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This year's conference will include both oral and poster (+) presentations. Learn more about the online conference format here.
The online platform will allow you to join a worldclass conference from the comfort of your own home or office and at the convenience of your own schedule all streamlined through one seamless interface. Prerecorded presentations will be available for viewing beginning nine days prior to the conference and for up to two weeks after the conference. Oral presenters will give a 10minute presentation and answer questions during live Q&A sessions. In addition to offering multimedia digital content, poster sessions scheduled over the three time blocks allow poster presenters to discuss their posters with the attendees via dedicated video chat rooms. All lectures will be recorded and available for viewing the day after each session and after the conference so that you don’t miss a thing – no matter where you are.
The single interface will provide aroundtheclock access to:
• All prerecorded presentations from 25 minisymposia
• Digital content from poster (+) presentations
• 10 invited lectures
• 4 keynote lectures
• Virtual exhibitor hall
• Breakout rooms for networking or further discussions 1on1 or in a group
• Engaging social & networking events
Join us for fascinating lectures, engage with fellow researchers from across the globe and discover cuttingedge exploration of porous media.
We look forward to welcoming you!
Topics and applications


Understanding the factors and mechanisms behind the trapping and immobilisation of residual saturations of carbon dioxide (CO2) and oil phases in the pore spaces of reservoir rocks during immiscible fluid displacement is vital for geological CO2 storage and enhanced oil recovery (EOR) (1). The extent of trapping that occurs determines the success and efficiency of such subsurface operations. Whilst the objective of CO2 storage operations is to maximise residual trapping of CO2, in EOR operations the objective is to supress and minimise trapping of the oil phase (2). Fluid displacement processes and residual trapping are strongly influenced by the topological roughness of the porous rock (3). Currently, there is very limited data on the effects of surface roughness on fluid displacement processes (4). Accordingly, in this study we aim to quantify the effects of microscale surface roughness on porescale fluid displacement processes.
To investigate the impact of surface roughness on porescale fluid displacement, immiscible displacement of air by water was conducted in a transparent glass micromodel at a flowrate of 8.33μL/min. The experiment was repeated three times to ensure reliability of results. The micromodel was fabricated using an ultrafast picosecond laser(5) and its pore network structure was comprised of cylindrical pillars 400 µm in diameter arranged in a rhombohedral type of packing. Due to the inherent nature of the laser fabrication process, the walls and surfaces of the laser machined porous structure were rough textured. The average hillock height to pore depth ratio (Ω) for this micromodel was determined to be 5µm/50µm (10%) and the average measured surface roughness (Sa) of the micromodel was 1.2µm. To isolate the effects of surface roughness on immiscible twophase fluid displacement, a Direct Numerical Simulation (DNS) of the waterair fluid displacement process was performed for the same porous structure assuming completely smooth surfaces in OpenFoam using the Volume of Fluid (VOF) method.
Comparing the experiments with the numerical simulation, our results demonstrate that microscale surface roughness has a strong and significant influence on porescale fluid displacement mechanisms and its contribution should not be ignored. We show that at a hillock height to pore depth ratio (Ω) of 10%, surface roughness can increase residual saturations in such a porous structure by up to 49% from 4% in the numerical simulation to 53% in the micromodel with rough surfaces. This implies that surface roughness can promote the isolation and trapping of clusters of CO2 in CO2 storage operations, thereby increasing efficiency of the process. In EOR operations, the effects of surface roughness are detrimental as the sweep efficiency of displacement process is significantly reduced.
Acknowledgements
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (MILEPOST, Grant agreement no.: 695070). This paper reflects only the authors’ view and ERC is not responsible for any use that may be made of the information it contains.
Coalbed methane (CBM) plays a critical role in transiting the global energy supply from fossil fuel to renewables in the next 30 years. To understand and forecast CBM reservoir performance, coal relative permeability curves are needed as a key input parameter in reservoir simulators. Currently， the relative permeability curves are normally measured using steadystate method at the laboratory conditions, where each effective flow capability of the coal core is then plotted against the corresponding water saturation. Field experience has constantly showed that the predicted results based on the curves from the steadystate method often overestimate field production.
In this work, the labonachip (LOC) method was adopted to measure the evolution of relative permeability under controllable and repeatable conditions, and meanwhile to visualize watergas twophase in microchannels to gain critical flow information that conventional laboratory measurements are unable to offer. As the start, a singlechannel microfluidics made of PDMS was first fabricated with a dimension of 100×100 µm (width by depth) and 24 mm in length. A number of tests were then conducted, including (i) the advancing contact angles of water with different wettability properties and the static contact angle to water and methane gas, (ii) similar to steadystate method, a series of injection tests with different gaswater volume ratios were conducted. Factors such as the flow velocity of each phase, the characteristics of flow field, and flow pressure of each phase, were also monitored; and (iii) the second step was repeated with different water wettability and injection rates.
The results show that the shape of water relative permeability from microfluidics tests is similar to that from conventional laboratory testing, but the gas relative permeability curve is very different between the two methods. The water relative permeability is 30 times lower than that predicted by Chima'model, and the gas relative permeability is even lower, 160 times. One reason, from our direct experimental observations, is that gas and water form discontinuous plug flow inside the microchannel and the interaction between the two phases along waterwetting surface significantly reduces gas flow capacity.
In additional, our results show that relative permeability values increase with injection rates and wettability, ranging from 10% to 20%. This work offers some interesting results that have rarely been captured and analyzed in core flooding measurements, and meanwhile the differences in relative permeability curves indicates that the data uncertainty associated with the steadystate method may be worth reassessing.
In this study, we investigate the dissociation pattern of CH4/CO2 mixed hydrate in porous media using highpressure micromodel. We formed CH4/CO2 mixed hydrate from gaseous CH4 and liquid/gaseous CO2 to mimic the scenario where a CH4 hydrate reservoir has been injected with CO2. Direct visualization was carried out using a highpressure, waterwet, siliconwafer based micromodel with a pore network of actual sandstone rock. Mixed hydrate was formed at reservoir conditions (P = 4475 bar and T = 1.73.6°C) from either a twophase system (liquid water and CH4/CO2 gas mixture) or a threephase system (liquid water, CH4 gas, and liquid CO2).
A stepwise pressure reduction method was applied to record multiple dissociation pressure points for a given mixed hydrate system, and the molar concentration of CH4/CO2 corresponding to each dissociation point was calculated. The effect of hydrate and fluid saturation on fluid flow during dissociation was also analyzed.
The results showed that liberated gas during stepwise pressure reduction was trapped by surrounding hydrate, and reformation of CO2 hydrate occurred rapidly when liquid water was present. The reformed CO2 hydrate shielded the CH4 hydrate that was still not dissociated and complete dissociation was accomplished when the pressure was brought below the stability pressure of pure CO2 hydrate.
Asphaltene is defined as the crude oil component, which is soluble in toluene and insoluble in lightnalkane [1,2]. In the development of oil fields, the deposition of precipitated asphaltene in a reservoir is a serious problem since it leads to clogging of the pores of the rock, resulting in a reduction in permeability [3]. Wang & Civan’s model, which was constructed based on DBF (deepbedfiltration) theory, has been commonly used in Darcyscale simulations to calculate the volume of asphaltene deposition [4,5]. In this model, the deposition rate of asphaltene is expressed by the summation of three terms: surface deposition caused by adsorption or gravity sedimentation, entrainment, and clogging of pores. Each term contains an empirical coefficient that needs to be tuned by comparing the experimentally measured permeability and the calculated one [6], which means that these coefficients cannot be determined without experiment. Porescale observation of the deposited asphaltene can directly evaluate the types of deposition. The observation using Xray microtomography showed that the cluster of deposited asphaltene clogged multiple pores after flooding with crude oil, which contains asphaltene, into a rock [7]. Although this shows the actual behaviour of the deposition, the transition of the clogging is still unknown. Several studies have been conducted with microfluidics experiments to capture the transient flow inside a transparent chip by a microscope. The process from precipitation to deposition of asphaltene at the wall of the chip [8] or dissolving behaviour of the asphaltene [9] have been visualised. However, the deposition process to clog the pores and the contribution of each type of deposition to the clogging is not well investigated.
In this study, the transition of asphaltene deposition inside porous media was visualised by a glassmade micromodel. In the micromodel, a latticelike porenetwork area with 6 cm in length and 1 cm in width was chemically etched. Each pore size was 100 μm in width and 110 μm in depth. Crude oil was mixed with nheptane as a precipitant of the asphaltene and injected into the micromodel at a rate of 0.7 ml/h, which was equivalent to a Darcy velocity of 1.94× 10–4 m/s. During the injection, the area composed of 2.5 mm length and 1.8 mm width was monitored with a microscope with a ten magnification lens to obtain twodimensional sequential images. Image analysis was conducted to identify deposited asphaltene.
We observed transitional processes from the deposition of asphaltene particles to the clogging of the pore spaces. At the initial stage, the deposition occurred at the local site of the pores. The deposited site grew by the accumulation. Finally, these local clusters were connected, resulting in the complete clogging of the area. The area of occupancy of the pores clogged with asphaltene linearly increased to 57.6%.
The ratio of deposition type to total deposition area was evaluated quantitatively to investigate each type's contribution to the permeability reduction.
Geological CO2 storage and CCS have a crucial role in reducing CO2 emission and therefore mitigating climate change. One of the prerequisites for selecting CO2 storage sites is a low permeability caprock preventing potential CO2 leakage and migration from the storage reservoir. The presence of fractures in the caprock can adversely affect the sealing capacity of caprocks. Chemical interactions between CO2, brine, and caprockforming minerals can cause fracture evolution, which results in changes in the transmissivity of fractures within the sealing layers. One factor that can affect the chemically induced fracture alterations is mineral heterogeneity in the caprock. In the present work, we investigate the effect of mineral heterogeneity on fracture geometry evolution when CO2rich brine flows through a single fracture scribed on different carbonaterich caprock samples. The rock samples have different carbonate contents and different levels of mineral heterogeneities. They can represent carbonaterich caprocks such as some intervals of the Upper Jurassic (Kimmeridgian) Draupne shales, the caprock for Smeaheia CO2 storage in Norway. An HPHT geomaterial microfluidic experimental setup is used to monitor the evolution of the fractures. Results indicate that the homogeneous caprock samples, i.e., the samples mainly composed of calcite, show a uniform fracture wall dissolution while fracture wall roughness increases for heterogeneous samples. The effluent chemistry analyses show that the samplescale calcite dissolution rate decreases over time, which can be due to the mass transfer limitations in the boundary layer near the fracture wall (for the homogeneous sample) or the altered layer formed around the fracture (for the heterogeneous samples). Microfluidic experiments were also done for one carbonaterich finegrained shale sample, which showed dissolution of calcite with no macroscopic fracture alteration during the tenday experiment. This indicates that in shale samples where the carbonate minerals, mainly calcite, are armored with other slow reacting minerals such as clays, the rate of fracture geometry evolution will be prolonged, which might be a positive point for the caprock integrity. However, the confirmed fluidrock geochemical interactions within the shaly sample in a short time frame call for further investigations on the consequent impacts on caprock samples' geomechanicalhydrological properties for more extended periods relevant for subsurface CO2 storage. The microfluidic experiments are also used to validate a reactive transport model. The model will then be utilized to study changes in transport properties of different samples during experiments. The LBMbased model outputs, such as porositypermeability relationships, can inform reactive models at larger scales to develop a better predictive numerical simulator for processes involved in CO2 storage projects.
While flow in porous media systems, such as in groundwater and rock fracture flow, is usually laminar (Re < 500), it has been increasingly recognized that recirculating flow structures can appear in these systems even at Re numbers less than one [1,2]. Furthermore, the structure of porous media leads to fluid stretching and folding that dramatically alters the fate of solutes, even in the absence of inertial forces and recirculating (vortical) flows [3]. These conditions should operate in tandem to significantly impact mixing and reaction in porous media, processes that are central to the fate of groundwater contaminants and biogeochemical cycling of nutrients. Previous work with a chemiluminescent reaction at a straight channel cross intersection showed that 3D vortical flow structures form and create reaction hot spots for Re numbers as low as 100 [4]. Another study showed that vortical flow structures can control transport processes even in low Re number (Re << 1) porous media flow, but further work is needed to examine how recirculating flows influence mixing and reaction in porous systems [5]. The overarching goal of this work is to identify the physical (pore structure), hydrodynamic (Re), and chemical (reaction rate) conditions where recirculating flows create reaction hot spots in a porous media.
Here, we combine 3D porescale numerical simulations and microfluidic experiments with a bimolecular chemiluminescent reaction to study the formation of recirculation induced reaction hotspots in low to moderate Re number flows. We use a microfluidic channel as a porous media analog where two reactants are injected into separate channels that converge to a central channel containing a sequence of pillars that represent grains of a porous media. By adjusting the flow condition (Re) and spacing of the pillars, recirculation can be readily induced within the space between the pillars. The apperance of the reaction hot spots then depends on the interplay between the factors creating recirculating flow, and the kinetics of the chemical reaction. The results of this work show that the critical Re to initiate recirculation is sensitive to pore geometries and well within the range of flow conditions common to natural soils and fractures. We also demonstrate that even once recirculation has formed, there is an optimal flow condition which enhances the reaction rate, which is controlled by the balance of flow velocity against reaction time scale. These results imply that typical soil porous media geometries, hydrodynamic conditions, and geochemical reactions will readily create vortical structures that induce reaction hot spots which will play a significant role in many natural porous media and fractured systems. During mineral precipitation and dissolution for example, recirculation induced reaction hot spots may drive preferential reaction in certain locations, which will influence evolution of porosity as the reactions proceed.
Ice crystallization and mechanical damage at the pore scale
Rosa Sinaasappel, Clémence Fontaine, Scott Smith, Daniel Bonn, Noushine Shahidzadeh
Institute of Physics, University of Amsterdam , Science Park, 904, 1098XH Amsterdam
Abstract
Frost in wintry weather conditions is one of the major causes of the degradation of roads, buildings and outdoor artworks that are all porous media and are prone to damaging. With the decrease of the temperature, the water present in the porous structure can crystallize; the formation of ice in the pore network or in cracks subsequently results in mechanical damage such as crack propagation or the delamination of the stone. The effect of ice crystallization in unconsolidated porous materials, known as frost heaving, results in an upward swelling of soils during freezing. Previous studies on freeze/thaw cycling in porous media have been done mostly on the macro and mesoscale. However, the detailed mechanism by which the damaging occurs is still ill understood; for instance, the mechanical properties of the ice and most porous media are such that one would expect the ice to break, and not the porous medium to be damaged.
Here, we present our results on ice crystallization in confinement at the microscale and investigate the conditions under which mechanical damage develop. In order to do so, micro scale experiments have been performed in a model microcrack/pore. Using glass micro capillaries of various sizes, parameters that cause fracture in the glass capillaries during freeze /thaw cycles are investigated; we are able to freeze water droplets inside the micro capillaries and simultaneously image the freezing and measure the deformation of the capillaries upon freezing, over multiple cycles. From the deformation of the capillaries we can estimate the pressure buildup by the ice in the confinement. The experimental results are compared with theoretical arguments in order to better understand the frost action at microscale on the resulting macroscale mechanical damage. The hoop stress responsible of the breaking of a single pore has been calculated considering the pressures induced by the crystallization process and the volume expansion of liquid water turning into ice.
Finally,we will discuss the importance of contact angle, volume of the confined water as well as the cycling on fracture observed in microcapillaries.
Velocity fields in flow in permeable media are of great importance to many subsurface processes such as geologic storage of CO2, oil and gas extraction, and geothermal systems. Steadystate flow is characterized by velocity fields that do not change significantly over time. The flow field transitions to a new steady state once it experiences a disturbance such as a change in flow rate or in pressure gradient. This transition is often assumed to be instantaneous, which justifies expressing constitutive relations as functions of instantaneous phase saturations. In this work, we examine the evolution of velocity fields in a surrogate quasi2D permeable medium using a microfluidic device and a highspeed camera. Tracer particles, i.e., microspheres with a diameter of one micrometer, are injected in to the medium along with DI water. The evolution of the velocity field is examined by tracing these particles in the captured images using a multipass particle image velocimetry algorithm. The results suggest that transition period between steadystates for an incompressible fluid takes a finite and nonnegligible amount of time. Finally, we examine the impact of the magnitude of the change in the pressure gradient on this transition period.
Carbonate rocks are multiscale systems where features in the order of few microns such as pores and throats interact with features on the order of a few millimetres, such as fractures and vugs. Fractures allow fluids to move at an extremely high speed through the reservoir and possibly leak out, which would undermine engineering efforts. We must thus be able to predict these fluid movements to ensure storage permanence of injected fluids. Recent advances in threedimensional (3D) printing allows for cheap and fast manufacturing of complex porosity models, allowing investigation of specific flow processes in repeatable manner and enabling sensitivity analysis for small geometry alterations. These 3D models can be printed with multiscale porosity structures that include large features such as fractures with smaller pores. Flow and transport in these multiscale structure can be modelled using high resolution porescale simulations, but these simulations are restricted to small domain (<10003 voxels). Darcy scale models with discrete fracture network can be applied, but they lack the exact representation of the fracture geometry. The DarcyBrinkmanStokes (DBS) equation gives a seamless transition between the Stokes and Darcy scales allowing us to solve the Navier stokes equation for the large features and Darcy’s equation for the small features. Although the use of the DBS equation for calculation of flow field and permeability has been widely applied, the validity of the transport equation remains to be investigated. Here we present an experimental investigation of species transport during single phase flow in custom 3D printed multiscale micromodels with fractured geometries. Different scenarios are examined where the connectivity of the fractures as well as the fracture shapes and apertures vary and their impact during single phase flow in the matrix is presented. The experimental results are then compared to highresolution pore scale modelling simulations, 2D depth averaged simulations, and 2D multiscale simulations. The results of this work can be used to benchmark multiscalesimulations solving the singlephase DarcyBrinkmanStokes equation.
The advent of deep learning marked a milestone in the reallife applicability of machine learning tools, as now very complex problems can be solved with unprecedented accuracy. Deep neural networks generally require little explicit prior knowledge and are distinctively efficient in extracting complicated patterns. These capabilities turn them into feasible candidates for replacing and/or assisting conventional timeconsuming and computationallyexpensive methods involved in porescale modelling, such as reconstruction, segmentation and single/multiphase simulations.
This work aims to show how the power of deep learning can be harnessed to both estimate porousmedia properties and develop new insights. Our main objectives are: (1) provide a general overview of how deep neural networks have already been used in terms of single/multiphase flow characterization; (2) demonstrate the potentials of deep learning in digital rock physics through case studies; (3) discuss deeplearningbased approaches to explore the physics of the porous media.
First, the relevant body of research is considered so that advancements, gaps and potentials can be identified. Then, an implementation map is laid out, encompassing the simplest to most comprehensive applications. Inputs can range from greylevel images to customized feature maps, while targets can span from static properties to complex, dynamic multiphase properties (e.g., resistivity index and fluid distribution). Secondly, case studies are presented where porosity, permeability and relative permeability are predicted from microCT (e.g., synchrotron beamline) images and rockfluid characteristics. A great challenge is to achieve the simulations at representative sample image sizes, which makes hyperparameter sweeping extremely taxing for the researcher and demanding on the hardware.
Thirdly, future research is discussed. It is proposed that to develop reliable multiphase predictors, large databases must be synthesized by collecting, resampling, augmenting, and grouping images and the corresponding properties. Consequently, deep neural networks can be trained for various rock types (e.g., carbonate) and processes (e.g., twophase unsteadystate drainage). Singular or ensembles of networks may either be used to make predictions or to serve as the base to be customized for other applications, i.e., transfer learning. Final models can be put to ultimate reallife testing by comparing against experimental data, e.g., phase distributions from synchrotron imaging.
Rather than trying to create mere blackbox estimators, one must strive to understand how the networks extract information, by looking at layer architectures, weights and other elements. The goal should be to gain insights into various flow functions (e.g., uncover the link between macroscopic properties and pore morphology and/or wettability) and the physics of certain flow behaviours (e.g., snapoff). This has already been done in such fields as object recognition, for instance, to figure out the level of feature abstraction at different layers. Furthermore, since trained models are very fast to run, they make perfect assets for such tasks as sensitivity/uncertainty analysis and backcalculation of input features, for instance, to see what wettability distribution can result in a specific flow parameter.
Natural gas hydrate has huge reserves and is one of the most potential carbon energy resources. In the process of natural gas hydrate production, the phase state changes in the formation. Until now, the gasliquid twophase flow mechanism is not well understood for gas hydrate formation. The permeability of gas and water determines the flow capacity of fluids in hydrate formation and directly affects the efficiency of natural gas production. Since gaswater twophase flow can cause changes of hydrate saturation and pore structure, the studies on the relative permeability is not inadequate. This study uses a combination of numerical simulation and machine learning to learn the relationship among pore statistical characteristic, the pore habits of hydrates, hydrates saturation and permeability. The goal is to reveal the seepage characteristics of hydrates at pore scale.
Using COMSOL Multiphysics software, porescale hydrate models are established, the NS equation is used to describe the gaswater flow. Gaswater twophase flow are simulated. A large number of data samples are generated and the porescale permeability prediction database is conducted. Based on the data samples generated by COMSOL Multiphysics, machine learning algorithms are used for permeability analysis. The hydrate permeability calculation model considering different hydrate pore habits (pore filling, particle coating, et al.) , pore statistical characteristic, and saturation is established. Then, the model is verified by comparing it with the classical capillary model and Kozeny particle model. The new model provides theoretical support for flow prediction of hydrate porous media.
Traditional flowbased twophase upscaling entails the computation of upscaled relative permeability functions for each coarse block or interface. It can be very timeconsuming especially for large models with a large quantity of coarse gird blocks or for cases that requires simulation runs over multiple geological realizations (as commonly used in uncertainty quantification or optimization). In this work, we introduce machine learning (ML) methods into the twophase upscaling procedure to significantly speed up the upscaling computations. In the new procedure, the flowbased relative permeability upscaling is performed only for representative coarse blocks/interfaces, while the upscaled functions for the majority of the coarse blocks are provided by the ML methods.
The new upscaling procedure entails a few steps. First, a ML method is applied to select the representative coarse blocks/interfaces based on the static permeability distribution associated with the target regions. Flowbased twophase upscaling is then performed for the selected blocks/interfaces to build a database. A different ML model can then be constructed to reveal the relationship between the upscaled relativepermeability functions and the corresponding static permeability distribution. This ML model is finally used to give the upscaled relative permeability functions for the rest of the coarse blocks/interfaces. In this work, both the local and extended local twophase upscaling approaches with generic pressure and saturation boundary conditions and effective flux boundary conditions are incorporated with the MLbased upscaling procedure.
We test the new upscaling procedure for generic (left to right) flow problems using 2D models for oilwater twophase systems. Both Gaussian and channelized permeability fields are considered. Extensive numerical results have shown that the coarsescale simulation results using the MLbased upscaling procedure are of similar accuracy compared to those using full flowbased upscaling. The relative errors of the total production rate and water cut are within 5%. Besides, at least one order of magnitude speedups achieved, which are quite significant. Higher speedup is observed for models with larger dimensions.
The ongoing work includes extending the procedure into 3D models, and testing it for actual field problems with more complex model geometry.
There are inherent resolution and fieldofview tradeoffs in XRay microcomputed tomography imaging, which limit the characterization, analysis and model development of porous systems with multiscale heterogeneities. In this work, we overcome these tradeoffs by utilising a deep convolution neural network to create enhanced, highresolution data over large spatial scales from lowresolution data.
We use paired highresolution (2 micrometres) and lowresolution (6 micrometres) images from two structurallydifferent Bentheimer rock samples to train an Enhanced Deep Super Resolution (EDSR) convolutional neural network. The generated highresolution images are validated against the true highresolution images through textual analysis, segmentation behaviour and porenetwork model (PNM) multiphase flow simulations. The final trained EDSR network is then used to generate highresolution digital rock cores of the whole samples with dimensions of 1.2cm × 1.2cm × 67cm. The 3D digital rock cores are populated with continuum properties predicted from subvolume PNMs, and used to simulate a range of experimental multiphase flow experiments. We present a consistent workflow to analyse multiscale heterogeneous systems that are otherwise intractable using conventional methods.
In this talk, we present an effective micromacro model for reactive flow and transport in evolving porous media exhibiting two competing mineral phases. As such, our approach comprises flow and transport equations on the macroscopic scale including effective hydrodynamic parameters calculated from representative unit cells. Conversely, the macroscopic solutes’ concentrations alter the unit cells' geometrical structure by triggering dissolution or precipitation processes on the distinct mineral surfaces. Gradually, such processes result in complex and hardly predictable geometries. Therefore, these do not allow for low dimensional parameter representations. Accordingly, associate effective parameters cannot be covered by simple heuristic laws. Hence, we derive hydrological parameters directly from the full geometry represented by levelset methods.
The numerical realization of such micromacro models poses several challenges, especially in terms of computational complexity due to the increased dimensionality of the problem. Costly computations of effective parameters directly from the representative geometry often constitute a bottleneck in the simulation of highly heterogeneous media. In this talk, the significant performance enhancements arising from machine learning techniques are evaluated. To this end, convolutional neural networks (CNNs) are trained on geometries derived from geological microCT scans to predict hydrodynamic parameters such as permeability and diffusivity. The pretrained networks are subsequently deployed in a micromacro simulation. We investigated the results in terms of computation time reduction and maintenance of high predictive quality.
The need of flow and transport characterization in underground fractured media is critical in many engineering applications, like fossil fuel extraction and water resources analysis. However, there is a lack of full knowledge (geometrical and hydrogeological) of these fracture systems and, therefore, statistical representations of the fractured media are given. In this context, we perform flow simulations in underground fractures with Discrete Fracture Network (DFN) models.
The stochastic representation of the fracture systems requires thousands of DFN generations and simulations to characterize the flow in a real fractured medium. For this reason, it is desirable to consider the application of Deep Learning models and use them as alternative model reduction methods to speed up the flow characterization process.
In this work we show the application of a set of Deep Learning models for flux regression in Discrete Fracture Networks, analyzing the regression quality and revealing suitable enhancements of the already existing encouraging results [1].
In a geological carbon storage project, management of reservoir pressure buildup is essential for longterm safe carbon storage. A reservoir pressure buildup caused by CO2 injection may lead to serious safety issues such as induced seismicity, caprock damage, and leakage of brine and CO2. Brine extraction is a practical solution to mitigate the reservoir pressure buildup. In heterogeneous reservoirs, the performance of brine extraction is significantly affected by where to place a brine extraction well because the mitigation of pressure buildup and the arrival time of injected CO2 to the brine extraction well are determined by the hydraulic connectivity map. The optimization of a brine extraction well location is computationally expensive because many reservoir simulation runs are required to seek optimal locations in potential well locations. We propose an efficient surrogate model that computes the optimality of a brine extraction well quickly using the fast marching method and a convolutional neural network. The arrival time map of a pressure pulse that the fast marching method provides rapidly can be used as a good representation of the hydraulic connectivity map for a brine extraction well location. The performance of our surrogate model is demonstrated in a CO2 injection site in the Pohang basin. The computational cost of optimization of a brine extraction well is significantly saved using our accurate surrogate model compared to a normal optimization process.
The study of particle transport in porous media is a research field of great interest as it is involved in a wide variety of applications [1]. The random nature of porous media systems makes it difficult to analytically correlate the impact and the synergy of the their geometrical parameters. Since these features make these systems a suitable candidate for machine learning (ML) approaches, in our work we employed neural networks for the realization of datadriven models. These techniques are able to grasp nonlinear correlations between data and to account for a large number of input parameters. Moreover in the case of convolutional neural networks the entire system geometry can be used as input for the model, in this way it is possible to avoid the selection of the geometrical features [23].
In this work we coupled computational fluid dynamics (CFD) simulations with machine learning models. The results of a CFD simulations campaign are employed as a training set for the neural networks in order to obtain a computationally inexpensive datadriven surrogate model which is able to replace the CFD simulation, while keeping a good accuracy. The aim of the CFD investigation is the flow, transport, and filtration at the porescale, in this framework the first step is the creation of the geometries. We designed bidimensional [4] and threedimensional [5] periodic packings of spheres via the opensource framework YADE DEM.
For each kind of geometry, hundreds of simulations are solved, each differing randomly in their geometrical parameters and input operating conditions. The CFD simulations are performed on the opensource code OpenFOAM. At first, the fluid flow is evaluated in the limit of small Reynolds numbers (<0.1), thus obtaining the medium permeability. Then the transport of dilute colloid particles is studied by solving the advectiondiffusion equation, and the filtration rate is calculated [6].
Two kinds of models have been built: both for the prediction of the permeability of the porous media, and the filtration rate of the colloid through the grains. The first one is a simple fullyconnected neural network whose input features are the geometric parameters and operating conditions. The second one is a convolutional neural network whose input is a porous medium geometry, in the form of a binary matrix. After the neural network training process, the end result is a surrogate blackbox model capable of predicting the output values when given a new set of input features, or a new geometry; notably, the accuracy of this datadriven model is onpar or better than other analytical or empirical correlations.
This simple datadriven models can then be reliably used in place of expensive CFD simulations (or in general, all “first principles” methods), as one single call of the neural network has a computational cost which is orders of magnitude lower than the full CFD simulation: in our test problems, under a second versus several hours – with a total neural network training time of around four minutes, for the fully connected one, and of several hours, for the convolutional one.
Artificial neural networks (ANNs) are well known for its strong learning ability and have been widely used in the petroleum industry, such as history matching, production optimization and productivity forecast. However, ANNs are also a typical kind of “black box” models for their weakness in the model interpretability, causing their results less reliable than those from other physics based models. This paper proposes an integrated model named intelligent connectivity model (ICM), which incorporates ANNs with the material balance equation within a machine learning (ML) framework. ICM is a modular model, and each module keeps correspondence with each item in the material balance equation, improving the model transparency and generalization capability significantly. The results of simulation experiments show that ICM enables to generate comparable prediction results and provide more reasonable characterizations on interwell connectivity than the classical physical model, and meanwhile ICM is more computationally efficient.
The performance of many industrial applications is largely based on the quality and reliability of the guidance and support systems (high rotational speeds, low friction torque, damping capability, etc.). The subject presented here is part of an ANR project, entitled SOFITT (Saturated Openpore Foams for Innovative Tribology in Turbomachinery) and aiming to find innovative technical solutions that break with current practices and provide highperformance support systems in terms of load capacity and damping. The project proposes a new concept of lubrication and correspondingly a new material (understood as a complex/composite material formed by the solid porous structure  compressible porous layers  and the imbibing fluid) in order to improve the quality and reliability of the guidance and supporting systems. The CFD (Computational Fluid Dynamics) simulations offer an economical solution to study the performance of this new concept of lubrication. The main objective is to understand the behavior of the porous complex structures, linked to microstructural properties of the solid material and their interactions with the fluid. In the scientific literature, the works studying the flow in compressible materials are essentially experimental because of their very complex geometrical shape [1], [2], [3]. The work proposed in this paper is a current challenge in the scientific community. The difficulty in performing CFD (Computational Fluid Dynamics) simulations in porous materials is to access the geometry of their structure. Thus, a first task is devoted to the simulation at the microscopic scale of the flow through a porous medium. The morphological structure of polyurethane foam samples is reconstructed at different levels of compression from 3D Xray microtomography. This is achieved by using a commercial software (Avizo) that allows to process 3D images and create FE/CFD models suitable for numerical analysis [4], [5]. A procedure allowing the passage between the microtomography measurements and the numerical models is developed. Then CFD modelling allows to study the impact of the material deformation on the pressure drop correlations [6], [7]. The numerical models are validated with experimental measurements conducted previously and presented in the reference [8].
Inkjet printing consists of the ejection and deposition of ink droplets on substrates that are moving underneath the printhead [1]. For printing on paper, waterbased inks have been developed that are beneficial from an environmental standpoint. The printing of semiinfinite lines on moving paper substrates lead to a steadystate distribution of moisture and heat, which are a suitable way to study the interplay between heat and masstransfer. Lateral wicking and evaporative mass loss are the dominant mass transfer mechanisms, while evaporative cooling reduces the temperature of paper by up to 6K.
Our goals were to develop an experimental setup and procedure to systematically measure the moisture content and temperature of paper as functions of the speed of the motion of the substrate and the frequency of droplet deposition. We use light transmission imaging and infrared thermography to measure the moisture content and temperature distributions, respectively. Our experimental setup consists of a sheet of paper, mounted 10 mm above an area light source and fastened onto a motorized translation stage. An inkjet printhead is placed a few mm above the paper surface. A CCD and an IR camera measure the transmitted intensity and the temperature of paper, respectively.
Besides conducting systematic experiments, we also developed a theoretical model for heat and mass transfer including evaporative cooling. The results of our simulations agree well with the measured data. Details of the model will be introduced in a separate presentation.
[1] H. Wijshoff, Physics Reports 491, 77177 (2010).
Surfactants play an important role in nearly the entire inkjet process including dispersion stability, jetting, spreading and absorption into porous media. In this work we used two main methods to extract the absorption dynamics of water and surfactant mixtures into porous media, namely Automatic Scanner Absorptiometer and a pico Liter drop watcher setup. Combining both methodologies it was possible to get information about the dynamics of liquid absorption into porous media.
The aim of this work is to study the consequences of surfactants on the absorption behaviour into porous media. For that, we used as surfactant the Surfynol series (104, 440, 465, and 485) mixed with water at CMC value. We studied in detail the increase of the hydrophilic part of the surfactant and correlate that with the absorption behaviour. This is performed for uncoated media and for coated media with a very different polarity (Inkjet vs Offset)
We have concluded that the structure of paper has a substantial effect on the interaction behaviour. For coated media we have seen little influence of the surfactant on the absorption behaviour; however for uncoated media we could have a difference on the absorption rate up to an order of magnitude. Furthermore we concluded that increasing the hydrophilic behaviour of the surfactant leads to a lower absorption rate.
The imbibition of liquids in thin, porous films is a widely studied phenomenon [1]. For example, in the print industry, understanding the penetration of ink inside paper provides tools for improving the quality of the print. However, measuring inside submillimeter opaque films like paper with a high temporal resolution is a challenging task. Here we introduce a Garfield Nuclear Magnetic resonance [2] (NMR) approach for measuring liquid imbibition into thin, porous films. Firstly, we were able to measure liquid distribution inside porous films with a spatial resolution of 10m on a time scale below 0.1s. Moisture profiles were measured for different model liquids inside PVDF and cellulose nitrate membranes. Secondly, microliter sized droplets were used to study the penetration process inside thin porous PVDF membranes (approx. 110 $\mu$m). Moisture profiles were measured with time frames as low as 25ms, which is to our knowledge the fastest NMR measurement used to study penetration ever reported. The front position inside the membranes, is determined from the liquid profiles, which allows to quantify the imbibition process. To illustrate the experimental power, the effect of viscosity and pore radius on the penetration process where investigated. To study the effect of pore size, two different PVDF membranes with a welldefined pore radius of 0.65 and 0.22$\mu$m where tested. The penetration process was performed with different water glycerol mixtures to study the effect of viscosity on the process. First results show a rather sharp imbibition front, additionally the imbibition dynamics obeys Stokes’ flow, but cannot be explained with the classical LucasWashburn equation [3]. The presented highspeed NMR imaging approach allows to measure the motion of liquid fronts on time and length scales that were not accessible before.
In printing industry research effort are currently focused on understanding evaporation and imbibition process of picoliter droplets [1, 2, 3]. In addition to new commercial inks and formulations, new machines and technologies are evolving. Understanding phenomena such as evaporation and imbibition of picoliter droplets into porous thin substrates, is therefore crucial in printing industry to achieve a higher printing quality and print speed.
In this contest we present an instrument which can print ondemand picoliter volume droplets of ink onto substrates, and then immediately record the evolution of the resulting dynamics when these two materials interact. The technique, High Speed Laser Speckle Imaging (HSLSI), evolution of standard LSI [4], has been developed to monitor nanometer displacement of the drying and imbibing ink droplet at high frame rate, up to 20kHz, given the short timescales of these interactions. We show the results obtained using two different inks printed on three substrates. Inks are homemade with two latices with different glass transition temperature (T$_g$), namely 16$^\circ$C and 37$^\circ$C. The substrates are glass filters, (PTFE) sheets and Teslin paper. The former material has been chosen following as it is unable to swell while the pore size and surface properties mimicking common printing paper. A substrate with no swelling ensures that the recorded dynamics are associated with the movement of the tested ink only. The second, PTFE, is hydrophobic: neither water nor watercontaining substances can wet it. Teslin paper is a singlelayer waterproof synthetic printing medium
In this talk, we will give one example of HSLSI’s usage for unraveling some dynamic printing features on each substrate which cannot be observed using other techniques.
A complete physiochemical description of the printing, imbibement, and swelling processes associated with commercial ink jet printing are currently under investigation using this HSLSI instrument
Nonwovens are highly porous media, typically used in industrial applications to transport and absorb fluids and/or to insulate against heat and noise. Moreover, they should be mechanically stable, especially under high compression. In the current talk, KimberlyClark and Fraunhofer ITWM present their joint work on modelling the mechanical compression behavior of thin nonwoven and the impact on the resulting material properties.
The focus lies on thin nonwoven structures consisting of different fiber types. We generate virtual geometry models that possess the essential properties of a given reference medium. These properties comprise the caliper, the basis weight, fiber orientations and fiber composition. Furthermore, based on µCT images, the pore size distribution of the reference structure is determined. It turns out that the first virtual models have all desired properties except for the pore size distribution. The real medium shows larger pores. Hence, we established a twostep generation algorithm. First, a packing of spheres is created whose size distribution resembles the larger pores. In a second step, a nonoverlapping fiber generator enters the desired fibers and, finally, deletes the spheres. By doing so, it is possible to validate the virtual medium against measured flow permeabilities.
KimberlyClark and Fraunhofer ITWM agreed on geometrical variations of the virtual reference medium to study the effects of changes in fiber diameters and fiber orientations. Moreover, based on this virtual models simulation studies of the mechanical compression behavior are performed. Of special interest is the impact of the number of bonding points between the fibers. In contrast to the number of fibers contained in the simulation box, the number of connection points between the fibers is not unique. Therefore, we present a procedure to compare the number of bond points in different structures.
The mechanical simulations are performed by ITWMs simulation tool FeelMath, which is also commercially available as the ElastoDict module in the software package GeoDict. This solver employs the LippmannSchwinger equations for elasticity in the Fourier space. Due to the voxelbased approach, large structures containing several thousands of highly resolved fibers and bonds are simulated. A further advantage of this method compared to FiniteElement approaches is the applicability to highly porous structures without the need of a mesh generation.
This effective approach allows for the numerical study of many virtual realizations, which are necessary to capture the variance of fiber networks with similar characteristics. In addition to the simulation of the mechanical effective stiffness of the nonwovens, the effective permeability is simulated and compared to experimental results.
The anode and cathode catalyst layers of protonexchange membrane fuel cell, a thin porous media of approximately 10μm thickness and 50% porosity, have a complex solid structure composed by a support matrix to conduct electrons and provide structural integrity, ionomer films to conduct protons, open pores to transport gases, vapor, and liquid water; and dispersed catalyst particles, typical Platinum. The behavior of the ionomer films adds complexity to the solid phase as it can retain water which causes swelling and therefore changing the porosity and the mass transport behavior for both gases and condensed liquid water. In this study, an experimental setup is used to investigate mass transport in catalyst layers at different relative humidity (RH). To decouple swelling and liquid water percolation phenomenon, an ionomer swelling neutral liquid, fluorinert FC3283, is utilized as the working liquid. The RH is then controlled by changing the water vapor content in the gas phase. The experimental results show that when fluorinert is injected into the catalyst layer at a constant flow rate, as the RH in the gas phase increases the injection pressure for both the liquid and gas increases due to swelling and reduction in porosity. Paradoxically, at high RH it takes a longer time to reach bubble point than at low RH. This unexpected observation could be a key feature in understanding the complex relationship between mass transport, swelling, and porosity in the catalyst layers.
The dynamic porenetwork modeling [13], as an efficient porescale tool, has been used to understand imbibition in porous media, which plays an important role in many subsurface applications. In this talk, we will present a dynamic porenetwork model for imagedbased modeling of spontaneous imbibition in porous media. The µCT scanning of a porous medium of sintered glass beads is selected as our study domain. We extract its pore network by using an opensource software of PoreSpy, and further project the extracted information of individual watersheds into multiform idealized pore elements. A number of case studies of primary spontaneous imbibition have been conducted by using both the porenetwork model and a VOF model, under different wettability values and viscosity ratios. We compare those model predictions in terms of imbibition rates and temporal saturation profiles along the flow direction. We show that our porenetwork model can well predict imbibition rates and temporal saturation profiles under different viscosity ratios and wetting conditions, in comparison to the VOF model. We explore the effect of viscosity ratio on the entrapment of nonwetting phase. Moreover, we discuss the difference between spontaneous imbibition and quasistatic imbibition in terms of porefilling mechanisms.
Complex fluid responses to external forces, imposed at specific lengthscales and forcing amplitudes, are intimately linked to their internal microstructure. Accordingly, microstructure deformation and relaxation history span lengthscales from the microscale to the macroscale. When complex, biological fluids are driven through porous media, a faithful model of the trapped vs. transported fluid mixture, and whether the material remains intact or preferentially separates (a version of material failure), is strongly dependent on multiple interacting chemical and transport processes. These dynamics processes are consequences of properties of the porous medium, the biological fluid, the relative lengthscales of the pore structure and the complex fluid, and mediumfluid component affinities. If the porous medium is fibrous with relative stiff fibers, a "simple" first step is to understand how the fluid behaves around a sphere or a cylinder. We start with a lambdaDNA solution to illustrate how complex even this simple model problem is, with a wide range of behavior. This study is a first step in our main goal of proposing an experimental strategy and analysis of the experimental data to learn the dominant mechanisms governing transport of complex fluids through porous media, and to build a predictive model.
Heat and mass transfer in nonNewtonian fluids through porous materials have wide applications in nature and engineering. Compared to nonNewtonian fluid flow in porous materials, solute and heat transport in porous materials have been less investigated. Specially, effect of heterogeneity of porous structure on flow and transport and upscaling the bulk fluid properties to the porous media averaged properties are not yet well understood.
To address these gaps in understanding, we proposed a GPUparallelized porenetwork model to simulate the flow and dynamic transport of nonNewtonian fluids in 3D unstructured networks with millions of pores at the centimetre level. The modified Meter model was used to properly model the relation between viscosity and shear stress of the nonNewtonian fluid under varying temperatures. We first validated the algorithm by comparing the thermal front from simulation results against the proposed analytical solution. Then both Newtonian and nonNewtonian fluids were studied in the spatially uncorrelated and correlated networks at varying injecting flow rates. The proposed modelling framework provides the possibility to control the injection rate as a function of porous media properties and fluids rheology. Additionally, effect of spatial heterogeneity and dynamic conditions on thermal fingering and upscaling transport properties will be presented in this work.
Flow and mixing at channel intersections are of broad interest because fluids with distinctive properties can efficiently mix and react at intersections, thereby controlling mixing and reaction processes in natural and engineered fractured and porous media. Recent studies showed that mixing and reaction hot spots are strongly linked with flow topological properties that form the backbone of underlying flow fields. In particular, stagnation points are related to strong stretching, folding, and flow separation, thereby governing overall mixing and reaction dynamics. Lee and Kang 2020 [Physical Review Letters, 124(14)] namely observed that inertia effects can induce recirculating flows at channel intersections and showed that the recirculating flows associated with stagnation points initiate local reaction hot spots, that is, locations where reaction rates are locally maximum. Nevertheless, there has been no systematic study on how diverse flow topologies emerge at channel intersections and how they control mixing and reaction dynamics at intersections.
In this study, we combine laboratory microfluidic experiments, porescale numerical simulations, flow topology analysis, and lamella mixing theory to establish a predictive framework that links flow topological properties to mixing and reaction properties. We systematically vary both the injection rate and injection rate ratio between the two inlets to elucidate how various flow topologies emerge at channel intersections as a function of the Reynolds number and injection rate ratio. We then establish a quantitative link between flow topology, mixing, and reaction rates. Finally, we upscale mixing and reaction at channel intersections using the lamella mixing theory and show how the key parameters of the upscaled model can be estimated from the flow properties.
Transport of dissolved substances through natural and engineered porous media is determined by the inherent complexity of the pore space, and diffusive mass transfer within and between pores. The interplay of porescale mixing and networkscale flow variability are key for the understanding of transport and contact processes in porous media with diverse applications ranging from groundwater contamination and geological carbon dioxide storage, to the design of batteries, and transport in brain microcirculation. Therefore, hydrodynamic transport has been the focus of research over decades in different disciplines. Nevertheless, questions of fundamental nature remain concerning both the evolution of hydrodynamic dispersion, and the dependence of asymptotic hydrodynamic dispersion coefficients on the Péclet number. We use a Lagrangian framework to identify and quantify three fundamental mechanisms of porescale mixing that determine the stochastic dynamics of pore and networkscale particle motion: (i) The smoothing of intrapore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion in terms of the characteristic pore length, Eulerian velocity distribution and P\'eclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in threedimensional digitized porous medium samples. Solute breakthrough curves are characterized by intermediate powerlaw behaviors and exponential cutoff, which reflect porescale velocity variability and intrapore solute mixing. Similarly, dispersion coefficients evolve from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Pécletdependence of asymptotic dispersion.
It is not constrained by transport measurements. The fundamental nature of the considered flow and transport processes allows application of the key elements of the derived theory to transport of dissolved chemicals, bacteria and colloids in a wide range of porous media also under different flow conditions.
Key words: porous media, haemodynamics, heterogeneity, modelling, microfluidics
Introduction
While extensive research has been devoted to fluid flows through porous media with comprehensive theories established ranging from porescale to fieldscale (singlephase or multiphase, inertial or noninertial, Newtonian or nonNewtonian, Darcy or nonDarcy), the underlying mechanisms for the flow and transport of blood and nutrients in biological organs/tissues such as the highly porous human placenta are still unclear [1]. As the size of flow channels within these systems becomes comparable with that of a red blood cell (RBC, about 8 μm in diameter), the particulate character of blood gives rise to complex nonlinearity by introducing spatiotemporal heterogeneities that require microscopic interrogation. In this work, we aim to characterise the microscopic blood flow within canonical porous media consisting of disordered pillar arrays. Both flow simulations at the microscale and corroborating experiments in a microfluidic analogue will be presented.
Methods
The porous media models are constructed by introducing different levels of disorder to regular obstacle arrays arranged on a square grid. Using the lattice Boltzmann and immersed boundary methods [2, 3], we simulate blood flow through the disordered geometry as a suspension of deformable RBCs in plasma. The volume fraction of RBCs (known as haematocrit) simulated is in the range of 20%30%. In parallel with the numerical model, a microfluidic analogue with equivalent conditions (e.g. confinement ratio and capillary number) is designed and fabricated, in which flow experiments are performed with monodisperse capsules (about 250 μm in diameter) that imitate the properties of RBCs.
Results
Our results show an intricate interplay of structural disorder, rheological uncertainty, and timedependent effects on the localisation of RBCs within a porous medium, which is highly heterogeneous presenting preferential paths subject to the “channelling effect” [4, 5] as well as emerging cell occlusion. We report for the first time the effect of incremental disorder within the porous media on the overall hydrodynamic resistance of the cellular blood flowing through, which markedly increases as the level of disorder introduced into the system, whereas in the Newtonian counterpart (for which only plasma is infused) a larger degree of disorder has a much weaker effect.
Discussion
The role of RBCs in the intervillous space within the human placenta is multifold. On the one hand, the RBCs facilitate the transport of oxygen, CO2 and other solutes. On the other hand, RBCs’ localisation can significantly affect the flow patterns in the porous media, which are not wellcaptured by Darcy’s law. Thus, more generalised constitutive relationships need to be derived based on crossvalidation of simulations and experiments to bridge microscopic characterisation and organlevel modelling.
