Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media
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Abstract
This paper presents a novel technique for upscaling multiphase fluid flow in complex porous materials that combines asymptotic homogenization approach with hydrodynamicand thermodynamic bounds. Computational asymptotic homogenization has been widely utilised in solid mechanics as a method for analysing multiscale expansion and convergence coefficients in heterogeneous systems. Computations are performed over several volumes by increasing the size until convergence of the material parameters under different load scenarios is achieved. It works by simplifying the problem with a homogenization method and is ideally suited for estimating the representative elementary volume of microporous material by expanding algorithms. The validity of the method to include complex multiphase hydrodynamic processes and their interaction with the matrix structure of porous media lacks a sound theoretical foundation. To overcome this problem, a variational thermodynamic approach is used. Upper and lower bounds of entropy production are proposed to provide effective material properties with uncertainties. This allows multiple possibilities to address dynamics via thermodynamically linked processes. This work utilizes volume of fluid approach to model multiphase porous media flow in models based on micro-computerized tomography x-ray data of Bentheimer sandstone and Savonnieres carbonate. It is found that the representative elementary volume sizes obtained by the conventional asymptotic homogenization methods do not satisfy thermodynamic bounds which consistently require larger representative elementary volume sizes. For the Savonnieres carbonate the entropic bounds have not converged fully questioning the reliability of the effective properties obtained from the classical method.
Document Type: Original article
Cited as: Hussain, S. T., Regenauer-Lieb, K., Zhuravljov, A., Hussain, F., Rahman, S. S. Asymptotic hydrodynamic homogenization and thermodynamic bounds for upscaling multiphase flow in porous media. Advances in Geo-Energy Research, 2023, 9(1): 38-53. https://doi.org/10.46690/ager.2023.07.05
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Aliseda, A., Heindel, T. J. X-ray flow visualization in multiphase flows. Annual Review of Fluid Mechanics, 2021, 53: 543-567.
Alpak, F. O., Berg, S., Zacharoudiou, I. Prediction of fluid topology and relative permeability in imbibition in sandstone rock by direct numerical simulation. Advances in Water Resources, 2018, 122: 49-59.
Al-Raoush, R., Papadopoulos, A. Representative elementary volume analysis of porous media using X-ray computed tomography. Powder Technology, 2010, 200(1-2): 69-77.
Aniszewski, W., Ménard, T., Marek, M. Volume of fluid (VOF) type advection methods in two-phase flow: A comparative study. Computers & Fluids, 2014, 152: 193-194.
Bear, J. Dynamics of fluids in porous media. Soil Science, 1975, 120: 162-163.
Bultreys, T., Stappen, J. V., Kock, T. D., et al. Investigating the relative permeability behavior of microporosity-rich carbonates and tight sandstones with multiscale pore network models. Journal of Geophysical Research: Solid Earth, 2016, 121(11): 7929-7945.
Bultreys, T., Van Hoorebeke, L., Cnudde, V. Multi-scale, micro-computed tomography-based pore network models to simulate drainage in heterogeneous rocks. Advances in Water Resources, 2015, 78: 36-49.
Costanza-Robinson, M. S., Estabrook, B. D., Fouhey, D. F. Representative elementary volume estimation for porosity, moisture saturation, and air-water interfacial areas in unsaturated porous media: Data quality implications. Water Resources Research, 2011, 47(7): W07513.
Dai, Z., Middleton, R., Viswanathan, H., et al. An integrated framework for optimizing CO2 sequestration and enhanced oil recovery. Environmental Science & Technology Letters, 2014, 1(1): 49-54.
Dautriat, J., Gland, N., Guelard, J., et al. Axial and radial permeability evolutions of compressed sandstones: End effects and shear-band induced permeability anisotropy. Pure and Applied Geophysics, 2009, 166(5): 1037-1061.
Deshpande, S. S., Anumolu, L., Trujillo, M. F. Evaluating the performance of the two-phase flow solver interFoam. Computational Science & Discovery, 2012, 5(1): 014016.
Diwakar, M., Kumar, M. A review on CT image noise and its denoising. Biomedical Signal Processing and Control, 2018, 42(1): 73-88.
Dong, H., Blunt, M. J. Pore-network extraction from micro-computerized- tomography images. Physical Review E, 2009, 80(3): 036307.
