Experimental design and model parameter estimation for locating a dissolving dense nonaqueous phase liquid pool in groundwater

Abstract

This paper investigates the experimental design problem in the context of estimating the location and dimensions of a dissolving dense nonaqueous phase liquid (DNAPL) pool in an aquifer. The design problem deals with the selection of the number and location of observation wells that minimizes the parameter uncertainty while minimizing installation and sampling costs. The solution of this multiobjective optimization problem is achieved by solving a series of combinatorial optimization problems in which, for each imposed budget constraint, the optimal combination of wells is found. The combinatorial optimization problems are solved by a genetic algorithm for two different design strategies: one where the prior estimates are not updated and one where the parameter updating is performed at the end of each design stage (sequential design). In the latter case, parameter updating is obtained by executing an inverse model based on concentration values collected at the locations specified by the previous optimal design. The algorithms are tested for a controlled, bench‐scale pool dissolution experiment. The results demonstrate that the sequential design performs better in terms of final parameter estimates. Three optimality criteria associated with experimental design for model parameter estimation are compared: the A optimality, D optimality, and E optimality. Among the three criteria, the A and E optimalities produce better estimates of the pool location and size, which is justified by appreciably different variances associated with the parameters and their high degree of correlation.