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Our analysis takes into account the viscous coupling between the pressure field and the saturation map. Although most of previously published stochastic homogenization approaches for upscaling two-phase flow in heterogeneous porous media neglect this viscous coupling, we show that it plays a crucial role on the dynamics of the front. In particular, when the mobility ratio is favorable, the viscous coupling induces a transverse flux that stabilizes the water–oil front, which follows a stationary behavior, at least in a statistical sense. Calculations are based on a double perturbation expansion of equations at first order: the local velocity fluctuation is defined as the sum of a viscous term related to perturbations of the saturation map, on one hand, plus the perturbation induced by the heterogeneity of the permeability field with a base-state saturation map, on the other hand. In this first paper, we focus on flows in stratified reservoirs, with stratification parallel to the mean flow. Our results allow to predict the evolution of large Fourier mode of the front, and the emergence of a stationary front, for favorable mobility ratios. Numerical experiments confirm our predictions. Our approach is applied to downscaling. Extension of our theory to isotropic media is presented in the companion paper.",{"EN":222},"Dynamics of the Water–Oil Front for Two-Phase, Immiscible Flow in Heterogeneous Porous Media. 1 – Stratified Media",{"VOID":224},"[\"7183996729464681517\"]",{"VOID":226},"10.1023\u002FB:TIPM.0000026085.38271.2e","PUBLICATION","VERIFIED","2024-05-03T20:26:23.448+00:00","Auto 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J.: 1997, Use of higher moments for the description of upscaled, process independent relative permeabilities, Paper SPE 37987 presented at the SPE Reservoir Simulation Symposium held in Dallas, Texas.",{"doi":354},{"id":22,"text":377,"url":22,"identifiers":378},"Dykstra, H. and Parsons, R. L.: 1950, Secondary Recovery of Oil in the US. API.",{},{"id":380,"text":381,"url":382,"identifiers":383},"d7e2998c-33bc-4c01-b707-3a4e4c736922","Ekrann, S. and Aasen, J. O.: 2000, Steady-state upscaling. Transport Porous Media 41, 245–262.","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1023\u002FA:1006765424927",{"doi":384},"10.1023\u002FA:1006765424927",{"id":350,"text":386,"url":352,"identifiers":387},"Fitzmorris, R. E., Kelsey, F. J. and Pande K. K.: 1992, Effect of crossflow on sweep efficiency in water\u002Foil displacement in heterogeneous reservoirs, Paper SPE 24901, 67th Annual Technical Conference and Exhibition of the SPE held inWashington, DC, 4–7 October.",{"doi":354},{"id":22,"text":389,"url":22,"identifiers":390},"Furtado, F. and Pereira, F.: Crossover from nonlinearity controlled to heterogeneity controlled mixing in two-phase porous media flows, Computational Geosciences (submitted).",{},{"id":22,"text":392,"url":22,"identifiers":393},"Gelhar, L. W.: 1993, Stochastic Subsurface Hydrology, Prentice Hall, Inc.",{},{"id":350,"text":395,"url":352,"identifiers":396},"Hagoort, J.: 1974, Displacement stability of water drives in water-wet connate-water-bearing reservoirs, Paper SPE 4268.",{"doi":354},{"id":350,"text":398,"url":352,"identifiers":399},"Hearn, C. L.: 1971, Simulation of stratified waterflooding by pseudo-relative permeability curves, J. Petrol. Technol. 805–813.",{"doi":354},{"id":22,"text":401,"url":22,"identifiers":402},"King, M. J. and Dunayevsky, V. A.: 1989, Why waterflood works: a linear stability analysis, Paper SPE 19648, 64th Annual Technical Conference and Exhibition of the SPE held in San Antonio, TX, 8–11 October.",{},{"id":350,"text":404,"url":352,"identifiers":405},"Kyte, J. R. and Berry, D. W.: 1975, New pseudo functions to control numerical dispersion, Paper SPE 5105.",{"doi":354},{"id":22,"text":407,"url":22,"identifiers":408},"Langlo, P. and Espedal, M. S.: 1975, Macrodispersion for two-phase, immiscible flow in porous media, Adv. Water Resour. 17, 297–316.",{},{"id":350,"text":410,"url":352,"identifiers":411},"Lenormand, R.: 1996, Determining flow equations from stochastic properties of a permeability field: the MHD model, SPE J. 179–190.",{"doi":354},{"id":22,"text":413,"url":22,"identifiers":414},"Le Ravalec, M., Noetinger, B. and Hu, L. Y.: 2000, The FFT moving average (FFT-MA) generator: an efficient numerical method for generating and conditioning gaussian simulations, Math. Geol. 32(6), 701–723.",{},{"id":22,"text":416,"url":22,"identifiers":417},"Quintard, M. and Whitaker, S.: 1988, Two-phase flow in heterogeneous porous media: the method of large-scale averaging, Transport Porous Media 3, 357–413.",{},{"id":419,"text":420,"url":421,"identifiers":422},"e83070c8-5260-4e7b-a6ab-d8fa9f6f7da0","Saffman, P. G. and Taylor, G.: 1958, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, Proc. Royal Soc. London A245, 312–329.","https:\u002F\u002Froyalsocietypublishing.org\u002Fdoi\u002F10.1098\u002Frspa.1958.0085",{"doi":423},"10.1098\u002Frspa.1958.0085",{"id":350,"text":425,"url":352,"identifiers":426},"Simon, A. D. and Koederitz, L. F.: 1982, An improved method for the determination of pseudorelative permeability data for stratified systems, Paper SPE 10975, Annual Fall Technical Conference and