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Computation of Type Curves for Flow to Partially Penetrating Wells in Water‐Table Aquifers
Author(s) -
Moench Allen F.
Publication year - 1993
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1993.tb00870.x
Subject(s) - computation , laplace transform , series (stratigraphy) , mathematics , convergent series , flow (mathematics) , algorithm , mathematical analysis , computer science , geometry , geology , paleontology , power series
Abstract Evaluation of Neuman's analytical solution for flow to a well in a homogeneous, anisotropic, water‐table aquifer commonly requires large amounts of computation time and can produce inaccurate results for selected combinations of parameters. Large computation times occur because the integrand of a semi‐infinite integral involves the summation of an infinite series. Each term of the series requires evaluation of the roots of equations, and the series itself is sometimes slowly convergent. Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical integration. In this paper it is proposed to use a method of numerical inversion of the Laplace transform solution, provided by Neuman, to overcome these difficulties. The solution in Laplace space is simpler in form than the real‐time solution; that is, the integrand of the semi‐infinite integral does not involve an infinite series or the need to evaluate roots of equations. Because the integrand is evaluated rapidly, advanced methods of numerical integration can be used to improve accuracy with an overall reduction in computation time. The proposed method of computing type curves, for which a partially documented computer program (WTAQ1) was written, was found to reduce computation time by factors of 2 to 20 over the time needed to evaluate the closed‐form, real‐time solution.