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Pompage d’une nappe libre rechargée: solutions pour la charge hydraulique et le temps de transfert

Pumping a recharged unconfined aquifer: solutions for the hydraulic head and the transfer time

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Résumé

Avec les hypothèses de Dupuit, une nouvelle solution analytique est établie pour le pompage permanent d’un aquifère idéal à nappe libre rechargé par infiltration. La nouvelle solution est complète pour les deux parties du domaine mathématique, ce qui n’était pas le cas des solutions partielles antérieures. Une autre nouvelle solution est alors fournie pour le temps qu’un traceur non réactif met pour atteindre le puits en régime permanent. L’intégrale donnant le temps n’a pas de primitive connue mais se calcule aisément, soit numériquement soit par une équation simplifiée. Le calcul numérique et l’équation simplifiée donnent des temps voisins de ceux obtenus avec des codes d’éléments finis pour l’écoulement souterrain saturé et non saturé et le suivi de particules.

Abstract

Using the Dupuit assumptions, a new closed-form solution is established for steady-state pumping of an ideal unconfined aquifer that is recharged by infiltration. This new solution is complete for the two-part mathematical domain, which was not the case for previously partial solutions. A second new solution is then provided for the travel time of a non-reactive tracer to the pumping well, under steady-state conditions. The travel time integral has no known closed-form solution, but is easy to calculate, either numerically or using a simplified equation. The numerical calculation and the simplified equation give travel times very close to those obtained using finite element codes for saturated and unsaturated groundwater flow and particle tracking.

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Remerciements

Cette recherche a été subventionnée par le Conseil de recherches en sciences naturelles et en génie du Canada. L’auteur remercie le Professeur Michel Deveughèle pour lui avoir signalé une erreur dans une première version du manuscrit.

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  1. Département des génies civil géologique et des mines, École Polytechnique, C.P. 6079, Succ. CV, Montréal, QC, H3C 3A7, Canada

    Robert P. Chapuis

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  1. Robert P. Chapuis
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Correspondence to Robert P. Chapuis.

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Chapuis, R.P. Pompage d’une nappe libre rechargée: solutions pour la charge hydraulique et le temps de transfert. Bull Eng Geol Environ 70, 309–316 (2011). https://doi.org/10.1007/s10064-010-0307-x

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  • DOI: https://doi.org/10.1007/s10064-010-0307-x

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