Optimal pumping test design for the parameter identification of groundwater systems

Abstract

The overall goal of this research is to identify a least cost pumping test design whose data will yield parameter estimates of a required reliability. The reliability is characterized by the statistical concept of the D optimality which in turn is used as the acceptability criterion for experimental design. Classically, D optimality seeks an experiment which minimizes the determinant of the parameter estimates' covariance matrix, thereby maximizing their reliability. An upper bound on the determinant of the covariance matrix is derived by using the assumed asymptotic normal distribution of the parameter estimates. As formulated, the least cost problem is a nonlinear, mixed integer programming problem where the decision variables are the location of the pumping/observation well(s), the number of wells, the pumping rate, and the frequency of observations. A heuristic design algorithm is developed. The algorithm seeks to minimize the number of pumping and observation wells. Since a heuristic algorithm is used and because the inverse problem is nonlinear, the algorithm will identify a local, D‐optimal pumping test design. This algorithm is then applied to a hypothetical aquifer system. A sequential design algorithm is developed for circumventing the nonlinearity of the inverse problem of parameter estimation. Two case studies are performed. The first case study verifies the sequential design algorithm under noiseless conditions. The second case study yields realistic results under noisy conditions.