Gharbi, O., Blunt, M. J. The impact of wettability and connectivity on relative permeability in carbonates: A pore network modeling analysis. Water Resources Research, 2012, 48(12): W12513.
Greenshields, C. OpenFOAM v10 User Guide, 2022.
Hansen, A., Sinha, S., Bedeaux, D., et al. Relations between seepage velocities in immiscible, incompressible twophase flow in porous media. Transport in Porous Media, 2018, 125(3): 565-587.
Hirt, C. W., Nichols, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 1981, 39(1): 201-225.
Hussain, F., Pinczewski, W. V., Cinar, Y., et al. Computation of relative permeability from imaged fluid distributions at the pore scale. Transport in Porous Media, 2014, 104(1): 91-107.
Hussain, S. T., Rahman, S. S., Azim, R. A., et al. Multiphase fluid flow through fractured porous media supported by innovative laboratory and numerical methods for estimating relative permeability. Energy & Fuels, 2021, 35(21): 17372-17388.
Jacquey, A. B., Regenauer-Lieb, K. Thermomechanics for geological, civil engineering and geodynamic applications: Rate-dependent critical state line models. Rock Mechanics and Rock Engineering, 2021, 54(10): 5355-5373.
Jiang, F., Tsuji, T. Estimation of three-phase relative permeability by simulating fluid dynamics directly on rock-microstructure images. Water Resources Research, 2017, 53(1): 11-32.
Joekar-Niasar, V., van Dijke, M. I. J., Hassanizadeh, S. M. Pore-scale modeling of multiphase flow and transport: Achievements and perspectives. Transport in Porous Media, 2012, 94(2): 461-464.
Karnakov, P., Litvinov, S., Koumoutsakos, P. A hybrid particle volume-of-fluid method for curvature estimation in multiphase flows. International Journal of Multiphase Flow, 2020, 125: 103209.
Khodadadi, B., Qadeer Siddiqui, M. A., Pirzada, M. A., et al. Direct observation of two-phase flow in deformable fractures of shales: A Utica shale example. Journal of Petroleum Science and Engineering, 2020, 194: 107487.
Kjelstrup, S., Bedeaux, D., Hansen, A., et al. Non-isothermal transport of multi-phase fluids in porous media. The entropy production. Frontiers in Physics, 2018, 6: 126.
Lanetc, Z., Zhuravljov, A., Armstrong, R. T., et al. Hybrid numerical methods for modelling multi-physics mass transport in coal. International Journal of Heat and Mass Transfer, 2023, 214: 124386.
Leu, L., Berg, S., Enzmann, F., et al. Fast X-ray microtomography of multiphase flow in berea Ssandstone: A sensitivity study on image processing. Transport in Porous Media, 2014, 105: 451-469.
Liao, Q., Xue, L., Wang, B., et al. A new upscaling method for microscopic fluid flow based on digital rocks. Advances in Geo-Energy Research, 2022, 6(4): 357-358.
Liu, T., Jin, X., Wang, M. Critical resolution and sample size of digital rock analysis for unconventional reservoirs. Energies, 2018a, 11: 1798.
Liu, J., Regenauer-Lieb, K. Application of percolation theory to microtomography of rocks. Earth-Science Reviews, 2021, 214: 103519.
Liu, J., Sarout, J., Zhang, M., et al. Computational upscaling of Drucker-Prager plasticity from micro-CT images of synthetic porous rock. Geophysical Journal International, 2018b, 212: 151-163.
Liu, T., Wang, M. Critical REV size of multiphase flow in porous media for upscaling by pore-scale modeling. Transport in Porous Media, 2022, 144(1): 111-132.
Liu, T., Zhang, S., Wang, M. Does rheology of bingham fluid influence upscaling of flow through tight porous media? Energies, 2021, 14(3): 680.
Mahmud, H. B., Khalifa, M., Shafiq, M., et al. Experimental investigation of the influence of carbonated water on sandstone and carbonate rock properties. Petroleum Research, 2022, in press, https://doi.org/10.1016/j.ptlrs.2022.10.007.
Mirzaei-Paiaman, A., Saboorian-Jooybari, H., Chen, Z., et al. New technique of trueeEffective mobility (TEMFunction) in dynamic rock typing: Reduction of uncertainties in relative permeability data for reservoir simulation. Journal of Petroleum Science and Engineering, 2019, 179: 210-227.
