A Comparison of Methods for Determining the Stream Depletion Rate for a Radial Collector Well

Abstract:

The stream depletion rate (SDR) for a radial collector well located near a stream can be calculated using analytical and semi-analytical solutions that either use the Dupuit assumption or include vertical flow. An analytical solution is developed for the SDR for a radial collector well in an unconfined aquifer with vertical flow and allows for stream bed permeability. The non-dimensional parameter χ = K′L/Kb relates the streambed thickness b and hydraulic conductivity K′ of the streambed with the aquifer hydraulic conductivity K and distance L between the stream and the well. As χ decreases, the time to reach steady state increases. While previous work on this problem suggests that the steady-state value of SDR decreases as K′/K decreases, our solution shows that the steady-state SDR is one as long as χ > 0—that is, the flow through the streambed induced by pumping is equal to the amount of water pumped from the aquifer. Also, the analytical solution results in a relatively simple equation to predict SDR in unsteady conditions.