STABLE PUMPING RATES FOR HORIZONTAL WELLS IN RIVER BANK FILTRATION SYSTEMS

We consider common river bank filtration systems and develop an explicit analytic solution representing steady, two-dimensional flow to a horizontal well near a river in an unconfined aquifer. We use the solution to investigate the behavior and stability of the free surface under varying well discharges to identify stable pumping rates for predicting well field capacity. For the problem investigated we find that a unique solution to the boundary-value problem exists for all negative discharges of the well. For positive discharges, a maximum value exists which corresponds to the formation of a cusp in the free surface. For positive discharges less than the maximum, the solution is not unique, consisting of two alternate configurations of the free surface. One solution includes a stable free surface on a single-valued physical plane, while the alternate solution includes a looped free surface lying on two sheets of a Riemann surface. Imposing a stability condition on the free surface results in a unique solution to the problem.