Multiscale modeling for multiphase flow and reactive mass transport in subsurface energy storage: A review
Abstract
Modeling of multiphase flow and reactive mass transport in porous media remains a pivotal challenge in the realm of subsurface energy storage, demanding a nuanced understanding across varying scales. This review paper presents a comprehensive overview of the latest advancements in multiscale modeling techniques that address the inherent complexity of these processes. Three cutting-edge approaches are presented: hybrid multiscale simulation, which leverages both continuum and discrete modeling frameworks to enhance model fidelity; approximated physics, which simplifies complex reactions and interactions to expedite computations without significantly sacrificing accuracy; and machine-learning-assisted multiscale simulation, which integrates predictive analytics to refine simulation outputs. Each method presents distinct advantages and hurdles, collectively advancing the precision and computational efficiency of subsurface modeling. Despite the substantial progress, we recognize the persistent challenges, such as the need for more robust coupling techniques, the balance between model complexity and computational feasibility, and effectively combining machine learning with traditional physical models. Promising directions for future work are discussed to address these challenges, aiming to push the boundaries of current multiscale modeling capabilities.
Document Type: Invited review
Cited as: Lyu, X., Wang, W., Voskov, D., Liu, P., Chen, L. Multiscale modeling for multiphase flow and reactive mass transport in subsurface energy storage: A review. Advances in Geo-Energy Research, 2025, 15(3): 245-260. https://doi.org/10.46690/ager.2025.03.07
Keywords:
Multiscale modeling, multiphase flow, reactive mass transfer, subsurface storage, porous mediaReferences
Abbaszadeh Shahri, A., Shan, C., Larsson, S. A novel approach to uncertainty quantification in groundwater table modeling by automated predictive deep learning. Natural Resources Research, 2022, 31(3): 1351-1373.
Abd, A. S., Abushaikha, A. S. Reactive transport in porous media: A review of recent mathematical efforts in modeling geochemical reactions in petroleum subsurface reservoirs. SN Applied Sciences, 2021, 3(4): 401.
Ahusborde, E., Amaziane, B., de Hoop, S., et al. A benchmark study on reactive two-phase flow in porous media: Part ii-results and discussion. Computational Geosciences, 2024, 28: 1-18.
Ajayi, T., Gomes, J. S., Bera, A. A review of CO2 storage in geological formations emphasizing modeling, monitoring and capacity estimation approaches. Petroleum Science, 2019, 16: 1028–1063. Amini, D., Haghighat, E., Juanes, R. Physics-informed neural network solution of thermo-hydro-mechanical processes in porous media. Journal of Engineering Mechanics, 2022, 148(11): 04022070.
Ardakani, S. H., Zingaro, G., Komijani, M., et al. An efficient reduced order model for nonlinear transient porous media flow with time-varying injection rates. Finite Elements in Analysis and Design, 2024, 241: 104237.
Awag, M., Mackay, E., Ghanbari, S. A numerical analysis of background flow velocity effects on long-term post-injection migration of CO2 plumes in tilted storage aquifers. Advances in Geo-Energy Research, 2024, 11(2): 103-114.
Balhoff, M. T., Thompson, K. E., Hjortsø, M. Coupling pore-scale networks to continuum-scale models of porous media. Computers & Geosciences, 2007, 33(3): 393-410.
Balhoff, M. T., Wheeler, M. F. A predictive pore-scale model for non-darcy flow in porous media. SPE Journal, 2009, 14(4): 579-587.
Bao, K., Yan, M., Allen, R., et al. High-performance modeling of carbon dioxide sequestration by coupling reservoir simulation and molecular dynamics. SPE Journal, 2016, 21(03): 0853-0863.
Baqer, Y., Chen, X. A review on reactive transport model and porosity evolution in the porous media. Environmental Science and Pollution Research, 2022, 29(32): 47873-47901.
Bauer, S., Beyer, C., Dethlefsen, F., et al. Impacts of the use of the geological subsurface for energy storage: An investigation concept. Environmental Earth Sciences, 2013, 70: 3935-3943.
