Kansas Geological Survey, Open-file Report 2003-60
Part of the Well Tests for Site Characterization Project

Mathematical Derivations of Semianalytical Solutions for Hydraulic Tests in Highly Permeable Aquifers

by Xiaoyong Zhan and James J. Butler, Jr.

Kansas Geological Survey, University of Kansas

KGS Open File Report 2003-60

Introduction

In this report, derivations of the transform-space solutions to the mathematical model describing the head response to a hydraulic test in a highly permeable aquifer are presented. For the sake of generality, the solutions are developed in a dimensionless form. The back transforms of these expressions are used by Butler and Zhan [in review] to develop new insights into the analysis of hydraulic tests in aquifers of high hydraulic conductivity. In Section II of this report, governing equations and auxiliary conditions for the aquifer and the test well are presented. Dimensionless variables are introduced in Section III and are used to rewrite the governing equations and auxilary conditions in a dimensionless format. The corresponding dimensionless equations in Laplace-Fourier space are derived in Section IV using standard integral transform methods, and Laplace-space solutions are presented in Section V. In Sections VI-IX, a parallel development is presented for an observation well. The method used to numerically invert the Laplace-space solutions is described in Section X.

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