Analyse automatique des données de pompage d'essai — Application aux hypothèses de Boulton et d'Hantush

Abstract

Classical analysis of pumping test curves under unsteady-state flow conditions with constant discharge rate in a fully penetrating well is based on a manual graphical comparison of drawdowns with theoretical standard curves. This procedure leaves a relative subjectivity to the operator. A more rigorous method is proposed: automatic analysis of drawdown curves. The principle of automatic analysis is based on the minimization of differences between observed drawdowns and those calculated theoretically according to a nonlinear law. We use the iterative process in successive degrees of Gauss-Newton applied to the evaluation of least-squares errors for a nonlinear regression. The application of this method to two hydrogeological mecanisms described by N.S. Boulton and M.S. Hantush permits a quick and direct evaluation of the hydraulic parameters of the aquifer by means of partial derivatives with relation to those parameters of the theoretical function. This latter is determined as a generalized integral of a function depending on four (first case) or five (second case) parameters. We justify here the permutations of the derivations and integration. At the level of numerical calculation, the difficulty is to evaluate with sufficient precision the generalized integrals containing Bessel function. Applications of automatic analysis have been carried out and are discussed.