Exhibition, New-Orlean, LA.",{"doi":354},{"id":350,"text":428,"url":352,"identifiers":429},"Stiles, W. M. E.: 1949, Use of permeability distribution in waterflood calculations, T. AIME, 9–13 January.",{"doi":354},{"id":22,"text":431,"url":22,"identifiers":432},"Stone, H. L.: 1991, Rigorous black oil pseudo functions, Paper SPE 21207, 11th SPE Symposium on Reservoir Simulation, Anaheim, California.",{},{"id":350,"text":434,"url":352,"identifiers":435},"Warren, J. E. and Cosgrove, J. J.: 1964, Prediction of waterflood behavior in a stratified system, SPE Journal 149–157.",{"doi":354},{"id":22,"text":437,"url":22,"identifiers":438},"Yortsos, Y. C.: 1992, Analytical studies for processes at vertical equilibrium, 3rd European Conference on the Mathematics of Oil Recovery, Delft University of Technology, The Netherlands, 17–19 June.",{},{"id":22,"text":440,"url":22,"identifiers":441},"Zapata, V. J. and Lake, L. W.: 1981, A theoretical analysis of viscous crossflow, Paper SPE 10111, 56th Annual Fall Technical Conference and Exhibition of the SPE of AIME, San Antonio, Texas, 3–7 October.",{},{"id":22,"text":443,"url":22,"identifiers":444},"Zhang, D.: 2001, Stochastic Methods for Flow in Porous Media. Academic Press.",{},{"id":350,"text":446,"url":352,"identifiers":447},"Zhang, D. and Tchelepi, H. A.: 1999, Stochastic analysis of immiscible two-phase flow in heterogeneous media, SPE J. 4(4), 380–388.",{"doi":354},false,{"id":450,"createTime":451,"updateTime":452,"relativeEntities":453,"slug":454,"properties":455,"entityType":227,"verifyStatus":228,"verifyTime":466,"verifyNote":230,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":467,"fullTextUrl":22,"authors":468,"publicationType":278,"publisherRelationship":486,"citationCount":538,"citationInfo":539,"publishDate":543,"publishYear":540,"citationAnalyzeStatus":21,"lastCitationAnalyze":544,"indexDatabases":545,"openAccess":22,"references":22,"isForceReanalyzing":448},"7a17aa38-cefd-42e7-80bd-56ad5df60298","2023-12-25T08:03:11.837+00:00","2026-07-27T07:47:32.378+00:00",[],"Modeling-species-transport-by-concentrated-brine-in-aggregated-porous-media",{"abstract":456,"title":458,"gsPaper":460,"references":462,"doi":464},{"EN":457},"Basic equations governing the transport of species by concentrated brine flowing through an aggregated porous medium are developed. Some simple examples are solved numerically. The medium is considered to be composed of porous rock aggregates separated by ‘macropores’ through which the brine flows and transport of salt and low-concentration species takes place. The aggregates contain dead-end pores, cracks, and stationary pockets collectively called ‘micropores’. The micropore space does not contribute to the flow, but it serves as a storage for salt and species. Adsorption of fluid species takes place at internal surface of aggregates where it is assumed that a linear equilibrium isotherm describes the process. The effects of high salt concentrations are accounted for in the brine density relation, the viscosity relation, Darcy's and Fick's laws, and the rate of mass transfer between macropores and micropores. Mass balance equations, supplemented by extended forms of Darcy's and Fick's laws, are employed to arrive at two sets of equations. One set consists of seven coupled equations for the salt mass fraction and fluid density in macropores, salt mass fraction in micropores, fluid velocity vector, and the fluid pressure. The other set consists of two coupled equations to be solved for the mass fractions of low-concentration species in micropores and macropores. Based on these equations, a mathematical model called TORISM is developed. Using this model, the potential significance of modifications to Darcy's Law are demonstrated.",{"EN":459},"Modeling species transport by concentrated brine in aggregated porous media",{"VOID":461},"[\"16646041483119764272\"]",{"VOID":463},"Bachmat, Y. and Bear, J., 1986, Macroscopic modelling of transport phenomena in porous media: 2. Application to mass, momentum and energy transport, Transport in Porous Media 1, 213–240.\nCrittenden, J. C., Hutzler, N. J., Geyer, D. G., Oravitz, J. L., and Friedman, G., 1986, Transport of organic compounds with saturated groundwater flow: Model development and parameter sensitivity, Water Resour. Res. 22, 271–284.\nde Marsily, G., Fargue, D., and Goblet, P., 1987, How Much Do We Know About Coupled Processes in the Geosphere and Their Relevance to Performance Assessment?, in Proceedings of the GEOVAL Symposium, Session 5, April 7–9, 1987, Stockholm, Sweden.\nHandbook of Chemistry and Physics, 1982, 63rd edn., edited by R. C. Weast, CRC Press, Cleveland, Ohio, p. D261.\nHassanizadeh, S. M., 1986a, Derivation of basic equations of mass transport in porous media, Part 1. Macroscopic balance laws, Adv. Water Resour. 9, 196–206.\nHassanizadeh, S. M., 1986b, Derivation of basic equations of mass transport in porous media, Part 2, Generalized Darcy's and Fick's laws, Adv. Water Resour. 9, 196–206.\nHassanizadeh, S. M., 1987, Transport of radionuclides by concentrated brine in a porous medium with micropore-macropore structure, in J. K. Bates and W. B. Seefeldt (eds.), Scientific Basis for Nuclear Waste Management, Material Research Society Symposium Proceedings, Vol. 84, 757–767.\nHassanizadeh. S. M. and T. Leijnse, 1988, On the modelling of brine transport in porous media, Water Resour. Res. 24, 321–330.