Estimating transmissivity from single‐well pumping tests in heterogeneous aquifers

Although aquifers are naturally heterogeneous, the interpretation of pumping tests is commonly performed under the assumption of aquifer homogeneity. This yields interpreted hydraulic parameters averaged over a domain of uncertain extent which disguises their relation to the underlying heterogeneity. In this study, we numerically investigate the sensitivity of the transient drawdown at the pumping well, to nonuniform distributions of transmissivity in confined aquifers. Frechet kernels and their time derivative are used to estimate two spatially averaged transmissivities, denoted the equivalent and interpreted transmissivity, Teq and Tin, respectively, for the case of single‐well pumping tests. Interrelating Teq and Tin is achieved by modeling Tin in terms of a distance dependent, radially heterogeneous field. In weakly heterogeneous aquifers, Teq approximates TPW, the local transmissivity at the pumped well. With increasing degree of heterogeneity, Teq deviates from TPW as pumping propagates. Tin starts at TPW, approaching the spatial geometric mean of transmissivity during late pumping times. Limits of the proposed spatial weighting functions are investigated by treating the interpreted storativity, Sest, as an indicator for flow connectivity. It is shown numerically that the spatial weights for Teq and Tin agree well to the underlying heterogeneity if Sest