*Result*: Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management.
Title:
Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management.
Authors:
Ur Rashid H; Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA. hrashid@lanl.gov., Pachalieva A; Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA., O'Malley D; Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA.
Source:
Scientific reports [Sci Rep] 2026 Feb 24. Date of Electronic Publication: 2026 Feb 24.
Publication Model:
Ahead of Print
Publication Type:
Journal Article
Language:
English
Journal Info:
Publisher: Nature Publishing Group Country of Publication: England NLM ID: 101563288 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 2045-2322 (Electronic) Linking ISSN: 20452322 NLM ISO Abbreviation: Sci Rep Subsets: MEDLINE
Imprint Name(s):
Original Publication: London : Nature Publishing Group, copyright 2011-
References:
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Buscheck, T. A. et al. Combining brine extraction, desalination, and residual-brine reinjection with co2 storage in saline formations: Implications for pressure management, capacity, and risk mitigation. Energy Procedia 4, 4283–4290 (2011).
Alabert, F. & Massonnat, G. Heterogeneity in a complex turbiditic reservoir: stochastic modelling of facies and petrophysical variability. In SPE Annual Technical Conference and Exhibition?, SPE–20604 (SPE, 1990).
Tavakoli, V. Carbonate reservoir heterogeneity: overcoming the challenges (Springer Nature, 2019).
Khalili, Y. & Ahmadi, M. Reservoir modeling & simulation: Advancements, challenges, and future perspectives. J. Chem. & Petroleum Eng. 57(2), 343–364 (2023).
Chen, B., Harp, D. R., Lin, Y., Keating, E. H. & Pawar, R. J. Geologic co2 sequestration monitoring design: A machine learning and uncertainty quantification based approach. Appl. energy 225, 332–345 (2018).
Sinha, S. et al. Normal or abnormal? machine learning for the leakage detection in carbon sequestration projects using pressure field data. Int. journal greenhouse gas control 103, 103189 (2020).
Yan, B., Harp, D. R., Chen, B., Hoteit, H. & Pawar, R. J. A gradient-based deep neural network model for simulating multiphase flow in porous media. J. Comput. Phys. 463, 111277 (2022).
Liu, M. et al. Prediction of co2 storage in different geological conditions based on machine learning. Energy & Fuels 38, 22340–22350 (2024).
Chu, A. K., Benson, S. M. & Wen, G. Deep-learning-based flow prediction for co2 storage in shale-sandstone formations. Energies 16, 246 (2022).
Cheraghi, Y., Kord, S. & Mashayekhizadeh, V. Application of machine learning techniques for selecting the most suitable enhanced oil recovery method; challenges and opportunities. J. Petroleum Sci. Eng. 205, 108761 (2021).
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Mahdaviara, M., Sharifi, M. & Ahmadi, M. Toward evaluation and screening of the enhanced oil recovery scenarios for low permeability reservoirs using statistical and machine learning techniques. Fuel 325, 124795 (2022).
Khan, W. A. et al. Application of machine learning and optimization of oil recovery and co2 sequestration in the tight oil reservoir. SPE J. 1–21 (2024).
Rezvanbehbahani, S., Stearns, L. A., Kadivar, A., Walker, J. D. & van der Veen, C. J. Predicting the geothermal heat flux in greenland: A machine learning approach. Geophys. Res. Lett. 44, 12–271 (2017).
Yan, B., Gudala, M. & Sun, S. Robust optimization of geothermal recovery based on a generalized thermal decline model and deep learning. Energy Convers. Manag. 286, 117033 (2023).
Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. physics 378, 686–707 (2019).
Wang, Y.-W. et al. A hybrid physics-informed data-driven neural network for co2 storage in depleted shale reservoirs. Petroleum Sci. 21, 286–301 (2024).
Pruess, K. TOUGH2-A general-purpose numerical simulator for multiphase fluid and heat flow. Tech. Rep., Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States) (1991).
Pettersen, Ø. Basics of reservoir simulation with the eclipse reservoir simulator. Lect. Notes. Univ. Bergen, Nor. 114, 81 (2006).