\nLever, D. A. and Jackson, C. P., 1985, On the equations for the flow of concentrated salt solution through a porous medium, U.K. DOE Report No. DOE\u002FRW\u002F85.100.\nRao, P. S. C., Jessup, R. E., and Addiscott, T. M., 1982, Experimental and theoretical aspects of solute diffusion in spherical and non-spherical aggregates, Soil Science 133, 342–349.\nRao, P. S. C., Jessup, R. E., Rolston, D. E. Davidson, J. M., and Kilcrease, D. P., 1980, Experimental and mathematical description of non-adsorbed solute transfer by diffusion in spherical aggregates, Soil Sci. Soc. Am. J. 44, 684–688.\nRasmussen, A., 1981, Diffusion and sorptionin particles and two-dimensional dispersion in a porous medium, Water Resour. Res. 17, 321–328.\nSkopp, J. and Warrick, A. W., 1974, A two-phase model for the miscible displacement of reactive solutes in soils, Soil Sci. Soc. Am. J. 38, 545–550.\nvan Eijkeren, J. C. H. and Loch, J. P. G., 1984, Transport of cationic solutes in sorbing porous media, Water Resour. Res. 20, 714–718.\nvan Genuchten M. Th. and Cleary, R. W., 1979, Movement of solutes in soil: computer-simulated and laboratory results, in G. H. Bolt (ed.), Soil Chemistry, Part B. Physico-Chemical Models, Elsevier, New York, Chap. 10.\nvan Genuchten M. Th. and Wierenga, P. J., 1976, Mass transfer studies in sorbing porous media I. Analytical solutions, Soil Sci. Soc. Am. J. 40, 473–480.\nvan Genuchten M. Th. and Wierenga, P. J., 1977, Mass transfer studies in sorbing porous media II. Experimental evaluations with Tritium (3H2O), Soil Sci. Soc. Am. J. 41, 272–278.",{"VOID":465},"10.1007\u002FBF00235333","2024-05-13T05:55:02.739+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF00235333",[469],{"id":470,"sortIndex":23,"researcher":22,"roles":471,"affiliations":472,"properties":481,"displayName":483,"givenName":22,"familyName":22},"08eb8bab-6b4c-43ff-b663-aa6b3a29c7ff",[236],[473],{"id":474,"sortIndex":23,"affiliation":475,"properties":22},"9d155d05-f204-4242-9c9f-7587a2b754f1",{"id":474,"createTime":22,"updateTime":22,"relativeEntities":476,"slug":22,"properties":477,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":480,"statistic":22},[],{"title":478},{"VI":479},"National Institute of Public Health and Environmental Protection (RIVM), Bilthoven, The Netherlands",[],{"title":482,"gsAuthor":484},{"VI":483},"S. 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We show how Henry’s law fits in a phase diagram and the problem is formulated as a set of nonlinear partial differential equations with complementarity constraints.",{"EN":556},"Henry’ Law and Gas Phase Disappearance",{"VOID":558},"[\"5755709146031872458\"]",{"VOID":560},"Abadpour, A., Panfilov, M.: Method of negative saturations for multiple compositional flow with oversaturated zones. Transp. Porous Media (2009) doi:10.1007\u002FS11242-008-9310-0\nBourgeat A., Jurak M., Smaï F.: Two phase partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository. Comput. Geosci. 13, 29–42 (2009)\nChavent, G., Jaffré, J.: Mathematical Models and Finite Elements for Reservoir Simulation, Studies in Mathematics and its Applications 17. North Holland, Amsterdam (1986)\nFacchinei F., Pang J.S.: Finite Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)\nKanzow C.: Inexact semismooth Newton methods for large-scale complementarity problems. Optim. Methods Softw. 19, 309–325 (2004)\nKraütle S.: General Multi-species Reactive Transport Problems in Porous Media: Efficient Numerical Approaches and Existence of Global Solutions. University of Erlangen-Nuremberg, Department of Mathematics, Erlangen (2008)",{"VOID":562},"10.1007\u002Fs11242-009-9407-0","2024-05-16T21:58:13.012+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11242-009-9407-0",[566,581],{"id":567,"sortIndex":23,"researcher":22,"roles":568,"affiliations":569,"properties":578,"displayName":580,"givenName":22,"familyName":22},"2efc34b6-88e9-486a-8911-dd1ce2d4c22b",[236],[570],{"id":571,"sortIndex":23,"affiliation":572,"properties":22},"b33458d4-764e-4494-9c56-6f1abd18c3d1",{"id":571,"createTime":22,"updateTime":22,"relativeEntities":573,"slug":22,"properties":574,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":577,"statistic":22},[],{"title":575},{"VI":576},"INRIA Paris–Rocquencourt, Le Chesnay cedex, France",[],{"title":579},{"VI":580},"Jérôme 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article presents the lattice Boltzmann simulation of viscous fingering phenomenon in immiscible displacement of two fluids in porous media. Such phenomenon generally takes place when a less viscous fluid is used to displace a more viscous fluid, and it can be found in many industrial fields. Dimensionless quantities, such as capillary number, Bond number and viscosity ratio between displaced fluid and displacing fluid are introduced to illustrate the effects of capillary force, viscous force, and gravity on the fluid behaviour. The surface wettability, which has an impact on the finger pattern, is also considered in the simulation. The numerical procedure is validated against the experiment about viscous fingering in a Hele-Shaw cell. The displacement efficiency is investigated using the parameter, areal sweep efficiency. The present simulation shows an additional evidence to demonstrate that the