Bauer, S., Dahmke, A., Kolditz, O. Subsurface energy storage: Geological storage of renewable energy-capacities, induced effects and implications. Environmental Earth Sciences, 2017, 76: 1-4.
Berger, M. J., Oliger, J. Adaptive mesh refinement for hyperbolic partial differential equations. Journal of Computational Physics, 1984, 53(3): 484-512.
Bijeljic, B., Blunt, M. J. Pore-scale modeling of transverse dispersion in porous media. Water Resources Research, 2007, 43(12): W12S11.
Bijeljic, B., Raeini, A., Mostaghimi, P., et al. Predictions of non-fickian solute transport in different classes of porous media using direct simulation on pore-scale images. Physical Review E, 2013, 87(1): 013011.
Blunt, M. J., Bijeljic, B., Dong, H., et al. Pore-scale imaging and modelling. Advances in Water resources, 2013, 51: 197-216.
Blunt, M. J., Jackson, M. D., Piri, M., et al. Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Advances in Water Resources, 2002, 25(8-12): 1069-1089.
Cai, J., Qin, X., Xia, X., et al. Numerical modeling of multiphase flow in porous media considering micro-and nanoscale effects: A comprehensive review. Gas Science and Engineering, 2024, 131: 205441.
Cant, R., Ahmed, U., Fang, J., et al. An unstructured adaptive mesh refinement approach for computational fluid dynamics of reacting flows. Journal of Computational Physics, 2022, 468: 111480.
Carrillo, F. J., Bourg, I. C., Soulaine, C. Multiphase flow modeling in multiscale porous media: An open-source micro-continuum approach. Journal of Computational Physics: X, 2020, 8: 100073.
Chen, L., He, A., Zhao, J., et al. Pore-scale modeling of complex transport phenomena in porous media. Progress in Energy and Combustion Science, 2022, 88: 100968.
Crotogino, F., Schneider, G.-S., Evans, D. J. Renewable energy storage in geological formations. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2018, 232(1): 100-114.
Cusini, M., Fryer, B., van Kruijsdijk, C., et al. Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media. Journal of Computational Physics, 2018, 354: 593-612.
De Barros, F., Colbrook, M., Fokas, A. A hybrid analytical-numerical method for solving advection-dispersion problems on a half-line. International Journal of Heat and Mass Transfer, 2019, 139: 482-491.
de Hoop, S., Jones, E., Voskov, D. Accurate geothermal and chemical dissolution simulation using adaptive mesh refinement on generic unstructured grids. Advances in Water Resources, 2021, 154: 103977.
de Hoop, S., Voskov, D., Ahusborde, E., et al. A benchmark study on reactive two-phase flow in porous media: Part i-model description. Computational Geosciences, 2024, 28(1): 175-189.
De Santis, A., Colombo, M., Hanson, B. C., et al. A generalized multiphase modelling approach for multiscale flows. Journal of Computational Physics, 2021, 436: 110321.
Duran, O., Devloo, P. R., Gomes, S. M., et al. A multiscale mixed finite element method applied to the simulation of two-phase flows. Computer Methods in Applied Mechanics and Engineering, 2021, 383: 113870.
Esler, K., Gandham, R., Patacchini, L., et al. A graphics processing unit-based, industrial grade compositional reservoir simulator. SPE Journal, 2022, 27(01): 597-612.
Estep, D., Ginting, V., Ropp, D., et al. An a posteriori-a priori analysis of multiscale operator splitting. SIAM Journal on Numerical Analysis, 2008, 46(3): 1116-1146.
Flyer, N., Fokas, A. A hybrid analytical–numerical method for solving evolution partial differential equations. i. the halfline. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2008, 464(2095): 1823-1849.
Gasanzade, F., Pfeiffer, W. T., Witte, F., et al. Subsurface renewable energy storage capacity for hydrogen, methane and compressed air-a performance assessment study from the north german basin. Renewable and Sustainable Energy Reviews, 2021, 149: 111422.
