Stochastic analysis of pumping test drawdown data in heterogeneous geologic formations

Abstract

Pumping tests are often used to estimate effective values of the transmissivity and the storativity of the perturbed aquifer portion surrounding the pumping well and observation points. The interpretation of such pumping tests is based on analytic or semi-analytic methods that are normally developed under the assumption of homogeneity in the vicinity of the well. The purpose of this paper is to examine the impact of the local-scale heterogeneity of the transmissivity on the transient drawdown due to pumping. The log-transmissivity field is modeled as a multi-variate Gaussian random spatial function. Using Monte Carlo simulations, the aquifer response to a pumping test is simulated for various parameter values of the log-transmissivity variance and integral scale. The transient drawdown of the heterogeneous system is compared to the drawdown of an equivalent homogeneous aquifer with transmissivity equal to the effective transmissivity. The results of this study indicate that the impact of local heterogeneity expressed by the log-transmissivity variance is most pronounced in the early-time drawdown rates at or near the pumping well. The integral scale of the log-transmissivity on the other hand influences the time needed for the drawdown rate of the heterogeneous system to approach that of the equivalent homogeneous system.