For solute transport through a porous medium, mechanical dispersion is typically described by a Fickian law. However, it is well known that under certain conditions mechanical dispersion is non-Fickian. Despite this, the standard Advection-Dispersion Equation (ADE) is usually employed in solute transport problems, primarily for its simplicity. This paper will look at simplifications of a general non-Fickian model to reduce it to a standard ADE with transport parameters that vary spatially or temporally. This allows the general non-Fickian properties of dispersion to be captured, while still having the simplicity of the standard ADE. The parameters can be estimated by fitting solutions of the ADE to experimental data and used to obtain better predictions of solute transport.


As mentioned previously, the coefficient of mechanical dispersion depends on velocity. Physically mechanical dispersion arises due to the tortuous paths that solute streamlines must travel (Bear, 1972). The tortuous paths result from the pore geometry of the porous medium. Mathematically advection is represented by a hyperbolic equation, which does not require a downstream boundary condition and the solution has a finite speed of propagation. As mechanical dispersion is an advective process, it would be expected to have similar mathematical properties. In essence, advection and mechanical dispersion should be represented by a hyperbolic equation. Fickian dispersion leads to a parabolic equation, which requires both an upstream and a downstream boundary condition and leads to an infinite speed of propagation of the solute plume (after an infinitesimal time there will be a finite amount of solute at infinity). The downstream boundary condition and infinite speed of propagation are a result of the Fickian assumption, but they do not physically occur in the advection/dispersion process. Many non-Fickian models for mechanical dispersion have been developed in the past (Hassanizadeh, 1996).

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