Gauthier, D. J., Bollt, E., Griffith, A., et al. Next generation reservoir computing. Nature Communications, 2021, 12(1): 1-8.
Ghassemzadeh, S., Gonzalez Perdomo, M., Haghighi, M. et al. A data-driven reservoir simulation for natural gas reservoirs. Neural Computing and Applications, 2021, 33(18): 11777-11798.
Golparvar, A., Zhou, Y., Wu, K., et al. A comprehensive review of pore scale modeling methodologies for multiphase flow in porous media. Advances in Geo-Energy Research, 2018, 2(4): 418-440.
Hajibeygi, H., Karvounis, D., Jenny, P. A hierarchical fracture model for the iterative multiscale finite volume method. Journal of Computational Physics, 2011, 230(24): 8729-8743.
Hajibeygi, H., Tchelepi, H. A. Compositional multiscale finite-volume formulation. SPE Journal, 2014, 19(02): 316-326.
Han, J., Jentzen, A. Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations. Communications in Mathematics and Mtatistics, 2017, 5(4): 349-
Heinemann, N., Alcalde, J., Miocic, J. M., et al. Enabling large-scale hydrogen storage in porous media-the scientific challenges. Energy & Environmental Science, 2021, 14(2): 853-864.
Icardi, M., Boccardo, G., Marchisio, D. L., et al. Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media. Physical Review E, 2014, 90(1): 013032.
Jacob, B., Howard, A. A., Stinis, P. Spikans: Separable physics-informed kolmogorov-arnold networks. arXiv preprint arXiv:2411.06286, 2024.
Joekar-Niasar, V., Van Dijke, M., Hassanizadeh, S. M. Pore-scale modeling of multiphase flow and transport: Achievements and perspectives. Transport in Porous Media, 2012, 94(2): 461-464.
Kabuth, A., Dahmke, A., Beyer, C., et al. Energy storage in the geological subsurface: Dimensioning, risk analysis and spatial planning: The angus+ project. Environmental Earth Sciences, 2017, 76: 1-17.
Kala, K., Voskov, D. Element balance formulation in reactive compositional flow and transport with parameterization technique. Computational Geosciences, 2020, 24(2): 609-624.
Karimpouli, S., Tahmasebi, P., Saenger, E. H. Ultrasonic prediction of crack density using machine learning: A numerical investigation. Geoscience Frontiers, 2022, 13(1): 101277.
Karniadakis, G. E., Kevrekidis, I. G., Lu, L., et al. Physics-informed machine learning. Nature Reviews Physics, 2021, 3(6): 422-440.
Khait, M., Voskov, D. Adaptive parameterization for solving of thermal/compositional nonlinear flow and transport with buoyancy. SPE Journal, 2018, 23(2): 522-534.
Kochkov, D., Smith, J. A., Alieva, A., et al. Machine learning-accelerated computational fluid dynamics. Proceedings of the National Academy of Sciences, 2021, 118(21): e2101784118.
Korneev, S., Battiato, I. Sequential homogenization of reactive transport in polydisperse porous media. Multiscale Modeling & Simulation, 2016, 14(4): 1301-1318.
Krevor, S., De Coninck, H., Gasda, S. E., et al. Subsurface carbon dioxide and hydrogen storage for a sustainable energy future. Nature Reviews Earth & Environment, 2023, 4(2): 102-118.
Ladd, A. J., Szymczak, P. Reactive flows in porous media: Challenges in theoretical and numerical methods. Annual Review of Chemical and Biomolecular Engineering, 2021, 12(1): 543-571.
Lasseux, D., Parada, F. J. V., Porter, M. L. An improved macroscale model for gas slip flow in porous media. Journal of Fluid Mechanics, 2016, 805: 118-146.
Li, L., Li, X., Zhu, Z., et al. Numerical modeling of multiphase flow in gas stirred ladles: From a multiscale point of view. Powder Technology, 2020, 373: 14-25.