lattice Boltzmann method is a useful method for simulating some multiphase flow problems in porous media.",{"EN":673},"LBM Simulation of Viscous Fingering Phenomenon in Immiscible Displacement of Two Fluids in Porous Media",{"VOID":675},"[]",{"VOID":677},"Babchin A., Brailovsky I., Gordon P., Sivashinsky G.: Fingering instability in immiscible displacement. Phys. Rev. E 77(2), 026301 (2008)\nBogoyavlenskiy V.A.: Mean-field diffusion-limited aggregation: a “Density” model for viscous fingering phenomena. Phys. Rev. E 64(6), 066303 (2001)\nBrailovsky I., Babchin A., Frankel M., Sivashinsky G.: Fingering instability in water-oil displacement. Transp. Porous Media 63(3), 363–380 (2006)\nBrailovsky I., Babchin A., Frankel M., Sivashinsky G.: A reduced model for fingering instability in miscible displacement. Phys. Lett. A 369(3), 212–217 (2007)\nChau J.F., Or D.: Linking drainage front morphology with gaseous diffusion in unsaturated porous media: A lattice Boltzmann study. Phys. Rev. E 74(5), 056304–056311 (2006)\nChau J.F., Or D., Sukop M.C.: Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods. Water Resour. Res. 41(8), W08410 (2005)\nChen S., Doolen G.D.: Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30(1), 329–364 (1998)\nChen J.-D., Dias M.M., Patz S., Schwartz L.M.: Magnetic resonance imaging of immiscible-fluid displacement in porous media. Phys. Rev. Lett. 61(13), 1489 (1988)\nChin J., Boek E.S., Coveney P.V.: Lattice Boltzmann simulation of the flow of binary immiscible fluids with different viscosities using the shan-chen microscopic interaction model. Philos. Trans. R. Soc. A 360(1792), 547–558 (2002)\nChuoke R.L., Meurs P.v., Poel C.v.d.: The instability of slow, immiscible, viscous liquid–liquid displacements in porous media. Trans. AIME 216, 188–263 (1959)\nDong B., Yan Y.Y., Li W., Song Y.: Lattice Boltzmann simulation of viscous fingering phenomenon of immiscible fluids displacement in a channel. Comput. Fluids 39(5), 768–779 (2010)\nEleanor S.D., Carpenter T.A., Laurance D.H., Christopher H.: NMR imaging of fractal fingering in Hele-Shaw cells. AIChE J. 39(3), 510–512 (1993)\nFan L., Fang H., Lin Z.: Simulation of contact line dynamics in a two-dimensional capillary tube by the lattice Boltzmann model. Phys. Rev. E 63(5), 051603 (2001)\nFernández J.F., Albarrán J.M.: Diffusion-limited aggregation with surface tension: scaling of viscous fingering. Phys. Rev. Lett. 64(18), 2133 (1990)\nFrette V., Feder J., Jøssang T., Meakin P., Måløy K.J.: Fast, immiscible fluid–fluid displacement in three-dimensional porous media at finite viscosity contrast. Phys. Rev. E 50(4), 2881 (1994)\nGrosfils P., Boon J.P.: Viscous fingering in miscible, immiscible and reactive fluids. Int. J. Mod. Phys. B 17(1\u002F2), 15–20 (2003)\nGrosfils P., Boon J.P., Chin J., Boek E.S.: Structural and dynamical characterization of Hele-Shaw viscous fingering. Philos. Trans. R. Soc. Lond. Ser. A 362(1821), 1723–1734 (2004)\nGunstensen A.K., Rothman D.H.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43(8), 4320–4327 (1991)\nHarrison S.E., Smith S.M., Bernsdorf J., Hose D.R., Lawford P.V.: Application and validation of the lattice Boltzmann method for modelling flow-related clotting. J. Biomech. 40(13), 3023–3028 (2007)\nHe X., Chen S., Zhang R.: A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J. Comput. Phys. 152, 642–663 (1999)\nHill S.: Channeling in packed columns. Chem. Eng. Sci. 1(6), 247–253 (1952)\nHuang H., Li Z., Liu S., Lu X.-y.: Shan-and-Chen-type multiphase lattice Boltzmann study of viscous coupling effects for two-phase flow in porous media. Int. J. Numer. Methods Fluids 61(3), 341–354 (2008)\nInamuro T., Yoshino M., Ogino F.: Lattice Boltzmann simulation of flows in a three-dimensional porous structure. Int. J. Numer. Methods Fluids 29(7), 737–748 (1999)\nInamuro T., Konishi N., Ogino F.: A galilean invariant model of the lattice Boltzmann method for multiphase fluid flows using free-energy approach. Comput. Phys. Commun. 129(1–3), 32–45 (2000)\nInamuro T., Ogata T., Tajima S., Konishi N.: A lattice Boltzmann method for incompressible two-phase flows with large density differences. J. Comput. Phys. 198(2), 628–644 (2004)\nJohns M.L., Sullivan S.P., Sederman A.J., Gladden L.F.: MRI verification of complex flow simulations. Magn. Reson. 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In the Knudsen regime, gas–gas collisions do not occur and molecular transport can be fully attributed to gas–wall collisions. It is commonly accepted that the mean free path probability distribution then becomes highly nontrivial. Therefore, we propose to analyze this function in terms of its first two moments. We show numerically that both the first and second moments of the path distribution are important in describing the transport of a rarefied gas. In case of the Smoluchowski thermostat, a thermal wall mechanism for the cylindrically shaped pore, the obtained values can be compared with the results that follow from kinetic gas theory.",{"EN":800},"A Numerical Investigation of the Mean Free Path Distribution in the Knudsen Regime",{"VOID":802},"[\"7866433209915800664\"]",{"VOID":804},"10.1007\u002Fs11242-018-1035-0","2024-04-29T07:03:39.761+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11242-018-1035-0",[808],{"id":809,"sortIndex":23,"researcher":22,"roles":810,"affiliations":811,"properties":820,"displayName":822,"givenName":22,"familyName":22},"5ba017ef-82e0-4bf7-b7ed-a74c047a24c5",[236],[812],{"id":813,"sortIndex":23,"affiliation":814,"properties":22},"73e4b457-b153-41fd-82b7-887cc38168a1",{"id":813,"createTime":22,"updateTime":22,"relativeEntities":815,"slug":22,"properties":816,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":819,"statistic":22},[],{"title":817},{"VI":818},"Hoorn, The Netherlands",[],{"title":821},{"VI":822},"Martijn G. 