Transport Mechanisms in Porous Media

8 DIFFUSION IN POROUS MEDIA 5.8.1 Transport Mechanisms in Porous Media 

We have discussed previously diffusion in dense crystalline materials. Now, we study the transport of molecules in porous media. According to the classification scheme proposed by the International Union of Applied Chemistry (IUPAC), pores are divided into three categories on the basis of size macropores (more than 50 nm), mesopores (from 2 to 50 nm), and micropores (less than 2 nm) [74,75], 

FIGURE 5.27 Transport mechanisms in porous media molecular or gaseous flow, (a) Knudsen flow, (b) surface diffusion, (c) multilayer diffusion, (d) capillary condensation, and (e) configurational diffusion. 

The Physical Chemistry of Materials Energy and Environmental Applications 

FIGURE 5.28 Relation between diffusivity and pore diameter. 

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There are four well-known types of diffusion in solids [10] gaseous or molecular diffusion [75], Knudsen diffusion [76-80], liquid diffusion [10], and atomic diffusion. In Figure 5.27, the possible transport mechanisms in porous media are schematically shown [77], Gaseous flow (Figure 5.27a)... 

Figure 4. Schematic representation of transport mechanisms in porous media (a) Poiseuille flow (b) Knudscn diffusion (c) surface diffusion (d) capillary condensation (e) molecular sieving...

Dybbs, A. and Edwards, R.V., A New Look at Porous Media Fluid Mechanics Darcy to Turbulent , in Fundamentals of Transport Phenomena in Porous Media, Bear. J. and Corapcigoln, M.Y., Eds., Martinus Nijhoff Publishers. The Hague. 1984. 

Advective transport alone does not account for all observed transport behavior. Transport observations in porous media exhibit characteristics indicative of a phenomenon beyond that described by advection only, such as breakthrough prior to and tailing after the advective front. This additional transport phenomenon is attributed to hydrodynamic dispersion, which is the sum of diffusive and mechanical dispersive processes. The former is attributed to concentration gradients, and the latter is attributed to variations in velocity at both micro and macro spatial scales. 

Hendricks DW (1972) Sorption in flow through porous media. In Bear J (ed) Transport phenomena in porous media. Elsevier, Amsterdam, pp 384-392 HiU R (1978) Aspects of invariance in solid mechanics. In Yih C-S (ed) Advances in applied mechanics, vol 18. Academic, New York, pp 1-73 Houlsby GT, Schofield AN (eds) (1993) Predictive soil mechanics. Thomas Telford, London Homung U (ed) (1997) Homogenization and porous media. Springer, New York Hughes TJR (1987) The finite element method. Prentice-HaU, Englewood CUffs... 

Figure 25.1 Heterogeneity is one of the main properties of porous media it not only characterizes the scales shown in the figure, but also occurs on larger scales up to the size of the whole porous system. Three important mechanisms of transport and mixing in porous media are (a) interpore dispersion caused by mixing of pore channels (b) intrapore dispersion caused by nonuniform velocity distribution and mixing in individual channels (c) dispersion and retardation of solute transport caused by molecular diffusion between open and dead-end pores as well as between the water and the...

Huyghe, J.M. and Janssen, J.D. (1999) Thermo-chemo-electro-mechanical formulation of saturated charged porous solids, Transport in Porous Media 34, 129-141... 

See, for example, M. L. Brusseau and P.S.C. Rao. Sorption nonideality during organic contaminant transport in porous media, Crit. Rev. Environ. Control 19 33 (1989) and W. W. Wood, T. F. Kraemer, and P. P. Hearn, Jr., Intragranular diffusion An important mechanism influencing solute transport in clastic aquifers Science 247 1569... 

In porous media, in addition to the intrinsic properties of the diffusing species, the structure of the solid has an important Influence on the transport mechanisms. Any description of the pro-cesses taking place should account for these features and the... 

Ideally, the zeolite membranes must be continuous with good cross-linking between crystals and free of pinholes and cracks to get high selectivities. However, most of the synthesis procedures render membranes with some intercrystaUine gaps and defects. The amount of these membranes and their sizes play an important role in the overall quahty of the membrane. Therefore, it has been considered illustrative to explain briefly the transport regimes in porous materials whatever the pore size, after which the mass transport mechanisms through microporous media will be fully described. 

A critical review of emulsion flow in porous media has been presented. An attempt has been made to identify the various factors that affect the flow of OAV and W/O emulsions in the reservoir. The present methods of investigation are only the beginning of an effort to try to develop an understanding of the transport behavior of emulsions in porous media. The work toward this end has been difficult because of the complex nature of emulsions themselves and their flow in a complex medium. Presently there are only qualitative descriptions and hypotheses available as to the mechanisms involved. A comprehensive model that would describe the transport phenomenon of emulsions in porous media should take into account emulsion and porous medium characteristics, hydrodynamics, as well as the complex fluid-rock interactions. To implement such a study will require a number of experi-... 

To predict the transport and fate of colloids in the subsurface, it is important to understand both the mechanism of particle deposition and that of remobilization in porous media. Experiments by MacDowell-Boyer (1992) and Monte Carlo simulations of Brownian particles near the surfaces of the media indicate that the secondary stability minimum (see physical model on colloid stability. Figure 14.10) can play an important role in the deposition and reentrainment of submicron particles at ionic strengths relevant to groundwater. 

Pores, and espjecially mesopores and micropores, play an essential role in physical and chemical properties of industrially important materials like adsorbents, membranes, catalysts etc. The description of transport phenomena in porous materials has received attention due to its importance in many applications such as drying, moisture transport in building materials, filtration etc. Although widely different, these applications present many similarities since they all depend on the same type of transport phenomena occurring in a porous media environment. In particular, transport in mesoporous media and the associated phenomena of multilayer adsorption and capillary condensation have been investigated as a separation mechanism for gas mixtures. 

In an aquifer, the total Fickian transport coefficient of a chemical is the sum of the dispersion coefficient and the effective molecular diffusion coefficient. For use in the groundwater regime, the molecular diffusion coefficient of a chemical in free water must be corrected to account for tortuosity and porosity. Commonly, the free-water molecular diffusion coefficient is divided by an estimate of tortuosity (sometimes taken as the square root of two) and multiplied by porosity to estimate an effective molecular diffusion coefficient in groundwater. Millington (1959) and Millington and Quirk (1961) provide a review of several approaches to the estimation of effective molecular diffusion coefficients in porous media. Note that mixing by molecular diffusion of chemicals dissolved in pore waters always occurs, even if mechanical dispersion becomes zero as a consequence of no seepage velocity. 

Dybbs, A., and Edwards, R. (1984) A new look at porous media fluid mechanics, Darcy to turbulent, In. Fundamentals of Transport in Porous Media, (Bear and Corapcioglu, eds.), 199-256. 

Kolditz, O. Computational Methods in Environmental Fluid Mechanics Springer Berlin, 2002. Parker, J.C. Multiphase flow and transport in porous media. Rev. Geophys. 1989, 27 (3), 311-328. 

Excellent texts are available that describe fundamental behavior, including Refs. . Current research is often published in Transport in Porous Media (which tends to have a mathematical focus). Water Resources Research, Journal of Fluid Mechanics, and the traditional chemical engineering journals. 

Whitaker, S. Volume averaging of the transport equations. In Fluid Transport in Porous Media] du Plessis, P., Ed. Computational Mechanics Publications Southampton, U.K., 1997. 

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