A well flow model for a stratified heterogenous unconfined aquifer in a round island with infiltration recharge

Abstract

Objective The Dupuit model of well flow is a classical steady-state well flow model for a homogeneous unconfined aquifer in a round island. However, it does not consider the widely existing infiltration recharge from precipitation, and is also inapplicable for stratified heterogeneous aquifer systems. Therefore, it must be modified to address these issues. Methods On the basis of the revised Dupuit well flow model which incorporates infiltration recharge, this study further extended its application to a stratified heterogeneous unconfined aquifer. The Girinskii's potential function was used to construct the differential equations for the radial groundwater flow according to the water balance principle, and the analytical solutions satisfying the boundary conditions are then obtained as formulas of the flow rate, water table and groundwater divide. Taking the bilayer structure as an example, typical groundwater level curves with respect to 30 scenarios of different parameter values were investigated. A special phenomenon was found in which the curves of different hydraulic conductivities intersect at a single point, which could also be proven in theory. This analytical model still adopted the Dupuit assumption and did not consider the "hydraulic jump" phenomenon on the wall of the pumping well. To check the impact of these constraints on the applicability of the analytical formulas, a two-dimensional numerical model for axially symmetric seepage was built for comparison. Results As indicated by the results, the relative error of the groundwater level estimated from the analytical solution is generally less than 4%, except for the zone near the pumping well. On the groundwater divide, where the Dupuit assumption is mostly invalid, the relative errors of the analytical solution to both the distance and height of the divide are smaller than 0.1%. Conclusion The Dupuit assumption does not significantly influence applicability of the analytical model.

Keywords

• dupuit equation
• precipitation infiltration recharge
• stratified heterogeneous
• groundwater divide
• hydraulic jump
• analytical solution
• numerical modelling