A five-layered confined-unconfined flow and transport models are developed and calibrated for the Alamitos seawater intrusion barrier in Southern California. The conceptual model is based on the geological structure of the coastal aquifer system, and the key parameters in the flow and transport models are calibrated using field measurements of hydraulic conductivity as well as head and concentration observations. Because of the abundance of point measurements of hydraulic conductivity, the heterogeneous and random hydraulic conductivity field for each of the five aquifers is estimated by the proposed geostatiscal method of natural-neighbor-kriging (NNK). The longitudinal and transverse dispersivities in the transport model are estimated by an inverse procedure that minimizes the least-squares error for concentration (LSE-CON). The minimum LSE-CON is achieved near 50 ft (15.2 m) and 5 ft (1.52 m) for the longitudinal and transverse dispersivities, respectively. The calibrated simulation model is linked with two optimization models to investigate alternatives for enhancing seawater intrusion barrier operations for the Alamitos Barrier Project in Los Angeles. Two types of management problems are analyzed the optimal scheduling problem (OSP) and the optimal well location problem (OWLP). The objective of the OSP is to minimize the total injected water subject to constraints on the state variables: hydraulic head and chloride concentration at target locations. Two OSP formulations are considered, a pure hydraulic gradient formulation, and a combined hydraulic and transport formulation. Optimization results suggest that algorithm performance is best when the number of decision variables can be limited to approximately ten wells. Next, a genetic algorithm is linked with the calibrated simulation model to determine the locations of new injection wells that maximize the marginal increase in head targets along the barrier. Parallel processing is also employed to improve algorithm efficiency.

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Increasing demand for water in urban areas and agricultural zones in arid and semi-arid coastal regions has urged planners and regulators to look for alternative renewable water sources. Seawater reverse osmosis desalination (SWRO) plants have become an essential supply source for the production of freshwater in such regions. However, the disposal of hypersaline wastes from these plants in many of these regions has not been fully and properly addressed. This study aims to develop and present a strategy for the analysis and design of an optimal disposal system of wastes generated by SWRO desalination plants.

After current disposal options were evaluated, the use of multiport marine outfalls is recommended as an effective disposal system. Marine outfalls are a reliable means for conveying wastes from process plants, to include wastewater treatment and power plants, into the coastal waters. Their proper use, however, in conjunction with SWRO desalination plants is still in its beginning stage.

A simulation-optimization approach is proposed to design a system for safe disposal of brine wastes. This disposal system is comprised of a marine outfall that is equipped with a multiport diffuser structure. A hydrodynamic model (CORMIX) is used to assess the initial dilution of hypersaline effluent discharged into coastal waters. A regression model is developed to relate the input and output parameters of the simulation model. This regression model replaces the simulation model. A mixed-integer linear programming (MILP) optimization model is then formulated to determine the design of the multiport marine outfall. The design parameters are the length, diameter and number of ports of the disposal system. Given the uncertainty of some parameter, such as current speed, wind speed and ambient temperature, a chance-constrained programming model is used to properly incorporate these stochastic parameters into the model. This simulation-optimization framework provides planners with effective tools that preserve a healthy coastal environment, meet environmental permitting requirements and restrictions, while achieving cost savings and adequate hydrodynamic performance. A case study demonstrates the applicability of the proposed methodology.

Understanding groundwater resources is enhanced through the application of mathematical models that simulate the dynamics of an aquifer system. Conducting advanced analyses such as inverse problems for parameter estimation or optimization of pumping schedules under different scenarios requires a large number of simulations. Such analyses are intractable for complex, highly-discretized models with large computational requirements. Reducing the computational burden associated with these simulation models provides the opportunity to perform more advanced analyses on a wider spectrum of groundwater management problems. Projection based model reduction via Proper Orthogonal Decomposition (POD) has been shown to reduce the state space dimension by several orders of magnitude and thus reduces the computational burden. Two new POD techniques have been developed that improve the computation of high dimensional groundwater modeled systems. The first method provides a framework for developing parameter independent reduced models for solving inverse problems of confined groundwater models. This methodology is validated using synthetic test cases to solve a traditional inverse problem and Bayesian inverse problem. The second method presents a novel technique that allows for model reduction of unconfined groundwater flow, a nonlinear system of equations, using the Newton formulation of MODFLOW. This method extends POD to nonlinear equations and reduces the computational burden of solving the inverse of the Jacobian required by the Newton formulation. Multiple test cases are presented to illustrate how a POD model is constructed and applied to different groundwater models. These two techniques result in several orders of magnitude of reduction in the state dimension and reduce to the total CPU time. For the case of the Bayesian inverse problem, the synthetic example’s parameter posterior distributions that are described with the Metropolis-Hastings Markov chain Monte Carlo method results in a time savings of 48 days when using the reduced model.

