Reactive transport modeling in porous media involves the simulation of several physical and chemical processes: flow of fluid phases, transport of species and chemical reactions between species. After discretization, one obtains a highly nonlinear system of partial differential for transport, coupled to algebraic equations for chemistry.
In [1], we have presented a globally coupled...
The stability of matter is one of the fundamental problems of physics. In this contribution, we examine phase stability. From the mathematical point of view, the problem of coexistence or separation of phases can be formulated as a global optimization problem. We consider $VTN$-stability testing, i.e. the phase compostion of a mixture under fixed concentrations and temperature. Our goal is to...
A numerical scheme of higher-order approximation in both space and time for the single-phase multicomponent flow in porous media is presnted. The mathematical model consists of Darcy velocity, transport equations for components of a mixture, pressure equation and associated relations for physical quantities such as viscosity or density. The discrete problem is obtained using a combination of...
In mathematical modeling of chemical enhanced oil recovery by polymer flooding, it is desirable that non-Newtonian effects of polymer are properly accounted for. The two distinct effects that polymers exhibit are shear-thinning (stiff polymer) and visco-elasticity (flexible polymer). The shear thinning effect is important as the polymers used in chemical oil recovery are usually stiff...
We present an efficient computational approach for simulating component transport within single-phase free flow over a soil. A numerical model based on this approach is validated using controlled experiments in a climate-controlled low-speed wind tunnel. The wind tunnel is interfaced with a soil tank to study problems of heat and mass flux across the land-atmospheric interface. The developed...
Flow in geological porous media is central to a wide range of natural and industrial processes, including geologic CO2 sequestration, enhanced oil recovery, and water infiltration into soil. Petroleum engineers use reservoir simulation models to manage existing petroleum fields and to develop new oil and gas reservoirs, while environmental scientists use subsurface flow and transport models...
Multi-phase multi-component flows are the key problems needing to be solved in the study of subsurface geological formation and fluid flows, which are essentially required in the understanding and description of complicated heat and mass transfer behaviors commonly seen in oil and gas reservoirs. A large number of chemical species have been detected in the reservoir fluids, which challenges...
Buoyant incompressible multiphase flow and transport in porous media typically is simulated by coupling an elliptic flow equation with a hyperbolic transport description. The tight coupling between flow and transport either requires a fully implicit solution algorithm or very small time steps, if solved sequentially. In any case, however, a large linear system has to be solved each time...
Porous media are complex domains involving hierarchically organized structures, where various processes take place at different scales. An example in this sense is the fluid flow through the pores of a porous medium and, in particular, the two-phase flow. Prominent real-life applications in this sense are geological CO2 sequestration or oil recovery.
In [1], a two-scale model for two-phase...
Two-Phase flow in porous media is relevant for many applications and accurately capturing of interfacial effects in an effective model is central to its modeling. The flow morphology can vary significantly for different physical settings and impact the effective behaviour.
We use phase-fields to model two-phase flow on the pore scale with an advective Allen-Cahn formulation coupled to a...
Porous media naturally exhibit a heterogeneous structure including two different spatial scales: The pore/micro-scale is the fundamental scale, on which flow and reactive transport processes take place whereas the macro-scale, i.e. the scale of the porous medium itself, is of practical relevance for many geoscientific applications. (Periodic) homogenization has been successfully applied for...
We develop a phase-field model for evaporation in a porous medium by explicitly considering a vapor component together with the liquid and gas phases in the system. The phase-field model consists of the conservation of mass (for phases and vapor component), momentum, and energy. In addition, the evolution of the phase field is described by the Allen-Cahn equation. In the limit of vanishing...
In complex multi-scale system analysis, macroscopic differential equations are used to significantly increase computational efficiency and accurately model physical processes across multiple scales. Such equations can be systematically generated through rigorous upscaling techniques, which provide a priori error estimates and conditions under which the equations are valid (i.e.,...
Evolution and dynamics of particles have great importance in environmental, industrial and biological applications. One of the most known way to model their behaviour is through the Population Balance Equation (PBE). The PBE describes the evolution of the size $\ell$ of a population of particles, $f(\mathbf{x},\ell;t)$, through the reciprocal interactions of the particles within the population...
Porous materials with heterogeneous porous structures possess a wide range of mechanical, thermal, or electrical properties. Therefore, they are widely used in different engineering fields, such as energy-storage technology, geothermal engineering, and bio engineering. Considering the strong influence of pore morphology on material properties and their diverse application, over the years...
