A game-theoretic parameter configuration technique for aquifer restoration design

Abstract

The problem of designing an active hydraulic system for remediation of a polluted aquifer is addressed for the case when parameters are not known with certainty. The design problem is cast as a game in which the protagonist-designer is pitted against an antagonist which alters the values of the uncertain parameters, within prescribed limits, so as to render the engineered system most ineffective. A solution method for the antagonist's problem, referred to as the parameter configuration technique (PCT), is developed and discussed in this paper. This technique selects spatially dependent values of the distributed parameter, transmissivity, such that the pattern of variation represents a pessimistic (but realistic) set of design conditions. The task of finding the “worst” set of parameter values is cast as a constrained optimization problem whose objective function is to thwart the remedial action design to the greatest degree possible. A rudimentary objective function is arbitrarily specified by the researchers. Several types of feasibility constraints restrict the distribution of parameter values to those combinations that are “realistic.” One type limits the variogram, another type, the mean, and a third type, the trend, of the log transmissivity. The resulting optimization problem is ill-behaved; difficulty was encountered obtaining a mathematically optimal solution. However, it may not always be necessary to find such a mathematically optimal solution in order to derive practical utility from the results. Two special heuristic techniques for obtaining a near-optimal solution are discussed. The technique is applied to a hypothetical contaminated aquifer with a simple single-extraction well flushing system. The solution is compared to a Monte Carlo approach applied to the same aquifer. The required pumping rate for a pessimistic parameter set generated by the new technique is about the same as the second largest of 100 Monte Carlo realizations.