Effective permeability of an immiscible fluid in porous media determined from its geometric state

Al-Zubaidi, Fatimah; Mostaghimi, Peyman; Niu, Yufu; Armstrong, Ryan T.; Mohammadi, Gelareh; McClure, James E.; Berg, Steffen

doi:10.1103/physrevfluids.8.064004

Title: Effective permeability of an immiscible fluid in porous media determined from its geometric state

Journal Article · Wed Jun 21 20:00:00 EDT 2023 · Physical Review Fluids (Online)

DOI: https://doi.org/10.1103/physrevfluids.8.064004 · OSTI ID:2424012

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Univ. of New South Wales, Sydney, NSW (Australia)
Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Shell Global Solutions International B.V. (Netherlands)

Based on the phenomenological extension of Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process or path dependent with an underlying dependency on pore structure and wettability. For applications (fuel cells to underground CO₂ storage), it is imperative to determine the effective phase permeability relationships where the traditional approach is based on the inverse modeling of time-consuming experiments. The underlying reason is that the fundamental upscaling step from pore to Darcy scale, which links the pore structure of the porous medium to the continuum hydraulic conductivities, is not solved. Herein, we develop an artificial neural network (ANN) that relies on fundamental geometrical relationships to determine the mechanical energy dissipation during creeping immiscible two-fluid flow. Finally, the developed ANN is based on a prescribed set of state variables based on physical insights that predict the effective permeability of 4500 unseen pore-scale geometrical states with R² = 0.98.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2424012

Journal Information:: Physical Review Fluids (Online), Journal Name: Physical Review Fluids (Online) Journal Issue: 6 Vol. 8; ISSN 2469-990X

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (55)