We develop a fully mixed formulation of the Stokes-Biot model for fluid poroelastic structure interaction and its mixed finite element approximation. The Stokes formulation is based on weakly symmetric deviatoric stress, velocity, and vorticity. The elasticity formulation is based on weakly symmetric stress, displacement, and rotation. The porous media flow formulation is based on Darcy...
Nonlinear advection-diffusion-reaction equations are used to model complex flow processes such as multiphase flow and flow through porous media/biological systems. When discretized in time, such equations result in a sequence of nonlinear degenerate elliptic problems which require linear iterative schemes to solve. The linear iterates can be used to provide upper/lower bounds to the error, and...
Nonlinear degenerate parabolic equations are the main core to study some complex problems arising from petroleum engineering and hydrology. In our study, the problem describes the infiltration of a single fluid through a porous medium with no gravity effects.
We carry out the convergence analysis of a positive DDFV (Dual Discrete Finite Volume) method for approximating solutions of...
We consider a coupled system of advection-diffusion-reaction PDEs modeling biofilm growth and nutrient consumption in porous media. One of the PDEs is subject to a constraint on the biomass density, so it can be formulated as a parabolic variational inequality (PVI). Moreover, the model is coupled to a heterogeneous Brinkman model of flow of an ambient fluid flowing within and outside the...
Biology is often explained in terms of biochemical pathways. In order for these pathways to work out, substantial logistics are needed to bring molecules to find their counterparts. Diffusion is typically the magic word that comes to rescue the transport mechanisms needed. Diffusion, however, results in homogenizing the medium, while differentiation is repeatedly the observed fact. This...
Momentum transport near porous media boundaries has been the subject of intense work for more than half a century since the pioneering work of Beavers and Joseph in 1967 [1,2]. Currently, there are two modeling strategies to study this subject: 1) A one-domain approach (ODA), where the spatial variations of average properties are accounted for in the transition zone and 2) a two-domain...
Lignin is one of the abundant polymers found in wood cell wall composite acting as the cohesive matrix that surrounds the wood holocellulose and provides increased hydrophobicity and chemical stability to the composite. Due to its less susceptibility to biological attack and high compatibility with holocellulose, synthesized lignin-like oligomers have been considered as potential consolidation...
The coupled simulation of frictional contact mechanics and fluid flow in fractured porous media is attracting more and more attention in many subsurface applications, such as geothermal energy production, carbon dioxide sequestration, and underground gas storage. In these contexts, large computational domains are usually required to achieve the desired accuracy, along with high resolution...
Many real-world applications involve interface-coupled processes and porous media. Common examples are the hydromechanical coupling of liquid in a fracture under high pressure and the resulting deformation of the surrounding porous medium or coupled free and porous-medium flow. These examples play an important role in hydraulic simulations or simulations of filters. Moreover, the underlying...
Flow in porous media with inclusions is a determining processes within natural and artificial materials [6]. One important feature of thin inclusions is that they represent fractures. In fractured formations, the equations are strongly coupled, so the accurate and robust numerical methods are of great importance.
Flow in fractured porous media is a typical example of non-local process,...
Developing efficient solvers for coupled PDE systems is often a non-trivial task, since one must to combine suitable schemes for time integration and linear solvers, which is suitable for HPC systems. In this study, we present a unified solver framework, which combines a linearly-implicit extrapolation scheme with a scalable multigrid solver.
The effectiveness of the approach is...
Growing global demand for renewable energy and reducing CO2 emissions drive researchers to materialize Carbon Capture and Storage (CCS) to achieve a net-zero emission by 2050. With several depleted offshore hydrocarbon fields, Denmark is taking this opportunity to reduce the CO2 levels during the energy transition from fossil fuels to renewable energy. However, most reservoirs in the Danish...
Concrete structures constitute a large portion of civil engineering constructions, such as building, hydroelectric dams and bridges, etc. Due to the relatively small permeability of concrete, the cores of these structures could remain quasi-saturated during most of their lifetime even though their facings dry very quickly. A heterogenetic distribution of free water content is then observed....
The dry-ice formation of CO2 near its triple-point can occur during a blowout event in plugged wells, and this process can impact the mass flux of the leaking CO2. From a risk assessment standpoint relating to geologic carbon sequestration, we wish to understand which scenarios will lead to the dry-ice formation, and how this process affects the CO2 flux. In the current work we present a...
