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 contamination 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 the 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. 28 refs., 7 figs., 10 tabs.

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