From connected pathway flow to ganglion dynamics Rücker, M.; Berg, S.; Armstrong, R. T. Geophysical Research Letters, Vol. 42, Issue 10 https://doi.org/10.1002/2015GL064007	journal	May 2015
On the dynamics and kinematics of two‐fluid‐phase flow in porous media Gray, W. G.; Dye, A. L.; McClure, J. E. Water Resources Research, Vol. 51, Issue 7 https://doi.org/10.1002/2015WR016921	journal	July 2015
Minkowski Tensor Shape Analysis of Cellular, Granular and Porous Structures Schröder-Turk, G. E.; Mickel, W.; Kapfer, S. C. Advanced Materials, Vol. 23, Issue 22-23 https://doi.org/10.1002/adma.201100562	journal	June 2011
Microfluidic Model Porous Media: Fabrication and Applications Anbari, Alimohammad; Chien, Hung-Ta; Datta, Sujit S. Small, Vol. 14, Issue 18 https://doi.org/10.1002/smll.201703575	journal	March 2018
The LBPM software package for simulating multiphase flow on digital images of porous rocks McClure, James E.; Li, Zhe; Berrill, Mark Computational Geosciences, Vol. 25, Issue 3 https://doi.org/10.1007/s10596-020-10028-9	journal	January 2021
Pore-Scale Characterization of Two-Phase Flow Using Integral Geometry Liu, Zhishang; Herring, Anna; Arns, Christoph Transport in Porous Media, Vol. 118, Issue 1 https://doi.org/10.1007/s11242-017-0849-5	journal	March 2017
Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic McClure, James E.; Ramstad, Thomas; Li, Zhe Transport in Porous Media, Vol. 133, Issue 2 https://doi.org/10.1007/s11242-020-01420-1	journal	May 2020
Sensitivity and Uncertainty Analysis for Parameterization of Multiphase Flow Models Berg, Steffen; Unsal, Evren; Dijk, Harm Transport in Porous Media, Vol. 140, Issue 1 https://doi.org/10.1007/s11242-021-01576-4	journal	March 2021
Pore-by-Pore Modelling, Validation and Prediction of Waterflooding in Oil-Wet Rocks Using Dynamic Synchrotron Data Foroughi, Sajjad; Bijeljic, Branko; Blunt, Martin J. Transport in Porous Media, Vol. 138, Issue 2 https://doi.org/10.1007/s11242-021-01609-y	journal	May 2021
Multiscale Characterization of Wettability in Porous Media Armstrong, Ryan T.; Sun, Chenhao; Mostaghimi, Peyman Transport in Porous Media, Vol. 140, Issue 1 https://doi.org/10.1007/s11242-021-01615-0	journal	May 2021
Approximation capabilities of multilayer feedforward networks Hornik, Kurt Neural Networks, Vol. 4, Issue 2 https://doi.org/10.1016/0893-6080(91)90009-T	journal	January 1991
Pore-scale imaging and modelling Blunt, Martin J.; Bijeljic, Branko; Dong, Hu Advances in Water Resources, Vol. 51 https://doi.org/10.1016/j.advwatres.2012.03.003	journal	January 2013
Linking pore-scale interfacial curvature to column-scale capillary pressure Armstrong, Ryan T.; Porter, Mark L.; Wildenschild, Dorthe Advances in Water Resources, Vol. 46 https://doi.org/10.1016/j.advwatres.2012.05.009	journal	September 2012
Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces Raeini, Ali Q.; Blunt, Martin J.; Bijeljic, Branko Advances in Water Resources, Vol. 74 https://doi.org/10.1016/j.advwatres.2014.08.012	journal	December 2014
Microfluidics-based analysis of dynamic contact angles relevant for underground hydrogen storage van Rooijen, Willemijn; Hashemi, Leila; Boon, Maartje Advances in Water Resources, Vol. 164 https://doi.org/10.1016/j.advwatres.2022.104221	journal	June 2022
Non-uniqueness and uncertainty quantification of relative permeability measurements by inverse modelling Berg, Steffen; Unsal, Evren; Dijk, Harm Computers and Geotechnics, Vol. 132 https://doi.org/10.1016/j.compgeo.2020.103964	journal	April 2021
A novel heterogeneous algorithm to simulate multiphase flow in porous media on multicore CPU–GPU systems McClure, J. E.; Prins, J. F.; Miller, C. T. Computer Physics Communications, Vol. 185, Issue 7 https://doi.org/10.1016/j.cpc.2014.03.012	journal	July 2014
Deep learning in pore scale imaging and modeling Wang, Ying Da; Blunt, Martin J.; Armstrong, Ryan T. Earth-Science Reviews, Vol. 215 https://doi.org/10.1016/j.earscirev.2021.103555	journal	April 2021
