Comparing a three-dimensional and a Dupuit-Forchheimer solution for a circular recharge area in a confined aquifer

Abstract

An exact, closed-form analytic solution is presented for three-dimensional steady-state flow due to a source disc. The solution is used to model a circular recharge area at the upper boundary of a confined aquifer. Streamlines and contour plots of equipotentials are compared with those obtained from a Dupuit-Forchheimer solution. The latter solution is approximate in that resistance to vertical flow is ignored. As a further illustration a groundwater contamination problem is solved; that of a leaching circular pond in a uniform flow field. Some streamlines and the shape of the downstream plume are plotted for both the three-dimensional and the Dupuit-Forchheimer solution. It appears that when the recharge area is sufficiently large the Dupuit-Forchheimer solution is quite adequate, particularly when tracing streamlines. The results, therefore, confirm the validity of the Dupuit-Forchheimer assumption when modeling regional flow, even under circumstances of areal recharge. However, when the size of the recharge area is in the order of the aquifer thickness a truly three-dimensional solution is needed.