Optimal parameter sampling for aquifer remediation design under uncertainty

Abstract

In restoring polluted aquifers by hydraulic means, the parameters that characterize the aquifer are rarely known with certainty. To address this uncertainty, one may conservatively design the remediation system, so that the probability of failure to restore the aquifer is small. Alternatively, one may sample the aquifer to determine parameter values so that a less conservative remediation design may be successful. In this thesis, a method is presented for optimal incorporation of a sampling strategy into a reliable aquifer remediation design. Taking transmissivity as the uncertain parameter, the method identifies the aquifer sampling location that has the largest expected impact on the system cost, given a set of statistical parameters and a required probability of success. The cost of sampling may be compared to the predicted expected value of sampling, in terms of system cost savings, to determine whether or not the optimal sample is worth taking.

The method uses a large number of equally likely realizations to represent the variation of the distributed parameter. The optimal remediation system design is determined for the set of realizations using a chance-constraint cost-optimization method. The method then calculates the expected design cost savings for each sampling location. This method is demonstrated through a hypothetical example case.