On the Requirements for Inferring Aquifer-Scale T and S in Heterogeneous Confined Aquifers

We study the sensitivity of aquifer-scale estimates of transmissivity (T) and storativity (S) to the variance and correlation length scale of aquifer heterogeneity, when such estimates are obtained by the traditional approach of analyzing pumping test data. We consider both constant-rate and variable-rate pumping tests, and a variety of Theis-based solution methodologies (single- and multiple-observation well methods, and interpreted single value or transient values for T and S parameters) applied in pumping test data analysis. Our results indicate that achieving reliable inference of effective T and S requires that pumping be continued until the radius of the test-induced cone of depression exceeds a “representative length” that corresponds to ∼15 times than the correlation length scale of the aquifer heterogeneity. Independent of solution type, pumping history, correlation length scale, magnitude of the sill, and location of observation well, the estimates for T will converge toward the geometric mean. For S, the estimation uncertainty is relatively large for observation wells that are close to the pumping well, but diminishes for observation wells located beyond the representative distance, resulting in convergence to the arithmetic mean. Given that these results have practical implications for how pumping tests should be carried out, we present a simple “rule-of-thumb” for estimating the correlation length scale of the heterogeneity of an aquifer.