InterPore2022

Session

MS07

31 May 2022, 10:30

73. Simulation of reactive transport in heterogeneous porous media with a Newton-Krylov method

Michel Kern (Inria)

31/05/2022, 10:30

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

148. An enhanced branch and bound algorithm for phase stability testing of multicomponent mixtures

Martin Jex (ctu fnspe)

31/05/2022, 10:45

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

153. Modeling of Multicomponent Flow in Porous Media using Higher-Order Methods

Petr Gális (Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague)

31/05/2022, 11:00

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

529. A numerical approach to incorporating shear thinning effects of polymer in polymer flooding.

Prof. Prabir Daripa (Texas A&M University)

31/05/2022, 11:15

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

230. Development and experimental validation of lattice Boltzmann method-based simulator for vapor transport in air over a moist soil layer

Jakub Klinkovský (Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague)

31/05/2022, 11:30

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

445. Phase-wise Conservative and Physics Preserving Algorithms for Porous Media Flow

Prof. Shuyu Sun (King Abdullah University of Science and Technology (KAUST))

31/05/2022, 11:45

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

484. Thermodynamics-Informed Neural Network for Phase Equilibrium in Subsurface Reservoirs

tao zhang (King Abdullah University of Science and Technology)

31/05/2022, 12:00

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

562. Tightly Coupled Hyperbolic Treatment of Buoyant Two-Phase Flow and Transport in Porous Media

Prof. Patrick Jenny (Swiss Federal Institute of Technology, Switzerland)

31/05/2022, 12:15

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

9. The numerical solution of the micro-scale phase-field equation and its role in a two-scale two-phase flow model.

Manuela Bastidas (Inria. Paris, France)

01/06/2022, 10:30

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

47. Upscaling of phase-field models for two-phase flow based on fluid morphology

Mr Mathis Kelm (University Stuttgart)

01/06/2022, 10:45

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

60. Micro-macro models for reactive two-mineral systems

Nadja Ray (Friedrich-Alexander Universität Erlangen-Nürnberg)

01/06/2022, 11:00

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

88. A phase-field approach to model evaporation in porous media: Upscaling from pore to Darcy scale

Mr Tufan Ghosh (Institute for Modelling Hydraulic and Environmental Systems (IWS), University of Stuttgart)

01/06/2022, 11:15

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

130. Upscaling and Automation: Pushing the Boundaries of Multiscale Modeling through Symbolic Computing

Kyle Pietrzyk (Stanford University)

01/06/2022, 11:30

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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.,...

501. Population Balance Equation for Porous Media: Upscaled Dynamics and Evolution

Nicodemo Di Pasquale (University of Manchester)

01/06/2022, 11:45

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

539. Influence of Pore Morphology on Mechanical Properties of Second Gradient Materials

Pania Newell (The University of Utah)

01/06/2022, 12:00

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

308. A multipoint stress-flux mixed finite element method for the Stokes-Biot fluid poroelastic structure interaction model

Ivan Yotov (University of Pittsburgh)

01/06/2022, 14:05

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

405. Reliable and efficient error estimates for nonlinear flow processes using linear iterative schemes

Dr Koondi Mitra (Radboud University)

01/06/2022, 14:20

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

517. Positive DDFV scheme for degenerate parabolic equations arising from infiltration problem

Prof. Mazen Saad (Ecole Centrale de Nantes)

01/06/2022, 14:35

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

232. Numerical Analysis of a Mixed Finite Element Approximation a Model of Biofilm Growth in Porous Media

Dr Azhar Alhammali (Imam Abdulrahman Bin Faisal University)

02/06/2022, 11:20

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

295. Differentiation in biological porous media: a role for diffusiophoresis and surface instabilities

Prof. Jacques Huyghe (University of Limerick, Eindhoven University of Technology)

02/06/2022, 11:35

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

316. A One-domain approach for flow near porous media boundaries

Dr Didier Lasseux (CNRS - Univ. Bordeaux)

02/06/2022, 11:50

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

548. Linear lignin as a potential consolidant for archaeological wood treatment: a hybrid Monte Carlo and molecular dynamics study

Ali Shomali (ETH Zurich)

02/06/2022, 12:05

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

65. An efficient preconditioning framework for the coupled simulation of contact mechanics with hydraulically active fractures

Laura Gazzola (University of Padova)

02/06/2022, 13:30

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

128. Simulation of interface-coupled porous-medium applications using partitioned coupling methods

Alexander Jaust (University of Stuttgart)

02/06/2022, 13:45

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

242. Coupled flow in porous media with thin inclusions: preconditioning based on rational approximations of the fractional interface operators

Prof. Svetozar Margenov (Institute of Information and Communication Technologies, BAS)

02/06/2022, 14:00

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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,...

498. Solvers for Coupled PDE Problems in Porous Media Science

Dr Arne Naegel (Goethe-University Frankfurt)

02/06/2022, 14:15

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

564. Coupled Thermo-Hydro-Mechanical-Chemical Analysis of CO2 Injection in a North Sea Chalk Reservoir

Mr Seyedbehzad Hosseinzadeh (Technical University of Denmark)

02/06/2022, 14:30

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...

201. Numerical modelling the hydromechanical behavior of undrained triaxial tests on saturated concrete

Mr Jinzhou Bai (Univ. Lille, CNRS, UMR 9013-LaMcube-Laboratoire de Mécanique, Multiphysique, Multi-échelle)

02/06/2022, 14:45

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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....

550. Numerical investigation of the flow and phase transitions of CO2 near its triple-point during a blowout from a plugged well

Pramod Bhuvankar (Lawrence Berkeley National Laboratory)

02/06/2022, 15:00

(MS07) Mathematical and numerical methods for multi-scale multi-physics, nonlinear coupled processes

Oral Presentation

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...