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Abstract

The present invention features a differential dynamic programming (DDP) method for computing optimal, time-varying pumping policies utilized in groundwater remediation. The strategy for treating the groundwater can use a feedback law generated by a constrained differential dynamic programming algorithm with penalty functions. The method has been tested in cases where there is uncertainty in the hydraulic conductivity. Confined transient aquifer flow and transport were modeled, using a two-dimensional Galerkin finite element scheme with implicit time differencing. Optimal policies were calculated using a given or 'measured' set of hydraulic conductivities and initial conditions. The optimal policies were applied using the same finite element model with a second, or 'true' set of conductivities The 'true' sets of conductivities were generated randomly from an autocorrelated lognormal distribution by the spectral method. The approach used had an advantage over other uncertainty approaches, because it was not necessary to specify precisely the probability distribution of each uncertain parameter. The method did not require any single probability distribution for each uncertain parameter. The relative weight assigned each penalty function was adjusted, which resulted in obtaining robust feedback laws that performed equally well under different, assumed error distributions. The water remediation method of this invention resulted in a cost savings within the approximate range of between 4% and 51% less than the cost of applying the calculated optimal policies without using a feedback law.

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