Background Reports

Mathematical Derivations of Semianalytical Solutions for Pumping-Induced Drawdown and Stream Depletion in a Leaky Aquifer System

by Xiaoyong Zhan and James J. Butler, Jr.
Kansas Geological Survey, University of Kansas, Lawrence, KS 66047
KGS Open-file Report 2005-10

Introduction

In this report, derivations of the transform-space solutions to the mathematical model describing the drawdown and stream depletion produced by a pumping well in a leaky aquifer system are presented. The back transforms of these expressions are used by Butler et al. [in review] to develop new insights into stream-aquifer interactions in a leaky aquifer system.

In Section II of this report, governing equations and auxiliary conditions for a leaky aquifer system hydraulically connected to a stream are presented. The corresponding equations in Laplace-Fourier space are derived in Sections III and IV using standard integral transform methods. The general transform-space solution is presented in Section V. In Sections VI and VII, simplified solutions for an unbounded domain and an unbounded homogeneous domain, respectively, are presented. The derivation of a solution for the stream-depletion rate is presented in Section VIII. The methods used to numerically invert the transform-space solutions are described briefly in Section IX.

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Kansas Geological Survey, Stream-Aqufer Interactions Project
Updated online April 26, 2005
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The URL is http://www.kgs.ku.edu/StreamAq/Reports/05/rep_10.html