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J. Heat Transf. (Trans. ASME) 132, 041006 (2010)",{"doi":354},{"id":350,"text":885,"url":352,"identifiers":886},"Canepa, P., Nijem, N., Chabal, Yves J., Thonhauser, T.: Diffusion of small molecules in metal organic framework materials. Phys. Rev. Lett 110, 026102 (2013)",{"doi":354},{"id":350,"text":888,"url":352,"identifiers":889},"Dongari, N., Zhang, Y., Reese, J.M.: Molecular free path distribution in rarefied gases. J. Phys. D Appl. Phys. 44, 125502 (2011)",{"doi":354},{"id":350,"text":891,"url":352,"identifiers":892},"Guo, Z.L., Shi, B.C., Zheng, C.G.: An extended Navier-Stokes formulation for gas flows in the Knudsen layer near a wall. Europhys. Lett. 80(2), 24001–24006 (2007)",{"doi":354},{"id":350,"text":894,"url":352,"identifiers":895},"Kennard, E.H.: Kinetic Theory of Gases. McGraw-Hill, New York (1938)",{"doi":354},{"id":350,"text":897,"url":352,"identifiers":898},"Skoulidas, A.I., Ackerman, D.M., Johnson, J.K., Sholl, D.S.: Rapid transport of gases in carbon nanotubes. Phys. Rev. Lett. 89, 185901 (2002)",{"doi":354},{"id":350,"text":900,"url":352,"identifiers":901},"Stops, D.W.: The mean free path of gas molecules in the transition regime. J. Phys. D Appl. Phys. 3, 685–696 (1970)",{"doi":354},{"id":350,"text":903,"url":352,"identifiers":904},"Verbeek, M.G.: Smoluchowski thermostat: A realistic introduction of the tangential momentum accommodation coefficient. Phys. Rev. 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The Darcy model (including the centrifugal, gravitational and Coriolis terms; and permeability anisotropy effects) and a modified energy equation (including the effects of thermal anisotropy) is used in the current analysis. The linear stability theory is used to evaluate the critical Rayleigh number for the onset of convection in the presence of thermal and mechanical anisotropy. It is shown that the preferred solution comprises roll cells aligned parallel to the vertical z-axis. As a result, it is found that the Coriolis acceleration (or Taylor number) and the gravitational term play no role in the stability of convection.",{"EN":915},"Coriolis Effect on the Stability of Centrifugally Driven Convection in a Rotating Anisotropic Porous Layer Subjected to Gravity",{"VOID":917},"[\"1460786465512842777\"]",{"VOID":919},"Bejan A. (1995). Convection Heat Transfer, 2nd ed. Wiley, New York\nEpherre J.F. (1975). 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Rock Eng. 40(1), 3–21 (2007)",{"doi":1404},"10.1007\u002Fs00603-006-0103-x",{"id":22,"text":1406,"url":22,"identifiers":1407},"Zhao, D., et al.: Synchronized control with neuro-agents for leader-follower based multiple robotic manipulators. Neurocomputing 124, 149–161 (2014a)",{"doi":1408},"10.1016\u002Fj.neucom.2013.07.016",{"id":22,"text":1410,"url":22,"identifiers":1411},"Zhao, D., Ni, W., Zhu, Q.: A framework of neural networks based consensus control for multiple robotic manipulators. Neurocomputing 140, 8–18 (2014b)",{"doi":1412},"10.1016\u002Fj.neucom.2014.03.041",{"id":1414,"createTime":1415,"updateTime":1416,"relativeEntities":1417,"slug":1418,"properties":1419,"entityType":227,"verifyStatus":228,"verifyTime":1430,"verifyNote":230,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":1431,"fullTextUrl":22,"authors":1432,"publicationType":278,"publisherRelationship":1461,"citationCount":1513,"citationInfo":1514,"publishDate":1518,"publishYear":1515,"citationAnalyzeStatus":339,"lastCitationAnalyze":1416,"indexDatabases":1519,"openAccess":22,"references":22,"isForceReanalyzing":448},"b55027ad-a411-4be5-813e-62abd8becb2e","2024-01-21T01:10:08.758+00:00","2026-07-20T12:37:53.301+00:00",[],"Method-of-Negative-Saturations-for-Modeling-Two-phase-Compositional-Flow-with-Oversaturated-Zones",{"abstract":1420,"title":1422,"gsPaper":1424,"references":1426,"doi":1428},{"EN":1421},"We examine the two-phase flow through porous media of multicomponent partially miscible fluids. The composition of both the phases is variable in space and time and is assumed to be in local thermodynamic equilibrium. One of the basic problems in modeling such systems is related to the appearance of single-phase zones occupied by the fluid which is over- (or under-) saturated, i.e., it is significantly remote from the equilibrium two-phase region. In an oversaturated zone, the two-phase flow equations degenerate and can no longer be used, which provokes serious numerical problems. We propose to describe the two-phase and oversaturated single-phase zone by a uniform system of classic two-phase equations while extending the concept of the phase saturation so that it may be negative and higher than one. Physically this means that we consider the oversaturated single-phase states as the pseudo two-phase states which are characterized