The effects of variable flow velocity on contaminant dispersion in porous flow

Abstract

The diffusion-like behaviour of contaminant dispersion that underlies the commonly used advection-dispersion equation (ADE), has been shown by the authors to follow rigorously from a model that uses stochastic displacements to represent porous flow in a homogenous medium. This paper extends the model, as in a realistic aquifer the velocity will vary due to flow geometry and inhomogeneity of the medium. An integral formulation of the solute mass conservation law involving the probability distribution of fluid elements is presented. This is first applied to several numerical examples involving transmission of a gaussian contaminant plume through discrete velocity steps. A net increase in dispersion is found even when the average velocity is maintained. This is the result of the interaction of kinematic effects and dispersion. Some results from an analytical calculation are also presented, which show that the effects of a velocity step decay away from the step location. This leads to an expression for a scaling length, and the conclusion that dispersion is only sensitive to velocity fluctuations on a similar length scale as that of the dispersion itself.