Partial Infeasibility Method for Chance‐Constrained Aquifer Management

A pump‐and‐treat system of extraction wells is modeled to create a hydraulic capture zone to immobilize a plume of contaminants in a confined aquifer with uncertain hydraulic transmissivity. The stochastic approach is used to model the transmissivity as a random field and to generate random realizations of the field. The linear‐response‐matrix method is used to address a joint chance‐constrained optimization problem in which constraints on velocities must be simultaneously satisfied with high probability. In the literature, the multiple‐realization approach provides a robust solution but does not allow for prespecification of a desired reliability. We develop a partial‐infeasibility method, in which the pumping strategy is obtained through heuristic methods that require the designed reliability level to be satisfied for a training set consisting of multiple realizations of the uncertain transmissivity. Empirical Monte Carlo testing shows that as the size of the training set increases, the actual reliability approaches the design criterion. Thus, the method combines the intuitive appeal of the multiple‐realization method with the ability to prescribe a desired reliability level.