A miscible horizontal interface separating two solutions of different solutes
can deform into convective fingerlike structures due to buoyancydriven
instabilities like the classical RayleighTaylor instability or the
doublediffusive instabilities, triggered by differential diffusion of the
solutes in the solutions. We analyse numerically for porous media flows the
scaling of the fingers vertical speed, defined as the slope of the temporal
evolution of the mixing length of the fingers. In the parameter space of the
problem, spanned by the buoyancy ratio R, and the ratio $\delta$ of diffusion
coefficients of the two species, the vertical speed is found to scale linearly
with the adverse density difference that drives the convective mixing in these
flows. The adverse density difference is the density jump across the spatial
domain where the density gradient of the diffusive basestate is negative along
the direction of gravity. It can be computed analytically from the diffusive
basestate density profile and can be significantly different from the initial
density difference when differential diffusion of the solutes are at play. Our
results evidence the possibility of controlling the nonlinear evolution of
mixing of buoyancydriven instabilities in twospecies stratifications
Many important subsurface processes and applications, such as geologic carbon sequestration, enhanced geothermal system, and magma flow in dykes, involve flows of variabledensity fluids in geologic fractures. Understanding the role of variabledensity flow on transport, mixing, and geochemical reactions is essential for the prediction, design, and operation of the subsurface activities. In reality, vertical fractures are common, and flow and transport in vertical or inclined fractures will determine the integrity of caprocks. However, the effects of density contrasts on flow and mixing in vertical fractures have rarely been studied.
In this study, we combine visual laboratory experiments and direct threedimensional (3D) numerical simulations to study the effects of fracture inclination angle (orientation relative to gravity), flow inertia, and density contrasts between fluids on the spatiotemporal distribution of miscible fluids in a fracture. Two miscible fluids with different densities are injected through two inlets at the bottom of the fracture and flowed out from the outlet at the top of the fracture. The density contrast between two injection fluids results in the lighter fluid being confined to a narrow path, which we term “runlet”, and the instability of this runlet is observed in both visual lab experiments and 3D numerical simulations. We investigate the underlying mechanisms triggering the instability in variabledensity fracture flows by systematically conducting numerical simulations for various combinations of flow rates, density contrasts, and fracture inclination angles. We first identify critical stagnation points that control the instability of the runlet through streamline and flow topology analysis. We then elucidate the effects of fluid stretching and mixing on the evolution of critical stagnation points by analyzing the spatiotemporal evolution of stretching and mixing measures. Our results show that the runlet is formed by the complex interplay between the density contrast, inertia effects, and mixing, and the runlet instability is controlled by 3D vortices.
The experimental work supported by the former Center for Nanoscale Controls on Geologic CO₂ (NCGC), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DEAC0205CH11231
The flow of dilute polymer solution in model porous media consisting of an array of cylinder is considered. Numerical [1] and experimental [2] studies show that such flows are subject to the intensification of preferential flow paths. These pathways tend to favour shear stress and thus increase viscous dissipation and decrease permeability.
We seek to study the mechanisms of reinforcement of these preferential flow paths which are crucial to the understanding of these flows. We consider here the OldroydB model of dilute polymer solutions.
The equations of the model are solved using a time predictioncorrection scheme and MAC discretization in finite volume in space.
The flow around two cylinders in a channel is first studied. As experimentally observed in [3], preferential flows appear, depending on the gap between the cylinders.
We show that the reinforcement mechanism of the preferential flow paths is linked to the appearance of elastic membranes which will interact with the flow. Like gates, they will guide the flow to areas where the velocity is initially high.
We then show how this mechanism works in the flow through an array of cylindres and study its impact on the flow and its macroscopic properties.
Many natural or industrial fluids exhibit nonNewtonian behavior. NonNewtonian fluids can therefore be found in different applications related to porous or fractured media such as mud flows, oil recovery, hydraulic fracturing or foam injection cleanup.
Although there are many different nonNewtonian fluids, we focus in this work on fluids that exhibit a change in regime: for low shearrate, their viscosity is constant (Newtonian) but it becomes shearthinning (or shearthickening) at higher shear rate.
And we are interested in understanding the flow of these fluids in large scale heterogeneous porous media, and particularly in the coupling between flow heterogeneity and the rheology.
Since the local viscosity changes above a certain velocity threshold, the flow field depends drastically on the mean flow rate or the applied pressure drop. In particular, one expects that the flow condition affects drastically the velocity field inhomogeneity, which is an important feature to understand the transport of species. We will show that, if the flow presents two asymptotic regimes of low and high flow rate corresponding to powerlaw fluids, the transition between these two regimes characterizes the heterogeneity of the permeability field. And, similarly to the case of yield stress fluids, the flow field presents interesting geometrical characteristics in this transitional regime, such as criticality and multiscale (fractal) properties which will be analyzed.
Experimental geomechanics highlights that the mechanical behavior of expansive porous media is variable depending on the pore water chemical composition. These porous media are typically characterized by clay particles, whose activity (Skempton, 1953) (and thus propensity to expand) is itself dependent on the pore water chemical composition. Chemicalinduced mechanical effects on both shear strength and volumetric behavior are highlighted in the literature (Di Maio, 1996; Castellanos et al., 2008). The physicalchemical origin of this mechanical dependence is still debated. Consequently, geomechanical approaches that can properly include these effects are still limited. The possibility of using a generalized effective stress concept for the mechanical modeling of these materials is an attractive proposition with the following advantages (Nuth and Laloui, 2008): (i) assured transition between saturated and unsaturated states, (ii) uniqueness of the critical state line irrespective of the degree of saturation, (iii) direct inclusion of hydraulic effects and corresponding hysteretic characteristics. In this contribution, we first account for the solid particlepore water interaction and distinguish the different types of ions and water characterizing expansive porous media (Tuttolomondo et al., 2021). Also, we highlight how the presence of both movable and nonmovable ions is essential in defining the pore water chemical composition. Second, we provide an analytical approach for determining the pore water pressure and replace the specified expression in the generalized effective stress definition. The effective stress also depends on a chemical variable related to the interaction between the solid particles and the pore water. The water retention curve (describing the evolution of matric suction at varying degree of saturation) and the effective solute suction curve (representing the evolution of the introduced chemical variable at varying degree of saturation) are essential to account for the retention state of the material and the chemical composition of the pore water at any state of interest. Existing experimental results in the literature, both at saturated and unsaturated conditions, are reinterpreted to investigate the advantages of the proposed geomechanical approach. The results obtained highlight, among others, the following additional benefits when using the proposed extension of the generalized effective stress concept: (i) the uniqueness of the failure envelope irrespective of the pore water chemical composition; (ii) the possibility of predicting elastic strain induced by pore water chemical composition changes (Tuttolomondo et al., 2021). Combined with the provided physicochemical explanation, these results bring the basis for an advanced stressstrain constitutive modeling.
Water scarcity is one of the biggest challenges of the 21st century. Using desiccants to harvest water from air is a promising way to address this challenge. However, most desiccants require considerable energy input to release absorbed water as vapor and then condense it. Here, we overcome this limitation by developing MoistureAbsorbent, TemperatureControlled Hydrogels (MATCHes) that absorb water from air at ambient conditions, and then release it in liquid form upon slight heating. Furthermore, we show that tuning the mesoscale porosity of the hydrogels dramatically impacts both the total amount and rate of water absorption and release — highlighting a previouslyoverlooked factor that regulates MATCH performance. Our work therefore demonstrates a new route to fabricating desiccants capable of harvesting water from air quickly, to a large extent, and with minimal energy cost.
Some crosslinked polymers, such as hydrogels, can absorb large quantities of solvents whilst undergoing a large change in volume. These chemically driven flows lead to a strong deformation of the polymer. In our experiments, we place a single droplet of water on a thin layer of strongly swelling polymer. Within minutes, a strongly swollen, very localised blister with a patterned surface forms. Over the next few hours, the pattern vanishes and the blister spreads radially whilst significant swelling remains.
We show that this process is driven by transport of solvent within the polymer and within the vapour contained in the surrounding gas phase. We also show how these two transport phenomena can be experimentally separated to enable the study of the transport within the polymer alone. The longtime dynamics of transport within the polymer is compared against a linear poroelastic model and a poroelastic model with porositydependent permeability which agrees well with the observed kinetics and blister shape.
Chemomechanical coupling in rock is known to result in the generation of cracks from volumetric changes in minerals caused by hydration, carbonation, oxidation, precipitation, and mineral dissolution. Alterations to the microstructures and changes in the chemical and mechanical properties of materials resulting from these processes can produce different types of acoustic activity as fracturing occurs. Here we examine the acoustic emissions (AE) in polymineralic synthetic rock samples during dehydration to distinguish the signals that arise from the movement of fluid through a rock, debonding of clay structures and, the development, nucleation, growth, and coalescence of fractures.
The synthetic rock was composed of Ordinary Portland Cement (OPC), Ottawa sand, and montmorillonite clays. Four types of samples were made which consisted of (1) OPC only, (2) OPC and Ottawa Sand (mortar), (3) mortar and Montmorillonite clay, and (4) embedded bodies of Montmorillonite clay in mortar. Samples with clay contained either a random distribution of clay (sample 3) or an architected structure (e.g. clay balls, thin sheet, etc.) (sample 4). Unbounded geoarchitected samples were also monitored during drying as moisture was removed from the medium, with intermittent 3D XRay Microscopy (Zeiss Xradia 510 Versa) to visualize the state of the system. The resolution of the Xray images was 40 micrometers pixel edge length. The AE were recorded using a Mistras  Physical Acoustics (PAC) AE recording system with a 10MHz sampling frequency, threshold amplitude of 27dB, and PAC F15alpha sensors which were connected to the AE system via preamplifiers and affixed to the sample with hot gorilla glue.
During drying fractures developed in the clayrich medium as a result of shrinkage, which coalesced into intricate fracture networks with distinct features. No fractures were observed in the samples with no clay and the same background medium. The peak frequencies of AE events generated during dehydration varied for the different samples. While the frequencies obtained for mortar samples occurred within a welldefined range (200250 kHz.), a wider frequency band (50 – 300 kHZ.) with lower frequencies was observed for the samples with distributed clay. The clayrich specimens were found to produce a significantly large number of AE resulting from the development and growth of the microfracture networks. The AE data are supported by 3D XRay Microscopy data which shows the progression of dense fracture networks in the clayrich samples during the period of dehydration.
Acknowledgment: This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences Research Program under Award Number (DEFG0209ER16022).
Complex clay systems are present all over the word and play a major role in many applications. In sedimentation processes for example, it is known that the settlement of clay particles is slow when they are exposed to fresh water. However, when exposed to salt water, the dynamics of the particles drastically change. The clay particles flocculate and results in a separation of an almost pure water section on top and a water and clay suspension below. This flocculation process starts within minutes with a formation of a clear concentration front. Once the flocculation is finished, a dense mass of clay (chemical bounded with positively charged salt ions) remains. On the other hand, if this dense mass of clay (also referred as salt rich glaciomarine salts), is uplifted and no longer exposed to saltwater, rainwater can infiltrate and diffuse the salts out of the clay. In some occasions this may result in massive landslides as the freshwater destabilizes the clay aggregate structures.
As another example, clay minerals such as bentonite are also widely present in various ore bodies, mainly as gangue minerals. For mining industries, the processing of those ore bodies is very challenging as the presence of clay results in poor flotation performance. The coating of the clay on the valuable ore minerals reduces the recovery of those minerals. The presence and addition of salt ions in water may have a significant effect on the slime coatings (Chen and Peng, 2018) and pulp rheology (Huang et al., 2020) enhancing for example chalcopyrite recovery (Jeldres et al., 2019).
In order to better understand the abovedescribed complex interactions of clay, salts and water, an in situ experiment was performed in a TESCAN CoreTOM, enabling 4D visualization and better understanding of the clay behaviour. By using high speed Xray microCT (dynamic CT) we were able to visualize the flocculation pattern, in three dimensions as a function of time, of bentonite clay in fresh water, NaCl solution, and KCl solution. In this study, 8 g bentonite was mixed with 2 g chalcopyrite in 1) 50 mL DI water, 2) 50 ml DI water + 1mol/L NaCl and 3) 50 ml DI water + 1mol/L KCl. The suspension was stirred for 15 min before subsampling. Microct was acquired using scans with a continuous speed of 5.8 sec/ rotation (0°360°) and a voxel size of 15 µm. In total 100 uninterrupted rotations were acquired with 400 projections each. Both temporal and spatial resolution was sufficient to visualize and analyse the dynamics in three dimensions showing clear differences between the systems. Motions of particles where analysed using the Software GeoDict.
Along with playing a critical role in soil stability and mining applications, bentonite is a widely used clay in many industrial products such as paints, ceramics, drilling fluids, etc. Although commonly used, the bentonitewater systems are not yet fully understood. The authors hope that these initial experiments may open doors towards many other applications and a better understanding of these, and similar, dynamic interactions.
Diffusion of water into plant materials is known to degrade their mechanical strength and stiffness, yet simultaneously enhance formability. Hence, the phenomenon is of both fundamental interest, and of importance for manufacture of ecofriendly products, e.g., foodware (plates, bowls). The existing literature on diffusion in plant materials (mainly woods) has focused on diffusion of water vapor (moisture) rather than liquid water. Furthermore, these studies have largely been restricted to estimating the macroscopic diffusion coefficient, using measurements of mass gain, with little focus on elucidating the micromechanisms of diffusion. Given the complex hierarchical structure of plant materials, the diffusion process may be expected to be strongly influenced by microstructural components such as fiber, matrix and porosity. Even a qualitative understanding of the role of microstructure in influencing diffusion of water will be of value for predicting the response of plant materials to water permeation, without extensive macroscopic measurements.
Here, we report on measurements of diffusion coefficient of water in areca palm sheath, a model plant material system, also used in ecofriendly foodware. The measurements account for the effects of material swelling and porosity, unlike prior characterization of this diffusion. Using in situ imaging, we show that the permeation of water through the sheath microstructure occurs heterogeneously, being several times faster in the matrix than in the fibers. Furthermore, using digital image correlation (DIC), we map the variation in the local strain during the diffusion process and show that it is significantly higher in regions of greater water penetration. The diffusion coefficient obtained from conventional mass gain measurements is shown to be consistent with the observations from the imaging experiments. The results highlight the critical need to include microstructure parameters, such as porosity and material swelling, to accurately estimate the diffusion coefficient. Implications of the results for diffusion in hierarchically structured materials, foodware manufacturing, and life of foodware products are discussed.
A poroelastoviscoplastic model for the consolidation of a twophase suspension is presented, motivated by the compaction and dewatering of woodfibre pulp. For that material, traditional twophase models of particulate porous media based upon plastic yielding of the particle network prove insufficient to capture the observed dynamics. The incorporation of viscous effects stemming from the compaction of the woodfibrenetwork assists the model in reproducing experimental dewatering tests at moderate rates of compaction. However, during more rapid dewatering there is clear emergence of an elastic behaviour in the woodfibre network. We present a poroelastoviscoplastic extension of the model, its calibration for woodpulp using quasistatic cycles of loading and unloading, and demonstrate its improved representation of the rapid dewatering experiments.
Transport in porous materials is a problem of relevance for several reallife applications such as disintegration of pharmaceutical tablets [1], groundwater contamination [2], and oil extraction [3]. In several cases the fluid changes the medium, and these changes are expected to feedback into the fluid flow. Examples of these changes are: i) erosion; ii) swelling; and iii) dissolution of solute. In a previous work, we focused on studying the dynamics of a porous medium that swells and erodes and showed that swelling can greatly impact the erosion of a porous medium [4]. Here, we study the competition between swelling and dissolution. We consider a porous medium composed of compacted nonoverlapping spheres of size dispersion 5%. We use the LatticeBoltzmann Method to resolve the fluid flow coupled to an advectiondiffusion equation for the solute, to obtain the velocity field and solute concentration. The fluid flows due to an imposed pressure drop. On the surface of each sphere there is a flux of solute that depends on the solute concentration gradient and on the solid dissolution mass transfer coefficient [5]. The implementation of the sphere swelling is based on the discretization of an empirical law [6] consisting of an exponential increase of the sphere volume. Swelling has two competing effects on the solute transport: i) swelling decreases the average velocity of the fluid which causes a decrease on the solute throughput; and ii) swelling causes an increase in the surface area of the porous medium which in turn enhances solute dissolution. We investigate the impact of this competition on the extracted solute over time and determine an empirical equation that describes the extracted solute concentration.
CO₂ injection into underground geological formations, particularly saline aquifers, causes the removal of water by evaporation into the CO₂rich phase. This process triggers salt nucleation and precipitation inside the pores, and therefore, alters the petrophysical properties of the formation rock.
In the context of CO₂ storage, several experimental studies have been conducted at pore and core scales to investigate salt precipitation. While micromodel experiments have provided a 2D insight into salt precipitates at the pore scale [1, 2], core flooding tests have been extensively employed to mimic this process in natural porous media. These corescale experiments have mostly been used to monitor the petrophysical alterations due to salt precipitation during CO₂ injection and have reported porosity and absolute permeability reductions [3, 4]. The advent of Xray microtomography (microCT) has facilitated the rapid, nondestructive, insitu 3D imaging of rockfluid systems. This technique provides a comprehensive porescale characterisation of rock samples down to microns, as well as the distribution, morphologies, and characteristics of the occupying fluids. However, using microCT scanning for monitoring such a flow process is challenging due to highpressure/hightemperature (HPHT) subsurface conditions, which need to be replicated because of the dramatic impact of such conditions on fluid properties and fluid/rock interactions.
In this work, we aim to investigate salt precipitation induced by CO₂ injection in natural porous media by providing direct, 3D porescale evidence using insitu HPHT microCT imaging. Although this technique has been extensively used to study many CO₂ storage related topics, it has rarely been utilised for imaging the potential petrophysical alterations due to salt precipitation during storage operations. Accordingly, we have designed and developed a unique HPHT microCT core flooding system, which is an excellent tool for providing valuable 3D information of flow processes at realistic subsurface conditions. The system consists mainly of two parts: (1) the microCT instrument itself capable of performing highresolution scans down to a nominal pixel size of 3 microns; and (2) the HPHT flooding system, the main part of which is an Xray transparent flow cell, capable of withstanding elevated pressures and temperatures to provide the conditions of typical deep saline aquifers.
Despite the numerous experimental studies published in this area, the impact of salt precipitation on the flow paths of the injected CO₂ and the potential alteration of its effective permeability is still a subject of discussion. Hence, the main objective here is to investigate the nucleation, precipitation, and dryout mechanisms, as well as the extent of injectivity reduction at the pore scale. Accordingly, microCT scanning of the drying process of a brinesaturated rock sample (diameter ≈ 5 mm) by dry gas injection is conducted. The analysis of the CT images taken before and after the experiments quantifies the precipitate particle sizes, the extent of pore size alterations, and the pattern of precipitation. Moreover, this presentation explores different injection conditions mimic the potential of salt precipitation at different distances from the injection well and analyses the resulting patterns of such a process.
In this study, an image processing framework was proposed for mapping Ca(OH)2 dissolution, CaCO3 precipitation, and pore volume change of wellbore cement samples exposed to high concentration CO2 under laboratorysimulated geologic CO2 storage conditions. The main workflow covered in this framework is to, 1) remove noises, artifacts, beam hardening effects, etc. from microCT images of cement samples before and after reaction with CO2; 2) register cement CT images before and after reaction; 3) generate grayscale intensity difference images showing CO2induced cement alteration, and convert grayscale intensity difference into Xray attenuation coefficient change; 4) calculate pore volume change and local content changes of Ca(OH)2 and CaCO3 at each voxel, given Xray attenuation coefficient change; 5) generate pore volume change and Ca(OH)2/CaCO3 content changes in 3D view. The effectiveness of the framework was validated through a stepbystep demonstration of results when deploying the framework to process the microCT images of six cement samples acquired before and after reaction with CO2. The 3D CaCO3 precipitation and Ca(OH)2 dissolution map was obtained, and the internal and external CaCO3 shells were visualized. Overall, the 3D precipitation and dissolution map gives more intuitive and interpretable results of CO2induced alteration of cement than the direct visual comparison from original CT images.
In enhanced oil recovery, gas injection often suffers from poor sweep efficiency due to conformance problems, such as gravity override, viscous fingering and channelling. Foam, composed of gas bubbles separated by continuous liquid films (lamellae), can effectively mitigate these problems. During foam flooding, the mobility of gas is reduced by a factor of hundreds or even more (Tang and Kovscek, 2006). As a result, the displacement front is more stable, and more gas is diverted to unswept zones, hence improving the sweep and recovery.
The ability of gas mobility reduction of foam is highly dependent on its texture. It has been found that foam with a finer texture implies a greater reduction of gas mobility (Lake et al., 2014). In the laboratory, computed tomography (CT) has often been used to study foam flooding in core plugs (Tang et al., 2019; Gong et al., 2020). The saturation of different phases is mapped, to evaluate the performance of the foam. However, foam texture at the microscopic level is still less understood.
In this study, we present a novel technique of image analysis on foam in two 1meterlong model fractures (analogous to microfluidic porous media). The fractures are made of glass plates (AlQuaimi and Rossen, 2018). Each model fracture has one flat wall and one rough wall. The gap between the two walls represents the aperture of the fracture. The distribution of aperture can be represented as a 2D map of pores and throats. The two fractures have different roughness distributions. One has a roughness in a regular pattern with a hydraulic aperture of 46 μm. The other one has an irregular pattern with a hydraulic aperture of 80 μm.
To quantify the roughness of the fractures, we profile the roughened surface (size: 2 × 2 cm, resolution: 1342 × 1342, pixel length: 14.9 μm) of the glass plate using a digital microscope. The fracture volume of the two models is also measured. The transparency of model fractures allows direct visualization of foam in the fractures, using a highspeed camera. A highparallelism backlight is used to provide stable lumination for the camera. The whole setup is placed in a tent to avoid outside reflection and refraction.
In this study, 2D image analysis of foam is performed using ImageJ software. We characterize foam texture by quantifying bubble density, bubble size and area fraction of water and gas. We also program macros to compute the velocity of flowing bubble trains. In addition, by using profiling data, we can convert phase area fraction to 3D volume fraction. We can also estimate the capillary pressure in the model fracture. From that we can estimate the lamella surface area available for foam coarsening by gas diffusion. Based on this information we can distinguish when diffusive coarsening stops because bubble pressures are equalized or slows nearly to a stop because bubbles lose contact through lamellae.
Magnetic resonance presents an array of unparalleled opportunities in probing fluids in porous media. Magnetic resonance methods are nowadays routinely employed in welllogging, monitoring underground water resources, laboratory analysis, and industrial process and quality control. Despite these widespread applications, there are significant problems associated with the inability of traditional magnetic resonance methods in observing shortlived signals typically observed in porous media. The University of New Brunswick (UNB) MRI Research Centre developed new methodologies to address these shortcomings and consolidated magnetic resonance imaging (MRI) as an excellent tool for in situ studies of a wide variety of materials, including rocks, sediments, wood, concrete, composites, foods, and microporous materials.
Innovations of UNB MRI Research Centre exploit (1) free induction decay as a means of signal formation for detecting shortlived signals, (2) low magnetic field intensities to reduce the effects of magnetic susceptibility difference of matrix/fluids, (3) pure phase encoding to avoid artefacts arising from susceptibility effects, chemical shift, B0 inhomogeneity and linewidth restriction on resolution, (4) the importance of information in the proximity of kspace origin on the quantitative quality of data, (5) nonmagnetic metallic environmental sample holders with integrated radiofrequency probes, and (6) correcting gradient waveforms or their effect. These innovations permitted quantitative and in vivo imaging of a variety of processes by a combination of specialized software and hardware. Several new discoveries and some interesting observations relevant to porous media applications were facilitated by these developments in the past few years:
(A) Magnetic resonance methods directly measured gas pressure in microscale pores of methane gas hydrates in a pioneering work. In a methane hydratebearing sand pack with 2.8% residual water at 2 MPa and 4°C, the elevated pore gas pressure was measured to be 59 MPa. (B) New models proposed for magnetic resonance relaxation in multicomponent mixtures in porous media were matched to experimental data on CO2/decane mixtures in Berea sandstone at 40°C and 6 MPa and 9 MPa, for miscible and immiscible conditions, respectively. The density of decane in the poresurface bound layer decreased during the miscible drainage of decane by CO2. In contrast, in immiscible displacement of decane by CO2, the poresurface area wetted by decane monotonically decreased only at saturations smaller than the residual saturation – consistent with the development of noncontinuous wetting films on the pore surface. (C) We established that nonground eigenvalues of the diffusionrelaxation equation indeed contribute to the magnetic resonance relaxation signal of common porous media, contrary to common belief. This discovery permits direct pore size estimation from common T1 and T2 distribution measurements. (D) The new T1T*2 method proposed as a 2D relaxation correlation experiment permits the detection of mobile and immobile 1H in porous materials, especially in shales and concrete material with significant susceptibility effects.
The recent addition of a variablefield superconducting magnet to the UNB MRI Research Centre is expected to further help the development of new methods and applications in porous media.
Moisture management in textiles is not only of importance for functional clothing, but also for medical fabrics. Understanding or even predicting the dynamics of spontaneous imbibition in textiles is challenging due to the heterogeneity of textile structures and thus the complexity of the fiber/water/air interfaces. The physics on the pore scale determine the macroscopic water transport. Contrary to some classes of porous media, e.g. sedimentary rock, stepwise uptake/imbibition dynamics have been observed for textiles and models in the style of Darcy's or Washburn's laws cannot always be applied. We employ timeresolved Xray tomographic microscopy (XTM) to study porescale filling processes and their impact on the overall imbibition dynamics.
Textiles are multiscale materials. Yarns are processed into fabrics, e.g. by weaving or knitting. The yarns are twisted bundles of fibers. The fibers can be porous themselves, but we focus in this study on dense fibers of polyethylene terephthalate (PET, not swelling) with uniform wettability and contact angle 48°. 32 continuous PET fibers with circular cross section and a diameter of 55 µm are manually spun to yarns with 200 twists per meter and mounted at given tension (2.5, 10 and 30 mN/tex) in a sample holder attached to a reservoir. The setup is placed on the rotating sample stage of the TOMCAT beamline for synchrotron XTM at the SLS, Paul Scherrer Institut, Villigen PSI, Switzerland. By remotely filling the reservoir, we image the full spontaneous water imbibition process in a 5 mm yarn segment from an unlimited reservoir in 4D with 2.75 µm voxel size and up to one tomographic scan per second. In a second experiment, equally prepared yarns are mounted in a configuration mimicking the contact of two yarns in the wale direction of a knit stitch. This configuration forces the water to pass the yarn contact to reach the top of the field of view.
XTM reveals the interfiber pore system and the dynamic evolution of the water configuration with its corresponding change in free energy. The imbibition process displays two very distinct time scales. While pores are filled in quick bursts, there are long periods of almost flow stagnation at pore transitions. It is found that these periods correspond to quasiequilibria of the water configuration with almost vanishing free energy gradient. The water reconfigures slowly until it reaches again a state with high free energy gradient that allows higher fluxes. Such high fluxes are supported by the longitudinal aspect ratio of the pores. Since these lowenergygradient periods can last up to minutes, the overall water uptake in yarns is not dominated by the wetting speed, but by the periods when water is (almost) not flowing. Since the fiber configuration at the yarn contact prevents the formation of continuous crossyarn pores, this yarn contact is the locus of many such slow water reconfigurations. Consequently, water uptake in both studied systems, namely single yarns and stitches, is characterized by twoscale stepwise dynamics with slowdowns at poretopore and yarntoyarn transitions, a crucial information for potential modeling approaches of textiles.
There are numerous challenges associated with measuring the wettability of a porous material. Surface roughness and chemical heterogeneity obscure representative characterisations via contact angle hysteresis. Micronresolution Xray CT imaging has enabled direct geometric measurements of contact angle inside core samples but due to uncertainty and error at the contact line, this method tends to skew values towards 90$^\circ$. The recent inception of an alternative topological approach has resulted in an approximate relationship between contact angle and interfacial curvature for individual clusters of the nonwetting phase, though its application has been limited to images of waterwet rocks at residual oil saturation. Here, previously published topological methods are demonstrated to be only applicable at these conditions. Furthermore, the wetting phase is not specified, leading to ambiguity for heterogeneous mixedwet samples. We present a more generalised model to include any wettability and saturations with high phase connectivity. A practical workflow has been developed for application to experimental porescale images, with processing parameters optimised using results from lattice Boltzmann simulations. Correcting for the relative orientation of the contact line with the solid surface, lacking from previous methods, is shown to significantly reduce error. Comparison of measurements from both techniques on experimental and simulated images at similar conditions suggests that the topological approach presented here provides the more accurate quantification of contact angle for both waterwet and mixedwet Bentheimer sandstone samples. Consistent 3D spatial distributions of contact angle for these images can now be observed, enabling wettability in porous media to be studied in much greater detail.
Understanding corrosion mechanisms and processes of UO2 fuel is essential for safe operation of nuclear reactors and storage of spent fuel [13]. We develop a 3D physicsbased numerical model to simulate the thermalchemical process during the corrosion of UO2 fuel pellets. Mass transfer, thermal conduction and solid chemical reactions are coupled in the model. The impact of temperature on uranium speciation during fuel corrosion is investigated. The UO2 pellets lifetime under corrosion is compared at same temperature but different reactions. The predicted reaction rates are shown to be dependent on the reaction types. The impact of microfractures on fuel pellets corrosion are studied by modelling reactions in fractured pellets. The composition change caused by radiation is also explored. The fuel with UO2U3O8 mixture is constructed. The results show the mixed fuel presents faster reaction rates in comparison with pure UO2 samples. The developed model will help quantify the effect of temperature on nuclear fuel dissolution and, help determine the key parameters controlling the physiochemical processes and ultimately inform the nuclear industry.
Ice formation in porous media is a phenomenon characterized by coupled heat and mass transport, which could lead to considerable deformations [1]. Studying such a process is important in many engineering applications. In cold regions where periodic freezing occurs, porous materials like road pavements and concrete are usually subjected to frost damage. Moreover, some techniques such as artificial ground freezing, which are widely used for groundwater control and temporary excavation support, can lead to heave and settlement of the ground surface.
In the underlying work, a numerical modeling framework that takes the multiphysical thermohydromechanical (THM) processes of ground freezing into account is presented. In this, an unsaturated soil is treated as a nonisothermal, deformable, triphasic porous material with a gas phase and a single fluid that can change depending on the thermal conditions between a solid ice and a liquid water state. The model is based on a coupled phasefieldporous media approach [2], where the main focus is laid on the temperaturedriven processes that lead to the phase transition between water and ice and the freezingrelated deformations. The governing equations of the macroscopic model are based on the wellfounded theory of porous media (TPM) [3] extended by the phasefield modeling (PFM) [4]. The model proceeds from a smallstrains assumption, whereas the porefluid can be found in liquid water or solid ice state with a unified kinematics treatment of both states [5]. Comparisons with the experimental data will demonstrate the ability and usefulness of the considered model in describing the freezing of unsaturated soils.
References
[1] J. Bluhm, T. Ricken, M. Bloßfeld (2011). Ice Formation in Porous Media. Advances in Extended and Multifield Theories for Continua, pp. 153174. Springer Berlin Heidelberg (ed.) B. Markert.
[2] A. H. Sweidan, Y. Heider, B. Markert (2020). A unified water/ice kinematics approach933for phasefield thermohydromechanical modeling of frost action in porous media. Computer Methods in Applied Mechanics and Engineering, 372, 113358.
[3] B. Markert (2011). Coupled Thermo and Electrodynamics of Multiphasic Continua. Advances in Extended and Multifield Theories for Continua, Springer Berlin Heidelberg, 129152.
[4] W. J. Boettinger, J. A. Warren, C. Beckermann, A. Karma (2010). PhaseField Simulation of Solidification. Annual Review of Materials Research 32:1639.
[5] A. H. Sweidan, K. Niggemann, Y. Heider, M. Ziegler, B. Markert (2021). Experimental study and numerical modeling of the thermohydromechanical processes in soil freezing with different frost penetration directions. Acta Geotechnica. Under revision.
Thermal protection systems (TPS) are used to ensure acceptable temperatures for the outer surface of a spacecraft during all mission phases and particularly during atmospheric reentry. Carbon fiber felt is widely used in TPS systems due to its high porosity and low thermal conductivity [1]. It is an anisotropic material. In local thermal nonequilibrium (LTNE) models, a heat transfer coefficient (HTC) is used to represent the internal heat exchange between the fluid and solid phases. Some correlations for metal foams, packed beds and ceramic foam are proposed in the literature for the prediction of the HTC [2]. However these correlations are not suitable for carbon fiber felt due to its geometric parameters, namely smaller fiber diameter (50μm), lower thermal conductivity (0.23W/(m3 K)) and its anisotropic structure. In this work, an inverse method was used to determine the anisotropic HTC between a gas stream and a carbon fiber felt sample. This method consists of three steps: transient singleblow technique (TSBT) experiments, macroscopic numerical simulation and error minimization between the results of the two first steps. To investigate the influence of the anisotropic structure of the materials on HTC, different experiments were performed by changing the orientation of the sample (ThroughThickness (TT), InPlane (IP) ), the inlet gas velocity varying from 0.23m/s to 0.94m/s. The experimental data are input into the macroscopic simulation process as initial and boundary conditions. The computational area includes a fluid (gas flow in the tube) and a porous domain. The energy conservation equations are solved using a finite volume method in the Porous material Analysis Toolbox based on OpenFoam (PATO) [3]. Besides, a numerical model of the thermocouple allowed to compute the temperature difference between the gas and the thermocouple probe. At last, a method for minimizing the error between calculated and measured temperatures is introduced, so that we can get the most suitable value of HTC. When the orientation of the sample is changed while keeping the same conditions, different values of the HTC are found. To take explicitly into account the flow direction, a new formulation with HTC has been proposed. This formulation will also be verified using porescale simulation in the future [4].
Keywords: Local thermal nonequilibrium; Anisotropic materials; Macroscopic numerical simulations; error minimization
Waste packages for disposal of radioactive waste originating from reprocessing of spent nuclear fuel typically include a stainless steel canister inside which the waste is immobilised in a (borosilicate) glass matrix. A potential disposal pathway for such wastes is in conventional mined geological disposal facilities (GDF) [1] or in deep boreholes [2]. In the latter concept, the packages are stacked in a disposal zone at a depth of several kilometres [3]. However, deep borehole disposal is still in its infancy requiring considerable Research, Development and Demonstration (RD&D) to bring the science to a similar level as for GDFs [4].
It is estimated that the total global inventory of radioactivity confined within (borosilicate) glass from reprocessing is on the order of $10^{20}$ Bq, with an approximate weight of 15,000 metric tonnes [5, 6]. The halflife of some of the radionuclides in nuclear waste is from the order of $10^{5}10^{9}$ y (e.g. $^{135}$Cs, $^{79}$Se, $^{238}$U, etc) [6]. This waste will generate heat for several hundred years [7, 8]. Any disposal container should have a lifetime long enough to survive (i.e. no breach therefore zero release) the heatproduction period.
For clay sediments, a porous mediumtype pore network is the path through which transport occurs [9]. For crystalline rocks on the other hand, transport is typically through a fracture network with concomitant matrix diffusion [1]. The nonlinear interaction between different transport phenomena and the very long time scales of the processes involved, necessitates modelling as the most realistic tool to assess the risks to humans and the environment [10]. Given the much greater disposal depth of a deep borehole concept compared to conventional GDFs, and the heatgenerating feature of the disposed waste, temperature evolution and its potential impact on radionuclide migration has to be accounted for in postclosure safety assessments.
For conventional GDFs, several studies have been conducted to model the thermal, hydraulic and mechanical interactions within the near field of the disposal environment [11]. The majority of these postclosure safety assessments consider isothermal transport of dissolved radionuclides, using simulation codes such as FRAC and PORFLOW [10, 12]. Some studies have also used TOUGH an TOUGHREACT to couple other transport phenomena [13]. However, few modelling studies exist for deep borehole disposal which include a proper linkage between the natural hydrostatic and temperature profiles to heat and solute mass transport at the Darcy scale [14, 15].
Here we present a coupled heat and solute mass transport modelling framework, subjected to depthdependent temperature, pressure and viscosity profiles  assuming an instantaneous release of all radionuclides. This is a very conservative assumption but is consistent with typical “what if?” scenarios undertaken in postclosure safety assessments [16]. The TOUGHREACT code [17, 18] was used in an axisymmetrical domain with a total depth of 3200 m. Several scenarios of heatgeneration were investigated to test if the additional heat produced by the waste containers affects radionuclide migration, e.g. by generating convectiondriven mass transport. Results show that the heat generation does not significantly affect the extent of the solute mass plume.
Thermal diffusion, the Ludwig – Soret effect, plays an important role in transport of heat and mass in fluid mixtures. The coupling between heat and mass transport extends Fourier’s law for heat conduction and Fick’s law for mass diffusion and is quantified by the Soret coefficient. The effect has applications in industrial processes, such as utilization of waste heat [1], analyses of composition gradients in oil reservoirs [2], as well as novel use in nanomachines [3]. Many experimental techniques have been used to measure Soret coefficients in bulk fluids [4]. It is known that a porous medium may have an impact on the Soret effect, but experimental data are not conclusive on its origin. For instance, porosity, permeability, wettability, and tortuosity will all change diffusion relative to bulk fluid, but the magnitude and mechanism of the coupling of mass diffusion and thermal diffusion is still unknown.
We will present results from nonequilibrium molecular dynamics simulations [5] of the Soret effect for a LennardJones model with two miscible fluid components in a porous medium. The medium has different porosity and wettability preferences for the two fluid components. We show that the wettability preferences change the Soret coefficient and discuss the mechanisms that lead to such change.
Marine sediments hosting methane hydrates (MH) cover pore sizes ranging from coarse‐grained sands to fine‐grained silts and clays. Coarsegrained sediments favour methane gas and methane saturated water flow and hence the formation of large concentrations of MH in pores (~6090%) (e.g., Weinberger and Brown, 2006). However, most of the world's MH inventory exists disseminated within finegrained sediments in very low saturations (below 10%) (e.g., Max et al., 2016). Experimental tests (e.g., Anderson et al., 2009; Chuvilin et al., 2005; Handa and Stupin, 1992; ∅stergaard et al., 2002; Uchida et al., 1999, 2004) and theoretical models (e.g., Clennell et al., 1999; Henry et al., 1999; Sun and Duan, 2007) have evidenced that MH confined in narrow pores (<100 nm) are subjected to capillary effects that disturb their thermodynamic stability. These studies show that capillary pressure hinders MH stability by decreasing the pore water activity and increasing aqueous methane solubility. Then, as pore size decreases, capillarity effects shift the MH equilibrium phase boundary towards higher pressures and/or lower temperatures than those predicted from bulk conditions (no sediment); similar and in addition to the shift generated by chemical inhibitors like salt. Understanding the stability conditions of natural MH is critical for a reliable prediction of the methane budget stored in hydrate systems as well as to assess the feasibility of its extraction for energy purposes (Ruppel and Waite 2020). Here, we first propose an equilibrium model to simulate MH formation conditions accounting for capillary effects. Analogously to water freezing behaviour in pores (e.g., Nishimura et al., 2009), our model assumes MH formation to be controlled by the sediment poresize distribution and the balance of the capillary forces developed at the liquidhydrate interface. Our model uses the ClausiusClapeyron relation for the thermodynamic equilibrium of methane and water chemical potentials in hydrate systems. It defines the thermodynamic equilibrium conditions that need to be satisfied by the liquid and MH phase pressures and the system temperature in a single pore size. Our model captures the depression of the MH equilibrium temperature observed experimentally during hydrate formation/dissociation tests performed in narrow pores (≤30.6 nm) (e.g., Deaton and Frost, 1946; Jhaveri and Robinson, 1965; McLeod and Campbell, 1961; ¬∅stergaard et al., 2002; Anderson et al. 2003, Anderson et al. 2009). Then, the model is combined with van Genuchten's capillary pressure (van Genuchten, 1980) to relate the thermodynamic properties of the hydrate system to the host sediment poresize distribution. The model is finally applied to simulate and quantify MH formation in sand, silt and clays with different content of fineparticles, under equilibrium conditions and without mass transfer limitations. The simulations evidence that capillary effects are negligible in sand and almost negligible in silty sediments but exert a key control in MH stability and saturation within clayey sediments. In particular, the results show that at thermodynamic conditions typically found in the seabed, capillary effects may reduce the maximum hydrate saturation expected in sediments with a high content of fines up to 50%.
*Arts et Metiers Institute of Technology, University of Bordeaux, CNRS, Bordeaux INP, INRAE, I2M Bordeaux, F33400 Talence, France.
+University of Bordeaux, CNRS, Arts et Metiers Institute of Technology, Bordeaux INP, INRAE, I2M Bordeaux, F33400 Talence, France
This presentation addresses heat transfer in porous media with the assumption of local thermal non equilibrium (LTNE). The macroscopic description makes use of a twoequation model featuring a heat transfer coefficient between the solid and fluid phases. This coefficient can be determined from direct pore
scale numerical simulations by computing the ratio of the heat flux at the solidfluid interface to the difference of the average temperatures [1]. When dealing with periodic materials, the resolution of the closure problems [2] obtained when using the volume averaging method can be considered for its evaluation. Both methods are widely used in the literature, but to our knowledge, no study has ever compared their predictions. For this reason, we have implemented both methods and applied them on basic periodic case where a creeping incompressible flow has been considered.
Results highlight two main facts. First, while the resolution of the closure problems provides a constant heat transfer coefficient, the method based on direct numerical simulations provides a timevarying coefficient that ends up to be equal to zero at steadystate. Special considerations are needed for a proper comparison of the two approaches. Second, as widely known, the heat transfer coefficient has shown to be a function of several parameters, mainly the Prandtl, Nusselt, and Biot numbers. The latter has been particularly investigated in this study by proposing a first analysis with homogeneous constant solid temperature and a second generic one with nonhomogeneous and varying solid temperature.
Finally, the method based on direct numerical simulations is applied on a 3D CMT of Calcarb, a carbon fiber preform used as thermal protection in space vehicle heat shields. The results in terms of heat transfer coefficient are compared to experimental results obtained elsewhere [3].
The numerical framework developed during this study is made available in the Porous material Analysis
Toolbox based on OpenFoam (PATO) released Open Source by NASA [4] (www.pato.ac).
Chemical exchange and energy storage devices utilize gas diffusion layers (GDLs) to facilitate the transport of gaseous reactants and liquid electrolytes to a catalyst site. The goal of the current work is to study the liquidgas interface dynamics that result in flooding in GDLs in the context of electrochemical CO2 reduction (CO2R). In CO2R reactors, flooding of the porous layer imposes a great challenge in expanding this technology to industrial applications. In fact, flooding of the GDL can happen within several hours of operation, leading to a reduction in selectivity toward CO2R reaction products. Generally, flooding is inhibited by hydrophobic coating applied to internal surfaces of the GDL, such as polytetrafluoroethylene (PTFE). However, recent innovations in additive manufacturing and catalyst design have enabled highperformance reactors with unprecedented rates of product conversion. Wettability and the potential for flooding increases as lower surface tension CO2R reaction products (e.g., formic acid, methanol, ethanol, and 1propanol) are introduced in high concentrations into the flowing liquid streams, thus challenging existing GDLs. If the GDL becomes flooded and pores start to fill up with liquid, gaseous CO2 is blocked from reaching the active site catalyst surface. It is hypothesized that the liquid electrolyte flooding the GDL under highconversion reactor operation leads to suboptimal performance or even failure of the electrochemical reactor.
We will present a threedimensional model incorporating the Hoffman expression for dynamic contact angle for CO2R products. Next the governing equations will be discretized numerically using the volume of fluid technique in OpenFOAM and executed on a parallel computing platform. The CFD core of this simulation serves as foundation to an optimization algorithm that iterates over the surface texture and morphology of the GDL to study the liquid saturation as a function of capillary pressure. Three morphologies of gyroids, lattice structures, and tubular arrays in combination with three surface textures of triangular waves, Voronoi embossment, and finned embossments are selected for the purpose of study. The designs are constrained to have equal liquidgas interface area and contact line length. However, surface texture parameters such as pattern density, chord height, and number of cells per unit volume are unconstrained variables that can be optimized. To update the geometry in each iteration, nTopology software has been used to create a new lattice structure with new sets of input variables. This unique software integration offers a significant advantage over geometry manipulation in OpenFOAM and could be applied to many similar problems involving complex geometry CFD calculations.
During the last couple of decades, interest in smallsized, singleuse, disposable devices such as rapid diagnostic kits (RDK’s) has dramatically soared [1]. Currently, such portable electronic devices rely heavily on conventional coin/button cell batteries for their operation. Although such batteries are very reliable and efficient, they become troublesome when such singleuse kits have to be disposed of. The problem is that the kits are usually discarded when the battery is not fully discharged. Evidently, this means a huge waste of energy, but, more importantly, it poses severe environmental hazards when the chemicals stored inside the battery diffuse into aquifers. In a world reimagined with biodegradable materials, it is of no surprise that in recent years we are witnessing a growing interest in cellulosic materials for the construction of such kits. Paper is cheap, recyclable, and biodegradable. An extra feature of cellulosic paper is that they can be used in the context of a flow battery to energize the printed circuitry of such kits [2]. That is to say that, while test fluid such as urine or blood is laterally spreading through the paper, they can serve as the fuel to energize the kit. As a matter of fact, the electrodes can be as simple as two parallel lines sketched by just a pencil on the two edges of the cellulosic paper. Fortunately, in recent years, novel paperbased, allquinone, flowthrough, microfluidic flow batteries such as PowerPAD have been developed for singleuse applications [3]. The cellulosic absorbent pad incorporated in the design of this flow battery establishes flow through its porous carbon electrodes via capillary action thereby eliminating the need for any type of micropump. The device is inherently transient as it relies on passive, dynamic wicking of electrolytes through the porous electrodes where electrochemical reactions occur. But, the power output of this promising flow battery should further be enhanced before it can be considered as a true contender to conventional batteries. And this requires that a mathematical model is available which can be used for its design. In this work, a general theoretical framework has been developed for designing such flow batteries. The proposed twostep methodology can be used for determining the polarization curves of such electrochemical cells at discrete times. Results obtained this way can then be used to investigate the effect of different parameters on the maximum power output of the cell and its efficiency as functions of time. In our twostep methodology, imbibition of electrolytes by electrode/pad is computed first using Richards equation combined with the BrooksCorey correlations. In the second stage, the saturation field so obtained is used to obtain the timedependent velocity field from which polarization curves can be obtained at discrete times. Using a twodimensional finiteelement analysis, we have been able to qualitatively predict the timedependent behavior of the PowerPAD battery [3]. The methodology developed in this work has also enabled us to qualitatively investigate the effect of pad’s thickness, pore size, poresize distribution, and contact angle on the power output of this battery.
Among the aqueous redox flow battery systems, redox chemistries using a zinc negative electrode have a relatively high energy density [1]. In this study, a new flow field design was applied in a zinciodide flow battery, with some of the electrolyte flowing over the electrode surface, and a fraction of the flow passing through the porous felt electrode in the direction of current flow. The flow battery was tested under constant current density and the efficiency, discharge energy density and power density of the battery were improved compared to conventional flow field designs. The morphology of the zinc deposition was studied using scanning electron microscopy and optical profilometry. It was found that the flow through the electrode led to a thinner zinc deposit with lower roughness on the surface of the electrode, in comparison to the case where there was no flow through the electrode.
During the charging process, metallic zinc is electroplated on the porous graphite felt in the negative side of the battery [2]. Exsitu tomographic measurements were used to image the zinc particles on the surface and inside the porous felt qualitatively and quantitatively. Information of porosity, thickness and distribution of the zinc in the porous felt were obtained from xray computed tomography (XCT) images. Volume rendering of graphite felt from XCT images showed that in the presence of flow through the electrode, more zinc deposition occurred inside the porous felt, resulting in a thinner surface deposit, and higher battery capacity and improved performance.
[1] Khor, A., P. Leung, M. R. Mohamed, C. Flox, Q. Xu, Liang An, R. G. A. Wills, J. R. Morante, and A. A. Shah. "Review of zincbased hybrid flow batteries: From fundamentals to applications." Materials today energy 8 (2018): 80108.
[2] Li, Bin, Zimin Nie, M. Vijayakumar, Guosheng Li, Jun Liu, Vincent Sprenkle, and Wei Wang. "Ambipolar zincpolyiodide electrolyte for a highenergy density aqueous redox flow battery." Nature communications 6, no. 1 (2015): 18.