Li, L., Voskov, D. A novel hybrid model for multiphase flow in complex multi-scale fractured systems. Journal of Petroleum Science and Engineering, 2021, 203: 108657.
Liu, H., Zhu, Z., Patrick, W., et al. Pore-scale numerical simulation of supercritical CO2 migration in porous and fractured media saturated with water. Advances in Geo-Energy Research, 2020, 4(4): 419-434.
Liu, M., Mostaghimi, P. High-resolution pore-scale simulation of dissolution in porous media. Chemical Engineering Science, 2017, 161: 360-369.
Liu, X., Zhang, S. Development of adaptive multi-resolution mps method for multiphase flow simulation. Computer Methods in Applied Mechanics and Engineering, 2021, 387: 114184.
Liu, Y., Wilcox, J. Molecular simulation of CO2 adsorption in micro-and mesoporous carbons with surface heterogeneity. International Journal of Coal Geology, 2012, 104: 83-95.
Liu, Y., Wilcox, J. Molecular simulation studies of CO2 adsorption by carbon model compounds for carbon capture and sequestration applications. Environmental Science & Technology, 2013, 47(1): 95-101.
Lu, R., Nagel, T., Poonoosamy, J., et al. A new operator-splitting finite element scheme for reactive transport modeling in saturated porous media. Computers & Geosciences, 2022, 163: 105106.
Luo, K., Xia, J., Monaco, E. Multiscale modeling of multiphase flow with complex interactions. Journal of Multiscale Modelling, 2009, 1(01): 125-156.
Lyu, X., Khait, M., Voskov, D. Operator-based linearization approach for modeling of multiphase flow with buoyancy and capillarity. SPE Journal, 2021, 26(4): 1858-1875.
Lyu, X., Voskov, D. Advanced modeling of enhanced CO2 dissolution trapping in saline aquifers. International Journal of Greenhouse Gas Control, 2023, 127: 103907.
Lyu, X., Voskov, D., R.Rossen, W. Numerical investigations of foam-assisted CO2 storage in saline aquifers. International Journal of Greenhouse Gas Control, 2021, 108: 103314.
Lyu, X., Voskov, D., R.Rossen, W. Numerical investigations of foam-assisted CO2 storage in saline aquifers. International Journal of Greenhouse Gas Control, 2021, 108: 103314.
Ma, Z., Ranjith, P. G. Review of application of molecular dynamics simulations in geological sequestration of carbon dioxide. Fuel, 2019, 255: 115644.
Marcato, A., Santos, J. E., Boccardo, G., et al. Prediction of local concentration fields in porous media with chemical reaction using a multi scale convolutional neural network. Chemical Engineering Journal, 2023, 455: 140367.
Martinez, M. J., Hesse, M. A. Two-phase convective CO2 dissolution in saline aquifers. Water Resources Research, 2016, 52(1): 585-599.
Meakin, P., Tartakovsky, A. M. Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Reviews of Geophysics, 2009, 47(3): RG3002.
Mehmani, A., Prodanovic, M. The effect of microporosity on ´ transport properties in porous media. Advances in Water Resources, 2014, 63: 104-119.
Meunier, F., Draye, X., Vanderborght, J., et al. A hybrid analytical-numerical method for solving water flow equations in root hydraulic architectures. Applied Mathematical Modelling, 2017, 52: 648-663.
Molins, S. Reactive interfaces in direct numerical simulation of pore-scale processes. Reviews in Mineralogy and Geochemistry, 2015, 80(1): 461-481.
Oyewole, I., Chehade, A., Kim, Y. A controllable deep transfer learning network with multiple domain adaptation for battery state-of-charge estimation. Applied Energy, 2022, 312: 118726.
Pau, G. S., Bell, J. B., Pruess, K., et al. High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers. Advances in Water Resources, 2010, 33(4): 443-455.
Raeini, A. Q., Blunt, M. J., Bijeljic, B. Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method. Journal of Computational Physics, 2012, 231(17): 5653-5668.
Ramesh Kumar, K., Makhmutov, A., Spiers, C. J., et al. Geomechanical simulation of energy storage in salt formations. Scientific Reports, 2021, 11(1): 19640.
