Successive equimarginal approach for optimal design of a pump and treat system

Abstract

An economic concept‐based optimization method is developed for groundwater remediation design. Design of a pump and treat (P&T) system is viewed as a resource allocation problem constrained by specified cleanup criteria. An optimal allocation of resources requires that the equimarginal principle, a fundamental economic principle, must hold. The proposed method is named successive equimarginal approach (SEA), which continuously shifts a pumping rate from a less effective well to a more effective one until equal marginal productivity for all units is reached. Through the successive process, the solution evenly approaches the multiple inequality constraints that represent the specified cleanup criteria in space and in time. The goal is to design an equal protection system so that the distributed contaminant plumes can be equally contained without bypass and overprotection is minimized. SEA is a hybrid of the gradient‐based method and the deterministic heuristics‐based method, which allows flexibility in dealing with multiple inequality constraints without using a penalty function and in balancing computational efficiency with robustness. This method was applied to design a large‐scale P&T system for containment of multiple plumes at the former Blaine Naval Ammunition Depot (NAD) site, near Hastings, Nebraska. To evaluate this method, the SEA results were also compared with those using genetic algorithms.