Dynamic optimal control for groundwater remediation with flexible management periods

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Abstract
A successive approximation linear quadratic regulator (SALQR) method with management periods is combined with a finite element groundwater flow and transport simulation model to determine optimal time‐varying groundwater pump‐and‐treat reclamation policies. Management periods are groups of simulation time steps during which the pumping policy remains constant. In an example problem, management periods reduced the total computational demand, as measured by the CPU time, by as much as 85% compared to the time needed for the SALQR solution without management periods. Conversely, the optimal costs increased as the number of times that the control can change is reduced. With two simulation periods per management period, the optimal cost increased by less than 1% compared to the optimal cost with no management periods, yet the computational work was reduced by a third. The optimal policies, including the number and locations of wells, changed significantly with the number of management periods. Complexity analysis revealed that the SALQR algorithm with management periods can significantly reduce the computational requirements for nonsteady optimization of groundwater reclamation and other management applications.