Fluid transport, in porous media

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. 

Because lattice-gases are entirely encoded with bit operations, they very efficiently employ computer memory, rendering their applications to fluid transport in porous media very attractive. These models have been successfully used to study flow in porous media for single and multiphase fluid flow, and for steady state and transient regimes (Balashubramanian et al., 1987 Rothman, 1988, 1989). 

Winter, A., Stability of Thin Wetting Films and Wettability Reversal in Reservoir Rocks, presented at the Symposium on Fundamentals of Fluid Transport in Porous Media organized by Institut Prancais du Petrole, May 14 18, 1990, Arles, Prance (in preparation). 

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. 

Darcy s law describes fluid flux in porous media, and must be combined with the continuity equation to develop flow equations. From the flow equations, the spatial and temporal pressure and velocity distributions can be estimated that are needed for the transport equations. The derivation of flow equations starts with the continuity equation, which states that the change in mass or volume within a control volume equals the net flux across the control volume boundary, plus sources and sinks within the control volume. For water within porous media, the continuity equation on a mass basis is ... 

A general overview was provided of porous media characteristics, fluid flow in porous media, advection and dispersion in porous media, and phase partitioning and reactive processes in porous media. Four questions were posed in the introduction, and it was suggested that the answers to those questions could be used to highlight the important features of a particular porous media transport problem. By the very nature of porous media, the answer to the first question (i.e., which phases are present ) will at least include a solid phase and one fluid phase, composed of either a liquid or a gas. If multiple phases are present in the void space, then the distribution of the liquid and gas in the pore space will be a function of capillary pressure. 

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. 

J. Bear, Dynamics of Fluids in Porous Media (American Elsevier, New York (1972 also available from Dover, New York, 1988 H. Brenner, Transport Processes in Porous Media (McGraw-Hill, New York, 1987) R. A. A. Greenkorn, Fluid Phenomena in Porous Media Fundamentals and Applications in Petroleum, Water and Food Production (Marcel Dekker, New York, 1983) A. Bejan, I. Dineer, S. Lorente, A. F. Miguel, and A.H. Reis, Porous and Complex Flow Structures in Modern Technologies (Springer-Verlag, New York, 2004). 

Assuming negligible conversion between hydromechanical and thermal energies and thermodynamic equilibrium between the fluid and solid phases, the equation for heat transport in porous media can be written (Combamous and Bories 1975) ... 

Problems involving transport through porous media occur in many disciplines. Although the most frequently studied individual problem is the movement of fluid through porous soils or rocks, examples of transport in porous media occur in many distinct types of systems. For example, tissues In the body are composed of cells and extracellular regions, two phases which often differ dramatically in resistance to diffusion of solutes. In recent years -as researchers have learned more about the structure of heterogeneous materials like soils, porous polymers, and animal tissues--the application of techniques developed to understand transport in porous media increase. 

Absorbency refers to the absorption of aqueous fluids by a porous, usually fibrous, polymer. Absorbency in polymers is an example of transport in porous media. While many important aspects of the science and engineering in absorbency have been described in a recent review [1] and elsewhere in this volume, this chapter will... 

The porosity or pore water volume fraction of total bed volume e (m m ) is obviously a key independent variable for assessing diffusive transport in porous media. The water that is contained in the bed is called the porewater or interstitial water because it fills the pores or interparticle spaces. It is the key phase for describing chemical mass transport interactions with the overlying water. Hence, all in-bed fluxes of dissolved constituents are transported in this fluid phase. 

Many investigators have studied diffusion in systems composed of a stationary porous solid phase and a continuous fluid phase in which the solute diffuses. The effective transport coefficients in porous media have often been estimated using the following expression ... 

The flow velocity, pressure and dynamic viscosity are denoted u, p and fj and the symbol (...) represents an average over the fluid phase. Kim et al. used an extended Darcy equation to model the flow distribution in a micro channel cooling device [118]. In general, the permeability K has to be regarded as a tensor quantity accounting for the anisotropy of the medium. Furthermore, the description can be generalized to include heat transfer effects in porous media. More details on transport processes in porous media will be presented in Section 2.9. 

The pore geometry described in the above section plays a dominant role in the fluid transport through the media. For example, Katz and Thompson [64] reported a strong correlation between permeability and the size of the pore throat determined from Hg intrusion experiments. This is often understood in terms of a capillary model for porous media in which the main contribution to the single phase flow is the smallest restriction in the pore network, i.e., the pore throat. On the other hand, understanding multiphase flow in porous media requires a more complete picture of the pore network, including pore body and pore throat. For example, in a capillary model, complete displacement of both phases can be achieved. However, in real porous media, one finds that displacement of one or both phases can be hindered, giving rise to the concept of residue saturation. In the production of crude oil, this often dictates the fraction of oil that will not flow. 

Camesano T, Logan B (1998) Influence of fluid velocity and cell concentration on the transport of motile and non-motile bacteria in porous media. Environ Sd Technol 32 1699-1708 Cary JW, Simmons CS, McBride JE (1989) CHI infiltration and redistribution in unsaturated soils. Soil Sci Soc Am J 53 335-342... 

Lichtner PC (1988) The quasistationary state approximation to coupled mass transport and fluid-rock interaction in porous media. Geochim Cosmochim Acta 52 143-65. 

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