Mostaghimi, P., Blunt, M. J., Bijeljic, B. Computations of absolute permeability on micro-CT images. Mathematical Geosciences, 2013, 45(1): 103-125.
Moukalled, F., Mangani, L., Darwish, M. The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab. New York, USA, Springer International Publishing, 2016.
Niederau, J., Clauser, C., Börsing, N., et al. Entropy production and attractors: Measures to quantify uncertainty and complexity introduced by convection. Paper Presented at the European Geothermal Conference, Strasbourg, France, 19-24 September, 2016.
Øren, P. E., Bakke, S., Arntzen, O. J. Extending predictive capabilities to network models. SPE Journal, 1998, 3(4): 324-336.
Patankar, S. Numerical Heat Transfer and Fluid Flow. Boca Raton, USA, CRC Press, 2018.
Pavuluri, S., Maes, J., Doster, F. Spontaneous imbibition in a microchannel: Analytical solution and assessment of volume of fluid formulations. Microfluidics and Nanofluidics, 2018, 22(8): 90.
Peksa, A. E., Wolf, K. H. A. A., Zitha, P. L. J. Bentheimer sandstone revisited for experimental purposes. Marine and Petroleum Geology, 2015, 67: 701-719.
Pirzada, M. A., Bahaaddini, M., Andersen, M. S., et al. Coupled hydro-mechanical behaviour of rock joints during normal and shear Loading. Rock Mechanics and Rock Engineering, 2023, 56: 1219-1237.
Ramstad, T., Berg, C. F., Thompson, K. Pore-scale simulations of single- and two-phase flow in porous media: Approaches and applications. Transport in Porous Media, 2019, 130(1): 77-104.
Regenauer-Lieb, K., Hu, M., Schrank, C., et al. Cross-diffusion waves resulting from multiscale, multiphysics instabilities: Application to earthquakes. Solid Earth, 2021a, 12: 1829-1849.
Regenauer-Lieb, K., Hu, M., Schrank, C., et al. Cross-diffusion waves resulting from multiscale, multi-physics instabilities: Theory. Solid Earth, 2021b, 12(8): 869-883.
Regenauer-Lieb, K., Karrech, A., Chua, H. T., et al. Time-dependent, irreversible entropy production and geodynamics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010, 368(1910): 285-300.
Regenauer-Lieb, K., Karrech, A., Chua, H., et al. Entropic bounds for multi-scale and multi-physics coupling in earth sciences. Beyond the Second Law, 2014: 323-335.
Regenauer-Lieb, K., Veveakis, M., Poulet, T., et al. Multiscale coupling and multiphysics approaches in earth sciences: Theory. Journal of Coupled Systems and Multiscale Dynamics, 2013, 1(1): 49-73.
Rusche, H. Computational Fluid Dynamics of Dispersed Two- Phase Flows at High Phase Fractions. London, UK, Imperial College London, 2003.
Ruspini, L. C., Øren, P. E., Berg, S., et al. Multiscale digital rock analysis for complex rocks. Transport in Porous Media, 2021, 139(2): 301-325.
Shapoval, A., Zhuravljov, A., Lanetc, Z., et al. Pore-scale evaluation of physicochemical interactions by engineered water injections. Transport in Porous Media, 2023, 148(3): 605-625.
Shikhov, I., d’Eurydice, M. N., Arns, J. Y., et al. An experimental and numerical study of relative permeability estimates using spatially resolved NMR. Transport in Porous Media, 2017, 118: 225-250.
Sidorenko, M., Orlov, D., Ebadi, M., et al. Deep learning in denoising of micro-computed tomography images of rock samples. Computers & Geosciences, 2021, 151: 104716.
Singh, A., Regenauer-Lieb, K., Walsh, S. D. C., et al. On representative elementary volumes of grayscale micro-CT images of porous media. Geophysical Research Letters, 2020, 47(15): e2020GL088594.
Urakov, D. S., Rahman, S. S., Tyson, S., et al. Conceptualizing a dual porosity occurrence in sandstones by utilizing various laboratory methods. SOCAR Proceedings, 2021, 2: 6-16.
Veveakis, E., Regenauer-Lieb, K. Review of extremum postulates. Current Opinion in Chemical Engineering, 2015, 7: 40-46.
DOI: https://doi.org/10.46690/ager.2023.07.05
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