Hostname: page-component-89b8bd64d-9prln Total loading time: 0 Render date: 2026-05-07T09:31:25.877Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiscale simulation of transport phenomena in porous media: from toy models to materials models

Published online by Cambridge University Press:  12 March 2018

Ulf D. Schiller Open the ORCID record for Ulf D. Schiller [Opens in a new window]  and
Fang Wang
Ulf D. Schiller*
Affiliation:
Department of Materials Science and Engineering, Clemson University, 161 Sirrine Hall, Clemson, SC 29634, USA
Fang Wang
Affiliation:
Department of Materials Science and Engineering, Clemson University, 161 Sirrine Hall, Clemson, SC 29634, USA
*
Address all correspondence to Ulf D. Schiller at uschill@clemson.edu
Get access

Abstract

Multiscale modeling and simulation techniques are transforming the way we can address questions concerning design, characterization, and optimization of novel materials. This transformation is enabled by advanced computational models that incorporate realistic geometries of porous media and serve as tools to predict flow and transport phenomena. Recent developments in mesoscopic and pore-scale modeling include workflows that combine experimental information and direct modeling into an integrated multiscale approach. This review surveys the progress, challenges, and future directions in predictive modeling and simulation of multiphysics phenomena in porous media.

Information

Type
Prospective Articles
Information
MRS Communications , Volume 8 , Issue 2 , June 2018 , pp. 358 - 371
Check for updates
Copyright
Copyright © Materials Research Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Khanafer, K. and Vafai, K.: The role of porous media in biomedical engineering as related to magnetic resonance imaging and drug delivery. Heat Mass Transf. 42, 939 (2006).Google Scholar
2.Tarascon, J.-M. and Armand, M.: Issues and challenges facing rechargeable lithium batteries. Nature 414, 359 (2001).Google Scholar
3.Yang, X.H., Lu, T.J., and Kim, T.: A simplistic model for the tortuosity in two-phase close-celled porous media. J. Phys. D: Appl. Phys. 46, 125305 (2013).Google Scholar
4.Chen, Z., Trofimov, A.A., Jacobsohn, L.G., Xiao, H., Kornev, K.G., Xu, D., and Peng, F.: Permeation and optical properties of YAG:Er3+fiber membrane scintillators prepared by novel sol–gel/electrospinning method. J. Sol-Gel Sci. Technol. 83, 35 (2017).Google Scholar
5.Roberts, S.A., Mendoza, H., Brunini, V.E., Trembacki, B.L., Noble, D.R., and Grillet, A.M.: Insights into lithium-ion battery degradation and safety mechanisms from mesoscale simulations using experimentally reconstructed mesostructures. J. Electrochem. En. Conv. Stor. 13, 031005 (2016).CrossRefGoogle Scholar
6.Blunt, M.J.: Flow in porous media — pore-network models and multiphase flow. Curr. Opin. Colloid Interface Sci. 6, 197 (2001).Google Scholar
7.Xiong, Q., Baychev, T.G., and Jivkov, A.P.: Review of pore network modelling of porous media: Experimental characterisations, network constructions and applications to reactive transport. J. Contam. Hydrol. 192, 101 (2016).Google Scholar
8.Gueven, I., Frijters, S., Harting, J., Luding, S., and Steeb, H.: Hydraulic properties of porous sintered glass bead systems. Granul. Matter 19, 28 (2017).Google Scholar
9.Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., and Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197 (2013).Google Scholar
10.Meakin, P. and Tartakovsky, A.M.: Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev. Geophys. 47, RG3002 (2009).Google Scholar
11.Shan, X. and Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47, 1815 (1993).Google Scholar
