Transport in Porous Media

In chemical micro process technology with porous catalyst layers attached to the channel walls, convection through the porous medium can often be neglected. When the reactor geometry allows the flow to bypass the porous medium it will follow the path of smaller hydrodynamic resistance and will not penetrate the pore space. Thus, in micro reactors with channels coated with a catalyst medium, the flow velocity inside the medium is usually zero and heat and mass transfer occur by diffusion alone. 

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At the present time there exist no flux relations wich a completely sound cheoretical basis, capable of describing transport in porous media over the whole range of pressures or pore sizes. All involve empiricism to a greater or less degree, or are based on a physically unrealistic representation of the structure of the porous medium. Existing models fall into two main classes in the first the medium is modeled as a network of interconnected capillaries, while in the second it is represented by an assembly of stationary obstacles dispersed in the gas on a molecular scale. The first type of model is closely related to the physical structure of the medium, but its development is hampered by the lack of a solution to the problem of transport in a capillary whose diameter is comparable to mean free path lengths in the gas mixture. The second type of model is more tenuously related to the real medium but more tractable theoretically. 

A number of different approaches have been taken to describing transport in porous media. The objective here is not to review all approaches, but to present a framework for comparison of various approaches in order to highlight those of particular interest for analysis of diffusion and electrophoresis in gels and other nanoporous materials. General reviews on the fundamental aspects of experiments and theory of diffusion in porous media are given... 

The objective of most of the theories of transport in porous media is to derive analytical or numerical functions for the effective diffusion coefficient to use in the preceed-ing averaged species continuity equations based on the structure of the media and, more recently, the structure of the solute. 

Kim, JH Ochoa, JA Whitaker, S, Diffusion in Anisotropic Porous Media, Transport in Porous Media 2, 327, 1987. 

Saez, AE Perfetti, JC Rusinek, I, Prediction of Effective Diffusivities in Porous Media Using Spatially Periodic Models, Transport in Porous Media 6, 143, 1991. 

Sahimi, M, Flow and Transport in Porous Media and Fractured Rock VCH Weinheim, Germany, 1995. 

Trinh, SH Arce, P Locke, BR, Effective Diffusivities of Point-Like Molecules in Isohopic Porous Media by Monte Carlo Simulation, Transport in Porous Media 38, 241, 2000. 

Whitaker, S, Flow in Porous Media I A Theoretical Derivation of Darcy s Law, Transport in Porous Media 1, 3, 1986. 

Whitaker, S, Transport Processes with Heterogeneous Reaction. In Concepts and Design of Chemical Reactors Whitaker, S Cassano, AE, eds. Gordon and Breach Newark, NJ 1986 1. Whitaker, S, Mass Transport and Reaction in Catalyst Pellets, Transport in Porous Media 2, 269, 1987. 

Surfactant Transport in Porous Media Dynamic Adsorption/Desorption Equilibria... 

Flow of trains of surfactant-laden gas bubbles through capillaries is an important ingredient of foam transport in porous media. To understand the role of surfactants in bubble flow, we present a regular perturbation expansion in large adsorption rates within the low capillary-number, singular perturbation hydrodynamic theory of Bretherton. Upon addition of soluble surfactant to the continuous liquid phase, the pressure drop across the bubble increases with the elasticity number while the deposited thin film thickness decreases slightly with the elasticity number. Both pressure drop and thin film thickness retain their 2/3 power dependence on the capillary number found by Bretherton for surfactant-free bubbles. Comparison of the proposed theory to available and new experimental... 

Gas-diffusion electrode metal-air cells gas-transport in porous media carbon-based catalysts. 

Quantum calculations are the starting point for another objective of theoretical and computational chemical science, multiscale calculations. The overall objective is to understand and predict large-scale phenomena, such as deformation in solids or transport in porous media, beginning with fundamental calculation of electronic structure and interactions, then using the results of that calculation as input to the next level of a more coarse-grained approximation. 

Steefel, C.I. and K.T. B. MacQuarrie, 1996, Approaches to modeling of reactive transport in porous media. In PC. Lichtner, C.I. Steefel and E.H. Oelkers (eds.), Reactive Transport in Porous Media, Reviews in Mineralogy 34, 85-129. 

E.A. Mason and A.P. Malinauskas, Gas Transport in Porous Media The Dusty-Gas Model, Elsevier, Amsterdam, 1983. 

Bear J, Cheng A, Sorek S, Ouazar D, Herrera I (eds.) (1999) Seawater intrusion in coastal aquifers concepts, methods and practices. In Theory and Applications of Transport in Porous Media... 

Redman JA, Grant SB, Olson TM, Estes MK (2001) Pathogen filtration, heterogeneity, and the potable reuse of wastewater. Environ Sci Technol 35 1798-1805 Redman JA, Walker SL, Elimelech M (2004) Bacterial adhesion and transport in porous media Role of the secondary energy minimum. Environ Sci Technol 38 1777-1785 Reeves CP, CeUa MA (1996) A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour Res 32 2345-2358 Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1 318-333... 

Moller, N., Greenberg, J. P. Weare, J. H. 1998. Computer modeling for geothermal systems predicting carbonate and silica scale formation, CO2 breakout, and H2S exchange. Transport in Porous Media, 33, 173-204. 

FIG. 1.1 A schematic illustration of colloid-mediated transport in porous media. The sketch illustrates the transport of molecular solutes by colloidal particles. The extent of such transport and its importance are determined by a number of factors, such as the extent of adsorption of molecular solutes on the colloids and on the grains, the deposition and retention of colloids in the pores, the influence of charges on the colloids and on the pore walls, and so on. 

Compared to rivers and lakes, transport in porous media is generally slow, three-dimensional, and spatially variable due to heterogeneities in the medium. The velocity of transport differs by orders of magnitude among the phases of air, water, colloids, and solids. Due to the small size of the pores, transport is seldom turbulent. Molecular diffusion and dispersion along the flow are the main producers of randomness in the mass flux of chemical compounds. 

Brusseau (1994) gives an overview on the real behavior of reactive contaminants in heterogeneous porous media. The reader can also find a large updated list of references on transport in porous media. Just a few phenomena are shortly mentioned here ... 

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