Abstract
Macroscopic properties, such as capillary pressure and permeability, are important variables for mathematical modeling of transport processes in porous media. However, most transport properties exhibit great variability which cannot be modeled using deterministic approaches. This chapter presents a brief description of some fundaments of porous structures, namely, cell models, digital reconstruction of porous structures (using Lattice Boltzmann Method), porous media generation, and the stochastic modeling of pore space and transport properties.
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Adler, P.M., Thovert, J.F.: Real porous media: local geometry and macroscopic properties. Appl. Mech. Rev. 51, 537–585 (1998)
Aharonov, E., Rothman, D.H.: Non-newtonian flow (through porous media): a lattice Boltzmann method. Geophys. Res. Lett. 20, 679–682 (1993)
Ahmadi, A., Quintard, M., Whitaker, S.: Transport in chemically and mechanically heterogeneous porous media. Part V: two-equation model for solute transport with adsorption. Adv. Water Resour. 22, 59–86 (1998)
Ammar, L., Hsieh, C.K.: Solution of the velocity and pressure fields for stokes flow inside an oblate hemispheroidal cap. Eur. J. Mech. B/Fluids 10, 171–178 (1991)
Bakke, S., Øren, P.E.: 3-D pore-scale modeling of sandstones and flow simulations in the pore networks. SPE. J. 2, 136–149 (1997)
Biswal, B., Manwart, C., Hilfer, R., Bakke, S., Øren, P.E.: Quantitative analysis of experimental and synthetic microstructures for sedimentary rock. Phys. A: Stat. Mech. Appl. 273, 452–475 (1999)
Boek, E.S., Chin, J., Coveney, P.V.: Lattice Boltzmann simulation of the flow of non-newtonian fluids in porous media. Int. J. Mod. Phys. B 17, 99–102 (2003)
Brinkman, H.C.: A calculation of the viscous force exerted by a bowing fluid on a dense swarm of particles. Appl. Sci. Res. Al, 27–34 (1947)
Bryant, S.L., Mellor, D.W., Cade, C.A.: Physically representative network models of transport in porous-media. AIChE J. 39, 387–396 (1993)
Cancelliere, A., Chang, C., Foti, E., Rothman, D.H., Succi, S.: The permeability of a random medium: comparison of simulation with theory. Phys. Fluids A: Fluid 12, 2085–2088 (1990)
Chen, S., Doolen, G.D.: Lattice Boltzmann method for fluid flow. Ann. Rev. Fluid. Mech. 30, 329–364 (1998)
Chiang, H.W., Tien, C.: Dynamics of deep bed filtration: analysis of two limiting situations. AIChE J. 31, 1349–1355 (1985)
Chiles, J.P., Delfiner, P.: Geostatisctics: Modeling Spatial Uncertainty. John Wiley and Sons, New York (1999)
Choo, C.U., Tien, C.: Simulation of hydrosol deposition in granular media. AIChE J. 41, 1426–1431 (1995)
Coelho, D., Thovert, J.F., Adler, P.M.: Geometrical and transport properties of random packings of spheres and aspherical particles. Phys. Rev. E 55, 1959–1978 (1997)
Coker, D.A., Torquato, S., Dunsmuir, J.H.: Morphology and physical properties of fontainebleau sandstone via a tomographic analysis. J. Geophys. Res-Sol. Ea. 101, 17497–17506 (1996)
Coutelieris, F.A., Kainourgiakis, M.E., Stubos, A.K., Kikkinides, E.S., Yortsos, Y.C.: Multiphase mass transport with partitioning and inter-phase transport in porous media. Chem. Eng. Sci. 61, 4650–4661 (2006)
Cunningham, M.A.: On the velocity of steady fall of spherical particles through fluid medium. In: Proceedings of the Royal Society, London, A83, pp 357–365 (1910)
Dassios, G., Hadjinicolaou, M., Payatakes, A.C.: Generalized eigenfunctions and complete semi-separable solutions for stokes flow in spheroidal coordinates. Quart. Appl. Math. 52, 157–191 (1994)
Dassios, G., Hadjinicolaou, M., Coutelieris, F.A., Payatakes, A.C.: Stokes flow in spheroidal particle-in-cell models with Happel and Kuwabara boundary conditions. Int. J. Eng. Sci. 33, 465–1490 (1995)
Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure, 2nd edn. Academic, San Diego (1992)
