Estimating stream filtration from a meandering stream under the Robin condition

Abstract

This study applies image well theory to estimate the stream depletion rate (SDR) due to pumping near a meandering stream with a clogged streambed treated as the Robin condition. The stream is considered as an irregular boundary represented by discrete nodes. Image wells are arranged along the stream and near those nodes. On the basis of the Theis (1935) solution and the principle of superposition, the solution for the aquifer drawdown subject to the stream can then be expressed as the sum of the Theis solution and a simple series representing the effect of those image wells. The discharge rates of the image wells are determined by solving a system of equations obtained by substituting the drawdown solution into the Robin condition. Quantitative criteria for assessing the applicability of the image well theory are provided. On the basis of the drawdown solution and Darcy\'s law, the analytical solution for SDR can then be obtained. A finite element solution is also developed to verify the SDR solution. Temporal SDR distributions predicted by both the analytical solution and finite element solution agree well over the entire period except at late time when the stream filtration rate approaches the pumping rate (i.e., SDR 1). It is found that a meandering stream has a significant effect on SDR compared with a rectilinear one and the effect should be taken into account in estimating SDR.