Geometric state function for two-fluid flow in porous media

McClure, James E.; Armstrong, Ryan T.; Berrill, Mark A.; Schlüter, Steffen; Berg, Steffen; Gray, William G.; Miller, Cass T.

doi:10.1103/PhysRevFluids.3.084306

Title: Geometric state function for two-fluid flow in porous media

Journal Article · Thu Aug 30 00:00:00 EDT 2018 · Physical Review Fluids

DOI:https://doi.org/10.1103/PhysRevFluids.3.084306· OSTI ID:1515702

McClure, James E. ^[1]; Armstrong, Ryan T. ^[2];

^[3]; Schlüter, Steffen ^[4]; Berg, Steffen ^[5]; Gray, William G. ^[6]; Miller, Cass T. ^[6]

Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
Univ. of New South Wales, Sydney, NSW (Australia)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Helmholtz-Centre for Environmental Research–UFZ, Halle (Germany)
Shell Global Solutions International B.V., Amsterdam (The Netherlands)
Univ. of North Carolina at Chapel Hill, Chapel Hill, NC (United States)

Models that describe two-fluid flow in porous media suffer from a widely recognized problem that the constitutive relationships used to predict capillary pressure as a function of the fluid saturation are nonunique, thus requiring a hysteretic description. As an alternative to the traditional perspective, we consider a geometric description of the capillary pressure, which relates the average mean curvature, the fluid saturation, the interfacial area between fluids, and the Euler characteristic. The state equation is formulated using notions from algebraic topology and cast in terms of measures of the macroscale state. Synchrotron-based x-ray microcomputed tomography and high-resolution pore-scale simulation is applied to examine the uniqueness of the proposed relationship for six different porous media. We show that the geometric state function is able to characterize the microscopic fluid configurations that result from a wide range of simulated flow conditions in an averaged sense. The geometric state function can serve as a closure relationship within macroscale models to effectively remove hysteretic behavior attributed to the arrangement of fluids within a porous medium. As a result, this provides a critical missing component needed to enable a new generation of higher fidelity models to describe two-fluid flow in porous media.

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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)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1515702

Alternate ID(s):: OSTI ID: 1467953

Journal Information:: Physical Review Fluids, Vol. 3, Issue 8; ISSN 2469-990X

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 77 works

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References (68)

