Simulation of Multiphase Flow in Hybrid-Scale Deformable Porous Media

This solver simulates two-phase flow in deformable porous media that contains two characteristic length scales: a large scale solid-free domain where flow is solved through the Volume-Of-Fluid Method, and a small scale porous domain where flow is solved through two-phase Darcy's Law and Biot Theory. The solver is able to include wetting and capillary effects at both scales. Both domains are coupled and are solved simultaneously with a single momentum equation and within a single mesh.

This repository was created by Francisco J. Carrillo with the support of Ian C. Bourg.

Conceptual Representation of the Modeling Framework.

---

Contents

• General Information
• Installation
• Running the Tutorials
• List of Included Cases
• List of Included Libraries
• Citing the Toolbox
• Authors' Publications

General Information

• This toolbox is compatible with OpenFOAM 7.0
• This toolbox needs only a standard OpenFOAM installation (see www.openfoam.org)
• Read the LICENCE_OPENFOAM file for information about OpenFOAM and this toolbox Copyrights.

Installation

First, make sure to source the OpenFOAM file, as shown in the following example code:

source /opt/openfoam7x/etc/bashrc

Then, in the main "hybridBiotInterFoam" directory, run:

./Allwmake

This compiles the libraries "lporousInterfaceProperties.so", "lporousModels.so","lporousTwoPhaseProperties.so", "lporousImmiscibleIncompressibleTwoPhaseMixture.so", and "Herschel-Bulkley-Quemada.so" in the standard OpenFOAM user directory: $FOAM_USER_LIBBIN;

The two solver executables "elasticHBIF" and "plasticHBIF" are also compiled in the standard OpenFOAM user directory $FOAM_USER_APPBIN.The former deals with multiphase flow through and around poroelastic solids, the latter does the same but for poroplastic solids.

---

To remove temporary files, dynamic libraries, and executables, run:

./Allwclean

Running the Tutorials

To test if the solver was installed correctly, you can run all the included tutorial cases by typing the following code within the "tutorials" subdirectory:

python runTutorials.py

Note that this will only run each case for a single time step. Still, it might take a while. Also make sure to use python2 to run the associated script.

---

Each tutorial directory contains "run" and "clean" files to test installation and validate the solver. To run a particular tutorial for more than a single time step just replace "writeNow" with "endTime" within its "system/controlDict" file. Then you can run said tutorial by typing:

./run

or equivalently, for linear elastic systems:

elasticHBIF

and for plastic systems:

plasticHBIF

To clean the directory:

./clean

List of Included Cases

Linear Elastic Cases

• Test cases related to the verification of the solver for poroelastic porous media (Terzaghi consolidation problem and pressure-oscillation in poroelastic core).

---

Plastic Cases

• Test cases related to the verification of the solver for poroplastic porous media (fracturing in a Hele-Shaw cell and in low-permeability formations).

---

Example Applications/Case Templates

• Sample cases that show the multi-scale nature of this solver by simulating systems with a combination of porous and free-fluid regions (wave absorption in poroelastic coastal barriers and fracture-driven surface deformation). Each variable within the "0/" directory and the "constant" directory is labeled to make it easier to understand. There is a template for both elastic and plastic systems.

List of Included Libraries

porousInterfaceProperties

• Implementation of a constant contact angle interface condition at the porous media-fluid interface.

---

porousImmicscibleIncompressibleTwoPhaseMixture

• Implementation of an immicisble incompressible two-phase fluid class that allows for the use of porousInterfaceProperties

---

porousTwoPhaseProperties:

• Defenition of two-phase fluid properties that allows for the use of porousInterfaceProperties

---

HerschelBulkleyQuemada:

• Implementation of the Herschel-Bulkley-Quemada plasticity rheology model

---

porousModels/capillarityModels ( adapted from from Horgue P. & Soulaine C. (2015) )

• Capillary pressure models (Brooks and Corey, Van Genuchten, Linear)

---

porousModels/phaseModels ( adapted from from Horgue P. & Soulaine C. (2015) )

• Incompressible phase model for porous media flows (constant density and viscosity)

---

porousModels/relativePermeabilityModels ( adapted from from Horgue P. & Soulaine C. (2015) )

• Relative permeability models (Brooks and Corey, Van Genuchten)

Citing the Toolbox

If you use this solver, please cite the following paper (theory) and the code (implementation):

Paper: Carrillo, F. J., & Bourg, I. C. (2021). Modeling multiphase flow within and around deformable porous materials: A Darcy-Brinkman-Biot approach. Water Resources Research, 57, e2020WR028734. https://doi.org/10.1029/2020WR028734

Code: https://doi.org/10.5281/zenodo.4013969 (DOI: 10.5281/zenodo.4013969)

Authors' Publications

1. Carrillo, F. J., Bourg, I. C., 2019. A darcy-brinkman-biot approach to modeling the hydrology and mechanics of porous media containing758 macropores and deformable microporous regions. Water Resources Research 55, 8096–8121
2. Carrillo F.J., Bourg, I. C., Soulaine, C., Multiphase flow modeling in multiscale porous media: An open-source micro-continuum approach, J. Comput. Phys. (2020), https://doi.org/10.1016/j.jcpx.2020.100073
3. Soulaine, C., Gjetvaj, F., Garing, C., Roman, S., Russian, A., Gouze, P., Tchelepi, H., May 2016. The impact of sub-resolution porosity of918 x-ray microtomography images on the permeability. Transport in Porous Media 113 (1), 227–243.919
4. Soulaine, C., Roman, S., Kovscek, A., Tchelepi, H. A., 2017. Mineral dissolution and wormholing from a pore-scale perspective. Journal of920 Fluid Mechanics 827, 457–483.921 URL https://www.cambridge.org/core/product/identifier/S0022112017004992/type/journal_article922
5. Soulaine, C., Roman, S., Kovscek, A., Tchelepi, H. A., 2018. Pore-scale modelling of multiphase reactive flow. Application to mineral923 dissolution with production of CO2. Journal of Fluid Mechanics 855, 616–645.924 Soulaine, C., Tchelepi, H.A., 2016.Micro-continuumapproachforpore-scalesimulationofsubsurface processes.TransportIn PorousMedia925 113, 431–456
6. Soulaine, C., Creux, P., Tchelepi, H. A., 2019. Micro-continuum framework for pore-scale multiphase fluid transport in shale formations.916 31 Transport in Porous Media.
7. Horgue, P., Soulaine, C., Franc, J., Guibert, R., Debenest, G., 2015. An open-source toolbox for multiphase flow in porous media. Computer810 Physics Communications 187 (0), 217– 226