Simulation models for the fate and transport of groundwater contaminants are important tools for testing our understanding of transport phenomena at long-term contaminated sites and for designing remedial action plans. A finite difference formulation for contaminant transport including a distribution of contaminant mass-transfer rates between the water and soil is developed. Optimal model simulations using both log-normal and γ distributions of mass transfer rates are compared to the two-site equilibrium/ kinetic model. In all cases, optimal sorption parameters were determined by best fit to laboratory data. For desorption of trichloroethene from long-term contaminated soils, the distributed mass-transfer rate model provided significantly improved simulations of aqueous concentrations, as compared to the two-site model, for both batch and soil column experiments. However, use of an apparent partition coefficient demonstrated that the performance of the two-site model was very sensitive to the value of the partition coefficient, while the performances of the distributed models were robust over a wide range of partition coefficients. Desorption studies in continuous-flow stirred tank reactors with laboratory-contaminated soils demonstrated that as the length of the contamination period increases, the simulation capability of the two-site model decreases.

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 !% 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. INTRODUCTION The design of pump-and-treat groundwater remediation projects is typically done by trial-and-error simulation of feasible combinations of pump locations and pumping rates. Given the countless number of feasible reclamation designs for a given site, the optimal management solution might never be identified by trial-and-error simulation. Mathematical optimization techniques combined with simulation can efficiently search through the possible design options and thus can be a useful tool for planning cost-effective pumpand-treat reclamation. Most mathematical optimization models for groundwater reclamation have determined static (or steady state) policies in which the pumping does not change over time. Given that groundwater remediation may occur over a period of decades, steady state policies would not be expected to be as cost-effective as dynamic policies in which the pumping policies are allowed to change as the contaminant plume moves. Control theory algorithms were developed specifically for dynamic systems and can readily handle timevarying pumping policies. In the few previous applications of control theory techniques to groundwater remediation [Andricevic and Kitanidis, 1990; Lee and Kitanidis, 1991; L.-C. Chang, C. A. Shoemaker, and P. L.-F. Liu, Application of a constrained optimal control algorithm to groundwater remediation, submitted to Water Resources Research, 1991 (hereinafter Chang et al., submitted, 1991)], the time steps of the optimization algorithms were identical to the time steps of the numerical models describing contaminant transport. The focus of this paper is the development of an algorithm for time-varying optimization of groundwater remediation in which the time steps in the optimization model (called "management periods") may be longer than the time periods in the numeri...

Rate-limited sorption and desorption strongly influence the fate, transport, and remediation of organic pollutants in subsurface environments. In this study, the rates of sorption and desorption were quantified for 1,2-dichlorobenzene to and from five natural sorbents using a batch methodology. Solute/sorbent contact times of 3, 7, 14, 49, and 99 d were studied for the desorption rate experiments. The sorption and desorption data were simulated with a distributed-rate model that used the Γ probability density function to generate the distribution of first-order rate coefficients. Ninety-five percent confidence intervals on the optimal model parameters were developed and translated into 95% confidence intervals on the various rate-coefficient distributions. Development of the confidence intervals on the rate coefficients facilitated a statistically rigorous evaluation of whether the rate of desorption was equal to the rate of sorption for the different sorbents. For three of the five sorbents studied, the rates of desorption were significantly slower than the rates of uptake for all solute/sorbent contact times studied. For the remaining two sorbents, the rates of desorption were significantly slower than the rates of uptake for solute/sorbent contact times greater than 2−3 d. For contact times greater than 2 d, a significant fraction of the 1,2-dichlorobenzene appeared to be resistant to desorption. However, the rate of desorption and the magnitude of the resistant fraction were independent of contact time for all but one sorbent. The rate observations for this study were consistent with an intraorganic matter diffusion mechanism.

[1] The determination of the pollutant load distribution among different pollutant sources in a watershed is a critical step in total maximum daily load (TMDL) development. Under current TMDL practices, TMDL allocations are typically determined through a trial-and-error approach of reducing pollutant loadings until a watershed simulation model predicts that water quality standards will be met given a margin of safety. Unfortunately, many feasible combinations of load reductions and significant uncertainties may exist. Therefore it is difficult and time-consuming to compare various allocation scenarios using a trial-and-error approach. A robust optimization model is developed in this study to incorporate the uncertainty of water quality predictions and to minimize pollutant load reductions given various levels of reliability with respect to the water quality standards. The generalized likelihood uncertainty estimation approach is used to explicitly address the uncertainty of a watershed simulation model, the Hydrological Simulation ProgramFortran. The uncertainty is integrated into TMDL allocations using a robust genetic algorithm model linked with a response matrix approach. The developed robust optimization model is demonstrated using a case study based on the Moore's Creek fecal coliform TMDL study. The trade-offs between reliability levels and total load reductions of allocation scenarios are evaluated, and the optimized load reduction scenarios are compared with the scenario generated by a trial-and-error approach and approved by the U.S. Environmental Protection Agency. The results show that the optimized load reduction scenario requires 30% less load reductions than the scenario approved by the U.S. Environmental Protection Agency at the same reliability level.

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