Estimating Aquifer Properties by Nonlinear Least‐Squares Analysis of Pump Test Response

In this study, nonlinear least-squares analysis of pump test data is used as a method for estimating aquifer parameters and choosing a conceptual model of the aquifer. The goal of this study is to investigate the potential advantages and disadvantages of using statistical algorithms for pump test analyses. Four different aquifer models were fitted to an extensive set of pump test data to characterize the aquifer at a single aquifer test site. These models were the Theis model, the equipotential boundary model, the confined leaky aquifer model, and the water-table aquitard model. For several of the data sets, more than one aquifer model was found to match the pump test response with the same residual least-squares error, and a review of the local hydrogeology was required to choose the leaky aquifer model as the most appropriate aquifer model. A few data sets, however, did not agree well with the leaky aquifer model. Using the fitting routine, the water-table aquitard model was found to significantly improve the fit to these data sets. Further analysis of hydrogeologic features at the site indicated that the duration of the pump tests which matched the leaky aquifer model was probably insufficient to exhibit deviation from the leaky aquifer model. The water-table aquitard model is, therefore, chosen as the most suitable model for this site, and parameters for the aquifer are estimated using the results from the fitting procedure. In comparison, an earlier graphical interpretation of these pump tests did not distinguish the improved fit which could be obtained with the water-table aquitard model. However, the graphical analyses were valuable as they did provide preliminary estimates of the aquifer transmissivity, aiding in accepting or rejecting the results of the fitting analysis. Thus, we found that nonlinear least-squares analysis can complement, but does not replace, graphical interpretation methods. The nonlinear least-squares analysis can provide a means for analyzing pump tests which may not have been easily interpreted using traditional techniques, as the nonlinear least-squares analysis attempts to match all the test data at both large and small values of time. However, this analysis also illustrates that fitting methods cannot be totally automated, but rather must be interpreted in light of other hydrogeologic data in order to arrive at a reasonable model for the aquifer.