Rashid, H., Olorode, O. & Chukwudozie, C. An iteratively coupled model for flow, deformation, and fracture propagation in fractured unconventional reservoirs. J. Petroleum Sci. Eng. 214, 110468 (2022).
Innes, M. et al. A differentiable programming system to bridge machine learning and scientific computing. arXiv:1907.07587 (2019).
Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. Automatic differentiation in machine learning: a survey. J. machine learning research 18, 1–43 (2018).
Ketkar, N., Moolayil, J., Ketkar, N. & Moolayil, J. Introduction to pytorch. Deep learning with python: learn best practices of deep learning models with PyTorch 27–91 (2021).
O’Malley, D. et al. Dpfehm: a differentiable subsurface physics simulator. J. Open Source Softw. 8 (2023).
Moyner, O. Jutuldarcy. jl-a fully differentiable high-performance reservoir simulator based on automatic differentiation. In ECMOR 2024, 1, 1–9 (European Association of Geoscientists & Engineers, 2024).
Pachalieva, A., O’Malley, D., Harp, D. R. & Viswanathan, H. Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management. Sci. Reports 12, 18734 (2022).
Wu, Y.-S. Multiphase fluid flow in porous and fractured reservoirs (Gulf professional publishing, 2015).
Rashid, H. U. & Olorode, O. A continuous projection-based edfm model for flow in fractured reservoirs. SPE J. 29, 476–492 (2024).
Harp, D. R., O’Malley, D., Yan, B. & Pawar, R. On the feasibility of using physics-informed machine learning for underground reservoir pressure management. Expert. Syst. with Appl. 178, 115006 (2021).
Von Rosenberg, D. U. Mechanics of steady state single-phase fluid displacement from porous media. AIChE J. 2, 55–58 (1956).
Aarnes, J. E., Gimse, T. & Lie, K.-A. An introduction to the numerics of flow in porous media using matlab. In Geometric modelling, numerical simulation, and optimization: applied mathematics at SINTEF, 265–306 (Springer, 2007).
Courant, R., Friedrichs, K. & Lewy, H. Über die partiellen differenzengleichungen der mathematischen physik. Math. annalen 100, 32–74 (1928).
LeCun, Y. et al. Backpropagation applied to handwritten zip code recognition. Neural computation 1, 541–551 (1989).
Simonyan, K. & Zisserman, A. Very deep convolutional networks for large-scale image recognition. arXiv:1409.1556 (2014).
Srinivasan, S. et al. A machine learning framework for rapid forecasting and history matching in unconventional reservoirs. Sci. Reports 11, 21730 (2021).
Zhuang, F. et al. A comprehensive survey on transfer learning. Proc. IEEE 109, 43–76 (2020).
Bengio, Y., Louradour, J., Collobert, R. & Weston, J. Curriculum learning. In Proceedings of the 26th annual international conference on machine learning, 41–48 (2009).
Simmenes, T. et al. Importance of pressure management in co2 storage. In Offshore Technology Conference, OTC–23961 (OTC, 2013).
Liu, G., Gorecki, C. D., Bremer, J. M., Klapperich, R. J. & Braunberger, J. R. Storage capacity enhancement and reservoir management using water extraction: Four site case studies. Int. J. Greenh. Gas Control. 35, 82–95 (2015).
Acuña, J. A., Stimac, J., Sirad-Azwar, L. & Pasikki, R. G. Reservoir management at awibengkok geothermal field, west java, indonesia. Geothermics 37, 332–346 (2008).
Barbour, A. J., Xue, L., Roeloffs, E. & Rubinstein, J. L. Leakage and increasing fluid pressure detected in oklahoma’s wastewater disposal reservoir. J. Geophys. Res. Solid Earth 124, 2896–2919 (2019).
Majer, E. L. et al. Induced seismicity associated with enhanced geothermal systems. Geothermics 36, 185–222 (2007).