Rigas, S., Papachristou, M., Papadopoulos, T., et al. Adaptive training of grid-dependent physics-informed kolmogorov-arnold networks. IEEE Access, 2024, 12: 176982-176998.
Scheibe, T. D., Schuchardt, K., Agarwal, K., et al. Hybrid multiscale simulation of a mixing-controlled reaction. Advances in Water Resources, 2015, 83: 228-239.
Sheng, Q., Thompson, K. Dynamic coupling of pore-scale and reservoir-scale models for multiphase flow. Water Resources Research, 2013, 49(9): 5973-5988.
Smith, E. R., Theodorakis, P. E. Multiscale simulation of fluids: Coupling molecular and continuum. Physical Chemistry Chemical Physics, 2024, 26(2): 724-744.
Soulaine, C. Micro-continuum modeling: An hybrid-scale approach for solving coupled processes in porous media. Water Resources Research, 2024, 60(2): e2023WR035908.
Soulaine, C., Tchelepi, H. A. Micro-continuum approach for pore-scale simulation of subsurface processes. Transport in Porous Media, 2016, 113: 431-456.
Steefel, C. I., Yabusaki, S. B., Mayer, K. U. Reactive transport benchmarks for subsurface environmental simulation. Computational Geosciences, 2015, 19(3): 439.
Subramaniam, S. Multiphase flows: Rich physics, challenging theory, and big simulations. Physical Review Fluids, 2020, 5(11): 110520.
Tang, H., Haynes, R., Houzeaux, G. A review of domain decomposition methods for simulation of fluid flows: Concepts, algorithms, and applications. Archives of Computational Methods in Engineering, 2021, 28(3): 841-873.
Tang, M., Liu, Y., Durlofsky, L. J. Deep-learning-based surrogate flow modeling and geological parameterization for data assimilation in 3D subsurface flow. Computer Methods in Applied Mechanics and Engineering, 2021, 376: 113636.
Tarkowski, R. Perspectives of using the geological subsurface for hydrogen storage in poland. International Journal of Hydrogen Energy, 2017, 42(1): 347-355.
Tartakovsky, A. M., Redden, G., Lichtner, P. C., et al. Mixing-induced precipitation: Experimental study and multiscale numerical analysis. Water Resources Research, 2008, 44(6): W06S04.
Toscano, J. D., Oommen, V., Varghese, A. J., et al. From pinns to pikans: Recent advances in physics-informed machine learning. arXiv preprint arXiv:2410.13228, 2024.
Tryggvason, G., Dabiri, S., Aboulhasanzadeh, B., et al. Multiscale considerations in direct numerical simulations of multiphase flows. Physics of Fluids, 2013, 25(3): 031302.
Vasilyeva, M. Efficient decoupling schemes for multiscale multicontinuum problems in fractured porous media. Journal of Computational Physics, 2023, 487: 112134.
Vialle, S., Druhan, J. L., Maher, K. Multi-phase flow simulation of CO2 leakage through a fractured caprock in response to mitigation strategies. International Journal of Greenhouse Gas Control, 2016, 44: 11-25.
Voskov, D. Operator-based linearization approach for modeling of multiphase multi-component flow in porous media. Journal of Computational Physics, 2017, 337: 275-288.
Wang, N., Chang, H., Zhang, D. Deep-learning-based inverse modeling approaches: A subsurface flow example. Journal of Geophysical Research: Solid Earth, 2021, 126(2): e2020JB020549.
Wang, W., Wen, J., Wang, C., et al. Current status and development trends of CO2 storage with enhanced natural gas recovery (CS-EGR). Fuel, 2023, 349: 128555.
Wang, W., Xie, Q., An, S., et al. Pore-scale simulation of multiphase flow and reactive transport processes involved in geologic carbon sequestration. Earth-Science Reviews, 2023, 247: 104602.
