Stream depletion rate for a radial collector well in an unconfined aquifer near a fully penetrating river

Abstract

The stream depletion rate (SDR) is computed for a radial collector well installed in a semi-infinite, anisotropic, homogeneous, unconfined aquifer near a fully penetrating stream with a streambed with reduced conductivity. For small pumping rates dimensional analysis and other arguments allow the SDR to be expressed as a function of eight parameters that describe the effect of properties of the aquifer and streambed as well as the configuration and placement of the well. The calculations employ some results from Huang et al. (2012, J. Hydrol.), who expressed the SDR as a quintuple integral, but by computing four of the integrals analytically, the present solution requires less computational effort. Analytical calculation shows that the SDR in steady state does not depend on the streambed properties (or any other parameters): Given enough time, the flow through the streambed will equal the pumping rate of the well. Values of SDR are supported by comparing to previous solutions for special cases corresponding to appropriate limiting values of the parameters. Effects of the eight dimensionless parameters are studied systematically: The properties of the streambed, anisotropy of the aquifer, and the position of the well affect the SDR more strongly than the orientation, length, and depth of the laterals.