Xray tomographic microscopy (XTM) has become a versatile tool for the analysis of the microstructure in fuel cells, lithium ion and redox flow batteries, as well as the transport processes therein. Advanced analysis tools like 3D interfacial curvature analysis have been developed to determine the capillary pressure in digital rock physics investigations [1] and were recently applied to exsitu XTM imaging experiments of the droplet release cycle in polymer electrolyte fuel cells [2]. Within this presentation, we will give insights into the water cluster formation using operando XTM imaging at a frequency of 1 Hz from liquid water emergence at the catalyst layer – gas diffusion layer interface until liquid water breakthrough and droplet formation in the gas channel of the flow field. With the help of interfacial curvature analysis as well as volume of fluid simulations [3], it was possible to obtain information about the capillary pressure evolution in the water phase. We will explain the nuanced interactions of water volume and pressure evolution during the growth of the percolation network within the GDL and the droplet formation and comment on the observed distinct differences to exsitu pressure evaluations.
References
[1] Q. Lin, B. Bijeljic, R. Pini, M. J. Blunt and S. Krevor, Water Resources Research, 54, (2018) 7046
[2] A. Mularczyk, Q. Lin, M. J. Blunt, A. Lamibrac, F. Marone, T. J. Schmidt, F. N. Büchi and J. Eller, Journal of The Electrochemical Society, 167, (2020) 084506
[3] D. Niblett, A. Mularczyk, V. Niasar, J. Eller and S. Holmes, Journal of Power Sources, 471, (2020) 228427
Transitioning to a sustainable energy economy is one of the greatest challenges of this century. Integrating renewables (e.g., wind and solar power) into the grid must be accelerated to limit the devastating effects of climate change. Due to their intrinsic intermittency, largescale energy storage must be deployed to balance the mismatch between supply and demand[1]. Redox flow batteries (RFBs) stand out as a promising candidate due to their ability to independently scale power and energy and projected lower costs[2,3]. The performance of RFBs largely depends on the porous electrodes microstructure and chemical composition as they must simultaneously provide high surface area for electrochemical reactions, low pressure drop, high electrical conductivity, and facile mass transport[4]. Stateoftheart electrodes are composed of carbon fibers which are arranged together using mechanical methods forming idiosyncratic structures such as papers, cloths and felts[5]. Their fabrication involves multiple complex subprocessing steps[6] impacting the final manufacturing cost and offering limited versatility to control the threedimensional structure of the material, which ultimately hampers widespread commercialization of the technology.
Here, we introduce the nonsolvent induced phase separation (NIPS) as a simple and versatile fabrication method for carbonaceous porous electrodes[7]. Drawing inspiration from membrane science and technology[8], the NIPS method has been leveraged to synthesize morphologicallydiverse microstructures (e.g., isoporous, macrovoids, porosity gradient) which are appealing to electrode manufacturing. A polymer solution, containing polyacrylonitrile (PAN, carboncontaining) and polyvinylpyrrolidone (PVP, poreforming agent) dissolved in N,Ndimethylformamide (solvent) was casted in a mold and subsequently immersed in water (nonsolvent). Finally, the polymeric scaffold is carbonized under inert conditions to form a conductive network. Easily adjustable parameters, such as solvent type, polymer concentration and temperature enable control of the final electrode microstructure. In this work, we study the influence of the PAN:PVP ratio on the electrode microstructure and its resulting effect on RFBs performance.
Microstructural characterization revealed a multimodal pore size distribution composed of fine, interconnected microvoids (pore diameter 215μm) coupled with through plane, fingerlike macrovoid channels (throat diameter > 50 μm) forming honeycomb networks. The unique microstructure, not attainable with traditional carbonfiber manufacturing techniques, enables large surface area at the membraneelectrode interface and fast electrolyte replenishing which reduces mass transfer resistance within the electrode. Flow battery tests with Fe2+/Fe3+ electrolyte revealed a considerable reduction of the charge transfer (RCT 0.016 Ω) and mass transfer (RMT 0.025 Ω) overpotentials of the novel electrodes compared to the commercial baseline (SGL29AA, RCT 0.326 Ω and RMT 0.151 Ω at a linear velocity of 5 cm s1) at the expense of a slight increase in pressure drop. In the final part, we demonstrate the use of NIPSelectrodes in a full allvanadium RFB. The polarization analysis revealed a ca. 70% improvement in power density compared to the baseline material, which can be attributed to reductions in the charge transfer and mass transport overpotentials. Although nascent, NIPS emerges as a promising platform to engineer porous electrodes for RFBs and other convectionenhanced electrochemical systems.
Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy and precision of the predictions are essential. Here, we consider an homogenized model for ionic electrodiffusion and osmosis comprising a nontrivial system of nonlinear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. We study numerical challenges related to approximating the system and validate the model against values from experimental studies in the physiologically relevant setting of cortical spreading depression (CSD). CSD is a wave of electrophysiological hyperactivity accompanied by substantial shifts in ionic concentrations and cellular swelling. We evaluate different associated finite elementbased splitting schemes in terms of their numerical properties, and find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution. Further, the data for several CSD hallmarks obtained computationally, including wave propagation speed, direct current shift duration, peak in extracellular potassium concentration as well as a pronounced shrinkage of extracellular space, are well in line with what has previously been observed experimentally. Finally, we note that the model considered within this work may be applied to study a wide array of phenomena in brain physiology and pathology.
Osteosarcoma is a primary bone tumour that occurs mainly in adolescents and young adults. The survival rate at 5 years is 70% and drops to 25% for patients with metastases or poor responders to treatment [1]. Therapeutic strategies have not evolved for more than three decades and new developments are needed to improve the specific management of patients.
Like the majority of complex genomic sarcomas, this type of tumours presents strong spatial heterogeneities. In the case of osteosarcoma, there are heterogeneities in bone microarchitecture, cell density but also in the response to treatment due to the potentially localised effect of chemotherapy [2]. Because of the cell populations involved in the evolution of osteosarcomas such as osteoblasts, osteoclasts or osteocytes, it is supposed that osteosarcoma is highly sensitive to the mechanical effects occurring at various spatial scales [3].
At the tissue scale, the osteosarcoma can be considered as porous medium involving various phases (bone, fluid and cells). It is admitted that transport mechanisms and structural deformations play a fundamental role in disease evolution but also on treatment efficiency. Therefore, it is important to determine accurately bone mechanical properties.
The aim of this work is to study different transport mechanisms (interstitial flow, diffusion), structural mechanics (linear elasticity) and poromechanics in the porous tumour at the tissue scale by an approach based on upscaling methods. This methodology rely on histological and immunohistological binarized sections of surgical specimens from a Toulouse patients cohort (CRB Cancer Toulouse). The statistical study of the osteosarcoma microarchitecture shows that the identification of characteristic lengths is complex and that a separation of spatial scales is not necessarily identified. To solve this problem, a sequential gridblock upscaling approach was therefore chosen [4].
We propose to study the 2step sequential GridBlock method for each physical mechanism mentioned above. In order to reduce the influence of boundary conditions on the sequential process, an extendlocal method has been developed for the first upscaling. These methods have been implemented with the finite element toolbox FEniCS [5]. The dependence to the various methods parameters (boundary conditions, GridBlock size etc) of the resulting tensors and their properties were studied.
Through this approach, mechanical properties and biological parameters (e.g. cell population density) can be correlated. It is then possible to obtain new quantitative mecanobiological information on bone tumours from patients followup images and potentially to obtain markers useful in patientspecific treatment management.
Deep tissue injury often results in contraction of skin due to mechanical pulling forces exerted by skin cells (fibroblasts) in the dermal layer. If contractions are morbid, then they are referred to as contractures. Contractures cause disabilities to patients, by, for instance, loss of mobility of a joint. By the use of modeling, we aim at understanding the mechanisms behind the formation of a contracture and at predicting which wound is likely to develop a contracture and which treatments can be employed in order to minimize the likelihood of a contracture. In most of our work, we used the immerse boundary approach based on a superposition of Dirac Delta functions to describe the forces exerted by individual skin cells, which results in a finite element solution that is not in H1. In [1, 2], we developed the smoothed particle approach as a replacement of the immersed boundary approach to improve the accuracy of the solution.
The smoothed particle approach is categorized as agentbased model, in which cells are considered as individuals. This class of models has the advantage of investigating the cellular activities of every single cell. Furthermore, for this modelling class, it is more straightforward to deduce parameter values from in vitro or in vivo experiments. However, once the number of cells is in the order of thousands and the wound scale is large (like centimeter square), these models become too expensive from a computational perspective. For the larger scales, continuumbased models are used. These models do not treat cells as separate entities, but treat cell behavior by the use of cell densities, which represent numbers of cells per unit volume. The resulting partial differential equations are easier to solve in terms of computational power.
We investigated the connections and consistency between these two types of models, regarding the momentum balance equation, which is used to describe the forces exerted by cells on the extracellular matrix (ECM) causing the deformation of the substrate. In one dimension, we establish the consistency between these approaches in both analytical solutions and finiteelement method solutions. In the multidimensional case, we have only computationally shown the consistency between the continuumbased and agentbased models.
Quantification of the full brain structural vasculature and physiological response is advantageous for improved understanding of cerebrovascular disease progression affecting the brain. In this respect, characterization of the whole brain angioarchitecture across multiple resolution scales from arteries and veins down to capillaries enables simulation of whole brain blood flow. In the current work we are pioneering a blood flow simulator for a complete in silico mouse brain model previously segmented for vasculature. We report structural and functional parameters of the mouse brain angioarchitecture that to date have not been reported elsewhere.
Capillaries are the most frequent vessel type of the brain’s vasculature. The dense and highly interconnected capillary bed is key to ensure a robust blood supply over the entire depth of the cortex, and during baseline and neuronal activation. Besides its relevance our knowledge of structural and functional properties of the capillary bed remains limited. We perform blood flow simulations in realistic microvascular networks and alter individual capillaries to improve our understanding of capillary perfusion and robustness. More precisely, we first investigate the impact of single capillary dilation (1), which has been suggested as a mechanism to contribute to upregulate flow during neuronal activation. Subsequently, we study flow changes in response to single capillary occlusion (2), because these microlesions are linked to dementia and Alzheimer’s disease. Both studies provide insights on the role of these alterations but importantly also regarding general characteristics of the cortical capillary bed. Additionally, thanks to our numerical model which tracks 100 thousands of red blood cells (RBCs) (3), we are able to comment on the impact of RBCs on these local changes.
Our results show that a capillary dilation of 10% leads to a flow increase of 23% (per 100 µm) and an increase in the number of RBCs of 20% in the dilated capillary. Interestingly, the precise response depends on the relative bulk flow velocity difference at the upstream divergent bifurcation. As such, single capillary dilation causes a local increase in flow rate and a redistribution of RBCs. However, to increase the total inflow by ~6% in a microvascular network embedded in a tissue volume of 1 mm3 all capillaries need to dilate by 10%. Consequently, capillary dilation is likely relevant for a localized redistribution of flow and RBCs, but is not the driving force to induce an overall flow increase.
Comparable to single capillary dilations, the effects of a microstroke are most pronounced in the direct vicinity of the microstroke capillary (MSC) and the severity is governed by the local vascular topology. The largest changes are observed for a MSC with a convergent bifurcation upstream and a divergent downstream (2in2out). Here, the flow rate drops by 80% in the directly adjacent vessels and is still reduced by 20% in generation ±3 from the MSC. Significantly, smaller changes are observed for a MSC with a divergent bifurcation upstream and a convergent bifurcation downstream (1in1out). Interestingly, MSCs of type 2in2out are considerably less frequent than MSCs of type 1in1out. Moreover, they supply a significantly smaller tissue volume with oxygen and nutrients. Taken together, our results suggest that the perfusion of the capillary bed is inherently robust to single capillary occlusions. Moreover, we hypothesize that the different topological configurations might fulfil distinct structural and functional tasks.
Due to the limited energy storage capabilities of the brain, maintaining a robust oxygen and nutrient supply to all regions of the brain is crucial. During healthy conditions, the interconnected network of blood vessels sustains blood flow to all brain areas. However, during stroke the overall blood supply is reduced drastically. This typically causes tissue damage, which often results in permanent disability or even death.
Generally, the microvasculature of the brain cortex consists of three vessel categories: (1) the surface vessels, (2) the penetrating trees and (3) the capillary bed. Collaterals are blood vessels connecting major feeding arteries at the surface of the brain, e.g. the middle and anterior cerebral arteries (MCA, ACA). If the primary flow path is blocked due to occlusion of the MCA, collaterals provide an alternative route for blood to partially maintain perfusion in the undersupplied brain region (MCA region). Therefore, vascular networks with collaterals are more robust towards tissue damage during stroke [El Amki & Wegener (2017)].
The goal of our work is to better understand the role of collaterals in redistributing flow during stroke and during the subsequent recanalization of the occluded vessel. To date, blood flow can only be quantified in a small number of vessels, hence in vivo measurements only provide limited insight on overall changes in perfusion and on the role of the collaterals. Consequently, we employ numerical simulations [Schmid et al. (2017)] to compute flow and pressure characteristics in large semirealistic microvascular networks. Here, we present a novel approach to generate such networks by combining realistic arterial networks with an artificial capillary bed. To achieve diameter and flow rate distributions consistent with sparse in vivo measurements, the diameters of the entire network are adjusted by solving an inverse problem using the adjoint method [Epp et al. (2020)]. This allows us to generate large microvascular networks which (a) represent the structure of the real vasculature and (b) are consistent with in vivo measurements in individual subjects with and without collaterals.
Our results confirm that the reduction of overall perfusion after MCA occlusion is less severe in networks with collaterals. Moreover, we show that the redistribution of flow is a direct consequence of the pressure changes initiated by the occlusion and occurs even without collateral dilation. This results in a substantial increase in flow in all collaterals and in the majority of surface arteries at the ACA side, as well as a directed flow from the ACA towards the MCAsupplied territory.
In summary, our approach allows to incorporate sparse experimental data into blood flow simulations. This strengthens the link between in vivo and in silico studies and allows quantitative and combined study designs. The developed simulation framework enables us to study transient changes during treatment as well as the role of changes at the capillary level during stroke. Both aspects are highly relevant for the recovery of the patient but difficult to study in vivo.
Percutaneous vertebroplasty is a medical procedure done for treating weakened or damaged vertebrae. In this procedure, a cementlike polymer (bone cement) is injected percutaneously into the inside of the vertebra, which is a porous trabecular structure. Upon curing, the bone cement restores the structural strength of the vertebra. While the procedure is fairly successful, there is a risk of bonecement leaking outside the vertebra, which could lead to severe problems like pulmonary embolism or paralysis. Towards this, a numerical model that can simulate the flow of bone cement inside the porous vertebra could be useful. Such a model could help mitigate the risk of leakage and help the surgeons determine optimum operating parameters, viz. the injection pressure, the cement viscosity, etc.
However, the problem is particularly challenging due to many factors like the complex geometry of the trabecular structure, the curing of the bone cement, nonNewtonian rheology of the bone cement and the bone marrow, and patienttopatient variation in material parameters. In order to tackle this, a continuummechanical approach based on the Theory of Porous Media is used to develop a multiphase model consisting of bone, bone marrow, and bone cement. The flow is modelled using a fully upwind Galerkin formulation. Rheological modelling of the fluids is done using nonNewtonian (shearthinning) constitutive equations. The viscosity at the macroscale is obtained using semiempirical models to upscale the shearrate. The curing of bone cement is modelled by adding a timedependence to its viscosity. Rheological characterisation of the bone cement is carried out to obtain the material parameters. For the validation of the model, an experiment is set up where the bone cement is injected into representative porous media (here, aluminium foam). The evolution of the flow is captured using a dynamic CT imaging setup. The results at the different stages of injection are then compared and studied.
Viruses are generally found as aggregates in the environment. The aggregation is a natural process which helps viruses to survive in soil and sediments and provides them resistance to disinfection, when they are suspended in water. Aggregation distinguishes between homogeneous and heterogeneous. In the former viruses agglomerate among themselves; whereas in the latter they nucleate around a foreign particle. The formation of viral aggregates may facilitate transport of viruses as well as cause clogging of porous media. Viral agglomeration dependents on the type of virus, solution composition, and the presence of particulate. If there are several works where the process is investigated experimentally, there are few attempts to describe it mathematically.
Here, we present a study which combines laboratory experiments and modeling to describe the formation and the evolution of viral aggregates. In particular, bacteriophage MS2 were used and tested under the effects of porous medium geometry, pH, ionic strength, and temperature. A microfluidic system was built with channels of various geometry and sinusoidal porethroat. A mathematical model of particle aggregation based on the population balance equation (PBE) of the number of viral particles coupled with extended DLVO theory was developed to determine the interactions among viruses and the evolution of the cluster size. Preliminary results show that, an early aggregation occurs which controls the later evolution of the cluster size. Given a type of virus, pH and porethroat shape are the important factors controlling the aggregation process.
Microbes in natural and engineering systems are often found as aggregates consisting of microbial communities, organic and inorganic matters, and water. Such bioaggregates play important roles in shaping biogeochemistry of soil and groundwater environments, clogging of porous media, biofilm formation, and human lung infections [1 – 3]. In addition, aggregated cells are reported to have enhanced protections against external stresses such as antibiotics, nutrient starvation, oxidative stress, etc., helping microbes to cope with environmental changes [3]. Therefore, understanding how bioaggregates are formed has been an active area of research in not only engineering and natural sciences but also in clinical and evolutionary standpoints. While bioaggregates are widely generated in porous systems, the role of porescale flow and porous media structure on aggregation is still poorly understood. In this study, we combine microfluidics experiments and threedimensional (3D) numerical simulations to demonstrate that the unique 3D flow structure at the constriction points of porethroats, which is ubiquitous in porous media, induces bioaggregate formation.
We use a single channel with a sinusoidal porethroat as an analog for a porous system (FIG. 1A). Upon injection of an E. coli suspension (OD600 = 0.1) at a constant flow rate (0.2 μl/min), we observed the formation of bioaggregates at the porethroat while in a straight channel only attachment and growth were detected (FIG. 1B  D). Pore clogging and pressure buildup occur as E. coli cells aggregate, which eventually lead to the detachment and flushing of bioaggregates. A series of laboratory and numerical experiments revealed that 3D secondary flows facilitate attachment and capture of cells at the porethroat, inducing aggregation. We further identified a critical shear stress value (~ 1.8 Pa) below which an aggregate forms and above which biofilm streamerlike morphology is found. Finally, we show that when the shear stress at the porethroat is maintained below the critical shear stress, the porethroat is rapidly clogged by bioaggregates.
Bacterial motility is central to processes in agriculture, the environment, and medicine. While motility is typically studied in bulk liquid or on flat surfaces, many bacterial habitats—e.g., soils, sediments, and biological gels/tissues—are complex porous media. Here, we use studies of E. coli in transparent 3D porous media to demonstrate how confinement in a heterogenous medium fundamentally alters motility. In particular, we show how the paradigm of runandtumble motility is dramatically altered by porescale confinement, both for cells performing undirected motion and those performing chemotaxis, directed motion in response to a chemical stimulus. Our porous media also enable precisely structured multicellular communities to be 3D printed. Using this capability, we show how spatial variations in the ability of cells to perform chemotaxis enable populations to autonomously stabilize largescale perturbations in their overall morphology. Together, our work thus reveals new principles to predict and control the behavior of bacteria, and active matter in general, in complex environments.
A meterscale tank test simulating twodimensional plane strain conditions was performed to evaluate the effectiveness of microbially induced desaturation & precipitation (MIDP) through denitrification for ground improvement applications in stratified soils. The process stimulates indigenous nitratereducing bacteria through the injection of a solution containing nitrate, calcium and a dissolved organic carbon source and results in the production of biogenic gas, biominerals and biomass. Entrapped gas bubbles can dampen pore pressures under cyclic loading, while biominerals form cementing bridges between existing grains, making MIDP a viable ground improvement technique for liquefaction hazards in granular soils. Desaturation of the soil requires a much lower amount of treatment than precipitation, however, precipitation may provide a more durable stabilizing effect as the entrapped gas may migrate and vent to the atmosphere. Previous studies have demonstrated the mechanical response for treated granular soils at bench scale, however limited knowledge is available on the impact of partial desaturation on the hydraulic properties of the soil, particularly in stratified formations. Further investigation into this area is important for the upscaling and future commercialization of the process as it may affect injection strategies, and the distribution of substrates and metabolic products. The process was monitored in terms of changes in electrical conductivity, moisture content, pore pressure and flow velocity. The results demonstrate how stratification affects the process performance and identify the challenges associated with treatment of layered soil systems.
Key functions of soils, such as permeability or habitat for microorganisms, are determined by structures at the microaggregate scale (< 250 $\mu m$).
Although advanced imaging techniques now allow snapshots even down to the nanoscale, the evolution of elemental distributions and dynamic processes still can often not be assessed experimentally. So mechanistic models operating at the pore scale can help to study and understand such phenomena.
We consider the complex coupling of biological, chemical, and physical processes in a hybrid discretecontinuum modeling approach. It integrates dynamic wetting (liquid) and nonwetting (gas) phases including biofilms, diffusive processes for solutes, mobile bacteria transforming into immobile biomass, and ions which are prescribed by means of partial differential equations. Furthermore the growth of biofilms as, e.g., mucilage exuded by roots, or the distribution of particulate organic matter in the system, is incorporated in a cellular automaton framework (CAM) presented in [1, 2, 3]. It also allows for structural changes of the porous medium itself (see, e.g. [4]). As the evolving computational domain leads to discrete discontinuities, we apply the local discontinuous Galerkin (LDG) method for the transport part.
Finally mathematical upscaling techniques are used to incorporate the information from the pore scale to the macroscale [1,5].
The model is applied for two research questions: Although a continuous reorganization of disintegrating and assembling soil aggregates can be observed, we still lack understanding of the mechanistic relationship between aggregation and organic matter sequestration in soils. We model the incorporation and turnover of particulate OM influencing soil aggregation. We hypothesize that soil mineral surfaces colocated with decomposing OM develop into spatially discrete ‘gluing’ hotspots that enhance aggregation locally and tested different numerical scenarios of OM input regimes, OM turnover, particle size distribution and ‘gluing’ hotspots.
As a second application, we quantify the effective diffusivity by upscaling on 3D geometries from CT scans of a loamy and a sandy soil. We see that conventional models for diffusivity cannot account for natural pore geometries and varying phase properties. Upscaling allows also to quantify how root exudates (mucilage) can significantly alter the macroscopic soil hydraulic properties.
Seawater flooding, is a widely used improved oil recovery technique in oil reservoirs. Due to presence of sulfate (SO42) in seawater, this technique can be associated with two side effects. The first side effect is the formation of various types of scale (e.g. BaSO4, CaSO4, and SrSO4) due to the incompatibility of seawater and formation brine that reduces permeability both in the reservoir and wellbore. For example, seawater containing SO42−, with field water rich in Ba2+ may cause BaSO4 scale precipitation both within the formation and also on coproduction at the wellbore[A]. Second, the activity of sulfate reducing bacteria (SRB) may result in bioconversion of sulfate into hydrogen sulfide, a hazardous[B] and corrosive gas. In case both of these processes are possible, they will compete for sulfate and one may limit the other. Therefore, it is important that the both are studied simultaneously. Furthermore, use of souring mitigation strategies can also affect the availability of sulfate through different pathways[C], which in turn calls for the necessity of a comprehensive simulation of all the processes. What makes this complex is that the microbial activity happens through oneway chemical reactions, which is the microorganisms consume sulfate among other things to generate the products, especially hydrogen sulfide in case of SRB. However, scaling happens through equilibrium processes, which mean the reaction path is determined based on the comparison of a state with the equilibrium state. Hence, the microbial reactions can heavily disturb possibly already existing equilibrium of sulfate with other ions and minerals in the reservoir.
In this work, we first present a model that simulates reservoir souring and mitigation together with scale formation simultaneously. Next, we use available experimental data in the literature to validate the model. A series of simulations are then conducted to identify the important parameters that control hydrogen sulfide production, scale formation, and the competition between them. The effect of scaling on porous media properties (porosity and permeability) is then discussed. Additionally, we discuss the possibility of optimizing souring mitigation strategies such that it doesn’t trigger sever scaling.
References:
[A]: K.S Sorbie, E.J Mackay, 2000. Mixing of injected, connate and aquifer brines in waterflooding and its relevance to oilfield scaling, Journal of Petroleum Science and Engineering, Volume 27, Issues 1–2, Pages 85106, ISSN 09204105.
[B]: Jiang, J. et al. 2016. Hydrogen sulfidemechanisms of toxicity and development of an antidote. Sci Rep 6, 20831.
[C] Veshareh, M.J., Nick, H.M., 2019. A sulfur and nitrogen cycle informed model to simulate nitrate treatment of reservoir souring. Sci. Rep. 9, 1–2.
In the present era marked by the desire to build a bioeconomy, plant biomass has a vast potential as a source of renewable and environmentally friendly molecules of interest. Deconstruction of biomass by a cocktail of enzymes is relevant at an industrial scale. However, achieving a better understanding of the intimate relationship between synergistic enzymatic activity and deconstruction of mechanisms of enzymatic degradation of such a complex, multiscale porous material is still needed.
In this work, we present some results regarding enzymatic degradation of a model biomass, raw wheat straw, obtained with experimental approaches such as XRay tomography or breakthrough curve analysis, which are usually dedicated to more “conventional” porous media.
First, we will present some results obtained using a laboratoryscale Xray tomograph. Fully hydrated wheat straw samples, placed in a homemade 3Dprinted thermostatically controlled bioreactor, are subjected to action of a commercial enzymatic cocktail. Enzymatic activity is monitored using state of the art techniques in enzymology. In spite of a rather limited spatial resolution (voxel size is 1.25 μm), 3D Xray tomography allows to highlight the selective effects of the enzymatic degradation. Notably, the disappearance of celluloserich cell walls as a function of the duration of the enzymatic attack, can be quantified over the full scale of the wheat straw sample (i.e. a few mm in length) offering 3D pieces of information on the degradation process, which contrasts with the 2D picture classically obtained from 2D imaging techniques.
Second, in order to probe the effects of the enzymatic degradation at a submicron scale, we analyse breakthrough curves obtained by 2D Xray radiography, when flushing with pure water a wheat straw initially saturated with a radioopaque molecular tracer. Experiments are conducted with untreated and degraded wheat straws. Breakthrough curve analysis is used to detect any differences between these two kinds of samples, which traduce an alteration of the transport properties of the tracer within the wheat straw. Modelling of the transport properties (e.g. through an effective diffusion coefficient) in relation with the enzymatic degradation mechanism (e.g. progressive disentangling of the polymer network constitutive of the plan cell walls, prior to its disappearance as imaged on 3D images) is a key point and preliminary results will be presented.
After decades of research on carbon capture and geologic sequestration (CCS), the world needs to finally move from pilot and demonstration experiments to industrialscale implementation. CCS at scale will involve unprecedented fluid injection volumes that can result in largescale pressure increases in the subsurface and may cause unwanted geomechanical effects, such as generating seismic events per reactivation of critically stressed faults. Understanding and predicting induced seismicity potential is critical in CCS projects for two reasons: (1) to avoid the potential for damaging earthquakes at the ground surface, and (2) to ensure that caprock integrity is not jeopardized by permeability increases of slipping faults. Also, in a future world with CCS being a fully deployed technology, sedimentary basins with interconnected reservoirs might host multiple storage sites between which pressure interference can be expected. Thus, largescale pressure buildup can be a limiting factor for CO2 sequestration capacity, because of induced seismicity concerns or because the possibility of distant pressurerelated impacts of individual projects needs to be considered. It has been pointed out that the subsurface storage capacity for CO2 may be increased via extraction of the native brines, a pressure management approach that of course comes with additional cost for the handling, treatment or disposal of the extracted brine and thus needs to be carefully optimized.
This presentation will start with a short description of the current worldwide status of CCS and its role as an important climatemitigation technology. We will then illustrate the basinscale pressure impacts expected from industrialscale implementation based on regional modeling studies of future CCS scenarios, and will discuss the potential for generating earthquakes from CCS at scale using the practice of waste water injection in Oklahoma and surrounding States in the U.S. as an analog. We will also present lessons learned from two field experiments—one being a controlledinjection fault slip experiment in a clay (caprock) formation which is highlighting the importance of aseismic leakage and its potential coupling to induced seismicity, the other a CO2 demonstration site where microseismicity has occurred along preexisting basement faults—and will finally evaluate brine extraction as a mitigation measure currently tested in a deep reservoir in the southern United States.
The potential of CO2 underground storage relies on the sealing efficiency of the overlaying caprock that acts as a geological barrier. Shales are extensively studied as potential caprock formations thanks to their favourable hydromechanical properties and their sealing capacity: low permeability, high sorption capacity, high swelling ability and high capillary entry pressure. The sealing capacity of a geomaterial is usually quantified based on its measured capillary entrypressure, i.e. the max. pressure difference that may exist across the interface that separates two immiscible fluids before the nonwetting fluid penetrated the pore space.
The water retention properties of shales have been previously studied in either gaswater or oilwater systems, however, no results for CO2water systems are reported to this day. In this work, the capillarity of a shaly caprock geometerial is investigated with a series of breakthrough tests (mesoscale). Based on these results, the capillary pressure (Pc)  saturation (Sw) relations of CO2 displacing water (drainage) and water rewetting (imbibition) are explored and modelled based on the basic principles of unsaturated soil mechanics. The final goal is to project the main findings of the work to possible implications for caprock integrity (entrypressure) and sealing properties (permeability) for safe CO2 storage. To this end, the transport properties of the material before and after CO2 injection are assessed and compared to previous results. The impact of the boundary conditions (pressure and temperature) to the retention, transport and sealing properties of the caprock material are evaluated. The interpretation of the obtained results is supported by an additional series of injection tests, this time in the microscale, the kinematics of which are observed and measured locally with insitu xray tomogrpahy.
Compositional flow is an important feature of numerical models in the context of gas storage in the subsurface. In practice, not only maximum inflow and outflow rates, development of reservoir pressure and gas plume shape in time are important, but because the gas is to be extracted and, e.g., combusted in a turbine, its molecular composition is of great interest. In addition, dissolution of the storage gas into the brine phase reduces the total amount of retrievable and thus commercially usable gas. Due to uncertainties associated with geological data, efficient and accurate models for energy storage in the underground need to be developed, which is additionally challenging since modeling compositional effects generally increases the complexity of models and with that the computational cost. The concept of vertical equilibrium (VE) [1,2] can be exploited in the context of compositional flow to develop fast models that give accurate solutions. In addition to phase equilibrium, which develops when a less dense gas phase is injected into the resident brine and moves upward to pool below an impermeable barrier, chemical equilibrium forms along the vertical direction driven by the chemical potential between the phases and diffusion within the phases.
In this talk we present a vertically integrated compositional model which is adaptively coupled to a compositional full multidimensional model. We use the compositional VE model in regions of the domain where the compositional VE assumption is valid, and the compositional full multidimensional model everywhere else. We develop and analyze local criteria to identify
where the compositional VE assumption is valid in the domain, including extraction and hysteretic effects on the coarse scale. During runtime of the multiphysics model, VE subdomains are identified by the local criterion and the models are assigned adaptively to those regions. We use two test cases: gas injection into a horizontal layer and gas storage with reversed flow in an idealized domeshaped aquifer, and show efficiency and accuracy of the compositional VE model and the compositional multiphysics model.
[1] Y. Yortsos. A theoretical analysis of vertical flow equilibrium. Transport in Porous
Media, 18(2):107–129, 1995.
[2] L. W. Lake. Enhanced oil recovery. Prentice Hall Englewood Cliffs, 1989.
In the CO2 sequestration process, the solubilitytrapping mechanism is one of the key mechanisms, which contributes to the safe eradication of injected supercritical CO2 (ScCO2). When ScCO2 is injected into the reservoir domain, it will start migrating upwards due to its low density as compared to reservoir water. During this migration, some amount of CO2 will be dissolved into the reservoir water. This process of CO2 dissolving in the reservoir water and getting trapped in the reservoir domain is known as Solubilitytrapping. The dissolution of CO2 in the reservoir domain can also occur due to the solubility fingering phenomenon. This solubility fingering phenomenon takes place due to the density differences between the CO2 dissolved water and connate reservoir water. Further, it will cause instability in the domain, which activates the diffusive convection process, which will increase the solubilitytrapping efficiency gradually [1].
The objective of this paper is to conduct a study on solubilitytrapping mechanisms during the CO2 sequestration process. The solubilitytrapping mechanism has a greater influence on the mineraltrapping mechanism, where the harmful CO2 can be permanently eliminated by mineral dissolution and precipitation reactions [2]. In this research, an effort is made to study the influences of petrophysical properties, geomorphological structures, and other CO2 sequestration parameters on the solubilitytrapping mechanism over a long geological time scale. The reactive transport modelling technique is used to perform this numerical analysis. It has the ability to predict the geochemical reactions in both spatial and temporal directions along with the fluid flow [3]. In the current numerical analysis, necessary assumptions are made so that only the solubility reactions are considered by neglecting the mineral reaction.
Firstly, the evidence of solubilitytrapping due to the instability created by density differences in the reservoir domain is evaluated. Then the initiation of densitydriven convective mixing is evaluated with the help of the RayleighDarcy number for an observable domain over a geological time scale. Secondly, the parametric analysis is carried out by analyzing the solubilitytrapping percentage at different injection points with a fixed injection rate so that the optimal injection point for CO2 sequestration is evaluated. Then the influences of petrophysical properties and geomorphological structure on the solubilitytrapping mechanism are studied by modelling individual synthetic domains.
Further, the analysis is carried out to study the trapping efficiency, storage capacity, and structural integrity. These simulation analyses are carried out based on the cumulative aqueous CO2 concentrations, average reservoir pressure, and reservoir temperature. The outcome of these results provide insights into the selection of the suitable range of petrophysical properties and optimal injection points for the safe and efficient implementation of CO2 sequestration.
Pilot projects to sequester CO$_2$ in geologic formations as part of Carbon Capture and Sequestration (CCS) efforts to mitigate anthropogenic climate change have obtained evidence of the mineralization of injected CO$_2$. Basalt aquifers like in CarbFix and the Wallula Basalt Pilot Project contain minerals like olivine which can liberate ions to mineralize and deposit the carbonates as they themselves dissolve. Flow through experiments in olivine show evidence for dual control of carbonation by reactive and transport processes [1] and the modification of the permeability of the host rock [2]. We have investigated the impact of porosity and permeability changes on the spatiotemporal dynamics of mineralization of calcium carbonate formed from the convective dissolution of carbon dioxide. We report our experimental study of convective dissolution of carbon dioxide in a modified vertical HeleShaw cell where the carbon dioxide is dissolved into host solutions of different concentrations of dissolved portlandite (Ca(OH)$_2$) which reacts to form solid CaCO$_3$. For the modification of the cell, glass beads of different diameters were packed into the cell in order to vary the porosity and permeability. We show that the precipitation front advances more slowly for the smaller beads as well as for the higher concentrations of reactant.
Using an evolutional pathway from disciplinary towards transdisciplinary science and research, I explore exciting opportunities that can lead to transdisciplinary research as society demands for our science expertise to be increasingly involved in developing solutions for global issues of sustainability. I do this by presenting excellent examples by way Dr. Harry Vereecken has taken this challenging path. Recommendations are presented to better train students and early‐career scientists so that they can be effective in participating and communicating their scientific knowledge to relevant stakeholders, the public, and decision makers when being part of the policy‐making process.
For more than 35 years, Harry Vereecken developed vadose science research, aiming primarily to improve the understanding and prediction of water and contaminant transport processes, supporting sustainable soil and water management. This research is key in the current sustainable development agenda, where multiple objectives are directly related to good and healthy status of soil and water systems. In this contribution, examples are given showing how combined methodologies based on pedotransfer functions, hydrogeophysics and modeling of the soilwatercrop continuum are implemented to generate information supporting sustainable soil and water management strategies. A first example deals with the evaluation of the impact of agricultural policies on groundwater quality in Belgium. In this example, long term groundwater pressures with nitrate on deep unconfined groundwater systems are simulated, allowing to evaluate the reaction time of the system for adapted agricultural policies. These policies were designed to reduce nitrate pressures on groundwater systems from the agricultural sector. In this study, the Belgian soil map, the Belgian geological map, soil physical analysis, Harry’s pedotransfer functions, and the WAVE model were used to perform the simulation study. The WAVE model (Vanclooster et al., 1996) was a revision of the SWATNIT model, developed earlier by Harry and coworkers in 1991 (Vereecken et al., 1991). A second example deals with the increase of food security in Benin. Benin inland valleys are currently underexploited and present unique opportunities to increase food production. Yet, the exploitation of these inland valleys requires a better understanding of the hydraulic behavior of these inland valley systems. In this example, it is shown how a combined approach, based on classical soil physical sampling, pedotransfer functions, and remote sensing is used to assess the infiltration characteristics of an experimental inland valley, supporting the design of an appropriate hydrological model of Benin inland valley systems. In both examples, approaches and methods inspired by Harry’s works were used.
References
Vereecken H., M. Swerts and M. Vanclooster, 1991. Description of the SWATNIT model. In : Soil and Groundwater Research Report II, Nitrate in soils. Commission of the European Communities, DGXII, 4th Environmental Research Programme: 262266.
Vanclooster M., P. Viaene, K. Christiaens and S. Ducheyne, 1996. WAVE: a mathematical model for simulating water and agrochemicals in the soil and vadose environment. Reference and user's manual (release 2.1), Institute for Land and Water Management, Katholieke Universiteit Leuven, Leuven, Belgium
In past 3 decades, Harry Vereecken has addressed a number of topics related to soil hydrology covering a range of scales from pore to catchment. To honor his outstanding efforts, here we present a new data fusion scheme to merge soil moisture from various insitu and satellite platforms. In this work, we develop a novel multiscale geostatistical algorithm which can combine massive remote sensing datasets at different spatiotemporal resolutions for enhanced understanding of the underlying physical processes. We apply the proposed algorithm combining soil moisture data from Soil Moisture Active Passive (SMAP) and Soil Moisture and Ocean Salinity (SMOS) with point data from U.S Climate Reference Network (USCRN) and Soil Climate Analysis Network (SCAN) across Contiguous US (CONUS) uncovering novel insights into soil moisture dynamics across scales. Using an underlying covariatedriven spatiotemporal process, the effect of dynamic and static physical controls—vegetation, rainfall, soil texture and topography—on soil moisture is quantified. We find that vegetation, rainfall and topography affect the mean soil moisture distribution across CONUS while soil texture determines the spatiotemporal covariance between soil moisture pixels. We successfully forecast 5day soil moisture across CONUS for multiple spatiotemporal scales accompanied by uncertainty metrics. Finally, we discuss the potential applicability of the algorithm to future soil moisture missions and broader EarthSystem processes.
Soil water content (aka soil moisture) influences many Earth surface processes, from surface runoff to ET to groundwater recharge. By combining pedotransfer functions (PTF’s) (e.g., Vereecken, 1995; Vereecken et al., 2010; van Looy et al. 2017), digital soil models, and highresolution weather forecasts, we can estimate future soil water states (content and storage), and then use them to solve practical problems like flood risk potential and irrigation needs. Especially where human wellbeing is concerned, errors in soil water state estimates need to be minimized. The questions we ask are: what is our current skill in forecasting soil water content and storage, and what is the role of soil hydraulic properties in reducing errors in these forecasts? To address these questions, we use data from the Texas Soil Observation Network (TxSON), which monitors soil water states and weather parameters from 40 sites, all located west of Austin, TX. Weather forecasts are available from the US National Weather Service (NWS) at time resolutions that vary between 112 hours, depending on forecast period, and initial soil hydraulic properties are obtained from PTF’s using SoilGrids250m (Hengl et al., 2017). The monitored field site(s) are found on thin, calcareous soils formed on limestone parent material. Vegetation consists of oak trees, woody plants, and a mixture of short and midheight grasses (Caldwell et al., 2019). Data are incorporated into HYDRUS1D, where we fine tune soil properties across several months that includes wet and dry periods. We then forecast soil water states between May 2020 – February 2021, using HYDRUS1D and 7day weather forecasts obtained from the NWS’s National Blend of Models (NBM). NBM provides highlyskilled weather forecasts, with data including probability of precipitation, temperature, wind speed and direction, dew point, etc. from which forecasts of ET—and soil water states—can be obtained. Forecasts of soil water content are compared sequentially to measurements from groundbased sensors. As simulations move forward in time, each 7 days long, multiple comparisons of observed and forecasted soil water states are determined as forecast lead time is reduced from 7 days to 0 days. Conducted over ~300 days, stacked results will indicate when errors in soil water forecasts drop below a specified threshold (e.g., +/ 0.03 m3/m3). Results will be presented in the form of ubRMSE and magnitude difference between observed and forecasted soil water content, as a function of forecast lead times.
Across the Mediterranean region, there is a need to obtain an indepth understanding of the impacts of climate seasonality (drought) and landuse (including wildfires) on ecosystem services related to the hydrological cycle (contaminant transport, soil erosion, etc.), especially in hillymountainous catchments that can be more sensitive to imbalances in the management of land and water resources. A valid contribution to the development of sustainable management strategies and the prediction of the future condition is the integration of ground, proximal, and remote sensingbased monitoring activities together with diverse scientific expertise in the “Alento” hydrological observatory (southern Italy). This observatory was established in 2016 to provide large soil and hydrological datasets for Mediterranean environments and comprises two study sites (MFC2, agricultural use on clay soil; GOR1, forested site on loamy andic soil) instrumented with soil sensor networks (SoilNet) and cosmicray neutron probes (CRNP). Hundreds of disturbed and undisturbed soil samples were collected along transects in the catchment and also in the test sites at the nodes of regular 25m25m grids to determine soil physical and hydraulic properties in these test sites. Here we will present the most recent investigations underway in the Alento observatory.
Data retrieved from the groundbased sensing systems are being integrated with dual polarimetric Sentinel1 Synthetic Aperture Radar (SAR) data to provide effective identification of fieldscale soil hydrological responses of sites with different characteristics. These activities have been firstly devoted to the development of a simplified calibration procedure of SARbased parameters using local terrain attributes and sparse surficial soil moisture values. The developed sitespecific calibrationdependent model was tested in MFC2 only for a short period in November 2018. Preliminary results show that the combined SAR + terrain model (R² 89%, RMSE 2.49 vol%) slightly outperforms the SARbased model (R² 86%, RMSE 2.23 vol%) in terms of accuracy and agreement between observed and estimated values of nearsurface soil moisture. Ongoing activities in MFC2 focus on the inverse modeling in Hydrus1D to simulate two supporting variables to calibrate SARbased parameters: (i) sparse soil moisture data measured at the soil depths of 15 cm and 30 cm over the SoilNet locations, and (ii) downscaled fieldscale soil moisture monitored with the CRNP. This task aims primarily at highlighting the effectiveness of integrating SARbased measurements, topographic attributes, and CRNP data for mapping the nearsurface soil moisture at a small scale with the advantage of being noninvasive and easy to maintain. Spaceborne information on biophysical properties (i.e., vegetation) adds to the current efforts to enlarge the dataset. In both MFC2 and GOR1, systematic campaigns are carried out to measure the water isotope compositions of rain, soil, plant, shallow aquifer, and streamflow. This dataset helps verify the hypothesis of ecohydrological separation whereby distinct soil water pools supply either plant transpiration or groundwater recharge and surface runoff. Finally, this bulk of integrated sets of soil and hydrological data will serve as input into one or threedimensional hydrological models to investigate the interactions and feedback in the soilvegetationatmosphere continuum and obtain reliable scenariobased projections.
Solute transport modeling at the hillslope scale warrants a detailed soil domain description. This is true even if we expect only matrix flow since variations in soil layering, like differences in the depth to impeding layer, could alter the location where preferential flow processes like funnel flow occur. The traditional pedological soil horizonbased representation may be inadequate to represent such processes and thus lead to incorrect transport dynamics such as travel time even if the average signature of solute concentration is adequately represented. On the other hand, there is a tradeoff to an increased representation of heterogeneity which is the problem of equifinality. In this study, we compare a parsimonious genetic horizon based model with a detailed model to assess the value of increasing heterogeneity representation for modeling transport of a conservative solute (chloride) at the hillslope scale. The study site is located in the Piedmont region of Georgia that is characterized by deep saprolite and variable bedrock depth. We developed the detailed model by estimating a high resolution soil texture map of the hillslope that was derived using soil electrical resistivity in an Artificial Neural Network (ANN) framework. The ERT driven soil layering model uses three easily measured inputs: soil resistivity, relative depth of investigation, and weekly antecedent rainfall. To train and test the model, we used soil samples, collected in 30cm increments up to 510 cm, from 11 different locations across a 42 m hillslope transect. Texture was measured using a laser particle size analyzer. We used bootstrapping to train and test the ANN framework to identify the minimum set of soil samples required to generate an acceptable dataset and concluded that models trained on 6 locations had the least uncertainty. The soil texture predictions had values of R2=0.74 and RMSE=0.4. From the obtained textures, we created a hillslope domain in HYDRUS 2D to predict hydrological and chloride transport at the hillslope scale. Both models are calibrated using water table elevations. In this presentation, we will discuss the soil texture determination process from ERT and the key differences in calibration and predictions for the two hydrologic models.
Introduction
Surfactant and foam processes have been widely used in enhanced oil recovery from the petroleumbearing geological formations [1, 2] and insitu subsurface remediation from shallow formation and aquifer [3, 4].
This study investigates the potential of using surfactant and foam processes for the insitu remediation of shallow subsurface NAPL phases within a field in a US/Korea military base, South Korea. It consists of two major components: the first is a history matching of surfactant enhanced aquifer remediation treatment and the second is a prediction of followup foam injection treatment. The site has a 5 m x 5 m treatment area with 3 m depth with 3 injection wells and 3 extraction wells.
Results
Surfactant treatment: Over 10days surfactant treatment exhibits a partial success in terms of NAPL removal. The relatively higherpermeability area contacted by the surfactant chemicals shows a mobilization of NAPL phases because of a reduced level of capillary trapping (i.e., low dimensionless capillary number). It is the area with relatively lowerpermeability values, however, that prevents a successful sweep from occurring. History matching from simulations shows why such an early breakthrough happens in some extraction wells, and what roles the subsurface heterogeneity plays in overall insitu treatment with surfactant solution.
Foam treatment: A foam treatment, proposed as a potential followup action, is evaluated see if how foam can overcome subsurface heterogeneity. The outcome seems very promising such that foam can improve the sweep and increase the recovery factor over 80  90%. The final results are shown to vary with foam strengths as summarized by using a sensitivity analysis. Foam field test is designed in the near future.
A reliable forecast of potential evapotranspiration (ET$_0$) and precipitation can be used for precision crop irrigation. A multiobjective evolutionary algorithm (MOEA) optimization followed by a sensitivity analysis (SA) of a crop model (HYDRUS1D) for two case studies was performed in order to assess the crop model sensitivity to weather forecast accuracy. A $\pm$5 % of ET$_0$ relative bias range was found to be a threshold for ET$_0$ forecast accuracy being a nondominant parameter for both spring potatoes growing in loamy sand and summer peanuts growing in silty clay. For both case studies soil hydraulic parameters dominated model output and increased with increasing ET$_0$ forecast accuracy. With respect to model output of actual transpiration, maximum root depth was also dominant for the first case study and although precipitation for the test cases was scarce, the rainfall bias parameter dominated excess drainage of water and solutes. This MOEA$$SA scheme for crop model analysis can help set priorities in irrigation management by ranking the data that is most important to be accurately determined in order to optimize crop production.
Membrane distillation (MD) using porous hydrophobic membranes finds applications in various areas such as desalination of seawater, industrial wastewater treatment, and pharmaceutical separation of mixtures. In this study, a direct contact membrane distillation (DCMD) module with commercially available polytetrafluoroethylene (PTFE) membranes (GEOsmonics/0.22um and MS3010/0.45um) is investigated with a multiscale approach. A 2D macroscopic, multiphysics model considering the conservation of species, momentum, and energy has been developed in the present study to gain an understanding of the processes in such a DCMD system. Instead of empirical correlations, this study uses a microscopic model to determine the effective transport properties, including effective mass diffusivity and thermal conductivity. The flowchart of workflow, the graphical representation of the multiscale approach used in the present study, is shown in Fig. 1. As illustrated in Fig. 1, a stochastic numerical reconstruction method is first developed to generate virtual membranes based on the membrane's pore size, fiber orientation distributions and the structure data of membranes presented by the manufacturers. To compute the transport properties subsequently needed in the macroscopic model, a finite volume operator in AVIZO and a finite volume solver in OpenFOAM, are employed to perform porescale simulations on the reconstructed geometries.