Synchrotron X-ray tomographic characterization of microstructural evolution in coal due to supercritical CO2 injection at in-situ conditions Zhang, Guanglei; Ranjith, P. G.; Wu, Bisheng Fuel, Vol. 255 https://doi.org/10.1016/j.fuel.2019.115696	journal	November 2019
Determination of the spatial distribution of wetting in the pore networks of rocks Garfi, Gaetano; John, Cédric M.; Rücker, Maja Journal of Colloid and Interface Science, Vol. 613 https://doi.org/10.1016/j.jcis.2021.12.183	journal	May 2022
Assessing the impacts of partial mass depletion in DNAPL source zones Falta, Ronald W.; Suresh Rao, P.; Basu, Nandita Journal of Contaminant Hydrology, Vol. 78, Issue 4 https://doi.org/10.1016/j.jconhyd.2005.05.010	journal	August 2005
Flow regimes and relative permeabilities during steady-state two-phase flow in porous media Avraam, D. G.; Payatakes, A. C. Journal of Fluid Mechanics, Vol. 293 https://doi.org/10.1017/S0022112095001698	journal	June 1995
Tracking interface and common curve dynamics for two-fluid flow in porous media McClure, J. E.; Berrill, M. A.; Gray, W. G. Journal of Fluid Mechanics, Vol. 796 https://doi.org/10.1017/jfm.2016.212	journal	April 2016
Machine Learning Force Fields Unke, Oliver T.; Chmiela, Stefan; Sauceda, Huziel E. Chemical Reviews https://doi.org/10.1021/acs.chemrev.0c01111	journal	March 2021
Giant Negative Compressibility by Liquid Intrusion into Superhydrophobic Flexible Nanoporous Frameworks Tortora, Marco; Zajdel, Paweł; Lowe, Alexander Rowland Nano Letters, Vol. 21, Issue 7 https://doi.org/10.1021/acs.nanolett.0c04941	journal	March 2021
Minimal Surfaces in Porous Materials: X-Ray Image-Based Measurement of the Contact Angle and Curvature in Gas Diffusion Layers to Design Optimal Performance of Fuel Cells Shojaei, Mohammad Javad; Bijeljic, Branko; Zhang, Yihuai ACS Applied Energy Materials, Vol. 5, Issue 4 https://doi.org/10.1021/acsaem.2c00023	journal	April 2022
Random Forests Breiman, Leo Machine Learning, Vol. 45, Issue 1, p. 5-32 https://doi.org/10.1023/A:1010933404324	journal	January 2001
Impact of relative permeability hysteresis on geological CO ₂ storage : IMPACT OF HYSTERESIS ON GEOLOGICAL CO Juanes, R.; Spiteri, E. J.; Orr, F. M. Water Resources Research, Vol. 42, Issue 12 https://doi.org/10.1029/2005WR004806	journal	December 2006
Relative permeability and trapping of CO ₂ and water in sandstone rocks at reservoir conditions : MULTIPHASE FLOW OF CO Krevor, Samuel C. M.; Pini, Ronny; Zuo, Lin Water Resources Research, Vol. 48, Issue 2 https://doi.org/10.1029/2011WR010859	journal	February 2012
Quantification of Nonlinear Multiphase Flow in Porous Media Zhang, Yihuai; Bijeljic, Branko; Gao, Ying Geophysical Research Letters, Vol. 48, Issue 5 https://doi.org/10.1029/2020GL090477	journal	March 2021
Red Noise in Steady‐State Multiphase Flow in Porous Media Spurin, Catherine; Rücker, Maja; Moura, Marcel Water Resources Research, Vol. 58, Issue 7 https://doi.org/10.1029/2022WR031947	journal	July 2022
Thermodynamic basis of capillary pressure in porous media Hassanizadeh, S. Majid; Gray, William G. Water Resources Research, Vol. 29, Issue 10 https://doi.org/10.1029/93WR01495	journal	October 1993
Deep learning for universal linear embeddings of nonlinear dynamics Lusch, Bethany; Kutz, J. Nathan; Brunton, Steven L. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07210-0	journal	November 2018
Improved protein structure prediction using potentials from deep learning Senior, Andrew W.; Evans, Richard; Jumper, John Nature, Vol. 577, Issue 7792 https://doi.org/10.1038/s41586-019-1923-7	journal	January 2020
The Flow of Gas‐Liquid Mixtures Through Unconsolidated Sands Wyckoff, R. D.; Botset, H. G. Physics, Vol. 7, Issue 9 https://doi.org/10.1063/1.1745402	journal	September 1936
The Flow of Heterogeneous Fluids Through Porous Media Muskat, Morris; Meres, Milan W. Physics, Vol. 7, Issue 9 https://doi.org/10.1063/1.1745403	journal	September 1936
Capillary fluctuations and energy dynamics for flow in porous media McClure, James E.; Berg, Steffen; Armstrong, Ryan T. Physics of Fluids, Vol. 33, Issue 8 https://doi.org/10.1063/5.0057428	journal	August 2021
