The effective resistance to vertical flow in Dupuit models

Analytic solutions are developed for two-dimensional flow in the vertical plane in a stratified aquifer of two strata. Vertical flow in the aquifer is created by a discontinuous impermeable boundary separating the two aquifer layers. The solutions are compared to Dupuit solutions for a two-layer aquifer system in which the two layers are separated by a fictitious leaky layer; the resistivity of the fictitious leaky layer represents the average vertical resistance to flow in the aquifer. By comparison of the exact and Dupuit solutions, the appropriate characteristic length of the leaky system (the leakage factor) is evaluated, such that the discharges in the Dupuit and exact solutions are identical and the heads converge a short distance from the discontinuity in the impermeable boundary. It is shown, for this flow case, that the effective leakage factor is not a function of the flow field or the hydraulic conductivity of the two layers and that the effective resistivity is about 20% of the total resistance to vertical flow of the aquifer. The results provide guidance for selecting the resistance to vertical flow in numerical or analytical Dupuit models with coarse vertical discretization.