For virtual reconstructed GEOsmonics/0.22um PTFE membrane, the effective thermal conductivity and the effective mass diffusivity in throughplane direction are determined 0.0582W/mK and 1.07e5 m2/s, respectively, while these transport properties are calculated 0.0571W/mK and 1.13e5 m2/s for virtual reconstructed MS3010/0.45um PTFE membrane. It shows a good agreement between the simulation results and published data as well as empirical relations.
Fig. 1. Workflow flowchart of the multiscale approach.
With the objective to understand the effect of transport properties computed by microscopic methods in macroscopic modeling, simulation results of the present study in relation to the experimental data with previous studies are compared and realized that the average error of flux of distillate water is reduced from 10.5% and 6% found in previous studies to 7.9% and 5.3% calculated in the present study for feed inlet temperatures of 333.15 and 313.15, respectively.
Fig. 2. Comparison of flux of distillate water for experimental and predicted responses by Hwang et al. and present model for different feed inlet temperatures and inlet velocities (permeate inlet temperature of 293 K, NaCl mass fraction of 1%, GEOsmonics/0.22um).
Furthermore, comparing two stochastically reconstructed membranes, GEOsmonics/0.22um and MS3010/0.45um, show that the average amount of produced freshwater in the DCMD module with MS3010/0.45um is 24% more than produced freshwater in the DCMD module with GEOsmonics/0.22um.
Fig. 3. Comparison of flux of distillate water for two stochastically reconstructed membranes, GEOsmonics/0.22um and MS3010/0.45um, for different inlet velocities (Feed inlet temperature of 333.15K permeate inlet temperature of 293K, NaCl mass fraction of 1%, Countercurrent flat sheet).
Increasing the contact area between roots and soil, root hairs are hypothesized to be a key plant strategy facilitating nutrient and root water uptake. Although future agriculture will have to deal with an increasing water and nutrient deficiency, there is still a lack of knowledge regarding root responses to soil drying. In particular, the effect of drought stress on rootsoil contact remains unknown. Hence, the objective of our study was to determine morphological responses of roots and root hairs to soil drying in situ.
For this purpose, we have grown maize plants (Zea mays L.) in 3Dprinted seedling holder microcosms. After a growing period of 8 days, plants were harvested and scanned using a synchrotron radiation CT in order to visualize root compartments as well as the elongated root hairs. The obtained images served as a basis for both image analysis and numerical modelling.
The results revealed that not only roots but also root hairs lose turgidity under dry soil conditions. Root hair shrinkage occurs at high soil water potentials and leads to a severe reduction of both the surface area and the soil contact area of roots. It represents the first step in a sequence of responses to progressive soil drying, followed by the formation of cortical lacunae and root shrinkage. The latter results in air filled gaps at the rootsoil interface and thus in a further loss of contact to the soil. Only minor cavitation within the xylem was observed at the corresponding soil water potentials meaning that xylem embolism occurs at even lower potentials.
The data suggest that there is a tremendous loss of rootsoil contact and consequently of hydraulic conductivity at the rootsoil interface before xylem cavitates and reduces water as well as nutrient fluxes in the axial root direction. Although it is not yet clear if shrunk root hairs are inactive in nutrient and water uptake, their enormous shrinkage due to soil drying might limit rhizosphere processes.
Additionally, we estimated the importance of root hairs on root water uptake by means of imagebased simulation of water flow through soil and roots, explicitly accounting for pore scale features such as: root hairs, rootsoil matrix contact and airfilled gaps at the rootsoil interface and within the root tissue.
Plant productivity is directly influenced by water and nutrient uptake. Therefore, functionalstructural root models need to accurately describe rhizosphere processes. Such models will enable better agricultural management strategies and improved root trait selection for plant breeding. Due to their complexity functionalstructural root models are hard to analyse. In Schnepf et al. (2020) various research groups developed a systematic framework for benchmarking individual root functional models and their individual components. In this work we will focus on root water uptake and how appropriate sink terms can be developed in macroscopic (plotscale) models.
Macroscopic water movement is commonly described by the Richards equation and the impact of root water uptake is described by a sink term. The sink term is either derived by some averaging or homogenisation procedure or by equations based on empirical observations. Common choices are to set the sink term proportional to the root surface density, or to use line sources which represent the root architecture. In Schnepf et al. (2020) various sink terms were benchmarked and compared to an exact 3dimensional solution of a small root system, where a mesh was calculated and refined towards the root surface. Results showed that local water depletion in the rhizosphere will affect total water uptake when the soil is sufficiently dry.
A solution to this problem was presented by Mai et al. (2019) who described the rhizosphere by a 1dimensional model around each root segment. The 1dimensional grid was refined at the root surface enabling an accurate representation of the pantsoil interface. In the following we describe and generalize the coupling steps, especially with a focus on the point of contacts between the different sub models (see Figure 1). The evolving root architecture is described by CPlantBox (Schnepf et al, 2018), macroscopic water movement as well as water movement in the 1D rhizosphere models are calculated in DuMux (Flemisch et al. 2011, Koch et al. 2020).
Using 1dcylindrical models to describe the plant rhizosphere is a promising approach for development of better functionalstructural root models. It enables us to separately develop and analyse the microscopic rhizosphere models. Such models can be directly used in the proposed coupling framework, where no additional upscaling is needed. This enables an analysis how changes of microscopic parameters will affect the macroscopic results.
Different land uses and wastewater discharges from point and diffuse emission sources result in accumulation of nutrients, or eutrophication of lakes and reservoirs, and water quality not meeting standards for different uses. Consequently, 70% of the approximately 300 lentic water bodies monitored in Mexico are in a eutrophic or hypereutrophic state [1]. Different methods have been proposed for the rehabilitation of eutrophic water bodies, where the following stand out (1) hypolimnetic oxygenation systems (HOS), where organic matter is expected to be more readily degrated and iron oxyhydroxides are formed that can immobilize nutrients, and (2) application of a phosphorus selective adsorbent (Phoslock) in water and sediment, that restrains this limiting nutrient [2]. The effectiveness of these treatments depends on the accessibility of these amendments to surfaces inside the porous structure of sediments, and the question arises if there are structural changes due to the application of these methods? We evaluated how these treatments affected mineralization rates of organic matter, immobilization of phosphorus, changes in pore volumes, distribution of pore areas in the sediment. The sediment had a predominant pore size of 5.2 ± 1.5 nm with an initial specific surface area of 46 m2/g, which increased to 58 m2/g with the HOS treatment and decreased to 41 m2/g or less with the Phoslock and combined treatments and without treatment (Control). The pore volume remained at 0.09 ± 0.01 cm3/g with no variation between treatments. It was determined that the mineralization rate of organic matter was higher in the Control reactor (44% of the organic matter in 220d) and lower in the reactors with treatments (32 ± 5% of the organic matter). The treatments did therefore not affect the pore volume or diameter. The different mineralization reactions identified through ion release and depletions during the treatments, were related to variations in surface areas of the sediment. The financial supports from IMTA (TH1913.1 and TH2012.1), Conacyt (scholarship CVU 780094) and the Office of International Affairs and External Cooperation of the University of Costa Rica, are acknowledged.
In the context of subsurface CO$_2$ storage, the mixing process is triggered by the local density increase in the ambient brine following the dissolution of CO$_2$. As a result, gravitational instabilities occur and characteristic, perpendicular elongated fingerlike patterns form that are enhancing the mixing between CO$_2$ and water compared to a purely diffusive process. This densitydriven mixing process is considered as a key trapping mechanism for subsurface CO$_2$ storage, because it accelerates the dissolution of CO$_2$ into brine and could eventually form a stable stratification in the aquifer, thereby reducing the chances of leakage.
Owing to the difficulty of imaging the timedependent convective process, experiments so far have largely focused on twodimensional systems (e.g., HeleShaw cells). However, the convective fingers are propagating into all three spatial directions and neglecting the third spatial dimension imposes a strong restriction on the lateral spreading of the plumes. To explore the dynamic flow pattern within a threedimensional medium, we developed an experimental procedure by applying Xray CT imaging and 3D reconstructions that allow visualisation of the evolution of the plumes noninvasively at a high spatial and temporal resolution. To imitate the dissolution process of CO$_2$ in brine under laboratory conditions, we use salt with a high Xray attenuation coefficient that dissolves in water and creates a heavier solution than pure water. We perform dissolution experiments for a range of Rayleigh numbers and infer several global quantities including the average mass fraction, dissolution flux and dilution index. We show that the threedimensional mixing evolves successively through three regimes, starting with a simple onedimensional diffusional profile, transit into a convectiondominated regime and continues to attain the maximum dissolution capacity of the system with the shutdown.
Results provide more representative information towards the investigation of convective mixing in the context of Carbon Capture and Storage. Insights into the complex threedimensional mixing structures will additionally support the elucidation if twodimensional scaling laws can successfully predict threedimensional behaviour.
In this study, we employ a ‘fillingbox’ model to experimentally investigate the flow of a dense, Boussinesq plume through a saturated porous medium characterized by a high permeability layer above and a low permeability layer below. The boundary, or permeability jump, separating the two layers is inclined to the horizontal. Upon striking the permeability jump, the discharged plume fluid propagates along the permeability jump as an unequal pair of up and downdip ‘$\it primary$’ gravity currents. As these gravity currents propagate, some fluid is lost by drainage through the permeable boundary. The associated (early time) spreading behavior has been theoretically investigated in our previous work (Bharath $\it et. al$, $\it J. Fluid Mech.$,$\bf902$, 2020). It was shown that the primary gravity current reaches runout (static state), wherein inflow from the plume is precisely matched by outflow due to draining. This static state can be maintained only so long as the discharged plume fluid falling through the lower layer does not itself collide with an impermeable boundary. Once such a collision occurs, there will form a pair of ‘$\it secondary$’ gravity currents, which, in turn, exert a significant dynamical influence over the entire depth of the heterogeneous porous medium. For instance, the secondary gravity currents will “tug” upon the primary gravity currents leading to a remobilization of this previouslyarrested front. At later times, primary and secondary gravity current flows are impeded by vertical sidewall boundaries. In characterizing the resulting fillingbox flow, we distinguish between two qualitatively different filling regimes, i.e., a sequential vs. simultaneous filling of upper and lowerlayers with contaminated fluid. Parameter combinations conducive to one or the other filling regime are also identified.
Through this work we attempt to address some of the key uncertainties in the field of underground hydrogen storage and carbondioxide/acidgas sequestration. These uncertainties include (i) the degree of asymmetry in the flow structure of the gravity current pairs as they propagate along an inclined and permeable boundary, (ii) the influence of impermeable boundaries encapsulating the porous media, and, (iii) the nature and time required to fill the porous medium in the presence of heterogeneities.
Due to the increasing challenges to preserve water quality and supply at global scale, groundwater flow modeling has become a tool of pivotal relevance for remediation, implementation of policies, and design of applications for recharge management. The strain towards faster and more reliable hydrogeological simulations triggered the development of upscaled and multiscale approaches employing different diffusion and dispersion models that are still the object of much debate in the community. Our ongoing study focuses on the up scaling of solute transport through heterogeneous geological domains by means of an extensive threedimensional simulation study, based on a new opensource C++ library, built on top of the wellknow finitevolume library OpenFOAM®. We integrate the whole workflow, from geostatistical random field generators to flow and transport solvers with integrated postprocessing capabilities. The robustness, scalability and flexibility of the library makes it suitable framework for the development, testing, and application of upscaling techniques.
Being the subsurface inaccessible by nature, the appeal to geostatistical techniques is a wellestablished approach to construct a realistic domain for flow and transport simulations. However, additional challenges are posed by the numerical simulation of highly heterogeneous materials. Indeed, the problem is twofold: on one side it is not always possible to characterize the heterogeneity in a deterministic way, while on the other side numerical methods which are effective for elliptic and parabolic equations solved over homogeneous domains might suffer in heterogeneous media. Both challenges were effectively tackled using the opensoruce library OpenFOAM whose implementation and capabilities will be illustrated. Preliminary results on flow and transport simulations performed on truncated pluriGaussian permeability fields will be shown and the influence of geostatistical metrics (e.g. correlation lengths, variance, geological entropy) on the flow and transport results (e.g. average velocity and breakthrough curves) analysed.
Extensions to variabledensity, mobileimmobile, and multirate mass transfer formulations are also presented in the context of the EU project “SECURe”.
Solute transport in unsaturated porous media is a key process for various applications, such as groundwater flow and building stone performance. The distribution of the immiscible fluids controls which parts of the pore space are accessible for solute transport. This may lead to a bimodal velocity distribution in the solvent phase with stagnant and flowing regions (JiménezMartinez et al., 2017), characterized by nonFickian solute transport. Hasan et al. (2019) showed that there are still fundamental inconsistencies between different modelling approaches, spurring the need for experimental validation. However, due to methodological challenges there are only few experimental studies that target unsaturated solute transport in rocks at the pore scale (Hasan et al., 2020).
In this study, we visualized the spreading of a solute through partially watersaturated sintered glass and Bentheimer sandstone samples. After a drainage and imbibition cycle with water and ndecane, leaving a significant amount of the latter trapped in the pore space, an aqueous tracer solution (10 wt% KI) was injected with a constant flow rate. Transient porescale concentration fields in the sample were imaged in 3D by using fast laboratorybased Xray microCT (time resolution of 15 s, voxel size of 13 µm). To determine the influence of the nonwetting phase on the solute transport, singlephase experiments were also performed on the same samples. By extracting a pore network and performing a porescale image analysis work flow (Van Offenwert et al., 2019) we investigated the existence of stagnant and flowing regions. Furthermore, we studied the influence of the fluid phase distribution on solute mixing and spreading. These results can improve our understanding of nonFickian solute transport. Our novel methodology can also be used to validate twophase solute transport simulations in rock types with different porescale heterogeneity.
Dispersion through unsaturated porous media plays an important role in several industrial and natural processes including those relevant to environmental and hydrogeological applications and chemical and petroleum engineering processes. During recent years, several direct numerical simulations at the pore scale explored dispersion and solute transport in immiscible twophase flow in porous media. Displacement patterns differ significantly depending on capillary number and viscosity ratios. Different invasion conditions impose important changes on the dispersion of the displacing fluid. Most of studies have not considered the effect of displacement patterns on dispersion through the displacing phase.
This study aims to understand and quantify dispersion in three distinct regimes of displacement including frontal displacement, capillary fingering, and viscous fingering. Hydrodynamic dispersion in all these regimes is modelled in the displacing phase using a volume of fluid (VOF) method in OpenFOAM and compared to a base case to categorize dispersion under different two phase flow regimes. Structure of velocity field and solute transport within the displacing fluid were investigated to compare dispersion phenomena for each domain. The shape of displacement in each regime causes changes and deviations in dispersion related parameters.
Hydrodynamic dispersion is separated and studied in two parts in our work: with and without diffusion. In the first part the effect of diffusion is investigated, and in the second part statistical parameters of the whole domain and Lagrangian parameters through the domain are explored. Results demonstrate that dispersion of a solute in frontal displacement behaves similar to the base case (i.e., a saturated media) with the same arrangement. Dispersion in the fingering regime is considerably different compared to the base case which can have a significant impact on dispersive behavior of solutes in porous media.
Transport in porous media is central in chemical engineering. Effective transport properties are required for evaluating and improving many processes and applications, typical example are catalysts, or porous membranes in separation processes. A widely used model to describe transport in porous media is the Dustygas model. This model accounts for permeation, Knudsendiffusion and binary diffusion. The model parameters are commonly determined from experiments, for instance, performed in a WickeKallenbach cell [1]. The parameters derived in this way are spatially averaged effective parameters.
In this contribution we present an approach to calculate transport parameters of the DustyGas model from a cross sectional image of a porous material. This reduces the currently large experimental effort, since only once a visualization of the microstructure is needed. For a structure this characterisation by a single highresolution image is less demanding than multiple experimental series to derive the parameter as in conventional procedures. In addition, the transport properties of very thin layers, of materials that are difficult to study in the WickeKallenbach cell, or of virtually designed materials for which structural information is available from simulations but no physical sample has yet been synthesized, can be determined. The presented approach can be applied to any porous material permeated by a gas (or multiple gases), e.g. membranes, filters in general, bulk material, column internals, etc.
The method applied here is asymptotic homogenization, which allows structural information on the micro scale to be lumped into effective transport properties. The key idea of asymptotic homogenization is based on expressing the real physical problem as a representative mathematical problem (the socalled cell problem). The solution of the cell problem is directly related to the effective transport properties on a macroscopic scale. By variation of characteristic geometric properties of a porous structure, various kinds of pore structures can be covered. The resulting basic functions are integrated to calculate the effective transport properties of the upscaled model. We applied this approach to porous media to derive the dustygas model parameters, namely permeability, Knudsendiffusion and binary diffusion coefficient. In our present work, as well as in our previous work [2], we compare the model predictions based on cross sectional images with experimental data and literature data to validate our results. A remarkable agreement between experiment and simulation is achieved.
A less viscous fluid invading into a more viscous immiscible fluid produces fingering patterns due to instabilities at the interfaces between them. In the space between two closely spaced parallel plates, the fingers appear to be smooth as there is essentially only one interface separating the fluids. In case of a porous medium, e.g. by filling the space between the plates with fixed glass beads, the fingers show fractal structures where many microscopic fluidfluid interfaces exist. These patterns are fractal in nature and characterized by different fractal dimensions depending on whether they are dominated by viscous or capillary forces [1].
In the largescale continuum limit where the pores are vanishingly small compared to the dimensions of the porous medium, the relative density of invading fluid in the fractal patterns approaches zero. Rather, it is the structures giving rise to nonzero saturation which will dominate. The local saturation is the proper quantity to characterize the fingers in this limit.
We now ask the following question: Is it possible to use the fractal structures on the pore scale to infer the saturation distribution in the continuum limit? We follow the experimental work of Løvoll et al. [1] and Toussaint et al. [2], using an averaging technique to map out a probability distribution for the position of the fingers. That is, each point is given a probability density for being part of a viscous finger. This creates a density profile and we conjecture that this density profile reproduces the saturation profile in the continuum limit. This conjecture is built upon the work of Arnéodo et al. [3] that demonstrated that averaging over DLA patterns reproduces the smooth fingers that SaffmanTaylor found analytically.
We perform our study with dynamical porenetwork modeling [4] and analytical derivations [5], and compare them with experimental observations.
Mineral dissolution is relevant to most subsurface processes, including CO2 storage, geothermal systems and enhanced oil recovery. Porescale simulation can be a useful tools to decipher the reactive transport within the porespace and estimate upscaled parameters such as permeability and reaction constants. These simulations may be challenging though as they involve the tracking of multiple solid interfaces. The microcontinuum method is an efficient approach as it does not involve complex algorithms for explicit reconstruction of the interface, but use volumeaveraging of the fluid and solid properties. However, there are two fundamental issues with the current formulation: the need of an interface localisation function to avoid local negative porosity, and concentration bleeding into the solid phase. These two issues lead to significant underprediction of the reaction rate, especially in the diffusionlimited regime, and the reaction constant usually needs to be fitted. To solve these issues, we propose new formulations using a mass conservative localisation function based on the divergence and using the Continuous Species Transfer (CST) method to insure a zero concentration in the solid phase. Our improved formulations are validated by comparison with experimental results and with numerical simulations using a direct method and using the standard microcontinuum approach. We then performed numerical simulations in porous media images and we show that our novel method is as accurate as direct methods and orders of magnitude faster.
Compositional flow and phase change dynamics in porous media play a central role in many industrial and geoscience applications including fuel cells, geologic CO2 sequestration, and hydrocarbon production. Though the interplay between transient twophase flow and phase change dynamics is of critical important, it remains not well understood limited by computational challenges especially for direct numerical simulations. We develop a novel dynamic porenetwork model to simulate twophase compositional flow and phase change dynamics in complex pore structures. The model formulation couples a thermodynamic phaseequilibrium model for multicomponent fluids in each individual pore to a dynamic porenetwork model for twophase compositional flow. The new coupled modeling framework allows us to investigate the interactions between compositional flow dynamics and phase change dynamics in highly disordered pore structures extracted from 3D digital images of rock samples. A series of example simulations of twophase displacements show that phase change (evaporation and condensation) can suppress fingering patterns generated during invasion.
For nanoconfined fluids, equilibrium properties such as adsorption, density, and surface diffusion are dependent on the layered structure of the fluid near the surface. This layered structure is also relevant to describe transport as the noncontinuum effect, such as slip velocity, depends on the nearwall density. While molecular dynamics simulations quantify the layered density profile in nanoconfigurations, a systematic theoretical development to calculate equilibrium properties remains challenging. We consider a grand canonical ensemble and include fluidsurface interaction exclusively in the configurational integral. Using LennardJones type interaction between the fluid and surface in the configurational integral, an approximation to the grand partition function for confined fluid is derived. Theoretically obtained density profiles are compared with grand canonical Monte Carlo simulations. While the focus of the present work is the density of the fluid, other static equilibrium properties and transport related quantities such as correction to slip can be derived using the surfaceinteraction corrected partition function.
Pore space properties such as pore shape, connectivity and pore size distribution are key to understanding porescale processes. Xray computed (micro) tomography (µCT) has become one of the dominant techniques to nondestructively investigate this pore space in three dimensions.
In conventional attenuationbased µCT, the rule of thumb is that the achievable resolution is about three orders of magnitude smaller than the sample size (Cnudde and Boone, 2013). For heterogeneous materials with pores from the nanometer scale up to the millimeter scale (e.g. mineral building materials), this makes it impossible to visualize the entire pore space without taking (multiple) smaller subsamples. This tradeoff between image resolution and sample size also forces modelers to make assumptions and generalizations about the unresolved, subresolution pore space.
In the last fifteen years, Xray darkfield tomography has been explored as a technique to overcome this tradeoff between resolution and sample size. Darkfield imaging is based on smallangle Xray scattering (as opposed to Xray attenuation) and has been shown to be sensitive to subresolution density variations (Pfeiffer et al., 2009). Such variations are typically caused by structures of interest like subresolution pores, inclusions, microcracks and other heterogeneities. Darkfield imaging can be performed using TalbotLau grating interferometry, specklebased imaging, or edge illumination. Although the published research on darkfield imaging is very promising, only limited use cases have been published on quantifying subresolution feature sizes (Lynch et al., 2011; Yashiro et al., 2010).
In this work, quantitative information on subresolution feature sizes in the nanometer regime has been extracted, based on this darkfield modality of Xray tomography using TalbotLau grating interferometry. A validation experiment was performed at the TOMCAT beamline (Swiss Light Source, Paul Scherrer Institut, Switzerland) (Stampanoni et al., 2007). Alumina particles with either pore sizes of 50 nm or 150 nm were mixed together in a tube with a diameter of 1.5 mm and imaged using grating interferometry at five correlation lengths ranging from 45 nm to 800 nm to cover the pore size ranges. The image voxel size was 1.62³ µm³. With conventional absorption µCT, it was not possible to distinguish particles with different pore sizes due to their very similar density. However, the behavior of the particles’ darkfield response over the range of correlation lengths allows to classify subresolution pore sizes. This suggests that darkfield imaging can be calibrated to quantify subresolution feature sizes inside porous materials, overcoming the resolution limitations of µCT.
In various natural and engineered systems, multiphase flow and mineralfluid interactions cooccur and their interplay controls the evolution of these systems. In continuum scale models, how multiphase flow dynamics affect mineral reactions are rarely accounted for or are corrected via reactive surface area and saturation of the aqueous phase. To evaluate the applicability of such treatment, understanding of the porescale dynamics is required. In this study, we developed a framework that couples the twophase flow simulator from OpenFOAM with the geochemical reaction capability of CrunchTope, to examine porescale dynamics of two phase flow and their impacts on mineral reaction rates. For our investigations, flat 2D channels and single sine wave channels were used to represent smooth and rough geometry. Calcite dissolution in these channels were quantified with single phase flow and two phase flows with different saturations. We observed that the bulk calcite dissolution rates were not only affected by the loss of reactive surface area as it becomes occupied by the nonreactive nonaqueous phase, but also largely influenced by the changes in local velocity profiles due to the presence of then nonaqueous phase. The extent of the changes in reaction rates in the twophase systems compared to the corresponding single phase system is dependent on the flow rate (i.e., capillary number) and channel geometry. The porescale simulation results can be used to better constrain reaction rate descriptions in multiphase continuum scale models.
Recently progress in the international infiltration studies has been stimulated and summarized by Harry Vereecken and colleagues in several international efforts. These developments created opportunities to expand the knowledge on infiltration to largescale projects by developing pedotransfer functions for infiltration equations. The complexity of relationships between parameters of infiltration equations and readily available soil and landscape data calls for the use of machine learning methods for the PTF development. This work's objective was to run a pilot project on pedotransfer for infiltration with the data from large international Soil Water Infiltration Global (SWIG) database and address the following questions:
1. Can soil basic properties and landuse inform about the most appropriate infiltration equation and, if yes, then what are the most influential predictors?
2. Can soil basic properties and landuse be used as predictors of infiltration equations' parameters, and if yes, then does the accuracy of the parameter estimation depend on the accuracy?
Research with 1830 SWIG datasets showed that which infiltration equation will perform the best depends on the input soil properties and land use domain. Inputs that predicted the Horton, KostiakovLewis (Mezencev) equation being the best, provided more reliable predictions than inputs that pointed to GreenAmpt, Philip, and Swartzendruber equation being the best. The infiltration measurement method was a dominant predictor, and using the textural class provided the accuracy of predicting the best equation comparable with using the silt, sand, and clay contents. The accuracy of predicting Horton and Mezencev equations' parameters did not depend on the performance of these equations. This accuracy strongly depended on the infiltration measurement method. Further research is needed to understand how to establish the threshold to consider the accuracy of two equations different. Also, the dependence of pedotransfer accuracy on affected by the observed infiltration stages needs to be studied. Overall, opportunities exist to provide additional means for infiltration modeling in multiple applications.
In models and estimates of unsaturated hydraulic properties, the wet range between field saturation and the airentry value is greatly oversimplified. Retention curves, for example, are often taken to be perfectly flat (unchanging water content) in this range, or are represented by an empirical formula that is unrelated to the active processes. Another example is diffusivity, which goes to infinity with a flat retention curve, making it both unrealistic and unusable. Though much neglected, the hydraulic properties of a nearly saturated medium are important in an increasing number of applications, for example:
• Macropore/matrix domain exchange, a major influence on preferential flow processes and control on rapid versus slow solute transport, which often occurs with the matrix domain at high water content.
• The precise timing of the transition from unsaturated to fieldsaturated conditions, as may be important to initiation of ponding, triggering of landslides, heightened vulnerability to erosion, and initiation of preferential flow.
• Subsurface initiation of preferential flow by seepage from nearly saturated matrix material into macropores.
• Hydraulic property measurement by tension infiltrometer, which frequently is done with the input condition at a very slight suction.
A new processbased model has been developed for the important case of a medium without macropores (i.e. having a distinct nonzero airentry value) that is exposed to repeated wetting and drying cycles. On wetting, the medium does not exceed field saturation, with trapped air occupying some of the pore space. Water retention in the range between airentry and field saturation is not dominated by capillarity but by trapped air expansion and contraction with change in matric pressure, and effects triggered by this process. Accordingly, the model represents this wet range by an augmented Boyles’ law variation of trapped air volume with matric pressure, amplified by an empirical factor to account for associated liquidbridge collapse or other mechanisms. Tests using highquality measurements in this range showed good fits with Boyles’ law amplified by a factor typically between 2 and 4.
This model can serve within a model of hydraulic conductivity, treated as saturated conductivity that varies with changes in effective porosity determined by the variable trapped air volume. Diffusivity can then be assigned a realistic value using the modeled retention and conductivity relations. Though few data are available for direct test of these dynamic properties, the model has value for exploring possible consequences of processes occurring under conditions close to field saturation.
Suction cups are widely used in agricultural and environmental research and monitoring under the hypothesis that the samples chemistry represents the soil pore water solute composition around the cup location. The objective of this study was to analyze the sampling procedures that lead to the most representative sample for soil aqueous phase composition when using a falling head suction cup. This was achieved by simulating simultaneously the hydraulic and geochemical response of the suction cup sampled soil solution and its immediate surroundings when evacuated by a systemdependent variable boundary condition. Different soils, water contents, vacuum applications and suction cup internal volumes, as well as variable hydraulic conductivities of the ceramic cup were evaluated and their effect on the sampling rate and sample chemical composition reported. Model results showed that potential extracted soil solution volume depends on a combination on internal suction cup volume and vacuum applied, independently from soil type or water content. A linear relationship was defined between the ratio of the extracted sample to suction cup volumes and the initial applied vacuum, for all simulations. pH values and general chemistry of the sampled solution were found to be more similar to those in the soil when a porous cup system is filled until hydraulic equilibrium is reached. Following this, a small volume suction cup system with a high initial applied vacuum, which allows for faster sample collection, could be optimal.
The RichardsonRichards equation (RRE), a nonlinear partial differential equation (PDE), is commonly used to describe soil water dynamics. Analytical solutions of RRE are available only when simplifying assumptions are made. Therefore, numerical methods, such as the finite difference, finite element, and finite volume methods, are employed when solving practical problems. Here, we introduce an alternative numerical method known as physicsinformed neural networks (PINNs), in which neural networks approximate the solution to the RRE. The PINN approach, which is rapidly gaining popularity in various fields of physics, is based on the universal approximation theorem that neural networks with at least one hidden layer with a finite number of weights can approximate any continuous function arbitrarily well. Furthermore, the automatic differentiation allows the evaluation of the residual of PDEs, which is incorporated into the loss function to be minimized. Although the forward solution of PDEs using PINNs is computationally more expensive than other numerical methods, the PINNs approach is expected to be more effective for the inverse problem because it does not require a repetitive solution of the forward problem as in other numerical methods. We will present a PINNs solver for the RRE and compare its approximations with analytical and conventional numerical solutions for homogeneous and layered soils. We also present a PINNs method for approximation of soil surface flux from only nearsurface soil moisture measurements, which demonstrates the superior potential of PINNs for solving inverse problems.
Data sets collected from field or laboratory experiments for the determination of unsaturated hydraulic parameterswater retention curves and unsaturated hydraulic conductivityare often uncertain, imprecise, incomplete or vague because of a vague delineation of subsurface heterogeneities and preferential flow zones. The other source of uncertainty is inconsistency between the real physical processes and the physics of the field and laboratory measurements. The use of soil physical and hydraulic parameters, which are commonly expressed using crisp relations, often leads to significant uncertainties in predictions.
One of the modern approaches to deal with uncertain data is the use of the fuzzy systems modeling. Fuzzy systems modeling, based on the application of the possibility theory, is a tool to evaluate the uncertainty of predictions of complex systems, given the uncertainty of input parameters. Possibility theory is concerned with event ambiguity, that is the extent to which some event occurs, given incomplete information expressed in terms of fuzzy propositions or fuzzy numbers.
The goal of this presentation is to present an approach to the prediction and uncertainty evaluation of hydrogeological systems based on a combination of the statistical and fuzzysystem modeling analyses. In particular, a rationale for representing heterogeneous soil and fractured rock systems as a fuzzy system will be presented. Fuzzy Cmeans clustering is applied to partition the 11 soil types of the UNSODA database into a series of overlapping clusters based on the fuzzy degree of membership. Fuzzy relations of the van Genuchten and BrooksCorey unsaturated hydraulic parameters are derived, and these fuzzy relations are then applied for the fuzzysystems time series predictions of the infiltration flux. Predictions are based on a fuzzyform of Darcy’s equation for unsaturatedsaturated subsurface media. Fuzzy modeling techniques are well suited to utilize the imprecise input information for the uncertainty evaluation of predictions, risk assessment, and management of soil and hydrological systems.
Many different equations have been proposed to describe quantitatively the infiltration process. These equations range from simple empirical equations to more advanced deterministic model formulations of the infiltration process and semianalytical solutions of Richards' equation. The unknown coefficients in these infiltration functions signify hydraulic properties and must be estimated from measured cumulative infiltration data, $\tilde{I}(\tilde{t})$, using curve fitting techniques. From all available infiltration functions, the twoterm equation, $I(t) = S\sqrt{t} + c K_\text{s} t$ of Philip (1957) has found most widespread application and use. This popularity has not only been cultivated by detailed physical and mathematical analysis, the twoterm infiltration equation is also easy to implement and admits a closedform solution for the soil sorptivity, $S$ (L/T$^{1/2}$), and multiple, $c$ (), of the saturated hydraulic conductivity, $K_\text{s}$ (L/T). Yet, Philip's twoterm infiltration function has a limited time validity, $t_\text{valid}$ (T), and consequently, the use of measured cumulative infiltration data, $\tilde{I}(\tilde{t})$, beyond $t = t_\text{valid}$ will corrupt the estimates of $S$ and $K_\text{s}$. Philip (1957) provides theoretical guidelines on the time validity, yet, these estimates need to corroborated experimentally. In this paper, we introduce a new method to determine simultaneously the values of the coefficient $c$, hydraulic parameters, $S$ and $K_\text{s}$, and time validity, $t_\text{valid}$, of Philip's twoterm infiltration equation. Our method is comprised of two main steps. First, we determine independently the soil sorptivity, $S$, and saturated hydraulic conductivity, $K_\text{s}$ by fitting the implicit infiltration equation of Haverkamp et al. (1994) to measured cumulative infiltration data using Bayesian inference with DREAM Package of Vrugt (2016). This step is made possible through a novel, exact and robust numerical solution of Haverkamp's infiltration equation, and returns as byproduct the marginal distribution of the parameter $\beta$. In the second step, the maximum likelihood values of $S$ and $K_\text{s}$ are used in Philip's twoterm infiltration equation, and used to determine the optimal values of $c$ and $t_\text{valid}$ via model selection using the Bayesian information criterion. To benchmark, test and evaluate our approach we use cumulative infiltration data simulated by HYDRUS1D for twelve different USDA soil types with contrasting textures. This allows us to determine whether our procedure is unbiased as the inferred $S$ and $K_\text{s}$ of the synthetic data are known before hand. Results demonstrate that the estimated values of $S$ and $K_\text{s}$ are in excellent agreement with their "true" values used to create the infiltration data. Furthermore, our estimates of $c$, $\beta$ and $t_\text{valid}$ depend strongly on texture and fall within the ranges reported in the literature. Our findings are corroborated by analysis of realworld data. Our study addresses four areas of active research by Prof. Vereecken, namely (1) measurement and modeling of water infiltration into variablysaturated soils, (2) development of numerical methods for subsurface flow and transport, (3) soil moisture measurement and characterization and (4) inverse methods and uncertainty quantification. As I have known Harry for about 15 years and visited him on several occasions, I'd be remiss if I did not share a few personal anecdotes about him (time permitting).
Swelling of Shalerocks create several problems [1] during underground drilling operations, such as stuckpipe/drillbit. However, swelling of shalerocks can close the gaps between rock (wellbore) and casing –therefore no cementing is needed – which can save a lot of time and money and such a “natural” closing ensures “noleakage” during further drilling and production phases. The field experience reveals that some shalerocks are good candidate for swelling and some are not. It is believed that, amount of clay is the most important factor for shaleswelling. There are several other parameters that can influence the swelling behavior, such as porosity, quartz contents, claycluster distribution, stress difference between field and drilling zone etc. Therefore, to plan a safe and efficient drilling through shalerocks, we should understand the swelling mechanism of clay.
To investigate swelling of clay, we have introduced a discrete element model (DEM), based on MonteCarlo technique. We define a probability of swelling for all the clay grains in the shalerock sample that includes the effect of stressdifference, porosity, temperature etc. The time evolution of grain swelling results in bulk swelling behavior of the sample and the simulation result qualitatively matches [2] with the observations of shale/clay swelling experiments [3,4]. The MonteCarlo based DEM code has been studied [5] for the entire parameter space by varying several important inputs like porosity, clayquartz contents, stress difference, temperature etc. In addition, the masstransport phenomenon has been implemented by considering clay grain movement through fractures (flow channels).
A major challenge in flow through porous media is to better understand the link between porescale microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a twodimensional microstructure comprising an array of circular obstacles, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scale to systematically upscale a novel problem that involves cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterized by the local porosity, an effective local anisotropic flow permeability, and an effective local anisotropic solute diffusivity. These macroscale properties depend nontrivially on both degrees of microstructural geometric freedom (obstacle size and spacing). We take advantage of this dependence to compare scenarios where the same porosity field is constructed with different combinations of obstacle size and spacing. For example, we consider scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters, or for studying the impact of deformation on transport in soft porous media.
The use of conventional techniques for soil stabilization often involves chemical compounds which are not environmentally friendly and can be hazardous. Moreover, newly introduced regulations which target zero CO2 emission demand new construction policies and alternative construction solutions. When it comes to soil improvement, reducing the level of greenhouse gas emission would mean searching for ecofriendly stabilizing agents rather than resorting to traditional ones such as lime and cement. Biological soil stabilization techniques which include the use of a variety of microorganisms such as bacillus, cyanobacteria, microalgae [e.g.,16], and/or the use of enzymes present in the microbial metabolic paths [e.g., 7], as well as biopolymers [e.g., 89] are among alternative solutions for soil improvement. In this contribution, a review on different biological soil stabilization techniques will be presented. The aim is to characterize different biological techniques and their strength and challenges. Then the focus is placed on the class of methods which is based on the microbial calcite precipitation (MICP) and its use for problematic soil engineering. The application of MICP for problematic soil engineering will be reviewed and the recent findings on the efficiency and efficacy of MICP to treat dispersive, expansive and collapsible soils [1014] are briefly explained and suggestions for future studies, on this topic, are put forward.
An innovative analytical 2D model for solvent injectionbased heavy oil recovery was generated with respect to complicated mass transfer mechanisms integrating diffusion and dispersion, dynamic viscosity reduction, and fluids mixture expansion. The high nonlinear process caused by coupled diffusion and fluids movement, viscosity reduction, and mixture volume expansion were analytically captured and analyzed in this model and applied in variable well configurations including single vertical wells and fractured wells.
This proposed analytical methodology is developed by use of the pseudopressure and pseudotime based diffusivity equation linearization, and integral image method (IIM) for whole reservoir scale modeling. The pseudotime can be converted to the realtime domain by evaluating reservoir average pressure in the region of investigation using IIM. Dynamic mixture volume expansion using linear expansion model was analytically treated as a kind of variablerate additional source/sink integral within each discretized reservoir domain. Dynamic mass transfer domain and fluids flow pressure domain was coupled analytically in this work and the systematically iterative method was used to make calculation in these two domains as a closedloop in Laplace domain. Dimensionless terms were used for providing universal solutions. Normalized transient pressure behaviors were calculated and discussed their features in loglog plots.
This method was validated against finely gridded commercial numerical simulation models under limiting cases. The results were well matched and clearly showed fluids mixture expansion acting as an additional source to increase the pressure in porous media compared with the conventional dispersion process. Accordingly, dimensionless pressure and pressure derivative type curves were developed to match flow behaviors, such as radial flow, linear flow, and boundary dominate flow. By comparing with the standard type curve, the mechanism of viscosity reduction and mixture expansion can be quantifiably captured to analyze the expansion features of the solvent and heavy oil mixture, which will become useful tools for accurately evaluating the solvent functional ability in heavy oil recovery methods. A typical coldoilproductionwithsand (CHOPS) well the configuration of a single fracture structure had been modeled using solvent injection process. Transient pressure behavior with respect to different time domains had been plotted and discussed based on its physical meaning.
This work proposed a new analytical methodology of modeling mass transfer integrating diffusion and dispersion in solvent injectionbased heavy oil recovery methods. Solvent diffusion and dispersion, dynamic mixture viscosity reduction, and mixture volume expansion were analytically captured and integrated into reservoir scale modeling using an additional source/sink integral method. This study will also help improve the PostCHOPS characteristics, and will directly provide operating companies the technique to analyze and have a better understanding of the transient pressure data of solvent injection process in heavy oil recovery methods.
Bacillus subtilis is a wellknown plantgrowthpromotingrhizobacteria (PGPR). It has been suggested that PGPR influences the hydrophysical properties of soil, but the mechanistic understanding of this is still scarce. As a stresstolerantbacteria, Bacillus subtilis can produce biosurfactant to create surfacetension and viscosity gradient and thus form and spread viscoelastic biofilm in order to cope with the fluctuating water conditions of the soil. This, in turn, can affect the hydraulic and interfacial properties of soil. Understanding the ecological significance of such a strategy and identifying some key missing links of the important physicochemical traits of EPS (Extracellular Polymeric Substances) and biofilm to soil physics and hydraulics were the motivation of this work. We conducted evaporation, percolation, and pellicle experiments on the wildtype and its EPSknock out (eps) and surfactinknock out (sfp) mutantstreated sands to identify key mechanisms responsible for EPS' (and PGPR's) potency on water retention. Our results show that EPS produced by the Bacillus subtilis can increase water retention of fine sands by reducing the upward (evaporation loss) and downward (percolation) flow of water. Interrupted capillarity, increased sorption and hydraulic decoupling are likely the causative mechanisms here. SEMimaging and water repellency data suggest that the occurrence of hydraulic stability rather than mechanical stability in imparting such an outcome. Our study highlights the importance of flowrelated variables of surface tension, viscosity, and water repellency to understand the water retention phenomena in a low Reynold's number condition. These research outcomes would contribute to the fundamental understanding of earlystagebiofim mediated hydrophysical changes of soil and thereby provide a scientific basis for developing biofilm strategies that could effectively manage soilwater in order to achieve sustainability in agriculture.
CO2plume geothermal (CPG) operations are considered for sufficiently permeable formations. Fluvial sedimentary reservoirs affect losses in pump energy in heat extraction from hot sedimentary aquifers (HSA). It has been shown previously that the losses for heat extraction from HSAs can be reduced by up to 10% by orienting a doublet well pair parallel to the paleo flow trend rather than orienting it in perpendicular. In this study, we examine the same orientationdependency of geothermal heat extraction for highly fluvial CPG operations. We use multiple realisations of highly channelized domains with control over the width, number, and straightness of the channels. We investigate the physical processes involved in CPG (such as salt precipitation, porositypermeability changes, and pressure buildup) for these realisations.
The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B$\to$C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemicalhydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.
Here, we consider a 3D axissymmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive nonuniform advection. The advective field $v_r(r,z)$ describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an earlytime regime where the amount of mixing is small and the dynamics is transportdominated, ii) a strongly nonlinear transient regime and iii) a longtime regime that exhibits Taylorlike dispersion, for which the system dynamics is similar to the 2D radial case.
Geochemical reactions in porous media can result in various patterns of flow channels and fractures which could potentially alter the properties of the porous media including porosity, permeability, tensile strength and tortuosity, etc. Enhancing our knowledge of these reactions at pore scale can help better predict the impacts of these reactions on the larger scales. Mineral surface area, as one of the controlling parameters in geochemical reactions, can be measured or estimated in various methods such as geometry, BET adsorption, imaging, etc. It has been reported in the literature that the estimated mineral surface area can vary up to 5 orders of magnitude. In addition, the knowledge on how mineral surface area evolves during the geochemical reactions is lacking. Currently, the commonly used theory assumes that mineral grains to be a smooth sphere and the surface area changes with changing sphere size. However, backscatter electron (BSE) images of rock samples revealed that most of the mineral grains are not spherical, and has different level of surface roughness. In this work, the evolution of mineral surface area will be evaluated for different mineral phases through coreflood experiments. Hydrochloric acid (HCl) will be used as the reacting fluid in the coreflood experiment with a halfinch core (Bandera Grey). Inductively coupled plasmaoptical emission spectrometry (ICPOES) will be used to determine the effluent chemistry, from which the reaction rate and reactive surface area can be estimated. Scanning electron microscopy (SEM) backscatter electron (BSE) images will be used to estimate mineral accessible surface areas and to compare the surface change of different mineral phases before and after experiments. Xray micro computed tomography (microCT) will be used to analyze the pore space change and newly formed flow channels. Based on the experimental data and observations, we aim to find a relationship among porosity, volume fraction and mineral surface areas.
Characterization of irreducible saturation of the wetting phase during multiphase fluid flow in porous media is essential for an accurate estimation of CO2 storage capacity and hydrocarbon recovery of the geological formations. Despite pore deformation has been shown to significantly control singlephase and multiphase fluid flow in porous media, the interactive controls of capillary number and mechanical pore deformation on irreducible saturation during multiphase fluid flow in geomaterials is not yet fully explored. In this study, the stressdependent shifts of irreducible water saturation (Swir) of a Berea sandstone and an Indiana limestone specimen are investigated through series of twophase (waterN2) coreflooding experiments (i.e., drainage) under increasing effective stress from 10 MPa to 30 MPa and isothermal (40⁰C) conditions. We used Xray computed microtomography to quantify changes in the topology of the porespace with effective stress. The controls of the capillary number on the stressdependent shifts of Swir is studied through experiments under constant injection rate and constant injection pressure conditions, independently. We find a 22% and 52% decrease in Swir of Berea sandstone and Indiana limestone, respectively, in response to an increase in effective stress under constant injection rate (i.e., increasing capillary number) condition. We further find a 27% increase in Swir of Indiana limestone with the same increase in effective stress under constant injection pressure (i.e., decreasing capillary number) condition. We reveal that the deformation of the pore throats, due to an excess effective confining stress, and changes in the driving energy for the gas phase to invade smaller channels, due to an increase/decrease in capillary number, leads to a decrease/increase in Swir of both specimens. These microscale and macroscale observations underscore the remarkable control of capillary number on deformationdependent fluidfluid displacement in porous media, which pave the way for relevant research in geoscience and engineering.
Low salinity waterflooding (LSWF) as an enhanced waterflood technique is applicable in secondary and/or tertiary oil production. The performance of LSWF depends on different factors including the volume of injected brine, its salinity and insitu mixing. Mixing is intensified due to adverse mobility ratio at low salinity (LS)  high salinity (HS) front. This research focuses on the impact of salinity of injection and resident brine (salinity gradient) on physical dispersion through singlephase (miscible) sandpack tests.
A systematic series of singlephase sandpack tests were performed. In this manner, the sandpack was initially saturated with high salinity brine (HS) and flooded with low salinity brine (LS), afterward. Consequently, the initially uniform salt distribution in the sandpack was altered gradually, leading to development of salinity gradient and mixing zone in the sandpack. The salinity of the effluent brine was measured as a function of injected pore volume. A coherent analytical approach was then carried out to estimate the length of mixing zone with respect to Peclet number and dispersivity. The salinity difference of the brines used in the tests were between 36,000 to 156,000 ppm.
It was observed that dispersivity and physical dispersion of salt during LSWF depends on the salinity of HS and LS. The higher the salinity difference, the higher the dispersivity. The maximum estimated dispersivity was observed for a test in which the salinity of HS and LS were 160,000 and 4,000 ppm, respectively. The estimated dispersivity of this test was 0.0071 ft. which is equivalent to a Peclet number of 116. The minimum dispersivity was obtained when the salinity difference was 36,000 ppm. The dispersivity of this test was estimated to be 0.0040 ft. which means the Peclet number is increased to 205. Putting all results together, it can be concluded that for a system with lower salinity difference, lower volume of LS will be required to establish low salinity conditions throughout the porous system.
The impact of salt concentration of resident HS and LS injection brine on physical dispersion/mixing of brines with different salinity was experimentally investigated for the first time, to the best of our knowledge. Moreover, visual evidence was provided to discuss the impact of salinity and salinity difference of brines on dispersivity of the system.