Wang, Y., Hajibeygi, H., Tchelepi, H. A. Algebraic multiscale solver for flow in heterogeneous porous media. Journal of Computational Physics, 2014, 259: 284-303.
Wang, Y., Lin, G. Efficient deep learning techniques for multiphase flow simulation in heterogeneous porousc media. Journal of Computational Physics, 2020, 401: 108968.
Wang, Y., Voskov, D., Khait, M., et al. An efficient numerical simulator for geothermal simulation: A benchmark study. Applied Energy, 2020, 264: 114693.
Wang, Y. D., Chung, T., Armstrong, R. T., et al. Ml-lbm: predicting and accelerating steady state flow simulation in porous media with convolutional neural networks. Transport in Porous Media, 2021, 138(1): 49-75.
Wu, Y., An, S., Tahmasebi, P., et al. An end-to-end approach to predict physical properties of heterogeneous porous me dia: Coupling deep learning and physics-based features. Fuel, 2023, 352: 128753.
Wu, Z., Wang, H., He, C., et al. The application of physics-informed machine learning in multiphysics modeling in chemical engineering. Industrial & Engineering Chemistry Research, 2023, 62(44): 18178-18204.
Xie, Q., Wang, W., Bakhshian, S., et al. Simulation of CO2 dissolution reactions in saline aquifers using lattice boltzmann method. Gas Science and Engineering, 2024, 125: 205284.
Xie, Q., Wang, W., Su, Y., et al. Pore-scale study of calcite dissolution during CO2-saturated brine injection for sequestration in carbonate aquifers. Gas Science and Engineering, 2023, 114: 204978.
Xu, C., Fu, L., Lin, T., et al. Machine learning in petrophysics: Advantages and limitations. Artificial Intelligence in Geosciences, 2022, 3: 157-161.
Yan, B., Harp, D. R., Chen, B., et al. A physics-constrained deep learning model for simulating multiphase flow in 3D heterogeneous porous media. Fuel, 2022, 313: 122693.
Yang, X., Kong, S.-C., Liu, Q. Smoothed particle hydrodynamics with adaptive spatial resolution for multiphase flows with large density ratio. Physical Review E, 2021, 104(5): 055308.
Yang, Y., Wang, J., Wang, J., et al. Pore-scale modeling of coupled CO2 flow and dissolution in 3D porous media for geological carbon storage. Water Resources Research, 2023, 59(10): e2023WR035402.
Yin, J., Medellín-Azuara, J., Escriva-Bou, A., et al. Bayesian machine learning ensemble approach to quantify model uncertainty in predicting groundwater storage change. Science of The Total Environment, 2021, 769: 144715.
Zha, W., Zhang, W., Li, D., et al. Convolution-based model-solving method for three-dimensional, unsteady, partial differential equations. Neural Computation, 2022, 34(2): 518-540.
Zhang, H., Diao, R., Mostofi, M., et al. Molecular simulation of enhanced CH4 recovery and CO2 storage by CO2-N2 mixture injection in deformable organic micropores. Journal of Natural Gas Science and Engineering, 2020, 84: 103658.
Zhang, X., Ma, F., Yin, S., et al. Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media: A critical review. Applied Energy, 2021, 303: 117603.
Zhou, X.-H., McClure, J. E., Chen, C., et al. Neural network-based pore flow field prediction in porous media using super resolution. Physical Review Fluids, 2022, 7(7): 074302.
Zhu, L.-T., Chen, X.-Z., Ouyang, B., et al. Review of machine learning for hydrodynamics, transport, and reactions in multiphase flows and reactors. Industrial & Engineering Chemistry Research, 2022, 61(28): 9901-9949.
Zhuang, X., Wang, W., Su, Y., et al. Spatio-temporal sequence prediction of CO2 flooding and sequestration potential under geological and engineering uncertainties. Applied Energy, 2024, 359: 122691.
Zhuang, X., Wang, W., Su, Y., et al. Multi-objective optimization of reservoir development strategy with hybrid artificial intelligence method. Expert Systems with Applications, 2024, 241: 122707.
Downloads
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Author(s)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.