12.Shan, X.W. and Chen, H.D.: Simulation of nonideal gases and liquid-gas phase-transitions by the lattice Boltzmann equation. Phys. Rev. E 49, 2941 (1994).Google Scholar
13.Capuani, F., Pagonabarraga, I., and Frenkel, D.: Discrete solution of the electrokinetic equations. J. Chem. Phys. 121, 973 (2004).CrossRefGoogle ScholarPubMed
14.Nabovati, A., Llewellin, E.W., and Sousa, A.C.M.: A general model for the permeability of fibrous porous media based on fluid flow simulations using the lattice Boltzmann method. Compos. A 40, 860 (2009).Google Scholar
15.Boek, E.S. and Venturoli, M.: Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries. Comput. Math. Appl. 59, 2305 (2010).Google Scholar
16.Ghassemi, A. and Pak, A.: Pore scale study of permeability and tortuosity for flow through particulate media using lattice Boltzmann method. Int. J. Numer. Anal. Meth. Geomech. 35, 886 (2011).CrossRefGoogle Scholar
17.Hilfer, R.: Transport and relaxation phenomena in porous media. In Advances in Chemical Physics, edited by Prigogine, I. and Rice, S.A. (John Wiley & Sons, Inc., Hoboken, NJ, USA, 1996), pp. 299–424.Google Scholar
18.Kwiecien, M.J., Macdonald, I.F., and Dullien, F.A.L.: Three-dimensional reconstruction of porous media from serial section data. J. Microsc. 159, 343 (1990).CrossRefGoogle Scholar
19.Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure (Academic Press, San Diego, 2nd ed., 1992).Google Scholar
20.Panda, M.N. and Lake, L.W.: A physical model of cementation and its effects on single-phase permeability. AAPG Bull. 79, 431 (1995).Google Scholar
21.Garrouch, A.A., Ali, L., and Qasem, F.: Using diffusion and electrical measurements to assess tortuosity of porous media. Ind. Eng. Chem. Res. 40, 4363 (2001).Google Scholar
22.Lucas, R.: Ueber das Zeitgesetz des kapillaren Aufstiegs von Flüssigkeiten. Kolloid-Zeitschrift 23, 15 (1918).Google Scholar
23.Washburn, E.W.: The dynamics of capillary flow. Phys. Rev. 17, 273 (1921).Google Scholar
24.Sing, K.: The use of nitrogen adsorption for the characterisation of porous materials. Colloids Surf. A 187, 3 (2001).CrossRefGoogle Scholar
25.Brunauer, S., Emmett, P.H., and Teller, E.: Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309 (1938).Google Scholar
26.Barrett, E.P., Joyner, L.G., and Halenda, P.P.: The determination of pore volume and area distributions in porous substances. I. Computations from nitrogen isotherms. J. Am. Chem. Soc. 73, 373 (1951).CrossRefGoogle Scholar
27.Ketcham, R.A. and Carlson, W.D.: Acquisition, optimization and interpretation of x-ray computed tomographic imagery: applications to the geosciences. Comput. Geosci. 27, 381 (2001).Google Scholar
28.Shannon, M.A., Bohn, P.W., Elimelech, M., Georgiadis, J.G., Mariñas, B.J., and Mayes, A.M.: Science and technology for water purification in the coming decades. Nature 452, 301 (2008).Google Scholar
29.Amin, M.T., Alazba, A.A., and Manzoor, U.: A review of removal of pollutants from water/wastewater using different types of nanomaterials. Adv. Mater. Sci. Eng. 2014, 825910 (2014).Google Scholar
30.Théron, F., Lys, E., Joubert, A., Bertrand, F., and Le Coq, L.: Characterization of the porous structure of a non-woven fibrous medium for air filtration at local and global scales using porosimetry and x-ray micro-tomography. Powder Technol.. 320, 295 (2017).Google Scholar
31.Lu, W.-M., Tung, K.-L., and Hwang, K.-J.: Fluid flow through basic weaves of monofilament filter cloth. Text. Res. J. 66, 311 (1996).Google Scholar
32.Gregor, E.C.. Primer on nonwoven fabric filtration media, 2003. https://www.chemicalprocessing.com/assets/Media/MediaManager/NonwvnFabricFiltrMedia.pdfGoogle Scholar