The heterogeneity of natural geologic samples presents significant challenges in furthering our understanding of geochemical reactions in porous media. This investigation explores the feasibility of fabricating reactive rocks through novel additive manufacturing techniques by integrating reactive materials with polymer filaments. Using 3D Xray Computed Tomography (Xray CT) images of a sandstone sample from the Paluxy formation in Mississippi, a template was created to 3D print a model of the system’s pore structure. Two methods for fabricating a rock structure consisting of a reactive phase that reflects the properties of the real sample are investigated here. The first method entails mixing calcite particles with HIPS pellets and extruding a customized reactive filament. The second method consists of dispersing calcite in THF and using the resultant mixture to coat segments of HIPS filament. The filaments were used to 3D print models, and the relative success of each method was evaluated via by optical microscopy, 2D Scanning Electron Microscopy, and 3D Xray CT imaging. For each set of images, calcite volume fractions and the exposed calcite surface area are determined using ImageJ and MATLAB. Results from the first method indicate that calcite surface areas are comparable to real samples, albeit most of the calcite is inaccessible. This will be compared with accessible surface areas of samples printed with the calcite coated filament. These findings will be used to inform further pathways for utilizing 3D printing as a means of modelling reactive porous media in pursuit of a solution that accurately reflects the pore structure and reactive properties of real samples.
The dissolution of fractures exhibits various patterns when a reactive fluid was injected into undergrounds. We performed a visual dissolution experiment on NaCl crystals to simulate the coupling of reaction and dissolution in natural environments. Three typical dissolution patterns including face dissolution, wormholes and uniform dissolution were observed. However, the theoretical foundation of transitions of dissolution patterns remains unclear. Here, we proposed a theoretical model to illustrate the transitions of dissolution patterns affected by flow rate and reaction rate. By comparing the length for unsaturated fluids saturates at the radial and transverse direction, the phase diagram predicted by the model shows that wormhole dissolution will dominates when. The phase diagram not only exhibits good agreement with our this and previous experiments, but also is highly consistent with experiments and simulations of existing works. This work extends the classic phase diagram for fracture dissolutions and provide improved insights for dissolving process in subsurface applications.
Root exudates stimulate microbial activity and functions as binding and adhesive agent that increases aggregate stability in the rhizosphere. The exudates produced from plant roots and microorganisms in rhizosphere plays a significant role in the formation of rhizosheath. A high viscosity stabilizes soil aggregates in the surrounding of the root and creates rhizosheath. The formation and stabilization of rhizosheath of maize plants under various soil water contents has been studied in the past but the influence of root exudates on the rhizosheath formation associated with other rheological properties still needs to be investigated and understood. Such knowledge will greatly enhance the understanding of how rhizosheath is formed under different root and seed exudates and effect of their physiochemical properties on the adhesion properties of mucilage. The aim of this study is to provide the first combined quantitative data on how root and seed exudates of different plants affects rhizosheath formation. We hypothesized that mucilage will contribute in the formation of rhizosheaths. For this we used the mucilage of chia seeds which acts as a modelled plant root mucilage and mix it with soil in a five different concentration. After preparing the soil with mucilage, artificial roots (flax cords) are incorporated in this soil. After 48 hours at 25oC roots are removed and rhizosheath is measured. For further studies, rhizosheath after drying and wetting cycles, mucilage adhesion, simulation and rheological properties will be investigated under various soil water contents, soil texture, soil type and soil compaction.
This talk will present a 3D, continuumlevel damage model for simulating Lithium diffusion within generated Li$_x$Ni$_{0.5}$Mn$_{0.3}$Co$_{0.2}$ (NMC 532) secondary cathode particles. The primary motivation of the particlelevel model is to inform cathodeparticle design and determine charging profiles that reduce cathode fracture. The model considers NMC 532 secondary particles containing an agglomeration of anisotropic, randomly oriented grains. The model predicts that secondaryparticle fracture is primarily due to nonideal grain interactions with slight dependence on highrate charge demands. The model predicts that small secondaryparticles with large grains develop significantly less damage than larger secondary particles with small grains. Finally, the model predicts most of the chemomechanical damage accumulates in the first highrate cycles. This chemomechanical "damage saturation'' effect indicates that initial secondaryparticle fracture occurs within the first few cycles, while longterm cathode degradation is not solely chemomechanically induced.
MetalOrganic Framework (MOFs) are functional crystalline porous material having an open metal site with organic linkers with a wide range of applications. Fundamental properties include a large surface area, the high degree of crystallinity. It is also known that MOFs are of low density and show high thermal stability. Their usage in gas hydrate field is unknown and has not been investigated previously.
In this study, we test different MOFs for their CH4 hydrate storage capability as well as storage stability below 0℃ for natural gas storage and transport. Experiments are performed under hydrate formation conditions using a highpressure chamber. Multiple temperature cycles are performed to check the memory effect as well as improvement in hydrate storage capability in memory run. Results show enhanced hydrate formation rate in the presence of MOF. During the study, crystals are found to remain stable over multiple dissociations and formation cycles, indicating a long life cycle and reusability of MOF as a hydrate carrier. Details discussion will be provided during the presentation.
Hydrogen for clean energy is in the national and international spotlight. Offshore wind presents an extensive renewable energy source in the UK, and a large green hydrogen resource, positioning the UK to be a major player in the emerging global hydrogen market. In the UK and around the globe there’s a handful of likely subsurface hydrogen storage sites and it is widely recognised that hydrogen storage in porous media (rocks) will be necessary to support the scale of production, storage and use anticipated for a global hydrogen economy.
A key component of subsurface risk management is the suite of geological controls needed to ensure that storage is efficient and secure (i.e. that injected fluids do not leak from the storage formation). The project will characterize, translate and test a suite of geological controls (including caprocks and hydraulic barriers) and explore the subprocesses which govern their ability to trap hydrogen. The aims is to better understand hydrogen flow through porous media (rocks) and hydrogen behavior in underground settings. In order to achieve the goal, the first approach was to map possible distribution of hydrogen density within the North Sea. A database of pressure, temperature, salinity and depth measurements for 191 gas and oil reservoirs within the North Sea was collected. Hydrogen density, brine density and buoyancy was calculated in order to understand its special variation in relation to pressure and temperature distribution. Sensitivity analysis were carried out to understand relationship and influentiality extent between the selected parameters.
Understanding of geological controls is critical to inform the selection of appropriate reservoir sites as well as designing safe and effective storage and recovery schemes. The project outcomes will inform (a) criteria to site selection, monitoring and assessment approaches for hydrogen geological storage, and (b) potential for engineered barriers for enhanced containment or leak remediation.
Coal beds are dual permeability systems characterized by a porous matrix enclosed within sets of orthogonal fractures known as cleats. Production of coalbed methane (CBM) consists of desorbing methane from the low permeable coal matrix to the high permeable cleat system. Unlike in conventional reservoir exploitation, sorption mechanisms cause shrinkage and swelling of the matrix which increases the complexity of the phenomena at stake, leading to complex reservoir behaviors in terms of production.
A 3D discrete element method (DEM) coupled to a porescale finite volume method (PFVM) is used here to better understand the different mechanisms at stake. The model, implemented in the opensource software Yade Open DEM (Smilauer et al., 2015), is an offspring of the hydromechanical model proposed by Catalano et al. (2014). The coal matrix is treated as an assembly of bonded particles interacting one with another through elasticbrittle contact laws. The pore space is discretized into tetrahedra, generated from a regular triangulation of the particle assembly. Both Knudsen and surface diffusions, as well as sorption processes, are modeled considering the coal matrix as a microporous material. The method is hydromechanically coupled in the sense that changes in pore pressure produce hydrostatic forces that deform the solid skeleton, while deformation of the pore space induces pore pressure changes that promote interporal flow. Besides, sorption induced deformations are taken into account by considering an additional pressure term related to the concentration of gas within the medium (the socalled solvation pressure).
In this work, we first present the model and its constitutive equations. We assess its capabilities by comparing its predictions to wellestablished solutions describing diffusive flow in porous media as well as to classic poroelasticity concepts. In particular, we focus on the influence of sorption induced deformations on the Biot coefficient estimation. Finally, we compare the model predictions to swelling test data from the literature to illustrate its consistency.
Studies of colloid transport during transient flow in variably saturated porous media are important to determine the roles of dominant processes on particle remobilization. The main objective of this study is to develop a model to describe transport, adsorption, and release of colloids during cycles of drainage and imbibition under various saturation conditions. For this purpose, two different modelling methods were investigated. In the first set of equations, the extensions of the model of Cheng and Saires1, which was proposed by Qiulan et. al.2 is examined. This model includes the empirical coefficients that quantify the kinetics of colloid mobilization during transient conditions. This formulation assumes that attachment and detachment at the airwater interface (AWI) occurs as a function of the available air–water interfacial area (a). In the second approach, we assumed that colloid exchange term from the AWI is a kinetic sorption process in which the amount of fluid saturations determines the magnitude of airwater interfacial area. To obtain the optimized values of parameters we employed a genetic algorithm optimization scheme in both approaches. We found rather similar results between the two approaches, while slightly more accurate results were obtained using the second model. The results of simulations revealed a promising description of column scale experiments, using Escherichia coli D21g particles, performed by wang et al3. Numerical simulations demonstrated that the amount of colloids release is a function of the number of drainage and imbibition cycles. Furthermore, the amounts of release during the imbibition cycle was much higher than that of drainage which would be related to the important role of AWI on particle remobilization. This finding is consistent with the outcomes of experiments.
Gravitydriven infiltration of fluids into heterogeneous soil controls the distribution of water in soil and the fate and transport of pollutants through the vadose zone. Infiltration into dry soil is hydrodynamically unstable, leading to preferential flow through narrow wet regions. These preferential channels concentrate water and solute fluxes and persist over cycles of wetting and drying.
In this work, we use numerical simulation to explore the impact of fingering and layered soil structure on solute transport in the vadose zone. We validate our unsaturated flow model by reproducing experimental results of infiltration of water into various configurations of layered soil. Our model can accurately reproduce the flow behavior at the transition between layers with contrasting grain sizes. We propose to calibrate our continuum unsaturated flow model using the changes in finger width as a function of infiltrating flux and grain size contrast between layers. We simulate the transport of a passive tracer through initially dry soil and after multiple infiltration cycles, and characterize the transport mechanisms in 2D and 3D layered soils.
Swimming microorganisms are often encountered in confined, porous geometries where also an external flow is present, e.g. in filters or inside the human body. To investigate the interplay between microswimmer motility, confinement and external flows, we developed a model for swimming bacteria based on point coupling to an underlying lattice Boltzmann fluid. With this implementation, straight swimming motion interrupted by random reorientation events reproduces the motility pattern of the runandtumble bacterium E. coli.
We present the application of the model to the study of bacterial dynamics in a simplified porous geometry: A rectangular channel with a single cylindrical obstacle. In accordance with experimental measurements, the results show asymmetric accumulation behind the obstacle only when the bacteria are active and an external flow is present[1]. We quantitatively compare bacterial densities from simulations to the experiments and investigate the physical mechanisms that lead to accumulation.
[1] M. Lee et al.: The Influence of Motility on Bacterial Accumulation in a Microporous Channel, Soft Matter advance article, 2021, DOI: 10.1039/D0SM01595D
Bacteria are ubiquitous in our daily life, frequently as surfaceattached biofilm communities. In some cases, biofilms serve a positive purpose, such as improving health or remediating polluted water; in other cases, they negatively impact our lives, such as by causing infection or fouling equipment. For both positive and negative purposes, understanding the factors that regulate the onset of biofilm formation is crucial in determining how to control or treat them. However, how bacteria transition between the freeswimming planktonic state to the sedentary biofilm state in these heterogeneous environments is poorly understood. Here, we use computational modeling to investigate how biofilm formation depends on bacterial properties as well as the properties of their environment. Specifically, by analyzing the competition between chemotactic dispersal and quorum sensing, we establish universal rules predicting how the onset and extent of biofilm formation depend on cell concentration and motility, nutrient diffusion and consumption, chemotactic sensing, and autoinducer secretion. The findings from this study therefore yield quantitative principles to predict biofilm formation.
Hydrogels hold promise in agriculture as reservoirs of water in dry soil, potentially alleviating the burden of irrigation. However, confinement in soil can markedly reduce the ability of hydrogels to absorb water and swell, limiting their widespread adoption. Unfortunately, the underlying reason remains unknown. Here, we report the first direct visualization of hydrogel swelling within a model threedimensional (3D) granular medium with tunable confining stresses and grain sizes. Our experiments enable us to measure, in situ, two key quantities that were previously inaccessible: the extent of hydrogel swelling and medium restructuring. Unlike an imposed osmotic or hydrostatic pressure, confinement in a granular medium subjects the surface of a hydrogel to a spatially nonuniform stress. We therefore extend the classic FloryRehner theory of hydrogel swelling by coupling it to Hertzian contact mechanics that explicitly treats the stresses exerted by the medium at the hydrogelgrain contacts. Using this approach, we show that the extent of hydrogel swelling is determined by the balance between the osmotic swelling force exerted by the hydrogel and the confining force transmitted by the surrounding grains. Furthermore, we demonstrate that a balance of the same forces, also including intergrain friction, determines the onset of restructuring of the surrounding medium. Our work therefore reveals the physical principles that describe how hydrogel swelling in and restructuring of a granular medium both depend on the properties of the hydrogel, the properties of the medium, and confining stress. We show that our theoretical framework not only describes our measurements but also helps to rationalize previous measurements of hydrogel water absorption in soil. Together, our results provide quantitative principles to predict how hydrogels behave in confinement, potentially improving their use in agriculture as well as informing other applications such as oil recovery, construction, mechanobiology, and filtration.
Reducing the carbon footprint and the commitment to achieve netzero targets will be the drivers of global environmental and energy policies in the years to come. Clean energy sources could soon become the premium choice for power generation and transportation. Hydrogen is an important clean and promising alternate energy option that is growing rapidly. Blue hydrogen is made from natural gas through the process of steam methane reforming coupled with CCS, while green hydrogen is produced from water using renewable power. Especially for the latter, there can be a mismatch between production and consumption, requiring intermittent storage in periods of low energy demand, that can be utilized in periods of high energy demand. Clean hydrogen can be stored in large volumes in underground formations, such as salt caverns, depleted hydrocarbon reservoirs and saline aquifers.
Although storage of gas in underground reservoirs has been vastly studied and implemented for natural gas and to a certain extent CO2, hydrogen storage poses its unique challenges due to its distinctive physical and chemical properties. Hydrogen is more prone to microbiological reactions, has a higher diffusivity and mobility and can have several chemical interactions with the subsurface fluids and rock formations, especially in the presence of clays. All these factors need to be considered before designing an underground hydrogen storage facility. Limited data is available on the feasibility of underground storage of hydrogen for extended periods of time and porescale interactions with reservoir fluids and rocks is still not well understood as there are no studies conducted to visualize or observe these interactions.
Recent advances in Xray µCT to image multiphase flow in porous media and perform insitu measurements, has allowed to visually observe and quantify the complex porescale displacement events occurring under reservoir conditions. These images and measurements have contributed enormously to developing the correct strategies for hydrocarbon recoveries and CO2 storage, and to comprehend the interactions between multiple reservoir fluids at different conditions.
Aiming to achieve a similar level of insight for hydrogen storage, this study discusses porescale imaging experiments to capture the interaction between hydrogen, reservoir fluids and rocks. These experiments allow us to visualize the flow patterns as hydrogen is injected into the porous rock in the presence of brine, and to measure insitu contact angles ascertaining the wettability at different points in porous media. Understanding the interactions between hydrogen and brine can be the first step towards designing an underground hydrogen storage facility in aquifers or depleted hydrocarbon reservoirs. Our research aims to provide an initial indication about the trapping mechanisms and therefore storage efficiency that will occur when large scale hydrogen injection is implemented on the fieldscale level. Further research is planned to understand these interactions under different pressure, temperature, and salinity conditions, and using different flow parameters.
Wind erosion is an ecological and environmental issue of global concern, with many adverse effects such as damage to infrastructure, economic loss, increased regional poverty, and social instability [1, 2]. Desertification directly caused by wind erosion affects 32% of the world’s population, 67% of countries, and 40% of the land area, making it a serious threat [3]. The United Nations Convention to Combat Desertification (UNCCD) calls for attention and action to be taken in the science of combating desertification [4]. Extensive research has shown that that natural vegetative and artificial windbreak forests are the most widely used measure to reduce wind velocity and trap sand [5]. However, the construction of natural vegetative in arid and semiarid areas is limited by scarce water resources and unique soil texture [6]. On the contrary, artificial windbreak forests have been successfully applied in wind and sand engineering projects with low cost and water demand that effectively reduce wind speed and trap sand particles. Although windbreak forests have been implemented to control wind erosion for many years as a wind erosion control measure in arid and semiarid areas, there are few studies on the comprehensive efficiencies between the geometric configuration and spatial arrangement of windbreak forests in terms of the nearsurface airflow field and soil grainsize variation, and there are still controversies regarding the optimal design of windbreak forests to maximize the efficiency of the windbreak forests. Given this, we designed a series of wind tunnel experiments with the first goal of clarifying the variations of the nearsurface airflow field and soil grainsize of simulated shrubs (equivalent to windbreak forests) with different spatial configurations that contain three form configurations (spindleshaped, broomshaped, and hemisphereshaped) and row spaces (17.5×17.5 cm, 17.5×26.25 cm, and 17.5×35 cm) under the net wind speeds of 8 m/s, 12 m/s, and 16 m/s. Our object was to reveal how to arrange the windbreak forests in terms of form configurations and row spaces for preventing desertification in the most convenient and efficient ways. A better understanding of the airflow field and soil grainsize around the simulated shrubs is essential to provide optimized design and maximize the efficiency of the windbreak forests. Simulated shrubs used in this study are not only polymerized by antiaging polymer compounds which are new windresistant materials but also it has beautiful visual effects in deserts.
To improve estimates of longterm average groundwater recharge in data sparse arid regions, we combined a numerical multimodel approach with centurylong time series of meteorological data and sitespecific regolith hydraulic properties. The numerical model was set up in the vadose zone simulator HYDRUS1D for a bare soil and a Mulga (Acacia aneura) savannatype soil in central Australia. Grain‐size analysis from regolith cores were used to generate contiguous 12m deep profiles of hydraulic properties by means of pedotransfer functions. In order to account for conceptual model uncertainty in generated hydraulic properties that are required as input for the physically based soil‐water balance model, eleven pedotransfer functions were applied. Three types of PTFs were used: point estimation (Bruand et al. (1994), Canarche (1993), Gupta and Larson (1979), Hall et al. (1977), Petersen et al. (1968), Varallyay et al. (1982)), parametric (Vereecken et al. (1989), Wösten et al. (1999)), and class PTFs (Meyer et al. (1997), Schaap et al. (2001), Wösten et al. (1999)). Climate data from three stations were used to account for spatial heterogeneity in local climate of the Ti Tree Basin case study area. Analysis of simulated water fluxes in the vadose zone indicated that only rainfall events of more than 200 mm resulted in noticeable fluxes at the bottom of the 12m deep regolith. Recharge events were linked to extreme rainfall associated with monsoonal cyclones. Based on the 130year climate records, longterm average recharge for the savannatype vegetation ranged from 4.3 to 7.4 mm/a across the three climate stations, with an overall mean of 4.6 mm/a. The bare soil had an overall mean recharge of 29.5 mm/a, ranging from 23.5 to 35.8 mm/a depending on climate station. Results from this study yield a better understanding of the highly episodic and spatially variable recharge in arid and semiarid environments and is critical input to sustainably manage groundwater resources.
The hydraulic and air conductivity and the water retention of porous media are nonlinear functions of the water (or air) content or capillary pressure (Van Genuchten, 1980; Vereecken et al., 1989, 1990; Assouline and Or, 2013), which results in nonlinear water and air, single and twophase flow equations that usually preclude analytical and necessitate numerical solutions. If assuming exponential dependence of the hydraulic (Gardner, 1958) or air (Philip, 1998) conductivity on the capillary pressure, the steady flow equations can be linearized when described in terms of the matric flux potential (the integral of the conductivity over the capillary pressure). If assuming also linear dependence of the hydraulic (or air) conductivity on the water (or air) content, the unsteady flow equations are also linear. The two major advantages of linear flow equations are that they facilitate analytical solutions to a variety of flow problems and that the action of multiple water (or air) sources can be described by linearly superposing the solutions describing their decoupled actions.
In the lecture, we will describe briefly a few applications of linear water (or air) flow equations for describing steady and unsteady, forced, water (or air) injection into porous media at different geometries and boundary conditions, relevant for several agricultural and environmental circumstances. These include: 1. Coupled point (or line) source irrigation and localized root water uptake (Communar and Friedman, 2010), which serves the major principle of; 2. The freeware DIDAS program for Drip Irrigation Design and Scheduling (https://app.agri.gov.il/didas, Friedman et al., 2016); 3. Evaluating the role of water availability in determining the yield/plant population density relationship (Friedman, 2016); 4. A proposed method for determining the soil hydraulic properties based on periodic point source irrigation (Communar and Friedman, 2014); 5. Simultaneous water uptake from an onsurface water source and from a shallow water table (in also laterally confined lysimeters) (Friedman and Gamliel, 2019); 6. Singlephase, air flow bounds (BenNoah and Friedman, 2019) to twophase, airwater flow in periodic air injection (BenNoah et al., 2020).
Overall, the solutions to the simplified, linear water and air flow equations, described reasonably well measured distributions of water and air contents (pressures) and fluxes in a wide range of water (and air) contents, making them constructive, practical tools for the design and assessment of irrigation and subsurface air injection operations.
The recharge from the soil to the groundwater is a crucial variable to simulate timevariable groundwater levels and gradients at a catchment scale. Although essential for groundwater modelling, no direct measurement methods are available. One way to estimate this variable is to calculate it from timeseries of atmospheric boundary conditions (precipitation, potential evaporation) for specific soil types, land uses, and ground water depths. In this study, we precalculated monthly and seasonally recharge rates as a function of three parameters for an area in Northern Belgium. Soil type and land use were inferred from geographic information systems. Soil hydraulic properties were derived from soil textural information for a soil information system (AARDEWERK) using pedotransfer functions. Vegetation parameters were taken from the literature. Recharge values were calculated using the HYDRUS1D model with timeseries of daily atmospheric input data for a period of 20 y. A series of models were ran for each soiltype/land use combinations with the fixed groundwater level type bottom boundary with depth in a range between 5 and 200 cm. Next, monthly recharge values were obtained for the complete period for each calculated ground water level. In additions, a future climate time series of atmospheric input data was obtained by applying monthly correction factors derived from a regional climate model (Ntegeka et al., 2008). Resulting lookup table with soiltype, landuse and groundwater depth combinations served as an input to a MODFLOW model recharge (RCH) and evapotranspiration (EVT) package to simulate transient ground water levels and fluxes at the current and future climate. We shortly discuss our MCMC calibration to ground water level and fluxes, validation and water budgets for current and future climate conditions.
Soil database was traditionally used to characterize unimodal soil water retention curve and hydraulic conductivity curve in the past decades. However, soil is often shown to have dualmodal property, being described by macropores/fracture pore system and matrix pore system, respectively, indicating structured soils/fractured rocks and microscopic soils. Here we employed widelyused pedotransfer function databases, including UNSODA 2.0, Vereecken, and HYPRES databases, to characterize both unimodal and dualmodal water retention curves and hydraulic conductivity curves. Only undisturbed samples were selected from the databases. We further required strict criteria to choose the soil samples to ensure that there is enough information in the measurement. A new fitting approach was then proposed to obtain the global minimal soil hydraulic parameters for both the unimodal and dualmodal Mualem van Genuchten (MvG) functions (van Genuchten, 1980; Mualem, 1976). Results suggested there is a decreasing trend of alpha (inverse of air entry parameters) and n (pore size distribution parameters) with the increasing of alpha values in the MvG functions. This trend seems to contradict our physical principles that larger alpha values usually correspond to larger n values. The decreasing trend between alpha and n were further verified analytically. We also find that the ratio of n parameters between macropore and matrix properties has an interesting relationship with the weighting factors obtained from the fitting of dualmodal soil water retention curve and hydraulic conductivity curve, respectively, for the two properties. We anticipate that the results will help to derive soil pedotransfer functions for macropore and matrix properties, which might alleviate unrealistic combinations of MvG parameters.
A new numerical approach is proposed for the simulation of coupled threedimensional and onedimensional elliptic equations (3D1D coupling). Possible applications are the interaction of a capillary network with the surrounding tissue, of tree roots with the soil, or of a system of wells with a reservoir in geological applications. In all of these cases, in which nearly 1D fractures are embedded in a much wider porous matrix, the generation of a 3D mesh inside the small inclusions can become extremely expensive, as well as the resolution of the resulting discrete problem. For these reasons we developed [1] a novel framework for 3D1D coupling based on a well posed mathematical formulation and with a high robustness and flexibility in handling geometrical complexities. This is achieved by means of a threefield domain decomposition [2] to split the reduced 1D problems from the bulk 3D problem, and then resorting to the minimization of a properly designed functional to impose matching conditions at the interfaces, following an approach similar to the one used for handling discrete fracture networks in [3]. Thanks to the structure of the functional, the method allows to use completely independent meshes on the various subdomains and on the interfaces.
Chronopotentiometry is a powerful technique to investigate transport phenomena in charged porous mediumelectrolyte interfaces, especially those associated with ion transport in the overlimiting regime. It allows to determine the transition time, which is an important characteristic of transient ion transport. Under certain conditions, the Sand equation can be applied to analyse fouling effects, the inhomogeneity of the surface or to determine ion transport numbers in polymeric ionexchange membranes. Even ionexchange membranes based on chemically homogeneous polymers can exhibit microheterogeneities disturbing the ion transfer. The surface heterogeneity of the membranes used in many electrochemical systems is an important issue and it has been actively studied, but usually aqueous electrolyte systems have been studied.
In this work we apply chronopotentiometry for studying polymeric ionexchange membranes in alcoholwater media. A nonreinforced homogenous membrane, Nafion 117, and two reinforced homogeneous membranes, Neosepta CMX and AMX, have been investigated in LiCl 0.005 M electrolyte solutions with 2M alcoholwater solution as solvent. Methanol and ethanol were used as alcohols. Limiting current values were determined from voltagecurrent curves. The transition times were obtained as a function of the density current and the agreement with the Sand theory has been analysed.
Financial support from Banco de Santander and Universidad Complutense de Madrid is gratefully acknowledged.
Fluid flow in fractured porous media is a common phenomenon in many engineering applications, and many numerical methods have been proposed to capture these processes. Here, a new discrete fracture model based on phase field method is presented. The common discrete fracture models represent fractures by sharp topology in an explicit way, regardless of using conforming or nonconforming mesh. Inspired by the definition of crack phase field, the sharp fracture topology is treated as a diffusive one in the solution of fluid flow problems, and the integration of fluid flow equation over fractures can be transformed to the one over the matrix. The algorithm to determine the fracture phase field and finite element discretization are described in detail. The performance of the proposed method is validated against the classic discrete fracture model on several numerical cases in both two and three dimensions. The convergency behavior of the proposed method is furtherly investigated through sensitivity analysis to mesh resolution and fracture parameters. Numerical results demonstrate that the proposed method is accurate, convergent and quite promising for simulating fluid flow in fractured porous media.
The simulation of flow and transport in porofractured media is a complex task, in particular from the point of view of mesh generation. Indeed, constructing good quality meshes that are conforming to the fractures internal to a rock matrix can be computationally expensive when the mesh has to be simplicial, as for standard Finite Element Methods.
In this talk we introduce novel strategies based on Virtual Element Methods (VEM) to perform simulations of flows in Discrete Fracture Matrix models. The flexibility of generalized polygonal meshes that can be handled by VEM, even allowing aligned edges and aligned faces, is a very useful tool for mesh generation. The presented strategies rely on the fast generation of polytopal meshes and on suitable refinement techniques designed for generalized polytopal meshes, that are used to adapt the mesh according to a posteriori error estimates, in order to reduce the number of degrees of freedom used to obtain high quality solutions.
Abstract
An investigation of drug release from granules linking structure, process and release performance
Faraj Shmam, Rachel Smith, Kate Pitt
Particle Technology Group, Department of Chemical and Biological Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK
Granulation is a particle enlargement process where coarse or fine particles are agglomerated into large granules. These large granules are further processed to form tablets for oral solid dosage forms. In a highshear granulation, the granule structure can be directly influenced by the granulation time and the amount of liquid binder added and this will have a strong influence on the dissolution rate of the granules. However, there is a lack of scientific understanding on the relationship between formulation, process and granule structure and performance. The aim of this work is to develop an experimental understanding of the relationship between granulation process parameters and granule structure and investigate the links between granule structure, granule dissolution and drug release profile.
In this study, microcrystalline cellulose was used as an excipient powder and polyethylene glycol as the binder. Acetyl salicylic acid (aspirin) was used as a model active component drug. When granulated, it was found that increasing of both the liquid to solid ratio (0.8, 1.0 and 1.2) and mixing time (2.5, 5 and 7 minutes) decreased the porosity of the granules. For the dissolution studies, a UV spectrophotometer at 270 nm was used to monitor drug release as a function of time. For the higher porosity granules, i.e. those produced at low granulation time and liquid to solid ratio, dissolution was found to be significantly more rapid. This demonstrates the importance of the granulation process and the resulting granule structure.
The Virtual Element Method (VEM), firstly introduced in [1], is a very recent extension of the Finite Element Method that allows the resolution of partial differential equations using general polygonal grids. This brings forth several advantages including better domain meshing and approximation of geometric features that are of great relevance in tackling problems characterized by complex geometries. Despite the growing interest in testing the performance of this new numerical method on physical and engineering problems characterized by challenging domains, still very few applications exist to complex and realistic geological flow models in porous media. In this framework, the aim of the present contribution [2] is to investigate the potentialities of the VEM in the contest of twophase flow of immiscible fluids in porous media, a problem described by a system of timedependent coupled nonlinear partial differential equations. In this work we discretize the equations in time and in space using an iterative IMplicitPressureImplicitSaturation method coupled with a primal $C^{0}$conforming VEM. We investigate the performance of the resulting fully discrete scheme showing its potentialities in terms of simplified construction of highorder approximations and mesh flexibility, a very attractive feature for the numerical modeling of twophase flow processes in fractured porous media. The method is tested both on a problem with known analytical solution and on some more realistic benchmark problems that are of interest for engineering applications in porous media [3].
During cycling, volumetric changes of the active material induce stresses on the micro and macroscale, leading to cracks and delamination, and deformation of the inactive layers and the casing [1]. The altered microstructure is said to “age” and it suffers from capacity loss and damaging effects like lithiumplating [2]. The quantitative simulation of this battery aging on a microstructural level is now jointly pursued by Math2Market and the MaDE group of Prof. Vanessa Wood (ETH Zürich) in the framework of the EUproject “SOLVED!”.
Our approach is to analyze NMC cathode and graphite anode microstructures via 3D invivo tomography and electrochemical characterization [3]. The experimental data is used to validate the degradation simulations in which local volumetric changes and damage due to lithium intercalation on the microscale are linked to the local Liion concentration in the active material and its mechanical deformation. In a dynamic process, the altered microstructure is considered for each charging and discharging step. In this way, the influence of structural changes on the electronic and ionic transport processes and on the macroscopic performance of the cell is digitally predicted and monitored.
The usage of reliable quantitative simulations allows for the timesaving and streamlined finding of new prototype materials with superior lifetime and performance. This unique workflow represents a new efficient, stateoftheart approach to digital R&D material design for energy materials in emobility and energy storage.
Oil and gas deposits are still the largest energy sources among all over the world. The most common and reliable method of their prospecting and exploration is the seismic survey process. It is based on the propagation of seismic waves in geological media and their interaction with heterogeneities (reflection, diffraction, attenuation). Recently, a lot of migration and inversion algorithms were developed: fullwaveform inversion, petrophysical inversion, stochastic inversion, etc. All of them are based on the numerical solution of the direct wave problem. That is why, the investigation of accurate and effective methods of the computer simulation is an important scientific task.
Previously, the usage of sophisticated mechanicalmathematical models for describing the dynamic behavior of geological media was strictly limited by the performance of available computers. In the last century, several models describing wave propagation in porous fluidsaturated media were proposed. Initially, the Gassmann model [Gassmann, 1951] has become widespread. Further, the Biot model [Biot, 1956], has grown more popular, since it describes the porous medium more accurately. For example, the Biot model considers two velocities of longitudinal waves that can be observed and measured experimentally [Winkler et al., 1989]. In 1989, V.N. Dorovsky proposed a nonlinear continual theory of filtration [1989]. The theory was expanded in the work [Blokhin and Dorovsky, 1995], and the twovelocity linearized model, known now as the Dorovsky model, was presented. The comparison of the continuum filtration theory with the BiotJohnson theory was done at [Dorovsky et al., 2012]. Both models show excellent agreement with each other. Another physical model of the multiphase medium was suggested in [Romensi et al., 2019]. Its governing equations form a hyperbolic system of PDEs that significantly differs from the Biot system [Biot, 1956] because of the different stressstrain relationships; however, the authors state that “the features of wavefields are qualitatively similar in both models, and in some cases, they are quantitatively close by a corresponding choice of the material parameters” [Romenski et al., 2019].
In this work we extended our novel approach for the simulation of seismic waves in hydrocarbon deposits [Golubev et al., 2020] to the case of fractured fluidsaturated medium described by the Dorovsky model. We relied on the method of incorporating fractures into the computation process presented in [Khokhlov et al., 2020] for isotropic elastic media, which replaces an inclined fracture with a number of small fractures tied to the mesh points and duplicates the corresponding nodes (containing the unknown functions). The feature of the method is the possibility to perform calculations on a structural computational grid, that avoids the construction of unstructured grids and drastically decreases computational costs. Physically correct internal contact conditions were derived for the two sides of the fracture, that eliminates the meshing process inside the crack volume. The presented approach allows us not only to simulate precisely the stressstrain state, but also to estimate the pore pressure inside the reservoir.
The reported study was funded by RFBR, project number 200100261.
Gas shales are partially water saturated with their pore space simultaneously filled with brine and liquid and/or gas hydrocarbons. Changes in water saturation can cause swelling or shrinkage, which is of significant importance to natural gas production from unconventional shale reservoirs and sample handling in the laboratory [1]. During hydraulic fracturing, a substantial amount of injected waterbased fluid is believed to imbibe into the shale matrix, driven by the high suction gradient between the well and the shale. Such imbibition has been evidenced in the field by large fluid loss during flowback operations and reproduced by many laboratory spontaneous imbibition tests [2], [3]. Also highlighted in recent research is that increasing water saturation can not only result in swelling [4] but also alter elastic and strength properties [5]. However, little is know about how suction and water saturation can be related to the resulting volumetric deformation in gas shales. Here we show our progress in characterizing the swelling and shrinkage of gas shales as stressstrain behavior. We found, in our controlled suction experiments on an organicrich shale, that the volumetric strain induced by suction variations is a strong function of imposed suction and water saturation. The nonlinear hysteretic relationship between the two was expressed by water retention curves. We discuss possible expressions for the average pore pressure and effective stress. We anticipate our results to be a starting point for a more sophisticated stressstrain framework with a proper definition of effective stress for partially saturated gas shales.
Different techniques were used for water shut off and conformance control in the mature oil fields whose sole purpose is to cut the water production and sweep the oil towards the producing wells. Many different types of gel systems were developed for the conformance control but all of them have the risk associated with them. It is common for the gel systems to not only block the water producing zone, but they also block the oil producing zone. To solve this problem an invert emulsion system with polyacrylamide (polymer) and polyethyleneimine (crosslinker) was developed. The emulsion system breaks into oil phase and gelant phase at high temperature of 105 ℃. The oil phase will provide a path for the oil to flow towards the producing well whereas the gel will prevent the water from flowing towards the production well. To understand this behaviour properly, microfluidic experiments were conducted in this work.
To understand the emulsion separation and conformance control behaviour of developed invert emulsion system, the glass micromodels were used. The developed emulsion was injected into the micromodel and heated at 105 ℃ for emulsion separation and gelation.
After the gelation in the glass micromodels, the injection of water and oil was carried out and the behaviour of water and oil flow was recorded using the microscopic camera. The video graphic analysis presented a unique way in which the developed emulsion systems prevents the water production but allows the oil to flow.
This work for the first time presented the mechanisms which were used by the emulsion system to provide efficient conformance control, the use of micromodel allowed to visually see how the emulsion system allows the oil flow but restricts the water production.
We report experiments in which hydrogels equilibrated with carbon dioxide at elevated pressure experience sudden decompression. The hydrogels remain stable until disturbed by a small impact, which initiates the formation of pennyshaped cracks within the hydrogel. The main radius of these oblate ellipsoids grows linearly in time with a growth rate of the order of 1 cm/minute.
Our quantitative model assumes the growth kinetics of the crack to be controled by gas diffusion from the bulk of the hydrogel to the crack boundaries. Crack propagation continously creates fresh crack surface whose high gas concentration supports continous crack growth. The model confirms the observed linear growth of the main crack radius and predicts the growth rate with high accuracy from the material properties.
This work might be of interest as catastrophic mechanism of tissue damage for decompression sickness and to study material properties via cavitation rheology.
Polymer electrolyte membrane (PEM) fuel cells are expected to play an integral role as lowemission energy converters in a future energy economy. Although technological maturity of these cells has been demonstrated, the challenge remains to achieve high power performance at drastically reduced platinum loading. So far, the attempts to reduce the platinum loading have been thwarted by severe voltage losses. A possible origin of these losses is the water flooding of porous gastransport media. The optimal water balance is of particular importance for the operation of the cathode catalyst layer (CCL), wherein liquid water is needed for efficient proton transport and high activity of the oxygen reduction reaction [1], whereas excessive water accumulation in pores (i.e., flooding) would block the porous pathways needed for the gaseous supply of oxygen. An optimal design of porous electrode media PEM fuel cells should thus account for heterogeneous wettability effects in them.
Conventional CCLs possess an agglomerate structure with a bimodal porous network morphology [2]. Primary pores (110 nm diameter) exist in the carbon support, which has platinum particles (15 nm diameter) attached to its surface. Secondary pores (10 – 50 nm diameter) form the space between Ptloaded carbon. An ionomersubphase is dispersed in this structure, forming a thin, skinlike layer that partially covers the surface of Pt/C particles or their agglomerates.
The CCL exhibits a highly heterogeneous wetting behavior. Various models [3, 4] account for the impact of the mixed wettability, parametrizing contact angles and fractions of hydrophilic/hydrophobic parts independently to match experimental data. We propose a novel approach that harnesses the correlations between the wetting behavior and the structure and composition of the layer. The main distinction is made between ionomerpenetrated and ionomerfree pores. The impact of the Pt particle density on the support is also explicitly considered. Moreover, a peculiar ionomer inversion effect that had been seen in previous experimental results plays a crucial role: where ionomer covers the Pt/C surface, previously hydrophilic surfaces turn hydrophobic [5]. Consequently, we developed a set of descriptors, including a statistical density function for wetting properties. Our analysis of the relations between structure, composition, wettability and performance supports the following hypothesis: lowering the Pt loading via reducing the Pt:C ratio evokes hydrophilic wetting behavior in secondary pores, leaving the CCL highly susceptible for flooding. Based on this finding, we derive design strategies to match lowPtloading with floodingresistant wetting behavior. The results of this work are embedded in larger framework of a comprehensive, structurebased model to link CCL recipe and material choices with performance.
A central component of the rhizosphere is root mucilage, a hydrogel exuded by plants that dramatically alters chemical and physical properties of the soil. It is characterized by its large water holding capacity and is hydrophilic or hydrophobic depending on its hydration status: when swollen, mucilage is hydrophilic but becomes hydrophobic when dry, forming local hydrophobic spots on the surface of soil particles. The morphology of these hydrophobic regions formed by dried mucilage is affected by the type of mucilage and microorganisms and can vary from isolated local spots, to networks spanning across larger areas of the soil particle surface. However, until now the understanding on how this heterogeneous distribution and its morphology affect infiltration and water repellency in soil is limited.
Therefore, the goal of this study is to investigate the impact of the spatially heterogeneous wettability distributions on the infiltration into soil. For this purpose, we utilize a twophase flow model based on the LatticeBoltzmann to numerically simulate the infiltration in porous media with a simplified geometry and for different selected heterogeneous wettability coatings. Additionally, we simulated the rewetting of dry rhizosphere of a sandy soil where dry hydrophobic mucilage depositions on the particle surface are represented via a locally increased contact angle.
Our simulations show that water repellency in porous media can occur not only when the soil particles are hydrophobic but also when their wettability is reduced on small local spots. In particular, we can show that the hydraulic dynamics and effective water repellency are determined by the specific location within the pore space where wettability is reduced or hydrophobic, rather than by the averaged contact angle. This raises questions about the applicability of the Cassie equation that considers only an averaged contact angle to most porous media, since for instance, coatings in the pore throat and pore body often have different effect strengths. Thus, within the rhizosphere, even relatively small areas coated with dry hydrophobic mucilage in the pore throats can cause water repellency in an otherwise wellwettable and waterconducting soil.
Assessing the land use and land cover change is crucial for sustainable natural resource management and understanding the changes in hydrologic processes and water cycle. In this study, we aim to quantify the land use and land cover changes in Gilan province of Iran between 1975 to 2015 using Landsat 2 MSS and Landsat 8 OLI/TIRS images, with spatial resolution of 80 m and 30 m, respectively. ArcGIS 10.5 and ERDAS Imagine 14 are utilized for image processing. Maximum likelihood supervised classification method is performed to generate the signature class of significant land cover classes including agriculture, plantation/orchards, moderate forest, urban settlements, water bodies, woodland, dense forest, good rangeland, and moderate rangeland. For each classified images, an accuracy assessment step is executed using error matrix and Kappa coefficient followed by the post classification change detection analysis. To provide detailed information about the spatial and temporal variation of land use and land cover, the statics of changes in 1975 relative to 2015 were delineated using transition probability matrix. Our analysis suggests that around 351,000 hectares in Gilan province (equivalent to nearly 25% of land cover) has changed between 1975 and 2015. The results show that dense forest and plantation/orchards are disappearing with obtained change ratio of 5.76%, and 5.88%, respectively. Agriculture and urban settlements have been expanded about 91,900 ha and 29,000 ha, respectively. The majority of the converted land use types to urban settlements are identified as plantation/orchards, agriculture, and water bodies. Forest conversion to other land uses, especially agriculture and plantation/orchards is highlighted in our analysis. The possible socioeconomic impacts of these changes as well as their consequences on hydrologic processes in the region are discussed. Our investigation offers new insights regarding the changes in the land cover and land use in Gilan province of Iran which can guide future decisions, restorative land use practices, and contribute toward sustainable management of land, water and natural resources.
Keywords: Land use, Land cover, Sustainable management, Geographic information system, Remote sensing
In the process of fractured reservoir development, fracture opening pressure, opening sequence, and reservoir fracture pressure are the factors that must be considered when formulating oil and gas development plans. Particularly in fracturing, refracturing, and water injection development measures for a lowpermeability reservoir, accurate prediction of structural fracture development law and reservoir fracture pressure is an important guarantee of improved oil and gas recovery and economic benefits. A reasonable injection pressure for oil and gas wells cannot exceed the fracture pressure of oil and gas reservoirs. Under this pressure condition, the structural fractures should be fully opened to maximize the oil and gas recovery efficiency. Through structural evolution analysis, combined with rock fracture criteria, the occurrence of fractures is predicted; based on the theory of fracture surface energy and rock strain energy in fracture mechanics, the linear fracture density is predicted. Using a core sound velocity experiment and microseismic monitoring technology, the in situ stress direction is determined. Combined with the fracturing data, the in situ stress of each well is calculated; by determining the rock mechanics parameters and a finite element model, the threedimensional distribution of the in situ stress can be predicted; with the aid of the fracture occurrence and the stress field numerical simulation results, the reservoir fracture pressure and the opening sequence of natural fractures in the reservoir are determined. We used the Paleogene Funing Formation in the T96 fault block of the Jinhu Sag in eastern China as an example to predict the reasonable water injection pressure of fractured lowpermeability reservoirs. Observations of core fractures in the Funing Formation in the T96 fault block show that the predominant orientation of fracture strikes is ENE and WNW conjugate fractures; the dip consists of mainly vertical fractures and highangle oblique fractures (87%). The simulation results of the stress field show that the horizontal minimum principal stress is between 21 MPa and 28 MPa, and the maximum horizontal principal stress is between 30 MPa and 40 MPa. The horizontal maximum principal stress of the T96 fault block is in the ENE direction; near the fault, the direction of the horizontal principal stress changes by 5° to 10°. During water injection, the fractures in the ENE direction open first, and the fractures in the SE direction open subsequently. The opening pressure of the fracture increases as the angle between the fracture strike and the horizontal maximum principal stress becomes larger; the depth of the fracture and the opening pressure are also positively well correlated. In the high part of the structure (1650 m2000 m), the fracture opening pressure is between 22 MPa and 42 MPa at the opening and between 41 MPa and 69 MPa in the lower portion of the structure (3150 m3800 m). By calculating the actual fracture pressure of the reservoir, it is proposed to use different water injection pressures in different blocks to ensure high and stable oil and gas well production.
The deformation of fruit tissue caused by drying typically results in consequent quality loss. To better understand the mechanism of heat and moisture transfer, a coupled thermohydromechanical model was developed at microscopic cell scale. Pear was chosen as the research object as this fruit suffers from great shrinkage after drying. A 2D geometric model of cortex tissue was obtained by a virtual fruit tissue generator that is based on cell growth modeling. The distribution of temperature and moisture in tissue cells were predicted using transport laws, and the different physical properties of the microstructural components were obtained experimentally or from literature. An equivalent microscale cell model that incorporates the dynamics of mechanical deformation of the cellular structure was implemented. It can not only predict the heat and moisture transport in tissue cells, but also obtain the deformation characteristics of different regions in the tissue, which further reveals the thermohydromechanical coupling mechanism during drying process. The results showed that the pore size of tissue cells gradually decreased with time. At a drying temperature of 70℃, the volume shrinkage ratio of tissue cells was about 50% after reaching a steady state. The intercellular spaces of tissue can be regarded as closed pores in porous media, and stress concentration tends to occur near these positions. A sensitivity analysis of water permeability, thermal conductivity of cell membrane and elastic modulus of cell wall on the tissue deformation showed that, the cell membrane permeability has a greater impact on the deformation during drying within a certain range of changes. It will then become feasible to evaluate measures to improve the quality of fruits and vegetables during drying using this model in a multiscale modeling framework.
Background: Coalbed methane (CBM) is an important natural gas resource of growing interest [1,2]. The injection of CO2 can enhance CBM recovery, meanwhile, CO2 can be stored in the coalbed layer. However, CO2 may induce coal matrix swelling, and an inappropriate injection design may result in the cleat closure of the coal system [3,4]. On the other hand, N2 was effective to promote CH4 desorption and improve sweep efficiency [5,6]. However, the major drawback associated with N2 injection is that it tends to lead to an early breakthrough. In the CBM reservoirs, the coal matrix is associated with a large number of micropores that are less than 2 nm. The swelling occurs is due to the adsorption behavior in the micropores [7,8]. Due to limitation of laboratory experiments to the gas adsorption status in the micropores, the replacement process of CH4 in the coal matrix and the swelling/shrinkage mechanism of the coal matrix are poorly understood.
Methods: In this paper, we studied the CH4 recovery process by injecting CO2, N2, or CO2–N2 mixture into the coal matrix using molecular dynamics simulations. The relationship between the swelling of coal matrix due to the adsorption, and permeability decline due to swelling, were then discussed. A model of a coal matrix filled with CH4 was constructed, and the CO2 (N2 or CO2–N2) molecules were added into a largesize fracture of the coal system. This system was equilibrated to investigate coal swelling and the replacement process. A long enough simulation was performed, to allow CO2 (N2 or CO2–N2) molecules enough time to enter the coal matrix and displace the CH4 molecules.
Findings: The calculated recovery factors were 79.9, 54.3, and 70.5% for CO2, N2, and CO2–N2 mixture injection, respectively. After equilibration, the specific volume (i.e. volume per unit mass) and thickness of the coal matrix were estimated and compared to those at the initial stage for estimation of the coal swelling. There is a swell of 12–17% in the pure liquid CO2 injection. There are no swell in the pure N2 case and CO2–N2 mixture case, shrinkage may be observed during N2 injection and negligible during the CO2–N2 mixture injection. The permeability change was also estimated by using the coal matrix swell data. The swelling estimated by the specific volume for the pure CO2 case is about 17%. Therefore, the estimated permeability will drop to 0.4% of the original one. The reported porosity of the actual field has some uncertainty, but, if the natural fracture porosity of 0.4% [5] was used, the cleat will be fully closed then. Apart from the micropores, the formation becomes almost impermeable. These findings agrees with previous reports [3,6,7]. In conclusion, in the case of pure liquid CO2, the permeability will reduce dramatically. For pure N2, it can be helpful to enhance the permeability. If we carefully choose the mole fraction of CO2–N2 mixture, the permeability reduction may be avoided, while keeping enough high CH4 recovery factor.
