Specification of the dispersion coefficient in the modeling of gravity-driven flow in porous media

Dispersion is an important component of transport in gravity-driven flow in porous media. However, its detailed modeling requires large computer powers and long calculation times. In this paper, we theoretically and experimentally investigate the conditions for which dispersion may be treated (1) as a simple constant or (2) as a more complex velocity-dependent term for flow in a homogeneous porous medium. The fundamental equations for fluid flow and solute transport in a porous medium are solved using an augmented Lagrangian algorithm. A general numerical code is developed in which the dispersion coefficient can be set as either a constant or as velocitydependent. The theoretical results predicted by these two models are compared with those of our new laboratory experiments. We also theoretically analyze case scenarios not easily realizable in the laboratory. On the basis of these results we propose a method for estimating representative constant dispersion coefficients and discuss the conditions for which such simplification is valid.