Epstein, N., Masliyah, J.H.: Creeping flow through clusters of spheroids and elliptical cylinders. Chem. Eng. J. 3, 169–175 (1972)
Fredlund, M.D., Fredlund, D.G., Wilson, G.W.: An equation to represent grain-size distribution. Can. Geotech. J. 37, 817–827 (2000)
Gabbanelli, S., Drazer, G., Koplik, J.: Lattice Boltzmann method for non-newtonian (power-law) fluids. Phys. Rev. E 72, 046312–046319 (2005)
Gunstensen, A.K., Rothman, D.H.: Lattice-Boltzmann studies of immiscible 2-phase flow through porous-media. J. Geophys. Res-Sol. Ea. 98, 6431–6441 (1993)
Happel, J.: Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles. AIChE J. 4, 197–201 (1958)
Heijs, A.W.J., Lowe, C.P.: Numerical evaluation of the permeability and Kozeny constant for two types of porous media. Phys. Rev. E 51, 4346–4352 (1995)
Hilfer, R.: Local porosity theory and stochastic reconstruction for porous media. In: Mecke, K.R., Stoyan, D. (eds.) Lecture Notes in Physics, 554th edn. Springer, Berlin (2000)
Hilfer, R., Manwart, C.: Permeability and conductivity for reconstruction models of porous media. Phys. Rev. E 64, 021304–021307 (2001)
Jin, G., Patzek, T.W., Silin, D.B.: Physics-based reconstruction of sedimentary rocks. In: Proceedings of the SPE Western Regional/AAPG Pacific Section Joint Meeting, SPE 83587, Society of Petroleum Engineers, Long Beach, USA (2003)
Kainourgiakis, M.E., Kikkinides, E.S., Steriotis, T.A., Stubos, A.K., Tzevelekos, K.P., Kanellopoulos, N.K.: Structural and transport properties of alumina porous membranes from process-based and statistical reconstruction techniques. J. Colloid Interf. Sci. 23, 158–167 (2000)
Kawaguti, M.: A hydrodynamical model for the sedimentation. J. Phys. Soc. Jpn. 3, 209–215 (1958)
Kuwabara, S.: The forces experienced by randomly distributed parallel circular cylinder or spheres in a viscous flow at small reynolds numbers. J. Phys. Soc. Jpn. 14, 527–531 (1959)
Latham, J.P., Lu, Y., Munjiza, A.: A random method for simulating loose packs of angular particles using tetrahedral. Geotechnique 51, 871–879 (2001)
Latham, J.P., Munjiza, A., Lu, Y.: On the prediction of void porosity and packing of rock particulates. Powder Techn. 125, 10–27 (2002)
Lerman, A.: Geochemical Processes: Water and Sediment Environments. Wiley, New York (1976)
Li, Y., LeBoeuf, E.J., Basu, P.K., Mahadevan, S.: Stochastic modeling of the permeability of randomly generated porous media. Adv. Water Resour. 28, 835–844 (2005)
Lock, P.A., Jing, X.D., Zimmerman, R.W., Schlueter, E.M.: Predicting the permeability of sandstone from image analysis of pore structure. J. Appl. Phys. 92, 6311–6319 (2002)
Lucia, F.J.: Carbonate Reservoir Characterization. Springer, Berlin (1999)
Manwart, C., Torquato, S., Hilfer, R.: Stochastic reconstruction of sandstones. Phys. Rev. E 62, 893–899 (2000)
Manwart, C., Aaltosalmi, U., Koponen, A., Hilfer, R., Timonen, J.: Lattice-Boltzmann and finite-difference simulations for the permeability for three dimensional porous media. Phys. Rev. E 66, 016702–016713 (2002)
Masliyah, J.H., Neale, G., Malysa, K., Van De Ven, G.M.: Creeping flow over a composite sphere: solid core with porous shell. Chem. Eng. Sci. 42, 245–253 (1987)
Moritomi, H., Yamagishi, T., Chiba, T.: Prediction of complete mixing of liquid-fluidized binary solid particles. Chem. Eng. Sci. 41, 297–305 (1986)
Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12, 513–522 (1976)
Neale, G.H., Nader, W.: Prediction of transport processes within porous media: creeping flow relative to a fixed swarm of spherical particles. AIChE J. 20, 530–538 (1974)
Okabe, H., Blunt, M.J.: Pore space reconstruction using multiple-point statistics. J. Petrol. Sci. Eng. 46, 121–137 (2005)
Øren, P.E., Bakke, S.: Reconstruction of berea sandstone and pore-scale modeling of wettability effects. J. Petrol. Sci. Eng. 39, 177–199 (2003)