Keranen, K. M., Weingarten, M., Abers, G. A., Bekins, B. A. & Ge, S. Sharp increase in central oklahoma seismicity since 2008 induced by massive wastewater injection. Science 345, 448–451 (2014).
McNamara, D. E. et al. Earthquake hypocenters and focal mechanisms in central oklahoma reveal a complex system of reactivated subsurface strike-slip faulting. Geophys. Res. Lett. 42, 2742–2749 (2015).
Baer, M. et al. Earthquakes in switzerland and surrounding regions during 2006. Swiss J. Geosci. 100, 517–528 (2007).
Deichmann, N. et al. Earthquakes in switzerland and surrounding regions during 2007. Swiss J. Geosci. 101, 659–667 (2008).
Buscheck, T. A. et al. Combining brine extraction, desalination, and residual-brine reinjection with co2 storage in saline formations: Implications for pressure management, capacity, and risk mitigation. Energy Procedia 4, 4283–4290 (2011).
Alabert, F. & Massonnat, G. Heterogeneity in a complex turbiditic reservoir: stochastic modelling of facies and petrophysical variability. In SPE Annual Technical Conference and Exhibition?, SPE–20604 (SPE, 1990).
Tavakoli, V. Carbonate reservoir heterogeneity: overcoming the challenges (Springer Nature, 2019).
Khalili, Y. & Ahmadi, M. Reservoir modeling & simulation: Advancements, challenges, and future perspectives. J. Chem. & Petroleum Eng. 57(2), 343–364 (2023).
Chen, B., Harp, D. R., Lin, Y., Keating, E. H. & Pawar, R. J. Geologic co2 sequestration monitoring design: A machine learning and uncertainty quantification based approach. Appl. energy 225, 332–345 (2018).
Sinha, S. et al. Normal or abnormal? machine learning for the leakage detection in carbon sequestration projects using pressure field data. Int. journal greenhouse gas control 103, 103189 (2020).
Yan, B., Harp, D. R., Chen, B., Hoteit, H. & Pawar, R. J. A gradient-based deep neural network model for simulating multiphase flow in porous media. J. Comput. Phys. 463, 111277 (2022).
Liu, M. et al. Prediction of co2 storage in different geological conditions based on machine learning. Energy & Fuels 38, 22340–22350 (2024).
Chu, A. K., Benson, S. M. & Wen, G. Deep-learning-based flow prediction for co2 storage in shale-sandstone formations. Energies 16, 246 (2022).
Cheraghi, Y., Kord, S. & Mashayekhizadeh, V. Application of machine learning techniques for selecting the most suitable enhanced oil recovery method; challenges and opportunities. J. Petroleum Sci. Eng. 205, 108761 (2021).
Krasnov, F., Glavnov, N. & Sitnikov, A. A machine learning approach to enhanced oil recovery prediction. In International conference on analysis of images, social networks and texts, 164–171 (Springer, 2017).
Kumar Pandey, R., Gandomkar, A., Vaferi, B., Kumar, A. & Torabi, F. Supervised deep learning-based paradigm to screen the enhanced oil recovery scenarios. Sci. Reports 13, 4892 (2023).
Mahdaviara, M., Sharifi, M. & Ahmadi, M. Toward evaluation and screening of the enhanced oil recovery scenarios for low permeability reservoirs using statistical and machine learning techniques. Fuel 325, 124795 (2022).
Khan, W. A. et al. Application of machine learning and optimization of oil recovery and co2 sequestration in the tight oil reservoir. SPE J. 1–21 (2024).
Rezvanbehbahani, S., Stearns, L. A., Kadivar, A., Walker, J. D. & van der Veen, C. J. Predicting the geothermal heat flux in greenland: A machine learning approach. Geophys. Res. Lett. 44, 12–271 (2017).
Yan, B., Gudala, M. & Sun, S. Robust optimization of geothermal recovery based on a generalized thermal decline model and deep learning. Energy Convers. Manag. 286, 117033 (2023).
Raissi, M., Perdikaris, P. & Karniadakis, G. E. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. physics 378, 686–707 (2019).
