Diffusion and dispersion in porous media

TLDR

The study derives a dispersion equation for a single, nonreacting, nonadsorbing species in incompressible, laminar flow through anisotropic porous media. By direct integration of the governing equations, the authors obtain dispersion and tortuosity vectors, expressing the dispersion vector in terms of velocity and concentration gradients, and requiring experimental evaluation. The resulting equation incorporates all features of earlier models without assuming flow characteristics, links microscopic and macroscopic behavior, and shows that experimental determination of tortuosity is only straightforward for pure diffusion.

Abstract

Abstract The dispersion equation for a single, nonreacting, nonadsorbing species is derived for incompressible, laminar flow in anisotropic porous media. Direct integration of the appropriate differential equations gives rise to a dispersion vector ψ i and a tortuosity vector τ i , both of which must be evaluated experimentally. For the dispersion vector, this is conveniently done by representing ψ i in terms of the velocity and gradients of the velocity and concentration. The experimental determination of τ i is not straightforward except for the case of pure diffusion. The analysis yields a result which contains all the features of previously presented dispersion equations without making any assumptions as to the nature of the flow, that is, bypassing, cell mixing, etc., except that it be laminar. Attacking the dispersion problem in terms of the differential diffusion equation provides a rational basis for the correlation of experimental data and illustrates the connection between the microscopic and macroscopic equations.