Semianalytical Solutions for Radial Dispersion in a Three‐Layer Leaky Aquifer System

Abstract

AbstractWaste water injected into aquifers bounded by aquitards can potentially leak into the aquitards and eventually reach other layers. Based on the mathematical framework of an earlier model, the current study deals with steady‐state and transient solutions for solute transport from an injection well into a three‐layer leaky aquifer system consisting of a pumped and an unpumped aquifer separated by an aquitard. Solutes are assumed to be transported by horizontal advection within the pumped aquifer, by advection and dispersion in a vertical flow field in the aquitard, and by molecular diffusion under hydrostatic conditions in the unpumped aquifers. Proper leaky aquifer well hydraulics are used to describe the ground‐water flow fields in the model, and radioactive (biological) decay and linear isotherm adsorption are considered. This model study shows that adsorption in the pumped aquifer has an overall retardation effect on solute movement in the whole system. Adsorption in the aquitard does not significantly affect solute movement in the pumped aquifer. Type curves are prepared to indicate whether the unpumped aquifer would be contaminated by the injection into the pumped aquifer. Pumping rate is an important hydraulic factor determining the leakage conditions of an aquifer (in addition to some hydrogeological conditions of the systems). Analytical solutions are obtained for steady‐state conditions. For transient conditions, however, only semianalytical solutions can be determined by numerically inverting the solutions of the model in the Laplace transform domain.