Relative permeability as a stationary process: Energy fluctuations in immiscible displacement McClure, James E.; Fan, Ming; Berg, Steffen Physics of Fluids, Vol. 34, Issue 9 https://doi.org/10.1063/5.0107149	journal	September 2022
Dynamic fluid connectivity during steady-state multiphase flow in a sandstone Reynolds, Catriona A.; Menke, Hannah; Andrew, Matthew Proceedings of the National Academy of Sciences, Vol. 114, Issue 31 https://doi.org/10.1073/pnas.1702834114	journal	July 2017
A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis Liang, Liang; Liu, Minliang; Martin, Caitlin Journal of The Royal Society Interface, Vol. 15, Issue 138 https://doi.org/10.1098/rsif.2017.0844	journal	January 2018
Pore-by-pore modeling, analysis, and prediction of two-phase flow in mixed-wet rocks Foroughi, Sajjad; Bijeljic, Branko; Lin, Qingyang Physical Review E, Vol. 102, Issue 2 https://doi.org/10.1103/PhysRevE.102.023302	journal	August 2020
Beyond Darcy's law: The role of phase topology and ganglion dynamics for two-fluid flow Armstrong, Ryan T.; McClure, James E.; Berrill, Mark A. Physical Review E, Vol. 94, Issue 4 https://doi.org/10.1103/PhysRevE.94.043113	journal	October 2016
Influence of wettability on phase connectivity and electrical resistivity Liu, Zhishang; McClure, James E.; Armstrong, Ryan T. Physical Review E, Vol. 98, Issue 4 https://doi.org/10.1103/PhysRevE.98.043102	journal	October 2018
Minimal surfaces in porous media: Pore-scale imaging of multiphase flow in an altered-wettability Bentheimer sandstone Lin, Qingyang; Bijeljic, Branko; Berg, Steffen Physical Review E, Vol. 99, Issue 6 https://doi.org/10.1103/PhysRevE.99.063105	journal	June 2019
Geometric state function for two-fluid flow in porous media McClure, James E.; Armstrong, Ryan T.; Berrill, Mark A. Physical Review Fluids, Vol. 3, Issue 8 https://doi.org/10.1103/PhysRevFluids.3.084306	journal	August 2018
Steady-State Two-Phase Flow in Porous Media: Statistics and Transport Properties Tallakstad, Ken Tore; Knudsen, Henning Arendt; Ramstad, Thomas Physical Review Letters, Vol. 102, Issue 7 https://doi.org/10.1103/PhysRevLett.102.074502	journal	February 2009
Permeability of Porous Materials Determined from the Euler Characteristic Scholz, Christian; Wirner, Frank; Götz, Jan Physical Review Letters, Vol. 109, Issue 26 https://doi.org/10.1103/PhysRevLett.109.264504	journal	December 2012
A short proof of Hadwiger's characterization theorem Klain, Daniel A. Mathematika, Vol. 42, Issue 2 https://doi.org/10.1112/S0025579300014625	journal	December 1995
Dynamics of Oil Ganglia During Immiscible Displacement in Water-Wet Porous Media Payatakes, A. C. Annual Review of Fluid Mechanics, Vol. 14, Issue 1 https://doi.org/10.1146/annurev.fl.14.010182.002053	journal	January 1982
Predictive Modeling of Relative Permeability Using a Generalized Equation of State Purswani, Prakash; Johns, Russell T.; Karpyn, Zuleima T. SPE Journal, Vol. 26, Issue 01 https://doi.org/10.2118/200410-PA	journal	September 2020
Effect of Wettability on Waterflood Recovery for Crude-Oil/Brine/Rock Systems Jadhunandan, P. P.; Morrow, N. R. SPE Reservoir Engineering, Vol. 10, Issue 01 https://doi.org/10.2118/22597-PA	journal	February 1995
A New Model of Trapping and Relative Permeability Hysteresis for All Wettability Characteristics Spiteri, Elizabeth J.; Juanes, Ruben; Blunt, Martin J. SPE Journal, Vol. 13, Issue 03 https://doi.org/10.2118/96448-PA	journal	September 2008
A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils1 van Genuchten, M. Th. Soil Science Society of America Journal, Vol. 44, Issue 5 https://doi.org/10.2136/sssaj1980.03615995004400050002x	journal	January 1980
Capillarity and phase-mobility of a hydrocarbon gas–liquid system Gao, Ying; Georgiadis, Apostolos; Brussee, Niels Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles, Vol. 76 https://doi.org/10.2516/ogst/2021025	journal	January 2021
Determination of Critical Gas Saturation by Micro-CT Berg, Steffen; Gao, Ying Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description, Vol. 61, Issue 2 https://doi.org/10.30632/PJV61N2-2020a1	journal	March 2020

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