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Miscible Displacement: An Interacting Flow Region Model

Dep. of Agronomy, Univ. of Nebraska, Lincoln, NE 68583

W. R. Gardner

Univ. of California, Berkeley, CA 94720

* Corresponding author.

ABSTRACT

No existing microscopically based models of solute transport in porous media are completely satisfactory. In particular, it is difficult to a priori provide an estimate of the hydrodynamic dispersion coefficient. We developed a model of solute movement in saturated porous materials that starts with a continuous velocity distribution instead of an average velocity. The model allows transfer of solute between regions of differing velocity. This transfer is characterized by an interaction coefficient. An approximate solution for large interaction is obtained using the method of moments. This technique shows the equivalence of the model moments to those of the classical dispersion equation. The second moment yields the dependence of the dispersion coefficient on average velocity. The empirical dependence of dispersion on average velocity is recovered if the interaction is assumed to be a linear function of the average velocity. The model also predicts the increase in dispersion observed for heterogenous materials over that for a similar homogeneous material.

Research supported by the College of Agricultural and Life Sciences, Univ. of Wisconsin, Madison, and by the Small Scale Waste Management Project.

Received for publication February 27, 1991.

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