Effect of a water table aquitard on drawdown in an underlying pumped aquifer

A theoretical derivation of the convolution integral produced by N. S. Boulton's originally empirical ‘delayed yield’ theory shows that it describes the vertical velocity at the base of a water table aquitard having negligible compressibility. The derivation requires that fluid compressibility be neglected and that water be obtained from storage by instantaneous desaturation (or saturation) with a declining (or rising) water table. An expression for the ‘delay index’ shows that it is a function of hydraulic conductivity, specific yield, and thickness of the aquitard. To evaluate the effect that gradual desaturation may have on flow in a water table aquitard, flow in the unsaturated zone was approximated by an analytical solution of Richards' equation assuming time invariant power law functions for change of both capillary conductivity and moisture content in the vertical. An equation was derived that shows that the length of time for which gradual desaturation could influence flow in the saturated zone is a function of the hydraulic conductivity and specific yield of the aquitard and the thickness of the capillary fringe. To investigate the effect that delayed yield could have on flow in the aquifer, analytical solutions were made for flow to a well pumping at a constant rate in a compressible aquifer overlain by a compressible water table aquitard. Comparison of results that consider delayed yield effects with those that do not suggests that the unsaturated zone has little effect on flow in the aquifer, and comparison of these solutions with numerical solutions that treat the unsaturated zone explicitly conforms with this result.