Capillary Behavior in Porous Solids Leverett, M. C. Transactions of the AIME, Vol. 142, Issue 01 https://doi.org/10.2118/941152-G	journal	December 1941
A model for hysteretic constitutive relations governing multiphase flow: 2. Permeability-saturation relations Lenhard, R. J.; Parker, J. C. Water Resources Research, Vol. 23, Issue 12 https://doi.org/10.1029/WR023i012p02197	journal	December 1987
Accurate and Efficient Implementation of Pore-Morphology-based Drainage Modeling in Two-dimensional Porous Media Adalsteinsson, David; Hilpert, Markus Transport in Porous Media, Vol. 65, Issue 2 https://doi.org/10.1007/s11242-005-6091-6	journal	November 2006
Introduction to the Thermodynamically Constrained Averaging Theory for Porous Medium Systems Gray, William G.; Miller, Cass T. Advances in Geophysical and Environmental Mechanics and Mathematics https://doi.org/10.1007/978-3-319-04010-3	book	January 2014
Trapping and hysteresis in two-phase flow in porous media: A pore-network study: Trapping and Hysteresis in Two-Phase Flow Joekar-Niasar, V.; Doster, F.; Armstrong, R. T. Water Resources Research, Vol. 49, Issue 7 https://doi.org/10.1002/wrcr.20313	journal	July 2013
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
A Simple Intrinsic Proof of the Gauss-Bonnet Formula for Closed Riemannian Manifolds Chern, Shiing-Shen The Annals of Mathematics, Vol. 45, Issue 4 https://doi.org/10.2307/1969302	journal	October 1944
Capillary Pressure Curve for Liquid Menisci in a Cubic Assembly of Spherical Particles Below Irreducible Saturation Bear, Jacob; Rubinstein, Boris; Fel, Leonid Transport in Porous Media, Vol. 89, Issue 1 https://doi.org/10.1007/s11242-011-9752-7	journal	March 2011
Pore-scale micro-computed-tomography imaging: Nonwetting-phase cluster-size distribution during drainage and imbibition Georgiadis, A.; Berg, S.; Makurat, A. Physical Review E, Vol. 88, Issue 3 https://doi.org/10.1103/PhysRevE.88.033002	journal	September 2013
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
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
Statistical mechanics of unsaturated porous media Xu, Jin; Louge, Michel Y. Physical Review E, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevE.92.062405	journal	December 2015
Real-time 3D imaging of Haines jumps in porous media flow Berg, S.; Ott, H.; Klapp, S. A. Proceedings of the National Academy of Sciences, Vol. 110, Issue 10 https://doi.org/10.1073/pnas.1221373110	journal	February 2013
Effect of fluid topology on residual nonwetting phase trapping: Implications for geologic CO2 sequestration Herring, Anna L.; Harper, Elizabeth J.; Andersson, Linnéa Advances in Water Resources, Vol. 62 https://doi.org/10.1016/j.advwatres.2013.09.015	journal	December 2013
A complete soil hydraulic model accounting for capillary and adsorptive water retention, capillary and film conductivity, and hysteresis Water Resources Research, Vol. 51, Issue 11 https://doi.org/10.1002/2015WR017703	journal	November 2015
Wettability Stabilizes Fluid Invasion into Porous Media via Nonlocal, Cooperative Pore Filling Holtzman, Ran; Segre, Enrico Physical Review Letters, Vol. 115, Issue 16 https://doi.org/10.1103/PhysRevLett.115.164501	journal	October 2015
Equation of State for Relative Permeability, Including Hysteresis and Wettability Alteration Khorsandi, Saeid; Li, Liwei; Johns, Russell T. SPE Journal, Vol. 22, Issue 06 https://doi.org/10.2118/182655-PA	journal	December 2017
Air-Water Interfacial Area and Capillary Pressure: Porous-Medium Texture Effects and an Empirical Function Peng, Sheng; Brusseau, Mark L. Journal of Hydrologic Engineering, Vol. 17, Issue 7 https://doi.org/10.1061/(ASCE)HE.1943-5584.0000515	journal	July 2012
Image processing of multiphase images obtained via X-ray microtomography: A review Schlüter, Steffen; Sheppard, Adrian; Brown, Kendra Water Resources Research, Vol. 50, Issue 4 https://doi.org/10.1002/2014WR015256	journal	April 2014
Calculation of Imbibition Relative Permeability for Two- and Three-Phase Flow From Rock Properties Land, Carlon S. Society of Petroleum Engineers Journal, Vol. 8, Issue 02 https://doi.org/10.2118/1942-PA	journal	June 1968
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
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
Fluid Configurations in a Random Sphere Packing McClure, James Digital Rocks Portal University of Texas at Austin https://doi.org/10.17612/P7TG68	dataset	January 2016
Miscible displacement of oils by carbon disulfide in porous media: Experiments and analysis Berg, S.; Oedai, S.; Landman, A. J. Physics of Fluids, Vol. 22, Issue 11 https://doi.org/10.1063/1.3516614	journal	November 2010
