Spring-depletion solution

Pumping from a well beside a spring also drains water from the spring in a process that is termed spring depletion. A solution is obtained for this problem by assuming that the spring partially penetrates an aquitard that overlies the pumped aquifer. The Boulton solution for delayed-yield flow to a well and the Duhamel superposition theorem are used to obtain a Volterra integral equation of the second kind, and the Laplace transform is used to solve this integral equation. Numerical values computed from this solution are checked with a direct numerical solution of the integral equation. Flow depleted from the spring depends upon dimensionless time and four dimensionless parameters, and the solution is illustrated by showing in plots the effect of changing time and one parameter while holding all other parameters constant. The plotted results appear physically reasonable.