Wang, Y.-W. et al. A hybrid physics-informed data-driven neural network for co2 storage in depleted shale reservoirs. Petroleum Sci. 21, 286–301 (2024).
Pruess, K. TOUGH2-A general-purpose numerical simulator for multiphase fluid and heat flow. Tech. Rep., Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States) (1991).
Pettersen, Ø. Basics of reservoir simulation with the eclipse reservoir simulator. Lect. Notes. Univ. Bergen, Nor. 114, 81 (2006).
Rashid, H., Olorode, O. & Chukwudozie, C. An iteratively coupled model for flow, deformation, and fracture propagation in fractured unconventional reservoirs. J. Petroleum Sci. Eng. 214, 110468 (2022).
Innes, M. et al. A differentiable programming system to bridge machine learning and scientific computing. arXiv:1907.07587 (2019).
Baydin, A. G., Pearlmutter, B. A., Radul, A. A. & Siskind, J. M. Automatic differentiation in machine learning: a survey. J. machine learning research 18, 1–43 (2018).
Ketkar, N., Moolayil, J., Ketkar, N. & Moolayil, J. Introduction to pytorch. Deep learning with python: learn best practices of deep learning models with PyTorch 27–91 (2021).
O’Malley, D. et al. Dpfehm: a differentiable subsurface physics simulator. J. Open Source Softw. 8 (2023).
Moyner, O. Jutuldarcy. jl-a fully differentiable high-performance reservoir simulator based on automatic differentiation. In ECMOR 2024, 1, 1–9 (European Association of Geoscientists & Engineers, 2024).
Pachalieva, A., O’Malley, D., Harp, D. R. & Viswanathan, H. Physics-informed machine learning with differentiable programming for heterogeneous underground reservoir pressure management. Sci. Reports 12, 18734 (2022).
Wu, Y.-S. Multiphase fluid flow in porous and fractured reservoirs (Gulf professional publishing, 2015).
Rashid, H. U. & Olorode, O. A continuous projection-based edfm model for flow in fractured reservoirs. SPE J. 29, 476–492 (2024).
Harp, D. R., O’Malley, D., Yan, B. & Pawar, R. On the feasibility of using physics-informed machine learning for underground reservoir pressure management. Expert. Syst. with Appl. 178, 115006 (2021).
Von Rosenberg, D. U. Mechanics of steady state single-phase fluid displacement from porous media. AIChE J. 2, 55–58 (1956).
Aarnes, J. E., Gimse, T. & Lie, K.-A. An introduction to the numerics of flow in porous media using matlab. In Geometric modelling, numerical simulation, and optimization: applied mathematics at SINTEF, 265–306 (Springer, 2007).
Courant, R., Friedrichs, K. & Lewy, H. Über die partiellen differenzengleichungen der mathematischen physik. Math. annalen 100, 32–74 (1928).
LeCun, Y. et al. Backpropagation applied to handwritten zip code recognition. Neural computation 1, 541–551 (1989).
Simonyan, K. & Zisserman, A. Very deep convolutional networks for large-scale image recognition. arXiv:1409.1556 (2014).
Srinivasan, S. et al. A machine learning framework for rapid forecasting and history matching in unconventional reservoirs. Sci. Reports 11, 21730 (2021).
Zhuang, F. et al. A comprehensive survey on transfer learning. Proc. IEEE 109, 43–76 (2020).
Bengio, Y., Louradour, J., Collobert, R. & Weston, J. Curriculum learning. In Proceedings of the 26th annual international conference on machine learning, 41–48 (2009).
Grant Information:
DE-SC0024721 U.S. Department of Energy,United States
Entry Date(s):
Date Created: 20260223 Latest Revision: 20260223
Update Code:
20260224
DOI:
10.1038/s41598-026-37063-3
PMID:
41730933
Database:
MEDLINE
*Further Information*
*Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compared to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then finetune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations - compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single phase simulations.
(© 2026. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.)*
*Declarations. Competing interests: The authors declare no competing interests.*