Asymptotic expansions for Moench's integral transform of hydrology
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 relat...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2023 |
| País: | España |
| Recursos: | Universidad Pública de Navarra |
| Repositório: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/46668 |
| Acesso em linha: | https://hdl.handle.net/2454/46668 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Water drawdown in aquifers Moench&apos s integral transform Asymptotic expansions Error function |
| Resumo: | 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. |
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