33.Vallabh, R., Banks-Lee, P., and Seyam, A.-F.: New approach for determining tortuosity in fibrous porous media. J. Eng. Fiber Fabr. 5, 7 (2010).Google Scholar
34.Schmieschek, S., Shamardin, L., Frijters, S., Krüger, T., Schiller, U.D., Harting, J., and Coveney, P.V.: LB3D: A parallel implementation of the Lattice-Boltzmann method for simulation of interacting amphiphilic fluids. Comput. Phys. Commun. 217, 149 (2017).Google Scholar
35.Zitha, P., Felder, R., Zornes, D., Brown, K., and Mohanty, K.: Increasing hydrocarbon recovery factors, 2011. http://www.spe.org/industry/increasing-hydrocarbon-recovery-factors.phpGoogle Scholar
36.Ghazanfari, E., Shrestha, R.A., Miroshnik, A., and Pamukcu, S.: Electrically assisted liquid hydrocarbon transport in porous media. Electrochim. Acta 86, 185 (2012).Google Scholar
37.Seccombe, J.C., Lager, A., Webb, K.J., Jerauld, G., and Fueg, E.: Improving Wateflood Recovery: LoSalTM EOR Field Evaluation, 2008. https://www.onepetro.org/conference-paper/SPE-113480-MSGoogle Scholar
38.Webb, K., Lager, A., and Black, C.: Comparison of high/low salinity water/oil relative permeability. In International Symposium of the Society of Core Analysts, volume 29 (UAE, Abu Dhabi, 2008). http://www.jgmaas.com/SCA/2008/SCA2008-39.pdfGoogle Scholar
39.Garrick, T.R., Kanneganti, K., Huang, X., and Weidner, J.W.: Modeling volume change due to intercalation into porous electrodes. J. Electrochem. Soc. 161, E3297 (2014).CrossRefGoogle Scholar
40.Abada, S., Marlair, G., Lecocq, A., Petit, M., Sauvant-Moynot, V., and Huet, F.: Safety focused modeling of lithium-ion batteries: A review. J. Power Sources 306, 178 (2016).Google Scholar
41.Smith, R.B. and Bazant, M.Z.: Multiphase porous electrode theory. J. Electrochem. Soc. 164, E3291 (2017).Google Scholar
42.Lee, S., Sastry, A.M., and Park, J.: Study on microstructures of electrodes in lithium-ion batteries using variational multi-scale enrichment. J. Power Sources 315, 96 (2016).Google Scholar
43.Kashkooli, A.G., Farhad, S., Lee, D.U., Feng, K., Litster, S., Babu, S.K., Zhu, L., and Chen, Z.: Multiscale modeling of lithium-ion battery electrodes based on nano-scale x-ray computed tomography. J. Power Sources 307, 496 (2016).CrossRefGoogle Scholar
44.Turner, J., Allu, S., Berrill, M., Elwasif, W., Kalnaus, S., Kumar, A., Lebrun-Grandie, D., Pannala, S., and Simunovic, S.: Safer batteries through coupled multiscale modeling. Proc. Comput. Sci. 51, 1168 (2015).Google Scholar
45.Darcy, H.: Les fontaines publiques de la ville de Dijon (V. Dalmont, Libraire des Corps imperiaux des ponts et chaussées et des mines, Paris, 1856).Google Scholar
46.Kozeny, J.: Über kapillare Leitung des Wassers im Boden. Sitzungsber. Akad. Wiss. Wien 136, 271 (1927).Google Scholar
47.Carman, P.C.: Fluid flow through porous rock. Trans. Inst. Chem. Eng. 15, 150 (1937).Google Scholar
48.Carman, P.C.: Flow of Gases Through Porous Media (Academic Press, New York, 1956).Google Scholar
49.Pan, C., Hilpert, M., and Miller, C.T.: Pore-scale modeling of saturated permeabilities in random sphere packings. Phys. Rev. E 64, 066702 (2001).Google Scholar
50.Ahmadi, M.M., Mohammadi, S., and Hayati, A.N.: Analytical derivation of tortuosity and permeability of monosized spheres: a volume averaging approach. Phys. Rev. E 83, 026312 (2011).Google Scholar
51.Duda, A., Koza, Z., and Matyka, M.: Hydraulic tortuosity in arbitrary porous media flow. Phys. Rev. E 84, 036319 (2011).Google Scholar
52.Xu, P. and Yu, B.: Developing a new form of permeability and Kozeny–Carman constant for homogeneous porous media by means of fractal geometry. Adv. Water Resour. 31, 74 (2008).Google Scholar
53.Matyka, M., Khalili, A., and Koza, Z.: Tortuosity-porosity relation in porous media flow. Phys. Rev. E 78, 026306 (2008).Google Scholar