by a negative saturation of the imaginary phase. Such an extension of the concept of the phase saturation requires the development of some consistence conditions that ensure the equivalence between the pseudo two-phase equations and the true single-phase flow model in the oversaturated zones. This method allows using the existing numerical simulators of two-phase flow for modeling single-phase zones by adding a simple plug-in with no modification of the structure of the simulators. The method is illustrated by several examples of hydrogene-water flow in a waste radioactive storage and of CO2 injection in an oil reservoir.",{"EN":1423},"Method of Negative Saturations for Modeling Two-phase Compositional Flow with Oversaturated Zones",{"VOID":1425},"[\"18394473337127184407\"]",{"VOID":1427},"Bedrikovetsky P.: Mathematical Theory of Oil and Gas Recovery. Kluwer Academic Publishers, Dordrecht (1993)\nBrusilovsky A.I.: Transition de Phases Under Exploitation of Oil and Gas Reservoirs. Graal, Moscow (2002)\nEntov V.M.: Nonlinear Waves in Physicochemical Hedrodynamics of Enhanced Oil Recovery, Multicomponent Flows. Nedra, Moscow (1997)\nOrr F.M.: Theory of Gas Injection Processes. Stanford University, California (2002)\nMichelsen M.N.: The isothermal flash problem: Part I: stability. Fluid Phase Equilibria 9(1), 1–19 (1982)\nRhee H., Aris R., Amundson N.R.: First-order Partial Differential Equations. Vol. 1. Printice-Hall, New Jersey (1986)",{"VOID":1429},"10.1007\u002Fs11242-008-9310-0","2024-08-30T07:32:04.388+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11242-008-9310-0",[1433,1448],{"id":1434,"sortIndex":23,"researcher":22,"roles":1435,"affiliations":1436,"properties":1445,"displayName":1447,"givenName":22,"familyName":22},"8ab34a5d-280c-4fe7-8c34-15f713dae29b",[236],[1437],{"id":1438,"sortIndex":23,"affiliation":1439,"properties":22},"80f08bc4-879d-47ec-99d7-16e5fea1f9d5",{"id":1438,"createTime":22,"updateTime":22,"relativeEntities":1440,"slug":22,"properties":1441,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1444,"statistic":22},[],{"title":1442},{"VI":1443},"LEMTA-UMR 7563: Laboratoire d’Energétique et de Mécanique Théorique et Appliquée - Nancy - Université, Vandoeuvre-lés-Nancy, France",[],{"title":1446},{"VI":1447},"Anahita Abadpour",{"id":1449,"sortIndex":172,"researcher":22,"roles":1450,"affiliations":1451,"properties":1458,"displayName":1460,"givenName":22,"familyName":22},"bb4fccc5-d98d-4d02-964f-6cb2b7642711",[236],[1452],{"id":1438,"sortIndex":23,"affiliation":1453,"properties":22},{"id":1438,"createTime":22,"updateTime":22,"relativeEntities":1454,"slug":22,"properties":1455,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1457,"statistic":22},[],{"title":1456},{"VI":1443},[],{"title":1459},{"VI":1460},"Mikhail Panfilov",{"url":1431,"publisher":1462,"properties":1508},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1463,"slug":10,"properties":1464,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":1468,"manageAffiliations":1477,"indexDatabases":1488,"url":22,"thumbnailPath":22,"statistic":1503,"gsStatistic":22,"type":207,"analyzePriority":22},[],{"issn":1465,"title":1466,"eissn":1467},{"VOID":15},{"EN":17},{"VOID":13},[1469,1473],{"id":26,"createTime":22,"updateTime":22,"relativeEntities":1470,"label":1471,"description":1472,"parentId":22,"standard":22,"scholarHubFieldId":22},[],{"EN":29},{},{"id":32,"createTime":22,"updateTime":22,"relativeEntities":1474,"label":1475,"description":1476,"parentId":22,"standard":22,"scholarHubFieldId":22},[],{"EN":35},{},[1478,1483],{"id":39,"createTime":22,"updateTime":22,"relativeEntities":1479,"slug":22,"properties":1480,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1482,"statistic":22},[],{"title":1481},{"EN":43},[45],{"id":47,"createTime":22,"updateTime":22,"relativeEntities":1484,"slug":22,"properties":1485,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1487,"statistic":22},[],{"title":1486},{"EN":51},[],[1489,1496],{"id":72,"indexDatabase":1490,"url":83,"indexYears":84,"academicFieldIds":1495,"indexDatabaseRanking":88},{"id":74,"createTime":22,"updateTime":22,"relativeEntities":1491,"label":1492,"description":1493,"key":80,"publicationTags":1494,"standard":22},[],{"EN":77,"VI":77},{"EN":77,"VI":79},[82],[86,87],{"id":55,"indexDatabase":1497,"url":68,"indexYears":22,"academicFieldIds":1502,"indexDatabaseRanking":22},{"id":57,"createTime":22,"updateTime":22,"relativeEntities":1498,"label":1499,"description":1500,"key":64,"publicationTags":1501,"standard":22},[],{"EN":60,"VI":60},{"EN":62,"VI":63},[66,67],[70],{"impactFactor":23,"impactFactorByYear":1504,"i10Index":103,"i10IndexLast5Year":104,"totalPublication":105,"totalPublicationByYear":1505,"totalCitation":142,"totalCitationByYear":1506,"totalCitationPerPublication":173,"totalCitationPerPublicationByYear":1507,"hindexLast5Year":206,"hindex":206},{"2012":91,"2013":92,"2014":93,"2015":94,"2016":95,"2017":96,"2018":97,"2019":98,"2020":99,"2021":100,"2022":101,"2023":102},{"1986":107,"1987":108,"1988":109,"1989":110,"1990":111,"1991":112,"1992":113,"1993":114,"1994":115,"1995":116,"1996":116,"1997":117,"1998":118,"1999":119,"2000":120,"2001":121,"2002":122,"2003":123,"2004":124,"2005":120,"2006":125,"2007":126,"2008":127,"2009":128,"2010":128,"2011":129,"2012":130,"2013":131,"2014":128,"2015":132,"2016":133,"