Thermoporoelasticity problem has many applications in science and engineering: geothermal energy systems, nuclear waste disposal, wellbore stability analysis, and others. However, most of the applied problems of thermoporoelasticity cannot be solved analytically. Therefore, it is essential to develop mathematical models and efficient numerical methods. The mathematical model is described by a coupled system of equations for pressure, temperature, and displacements. We consider heterogeneous and fractured media. We apply a multiscale model reduction to reduce the size of the discrete system. We use a continuous finite element method with a Discrete Fracture Model (DFM) for fine grid approximation. For coarse grid approximation, we apply the Generalized Multiscale Finite Element Method (GMsFEM). We present numerical results for two and threedimensional model problems in heterogeneous and fractured media. We compute errors between the multiscale solution with the finescale solution for different numbers of multiscale basis functions. The results demonstrate that the proposed method can provide good accuracy with a few degrees of freedom.
Raising crop production and at the same time reducing environmental spreading of agrochemicals are two current priorities in agriculture. Balancing these needs a quantitative understanding is needed of infiltration phenomena and agrochemical leaching into the subsoil. To this aim, field studies are undoubtedly the most reliable approach to retrieve representative data. Lysimeters are specific devices installed in fields used for studying percolation of water and, to a lesser extent, of contaminants through the unsaturated zone (Howell et al., 1991). However, fullscale detailed monitoring of water infiltration and more importantly leaching of chemical substances may be complex. To overcome this problem, laboratory flow and transport tests in small scale soilpacked columns (typical size, few cm in diameter, 10 to 20 cm in length) have been traditionally applied to study into details key processes controlling, in general, solute transport (Dontsova et al., 2006), and more specifically the effects of agrochemical applications (Masipan et al., 2016). However, under some circumstances, the reduced size may limit the representativeness of the results, and upscaling to the field could be limited. This work aims at linking these different experimental scales via a set of infiltration tests performed at three different laboratory scales, namely small columns (1.6 cm in diameter, 11 cm long), intermediate columns (10 cm in diameter, 25 cm long), and laboratory lysimeter (30 cm in diameter, 70 cm long), all packed with the same porous medium (Dorfner silica sand for a set of tests, and a Lufa standard soil for another set). Water flow and transport tests of solutes and of a pesticide (Dicamba) have been carried out to investigate the differences among the scales in terms of operating conditions, hydrodynamic dispersivity, hydraulic conductivity, pesticide interaction with the soil. The transport tests have been performed applying the solute or Dicamba to the top of the columns, followed by a flushing with water (mimicking irrigation and rain events). Injection rates have been properly selected at the three scales to have the same Darcy velocity, thus ensuring comparability. Outflow water has been collected and analyzed at all scales to reconstruct the breakthrough curve. Moreover, in the lab lysimeter, water content, matric potential, pH, EC and ORP have been measured at different depths for a correct reconstruction of the flow field, concentration profiles and breakthrough curves. The experimental data have been fitted using HYDRUS to obtain unsaturated flow and transport parameters. Dicamba showed little interaction with the soil at all scales, and results are comparable among all setups, suggesting that even small columns can be representative of largescale processes provided that operating conditions are properly selected, even though largescale setups are necessary while investigating the influence of unsaturated flow in the top soil on pesticide leaching.
Gaseous matter exchanges in soil are determined by the connectivity of the pore system which is easily clogged by fresh root exudates. However, it remains unclear how a hydrogel (e.g. mucilage) affects soil pore tortuosity when drying. The aim of this study is to obtain a better understanding of gas diffusion processes in the rhizosphere by explaining patterns formed by drying mucilage.
We measured oxygen diffusion through a soilmucilage mixture after drying using a diffusion chamber experiment. Therefore we mixed soil with different particle size with various amounts of mucilage. Afterwards we saturated the soil and measured the gas diffusion coefficient during drying.
We found that mucilage decreases gas diffusion coefficient in dry soil without significantly altering bulk density and porosity. Electron microscopy indicate that during drying mucilage forms filaments and interconnected structures throughout the pore space. Exudation of mucilage may be a plant possibility to actively alter gas diffusion in soil.
Compared to bulk soil, the rhizosphere has different properties because of the existence of root mucilage which affects the physical, chemical, and also microbial processes. Hydraulic phenomena like limiting water flow at certain dry soil conditions, modulating extreme water contents by slow response to water potential changes; and also influencing solute transport and gas diffusion by varying the connectivity of liquid and gas phases are all classified under the set of the physical processes which are affected by mucilage in the rhizosphere.
Overview of the literature and previous models shows the lack of a threedimensional porescale dynamic model for a better understanding of the connectivity between different phases during imbibition and drainage processes. A major challenge is that mucilage shows a complex behavior which at low concentrations is more like a liquid while at higher concentration when it is almost dry, it becomes a solid. In between, a viscoelastic state is observed and then, mucilage can be considered as a hydrogel.
In particular, this study will use the Lattice Boltzmann method as a powerful tool for fluid dynamics studies and the Discrete Element method for describing solids to present a threedimensional porescale model to simulate the drainage of mucilage between two soil particles. The model will be examined by comparing simulation results and ESEM images of real systems. In real systems, due to the concentration of mucilage and the distance between soil particles, different structures may be formed such as thin filaments or hollow cylinders. This model is able to reproduce observed structures, successfully.
The proposed model may provide us with a new perspective on hydrodynamic processes within the pore space in the rhizosphere. In addition, some other valuable data such as liquid bridges, connectivity of phases, solute transport and etc. would be resulted out of this model.
Understanding deformation and fluid flow in a fractured rock mass is of central importance for geothermal energy extraction, wastewater disposal, and hydrocarbon exploration. Thermal strain or fluid pressure  induced shear displacements in the fracture system lead to hydraulic aperture changes that affect the flow field. To predict these, numerical frameworks are needed that can accurately and efficiently capture this coupled mechanical and hydraulic behavior even in complex natural fractured reservoirs. For this purpose, we use the extended finite volume method (XFVM). In XFVM, the flow and mechanics solvers are iteratively coupled with the fixed stress method, modelling fractures in a poroelastic damaged rock matrix. Fractures are represented as embedded lower dimensional manifolds. The displacement of individual fractures and fracture manifolds is resolved by discontinuous basis functions, modeling slip and tensile displacements as piecewise constant on each fracture segment. Tractions, including compressive forces are calculated for each fracture segment and failure criteria are evaluated.
Here we apply the described framework to analyse shear displacements in a natural fracture network under in situ conditions. The selected fracture pattern consists of approximately 200 nonsystematic fractures mapped at Dounreay in Scotland. In a grid convergence study we investigate which grid resolution is needed to accurately resolve the stress field in the damaged rock matrix as well as the shear slip of the embedded fractures. The sensitivity of shear displacements to fracture characteristics such as for length, orientation or abutting relationships is studied.
The fate and transport of agrochemicals in soils have important implications for groundwater quality and public health. Land management practices deliberately change the pore structure, which consequently controls how mass is transported through the subsurface of agricultural lands. This study employs direct numerical simulations (DNS) to investigate the differences in transport behavior in porous media sampled from a longterm agricultural research station. Millimetersize samples of soils characterized as ploughed and no tillage are analyzed. The velocity field in each soil domain is solved from the full NavierStokes equations and massless particle tracers are tracked accordingly. A statistical analysis of the Lagrangian tracks is presented to compare the velocity variability, breakthrough curve and evolution of displacement moments that characterize each land management practice. Statistical rules for particle motion at the porescale are then applied to parameterize an upscaled transport model based on Continuous Time Random Walk theory. Such a modeling framework shows promise in capturing the nonFickian behavior that is ubiquitous in all heterogeneous media. An improved understanding of the controls for contaminant transport in agricultural soils and of the predictive tools to model contaminant transport are key to helping decision makers implement sustainable strategies in agriculture.
Low salinity waterflooding (LSW) attracts increasingly attentions in recent years. It has been proposed that the enhanced oil recovery by LSW (or low salinity response) is triggered by the electrochemical interactions (e.g., electrostatic interactions, multiple ion exchange, chemisorption, etc.) between brine, rock, and oil. This study used the methodology of surface complexation modeling to characterize those electrochemical interactions when LSW was applied in a sandstone reservoir, as well to investigate the influential factors (e.g., ionic chemistry, quartz and kaolinite contents, acid and base numbers of oil, etc.) of low salinity response. The modeling results indicated that the electrical repulsions of sandstone and oil surfaces contributed to the detachment of oil from sandstone surface and hence the low salinity response. The results also suggested that (1) the negativity of sandstone showed a complex change with the increase of NaCl concentration (0.00110.0 mol/L) and its maximum value reached at 0.1 mol/L NaCl concentration, while the negativity of oil decreased with the increase of NaCl concentration, especially, the decrease became very pronounced below 0.1 mol/L NaCl concentration, which resulted in a salinity threshold for low salinity response; (2) Both the negativities of sandstone and oil were enhanced with the presence of SO42 ions in the salt solution but were compromised by Ca2+ and Mg2+ ions; (3) The negativities of sandstone and oil increased with the increase of pH, especially from pH=5 to pH=7; (4) The negativity of kaolinite was extremely small in high salinity water, however, it was moderately smaller than that of quartz in low salinity water, indicating that the kaolinite charge change played important roles in low salinity response; (5) The negativity of oil seems to be greatly influenced by the base number compared to the acid number. The findings of this study might theoretically guide the application of LSW in sandstone reservoir.
Agrochemicals and fertilizers are central to modern agriculture and are credited with the large increase of crop yield as part of the Green Revolution of the 1960’s. Timely and targeted fertilizer application is an important component for reducing costs and minimizing unintended release to the environment and water resource pollution. The efficiency of highly mobile fertilizers (i.e., nitrate) is affected by drainage and preferential flow pathways that bypass root bearing soil volumes. We report a novel liquid fertilizer delivery method using foam as carrier. The highly controlled transport of foam (defined as a dispersion of gas in a continuous liquid phase) in coarse soils (most susceptible to unstable flows) offers a means for targeted delivery to desired root zone volumes at concentrations and floe geometry that minimizes losses and promote its uptake. As proof of concept we conducted transport experiments in cylindrical soil columns using foam and conventional fertilizer application. Our results show that foamassisted fertilizer application decreased the leaching of fertilizer and improved its retention in the soil column potentially offering a vehicle for fertilizer delivery in soil.
The transformation of the liquid menisci at pore throats is of great importance for mitigating the liquidblocking effect of condensate reservoirs. Here, we reported a super gaswetting peanutlike nanoparticle which can facilitate the liquid menisci to transform from concaveshape to convexshape by coating a super gaswetting adsorption with high surface roughness. The morphology and surface chemistry of gaswetting nanoparticles were investigated by SEM, AFM, and XPS analysis. The mechanism of surface modification was further explored by TEM, the adsorption layer coated on the nanoparticle surface can be recognized as monolayer absorption. Gaswetting model is recommended as the combination of the Wenzel model and CassieBaxter model, which is in close agreement with the results of AFM and Contactangle measurement. Core flooding visualization was performed to identify the effect of gaswetting alteration on the transformation of liquid menisci in porous media. Results showed that the addition of gaswetting nanoparticles could decrease the liquid saturations by inducing the transformation of liquid menisci in the pore throat. Additionally, a unique “Amoeba effect” and miscibility effect can synergistically improve the mobility of the oil phase, further enhance the oil recovery.
Integrating renewable energy technologies into the grid is necessary to enable a sustainable energy economy but is currently challenged by their intrinsic intermittency. Redox flow batteries (RFBs) are rechargeable electrochemical reactors that are promising for gridlevel energy storage due to their ability to decouple energy and power. However, current RFB systems remain too costly for widespread deployment [1]. Porous electrodes are performancedefining components as they must facilitate mass transport, provide surfaces for electrochemical reactions, and conduct electrons and heat. Thus, optimizing the porous electrode microstructure offers a promising pathway to cost reduction by increasing power density [2], [3]. Traditional, empirical design of electrodes is time and resourceintensive and does not enable exploration of the wider design space but is currently limited to carbonaceous fibrous structures. To accelerate progress, microstructureinformed multiphysics simulations (e.g. pore network modeling, lattice Boltzmann) can be leveraged to aid the theoretical understanding and design of advanced electrode architectures but has been limited to exploration of existing, carbonfiber based electrodes [4]–[6]. In this work, we explore the following scientific question: Can we deploy threedimensional simulations in combination with evolutionary algorithms to enable artificial generation of electrodes from the bottomup?
In the first part of this talk, the modeling framework will be introduced. We developed a microstructureinformed, electrolyteagnostic electrochemical pore network model (PNM) integrated in an open access platform (OpenPNM) [6], [7]. The model was validated using a symmetric flow cell for two distinct electrolytes (an aqueous Fe2+/Fe3+ and a nonaqueous TEMPO./TEMPO+) and two types of porous electrodes (a carbon paper Freudenberg H23 and a carbon cloth ELAT Cloth). The dry electrode microstructure was obtained with xray computed tomography and converted into a network of spherical pores and cylindrical throats using the SNOW algorithm [8]. The electrochemical model is solved for the electrolyte fluid transport, species transport, and charge transport with low computational cost (123,335 pores, 60120 min on an Intel® Core(TM) i78750H CPU). For the nonaqueous electrolyte, the model accurately predicts the electrochemical performance without fitting parameters, allowing rapid benchmarking of porous electrode microstructures in a timeefficient manner. For the aqueous electrolyte, we find that incomplete wetting of the electrode results in overprediction of the electrochemical model that assumes onephase flow and employ thermal pretreatment to demonstrate the importance of complete wetting on the modeling validation [9]. Fitting of the nearsurface mass transfer coefficient enables accurate representation of the experimental data. Finally, the PNM framework was coupled with a genetic algorithm based on Darwin’s evolutionary theory that is used to perform artificial generation of porous electrodes for RFBs from the bottomup. With this method, chemistryspecific electrode architectures can be optimized based on the electrolyte properties alone.
Preferential flowpaths are wellknown features in fractured rock masses, often allowing rapid movement of fluid and early breakthrough of solutes and/or heat/cold in a small fraction of void space, compared to nonfracturedominated porous media. These preferential flowpaths can change as the configuration of fractures varies, due to, for example, shear displacement (Yeo et al.,1998; Kluge et al.,2017) or bifurcations (Li,2002; Johnson et al.2006). Such changes could become particularly important for subsurface projects, such as geothermal energy utilization, reservoir enhancement, and hydrometallurgy. Although numerical studies have shed some light on the preferential flow path and fluid behavior in rough fractures, experimental visualization and, more importantly, quantification of flow paths in roughwalled fractures still remains a challenge.
In this work, we show how to record and quantify fluid velocities and solute transport rates through a rough fracture using Particle Imaging Velocimetry (PIV) measurements, which have been rarely applied in the geosciences (S.H. Lee et al.,2015; Ahkami et al., 2018). During PIVmeasurements, a solution of mineral oil and transanethole is prepared to match the refractive index of the clear 3Dprinted fractures. This solution serves as the working fluid, seeded with nearly neutrallybuoyant fluorescent particles. In the first study, the PIV results on a single, rough, shearable fracture will be compared to numerical simulations using the local cubic law. In the second study, we visualize solute transport and fluid flow through a bifurcating roughwalled fracture, quantified by PIV measurements and latticeBoltzmann simulations.
This paper establishes a comprehensive model to describe the deformation of hydrate sediment involved in the hydrate recovery process. It combines two parts: phase transition of hydrate in porous media and unsaturated poromechanics. This model considers that the substances in the pores are modeled as two phases: the hydrate solid phase, and free gas stay in continuous liquid water as individual gas bubbles namely the equivalent fluid phase. Because of capillary effects between hydrate and fluid, the phase equilibrium conditions in fine sediments are shown as a zone rather a line in pT diagram. When recovery hydrate by different stimulation methods, we calculate the deformation of hydrate sediment respectively by using this comprehensive model. In undrained condition, the pore pressure rises significantly during the hydrate dissociation process. This is because the gas released from the melting hydrate cannot be expelled from pores. This buildup of pore pressure lead to the deformation of the sediment, it also increases the hydrate dissociation temperature, and thus more heat supply is required when all the hydrates are dissociated. Finally, we compared the results of different recovery methods and got those conclusions: the thermal stimulation method in drained condition that leads to least deformation, and thus it’s the favorable way. But in undrained condition, the thermal stimulation method results in the largest deformation and so it’s the dangerous way in low permeability hydrate sediment.
Cemented granular materials is a general class of geomaterials composed of grains connected by cement partially or completely filling the void inbetween the grains. After deposition and consolidation phases of the sediments, cementation happens during diagenesis when mineral matter precipitates at the poregrain interface. This process is known to increase the strength of the geomaterial by creating a cohesion between the particles. As such, it is critical to characterize for material stability applications in geotechnical engineering and geophysical processes. However, no quantitative law can be directly derived between the amount of cement and rock strength because cementation depends heavily on the rock microstructure and the initial distribution of chain forces. On top of that, this process takes place at a geological timescale, which makes it complicated to reproduce experimentally. Eventually, only direct numerical simulation of elastoplasticity performed at the microscale level and coupled with microstructure evolution can be used to determine the strength of cemented materials. In this study we provide for the first time a comprehensive parametric study on the impact of cementation on rock strength for real microstructures of granular materials. Compared to most previous studies, the whole yield surface is determined numerically in order to assess the influence of cementation for different stresspaths. The previously known tendency of rock to strengthen with increasing cementation volume is verified. New results on the influence of cement property namely Young’s modulus, friction and cohesion on the rock’s yield surface are explored. While most studies use Discrete Element Modelling to consider grain contacts explicitly, our simulator uses Finite Element Modelling which allows more flexibility in the approach to model the precipitation of the pressuresensitive layer of cement. The contacts are modelled as an upscaled plastic law. The framework presented in this study showcases the possibility of determining rock yield surfaces from their microstructures. While the current contribution focuses on cementation, other phenomena of interest can also be investigated such as dissolution from reactive transport.
Accurately characterizing fracture network morphology is necessary for flow simulation and fracturing evaluation. The complex natural fractures and reservoir heterogeneity in shale gas reservoirs make the induced fracture network resulting from hydraulic fracturing more difficult to describe. Existing fracture propagation simulation and fracture network inversion techniques cannot accurately match actual fracture network morphology. Considering the process of lightning breakdown similar as fracture propagation, a new efficient approach for inversion of fracture network morphology is proposed. Based on the dielectric breakdown model (DBM) for lightning breakdown channel simulation and similarity principle, an induced fracture growth algorithm integrating reservoir insitu stress, rock mechanical parameters, and stress shadow effect is proposed. The fractal index and random function are coupled to quantitatively characterize the probability distribution of induced fracture growth path. At the same time, a matching rate function is proposed to quantitatively evaluate the fitting between fracture network morphology and the micro seismic data. Combined with automatic history matching method, the actual fracture network morphology can be inverted with the matching rate as objective function. The proposed approach is applied to fracture network simulation of fractured horizontal wells of shale oil reservoir in the Lucaogou Formation in Xinjiang of China, and the fracture networks from inversion fit well with the micro seismic data. A simulation of 94 fractures in the 32 section of Well X2 in Xinjiang Oilfield shows that the well develops more obvious branch fractures. The singlewing fracture network communicates approximately 200m horizontally and approximately 10m vertically. When simulating a single fracture in a production well, it is necessary to consider the influence of complex fracture network morphology, but when simulating a single well or even a reservoir, only the main fracture needs to be considered. This paper proposes an induced fracture growth algorithm that integrates reservoir insitu stress, rock mechanical parameters, and stress shadowing effects. This algorithm greatly improves the calculation efficiency on the premise of ensuring the accuracy of induced fracture network morphology. The approach in this paper provides a theoretical basis for flow simulation of fracturing reservoirs and optimization of fracture networks.
Fracture propagation in porous media is essential to many complex subsurface geoengineering systems, such as geological fault rupture, hydraulic fracturing, geothermal energy exploitation and waste water management and so on. Numerical methods have become more and more important in better understanding the coupled physics of those complex subsurface systems. In this work, an AES finite element approach is proposed to simulate fracture propagation in the partially saturated porous media. Compared with traditional finite element method, the AES approach allows the fracture to propagate inside the elements, does not require the element edges to be aligned with the fracture. Compared with the extended finite element method, the AES approach does not introduce new degrees of freedom into the global system of equations. The fractures in AES approach can be modeled locally at the Gauss point level and the explicit geometrical description of fractures can be avoided. The presentation will cover the formulation and some numerical aspects in implementing AES approach, and demonstrate its capability in simulating fracture propagation in the porous media with several numerical examples.
Continental shale oil in China is mainly of lowmedium maturity. The formation is filled with heavy oil of low mobility and organic matter that unconverted. Horizontal drilling and hydraulic fracturing are insufficient to obtain economic production in such reservoir, thus insitu heating and transform technology should be applied. To describe the decomposition of solid organic matter, cracking of heavy hydrocarbon, phase behavior and composition evolution, we developed a multiphase multicomponent hydrothermal coupled numerical model and numerical solution method by considering multistage kinetic reactions. Then the impact of parameters including heating temperature, kerogen concentration, well bottom hole pressure, heating space and initial water saturation on cumulative production is analyzed. The results are summarized as: kinetic reaction rate is controlled by temperature and different reactions take place at variety heating temperature; higher kerogen concentration can enhance cumulative hydrocarbon production after insitu conversion; low bottom hole can extract oil and gas quickly to prevent from coking; larger heating spacing would weaken the effect of insitu conversion process, while the product will further crack with too small heating spacing; high water saturation will enhance energy consumption to heat water and reduce the utility ratio of energy, thus dewater process is required to reduce water saturation. This study analyzed shale oil insitu conversion process based on thermalreactive flow. The model developed can be used to evaluate the heating process and provide theoretical support for the efficient development of shale oil reservoir.
The energy storage technology is capable to fill the gap between energy demand and supply and make the renewable energy more efficient, which have also become the research emphasis recently. Among three existing energy storage techniques, thermochemical energy storage has the highest energy density and longest storage period. In this study, we constructed a twodimensional numerical model of a CaO/Ca(OH)2 thermochemical energy storage reactor, using lattice Boltzmann method to calculate the whole process. This method is efficient and able to deal with complex boundaries. With regard to CaO/Ca(OH)2 energy storage process, it is based on the reaction of CaO with water vapor, which can be considered as heterogeneous gassolid reaction. According to previous relevant researches, the model in this study consists of two parts, fluid area and solid area. The fluid (H2O) flows in from one side and out the other, which interacts with the solid particles (CaO), which is similar to previous model. A few reasonable assumptions were taken: the diffusion of fluid in solid phase was ignored; the gassolid interface followed the firstorder kinetics model; the heterogeneous reactions only happened at the interface. Besides, the solid update algorithm was adopted in order to describe the phenomenon that the mass and volume of solid changes during the reaction, which means the flow state also changes as the reaction goes. When the result reached steady state, the reaction stopped. Additionally, the heat emitted by the reaction was determined by the reaction condition of each solid node, so this study is composed of flow, mass and heat transfer problems. It can help researchers to learn about more mechanisms of CaO/Ca(OH)2 energy storage and find out better solutions of promoting the efficiency of thermochemical storage reactor, which has great significances.
Drying or evaporation in porous media is always modeled as special scenario of classic fluidfluid displacement. However, when the evaporation is extensive, the temperature at drying front can be much lower than other regions in the porous media and thus resulting in significant temperature gradient. Consequently, Marangoni effect may appear and reshape the fluid flow pattern, which has not been well investigated before. Such extensive drying in porous media normally occurs in CO2 sequestration, gas condensate reservoir and shale gas recovery, fuel cell, water management, etc.
In this study, we conduct micromodel experiments to visualize the Marangoni effect during extensive drying in porous media. We fabricate a 2D transparent porous medium with an adjacent open fracture. The porous medium is saturated first with pentane, and air is then continuously injected to flow through the open fracture at different rates to control the pentane evaporation rates. Direct microscopic visualization is conducted to analyze the fluid flow pattern, and infrared camera is used to record the realtime temperature distribution.
We show that the drying pattern could be reshaped by the interplay between evaporationinduced Marangoni effect and viscous dissipation for liquid to supply the drying front. At high evaporation rate extreme, the main drying front stably moves inward to deep porous medium, as evaporation is much faster than liquid supply from deep; at low evaporation rate extreme, the main drying front moves in a classic capillary fingering pattern, as both the viscous dissipation and Marangoni effect are negligible. However, at intermediate evaporation rate, the air first invades deep into the porous medium through one single preferential path, and then scatters from the tip of this path to inner porous medium, while the main drying front keeps unmoved. In other words, the drying and displacement front are separated. Infrared camera records this phenomenon and support the above hypothesis of mechanism.
We further quantify the relationships of invaded pore sizes and distance from the initial invading front, with pore invasion trajectory, which illustrates the mechanisms laying under these three drying patterns. Dimensionless criterion that depicts the transitions among these regimes and therefore a phase diagram is yielded that matches experimental observation well. Further research will focus on how this Marangoni effect can impact Darcyscale flow pattern.
Storing energy in the form of heat has been under longstanding investigation for prospective applications, such as the capturing of excess heat from industrial processes as well as storing energy in concentrated solar power plants. Investigated mechanisms for the heat storage include the adsorption in porous media, materials undergoing phase changes and thermochemical reactions. Among these, thermochemical heat storage provides a large energy capacity and next to perfect reversibility. More specifically, storage in the CaO/Ca(OH)2System is investigated because of the low price and environmental friendliness of the reactants. In the project THEMSE, DLR is developing models and simulations for thermochemical heat storage in the CaO/Ca(OH)2System on the microscopic level. In this talk, we shall give an overview over the project and the materials involved.
The geometrical microscale characterization of the material is done using a combination of micro computed tomography (µCT) and scanning electron microscopy (SEM). Both methods are complementary in the sense that SEM can be used to resolve fine scale details, up to crystallites, while µCT can resolve powder particles as well as agglomerates of numerous single particles. This is complemented by kinetics measured by thermogravimetric analysis (TGA).
The first goal in the project is to explain the measured kinetics using a spatially resolved model, which takes the threedimensional morphology of the storage material into account. In general, this involves, thermal, hydrodynamic, mechanical, and chemical modeling. However, the first investigations involve a single crystallite model, where the thermal and hydrodynamic effects can be neglected, and which is solved using finite element simulations. Further models are developed to investigate the heat and mass transport in the powder bed inside the reactor. Heat transport being the limiting factor, modeling the thermal conductivity of the powder bed on the microscale, is given special attention. This is done, the using simulations based on µCTData. Finally, it is investigated how the cycling of the material influences the heat and mass transport in the powder bed inside the reactor. This happens through agglomeration of powder particles the cause of which, and the modeling of which, are under investigation and under development, respectively.
We will show results from experiments and from kinetic and microscale transport simulations. Finally, an outlook will be given on the upscaling of the micro scale model to the reactorscale and computational optimization methods for reactor design.
Lithium ion batteries consist of three main porous components: anode, cathode and an electronically isolating membrane in between. This socalled separator prevents physical contact between the two electrodes while the pore space is filled with electrolyte to allow ionic transport. Therefore, the separator is considered to be a crucial part in battery safety.[1] Filling of the electrode and the separator with an electrolyte is a crucial and timeconsuming step in the lithium ion battery manufacturing process and incomplete filling negatively impacts electrochemical performance, cycle life, and safety of cells.
Our research group has developed an approach to visualize and quantify a polyethylene (PE) separator with focused ion beam scanning electron microscopy (FIBSEM).[2,3] The soobtained 3D structure is used as a model system for typical polyolefin lithium ion battery separators, since it consists of a single solid phase with relatively uniform pore size and isotropic pore structure.
The 3D data set allows us to simulate the wetting of the separator membranes with liquid electrolyte. We perform quasistatic infilling simulations on the separator and show that during this imbibitionprocess up to 30% gas is entrapped in the separator. Using partial wetting theory, we show that the specific pore structure of the separator is responsible for this incomplete wetting.
A traditional parameter to characterize the performance of a separator is the effective transport coefficient (ratio between tortuosity and porosity). This value can be experimentally measured by electrical impedance spectroscopy (EIS).
Comparing the wetting simulations to these separator performance measurements, we demonstrate, that incomplete wetting can explain the discrepancy between theoretically predicted and experimentally measured transport coefficients. We also show that quasistatic wetting models overestimate the amount of residual gas in the membranes and that realistic wetting models have to consider both, the physiochemical properties of the liquid electrolyte and the 3D structure of the separator pore space. Our work highlights the importance of pore structure in determining the amount of residual gas in a structure and provides insights into the pore structures, infilling conditions, and electrolyte formulations that are advantageous for battery technology.[4]
Porous media are an integral part of energy conversion and storage electrochemical devices. Among them, we have gas diffusion layers (GDLs) and catalyst layers used in polymer electrolyte membrane fuel cells (PEMFCs), as well as fibrous electrodes used in redox flow batteries (RFBs) [110]. These porous media must fulfill several critical functions, such as providing a transport pathway for reactants/products through its pore volume and ensuring charge and heat conduction through its solid structure. Catalyst layers and active electrodes have the added functionality of providing a reactive surface area. Conduction in protonexchange membranes (PEM) through waterfilled ionic channels can also be modeled using percolation theory [11].
In this talk, an overview of mesoscopic modeling approaches applied to transport in GDLs and PEMs is presented. A composite continuumpore network formulation is used to model twophase transport in GDLs [9,10]. The composite model incorporates a control volume mesh at the layer scale, which embeds a structured cubic pore network. Capillary transport is simulated using the discrete pore network, considering the Purcell toroid model to determine the local entry capillary pressures of the fibrous material. The porenetwork model is also used to determine analytically local anisotropic effective transport properties (local effective diffusivity and permeability), which are mapped onto the CV mesh to simulate transport within the porous layer using a continuum formulation. As a second example, proton conduction in multiblock copolymer membranes is modeled based on percolation theory [11]. The mesoscopic model solves simplified NernstPlanck and charge conservation equations on a random cubic network. To mimic experimental conditions, hydrated sulfonated sites not connected to the edges of the domain are excluded from the network.
A comparison with experimental data is presented in terms of capillary pressure curves, water distribution and effective diffusivity in carbonpaper GDLs, as well as proton conductivity and water uptake in multiblock copolymer membranes of sulfonated polysulfone and polyphenylsulfone.
Temperature is known to be of importance for the ageing, performance, and safety of lithiumion batteries. The heat released or absorbed inside a battery has therefore been a topic of much interest. The heat released or absorbed with the cell reaction, the reversible heat effect, is commonly included in thermal models through the entropy change of the reaction. The total reversible heat is then distributed evenly over the cell. However, the cell reactions are occurring at the two electrode interfaces resulting in two local effects known as the Peltier heats. [1]
An anodic electrode surface reaction with a positive Peltier heat will be cooling down, while a negative Peltier heat means it is heating up. For lithiumion batteries this means that an electrode which heats during discharge, will cool during charging. The two local Peltier heats combine under the assumption of isothermal conditions to give the entropy change of the reaction. [2] If the entropy change is small, the Peltier heat of the individual electrode surfaces may still be large. [1,2] In such a situation one electrode surface would cool while the other heats. To distribute the reversible heat effect uniformly, would therefore give an inaccurate temperature profile.
We will show how entropy measurements of lithiumion batteries with a lithium metal counter electrode can be used to predict the Peltier heats of electrode materials of various chemistries and lithium content if the Peltier heat of Limetal is known. These data are already available in literature [3,4] and has heretofore been unexploited. We will see that one electrode surface will cool while the other releases heat. [5] The importance of these local effects will be for the temperature profile on a singlecell level and a stack will shown. [1]
Acknowledgment
The authors are grateful to the Research Council of Norway through its Centres of Excellence funding scheme, project number 262644, PoreLab.
References
1. L. Spitthoff, A. F. Gunnarshaug, D. Bedeaux, O. S. Burheim, S. Kjelstrup, Peltier effects in lithiumion battery modelling, submitted
2. K. S Førland, T. Førland, S. K. Ratkje., Irreversible thermodynamics: theory and applications, John Wiley & Sons Incorporated, 1988.
3. K. E. Thomas, J. Newman, Heats of mixing and of entropy in porous insertion electrodes, Journal of Power Sources 119–121 (2003) 844–849
4. Q. Huang., Y. Manming and J. Zhiyu, Thermal study on single electrodes in lithiumion battery, Journal of Power Sources 156 (2) (2006) 541546.
5. A. F. Gunnarshaug, S. Kjelstrup, D. Bedeaux, F. Richter, O. S. Burheim, The reversible heat effects at lithium iron phosphateand graphite electrodes. Electrochimica Acta 337 (2020) 135567
Simulations based on the Lattice Boltzmann method are a powerful and efficient tool for the investigation of mesoscopic processes that are hard to study experimentally. Such simulations have been used successfully to study redox flow batteries [1]. But they have rarely been used to study transport mechanisms in other battery systems [2,3]. In the present work, the wetting process during the electrolyte filling in the battery production is investigated by means of the flow of electrolyte through realistic threedimensional porous battery electrodes. The electrode microstructures are generated using a sophisticated stochastic model [4] for the active material which is complemented by an additional binder phase. The focus of the study is on determining the capillary pressuresaturation relation during electrolyte intrusion and drainage. The main influencing factors investigated in the present work, are the porosity of the electrodes, the proportion of the binder phase as well as the wetting behavior of both the active material and the binder. Besides, also the effect of spatially nonresolved nanopores in the binder is studied using a homogenization approach. Lattice Boltzmann simulations with different multiphase flow methods, i.e. the ShanChen pseudopotential method [5] and the color gradient method [6], are conducted. Results from both methods are compared with each other. For validation purposes, they are also compared against results determined using the pore morphology method. The results from the present study are shown to agree well with results from the literature. They are especially useful for optimizing the electrolyte filling process which is a timedetermining step in the battery production.
In this talk, we consider a twophase Darcy flow in a fractured and deformable porous medium for which the fractures are described as a network of planar surfaces leading to socalled hybriddimensional models. Fractures are assumed open and filled by the fluids, and small deformations with a linear elastic constitutive law are considered in the matrix. At matrixfracture interfaces, phase pressures can be continuous or discontinuous, corresponding to two different models. Unlike singlephase flow, discontinuous pressure models for twophase flows provide a better accuracy than continuous pressure models even for highly permeable fractures. This is due to the fact that fractures fully filled by one phase can act as barriers for the other phase, resulting in a pressure discontinuity at the matrix fracture interface. The model is discretized using the gradient discretization method, which covers a large class of conforming and nonconforming schemes. This framework allows for a generic convergence analysis of the coupled model using a combination of discrete functional tools. Numerical solutions provided by the continuous and discontinuous pressure models are compared on gas injection and suction test cases using a TwoPoint Flux Approximation (TPFA) finite volume scheme for the flows and $\mathbb P_2$ finite elements for the mechanics.
Coupled thermalhydrologicalmechanicalchemical (THMC) processes can significantly impact fracture permeability, immediately influencing the productivity/injectivity of fracturedominated reservoirs, associated with geothermal energy extraction, hydrocarbon production, nuclear waste disposal, and geologic storage of carbon dioxide (CO2). It is, therefore, necessary to investigate the THMC coupling processes in natural fractures to develop wellcalibrated models and predict the changes in hydraulic and transport properties of deep geological reservoirs.
In this presentation, results of flowthrough experiments on fracture granite samples were reported to examine permeability evolution induced by THMCcoupled processes. We used two types of granite samples, naturally fractured granodiorite cores from the Deep Underground Geothermal Lab at the Grimsel Test Site (GTS) in Switzerland, and hydrothermallyaltered fractured granite from Borehole EPS1 of the Soultz geothermal system and power plant site in France.
The GTS granite samples were subjected to flowthrough experiments using DI water at temperatures varying 25140 °C to characterize the evolution of fracture permeability. Periodic measurements of the efflux of dissolved minerals yield the net removal mass, which is correlated to the observed rates of fracture closure. Changes measured in hydraulic aperture are significant, exhibiting reductions of 2075 % over the heating/cooling cycles.
The Soultz granite sample was first opened along the calcitefilled fracture, and then subjected to flowthrough experiments using HCl solution at a temperature of 100 °C to evaluate the the evolution of fracture permeability and the fracture shear displacements due to calcite dissolution. Periodic fluid samples were also taken to infer the efflux of dissolved minerals. A strong correlation can be observed between permeability and shear displacement of the fracture.
Our experimental observations in this study should certainly contribute to the interpretations on coupled THMC evolutions during processes such as chemical/thermal stimulation of enhanced geothermal systems and carbon capture, utilization, and storage.
A model for homogenized flow in porous media with large inhomogeneities is presented. Classical homogenization relies on representative elementary volumes (REV) large enough that asymptotic macroscopic parameters, e.g. effective permeabilites, can be employed to describe the expected or mean behavior. In this way, Darcy's law, which describes the relationship between macroscopic pressure gradient and volumetric flow rate, was derived. In the presence of large features, however, the required REV size may reach the same order as the geometric reference scale of the problem, and thus effective permeabilities obtained from classical homogenization studies may be unsuited. This is in particular the case for reservoirs with isolated, highly conductive fractures. To see this, consider flow from left to right through a block of finite size. If the latter is small enough, such that some fractures are connected to both left and right boundaries, then the resulting flow will be larger for the same average pressure gradient than through a wider block. In this paper, a new subREV continuum model to describe this preasymptotic flow behavior is presented. The model relies on a nonlocal multimedia description based on coupled integraldifferential equations. The only empirical information required for calibration is the effective permeability of an infinitely large domain, e.g. as obtained from classical homogenization. With a series of numerical studies and comparison with Monte Carlo reference data it is demonstrated that the devised subREV model accurately captures mean flow rates and pressure profiles for arbitrary domain sizes.
Although significant progress has been made in the tight gas exploration and development, there is still a limited understanding of the fluid charging and hydrocarbon accumulation in the sweet spot. In this study, a novel method is proposed to generate the stochastically constructed porous media which represents the transition region between tight surrounding sandstone and sweet spot. Based on the constructed porous media, the fluid charging and hydrocarbon accumulation processes of the tight reservoir are simulated by the lattice Boltzmann method (LBM). The numerical simulation results show that, although a pistonlike pattern can be observed in fieldscale simulation or laboratory experiments, at the microscale, due to the inherent heterogeneity of the porous media, the fluid charging pattern tends to be fingeringlike. The existence of the transition region between tight surrounding sandstone and sweet spot becomes a waterbearing gas layer or even gasbearing water layer at the top/bottom of the gas layers (sweet spot). The existence of fractures is favorable for hydrocarbon charging into the reservoir rocks, but not for the hydrocarbon accumulation due to the gas escaping through the fractures. Combined with well logging interpretation results, three typical water bodies (isolated water body, water body at the top, or bottom of the gas layer) are identified from the view of fluid charging and hydrocarbon accumulation.
Porous media naturally exhibit a heterogeneous structure including two different spatial scales: The pore/microscale is the fundamental scale, on which flow and reactive transport processes take place whereas the macroscale, i.e. the scale of the porous medium, is of practical relevance for geoscientific applications. What is more, mineral dissolution and precipitation alter a porous medium’s structure and its bulk properties. Due to the medium’s heterogeneity and lack in dynamic porescale measurements, there has been an increasing interest in effective models accessing such phenomena on the macroscale without disregarding available microscale information.
In this talk, we start from a porescale model for reactive flow and transport in evolving porous media and derive an effective micromacro model by formal twoscale asymptotic expansion in a levelset framework. As such, our approach comprises reactive flow and transport equations on the macroscopic scale including effective hydrodynamic parameters (porosity, reactive surface, diffusion, and permeability). These are calculated from representative unit cells. On the other hand, the macroscopic solutes’ concentrations trigger mineral reactions, which alter the unit cells' geometrical structure.
Finally, we present numerical simulations of the fully coupled micromacro problem with application to dissolution of calcite and dolomite.
In this talk we derive a homogenized model for a reactiondiffusion equation describing mineral precipitation/dissolution in an evolving porous microdomain, consisting of a fluid phase and a solid phase build by periodically distributed spherical solid grains. The evolution of the microdomain depends on the concentration at the surface of the grains, leading to a free boundary value problem on the microscale. The periodicity and the size of the grains is of order $\epsilon$, where the parameter $\epsilon$ is small compared to the size of the whole domain. The radius of every micrograin depends on the concentration at its surface, leading to a nonlinear problem. The aim is to pass to the limit $\epsilon \to 0$ and rigorously derive a macroscopic model, the solution of which approximates the solution of the microscopic model.
In a first step we transform the problem on the evolving microdomain to a problem on a fixed periodically perforated domain by using the Hanzawatransformation, depending on the radius of the grains and therefore the concentration. This leads to a change in the coefficients of the equations, which now depend on the radius and the concentration, leading to a nonlinear problem. We prove existence using the Rothemethod and derive \textit{a priori} estimates for the solutions uniformly with respect to the parameter $\epsilon$. For the derivation of the macroscopic model in the limit $\epsilon \to 0$ we use rigorous homogenization methods like the twoscale convergence. For the treatment of the nonlinear terms we need strong compactness results.
Singlephase macroscopic flow in a rigid porous medium is traditionally described by classical Darcy's law which can be formally derived by upscaling the porescale flow equation in the creeping incompressible flow regime and the noslip condition at the solidfluid interfaces. However, there are many situations for which fluid release from the surface into the pores or, conversely, absorption from the pores into the solid through the interfaces may occur. To cite some but a few, this case is encountered in drying (Vu & Tsotsas, 2018) and pyrolysis (Mahmoudi et al., 2014) of porous materials, vapor bubble migration in ice due to temperature gradient (Shreve, 1967) or processes for which a chemical reaction in a porous material leads to a net production of fluid from the surface into the pores or, conversely, absorption from the pores into the solid through the interfaces. This translates into a local normal flux at the solid fluidinterface, featuring a generic problem which may be referred to as flow in exuding porous media. Although classical Darcy's law has been widely heuristically employed to describe this type of flow, the question remains on the physical relevance of such an assumption.
In this work, the upscaling of low Reynolds number incompressible Newtonian flow in a rigid homogeneous exuding porous medium is performed using a mixed volume averaging/adjoint method. The upscaled model shows that the macroscopic velocity is nonsolenoidal despite incompressibility. Moreover, the macroscopic momentum equation involves a Darcy term with the classical intrinsic permeability tensor corrected by a vectorial term including an effective component related to the local fluid displacement induced by exuding effects and, in some special cases, a compensation to nonlocality. The two effective coefficients are obtained from a single intrinsic ancillary (closure) problem (Lasseux et al., 2021). The relevance of the macroscopic model is illustrated in many different examples through comparison between porescale numerical simulations and the macroscopic model predictions, showing excellent agreement. The results of this work motivate further research about the influence of internal flow sources in transport phenomena in porous media.
Multiphase flow and reactive transport are important in many applications, in particular in porous media. We consider the incompressible flow of two immiscible fluids in the presence of a solid phase changing due to precipitation and dissolution. We employ a ternary phasefield model on the pore scale, extending widespread models for two fluid phases by including a solid phase.
We upscale this model in the geometry of a thin strip. In the context of porous media the thin strip can be seen as the representation of a single pore throat. For scale separation we introduce $\beta$ as the ratio between width and length of the strip. Using asymptotic expansions we investigate $\beta \to 0$ under moderate assumptions on Peclet number and Capillary number. The resulting multiscale model consists of upscaled equations for total flux and ion transport, while the phase field equation has to be solved in cellproblems on the pore scale to determine the position of interfaces.
We also investigate the sharp interface limit of the multiscale model. Here the diffuse interface width $\varepsilon$ approaches zero and a sharp interface model is recovered. The resulting model consists only of Darcyscale equations, as the cellproblems can be solved explicitly. The model is of hyperbolic nature, and we use numerical results to investigate the validity of the upscaling when discontinuities form in the upscaled model.
Professor Andro Mikelić is known for his seminal mathematical contributions to flow in porous media. In this presentation we summarize how his work has impacted the development of numerical models coupling flow and poromechanics arising in geosciences and biosciences applications such as subsidence events, carbon sequestration, groundwater remediation, hydrocarbon production, and hydraulic fracturing, enhanced geothermal systems, solid waste disposal, and biomedical multiplenetwork poroelastic theory MPET modeling. We focus on the Biot model that consists of a poromechanics equation coupled to a flow model with the displacement and pressure as unknowns. In contrast to solving the Biot system fully implicitly, we consider a fixed stress iterative scheme that allows the decoupling of the flow and mechanics equations. The decoupling scheme offers several attractive features such as the use of existing flow and mechanics codes, use of appropriate preconditioners and solvers for the two models, and ease of implementation. The design of this approach is currently quite popular in engineering studies due to its importance in the formulation of efficient, convergent, and robust schemes. Professor Mikelić’s work on establishing a contractive property of this and several other iterative schemes has led to many theoretical and computational practical extensions, one of which we discuss in detail.
In this presentation we discuss the Biot system solved with a fixedstress split, Enriched Galerkin (EG) discretization for the flow equation, and Galerkin for the mechanics equation. Residualbased a posteriori error estimates are established with both lower and upper bounds. These theoretical results are confirmed by numerical experiments performed with the Mandel’s problem. The efficiency of these a posteriori error estimators to guide dynamic mesh refinement is demonstrated with a prototype unconventional reservoir model containing a fracture network.
In this presentation we consider the equations of nonlinear poroelasticity derived from mixture theory. They describe the quasistatic mechanical behavior of a fluid saturated porous medium. The nonlinearity arises from the compressibility of the fluid and from the dependence of porosity and permeability on the divergence of the displacement. We point out some limitations of the model. In our approach we discretize the quasistatic formulation in time and first consider the corresponding incremental problem. For this, we prove existence using Brezis’s theory of pseudomonotone operators. Generalizing Biot’s free energy to the nonlinear setting we construct a Lyapunov functional, yielding global stability. This allows us to construct bounds that are uniform with respect to the time step. If dissipative effects between the fluid and the solid are taken into account, resulting in an additional time derivative, we obtain the continuous time case in the limit when the time step tends to zero. This yields existence of a weak free energy solution. This is joint work with Andro Mikelic to whom this minisymposium in dedicated.
We derive the new effective boundary condition for the fluid flow in domain with porous boundary. Starting from the Newtonian fluid flow through a domain with an array of small holes on the boundary, using the homogenization and the boundary layers, we find an effective law in the form of generalized Darcy law. If the pores geometry is isotropic, then the condition splits in BeaversJoseph type condition for the tangential flow and the standard Darcy condition for the normal flow.
The result is rigorously justified by an appropriate error estimate.
We study the behaviour of a system of equations that describes diffusion with chemical reactions caused by microorganisms in a double porosity medium. The objective is to find various classes of nontrivial limit solutions at large time (the patterns), especially simultaneous spatialtemporal patterns. In contrast to a classical reactiondiffusion system (RDS), our system contains four reactiondiffusion equations (RDE) describing the transport of nutrients and the dynamics of bacteria in fractures and blocks, with exchange terms. This system occupies an intermediate place between the Turing's RDS, which can have only spatial or temporal patterns separately, and a wavy RDS, which can have simultaneous spatialtemporal patterns in the form of standing waves. We show analytically, for a reduced version of the system, that spatialtemporal patterns can exist but in another form than a standing wave. The full system has been analysed numerically. Among with known patterns, we have detected a nontrivial simultaneous spatialtemporal pattern that has the form of travelling flashes. They correspond to the HopfAndronov temporal oscillations in blocks and to Turing’s spatial fluctuations in fractures.
There results have been used to analyse the behaviour of an underground storage of hydrogen. We show several different scenarios of the evolution of such a storage and discuss the optimal regime.
A threescale model for flow in karst conduit networks in carbonate rocks is constructed based on a reiterated homogenization procedure. The first upscaling, performed from the highfidelity flow model, is based on a topological model reduction considering a discrete network of conduits. The subsequent macroscopization procedure projects the reduced model into the cells of a coarse computational grid, where homogenized equivalent properties are numerically constructed. Such a twolevel upscaling gives rise to a macroscopic flow model characterized by masstransfer functions between the geological structures. A notable consequence of the approach proposed herein is the appearance of a new karst index concept, based on the generalization of the traditional Peaceman’s theory of well index, along with two skin factors. The former skin is of geometrical nature, and stems from noncircular crosssection, whereas the latter captures the presence of the damage zone arising from the presence of collapsedbreccia in the vicinity of the conduit network. Computational simulations are obtained by discretizing the coupled 1D/3D flow model by a Mixed Multiscale Method in its recursive form seated on a domain decomposition approach.
