Optimization of pump-treat-inject (PTI) design for the remediation of a contaminated aquifer: multi-stage design with chance constraints

A large scale groundwater remediation project using pump-and-treat (PAT) or pump-treat-inject (PTI) cannot be designed as a single time-step operation, because of uncertainties associated with the system. The changes in concentrations in reality may differ significantly from predicted ones. Instead, a multi-stage decision process is formulated and solved as a two-level hierarchical optimization model. Cost serves as the objective function, while contaminant concentration and total cleanup time are constraints. The entire cleanup time is divided into several stages. The number of wells for both pumping and injection is treated as a decision variable in each design stage. At the basic level, well locations and pumping/injection rates are sought so as to maximize mass removal of contaminants. At the upper level, the number of wells for pumping and injection is optimized, so as to minimize the cost, taking maximum contaminant level (MCL) as a constraint. Indices for the equivalent centroid and areal extent of a contaminant plume are proposed and used to initiate well locations at each design stage.