Optimization of the pumping schedule in aquifer remediation under uncertainty

A common method of aquifer decontamination is through “pump and treat” systems. Mathematical models of flow and transport can be incorporated into an optimization scheme to determine the most cost‐effective pumping pattern and schedule, provided that the parameters of the system are somehow known. In practice, however, there is seldom enough information to specify with certainty all the parameters of the system. Parameters are obtained from measurements through inverse modeling and are subject to error. This work presents an optimization methodology which accounts for and reduces parameter uncertainty. It is shown that in an average sense the cost consists of two parts: one which depends only on the best estimates and another which increases with the error in parameter estimation. A policy which minimizes the sum of the two parts is developed. The proposed methodology elucidates the dual control aspect of stochastic control, i.e., the control policy (pumping schedule) optimizes the objective function by, among other things, improving the accuracy of estimation of system parameters (i.e., dispersivity, transmissivity). For purposes of illustration, the proposed method is applied to a simple case. Comparison with an optimization method which neglects uncertainty in parameter estimation shows the superiority of the proposed algorithm.