Water resources systems management often requires complex mathematical models whose use may be computationally infeasible for many advanced analyses. The computational demand of these analyses can be reduced by approximating the model with a simpler reduced model. Proper Orthogonal Decomposition (POD) is an efficient model reduction technique based on the projection of the original model onto a subspace generated by full-model snapshots. In order to implement this method, an appropriate number of snapshots of the full model must be taken at the appropriate times such that the resulting reduced model is as accurate as possible. Since confined aquifers reach steady state in an exponential manner, a simple exponential function can be used to select snapshots for these types of models. This selection method is then employed to determine the optimal snapshot set for a

unit, dimensionless model. The optimal snapshot set is found by maximizing the minimum eigenvalue of the snapshot covariance matrix, a criterion similar to those used in experimental design. The resulting snapshot set can then be translated to any complex, real world model based on a simple, approximate relationship between dimensionless and real-world times. This translation is illustrated using a basin scale model of Central Veneto, Italy, where the reduced model runs approximately 1,000 times faster than the full model. Accurate reduced modeling can be significantly beneficial for advanced analyses such as parameter estimation. A new parameter estimation algorithm is proposed that is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. POD is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

Proper Orthogonal Decomposition (POD) is a method used to reduce the dimension of a highly discretized groundwater model. The reduced model is sometimes several orders of magnitudes smaller than the original model and can run several orders of magnitude faster. The key advantage of utilizing a POD reduced model is its ability to drastically reduce the computational burden of repeated model calls, which are required in Monte Carlo simulation, uncertainty analysis, and heuristically searched experimental design. Although POD has been applied to many areas of research, there continues to be room to improve its implementation. This dissertation consists of six chapters. After an introductory chapter, the second chapter discusses a method that can be used to improve the efficiency of constructing complex POD reduced models. The third through fifth chapters develops methodologies by which POD reduced models are used to solve the experimental design problem of optimizing a network of observation wells to gain information about the modeled aquifer. The final chapter offers some conclusions, discussions, and potential future research opportunities.

This report develops a systematic approach for solving the problem of conjunctive use of surface water and ground water in which both supply water quality and ground water quality are of major concern. The new approach utilizes a two-step nonlinear optimization. A test problem typical of a semiarid river basin with a seasonal agricultural demand and an increasing municipal and industrial demand is presented. Seasonal variations in demand, precipitation and recharge are handled by dividing each modeling year into a wet season and a dry season in the management model. Sustainable pumping and injection rates that would satisfy both the head and water quality constraints are obtained in the management model for each demand-supply scenario. An iterative technique is then used to solve the optimal pumping and injection rates within the planning horizon using the sustainable rates as upper bounds. Nonlinear programming solver MINOS is used to solve the management problem. MODFLOWand MT3D simulate the flow and transport in the ground water basin.

This report develops a multicommodity flow model to optimize water distribution and water quality in a regional water supply system. Waters from different sources with different qualities are considered as distinct commodities, which concurrently share a single water distribution system. Volumetric water blend is used to represent water quality in the model. The model can accommodate two-way flow pipes, represented by undirected arcs, and the perfect mixing condition. Additionally, blending requirements are specified at certain control nodes within the system to ensure that downstream users receive the desired water quality. The optimization model is highly nonlinear and solved by a hybrid genetic algorithm (GA). We first use GA to globally search for the directions of all undirected arcs. We then use a generalized reduced gradient (GRG) algorithm, which is embedded in GA, to optimize the objective function for fitness evaluation. The proposed methodology was first tested and verified on a simplified hypothetical system and then applied to the regional water distribution system of the Metropolitan Water District of Southern California (MWD). The results obtained indicate that the optimization model can efficiently allocate waters from different sources with different qualities to satisfy the blending requirements, perfect mixing and two-way flow conditions.

### Optimization of groundwater remediation strategies in aquifers affected by slow desorption processes

Most of the major groundwater contamination in California, including that inundating the San Fernando, San Gabriel and San Bernadino Valleys, will be addressed using some variation of the pump-and-treat technology. The pump-and-treat strategy is often judged to be unsuccessful because of difficulties encountered in recovering the contaminants from relatively stagnant zones within stratified aquifer systems. These zones can exist at the particle scale, as intraparticle or intra-aggregate porosity, and at the larger scales, as low permeability layers or lenses interspersed in substantially more permeable layers. This work focuses first on achieving an efficient numerical solution to a system of groundwater flow and contaminant transport equations that sufficiently captures the dynamics of slow desorption in a two-dimensional porous medium. The upstreamweighted, multiple cell balance (UMCB) method is developed and verified here to provide such a solution. Next, this work focuses on coupling the simulation model with a management model to provide a design tool for pump-and-treat remediation of real aquifer systme. Zeroth, first and second moments are calculated for mobile and immobile aqueous concentration distributions, and tested as potential design objectives. In a departure from conventional approaches, spatial moment analysis is also applied to local differences between simulated mobile and immobile aqueous concentrations.

Results suggest that pump-and-treat systems in heterogeneous domains might best be designed as two phase operation. The first phase addresses the early time removal of mobile (i.e., readily accessible) phase contaminant, and suggests the conventional approach of placing extraction wells slightly downgradient of the plume centroid. The second attacks fractions of the contaminant plume that are either harbored within immobile porosity, or that have penetrated impermeable layers. The latter stage can be accomplished through maximizing the desorption driving force distribution, or be minimizing the spreading (variance) of this distribution. It is recommended that the techniques developed in this research be applied to one or more of California's on-going pump-and-treat systems.