54.Valdés-Parada, F.J., Porter, M.L., and Wood, B.D.: The role of tortuosity in upscaling. Transp. Porous. Med. 88, 1 (2011).Google Scholar
55.Ghanbarian, B., Hunt, A.G., Ewing, R.P., and Sahimi, M.: Tortuosity in porous media: a critical review. Soil Sci. Soc. Am. J. 77, 1461 (2013).Google Scholar
56.Allen, R. and Sun, S.: Computing and comparing effective properties for flow and transport in computer-generated porous media. Geofluids 2017, 4517259 (2017).Google Scholar
57.Dias, R., Teixeira, J.A., Mota, M., and Yelshin, A.: Tortuosity variation in a low density binary particulate bed. Sep. Purif. Technol. 51, 180 (2006).Google Scholar
58.Rumpf, H.C.H. and Gupte, A.R.: Einflüsse der Porosität und Korngrößenverteilung im Widerstandsgesetz der Porenströmung. Chem. Ing. Tech. 43, 367 (1971).Google Scholar
59.Bourbié, T. and Coussy, O.: Acoustics of Porous Media Editions (TECHNIP, Paris, 1987).Google Scholar
60.Koponen, A., Kataja, M., and Timonen, J.: Permeability and effective porosity of porous media. Phys. Rev. E 56, 3319 (1997).Google Scholar
61.Mcgregor, R.: The effect of rate of flow on rate of dyeing II–The mechanism of fluid flow through textiles and its significance in dyeing. J. Soc. Dyers Colour. 81, 429 (1965).Google Scholar
62.Rodriguez, E., Giacomelli, F., and Vazquez, A.: Permeability-porosity relationship in RTM for different fiberglass and natural reinforcements. J. Compos. Mater. 38, 259 (2004).Google Scholar
63.Costa, A.: Permeability-porosity relationship: A reexamination of the Kozeny–Carman equation based on a fractal pore-space geometry assumption. Geophys. Res. Lett. 33, L02318 (2006).Google Scholar
64.Clague, D.S., Kandhai, B.D., Zhang, R., and Sloot, P.M.A.: Hydraulic permeability of (un)bounded fibrous media using the lattice Boltzmann method. Phys. Rev. E 61, 616 (2000).Google Scholar
65.Gebart, B.: Permeability of unidirectional reinforcements for RTM. J. Compos. Mater. 26, 1100 (1992).Google Scholar
66.Archie, G.E.: The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. Am. Inst. Min., Metall. Pet. Eng. 146, 54 (1942).Google Scholar
67.Plessis, J.P.D. and Masliyah, J.H.: Mathematical modelling of flow through consolidated isotropic porous media. Transp. Porous. Med. 3, 145 (1988).Google Scholar
68.Plessis, J.P.D. and Masliyah, J.H.: Flow through isotropic granular porous media. Transp. Porous. Med. 6, 207 (1991).Google Scholar
69.du Plessis, E., Woudberg, S., and Prieur du Plessis, J.: Pore-scale modelling of diffusion in unconsolidated porous structures. Chem. Eng. Sci. 65, 2541 (2010).CrossRefGoogle Scholar
70.Iversen, N. and Jørgensen, B.B.: Diffusion coefficients of sulfate and methane in marine sediments: influence of porosity. Geochim. Cosmochim. Acta 57, 571 (1993).Google Scholar
71.Weissberg, H.L.: Effective diffusion coefficient in porous media. J. Appl. Phys. 34, 2636 (1963).CrossRefGoogle Scholar
72.Comiti, J. and Renaud, M.: A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles. Chem. Eng. Sci. 44, 1539 (1989).CrossRefGoogle Scholar
73.Barrande, M., Bouchet, R., and Denoyel, R.: Tortuosity of porous particles. Anal. Chem. 79, 9115 (2007).Google Scholar
74.Mauret, E. and Renaud, M.: Transport phenomena in multi-particle systems—I. Limits of applicability of capillary model in high voidage beds-application to fixed beds of fibers and fluidized beds of spheres. Chem. Eng. Sci. 52, 1807 (1997).Google Scholar
75.Koponen, A., Kataja, M., and Timonen, J.: Tortuous flow in porous media. Phys. Rev. E 54, 406 (1996).Google Scholar
76.Chen, Z.: Recent advances of upscaling methods for the simulation of flow transport through heterogeneous porous media. J. Comput. Math. 24, 393 (2006).Google Scholar