Linking pressure and saturation through interfacial areas in porous media Cheng, J. -T. Geophysical Research Letters, Vol. 31, Issue 8 https://doi.org/10.1029/2003GL019282	journal	January 2004
Toward an improved description of the physics of two-phase flow Majid Hassanizadeh, S.; Gray, William G. Advances in Water Resources, Vol. 16, Issue 1 https://doi.org/10.1016/0309-1708(93)90029-F	journal	January 1993
Magnitude and Detailed Structure of Residual Oil Saturation Chatzis, Ioannis; Morrow, Norman R.; Lim, Hau T. Society of Petroleum Engineers Journal, Vol. 23, Issue 02 https://doi.org/10.2118/10681-PA	journal	April 1983
Measurement and prediction of the relationship between capillary pressure, saturation, and interfacial area in a NAPL-water-glass bead system: CAPILLARY PRESSURE, SATURATION, AND IFA Porter, Mark L.; Wildenschild, Dorthe; Grant, Gavin Water Resources Research, Vol. 46, Issue 8 https://doi.org/10.1029/2009WR007786	journal	August 2010
Impact of structured heterogeneities on reactive two-phase porous flow Reeves, Daniel; Rothman, Daniel H. Physical Review E, Vol. 86, Issue 3 https://doi.org/10.1103/PhysRevE.86.031120	journal	September 2012
Pore-morphology-based simulation of drainage in totally wetting porous media Hilpert, Markus; Miller, Cass T. Advances in Water Resources, Vol. 24, Issue 3-4 https://doi.org/10.1016/S0309-1708(00)00056-7	journal	February 2001
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
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
Lifetime of carbon capture and storage as a climate-change mitigation technology Szulczewski, M. L.; MacMinn, C. W.; Herzog, H. J. Proceedings of the National Academy of Sciences, Vol. 109, Issue 14 https://doi.org/10.1073/pnas.1115347109	journal	March 2012
Specific interfacial area: The missing state variable in two-phase flow equations?: INVESTIGATION OF EXTENDED DARCY'S LAW Joekar-Niasar, V.; Hassanizadeh, S. M. Water Resources Research, Vol. 47, Issue 5 https://doi.org/10.1029/2010WR009291	journal	May 2011
Curvature measures Federer, Herbert Transactions of the American Mathematical Society, Vol. 93, Issue 3 https://doi.org/10.1090/S0002-9947-1959-0110078-1	journal	March 1959
Network model investigation of interfacial area, capillary pressure and saturation relationships in granular porous media: NEW NETWORK MODEL FOR CAPILLARY FLOW Joekar-Niasar, V.; Prodanović, M.; Wildenschild, D. Water Resources Research, Vol. 46, Issue 6 https://doi.org/10.1029/2009WR008585	journal	June 2010
History effects on nonwetting fluid residuals during desaturation flow through disordered porous media Chevalier, Thibaud; Salin, Dominique; Talon, Laurent Physical Review E, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevE.91.043015	journal	April 2015
Reservoir Simulation With History-Dependent Saturation Functions Killough, J. E. Society of Petroleum Engineers Journal, Vol. 16, Issue 01 https://doi.org/10.2118/5106-PA	journal	February 1976
Network Generation Comparison Forum Sheppard, Adrian; Schroeder-Turk, Gerd Digital Rocks Portal University of Texas at Austin https://doi.org/10.17612/P7059V	dataset	January 2015
Mercury Porosimetry: A General (Practical) Overview Giesche, Herbert Particle & Particle Systems Characterization, Vol. 23, Issue 1 https://doi.org/10.1002/ppsc.200601009	journal	June 2006
Capillary saturation and desaturation Hilfer, R.; Armstrong, R. T.; Berg, S. Physical Review E, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevE.92.063023	journal	December 2015
Influence of phase connectivity on the relationship among capillary pressure, fluid saturation, and interfacial area in two-fluid-phase porous medium systems McClure, James E.; Berrill, Mark A.; Gray, William G. Physical Review E, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevE.94.033102	journal	September 2016
Micromodel study of two-phase flow under transient conditions: Quantifying effects of specific interfacial area Karadimitriou, N. K.; Hassanizadeh, S. M.; Joekar-Niasar, V. Water Resources Research, Vol. 50, Issue 10 https://doi.org/10.1002/2014WR015388	journal	October 2014
Consistent thermodynamic formulations for multiscale hydrologic systems: Fluid pressures: MULTISCALE FLUID PRESSURES Gray, W. G.; Miller, C. T. Water Resources Research, Vol. 43, Issue 9 https://doi.org/10.1029/2006WR005811	journal	September 2007
Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter Golub, Gene H.; Heath, Michael; Wahba, Grace Technometrics, Vol. 21, Issue 2 https://doi.org/10.1080/00401706.1979.10489751	journal	May 1979
