Validation of an inverse numerical model for interpretation of pumping tests and a study of factors influencing accuracy of results

Abstract

An inverse numerical model was developed for the interpretation of simple or multiple pumping tests in layered groundwater reservoirs. This model was obtained by the combination of a numerical model and a nonlinear regression analysis. The numerical model is an axisymmetric hybrid finite-difference finite-element model. In the nonlinear regression analysis the residuals are defined as the differences between the logarithms of the calculated and observed drawdowns, and the hydraulic parameters are estimated within log space. The inverse numerical model is validated using a hypothetical example. From the study of the factors which influence the hydraulic parameter estimates and their joint confidence region, the following conclusions can be drawn. Use of a simplified representation of the flow system in the inverse model can cause erroneous estimates. The closer the simulated flow approximates the actual flow, the closer are the estimates. Hydraulic parameter estimates obtained by fitting data from a single observation well to type curves can result in very different values for the parameters if the actual flow is different from the model from which the type curves are derived. These different values are not due to the heterogeneity of the formation as is often concluded in many pumping test analyses. The number of parameters that can be reliably estimated decreases and the joint confidence region of the estimates enlarges when the relative error of the observed drawdowns increases. Increasing the duration of observations reduces the joint confidence region and increases the number of parameters that can be reliably estimated.