Solute Transport in Porous Media. Media with Capillaries as Voids

We study solute transport in porous media with periodic microstructures consisting of interconnected thin channels. We discuss a local physical mechanism that occurs at the intersections of channels and promotes mixing of the solute with the solvent (i.e., the host liquid). We identify the parameter regime, where this mechanism is the dominant cause of dispersion, and obtain the effective or macroscopic transport equation that the concentration of solute satisfies when the medium is subjected to a time periodic applied pressure gradient. We conclude with illustrative examples.

[1]  Muhammad Sahimi,et al.  Dynamics of Fluids in Hierarchical Porous Media. , 1992 .

[2]  J. Feyen,et al.  Modelling Water Flow and Solute Transport in Heterogeneous Soils: A Review of Recent Approaches☆ , 1998 .

[3]  Wilkinson,et al.  Hydrodynamic dispersion in network models of porous media. , 1986, Physical review letters.

[4]  Brian Berkowitz,et al.  PERCOLATION THEORY AND ITS APPLICATION TO GROUNDWATER HYDROLOGY , 1993 .

[5]  G. Dagan.  Flow and transport in porous formations , 1989 .

[6]  Gedeon Dagan,et al.  Theory of Solute Transport by Groundwater , 1987 .

[7]  W. R. Gardner.  Physics of Flow through Porous Media , 1961 .

[8]  K. H. Coats,et al.  Dead-End Pore Volume and Dispersion in Porous Media , 1964 .

[9]  E. Charlaix,et al.  Hydrodynamic Dispersion in Networks of Capillaries of Random Permeability , 1991 .

[10]  John F. Brady,et al.  Dispersion in Porous Media , 1988 .

[11]  John H. Cushman,et al.  A primer on upscaling tools for porous media , 2002 .

[12]  Muhammad Sahimi,et al.  DISPERSION IN DISORDERED POROUS MEDIA , 1983 .

[13]  Pierre M. Adler,et al.  Taylor dispersion in porous media. Determination of the dispersion tensor , 1993 .

[14]  John F. Brady,et al.  Dispersion in fixed beds , 1985, Journal of Fluid Mechanics.

[15]  M. K. Knothe Tate,et al.  An ex vivo model to study transport processes and fluid flow in loaded bone. , 2000, Journal of biomechanics.

[16]  I. Fatt.  The Network Model of Porous Media , 1956 .

[17]  P. Niederer,et al.  Experimental elucidation of mechanical load-induced fluid flow and its potential role in bone metabolism and functional adaptation. , 1998, The American journal of the medical sciences.

[18]  H. Brenner,et al.  Transport processes in porous media , 1986 .

[19]  Ian G. Main,et al.  Relating flow channelling to tracer dispersion in heterogeneous networks , 2004 .

[20]  P. Saffman,et al.  Dispersion in flow through a network of capillaries , 1959 .

[21]  H. Brenner,et al.  Generalized Taylor-Aris dispersion in discrete spatially periodic networks: microfluidic applications. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Pierre M. Adler,et al.  Porous media : geometry and transports , 1992 .

[23]  Gedeon Dagan,et al.  Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion , 1990 .

[24]  Ulrich Hornung,et al.  Miscible displacement , 1996 .

[25]  P. Niederer,et al.  In vivo tracer transport through the lacunocanalicular system of rat bone in an environment devoid of mechanical loading. , 1998, Bone.

[26]  Helio Pedro Amaral Souto,et al.  Dispersion in periodic porous media. Experience versus theory for two-dimensional systems , 1997 .

[27]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[28]  Arthur W. Rose,et al.  Porous media: Fluid transport and pore structure (2nd Ed.) , 1993 .

[29]  D. A. Edwards,et al.  Dispersion of inert solutes in spatially periodic, two-dimensional model porous media , 1991 .

[30]  H. Brenner,et al.  Dispersion resulting from flow through spatially periodic porous media , 1980, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[31]  J. Bear.  On the tensor form of dispersion in porous media , 1961 .

[32]  H. Brenner,et al.  A general theory of taylor dispersion phenomena. VI. Langevin methods , 1983 .

[33]  Yves Bernabé,et al.  Network modeling of dispersion: Transition from Taylor Dispersion in homogeneous networks to mechanical dispersion in very heterogeneous ones , 2001 .

[34]  Mark L. Brusseau,et al.  Transport of reactive contaminants in heterogeneous porous media , 1994 .

[35]  J. Kärger,et al.  Flow and Transport in Porous Media and Fractured Rock , 1996 .

[36]  B. Berkowitz.  Characterizing flow and transport in fractured geological media: A review , 2002 .

[37]  V. Vinokur,et al.  On the stochastic transport in disordered systems , 1988 .

[38]  F. Horn.  Calculation of dispersion coefficients by means of moments , 1971 .

[39]  C. Harwood.  Groundwater contaminant transport , 1988 .

[40]  Guillermo H. Goldsztein.  Transport of Nutrients in Bones , 2005, SIAM J. Appl. Math..

[41]  Chiang C. Mei,et al.  Method of homogenization applied to dispersion in porous media , 1992 .

[42]  P. Saffman,et al.  A theory of dispersion in a porous medium , 1959, Journal of Fluid Mechanics.

[43]  Stephen C. Cowin,et al.  Modeling Tracer Transport in an Osteon under Cyclic Loading , 2004, Annals of Biomedical Engineering.

[44]  S. Wheatcraft,et al.  Fluid Flow and Solute Transport in Fractal Heterogeneous Porous Media , 1991 .

[45]  P. Saffman,et al.  Dispersion due to molecular diffusion and macroscopic mixing in flow through a network of capillaries , 1960, Journal of Fluid Mechanics.

[46]  M. Sahimi,et al.  Dispersion in Flow through Porous Media , 1982 .

[47]  K. Piekarski,et al.  Transport mechanism operating between blood supply and osteocytes in long bones , 1977, Nature.

[48]  Roberto Mauri,et al.  Dispersion, convection, and reaction in porous media , 1991 .

[49]  Terukatsu Miyauchi,et al.  Axial dispersion in packed beds , 1975 .

[50]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[51]  Feike J. Leij,et al.  Modeling the Nonequilibrium Transport of Linearly Interacting Solutes in Porous Media: A Review , 1991 .

[52]  G. Taylor.  Dispersion of soluble matter in solvent flowing slowly through a tube , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[53]  J. Parlange.  Porous Media: Fluid Transport and Pore Structure , 1981 .

[54]  R. Carbonell.  Effect of pore distribution and flow segregation on dispersion in porous media ag , 1979 .

[55]  Jacob Rubinstein,et al.  Dispersion and convection in periodic porous media , 1986 .

[56]  H. Brenner,et al.  General theory of Taylor dispersion phenomena. Part 3. Surface transport , 1982 .

[57]  Brian Berkowitz,et al.  Percolation Theory and Network Modeling Applications in Soil Physics , 1998 .

[58]  G. Gavalas,et al.  Periodic capillary models of diffusion in porous solids , 1981 .

[59]  Wilkinson,et al.  Transport and dispersion in random networks with percolation disorder. , 1988, Physical review. A, General physics.

[60]  V. Kadet,et al.  Percolation Models for Transport in Porous Media , 1996 .

[61]  Harry R. Cedergren,et al.  Seepage, drainage, and flow nets , 1967 .