Generalized nonequilibrium capillary relations for two-phase flow through heterogeneous media Amaziane, Brahim; Milišić, Josipa Pina; Panfilov, Mikhail Physical Review E, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevE.85.016304	journal	January 2012
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
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
Averaging theory for description of environmental problems: What have we learned? Gray, William G.; Miller, Cass T.; Schrefler, Bernhard A. Advances in Water Resources, Vol. 51 https://doi.org/10.1016/j.advwatres.2011.12.005	journal	January 2013
Nonlocal Interface Dynamics and Pattern Formation in Gravity-Driven Unsaturated Flow through Porous Media Cueto-Felgueroso, Luis; Juanes, Ruben Physical Review Letters, Vol. 101, Issue 24 https://doi.org/10.1103/PhysRevLett.101.244504	journal	December 2008
Generalized additive models for large data sets Wood, Simon N.; Goude, Yannig; Shaw, Simon Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 64, Issue 1 https://doi.org/10.1111/rssc.12068	journal	May 2014
Pore-scale studies of spontaneous imbibition into oil-saturated porous media Hatiboglu, Can Ulas; Babadagli, Tayfun Physical Review E, Vol. 77, Issue 6 https://doi.org/10.1103/PhysRevE.77.066311	journal	June 2008
Synchrotron Computed Microtomography of Porous Media: Topology and Transports Spanne, P.; Thovert, J. F.; Jacquin, C. J. Physical Review Letters, Vol. 73, Issue 14 https://doi.org/10.1103/PhysRevLett.73.2001	journal	October 1994
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
Wettability control on multiphase flow in patterned microfluidics Zhao, Benzhong; MacMinn, Christopher W.; Juanes, Ruben Proceedings of the National Academy of Sciences, Vol. 113, Issue 37 https://doi.org/10.1073/pnas.1603387113	journal	August 2016
Hysteretical models for prediction of the hydraulic conductivity of unsaturated porous media Mualem, Yechezkel Water Resources Research, Vol. 12, Issue 6 https://doi.org/10.1029/WR012i006p01248	journal	December 1976
Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media: FLUID TOPOLOGY Schlüter, S.; Berg, S.; Rücker, M. Water Resources Research, Vol. 52, Issue 3 https://doi.org/10.1002/2015WR018254	journal	March 2016
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
Macroscopic capillarity and hysteresis for flow in porous media Hilfer, R. Physical Review E, Vol. 73, Issue 1 https://doi.org/10.1103/PhysRevE.73.016307	journal	January 2006
Uniqueness of Reconstruction of Multiphase Morphologies from Two-Point Correlation Functions Rozman, M. G.; Utz, Marcel Physical Review Letters, Vol. 89, Issue 13 https://doi.org/10.1103/PhysRevLett.89.135501	journal	September 2002
Connected pathway relative permeability from pore-scale imaging of imbibition Berg, S.; Rücker, M.; Ott, H. Advances in Water Resources, Vol. 90 https://doi.org/10.1016/j.advwatres.2016.01.010	journal	April 2016
An integral-geometric approach for the Euler-Poincare characteristic of spatial images Journal of Microscopy, Vol. 198, Issue 1 https://doi.org/10.1046/j.1365-2818.2000.00668.x	journal	April 2000
Pore-scale modeling extension of constitutive relationships in the range of residual saturations Held, Rudolf J.; Celia, Michael A. Water Resources Research, Vol. 37, Issue 1 https://doi.org/10.1029/2000WR900234	journal	January 2001
Mesh free Estimation of the Structure Model Index Ohser, Joachim; Redenbach, Claudia; Schladitz, Katja Image Analysis & Stereology, Vol. 28, Issue 3 https://doi.org/10.5566/ias.v28.p179-185	journal	November 2009
Characterisation of irregular spatial structures by parallel sets and integral geometric measures Arns, C. H.; Knackstedt, M. A.; Mecke, K. R. Colloids and Surfaces A: Physicochemical and Engineering Aspects, Vol. 241, Issue 1-3 https://doi.org/10.1016/j.colsurfa.2004.04.034	journal	July 2004
Consistent thermodynamic formulations for multiscale hydrologic systems: Fluid pressures G., Gray, W.; T., Miller, C. The University of North Carolina at Chapel Hill University Libraries https://doi.org/10.17615/gfvk-3e11	text	January 2007
Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media Schlüter, S.; Berg, S.; Rücker, M. American Geophysical Union https://doi.org/10.5167/uzh-128246	text	January 2016
Permeability of porous materials determined from the Euler characteristic Scholz, Christian; Wirner, Frank; Götz, Jan arXiv https://doi.org/10.48550/arxiv.1211.6885	text	January 2012

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