77.Renard, P. and de Marsily, G.: Calculating equivalent permeability: a review. Adv. Water Resour. 20, 253 (1997).Google Scholar
78.E, W. and Engquist, B.: The heterogeneous multiscale methods. Commun. Math. Sci. 1, 87 (2003).Google Scholar
79.Fatt, I.: The network model of porous media. I. Capillary pressure characteristics. Petrol. Trans. AIME 207, 144 (1956).Google Scholar
80.Obliger, A., Duvail, M., Jardat, M., Coelho, D., Békri, S., and Rotenberg, B.: Numerical homogenization of electrokinetic equations in porous media using lattice-Boltzmann simulations. Phys. Rev. E 88, 013019 (2013).Google Scholar
81.Obliger, A., Jardat, M., Coelho, D., Bekri, S., and Rotenberg, B.: Pore network model of electrokinetic transport through charged porous media. Phys. Rev. E 89, 043013 (2014).Google Scholar
82.Blunt, M.J., Jackson, M.D., Piri, M., and Valvatne, P.H.: Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Adv. Water Resour. 25, 1069 (2002).Google Scholar
83.Mehmani, Y. and Balhoff, M.T.: Mesoscale and hybrid models of fluid flow and solute transport. Rev. Mineral. Geochem. 80, 433 (2015).Google Scholar
84.Bryant, S. and Blunt, M.: Prediction of relative permeability in simple porous media. Phys. Rev. A 46, 2004 (1992).Google Scholar
85.Bryant, S.L., King, P.R., and Mellor, D.W.: Network model evaluation of permeability and spatial correlation in a real random sphere packing. Transp. Porous. Med. 11, 53 (1993).Google Scholar
86.Bryant, S.L., Mellor, D.W., and Cade, C.A.: Physically representative network models of transport in porous media. AIChE J.. 39, 387 (1993).Google Scholar
87.Biswal, B., Held, R.J., Khanna, V., Wang, J., and Hilfer, R.: Towards precise prediction of transport properties from synthetic computer tomography of reconstructed porous media. Phys. Rev. E 80, 041301 (2009).Google Scholar
88.Bouzidi, M., Firdaouss, M., and Lallemand, P.: Momentum transfer of a Boltzmann-lattice fluid with boundaries. Phys. Fluids 13, 3452 (2001).Google Scholar
89.Ginzburg, I. and d'Humières, D.: Multireflection boundary conditions for lattice Boltzmann models. Phys. Rev. E 68, 066614 (2003).Google Scholar
90.Rotenberg, B., Pagonabarraga, I., and Frenkel, D.: Dispersion of charged tracers in charged porous media. Europhys. Lett. 83, 34004 (2008).Google Scholar
91.Rotenberg, B. and Pagonabarraga, I.: Electrokinetics: insights from simulation on the microscopic scale. Mol. Phys. 111, 827 (2013).Google Scholar
92.Toschi, F. and Succi, S.: Lattice Boltzmann method at finite Knudsen numbers. Europhys. Lett. 69, 549 (2005).Google Scholar
93.Horbach, J. and Succi, S.: Lattice Boltzmann versus molecular dynamics simulation of nanoscale hydrodynamic flows. Phys. Rev. Lett. 96, 224503 (2006).Google Scholar
94.Dünweg, B. and Ladd, A.J.C.: Lattice Boltzmann simulations of soft matter systems. Adv. Poly. Sci. 221, 89 (2009).Google Scholar
95.Koponen, A., Kandhai, D., Hellén, E., Alava, M., Hoekstra, A., Kataja, M., Niskanen, K., Sloot, P., and Timonen, J.: Permeability of three-dimensional random fiber webs. Phys. Rev. Lett. 80, 716 (1998).CrossRefGoogle Scholar
96.Math2Market GmbH: The GeoDict Software, 2015. https://www.geodict.com/Solutions/aboutGD.phpGoogle Scholar
97.Kanit, T., Forest, S., Galliet, I., Mounoury, V., and Jeulin, D.: Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int. J. Solids Struct. 40, 3647 (2003).Google Scholar
98.Alowayyed, S., Groen, D., Coveney, P.V., and Hoekstra, A.G.: Multiscale computing in the exascale Era. J. Comput. Sci. 22, 15 (2017).Google Scholar
Supplementary material: File

Schiller and Wang supplementary material

Schiller and Wang supplementary material 1

Download Schiller and Wang supplementary material(File)
File 68.4 MB