Hydrologic Theory of Dispersion in Heterogeneous Aquifers

Abstract

A general methodology to develop dispersion models in three-dimensional heterogeneous aquifers under nonstationary conditions is presented. Under this procedure, fundamental hydrologic processes influencing chemical dispersion in porous media, such as recharge rate, ground-water flow boundary conditions, regional hydraulic gradients and their transient behavior, as well as nonstationary statistical properties of the flow and dispersion parameters (if known), may be included in the analysis. The method of decomposition, which is a general analytic technique not requiring many of the restricting assumptions of the current small perturbation methods, is used as a basic tool to solve the resulting stochastic partial differential equations. A special application that reproduces the enhanced dispersion of the Borden aquifer tests is presented. The results suggest that the longitudinal and transverse field dispersion coefficients do not exhibit asymptotic values, even in the absence of recharge, and rather grow as linear functions of time and the corresponding longitudinal and transverse velocity variances. If the regional recharge rate is important, the rate of growth of the dispersion coefficients is expected to increase, and the corresponding mean concentration plume would be nonsymmetric with respect to its center of mass. Finally, a comparison between perturbation and decomposition solutions to ground-water equations, for the case of large conductivity variance, is presented.