Optimal time‐varying pumping rates for groundwater remediation: Application of a constrained optimal control algorithm

A numerically efficient procedure is presented for computing optimal time‐varying pumping rates for remediation of contaminated groundwater described by two‐dimensional numerical models. The management model combines a pollutant transport model with a constrained optimal control algorithm. The transport model simulates the unsteady fluid flow and transient contaminant dispersion‐advection in a two‐dimensional confined aquifer. A Galerkin's finite element method coupled with a fully implicit time difference scheme is applied to solve the groundwater flow and contaminant transport equations. The constrained optimal control algorithm employs a hyperbolic penalty function. Several sample problems covering 5–15 years of remediation are given to illustrate the capability of the management model to solve a groundwater quality control problem with time‐varying pumping policy and water quality constraints. In our example, the optimal constant pumping rates are 75% more expensive than the optimal time‐varying pumping rates, a result that supports the need to develop numerically efficient optimal control‐finite element algorithms for groundwater remediation.