Simulating groundwater flow in multi-aquifer systems with analytical and numerical Dupuit-models

Abstract

Analytic Dupuit solutions for multi-aquifer flow are compared to exact solutions for two-dimensional flow in the vertical plane to determine the error in discharge that is introduced by adopting the Dupuit approximation. Specifically, the problem of flow in the bottom aquifer of a two-aquifer system is studied where flow is caused by a piecewise constant head in the top aquifer. The difference between the exact and Dupuit solutions is small if the leakage factor (a characteristic length of the aquifer system) is large relative to the thickness of the aquifer, even for anisotropic hydraulic conductivities. The accuracy of discharges obtained with a Dupuit solution improves when the aquifer is divided up in a number of layers, separated by leaky layers representing the vertical resistance to flow of the aquifer. In a second comparison, analytic Dupuit solutions are compared to numerical Dupuit solutions obtained with the finite difference method to determine reasonable cell sizes and domain sizes for finite difference models. Accurate discharges were obtained with the finite difference method when the cell size is chosen equal to or smaller than the smallest leakage factor and the domain size is at least six times the largest leakage factor. Both a two-aquifer system (with one leakage factor) and a three-aquifer system (with two leakage factors) were studied.