Optimal Estimation and Scheduling in Aquifer Remediation With Incomplete Information

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Abstract
This work presents new results on a method for optimal aquifer remediation when available information is limited. The methodology combines computer simulation models of solute transport and fate, descriptions of spatial variability, probabilistic analysis of uncertainty, and optimization. The objective is to find the most cost‐effective management policy for aquifer decontamination. Advantages of the method include the following: (1) it utilizes measurements in real time, (2) it simultaneously estimates aquifer parameters and makes decisions for remediation, and (3) it devises a more cost‐effective and reliable aquifer remediation strategy than deterministic optimization, specifically, the method known as deterministic feedback control. Subject to constraints and for a given reliability of meeting water quality standards, this method minimizes the expected value of the cost in the remaining periods. That is, because of incomplete information about the site the cost of a decontamination strategy is not known a priori. The objective is to minimize the cost weighted by the probability that it will be incurred. The optimal aquifer management policy is expressed as the sum of a deterministic and a stochastic control term. The former is obtained by solving a deterministic optimization problem through constrained differential dynamic programming, and the latter is obtained by a perturbation approximation to the stochastic optimal control problem. Extended Kalman filtering is incorporated into the optimization method to improve the accuracy of the estimated state and parametric variables using available measurements. A hypothetical contamination case with two‐dimensional unsteady flow and transport for a persistent solute is studied to illustrate the applicability of the methodology. The effectiveness in terms of cost and reliability of the proposed method is studied under various conditions and then compared with the cost and reliability of the deterministic feedback control method through Monte Carlo simulations. The proposed methodology is shown to be superior to deterministic feedback control.

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