2017":134,"2018":135,"2019":136,"2020":137,"2021":138,"2022":139,"2023":140,"2024":141},{"1986":144,"1987":125,"1988":145,"1989":146,"1990":147,"1991":148,"1992":149,"1993":150,"1994":151,"1995":152,"1996":131,"2004":153,"2005":154,"2006":155,"2007":156,"2008":157,"2009":158,"2010":159,"2011":160,"2012":161,"2013":155,"2014":162,"2015":163,"2016":164,"2017":165,"2018":166,"2019":167,"2020":168,"2021":169,"2022":170,"2023":171,"2024":172},{"1986":175,"1987":176,"1988":177,"1989":178,"1990":179,"1991":180,"1992":181,"1993":182,"1994":183,"1995":184,"1996":185,"2004":186,"2005":187,"2006":188,"2007":189,"2008":190,"2009":191,"2010":192,"2011":193,"2012":194,"2013":195,"2014":196,"2015":197,"2016":198,"2017":199,"2018":200,"2019":201,"2020":202,"2021":203,"2022":204,"2023":95,"2024":205},{"pages":1509,"volume":1511},{"VOID":1510},"197-214",{"VOID":1512},"79",76,{"total":1513,"publishYear":1515,"statisticByYear":1516},2008,{"2009":172,"2010":542,"2011":337,"2012":1517,"2013":660,"2014":1517,"2015":336,"2016":266,"2017":335,"2018":660,"2019":336,"2020":660,"2021":337,"2022":172,"2023":336,"2024":172,"2025":172},9,"2008-12-09",[66,88],{"id":1521,"createTime":1522,"updateTime":1523,"relativeEntities":1524,"slug":1525,"properties":1526,"entityType":227,"verifyStatus":228,"verifyTime":1537,"verifyNote":230,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":1538,"fullTextUrl":22,"authors":1539,"publicationType":278,"publisherRelationship":1615,"citationCount":1667,"citationInfo":1668,"publishDate":1671,"publishYear":1669,"citationAnalyzeStatus":1672,"lastCitationAnalyze":1523,"indexDatabases":1673,"openAccess":22,"references":22,"isForceReanalyzing":448},"bada2b64-22b3-403a-8146-a6ade7b55fea","2023-12-26T03:05:41.736+00:00","2026-07-16T23:15:50.758+00:00",[],"Comparative-Analysis-of-Imaging-and-Measurements-of-Micrometer-Scale-Fracture-Aperture-Fields-Within-a-Heterogeneous-Rock-Using-PET-and-X-ray-CT",{"abstract":1527,"title":1529,"gsPaper":1531,"references":1533,"doi":1535},{"EN":1528},"Knowledge of the spatial distribution of fracture apertures is essential for reliable characterization of flow and transport processes in fractured systems and for better understanding of physicochemical matrix–fracture interactions. Here, we propose and test two image-based methods, thereby extending the current experimental capabilities to characterize aperture size distribution in structurally heterogeneous geologic porous media noninvasively. The first approach utilizes an inversion method based on the dataset acquired from positron emission tomography (PET) and the second approach considers an extension of the classic missing attenuation technique that relies on clinical X-ray computed tomography (X-ray CT). Independent sets of imaging experiments are conducted on a fractured basalt core with heterogeneous matrix properties and aperture distributions to compare the two methodologies. A repeat of each experiment is conducted to verify the proposed workflows. The performance of these two imaging techniques is systematically evaluated through the analysis of signal-to-noise ratio, minimum fracture size detectability, and measurement errors. While both approaches provide a reliable estimation of fracture aperture distributions, PET yields a signal-to-noise ratio that is substantially higher than the corresponding X-ray CT measurements. Furthermore, uncertainties of the aperture values for PET are considerably lower (\n                \n                  \n                \n                $$\\overline{\\sigma }_\\textrm{d}=15$$\n                \n              %) compared to those obtained from X-ray CT (\n                \n                  \n                \n                $$\\overline{\\sigma }_\\textrm{d}=29$$\n                \n              %), allowing for the detection of minimum aperture sizes of 20 \n                \n                  \n                \n                $$\\mu$$\n                \n              m with 70% confidence level. These approaches provide key experimental tools for better understanding dynamic hydromechanical fracture properties in geologic systems.",{"EN":1530},"Comparative Analysis of Imaging and Measurements of Micrometer-Scale Fracture Aperture Fields Within a Heterogeneous Rock Using PET and X-ray CT",{"VOID":1532},"[\"5897769151234875707\"]",{"VOID":1534},"Akin, S., Kovscek, A.R.: Computed tomography in petroleum engineering research. Geol. Soc. 215(1), 23–38 (2003). https:\u002F\u002Fdoi.org\u002F10.1144\u002FGSL.SP.2003.215.01.03\nAlRatrout, A., Blunt, M.J., Bijeljic, B.: Wettability in complex porous materials, the mixed-wet state, and its relationship to surface roughness. Proc. Natl. Acad. Sci. U.S.A. 115(36), 8901–8906 (2018). https:\u002F\u002Fdoi.org\u002F10.1073\u002FPNAS.1803734115\nAmeli, P., Elkhoury, J.E., Detwiler, R.L.: High-resolution fracture aperture mapping using optical profilometry. Water Resour. 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Porous Media 70(1), 25–42 (2007). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs11242-006-9080-5",{"VOID":1536},"10.1007\u002Fs11242-023-01922-8","2024-06-26T11:26:21.164+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11242-023-01922-8",[1540,1557,1574,1587,1602],{"id":1541,"sortIndex":23,"researcher":22,"roles":1542,"affiliations":1543,"properties":1552,"displayName":1554,"givenName":22,"familyName":22},"3634e68a-3b52-467e-824a-8e410f8307d3",[236],[1544],{"id":1545,"sortIndex":23,"affiliation":1546,"properties":22},"d81106e1-934f-44ee-959b-c4d72bb53392",{"id":1545,"createTime":22,"updateTime":22,"relativeEntities":1547,"slug":22,"properties":1548,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1551,"statistic":22},[],{"title":1549},{"VI":1550},"Department of Energy Science & Engineering, Stanford University, Stanford, USA",[],{"title":1553,"gsAuthor":1555},{"VI":1554},"Takeshi Kurotori",{"VOID":1556},"[\"B9EcaXoAAAAJ\"]",{"id":1558,"sortIndex":172,"researcher":22,"roles":1559,"affiliations":1560,"properties":1569,"displayName":1571,"givenName":22,"familyName":22},"91dd4b51-c25b-49f0-9f96-1afeeb584224",[236],[1561],{"id":1562,"sortIndex":23,"affiliation":1563,"properties":22},"abde25b0-e280-4244-a947-70249d5d01f8",{"id":1562,"createTime":22,"updateTime":22,"relativeEntities":1564,"slug":22,"properties":1565,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1568,"statistic":22},[],{"title":1566},{"VI":1567},"Department of Geoscience, University of Wisconsin-Madison, Madison, USA",[],{"title":1570,"gsAuthor":1572},{"VI":1571},"Christopher Zahasky",{"VOID":1573},"[\"Zw5xmqkAAAAJ\"]",{"id":1575,"sortIndex":266,"researcher":22,"roles":1576,"affiliations":1577,"properties":1584,"displayName":1586,"givenName":22,"familyName":22},"62da6bb8-0c01-4566-8553-b6734b8921c3",[236],[1578],{"id":1545,"sortIndex":23,"affiliation":1579,"properties":22},{"id":1545,"createTime":22,"updateTime":22,"relativeEntities":1580,"slug":22,"properties":1581,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1583,"statistic":22},[],{"title":1582},{"VI":1550},[],{"title":1585},{"VI":1586},"Meritxell Gran",{"id":1588,"sortIndex":337,"researcher":22,"roles":1589,"affiliations":1590,"properties":1597,"displayName":1599,"givenName":22,"familyName":22},"2aeb3e40-bad9-4e97-8d51-c0cc9e33b565",[236],[1591],{"id":1545,"sortIndex":23,"affiliation":1592,"properties":22},{"id":1545,"createTime":22,"updateTime":22,"relativeEntities":1593,"slug":22,"properties":1594,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1596,"statistic":22},[],{"title":1595},{"VI":1550},[],{"title":1598,"gsAuthor":1600},{"VI":1599},"Anthony R. 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This paper reviews the principles of shrinkage and stress development during drying of cement paste and concrete, taking particular account of the changes in microstructure as the cement hydrates, which profoundly influence the transport and mechanical properties of the body.",{"EN":1684},"Drying, Shrinkage, and Cracking of Cementitious Materials",{"VOID":1686},"[\"9207626366899530967\"]",{"VOID":1688},"Acker, P.: Swelling, shrinkage and creep: a mechanical approach to cement hydration. Mater. Struct. 37(May), 237–243 (2004)\nBarcelo, L., Kline, J., Walenta, G., Gartner, E.: Cement and carbon emissions. Mater. Struct. 47, 1055–1065 (2014)\nBaroghel-Bouny, V.: Water vapour sorption experiments on hardened cementitious materials. Part I: essential tool for analysis of hygral behaviour and its relation to pore structure. Cem. Concr. Res. 37, 414–437 (2007a)\nBaroghel-Bouny, V.: Water vapour sorption experiments on hardened cementitious materials. Part II: Essential tool for assessment of transport properties and for durability prediction. Cem. Concr. Res. 37, 438–454 (2007b)\nBaroghel-Bouny, V., Mainguy, M., Lassabatere, T., Coussy, O.: Characterization and identification of equilibrium and transfer moisture properties for ordinary and high-performance cementitious materials. Cem. Concr. Res. 29, 1225–1238 (1999)\nBaroghel-bouny, V., Mainguy, M., Coussy, O.: Isothermal drying process in weakly permeable cementitious materials—assessment of water permeability. In: Hooton, R.D., Thomas, M.D.A., Marchand, J., Beaudoin, J.J. (eds.) Materials Science of Concrete Special Volume: Ion and Mass Transport in Cement-Based Materials, pp. 59–80. American Ceramic Society, Westerville (2001)\nBaroghel-Bouny, V., Mounanga, P., Khelidj, A., Loukili, A., Rafai, N.: Autogenous deformations of cement pastes Part II. W\u002FC effects, micro-macro correlations, and threshold values. Cem. Concr. 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National Institute of Standards and Technology Internal Report, NISTIR 7765, February 2011\nBentz, D.P., Geiker, M.R., Hansen, K.K.: Shrinkage-reducing admixtures and early-age desiccation in cement pastes and mortars. Cem. Concr. Res. 31, 1075–1085 (2001)\nBeyea, S.D., Balcom, B.J., Bremner, T.W., Prado, P.J., Green, D.P., Armstrong, R.L., Grattan-Bellew, P.E.: Magnetic resonance imaging and moisture content profiles of drying concrete. Cem. Concr. Res. 28(3), 453–463 (1998)\nBeyea, S.D., Balcom, B.J., Bremner, T.W., Armstrong, R.L., Grattan-Bellew, P.E.: Detection of drying-induced microcracking in cementitious materials with space-resolved \\(^{1}\\)H nuclear magnetic resonance relaxometry. J. Am. Ceram. Soc. 86(5), 800–805 (2003)\nBisschop, J., van Mier, J.G.M.: Effect of aggregates and microcracks on the drying rate of cementitious composites. Cem. Concr. Res. 38, 1190–1196 (2008)\nBisschop, J., Wittel, F.K.: Contraction gradient induced microcracking in hardened cement paste. 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