Dynamic optimal ground water remediation by granular activated carbon

Objective functions to describe the operating and capital costs of granular activated carbon (GAC) treatment are incorporated into a management model for dynamic optimal pump-and-treat groundwater remediation design. The optimization approach, quasi-Newton differential dynamic programming including a constant shift in the Hessian Matrix, could not reliably handle the nonconvex objective functions for GAC system. To avoid the nonconvexity, linearized iterative approximations of operating costs were used to solve the multiple management period problem, although this approach does not guarantee global optimality for the original nonconvex objective function. Repeated optimizations assuming different size absorbers were required to consider the fixed costs of the GAC system. Basing the cost function on concentrations at the beginning of each management period provided reasonable conservative cost estimates. Dynamic policies were found to be superior to steady-state policies even when capital costs of treatment were included. This work suggests that improvements in the differential dynamic programming algorithm may be needed for it to be a robust technique for realistic nonconvex objective functions.