Pan, C., Hilpert, M., Miller, C.T.: Pore-scale modeling of saturated permeabilities in random sphere packings. Phys. Rev. E 64, 0066702-1–0066702-9 (2001)
Paraskeva, C.A., Burganos, V.N., Payatakes, A.C.: Three-dimensional trajectory analysis of particle deposition in constricted tubes. Chem. Eng. Commun. 108, 23–48 (1991)
Payatakes, A.C., Tien, C., Turian, R.M.: A new model for granular porous media. Part I: model formulation. AIChE J. 19, 58–67 (1973)
Payatakes, A.C., Tien, C., Turian, R.M.: Trajectory calculation of particle deposition in deep bed filtration. Part I: model formulation. AIChE J. 20, 889–900 (1974)
Payatakes, A.C., Brown, D.H., Tien, C.: On the transient behavior of deep bed filtration. In: Proceedings of the 83rd National AIChE Meeting, Houston, USA (1977)
Pilotti, M.: Reconstruction of clastic porous media. Transport. Porous Med. 41, 359–364 (2000)
Prasad, D., Narayan, K.A., Chhabra, R.P.: Creeping fluid flow relative to an assemblage of composite spheres. Int. J. Eng. Sci. 28, 215–230 (1990)
Quintard, M., Whitaker, S.: One- and two-equation models for transient diffusion processes in two-phase systems. Adv. Heat Transf. 23, 369–464 (1993)
Quintard, M., Whitaker, S.: Convection, dispersion, and interfacial transport of contaminants: homogeneous porous media. Adv. Water Resour. 17, 221–239 (1994)
Quintard, M., Whitaker, S.: Transport in chemically and mechanically heterogeneous porous media I: theoretical development of region-averaged equations for slightly compressible single-phase flow. Adv. Water Resour. 19, 29–47 (1996)
Rajagopalan, R., Tien, C.: Trajectory analysis of deep bed filtration using the sphere-in-cell model. AIChE J. 22, 523–528 (1976)
Richardson, J.F., Zaki, W.N.: The sedimentation of a suspension of uniform spheres under conditions of viscous flow. Chem. Eng. Sci. 3, 65–73 (1954)
Rothman, D.H.: Cellular-automaton fluids: a model for flow in porous media. Geophysics 53, 509–518 (1988)
Scheidegger, A.E.: General theory of dispersion in porous media. J. Geophys. Res. 66, 3273–3278 (1961)
Strebelle, S.: Conditional simulation of complex geological structures using multiple-point statistics. Math. Geol. 34, 1–21 (2002)
Succi, S.: The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, Oxford (2001)
Suciu, N., Vamos, C., Vanderborght, J., Hardelauf, H., Vereecken, H.: Numerical investigations on ergodicity of solute transport in heterogeneous aquifers. Water Resour. Res. 42, W04409–W04419 (2006)
Sukop, M.C., Thorne Jr, D.T.: Lattice Boltzmann Modeling an Introduction for Geoscientists and Engineers. Springer, Berlin (2006)
Sullivan, S.P., Gladden, L.F., Johns, M.L.: Simulation of power-law fluid flow through porous media using lattice Boltzmann techniques. J. Non-Newton. Fluid Mech. 133, 91–98 (2006)
Tien, C.: Granular Filtration of Aerosols and Hydrosols. Butterworths, USA (1989)
Tien, C., Turian, R.M., Pendse, H.P.: Simulation of the dynamic behavior of deep bed filters. AIChE J. 25, 385–395 (1979)
Thovert, J.F., Yousefian, F., Spanne, P., Jacquin, C.G., Adler, P.M.: Grain reconstruction of porous media: application to a low-porosity fontainebleau sandstone. Phys. Rev. E 63, 061307–061323 (2001)
Van Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898 (1980)
Wolf-Gladrow, D.A.: Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction. Lecture Notes in Mathematics. Springer, New York (2000)
Yang, A., Miller, C.T., Turcoliver, L.D.: Simulation of correlated and uncorrelated packing of random size spheres. Phys. Rev. E 53, 1516–1524 (1996)
Yeong, C.L.Y., Torquato, S.: Reconstructing random media. Phys. Rev. E 57, 495–506 (1998)
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Coutelieris, F.A., Delgado, J.M.P.Q. (2012). Fundamentals of Porous Structures. In: Transport Processes in Porous Media. Advanced Structured Materials, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27910-2_2
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