In this talk, we present an extension of the phasefield fracture propagation model to the immiscible twophase flow fracture model, and with a transport problem. The flow model is derived by using the lubrication theory, and we provide the absolute and relative permeabilities with nonzero capillary pressure. The contribution in solid mechanics consists of displacements and a phasefield variable. Both systems are coupled employing a fixedstress splitting and discretized by employing continuous Galerkin finite element methods. The flow and transport system has resident and injected pressures and saturations, and concentration of transported species. The flow problem is treated with a locally conservative enriched Galerkin finite element method to provide accurate flux to the transport problem. Modeling and algorithms are substantiated with several numerical tests.
Building on the work of Andro Mikelic and Mary WHeeler, we propose a numerical scheme for an ellipticparabolic system involving deformation and pressure in porous media. Existence and uniqueness of the solution have been proved by Mikelic et al; we will add some convergence results for ou numerical scheme.
This is joint work with Ludovic Goudenège and Danielle Hilhorst
We prove the existence of a weak solution to a fluidporoelastic structure interaction problem in which the structure consists of two layers: a thin poroelastic plate layer in direct contact with Stokes flow, and a thick Biot layer sitting on top of the thin layer. In the (quasistatic) Biot layer the permeability is a nonlinear function of the fluid content. Existence of a weak solution is obtained using a constructive proof based on Rothe's method. We provide uniqueness criteria and show that the constructed weak solutions are indeed strong solutions if one assumes additional regularity. We show how this result impacts the design of drugeluting stents for the treatment of coronary artery disease.
The presence of drugeluting stents alters the permeability of the arterial walls and impacts advection, reaction and diffusion of antiinflammatory drugs, such as sirolimus, into the poroelastic arterial walls. This information helps alter the design of drugeluting stents for improved longterm efficacy. The results presented in this talk were obtained in part with Lorena Bociu, Boris Muha, Yifan Wang, and Justin Webster.
Fractures can provide principal fluid flow pathways in the Earth’s crust, making them a critical feature influencing subsurface geoenergy applications, such as the storage of anthropogenic waste, emissions or energy. In such scenarios, fluidconductive fault and fracture networks are synonymous with twophase flow, due to the injection of an additional fluid (e.g. CO2) into an already saturated (e.g. brine) system. Predicting and modelling the resulting (partly)immiscible fluidfluid interactions, and the nature of fluid flow, on the fieldscale, requires an understanding of the constitutive relationships (e.g. relative permeability and capillary pressure) governing fluid flow on the singlefracture scale. In addition to capillary and viscous forces, fracture relative permeability is influenced by aperture heterogeneity, arising from surface roughness. The degree to which surface roughness controls relative permeability behaviour in fractures remains unclear. As all fractures display roughness to various degrees, furthering our understanding of twophase flow in fractures benefits from a systematic investigation into the impact of roughness on flow properties. To this end, we performed coinjection experiments on two 3Dprinted (polymeric resin) fractures with different controlled and quantified surface roughness distributions (Joint Roughness Coefficients of 5 & 7). Brine and decane were simultaneously injected at a series of incrementally decreasing brine fractional flow rates (1, 0.75, 0.5, 0.25, and 0), at low total volumetric flow rates (0.015 mL/min). Steadystate fluid occupancy patterns, preferential flow pathways and overall fluid saturations in each fracture were imaged and compared using an environmental laboratorybased μCT scanner with a 5.8 μm voxel size (EMCT; Ghent University Centre for Xray Computed Tomography). Experimental results highlight the importance of roughness on the relative permeability behaviour of fractures, which is, for example, a principal control on leakage rates from geological stores.
Analysis of consistent experimental sets of hydromechanical data recorded during hydraulic experiments on single fractures or fractured reservoirs require a consistent numerical model to determine fracture properties with a high accuracy. Hence, this work briefly discusses the derivation and numerical implementation of a consistent, fully coupled hydromechanical model for flow in deformable fractures. The computational efficiency of the model is demonstrated in a complex fracture network setting in three dimensions before specific hydromechanical phenomena are discussed. One prominent phenomenon is the occurrence of overtones in the frequency domain recorded during harmonic excitation tests and their dependence on the specific normal stiffness characteristic of a single fracture. The relevance of the numerical findings for experimental investigations is demonstrated on different scales consulting results obtained from laboratory and insitu field tests. Laboratory studies have been performed on single fractures embedded in a cylindrical sample using a recently designed triaxial setup and transient insitu measurement data was recorded during harmonic excitation tests at Reiche Zeche underground research laboratory.
Reduced Basis (RB) methods are wellknown and widely used techniques applied to complex parameterized simulation problems to obtain reliable discrete results for a particular choice of parameters, largely reducing the computational time to obtain the numerical solutions.
Flow simulations in underground fractured media seems to be a perfect application for the RB framework, due to the stochastic nature of the mechanic properties and the complex geometries of the domain obtained by random probability distributions.
Unfortunately, standard RB tools proved to be ineffective in the robust PDEconstrained optimization formulation proposes in [1], because of the use of nonconforming meshes for the computation of the underground flow on Discrete Fracture Network (DFN).
Thus, with the help of the residualbased a posteriori error available in [2], we propose an aggregated trial reduced space [3] reduced with an alternative RB greedy technique which requires no infsup lower bound estimation.
Numerical tests will be presented to show the ability of the technique to recover the right RB space dimension with a smart stopping criterion which relates the accuracy of RB approximation with the accuracy of the high fidelity solution.
It remains challenging to fully understand the granular transport mechanisms in confined geometries like fractured media. Here, by performing massively parallel simulations based on a coupled computational fluid dynamics and discrete element method (CFDDEM) approach, we systematically investigate the particle transport patterns and mechanisms driven by fluid flow in both smooth and rough fractures. In smooth fractures, depending on the local drag force, the particles can settle or suspend in the fluid, leading to fluiddriven particle transport by creeping or by suspension. Fluidinduced fingering patterns are observed in the upper layer of settled particles during the sliding. It is shown that the fingering pattern is affected by the flow rate and particle volume fraction. In rough fractures, increasing the standard deviations of the aperture shifts the particle migration from uniform to fingering behavior, which leads to earlier breakthrough and increased particle trapping.
In this presentation we introduce an innovative mathematical model that is able to describe chemical processes that may occur in fractured porous media. A solute is carried by a fluid in the porous medium, that reacting precipitates forming a salt that might alter the physical properties of the system, creating zone of low flow. Conversely, if the salt dissolves it might open up new pathways especially through previously clogged fractures. These chemical reactions depends also on the temperature, which controls their speed. We consider thus a fullycoupled and nonlinear system of mixeddimensional equations that is able to describe such phenomena. Numerical examples show the applicability of the proposed model.
The thermal treatment of rocks is a frequently used method to initiate microcracks. This is done to study experimentally different physical phenomena related to microcracks. The effect of microcracks on the effective macroscopic properties can be quantified, for instance, by wave propagation measurements or porosity measurements. Micro XRay Computed Tomography (µXRCT), as a noninvasive imaging method, offers the possibility to have an insight into the 3D microstructure. With this method, it is possible to improve the understanding of the relation between the microscale and the effective properties. Since microcracks have a disadvantageous ratio between the crack aperture and the crack length, the imaging, as well as the subsequent segmentation, is a challenging task. In particular, the spatial resolution of µXRCT devices often come to its limitation to resolve the crack aperture reliable. Furthermore, an inherent noise and low contrast of the resulting dataset cause difficulties to achieve an accurate segmentation. Based on an inhouse created µXRCT data set of a thermally treated Carrara marble sample, we applied and compared different segmentation methods. By all methods, the full 3D crack network can be successfully segmented. However, an approach based on a 2D Convolutional Neural Network (CNN) model shows the most promising result among the adopted methods. The segmented data is frequently used as direct input, for instance, in digital rock physics. Consequently, all the results depend on the quality of the imaging and the segmentation. Therefore, it is crucial to evaluate the quality of the segmentation. For this, a link back to macroscopic measurement results, for instance, the porosity can be used as an indicator. Besides different segmentation approaches, this contribution shows the importance of combining measurements of different scales, especially to evaluate segmentation methods.
This work provides new experimental evidence regarding twophase fluid flow in damaged porous media. The results aim to provide novel cases towards leakage rate modelling dedicated to the wellprediction of reliability and durability of the pressurised concrete structures such as nuclear containment buildings.
Previous experimental works on the structural scale, e.g. reinforced concrete slabs tested at MPA Karlsruhe$^1$ and in MAEVA model$^2$ show that the airvapour leakage rate is lower than the leakage rate of dry air. The accurate prediction of the complex interplay of multiphysics phenomena necessitates the use of sophisticated numerical models. The adaptation of such models demands the calibration and validation in simple yet realistic experiments whose thermohydric boundary conditions are welldefined.
With this regard, we present an experimental study, where, here a wellcontrolled flux and saturation of the hotsteam and air mix is injected through a cracked cylindrical concrete specimen of diameter and length 40mm. Brazilian test is conducted on the specimen, equipped with LVDTs on both circular faces, to create $\approx 150 \mu m$ crack opening displacement (COD). The required COD is achieved by progressive crack opening with several loading/unloading cycles.
Dry and saturated cracked specimen states, representative of the insitu limiting conditions, are examined for interaction with the injected vapour. Temporal evolution of temperature and pressure at both specimen boundaries are recorded and the whole process is visualised with sequential inoperando neutron tomographies of 30secs. The speed of vapour travel along the crack is reported higher for saturated specimen state in comparison to the dry state. The capillary suction around the crack is prominent for dry specimen and comparatively negligible for the saturated specimen. A relationship between the material microstructural damage and the vapour flow is presented with emphasis on the initial state of saturation in the specimen.
In order to model mechanics of porous media, the elastoplastic behaviour of materials, such as rocks and soils, plays an important role. In this work, we study Virtual Element Methods for 3D elastoplastic simulations. We focus on the equations that characterize the elastoplastic 3D model in the framework of small deformations theory. We especially deal with the MohrCoulomb plasticity model, which is suited to describe the plasticity behaviour of materials in which we are interested. We apply its yield function and flow potential to define associative and non associative plasticity. Due to numerical problems of the model, we study and implement a 'smooth' version of the MohrCoulomb model, proposed by Abbo and Sloan (2011). This aspect requires the study of a suitable generalized Return Mapping Algorithm. Moreover, we have to tackle with a strong nonlinearity involved in the model. This issue requires the study and the application of a proper globalization strategy for Newton method, for instance line search methods. Furthermore, as regards the variational discretization framework, we focus on the VEM formulation of the 3D primal elastoplastic equation, combined with the stress estimation through the Return Mapping Algorithm. We study a suitable stabilization for the problem with respect to the one introduced by Beirão da Veiga et al (2015). Finally, we present a 3D numerical experiment of limit analysis on slope stability, which is a classical benchmark problem for MohrCoulomb plasticity model, and other results in order to discuss numerical problems of the model and the strategies to deal with them.
Foam is composed of gas bubbles separated by continuous liquid films. The films, called lamellae, are stabilized by surfactants. Foam has many applications in underground resources, such as acid stimulation (Thompson and Gdanski 1993), aquifer remediation (Hirasaki et al. 1997) and enhanced oil recovery (Kovscek and Radke 1994; Rossen 1996). In enhanced oil recovery, foam injection can improve sweep efficiency by reducing the mobility of gas. To achieve an optimized mobility control, the stability of foam must be maintained while it propagates deep into the reservoir. At the pore scale, the coalescence of foam can take place due to different mechanisms including capillary coalescence and diffusive coarsening. Coarsening behavior has been well studied in bulk foam (Weaire and Glazier, 1993; Weaire and Hutzler, 1999). However, it is less understood in porous media.
In this study, we have built two 1meterlong model fractures analogous to microfluidic porous media, and investigate the effects of coarsening on static foams in the models. The model fractures are made of glass plates. Direct observation and analysis of the foam structure inside the fractures are facilitated using a highspeed camera. Each model fracture has one flat wall and one rough wall. The gap between the two walls represents the aperture of the fracture. The distribution of aperture can be represented as a 2D map of pores and throats. We use two model fractures with different roughness distributions. One model has a roughness in a regular pattern with a hydraulic aperture of 46 μm. The other one has an irregular pattern with a hydraulic aperture of 80 μm.
Prior to coarsening, foam is pregenerated, and then injected into the fractures. After foam flow reaches steadystate, the injection and production valves are closed. Once foam stops flowing, as the residual pressure gradient dissipates, the coarsening process commences.
In this study, we have observed that the foam coarsens due to gas diffusion in both model fractures. Due to coarsening, bubble numbers decrease and bubble size increases. The time scale of coarsening in our models is much larger than what has been reported elsewhere (Marchalot et al., 2008; Jones et al., 2018). In the regular model, coarsening stops after 2 hours. At the end of coarsening, all lamellae have zero curvature and rest at pore throats. Bubbles attain the same size as pores and almost all the liquid accumulates in plateau borders at throats. Compared to the regular model, the coarsening process is slower in the irregular model. Bubbles coarsening slows down to a barelymeasurable diffusion rate after 7 hours. However, small bubbles exist and the average bubble size increases even after 24 hours of coarsening. A possible explanation is that, for these small bubbles, the lamella area available through which gas can diffuse to a neighbouring larger bubble is greatly reduced. In both models, the capillary pressure increases to 1.3 kPa, which is too low to cause lamellae to break.
We consider a model for the flow of two immiscible fluids in a twodimensional thin strip and in a threedimensional tube of varying width. This represents an idealization of a pore in a porous medium. The interface separating the fluids forms a freely moving interface in contact with the wall and is driven by the fluid flow and surface tension. The contact line model incorporates Navierslip boundary conditions and a dynamic and possibly hysteretic contact angle law.
We assume a scale separation between the typical width and the length of the thin strip. Based on asymptotic expansions, we derive effective models for the twophase flow. These models form a system of differential algebraic equations for the interface position and the total flux. The result is Darcytype equations for the flow, combined with a capillary pressure  saturation relationship involving dynamic effects.
Finally, we provide some numerical examples to show the effect of a varying wall width, of the viscosity ratio, of the slip boundary condition as well as of having a dynamic contact angle law. Furthermore, we compare the effective model to experimental data for the capillarity rise in tubes.
Gas injection is one of the most effective enhanced oil recovery (EOR) methods, in which the gas–alkane interfacial tension (IFT) is an important parameter. Thus, to accurately estimate gas–alkane mixture IFT plays an imperative role in both chemical and petroleum engineering. Various empirical correlations by fitting the experimental results have been developed in the last several decades, which are convienent to use. However, their accuracies are inconsistent over a wide range of compositions, while some of them also need inputs from the equation of state (EOS) modeling. Statistical mechanics models and molecular simulations are other popular choices for IFT prediction, whereas they can be timeconsuming. Recently, the extended Connors–Wright (ex–CW) model has been proposed to accurately predict gasalkane IFT over a wide range of pressure, temperature, and composoition. In this work, the ex–CW model is used to provide enormous IFT data to be paired with machine learning (ML) approaches to construct simple yet highlyaccurate gasalkane binary mixture IFT prediction equations (i.e. linear equations) which are functions of temperature, pressure, and molecular weight. The linear equations for gasalkane binary mixture IFT based on ML are calibrated by comparing with experimental data, the ex–CW model, and the Parachor model. We find that the linear equations from ML approach largely outperforms the Parachor model, while they have a comparable performance with the ex–CW model. In addition, while both the Parachor model and the ex–CW model need the imputs from the EOS modeling, the linear equations from ML approach only use temperature, pressure and molecular weight. The proposed idea shows a great potential in terms of highlyefficient and highlyeffective gasalkane binary mixture IFT predictions which can be further extended to morecomplicated multicomponent gasoil IFT predictions for gas injection EOR processes.
Multiphase flow in particle–gas–fluid systems is relevant to many geophysical processes and subsurface engineering applications, such as hydrate production, methane venting, volcanic eruption, etc. Previous researches have investigated the pattern formation in frictional fluid dynamics, viscous fingering instability, wettability alteration, providing the basic understanding of the complex flow mechanisms. Here, we perform laboratory experiments of drainage of liquid–particle mixtures to study morphological patterns and interface stability. We consider both homogeneous and heterogeneous particle distributions. We characterize the flow regime transition from stable displacement to viscous fingering based on morphology and macroscopic metrics, and we compare the onset of fingering with prediction based on the linear stability theory. Compared with homogeneous mixtures, particle clusters and bands in the heterogeneous mixtures evidently promote fingering instability. Furthermore, we find that slow drainage leads to particle compaction bands due to interface ploughing effect. This work provides an improved understanding of the physical mechanism of particle–gas–fluid multiphase flow and is of relevance for practical applications in the subsurface.
One of the problems in EOR methods is the instability that occurs on the interface between two fluids with high viscosity contrast. The usage of viscous polymer agent can partially solve the problem by making the wateroil front stable. However the subsequent displacement of polymer by water produce a lot of long thin "water fingers" on the rear end of the polymer slug. The breakthrough of the polymer slug reduces the oil recovery factor. In the talk we will discuss how to calculate the size of polymer slug and consider the technology of graded viscosity banks (GVB) which helps to reduce the amount of polymer mass without loss of it's effectiveness.
GVB technology was proposed by Claridge and consists in injecting several subsequent polymer slugs of decseasing concentrations. As viscosity ratio reduces, the instabilities start to grow slowly and one can inject less amount of polymer with the same positive effect on oil recovery.
The main assumption of GVB technology is the linear growth of the front and rear ends of the mixing zone. There are a lot of numerical works that confirm linear behavior of fingers at intermediate times, but unfortunately no rigorous results exist up to now. However it is possible to get pessimistic estimates on velocities of the mixing zone by analyzing the mathematical model of the miscible displacement (the socalled Peaceman model) under transverse flow equilibrium assumptions. Unlike the wellknown Koval and ToddLongstaff models, these estimates take into account not only the viscosity ratio, but the whole viscosity curve. I the talk we will give an overview of the existing models and present our results in this direction.
From practical point of view a natural question arises: "How many slugs should one inject?" To answer this question we calculate the amount of saved polymer for n slugs and prove a theorem that there exists a limiting injection profile as number of slugs tends to infinity. This gives an upper bound on the possible amount of saved polymer. Analyzing the result for different viscosity curves and finger velocity models we conclude that for many practical situations it is enough to inject 25 slugs.
We verify the GVB technology with our numerical experiments in DuMuX.
In this work, a coupled finite element method based on porous media theory (TPM), see e.g. [1] [2], for direct modeling of the phase transition of ice and water is presented. In detail, the presented model investigates ice deformation, temperature evolution, and the evolution of energy, enthalpy, and mass exchanges between its constituents. The main idea is based on a theoretically motivated evolution equation for the phase transition of ice and water, which guarantees thermodynamic consistency and is mainly determined by the local temperature rate, see e.g. [3], where it is assumed that the local temperatures of the phases are equal. The resulting finite element is a fourfield formulation in terms of ice displacements, fluid pressure, volume fraction of ice, and temperature. Here, we use quadratic interpolation of the ice displacements and linear interpolation for the other degrees of freedom. The model is investigated in the context of first academic simulations of freezing processes of ice floes.
Multiphase flow is controlled by the pore geometry of the porous domain, which is formed by the grain morphology. Grain morphology not only influences fluid behavior and transport but also affects the development of interfacial area over time. One quantitative measure of grain morphology is circularity, i.e., how closely a grain resembles a perfect sphere. The objective of this work is to quantify how grain circularity affects the temporal development of interfacial area during multiphase flow through porous media. A multiphase lattice Boltzmann method (Guntensen et al., 1991; Reis and Phillips, 2007) is used to simulate oilwater drainage and imbibition in an ensemble of twodimensional porous media samples (Mollon and Zhao, 2012). We conducted multiphase simulations on 3 groups of porous media which involved: 20 realizations of spherical grain shapes, 20 realizations of intermediate grain shape, and 20 realizations of elongated grain shapes. Interfacial area was periodically monitored during drainage and imbibition simulations in 60 samples, until the samples acquired steadystate fluid saturations. During drainage and imbibition, the interfacial area increases with time, acquires a peak value, and then decreases before reaching a plateau at steadystate. All three groups of porous media showed the same temporal trend, with no major differences. However, the domains with highly circular groups showed an average 16 percent residual water saturation at the end of drainage, while only a 10 percent average residual water saturation was observed in the other two groups. The results indicate that grain circularity does not strongly affect the temporal evolution of interfacial area but influences the residual fluid volumes in the system. This implies that in case of oil spills in groundwater, spherical grains would be expected to have more water residual than an elongated grain system. Therefore, the results of this work can help understand oil contamination in groundwater and improve soil remediation efforts.
The flow of colloidal particle suspensions in multiphase systems have become widely studied in applications such as oil recovery, drug delivery, and contaminant transport. In oil extraction processes, about twothirds of the original oil in place remains underground after primary or secondary production. An important key factor contributing to the deficiency of recovery methods is the heterogeneity of the oil reservoirs. The morphology of the porous medium is heterogeneous with many distinct pore configurations, both in size and shape. For instance, oil may get trapped in cavities (deadend pores) connected to conductive channels. The inherent geometrical restriction of a deadend pore configuration inhibits the possibility to liberate the trapped fluid by displacement methods. Nanoscale particles placed at oilwater interfaces may produce a more uniform and elastic interfacial configuration when subjected to deformation. This elasticity may help oil to be drained from cavity confinements. Most nanoscale particles are either hydrophilic or hydrophobic and do not settle at the interfaces. Enabling particles to be surface activate by means of physicochemical interactions with natural surfactant molecules present in the crude oil such as asphaltenes, resins, and organic acids is a provident and not welldocumented alternative.
In this work, we examine the insitu particle activation at the oilwater interfaces subjected to a shearing flow field. We fabricate microfluidic chips with a welldefined pattern consisting of a main flow channel connected to multiple deadend pores. We orchestrated a displacement methodology in which fumed silica particles in a carrier aqueous solution bypass a series of cavities saturated with an oil phase doped with surfactant. The interactions of silica suspensions at 1, 2, and 4 wt.% concentrations and oilsoluble surfactants above critical micellar concentrations are examined. We use a color camera and a confocal laser scanning microscopy to monitor and visualize the displacement process. We measure the dilatational interfacial viscoelasticity and dynamic interfacial tension of oilwater systems by means of a drop shape analyzer and the Spinning Drop Tensiometer.
The results show that notable particlecoated wateroil interfaces developed in the presence of surfaceactive particles. When dispersed particles on injecting water enter cavities saturated with the trapped micellar solution, oil in water emulsions at the oilwater interface are instantaneously formed. As water penetrates the cavity area, the residual oil films left behind the interface interact with the particles in the aqueous phase forming rigid and well packed microsize droplets. The growth of the emulsion zone in cavities is a function of oil viscosity and decreases as the oil viscosity increases. A relationship between the oilwater interfacial viscoelasticity, dynamic interfacial tension, surfactant and particle concentrations, oil viscosity spontaneous insitu emulsification, and consequently oil discharge from cavities is established and discussed.
A porous medium is a highly complex domain, in which various processes can take place at different scales. Here we consider a phasefield approach to model the evolution of the evolving interfaces at the microscale. After applying a formal homogenization procedure, a twoscale phasefield model is derived, describing the averaged behavior of the system at the Darcy scale (the macroscale). In this twoscale model, the micro and the macro scale are coupled through the calculation of the effective parameters.
Although the resulting twoscale model is less complex than the original, the usual numerical strategies remain computationally expensive. Here, we propose an adaptive twoscale scheme involving different techniques to reduce the computational effort without affecting the accuracy of the simulations. These strategies include iterations between scales, an adaptive selection of the elements wherein effective parameters are computed, adaptive mesh refinement, and efficient nonlinear solvers.
There is an increasing interest in solvers for phasefield models of brittle fracture [2]. The
governing equations for this problem originate from a constrained minimization of a nonconvex energy functional, and the most commonly used solver is a staggered scheme. This method shows robustness in comparison to the monolithic Newton method, however, the staggered scheme often requires many iterations to converge when fractures are evolving. The focus of our work is to accelerate the solver through a scheme that combines Anderson acceleration and overrelaxation. The method is applied as a postprocessing technique, and therefore, already available software can be modified to include the acceleration method. Moreover, the activation of the scheme has a negligible cost. A numerical study, including wellknown benchmark problems, that demonstrates the efficiency, and robustness of the method will be presented [1].
[1] Storvik, E., Both, J.W., Sargado, J.M., Nordbotten, J.M. and Radu, F.A. An accelerated staggered scheme for phasefield modeling of brittle fracture. arXiv:2008.11787 [math.NA] (2020).
[2] Brun, M.K., Wick, T., Berre, I., Nordbotten, J.M. and Radu, F.A. An iterative staggered scheme for phase field brittle fracture
propagation with stabilizing parameters Comput. Methods Appl. Mech. Engrg. 361 (2020) https://doi.org/10.1016/j.cma.2019.112752.
The development of continuum reactive transport models in porous media traces back to mid80’s when the theoretical framework to consider reactions in mass transport equations was outlined. Since their establishment, the operatorsplitting (OS) approach has been frequently used due to its easy implementation and computational efficiency in large scale simulations including complex chemical processes. Existing and widely used OSfinite element framework in reactive transport normally adopts different collocation schemes for spatially discretizing the transport (i.e. advection and diffusion) and the reaction term of the advectiondiffusionreaction equation. While this numerical approach in general works well in homogeneous systems, it may fail if the field variables (i.e. concentration, hydraulic pressure) vary rapidly, for example, close to the domain boundaries or in the interfaces between different materials. In these cases sharp gradients exist and standard numerical schemes normally lead to inaccurate and unstable numerical results.
A novel OSfinite element framework adopting a consistent collocation scheme of all the field variables in the integration points has been recently developed in our group, validated and implemented in OpenGeoSys6 (Lu et al. (2021). Contrary to previous finite element OSschemes, the reaction term was calculated at the integration point level, instead of the nodes where a chemical solver (i.e. Phreeqc) was called for the chemical speciation calculation. Verification of the new implementation was done by comparing the results with different analytical solutions including a first order biodegradation reaction and a coupled transportdissolution processes and feedback on porosity changes. In this study, we extend the validation of the method by benchmarking different numerical coupling schemes and comparing the results to experimental observations obtained in a) a wellcontrolled laboratory scale column experiment including a dissolution reaction with feedback on porosity changes and b) through diffusion experiments of sorbing cations in clay.
The simulation of coupled fracture flow and deforming porous medium is a
challenging problem in reservoir engineering. Common examples are
hydraulic simulations or hydrofracking. Some of the challenges arise
due to the difference in properties of the mathematical models used in
each of the subdomains. Solving the problem using a monolithic approach
leads to an illconditioned system of equations implying the necessity
of using a direct solver for the resulting linear system of equations.
We investigate a partitioned blackbox coupling approach based on the
idea of domain decomposition techniques. The individual problems are
solved separately in an iterative manner such that we can use standard
iterative solvers for the linear systems. Our approach is based on the
opensource library preCICE (www.precice.org) allowing us to reuse
existing solver software and simplifying the setup of new solvers that
are immediately prepared for highperformance parallel computations.
Whereas extraction of hydrocarbons from the subsurface typically involves transport phenomena over large distances (e.g, inbetween injection and production wells), transport of geothermal heat during extraction and storage is chiefly confined to the proximity of wells. This indicates significantly reduced computational efforts by considering only a region of interest around the wells. In this work, we investigate a dynamic coarsening approach that uses aggregation of cells in an underlying finescale geomodel to form a coarse representation with refinement only in regions of interest. The dynamic grid is constructed from a predefined set of nested partitions of the underlying fine grid, and constructed at each timestep based on a set of suitable indicators. The approach is highly flexible, since it applies to any underlying fine grid consisting of nonoverlapping cells, and efficient, since properties of the dynamic grids can be computed in a preprocessing step.
We assess the method on a number of test cases, and compare and contrast the results to finescale simulations using different refinement indicators and coarsening strategies. All numerical experiments will be conducted using the newly developed geothermal module of the opensource MATLAB Reservoir Simulation Toolbox.
Modeling and simulation of flow, transport and geomechanics in the subsurface porous media is an effective approach to help make decisions associated with the management of subsurface oil and gas reservoirs, as well as in other wide application areas including groundwater contamination and carbon sequestration. Accurate modeling and efficient, robust simulation have always been the main purposes of reservoir researches, and a 6M digital twin (multiscale, multidomain, multiphysics and multinumerics numerical modeling and simulation of multicomponent and multiphase fluid flow in porous media) is designed, equipped with the following six pronounced features, to better digitally model and simulate the engineering processes and procedures in physical reality and further control and optimize such processes and procedures: 1. Efficient and reliable flash calculation; 2. Advanced phase interface modeling; 3. Fully conservative boundpreserving Darcys scale flow simulation; 4. Reactive flow and transport in porous media; 5. Molecular simulation of microscopic mechanisms; 6. Highperformance computation based on fullyImplicit and boundpreserving algorithms.
Whether naturally or artificiallyinduced due to human activities, decreasing or increasing of suction in multiphasefluidsaturated porous materials can lead to enormous changes in their thermohydromechanical properties. In this, both the mathematical description and the numerical modeling of the coupled problem present a challenging task. The presentation considers the following two instances related to suctioninduced fractures. (1) The dryinginduced fracturing, which occurs due to increasing of the capillary pressure (air pressure minus water pressure) in lowpermeable, unsaturated porous materials. (2) The microcryosuctioninduced fractures, which can be observed in saturated and unsaturated porous materials under freezing conditions.
In both cases, the macroscopic modeling of the induced fractures is based on continuum porous media mechanics extended by a diffusive phasefield fracture method. For the dryinginduced fractures of unsaturated porous media, one has to deal with more than one pore fluid (e.g., water and air). In this case, the mechanical behavior can be expressed by using Bishop’s effective stress principle, which considers the total stress, the capillary pressure, and saturation degree. For the microcryosuctioninduced fractures in saturated porous media, the water freezing is treated as a phasechange process. This is modeled using a different phasefield approach, in which the thermal energy derives the phase change and, thus, leads to occurrence of microcryosuction due to the formation of the ice phase.
In addition to the continuum mechanical modeling and the conventional constitutive relations, machine learning (ML) presents a powerful tool in bridging the gap between the micro and the macro scales. In this, we employ selfdesigned/selfimproved neural networks, which can be trained using datasets of microscale simulations, to produced constitutive relations for the macroscopic scale simulations. For instance, ML via deep recurrent neural networks (RNN) allows to generate of pathdependent retention curve models, which can capture the challenging hysteresis behavior. Numerical examples will be presented and include qualitative and quantitative comparisons with experimental data.
REFERENCES
[1] Heider, Y.; Sun, W. (2019): A phase field framework for capillaryinduced fracture in unsaturated porous media: Dryinginduced vs. hydraulic cracking, Comput Methods Appl Mech Eng; DOI: j.cma.2019.112647.
[2] Sweidan, A.H.; Niggemann, K.; Heider, Y.; Ziegler, M.; Markert, B. (2021): Experimental study and numerical modeling of the thermohydromechanical processes in multidirectional soil freezing. Acta Geotechnica (under review).
[3] Heider, Y.; Suh, HS; Sun, W. (2021): An offline multiscale unsaturated poromechanics model enabled by selfdesigned/selfimproved neural networks, Int J Numer Anal Methods Geomech; (accepted).
Modeling and simulation of multiphase flow in porous media have been a major effort in reservoir engineering and in environmental study. One basic requirement for accurate modeling and simulation of multiphase flow is to have the predicted physical quantities sit within a physically meaningful range. For example, the predicated saturation should sit between 0 and 1 while the predicated molar concentration should sit between 0 and the maximum value allowed by the equation of state. Unfortunately, popular simulation methods used in petroleum industries do not preserve physical bounds. Another major issue with common algorithms for twophase flow, especially common semiimplicit algorithms, is that they are (locally) conservative to just one phase only, not all phases.
In this talk we present our work on both fully implicit and semiimplicit algorithms for twophase and multiphase flow in porous media with capillary pressure. Our proposed algorithms are locally mass conservative for all phases. They are also able to accurately reproduce the discontinuity of saturation due to different capillary pressure functions, and the produced total velocity is continuous in the normal direction. Moreover, the new schemes are unbiased with regard to the phases and the saturations of all phases are boundspreserving (if the time step size is smaller than a certain value for semiimplicit algorithms). We also present some interesting examples to demonstrate the efficiency and robustness of the new algorithms. The semiimplicit algorithms are based on our novel splitting of variables, and the fully implicit algorithms are based on the two nonlinear preconditioner of activeset reducedspace method and nonlinear elimination, as well as the linear preconditioner of overlapping additive Schwarz type domain decomposition. The semiimplicit part of this presentation is based on our joint work with Huangxin Chen (Xiamen University), Jisheng Kou (Shaoxing University), Xiaolin Fan (Guizhou Normal University), and Tao Zhang (KAUST), and the fully implicit part is based on our joint work with Haijian Yang (Hunan University), Chao Yang (Beijing University), and Yiteng Li (KAUST).
Low resistivity pays (LRPs) are reservoirs from which dry hydrocarbons are produced in the presence of erroneously interpreted water saturations. LRPs are often identified within laminated reservoir sequences, shaley lithologies, and formations with multimodal poresize characteristics or containing fresh formation waters identified on the basis of well logging, testing and core observations. The following study addresses the characterization of a microporous carbonate LRP formation using digital rock physics (DRP) analysis in various facies identified in 62 core plugs through digital imaging.
A comprehensive DRP workflow was utilized to produce 3D digital rock models of rock samples through multiresolution Xray tomographic imaging and application of a machinelearning algorithm to characterize the internal fabric of the rock samples based upon the abundance of microporosity. The physical samples were also analyzed using mercury injection capillary pressure (MICP) to allow calibration and validate the 3D digital rock models. Numerical simulation of the electrical current flow through the samples showed the variation of Archie’s saturation exponent “n” with water saturation, i.e., the increasing influence of the microporous regions as water saturation is decreased. The meso and macropores were found to produce the moveable hydrocarbons due to their lower capillary pressure; the micropores holding immobile formation water. The DRP models were then used to simulate the drainage relative permeability curves to identify the water saturation causing the first water inflow, and separate immobile and freefluids. The wireline logs saturation profile was updated with these results.
As shown by digital experiments, conducted on LRP the waterfilled micropores provide a continuous path for electric current, masking the hydrocarbons and overestimating the water saturation. Saturation calculation could be significantly refined, if LRP wireline petrophysical models are calibrated using DRP data incorporating the modelled Archie’s saturation exponent and first water inflow from relative permeability curves.
Over the past years, tomographic scanning techniques like microCT have enabled the acquisition of highfidelity voidspace geometries of natural porous media [e.g., Raeini, Bijeljic, and Blunt, Physical Review E, 96, 1 (2017)]. There are, however, experimental/computational limitations in the sample size, respectively level of detail or voxel count, that can be acquired [Section 2.3 in Cnudde and Boone, EarthScience Reviews, 123 (2013)]. Moreover, limitations both in computing time and memory prohibit direct numerical simulation (DNS) of flow and transport in large resp. detailed sample geometries. Pore networks derived from scans alleviate this second limitation or computational burden, but introduce model assumptions and still necessitate a methodology to extrapolate to larger samples. Such a methodology is needed, especially for relatively inhomogeneous rocks like carbonates, as the scales of representative elementary volumes (REV) for flow and transport theories are often larger than the sample sizes that are currently scanned/postprocessed [Meyer and Bijeljic, Physical Review E, 94, 1 (2016)].
In this work, we address this need by presenting a new pore network generation algorithm. While emulating from an existing base network new networks of equal or larger sizes, the new algorithm scales approximately linearly with the pore count and maintains (1) pore coordinationnumber statistics, (2) geometrical pore/throat properties, as well as (3) the potentially inhomogeneous spatial clustering of pores. While existing methods address the first two properties [Idowu, PoreScale Modeling: Stochastic Network Generator and Modeling of Rate Effects in Waterflooding, Imperial College London (2009)], the third point is crucial to match flow/transport properties such as the permeability in inhomogeneous media.
Nucleation is the first step of any mineral precipitation and crystal growth process. It is often overlooked in studying the reactive transport phenomena. Nucleation controls the location and timing of crystal formation in a porous structure. The spatial distribution of stable secondary nuclei is crucial to predict hydrodynamics of the porous medium after mineral precipitation precisely. To better understand the nucleation process, we developed a new probabilistic nucleation approach in which the induction time is considered a random variable. The random induction time statistically spreads around the measured or reported induction time, either obtained from experiments or approximated by the exponential nucleation rate equation suggested by the classical nucleation theory. In this work, we utilized inputs from the classical nucleation theory. In our model, both location and time of nucleation are probabilistic, affecting transport properties in different time and lengthscales. We developed a porescale Lattice Boltzmann reactive transport model and implemented the new probabilistic nucleation model to investigate the effect of nucleation rate and reaction rate on the extent, distribution, and precipitation pattern of the solid phases. The simulation domain is a 2D substrate with an infinite source of the supersaturated solution. We use Shannon entropy to measure the disorder of the spatial mineral distributions. The results of the simulations show that all the reactions follow similar random behavior with different GaussLaplace distributions. The simulation scenarios start from a fully ordered system with no solid precipitation on the substrate (entropy of 0). Entropy starts to increase as the secondary phase precipitates and grows on the surface until it reaches its maximum value (entropy of 1). Afterward, the overall disorder declines as more surface areas are getting covered, and eventually, entropy approaches a constant value. The research results indicate that the slower reactions have longer windows of the probabilistic regime before entering the deterministic regime. The outcomes provide the basis for implementing mineral nucleation and growth for reactive transport modeling across timescales and lengthscales.
In this study, a porenetwork model as an upscaled representation of the pore space and fluid displacement is used to simulate and predict twophase flow through porous media. The results of microCT porescale imaging experiments are used to calibrate the model, and specifically to find the porescale distribution of wettability. As wettability is an uncertain parameter in twophase flow modeling, we employ energy balance to estimate an average, thermodynamic, contact angle in the model. This thermodynamic contact angle is used as the initial estimate of wettability. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment at the pore level as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steadystate microcomputedtomography experiments for waterwet and mixedwet Bentheimer sandstone. As a result of the optimization, the porebypore error of fluid distribution between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for upscaled parameters of capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angles around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oilwet. Using randomly assigned distributions of optimized contact angles in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixedwet case. Also, analyzing the spatial correlation show a stronger for mixedwet Bentheimer sandstone.
Drying in porous media is a complicated multiphysical process including liquid/vapor multiphase flow, phase change and heat and vapor transport, occurring with the complex geometry of porous media. Contact angle hysteresis induced by surface roughness is shown to influence drying of liquid or colloidal droplet, resulting in a stickslip drying mode and the formation of coffee ring after drying in constant contact radius mode. However, the influence of contact angle hysteresis on liquid drying in porous media still lacks exploration, either experimentally or numerically.
Lattice Boltzmann model (LBM) is an advanced numerical approach that can model phase change problems such as evaporation and boiling. In this paper, utilizing a geometric formulation scheme to prescribe contact angle, we present a contact angle hysteresis model within the framework of a twophase pseudopotential LBM. First, we simulate droplets sitting on flat and curved surfaces, to validate the capability and accuracy of prescribing and automatically measuring contact angles over a large range. The proposed contact angle hysteresis model is further validated by modeling droplet drying on flat and curved surfaces. It is found that by considering contact angle hysteresis a stickslip mode on both surfaces can be captured. Drying of two connected capillary tubes is studied, considering the influence of different contact angle hysteresis ranges on the evolution of liquidvapor interface. The model is finally applied to study drying of a dualporosity porous medium with/without considering contact angle hysteresis, where liquid configuration and drying rate are compared showing important differences. The proposed model is shown to be capable of dealing with different contact angle hysteresis ranges accurately, and of capturing the physical mechanisms during drying in different porous media.
Coupled freeflow and porousmedium systems described by the StokesDarcy equations are intensively studied in the last decade. Most of the coupling concepts are based on the BeaversJoseph interface condition, which is developed for onedimensional flows parallel to the fluidporous interface. However, this condition is unsuitable for arbitrary flow directions [2], e.g. for industrial filtration problems. Alternative coupling concepts existing in the literature, e.g. [1] contain unknown coefficients, which need to be calibrated before they can be used in computational models. Porescale simulations play here an important role, both for the validation of the coupled macroscale models and for the computation and calibration of the effective model parameters.
In this talk, we present a comparison study of several coupling concepts for the StokesDarcy problem [3, 4]. Coupled macroscale models are validated numerically by comparison of the macroscale simulation results against the porescale resolved models. Effective parameters appearing in the alternative interface conditions [3] are computed numerically based on the geometrical configuration of the underlying problem. The exact location of the sharp fluidporous interface and the BeaversJoseph parameter in the classical conditions are optimized for different pore geometries. We show that the coupling conditions proposed in [3] are the most accurate ones and the BeaversJoseph parameter cannot be fitted for arbitrary flows to the fluidporous interface.
Plant roots and bacteria alter the soil physical properties by releasing a polymeric blend of substances (e.g. extracellular polymeric substances and mucilage). Despite experimental evidence of the impact of such polymer solutions on water fluxes across the root zone, the physical mechanisms controlling the spatial distribution in complex porous media (soils) have not yet been addressed. In particular, it is not clear how the physical properties of polymer solutions (viscosity, surface tension and water adsorption, all depending on the polymer concentration) shape the configuration of the liquid phase in porous media. In this study, we present a new approach by modeling the (polymer concentration dependent) force balance between viscous flow and water adsorption, defining a threshold for the immobilization of the polymeric network. At this critical point, the polymers are deposited as twodimensional surfaces, such as hollow cylinders or interconnected surfaces. We implement this force balance in threedimensional simulations of drying in porous media to determine the polymer deposition at the critical point. Simulations are conducted for different drying rates, polymer concentrations and particle size distributions. Simulations are compared with results of scanning electron microscope and Xray imaging to improve our understanding of the rules defining the polymer deposition.
Multiphase flow in porous media is a subject with important technical applications, such as in oil recovery from petroleum reservoirs or in Liquid Composite Molding Processes. In the Liquid Composite Molding and in other applications, macroscopic resin flow is modelled by postulating a multiphase generalization of Darcy’s law. However, modelling of multiphase flow remains an important technical challenge and a thorough understanding of porescale physics and robust upscaling methods are of great importance.
This work addresses microporescale multiphase flow, in which different pressures are defined in each constituent phase with the differences, called capillary pressure, obtained by the micropore geometry and the interfacial tension. Consequently, the study of forces acting inside a fluid or at the interfaces liquid/liquid, liquid/vapor or liquid/solid is very significant to improve the understanding of multiphase flows in porous media [1, 2].
The aim of this work is to study the dependence between the contactline velocity and the slip length in a Generalized Navier Boundary Condition (GNBC) [3, 4], by confronting numerical simulations to experimental data. Experiments were performed by a liquid/gas crossflowing mechanism inside a pore Tjunction device. For typically small capillary numbers (between 10E6 and 10E2) of the continuous shear stream, the dynamic contact angle is found to have a significant effect on the bubble size. This can be explained by the nonuniform displacement of the contact line at the solid wall. Computer fluid dynamics (CFD) simulations of dynamic wetting were performed using a slip model on the substrate. Realistic values of the slip length were chosen by matching the numerical dynamic contact angles obtained by the GNBC Model and experimental ones.
Reactive transport in porous media is a dynamic field of research with open questions particularly at porescale. Despite our detailed understanding of nonreactive multiphase flow in porous media, across scales, little is known about the porescale dynamics of processes involving chemical reactions alongside fluid flow in porous media. Reactive flow plays a key role in a rage of application including groundwater remediation, CO2 sequestration, metal recovery, and heavy oil recovery. In these processes a chemical reaction is engineered to impact the structure/properties of the host porous medium or the arrangement of fluids it confines. In this contribution we study the classic problem of groundwater contamination with chlorinated solvents but from a porescale perspective. Chlorinated solvents are known as a persistent family of aquifer contaminants which, over the past decades, have caused serious health problems (e.g. kidney and liver damage) and some are considered as carcinogenic. Being denser than water, when a leakage occurs at the surface these contaminates sink into the groundwater system and create a source of contamination in form of trapped DNAPLs (i.e. dense nonaqueous phase liquids). The scale of the problem posed by these contaminants is globally significant due to their wide industrial use since the beginning of 20th century e.g. in metal processing plants and dry cleaning.
In this work we performed a synchrotronbased microtomography imaging experiment to study the dynamics of the reactive transport process during application of nanoremediation1. Nanoremediation is a new technology that injects aqueous suspensions of zero valent iron nanoparticles (nZVI) into contaminant bearing subsurface sediments. These nanoparticles are highly reactive and excellent electron donors (Fe0 > Fe2++ 2e¯). Chlorinated solvents accept those electrons and release their chlorine atoms in form of ions. Example reaction: (C2H2Cl2+ Fe0 + 2H+>C2H4 + 2Cl¯+ Fe2+). While nanoremediation concept is proven to be successful at laboratory, pilot, and field scales, the existing practice is far from optimised. A contributing factor to this is the lack of understanding around porescale mechanisms that control the nanoremediation process.
Our 4D (timeresolved, 3D) experiment comprised of fluid injections in a column (packed with glass beads) and simultaneous 3D imaging using Xray microCT technique. The study was conducted at the Brazilian synchrotron. For the first time, we captured the evolution of the DNAPL phase structure/distribution, in 3D, during the nanoremediation process. Our data show that a gas phase is released during nanoremediation which remobilises the trapped DNAPL phase, facilitating its complete removal in subsequent soil flushing processes. Our findings also show the evolved gas reduces the relative permeability of the contaminated water phase from 60% to less than 1%. This suggests that the gas evolution provides a temporary control on the contamination plume propagation. This favourable outcome is caused by porescale blockage of water flowpathways by the released gas. In field applications of nanoremediation (or similar insitu remediation technologies) gas formation is considered as a sign of effectiveness of the process. This study provides a quantitative evidence on how this gas release can impact the contamination removal and limit its propagation.
Fluids involved in activities occurring in fractured underground reservoirs, either related to natural resource recovery (e.g., hydrofracturing, drilling, geothermal exploitation) or environmental remediation schemes, often exhibit complex rheology. The microstructure of foams, muds, emulsions, or colloidal suspensions induces shearthinning in the continuum scale mechanical behaviour, which can be described by the Ellis rheology. This threeparameter model has a Newtonian lowshear rate behaviour of apparent viscosity $μ_0$, a highshear rate powerlaw trend with exponent $n$, and a transition between the two regulated by a characteristic stress $τ_{1⁄2}$. Such fluids often flow in rock fractures having rough walls characterized by longscale correlations in the topography, i.e., a selfaffine scale invariance at all scales. The facing walls of a given fracture are also mated at scales larger than a characteristic correlation length scale. Such geometries can be reproduced numerically utilizing an FFTbased algorithm. The fracture closure is then measured as the ratio of the aperture field’s roughness amplitude to the mean fracture aperture. The investigation of the nonNewtonian hydraulic behaviour of such natural or artificial fractures implies a considerable mathematical and numerical effort to properly account for nonlinearities and medium geometry. A full stochastic analysis of large fractures with a variety of statistical descriptive parameters via Monte Carlo simulations is almost prohibitive considering a fully 3D simulation of the flow. The flow of a shearthinning fluid through a variable aperture fracture can instead be described under the assumptions of the lubrication theory, a depthaveraged formalism that reduces the model formulation to a single twodimensional nonlinear PDE. A numerical code has been implemented adopting the finite volume method, with the fracture discretized on a staggered grid, defining the pressures at the centre of each finite volume and the aperture at each side. The system of nonlinear equation is solved adopting the NewtonKrylov method, considering a continuation strategy to face strong nonlinear cases (very low $n$ values), and solving the linearized symmetric system of equations via variablefillin incomplete Cholesky preconditioned conjugate gradient algorithm. A Monte Carlo framework is adopted to study the influence of rheology, fracture dimension and pressure gradient on fracture hydraulic behaviour, generating $NMC=1000$ realizations of the aperture field. The approach allows characterizing the hydraulic behaviour via ensemble statistics, such as the PDFs of the velocity fields and the dependence of the fracture transmissivity on fracture closure, and how it is impacted by the fluid’s shear thinning behaviour. Fracture flow is mainly cocurrent, presenting narrow PDFs with nearly exponential decay. Evident channelling and localization effects are associated with strongly heterogeneous aperture fields and very shearthinning fluids. In these cases, the probability distributions of velocity components PDFs show wide tails deviating from the exponential decay, and the fracture transmissivity is much higher compared with the Newtonian case of identical mean aperture.
