The form of the dispersion equation under recharge and variable velocity, and its analytical solution

Abstract

In this article an attempt is made to describe field scale solute transport parameters in terms of regional hydrologic and aquifer hydraulic properties, such as recharge rate, transmissivity, hydraulic gradient, aquifer thickness and soil porosity. Aquifers subject to natural recharge from rainfall exhibit groundwater velocities which vary with distance and with the recharge intensity. This in turn generates an evolving transport dispersion coefficient which increases with distance even in a homogeneous aquifer with constant dispersivity. The dispersion equation in an aquifer subject to recharge and variable groundwater velocity is one with coefficients given as variable functions of distance. A new stable analytical solution of this equation is presented along with numerical comparisons with the classical convection dispersion equation and sensitivity tests on the effect of hydrologic‐hydraulic variables on the contaminant evolution. It was found that the recharge rate substantially affects the contaminant distribution and may partially explain the scale dependence of dispersion parameters. Transmissivity and hydraulic gradient values also determine the velocity distribution and therefore the rate of migration. It would appear that constant, laboratory scale, dispersivities may be sufficient for the modeling of field scale concentrations if an equation which accounts for the effects of hydrologie and hydraulic variables is used.