Asymptotic Expansions for Moench’s Integral Transform of Hydrology

José L. López (), Pedro Pagola and Ester Pérez Sinusía
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José L. López: Departamento de Estadística, Informática y Matemáticas and INAMAT 2 , Universidad Pública de Navarra, 31006 Pamplona, Spain
Pedro Pagola: Departamento de Estadística, Informática y Matemáticas and INAMAT 2 , Universidad Pública de Navarra, 31006 Pamplona, Spain
Ester Pérez Sinusía: Departamento de Matemática Aplicada, IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain

Mathematics, 2023, vol. 11, issue 14, 1-14

Abstract: Theis’ theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H [ g ] ( r , t ) of the pumping function g that depends on the time t and the relative position r to the pumping point as well as on other physical parameters. Several analytic approximations of H [ g ] ( r , t ) have been investigated in the literature that are valid and accurate in certain regions of r , t and the mentioned physical parameters. In this paper, the analysis of possible analytic approximations of H [ g ] ( r , t ) is completed by investigating asymptotic expansions of H [ g ] ( r , t ) in a region of the parameters that is of interest in practical situations, but that has not yet been investigated. Explicit and/or recursive algorithms for the computation of the coefficients of the expansions and estimates for the remainders are provided. Some numerical examples based on an actual physical experiment conducted by Layne-Western Company in 1953 illustrate the accuracy of the approximations.

Keywords: water drawdown in aquifers; moench’s integral transform; asymptotic expansions; error function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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