This paper investigates the spatial patterns of metal deposit on battery cathode by electrodeposition during use. This is done by modelling with a reactiondiffusion system on a finite twodimensional domain and examining the conditions required for Turing instability. Turing instability requires analysing the stability of the system allowing for diffusion and also without diffusion. Phase portraits are produced as well as basins of attractions for parameter values for the diffusionless system. The full system is discretised using the Finite Element Method and then solved numerically. Tests are carried out to see the effects of different variable values on the resulting spatial patterns.
With the development of large quantities of gas injection in shale and tight reservoirs, the multiphase behavior in nanoscale pores before and after gas injection has gradually attracted people's attention. A large number of published literature have shown that due to wall adsorption and capillary force, the phase behavior of confined fluid in micro and nano pores is significantly different from that of conventional reservoirs, such as phase transformation hysteresis. The existing EOS equation, especially the PREOS method for the calculation of gasliquid equilibrium, has been unable to accurately describe the change of gasfluid phase state in nanopores. Therefore, it is necessary to modify the EOS equation according to the relevant terms introduced in the phase state mechanism of corresponding nano pores or combining with other methods. Our discussion focuses on three kinds of correction methods for phase state calculation in nanoscale pores, including: correction of gravitational phase and volume parameters in the equation of state; The capillary force and critical parameters in micronano pore channels were considered; Engineering Density Functional Theory (DFT) is combined with equations of state. Although the above methods in the literature are in order to improve the EOS model in the prediction of phase behavior change in a nanoscale pore precision for the result, but in the case of a given component simulated calculation, in the process of gas injection, the component concentration changing, each part of the existing EOS correction method adaptability to variable components is unknown, and they lack of contact with each other between various correction method. This discussion through the three kinds of PR  EOS correction method of micro/nano pores in the process of gas injection gas  liquid phase change contrast the actual situation of deviation rate, consider in the process of high temperature and high pressure gas injection with different pore scale, selection and analysis of the influence of key parameters on the phase behavior change and its sensitivity, finially,we can obtainted gas fluid EOS correction method of the accuracy and applicability after gas injection in the micro/nano pores. The results show that the three nanoscale pores phase state correction methods can reflect the phase state change better to a certain extent. Considering the change of composition, the changes of capillary force and critical parameters in micro and nano pores are more concise and the adjustable parameter range is larger. The fitting results can better reflect the changes of fluid phase state in micro and nano pores. The other two methods can clearly consider the intermolecular and fluidsurface interaction forces and can explain the restricted fluid phase behavior in micro and nano pores from the molecular perspective, but the calculation process involves largescale calculation and is relatively complex.
Polymer flooding is an enhanced oil recovery technique applied to reduce mobility ratio and improve sweep efficiency [7]. In addition, polymer solutions can be used as relative permeability modifiers (RPM) in order to increase the recovery factor due to flow diversion [1]. In the applications mentioned above, high viscosity and polymer retention (mechanical retention and adsorption) may cause injectivity problems in cases where there are limitations on injection pressure [7]. In the techniques mentioned above, accurately modeling the coupling between the nearwell region and the rest of the reservoir phenomena in different spatial and temporal scales is essential. For instance, a local spatial and temporal mesh refinement is necessary near the well to capture the formation damage and nonNewtonian behavior. However, refining the entire reservoir is impractical due to the high computational cost [5]. Therefore, an alternative to efficiently couple these regions is to apply a spacetime domain decomposition technique. The main idea is to split the reservoir domain into subdomains with appropriate spacetime refinement, taking advantage of the parallel computational architecture to reduce computational cost. This work aims to deduce an innovative mathematical and computational model for polymer flooding in oil reservoirs based on domain decomposition techniques to efficiently couple the nearwell region and the reservoir. The governing twophase flow equations consist of Darcy's law and mass balance for fluid (oil and water) together with the transport equation for the polymer movement in the aqueous phase [7]. Additional closure equations are applied to describe adsorption, mechanical retention, formation damage, and the nonNewtonian pseudoplastic behavior. For the computational model, Darcy's law and total mass balance are discretized by applying the mixed finite element method [3]. Moreover, the aqueous phase and polymer transport equations are approximated using the central upwind finite volume scheme [4]. To the domain decomposition method, we consider the reservoir domain partitioned into nonoverlapping subdomains. Then, for the hydrodynamics equations, the mortar finite element method is applied to ensure continuity of pressure and fluxes across the interfaces [2]. For the transport equations, due to the hyperbolic PDE nature, the explicit finite volume method is applied assuming Dirichlet interface conditions to compute the solution for saturation and polymer concentration [6]. To validate the accuracy and stability of the proposed computational model, we propose some numerical simulations by comparing the discrete solutions with analytical and highfidelity solutions. We also simulate the dependence of the injectivity and production curves with the nonNewtonian behavior, mechanical retention, and formation damage considering more general domains, such as the fivespot reservoir in the presence of perforated wells. The numerical simulations show that the proposed computational model has a low computational cost and accurately captures the solutions in several scenarios for polymer flooding in oil reservoirs.
Viscous fingering commonly takes place when a low viscosity fluid displaces a higher viscosity fluid. Although the fundamental principles governing the interfacial pattern in HeleShaw cell are well understood, their manifestation in porous media remains elusive. Here, we study viscous fingering in hierarchal porous media (HPM) consisting of a spatiallyorganized bimodal pore size distribution, namely patches of small and large pores. We use direct numerical simulations and microfluidic experiments to show that viscous fingering, typically highly random, develops into structured interfacial patterns in HPM, in contrast to its random nature in random media. We show that this invasion selectivity highly depends on the flow rate and the pore size contrast. Our results demonstrate that HPM provides a mean to control the morphology of displacement patterns, paving the way towards improved designs of chromatographic columns, membranes, microfluidic devices, and other applications where controlling interface morphology of the displacement pattern in porous materials is desirable.
The thermal energy distribution of the Yellowstone terrestrial hydrothermal system is driven by a mantlederived magmatic plume which has both IronMagnesium rich and AluminumSilicate rich phases and supplies thermal energy to the surface (Crough, 1978). The Yellowstone hydrothermal system is in steadystate within neighborhood of geologic time (10's Ka) and steadystate diffusive nature predominates as the hydrothermal system marches closer towards eruption(Faust, C.R. and Mercer, J.W., 1977). The Yellowstone Plateau Volcanic Field (YPVF) with area on the order of 90,000$km^{2}$ is the location of numerous active thermal areas. Since the domains observed during field reconnaissance (2019 and 2020) were relatively small ( \approx $1.6km^{2}$) compared to the overall area impacted by thermal energy within the global system (i.e. 90,000$km^{2}$), care was taken to ensure energy minimization $1/2\bigtriangledown(u)^{2}\approx0$ within the spatial domain was satisfied during numerical model's implementation of the coupled set of nonlinear hydrodynamic governing euqations (i.e. advectiondiffusionreaction) for the observed domain (i.e. Cule Basin). The FEniCSDolfinPETSc numerical libraries were used in the implementaiton of numerical simulations of spatial distributions for heat, water isotopes (i.e. $\delta D, \delta ^{18}O$), and saturation silica ($SiO_{2}$) concentration estimations of the fluidrock interface observed from Culex Basin hydrothermal features. Energy distributions, thermal and chemical gradient($\bigtriangledown (u)$)/numerical flux ($K \bigtriangledown (u)$) fields estimated within the observed fluidrock interface domain ($\Omega_{CB}$) are the result of the local buoyancy forces (Smith and Chapman, 1983).
If the locally observed hydrothermal systems at Yellowstone interact as energy conservative space time balances, that minimize the distribution of spatial potential energy in the observed phases, then this could be numerical evidence that the global Yellowstone hydrothermal system is in steadystate diffusive energy flux. This would imply that the fluidrock interface of a terrestrial hydrothermal system is driven by buoyancy forces which determine fluid velocity fields and thus the elliptic plane of thermal energy distribution decoupled from the physical ground surface (Smith and Chapman, 1983). The finite element numerical results of the nonlinear LagrangeGalerkin diffusive model for variables measured during field reconnaissance will be discussed for temperature based estimations, and measured spatial distributions and associated flux fields (Sorey et al., 1978).
On terrestrial hydrothermal systems found on Earth, this approach could reduce the amount of exploration drilling needed during geothermal development. Less drilling during said geothermal development could reduces the cost ($\$$) on the order of hundreds of thousands of dollars. Additionally less drilling could reduce the environmental impact in the surrounding biomes. Integrated with LiDar, and other types of spatially distributed signal data taken as discrete points, this approach completes the data driven approach to the numerical conservation of energy in natural systems. Upon further development, if Peclet convergence can be determined for the LagrangeGalerkin methods presented, terrestrial hydrothermal system models could be used to compare the data collected from other terrestrial hydrothermal systems where drilling might be a challenge such as other planetary bodies (i.e. Titan, I.O. Venus, Europa, Triton, etc.) since it would take an observation based approach with respect to the overall system.
Solute transport plays an important role in many soft porous materials, including the movement of contaminants in soils and the movement of nutrients and waste in living tissues and tissueengineering scaffolds. These systems are also often exposed to large, periodic loading and deformation, which drives nontrivial fluid motion and changes in pore structure. Here, we study the strong coupling between fluid flow and mechanical stimulation during periodic deformations using a 1D continuum model based on largedeformation poroelasticity. We show that these reversible deformations lead to nonreversible spreading and mixing, even in a homogeneous medium. We analyse the three primary mechanisms of solute transport (advection, molecular diffusion, and mechanical dispersion) and study their separate impacts on the solute distribution. We also identify the key dimensionless parameters that govern deformationdriven transport, and we study their qualitative and quantitative impacts on solute spreading and mixing.
Cellulose has a very large range of applications in many aspects, and the drying of cellulose are widely adopted in many industrial processes. The deformable property of cellulose fibers, along with water adsorption capacity, add complexity to its drying mechanisms. In this work, we study the global mass loss and the spatial evolution of the internal water content of cellulose during its convective drying. Two complimentary approaches were adopted for this objective: macroscopic drying manipulations and nuclear magnetic resonance (NMR) For cellulose slurry, different concentrations of watercellulose suspensions are dried under constant convection boundary conditions. Two obvious regimes are observed, corresponding to constant drying rate and decreasing drying rate. Meanwhile, the Magnetic Resonance Imaging results present three stages during the whole process: firstly, free water extracted accompanied with shrinkage of structures; followed by a second stage of homogeneously desaturation of all the bulk water; these stages correspond to the constant drying rate period. The last stage is assumed to be the confined water extraction, during which a slightly further shrinkage is observed as well. Complimentary experiments are carried out starting the drying test from cellulose powder prepared at saturated relative humidity, in order to capture the drying mechanism for confined water (possibly bound water). The profiles of NMR signal intensity, which is equivalent to water content inside cellulose, evolve in time in a way which appears consistent with a process of diffusion of vapor all along the sample interior (down to its bottom), in contrast with drying processes with liquid present inside the sample.
We model the displacement of oil from idealized porous media by simulating the quasistatic injection of gas into oilfilled channels with uniform crosssection under different wetting conditions.
We consider channels with triangular or rectangular crosssection that are initially filled with a single fluid (e.g. oil). A second, displacing, fluid (e.g. gas) is introduced at one end of the channel, first having to overcome the capillary entry pressure pce; we estimate pce based on the largest hemisphere that fits inside the crosssection of the channel.
The Surface Evolver software [1] is then used to simulate the invasion of the pore space by this second fluid. It allows us to find the shape of the interface with minimum surface energy separating the two fluids, for a given contact angle at which they meet the pore walls, and a highlyaccurate measurement of the capillary pressure. By making small changes in the gas volume and repeating the minimization, we predict in a quasistatic manner the variation of capillary pressure during the displacement flow. As well as neglecting viscous losses, we assume that the effects of gravity are negligible (small Bond number, based on the usual pore size being small).
When the interface is far from the ends of the channel the flow reaches a steady state. In this regime we predict the oil recovery factor, i.e. the proportion of the first fluid that is displaced by the second. We show that in any channel:
• The capillary pressure decreases as the oil volume increases, for given contact angle;
• The capillary pressure decreases as the contact angle increases, for given oil volume;
and hence that the volume of oil that remains in the corners of the channel is greater for smaller contact angles, decreasing the recovery factor.
RayleighTaylor (RT) convection is a buoyancydriven instability arising when a denser fluid overlies a less dense one in a gravitational field. In this work, we study RT instability in porous media where the denser fluid on the top is also more viscous. We perform highresolution numerical simulations through hybridization of pseudospectral and compact finite difference methods. Using our simulations, we study RT instability for a wide range of viscosity ratios, up to 3000. For the first time, we find that there is a critical viscosity ratio beyond which the updown symmetry of fingers breaks down such that the downward fingers become more extended than upward fingers as the viscosity ratio increases. In this regard, we develop universal scaling relations for the spreading rate of fluids and the convective mass flux at the interface. Finally, we introduce a new secondary fingering instability and verify our finding by comparing the results with a set of previous experiments. Our study provides a more realistic understanding of miscible RayleighTaylor convection in porous media by accounting for the viscosity variations.
Darcy’s Law, an important equation relating flow velocity in a porous medium to the permeability of the medium and the viscosity of the fluid, can be extended to form flow models for petroleum fluids in a reservoir by combining it with a fluid model and conservation of mass. The resulting models are central to reservoir engineering. Analytic solutions to these flow models, developed by Van Everdingen and Hurst, are used in well testing and water influx calculations and their numerical solutions form the basis of many reservoir simulation programs.
However, as interest grows in low permeability reservoirs, Darcy’s Law might not be the appropriate starting place. Alternatives to Darcy’s Law include include threshold pressure models and nonlinear pressure models [1]. In this work new flow models are developed by combining these alternatives with conservation of mass, various fluid models and bulk/boundary fluid viscosity models [2].
Future work will involve using finite difference methods to develop numerical simulations of these models to compare to conventional simulation and historical data in petroleum and CO2 sequestration applications.
In order to study the efficacy of mineral trapping scenarios for CO$_2$ storage behaviour in deep layers, demanding highly nonlinear coupled diffusionadvectionreaction partial differential equations (PDEs) have to be solved.
The chemistry includes both general kinetic and equilibrium reactions.
Realistic scenarios further ask to simulate the inflow of various gases into the deep layers.
We solve the multiphase multicomponent flow equations by means of a fully globally implicit PDE reduction method (PDERM) for the case of an arbitrary number of species in gaseous phase which are injected into a deep layer.
The Finite Element discretized / Finite Volume stabilized equations are split into a local and a global system coupled by the resolution function and evaluated with the aid of a nested semismooth Newton solver.
Our methods are implemented within the free open source software M++.
We present realistic scenarios of gas injection into deep layers and study the mineral trapping effects of the storage technique.
Finally, the PDERM reduction method can be applied not only to CO$_2$ storage processes, but also to e.g. oil recovery and nuclear waste storage.
Archaeological wood of shipwrecks buried for centuries under sea sediments is highly degraded due to the chemical changes and material loss. Uncontrolled or rapid drying of such artifacts results in drastic distortion and collapse of material due to high drying stress, therefore consolidation methods and drying processes have been developed to preserve these culturally valuable artifacts. As a consolidation technique used for both Swedish warship Vasa [1] and Henry VIII’s warship the Mary Rose [2], polyethylene glycol (PEG) solution was sprayed for decades on the surface of both shipwrecks to penetrate the wood and stabilize the wood structure [1]. While the experimental results show higher stability in PEGtreated samples [1], many questions regarding the impact of PEG polymers on the stability of wood polymers remain unanswered due to the microscopic nature of complex nanoscale phenomena involved. In this study, we combine the data obtained from molecular dynamics (MD) and grand canonical Monte Carlo (GCMC) simulation with a poromechanical model to examine the PEGcellulose synergic interaction in amorphous mixtures as observed in sorption isotherms, mechanical moduli and hydrogen bonding network. To this aim, mixtures of amorphous cellulose and PEG200 are constructed as simple models representing the interaction of PEG200 consolidant with cell wall holocellulose component. Mixtures with different mass ratios of cellulose and PEG are modeled using the OPLSAA force field and prepared by hightemperature relaxation followed by quenching at room temperature. Hybrid MD/GCMC is then employed to obtain the sorption isotherms and PEGcellulose mixtures at different levels and regimes of hydration. Following the GCMC simulations, mechanical tests are performed on resultant structures to examine the sorptioninduced mechanical softening in the wood structure for both treated and untreated samples. The data are then introduced into a poromechanical model which allows analyzing the change in the coupling between sorption and deformation by adding PEG to cellulose. The presented model, methodology, and the choice of simulation parameters such as system size are validated through comparison with available simulation and experimental data on amorphous cellulose sorption isotherms and mechanical properties. As indicated by sorption isotherms and swelling curves, the PEGcellulose mixture shows deviation from the ideal mixture rule referring to a synergic interaction between PEG and Cellulose. This synergic behavior can be examined by investigating the confinement of PEG molecules in the nanoporous structure of amorphous cellulose and by the hydrogen bonding network between cellulose and PEG. The PEG molecules rearrange the existing hydrogen bonding network by forming new hydrogen bonds with the cellulose chains reducing the sorption sites available for moisture adsorption. In addition, the amorphous cellulose limits the free swelling of PEG observed in its pure liquid form. These two mechanisms can describe the reduction in moisture content and its outcome: less swelling/shrinkage in treated samples and thus higher stability in museum conditions.
Numerous experimental observations and field applications have confirmed that lowsalinity water flooding is an effective technique for enhanced oil recovery. Given the complex physical and chemical processes, several controlling mechanisms have been proposed to explain the oil remobilization due to lowsalinity effects. Osmosis and waterinoil emulsification are among these mechanisms. However, our knowledge of these processes is limited and their associated time scales are not well understood.
To verify their roles, we conducted a series of microfluidic experiments by sequentially injecting highsalinity water, pure or surfactantadded synthetic oil, lowsalinity water into the hydrophobized glassbased microchips. Several selected specific areas were continuously observed for over 48 hours, with systems of trapped highsalinity water along the solid grains, lowsalinity water in bulk, and sandwiched oil. The systems mimicked the contact status of these three fluids in the natural reservoir. In the experiments using pure oil, we found that the trapped highsalinity water gradually squeezed the sandwiched oil phases out of the pores due to the osmosis induced expansion. The volume of highsalinity water increased by 22.73% with an average rate of 141.88 μm2/hr, which was difficult to rely solely on the diffusion of water in the oil. Therefore, we proposed a hyperthesis and developed a coupled water transport model to explain the highsalinity water expansion with a water flux in the oil phase. In the experiments with adding surfactant (SPAN 80) in oil, we observed that the expansion rate of highsalinity water was 2.72 times higher than it without surfactant, meaning that the emulsification contributed to accelerating water transport in the oil phase.
On the other hand, a corresponding series of experiments were carried out using Zetasizer to capture the size trend in waterinoil emulsion around the oil/salinitywater interface under different salinity conditions. In the case of 1,700 ppm salinity, we found that the waterSPAN80dodecane emulsions kept a primary size of around 50 nm for the first 4 hours, then generated a second primary size of 2 nm during 420 hrs. Finally, the small emulsions progressively dominated the size distribution around the interface, and relative big emulsions, e.g., 4,800 nm, occurred with the coalescence until the emulsification process reached equilibrium. This tendency matched well with the observation on the emulsion transformation in the microfluidic experiments and helped explain the process of highsalinity water expansion.
Stability of foam in the presence of hydrocarbons is a crucial factor in the success of its use in various applications in porous media, such as soil remediation and enhanced oil recovery. (EOR).In this study, we investigate the effect of surfactants with different charges (anionic, cationic, and nonionic) on foam stability in the presence of chargestabilized silica (SiO2) nanoparticles. Toward this aim, a comprehensive series of experiments on a HeleShaw cell and a foam column is conducted at bubble and bulkscale respectively, that is, investigating phenomenologies of foam coarsening separately by gas diffusion and gravitational drainage. Our results show nanoparticles, despite their ability to position themselves at liquidgas interfaces and thus limit the resulting surface tension coefficient, do not necessarily have a positive effect on foam stability; the nature and magnitude of this effect depends strongly on the nature of the surfactant, its concentration and the concentration of nanoparticles. Both results from bubblescale and the bulkscale experiments suggest that compatibility experiments are prerequisite to foam stability analysis to test the compatibility between surfactants and nanoparticles.
Among the demanding challenges of the 21st century, clean energy supply is still challenging to the scientific community to mitigate global warming. In this regard, transforming renewable energy into a stable and reliable fuel form by electrochemical methods is a promising technology. The polymer electrolyte membrane (PEM) water electrolysis is a key technology which uses water as feedstock for hydrogen production. The efficiency of PEM electrolysers is mainly due to wellcoupled kinetics of flow and reaction that occur inside the porous electrodes. The microstructure inside the anodic PTL plays a major role for favourable kinetics by facilitating countercurrent transport of water and oxygen. In this study, we elucidate the transport mechanisms inside the PTL for invasion of oxygen using Lattice Boltzmann method (LBM). A multiphase and multicomponent LBM (Shan Chen LBM) [1] is applied based on BGK collision operator. LBM simulations are used in optimising the structural parameters of PTL (i.e. pore structure, pore connectivity, pore shape) for efficient operation of water electrolyser. As a first step, LBM simulation for titanium felt PTL is compared with experimental data from literature as well as pore network modelling (PNM), see Figure 1. The Capillary number (Ca) and Bond number (Bo) are used to study the competitiveness between the capillary and viscous forces and gravity for understanding the evolution of invasion patterns. Further, LBM simulations for imbibition and drainage phenomena inside the anodic PTL will be shown and discussed based on a titanium felt PTL.
Figure 1: LB simulation invasion patterns for titanium felt PTL, comparison with experimental results from literature [2] and PNM simulations [3].
Permeability is a parameter introduced by Darcy’s Law, which is believed to be an intrinsic property of the porous medium and should be independent of the nature of the fluid flowing through it. However, Darcy’s Law has specific conditions. The assumptions inherent to Darcy's law are (1) a single, incompressible fluid is flowing; (2) flow is in the laminar regime; (3) the fluid is immobile at the pore walls; (4) isothermal conditions exist; (5) the fluid and medium are nonreactive. In this study, isothermal and nonreactive flow is considered. The dimensionless numbers corresponding to condition (1), (2) and (3) are Mach number (Ma), Reynolds number (Re) and Knudsen number (Kn) respectively. Only two of these three dimensionless numbers are independent since they are connected by Kn=$\frac{Ma}{Re}$$\sqrt\frac{\gamma\pi}{2}$. Therefore, and can be chosen as conditions for the establishment of Darcy’s Law when isothermal and nonreactive flow is considered, where represents the gas slip effect and represents the inertial effect.
The inertial effect is studied by many researchers. The most famous and successful model is proposed by Forchheimer, which is expressed in 1D by $\frac{dp}{dx}$=($\frac{\mu}{\kappa}$V+$\beta\rho$$V^2$) , where $\frac{dp}{dx}$ is pressure gradient which is imposed on the both ends of porous medium, $\mu$ is dynamic viscosity of fluid, $\kappa$ is intrinsic permeability of porous medium, $\rho$ is density of fluid, V is Darcy velocity of fluid and $\beta$ is Forchheimer coefficient. Except this, some researchers argued that the cubic term of Darcy velocity, $V^3$ , or the nth power, $V^n$ , should be included in the expression rather than the squared term. All of them have a similar coefficient as Forchheimer coefficient and the focus of related research is the expression of such coefficient. However, all of the expressions are too complicated to be applied in engineering.
In this study, we are trying to derive a concise expression of modified Darcy’s Law by considering the inertial effect. The idea is to propose a suitable modified boundary condition which can account for the derivation due to the moderate inertial effect. Suitable numerical cases will be conducted and results will be carefully analyzed in order to get the suitable modified boundary condition.
Porous electrodes are an essential component of Vanadium Redox Flow Batteries (VRFBs), which are one of the most promising technologies among the energy storage systems required for the integration of the growing supply of renewable energies into the electric grid. Vanadium RFBs have been engineered for decades and currently exhibit some early commercial scale implementations. In this context, mathematical modelling offers a great opportunity for the optimization of current VRFB performance [15].
In this work, a twodimensional, macroscopic, isothermal, steadystate model of a VRFB cell is presented. It incorporates comprehensive descriptions of charge transport and mass transport of ionic species in the electrolyte and membrane, as well as of the electrochemical kinetics in the porous electrodes. The resulting model enables an extensive understanding of the coupled phenomena that take place in VRFBs, being able to predict the performance under different operating conditions and to identify the critical parameters for the optimization of the cell design.
The electrolyte properties are characterized as a function of the State of Charge (SOC) using inhouse experimental data, thus providing a more accurate description of species transport. The computed ionic conductivities are corrected and compared with experimental measurements. Besides, an experimental campaign was conducted to validate the model. Polarization curves are obtained at ambient temperature varying operating conditions such as SOC and volumetric flow rate, and OCV data is obtained as a function of the battery SOC.
Gas hydrates are ubiquitous in seabed and submarine rocks in continental slopes around the world. Formation and dissociation of hydrates in porous spaces can alter the geomechanical strength of hydratebearing rocks. Dissociation of hydrates in submarine slopes decreases the elastic moduli and cohesion of rocks and can trigger slope failure. Failure of submarine slopes can cause damage to seafloor infrastructures, cause tsunamis, and release methane gas into the atmosphere. The bottom of hydratebearing rocks that are indicated by bottomsimulating reflector (BSR) plane can act as the glide plane for failure when large quantities of hydrate dissociate. Based on field observations from Cascadia Margin, a simple twodimensional bench model is created in FLAC3D, and natural tectonic stress regime is applied. Dissociation of gas hydrate is simulated by a steady depressurization of hydratebearing sediments and moduli of elasticity and cohesion are updated based on saturation of gas hydrate. MohrCoulomb failure criterion is applied on the poroelastic model to calculate the factor of safety and failure slope as hydrate saturation decreases. Results from the numerical simulation indicate that the failure slope coincides with the bottom of the hydratebearing rock layer. Factor of safety is the ratio between internal frictional angle of the rock to the angle of the slope failure plane relative to the horizon. The factor of safety decreases as hydrate saturation decreases in the hydratebearing rock layer. A factor of safety lesser than 1.0 to 1.15 indicates a high probability of slope failure. Results of this numerical simulation is used for validation and verification of field observations, and visualization of slope failure due to hydrate dissociation in continental slopes.
Due to recent advances in imaging technology, calculating the macroscopic properties of a porous medium through porescale simulation has become very common. There are several methods to simulate pore scale flow patterns [1], [2]. Among those, lattice Boltzmann method (LBM) has been widely used by scientists because of its simple approach in modeling the complex pore space boundaries, a key challenge in porescale simulation [3]. One of the main concerns about the LBM is high compressibility errors that reduce the prediction capacity of the method at high Reynolds numbers. [4]. In this study, we have tried to minimize the prediction error generated by the variation of the compressibility via adjusting the solution conditions and without the need to refine the lattice size. This makes it possible to employ the LBM to reliably predict transition to the nonDarcy flow regime in real samples with complex pore structure. For this purpose, a multirelaxation time collision model in the PALABOS library [5] is employed, and the fluid viscosity in the lattice unit is optimized. Thus, the effects of viscosity change on the bounce back boundary condition is minimize [6]. This enables us to predict the nonDarcy flow for fluids with LBM. Through these simulations it is concluded that the effect of the compressibility is significantly more important than the effect of the maximum velocity condition on the reliability of the LBM simulations.
Predicting the induced change of fluid pressure in an unsaturated porous medium during undrained loading/unloading processes is challenging because two different fluids (a liquid and a gaseous solution) and a mixture of solid particles are involved. The relative presence of the two fluids and solid particles in the medium of interest, their stiffness, and the initial conditions in terms of liquid and gaseous pressure can play a crucial role in dictating the fluid pressures to be expected at the end of an undrained process. Knowledge of these pressure changes is essential because they affect the mechanical behavior of the porous medium, involving, for instance, its shear strength and volume. In this context, the analytical formulations of the socalled “pore pressure coefficients” proves to be a useful tool for making such predictions. A pore pressure coefficient is defined as the change in pressure of a fluid per unit change in total stress (the latter is the stress component of interest) (Lambe and Whitman, 1969). In contrast to existing models (Skempton, 1954; Hasan and Fredlund, 1980), this contribution proposes an analytical approach for determining unsaturated pore pressure coefficients, which adopts the generalized effective stress (Nuth and Laloui, 2008). It refers to an isotropic elastic unsaturated soil, and total stress changes under isotropic and oedometer conditions. It is shown that it is possible to define a unique pore pressure coefficient for an equivalent fluid. This has advantages in ensuring a direct transition between saturated and unsaturated state predictions. The proposed formulation also includes the analytical expression of the liquidgas mixture stiffness; the latter is a function of the unique pore pressure and individual pore fluid coefficients. The number of constitutive parameters required for the applicability of the approach is lower than that needed to apply the currently existing approach for unsaturated soils (Hasan and Fredlund, 1980; Fredlund and Rahardjo, 1993). The proposed formulation also makes it easy to define the change in the soil water retention state resulting from the undrained process. Existing results in the literature are interpreted or predicted, highlighting the advantages and suitability of the proposed methodology.
Nonlinear oil flow through porous media near a sealing fault has a key role in reservoir engineering because the existence of sealed zones in many types of reservoir rocks present in the world. This work proposes a new unsteady 2D permeability pore pressuredependent model for a wellbore near a sealing fault, where analytical solution is based on an integrodifferential solution of the Nonlinear Hydraulic Diffusivity Equation (NHDE) through Green's Functions (GF's). The model also considers the variation in the properties of the rock and the fluid present inside its pores. The unsteady 2D pressure field is described by the sum of two exponential integral functions Ei(xD, yD, tD), that constitute a combined flow (radial, near to the wellbore) and linear (near to the sealing fault). This type of flow in geosciences and petroleum engineering literature is known as pseudoradial flow. Authors also implement the new model in Matlab® software in order to evaluate the general solution, so as initial and boundary conditions. The model calibration is performed through a porous media oil flow simulator, which showed a high convergence. The permeability functions for some types of reservoir rock are obtained through laboratory correlations, generated from synthetic field data. Authors conclude that general solution of NHDE is given by the sum of linesource solution PwD(tD) and the first order term of the series asymptotic expansion, mwD(1)(tD). This second term of the series expansion is obtained by solving a Volterra's second kind integrodifferential equation in Matlab and is responsible for all the nonlinearities of the combined oil flow. Results of this research showed that when the fault presence begins to contribute to the pressure drop at the well, the drawdown data increasingly departs from the semilog straight line. After a long transitional period, a second straight line with slope 2m can be noticed. Authors also realized that the pressure graphs showed excellent agreement when compared to a numerical simulator and presented errors less than 0.5%.
Understanding mineral reaction rates in porous material is crucial in many environmental systems such as natural weathering process, enhanced oil recovery, radioactive waste disposal etc. Prediction of insitu mineral reaction rates is challenging, and a significant variation is observed between laboratory data compared to field data due to factors like variation in the physicochemical properties of minerals, spatial heterogeneities, chemical composition of the fluid, etc. Previous studies have suggested that this discrepancy is mostly due to the imprecision in determining the mineral reactive surface areas. Even in many cases, the evolution of surface areas of different mineral phases during the reaction gets ignored. Core flood experiments under acidic condition can provide information about the geochemical reactions, mineral dissolutionprecipitation kinetics, and surface area evolution. In this study, a brine solution mixed with HCl is injected into a sandstone core sample from the Torrey Buff formation. 3D Xray nanocomputed tomography (Xray nanoCT) imaging and Scanning Electron Microscopy (SEM) Backscattered electron (BSE) and Energydispersive Xray spectroscopy (EDS) images are used to determine the mineral volume fractions, connected porosity, and accessible mineral surface areas as reactions progress. A reactive transport simulation is carried out in a multicomponent reactive flow and transport modeling tool, CrunchFlow, to simulate reaction rates and the evolution of mineral volume fractions and accessible surface areas. Finally, simulation results are compared with results achieved from the core flood experiment and Xray imaging outputs.
This work aims to understand the relationship between the spatial flow distribution and its underlying pore structure in heterogeneous porous media. Thousands of twodimensional samples of polydispersed granular media are used to 1) obtain the velocity field via direct numerical simulations, and 2) conceptualize the porenetwork as a graph in each sample. Analysis of the flow field allows us to first identify the primary flow paths. Then, the graph edges are weighted by structural attributes of the individual pores to find the shortest path through the sample. Overlap between the primary flow paths and the predicted shortest path determines the accuracy of the weighting scheme tested. A differential evolution genetic algorithm is employed to determine the “fittest” weighting scheme that maximizes accuracy while minimizing overparameterization. Our results demonstrate that the path of least resistance is accurately predicted in all samples for single phase flow and is independent of the flow distribution (uniform to preferential). The results of this work could be used for fast – relative to computationally expensive direct numerical simulations — characterization of porous media heterogeneity, which in turn can be used to predict the time of first arrival and location based on structural information alone.
Producing energy from intermittent renewable energy sources has been developed over the past decades. One of the goals at the gridscale is to provide sustainable energy output to the endusers [1]. To this end, efforts must be done to store a huge amount of energy in robust batteries to provide stable and flexible electricity to the customers during peak hours. Redox flow batteries (RFBs) have been attracted attention to be one of the best candidates amongst electrochemical technologies [2]. RFBs are a highly efficient energy storage technology that uses reduced/oxidized states of species for charge/discharge purposes. The performance of RFBs is evaluated using a polarization curve which describes the relationship between the cell voltage and the current density [3]. At higher current densities, the cell voltage drops drastically as a result of mass transport loss, meaning that the mass transport controls the performance and power range of RFBs [4]. The poor design of electrode microstructure is one of the main causes of this occurrence. Hypothetically, it can be overcome by tailoring or engineering the microstructure of the electrode. Therefore, the reactive transport of ionic solution in RFBs has been simulated in porescale using Pore Network Modelling (PNM) to investigate the effect of the electrode microstructure on the performance of RFBs. This work focused on Hydrobromic Acid (HBr) RFBs that hydrogen gas is oxidized in the anode and the produced protons are transferred to the cathode to reduce bromine in the cathode. By use of two unstructured and structured pore networks and two interdigitated and flowthrough flow patterns, the performance of RFBs were investigated. This work aims to optimize the electrode microstructure to broaden the power output of RFBs. Initial results show that species are mostly consumed in the outlet and the proximity of the membrane, mainly as a result of lower advective force in these areas. Consequently, bigger overpotentials were observed in these regions due to the lack of species supply. Also, concentration distribution in the flowthrough pattern was more uniform than the interdigitated one. This can be explained by the electrolyte flow direction in the electrode and greater advection force in the flowthrough pattern.
The process of indentation by a rigid tool has been widely studied for its versatility as an experimental technique to probe constitutive properties of materials of various kinds across multiple scales. Recently the technique has been applied to characterize poroelasticity of soft materials such as polymeric gels via load relaxation experiments, where an indenter is pressed instantaneously to a fixed depth and held until the indentation force approaches a horizontal asymptote. Assuming incompressibility in both the solid and fluid phases, elastic constants are determined from the early and late time responses, while the hydraulic diffusivity is obtained from the transient response by matching the experimentally obtained indentation force as a function of time against a master curve obtained from FEM simulations [1]. The numerical analysis assumes a negligible effect of the Poisson’s ratio and a mixed drainage surface condition where the area underneath the indenter is impermeable while the region outside is fully drained.
Motivated by these experimental advances in soft materials, we analyze indentation of a poroelastic solid by a sphericaltip tool within the framework of Biot’s theory. The McNameeGibson displacement function method is employed to solve the cases where the indenter is subjected to a step displacement loading. Three types of surface drainage conditions, namely, fully drained, fully undrained and mixed drainage, are analyzed. Compressibility of both the fluid and solid phases is considered in these solutions. Though derivation of these theoretical solutions requires the aid of a variety of mathematical techniques to overcome the difficulties related to integrals with rapidly oscillating kernels and solving the Fredholm integral equation of the second kind, the results in terms of the normalized indentation force relaxation with time are remarkably simple. The transient force responses show only weak dependence on one derived material constant and can be fitted by elementary functions, which lend themselves to convenient use for material characterization in the laboratory.
In this work we present opensource solvers, based on the finite volume library OpenFOAM, for solving the StokesPoissonNernstPlanck (SPNP) system of equations for single or multidomain ionic transfer. Many applications that involve said ionic transport, e.g reinforced concrete [1], batteries [3] and oil extraction [2], also involve heterogeneous reactions between domains. As such, interface conditions have been formulated and implemented to model this mass exchange between ionic species.
After outlining the governing equations, a dimensional analysis will be presented to note the various transport regimes capable of being seen under different scenarios by quantifying ratios between transport phenomena. We then discuss the features and capabilities of the porescale solvers (pnpFoam and pnpMultiFoam), as well as the heterogeneous reactive conditions (mappedChemicalKinetics). These solvers and conditions will then be verified under different test cases by comparing results against highorder spectral results obtained with the
MatLab toolbox Chebfun. Since a large number of applications of SPNP involve complex porous geometries (e.g., batteries involve a porous solid electrode flooded with fluid electrolyte), we consider the case of two and threedimensional randomly generated porous domain of solid and fluid [5]. Preliminary results will be presented to determine the set of geometrical parameters, through uncertainty quantification, that have significant effect on the ionic transport.
Solving at the microscale over complex porous mediums involving large scales seen in many applications is computationally intensive. Later work will be outlined to accommodate this by formulating homogenized models, parametrising the geometrical complexity, and developing therefore novel macroscopic model suitable for dominant reaction and fast ionic transfer regimes [4].
[1] Nmeek, J., Kruis, J., Koudelka, T. and Krej, T. (2018). Simulation of chloride migration in reinforced concrete. Applied Mathematics and Computation, 319, 575585. https://doi.org/10.1016/j.amc.2017.07.029
[2] Mohammadi, S., Mahani, H., Ayatollahi, S. and Niasar, V. (2020). Impact of Oil Polarity on the Mixing Time at the Pore Scale in Low Salinity Waterflooding. Energy and Fuels, 34(10), 1224712259. https://doi.org/10.1021/acs.energyfuels.0c01972
[3] Richardson, G., Foster, J., Ranom, R., Please, C. and Ramos, A. (2020). Charge transport modelling of lithium ion batteries. arXiv:2002.00806
[4] Municchi, F. and Icardi, M. (2020). Macroscopic models for filtration and heterogeneous reactions in porous media. Advances in Water Resources, 141, 103605. https://doi.org/10.1016/j.advwatres.2020.103605
[5] F. Municchi, N.D. Pasquale, Dentz M. and Icardi, M., Heterogeneous MultiRate mass transfer models in OpenFOAM, Computer Physics Communications, https://doi.org/10.1016/j.cpc.2020.107763
Geomechanical deformation can alter the flow field which impacts solute mass fluxes. Despite its importance, the effects of the coupling between geomechanical deformation and the flow field on solute transport behavior are not fully known. In this work, we study the impact of this coupling on the solute concentration distribution. The concentration field is semianalytically derived by making use of the Generalized Integral Transform Technique. We apply the semianalytical solution to two uniaxial consolidation problems, the classical Terzaghi's problem with a constant load and the case of periodic loading of a porous deformable layer. Our results indicate that geomechanical parameters, such as the Skempton's coefficient and the soil compressibility, can affect the peak concentration as well as the spatial moments of solute plume. In case of periodic loading, we show that the frequency of loading also plays a key role in regulating the temporal dynamics of the concentration field.
We consider a mathematical model for twophase immiscible flow in a porous medium. A solute is present in and transported by one fluid phase, leading to a nonconstant surface tension. At the scale of pores, the main challenge is to account for the movement of the fluidfluid interfaces, depending on the velocities and pressures of the two fluids, and on the concentrationdependent surface tension.
Using asymptotic methods, an upscaled, Darcyscale model is derived. This is expressed in terms of effective macroscopic quantities, like saturation, concentration, pressure or Darcy velocity. In view of simplicity, we use first a twodimensional strip as starting geometry at the pore scale. Then we consider a periodically perforated medium as a more general representation of a porous medium. In the former case, the evolving fluidfluid interface is modelled as a freely moving sharp interface. In the latter case, a phasefield formulation is used. Employing asymptotic expansion methods and periodic homogenization, the corresponding Darcyscale models are derived. For validating the results, we compare the numerical results for the Darcy scale models with those obtained by averaging the numerical results obtained for the porescale models.
We present a new concept for modelling singlephase flow and energy transport in porous media including conditions under which local thermal equilibrium cannot be assumed. A dual network model is introduced based on a recently developed algorithm to represent both the pore space and the solid grain matrix in a porous medium by interconnected networks.
Heat and mass transfer are considered simultaneously, allowing to naturally model scenarios with heterogeneous temperature distributions in both void space and solid matrix. We suggest a discretisation of mass, momentum, and energy balance equations using a dual network representation.
The new approach is compared with 3D conjugate heat transfer simulations
for both conduction and convectiondominated scenarios.
Wetting films can develop in the corners of pores in porous media under strong wetting conditions where the contact angle allows the wetting phase to invade the corner. Such corner flow has a significant influence on the twophase flow dynamics. Compared with the main meniscus rising within a pore, the wetting corner film is much thinner and can lie significantly ahead. Modeling the dynamics of corner film remains elusive using direct numerical simulation method because of the significant scale difference between main meniscus flow and corner film flow. In this presentation, we propose a dynamic pore network model for imbibition simulation which can accurately account for corner flow. First, a modified interacting capillary bundle model is presented to describe the liquid imbibition dynamics in a single angular tube with corner films. In this model, a square tube is decomposed into several interacting subcapillaries with the first subcapillary representing the main meniscus and the other ones representing the corner films. The conductance of each subcapillary is calculated based on singlephase lattice Boltzmann simulation. The modified interacting capillary bundle model is validated by comparing its results with the twophase lattice Boltzmann simulation results for the same geometry. Then this modified interacting capillary bundle model is incorporated into a dynamic pore network model with singlepressure algorithm. Thus the pore network is decomposed into several layers of interacting subporenetworks where the first layer of subporenetwork simulates the main meniscus flow in the porous media while the other sub layers simulate the corner film flow. The snap off mechanism is also introduced into the model, which plays an important role under low flow rate condition. Finally, both the proposed dynamic pore network model and a twophase lattice Boltzmann model are used to simulate wetting fluid redistribution in a porous medium induced by capillary force and corner film flow. The good agreement between the simulation results of both methods demonstrates the accuracy of the proposed dynamic pore network model in considering corner flow.
The modelling of multiphase flow and mechanical response in fractured chalk formations due to oil and gas explotation is of major importance in the understanding of the subsurface processes and the environmental impact associated with such activities. In addition, this knowledge is highly essential to predict unwanted effects from future carbon capture and storage (CCS) practices [13] and geothermal applications [46]. On the modelling of the fractures in porous media there are basically two classes of methods: (a) continuum methods [79] (or implicit methods), in which fractures and porous matrix are represented by two overlapping continua and a transfer function is used to model the interaction between these two, and (b) discrete methods [10–13] (or explicit methods), in which two different grids are used for fractures and porous matrix and the interplay between these two is represented explicitly. Employing a discrete method allows a more accurate representation of the fractures and subsequently the interplay between these and the porous matrix, but at the expense of a larger computational cost. The continuum approach presents a much lower computational cost. However, the existence of a representative elementary volume (REV) and accurate homogeneous parameters cannot be guaranteed [14]. Furthermore, previous works have shown that averaging the heterogeneous aperture to scale up permeability results in an underestimated fluid flow pattern [15], indicating the necessity of incorporating full aperture distributions rather than simplified aperture representations in reservoirscale flow models [16–18]. Given the importance of the fractures modelling for accurate predictions of the fluid flow patterns and the extra cost involved in employing a discrete method, mixeddimensional models [10,12,19], in which porous matrix is modelled as a $d$dimensional entity, whereas fractures are modelled as $(d1)$dimensional entities, were developed aiming a cheaper but accurate framework. This work explores the reduction of twodimensional fracture objects obtained from images to onedimensional objects, such that a mixeddimensional model might be employed. A skeletonization technique [20] along with a skeleton network generation [21] are employed for extraction of the onedimensional fracture object, while medial axis [22] is used for aperture distribution calculation. The mesh generated through this framework is used in numerical simulations carried with the mixeddimensional model for fluid flow in fractured porous media.
This study proposes and demonstrates a new porenetwork modeling approach to simulate singlephase reactive transport and mineral dissolution in porous media. A new algorithm for the merging of pores and throats resulting from solid dissolution is introduced to guarantee the conservation of the main variables of interest during the merging process. Pore surface areas and throat conductances are modeled accurately using a novel application of correction factors and effective properties. Hence, the main objective of this presentation is to discuss this novel merging methodology and some applications in regular and random porenetwork models. Our approach solves a coupled transport and reaction porenetwork model that implements a kinetic model with a single heterogeneous chemical reaction describing the dissolution of calcite by acidic solutions. The reactive transport problem is described by the acid advectiondiffusion transient equation in control volumes represented by pores and throats. The network geometry is updated based on the dissolution process happening at the mineral surface. Pores and throats are enlarged due to mineral consumption. The merging method is performed when two connected pores reach each other. Pore spaces are relocated in the network and correction factors are updated to conserve the effective surface areas and effective conductance of throats. The fluid flow field is also updated due to these new larger sizes of pores and throats. A wide range of porenetwork models are used to study the reactive transport problem. The main results include the exploration of different dissolution regimes through porositypermeability evolution curves, acid concentration profiles, and the use of statistical criteria to differentiate regimes. Importantly, this methodology has the ability to simulate permeability increases larger than 100fold during the formation of preferential pathways through the network. The innovative approaches presented may be used to improve the representation of many subsurface applications where reactive transport and mineral dissolution are the fundamental phenomena at the porescale, including performance of acidizing for stimulation, geological storage of carbon dioxide ($CO_2$), and enhanced oil recovery.
Anthropogenic and natural fractured aquifers are common examples of dual porosity matrixfracture systems, where the fracture network provides highlyconductive flow pathways and the lowpermeability matrix stores most of the fluid. Fluid production or extraction leads to land subsidence and potentially to induced seismicity. Mechanical deformations have recently been proposed as effective monitoring tools for reservoir characterization, complementing flow data.
Coupled flow and mechanical deformation in fractured media is often modeled using the classical theory of dualporosity poroelasticity (DPP), based on Barenblatt's hypothesis of pressure equilibrium inside the rock matrix blocks. However, classical DPP cannot be expected to upscale flow and deformation in fractured rocks when nonequilibrium effects are relevant. Equilibrium can be expected to appear if the matrix blocks are small, so that the matrix diffusion time is comparable to the flow time scales along the fractures. In practice, matrix blocks may be large enough so that diffusion time scales are long, and the equilibrium hypothesis breaks down.
We study nonequilibrium effects in coupled flow and deformation in fractured media through a theoretical nonequilibrium, dualporosity model. We use this theory to obtain the scalings for drainage and displacement to be expected for coupled flow and deformation in highlyheterogeneous, fractured porous media. The theoretical model allows to identify what behavior to expect in fractured aquifers and reservoirs, revealing the limitations of classical DPP formulations.
We compare analytical predictions and scalings with highfidelity numerical simulations, where we describe the coupled flow and deformation for both the rock matrix and a network of discrete fractures, explicitly represented by lowerdimensional (1D) objects. The results show strong tailing in land subsidence and fluid fluxes that cannot be captured by classical DPP or single porosity effective medium approaches. Conversely, theoretical predictions from the multirate DPP model and the highfidelity numerical simulations agree, even for highly heterogeneous matrixfracture systems.
Acknowledgements
Sandro Andrés gratefully acknowledges funding from the Spanish Ministr