Alex S. Mayer

Pump‐and‐treat optimization using well locations and pumping rates as decision variables

A new optimization formulation for dynamic groundwater remediation management is developed by simultaneously using well locations and the corresponding pumping rates as the decision variables. The genetic algorithm is applied to search for optimal pumping rates and the discrete space of well locations. The optimization model is applied to hypothetical, three-dimensional, contaminated aquifer systems with homogeneous and heterogeneous porous media properties. Optimal well locations and pumping rates obtained with the moving-well model are less expensive than solutions obtained with a comparable fixed-well model. Optimization with a linear objective function formulation identifies some of the optimal well locations obtained with a nonlinear formulation but results in higher pumping rates than the nonlinear formulation and ignores the higher drawdowns produced in low-permeability areas. Optimal well locations are found along the mass centerline of the contaminant plumes and in high-permeability areas in the heterogeneous system. Dynamic pumping rates and well locations produce more cost-effective solutions relative to a static model. The well location search path and convergence behavior indicate that the genetic algorithm is an effective alternative solution scheme and that well location optimization is more important than pumping rate optimization.

The Niched Pareto Genetic Algorithm 2 Applied to the Design of Groundwater Remediation Systems

We present an evolutionary approach to a difficult, multiobjective problem in groundwater quality management: how to pump-and-treat (PAT) contaminated groundwater to remove the most contaminant at the least cost. Although evolutionary multiobjective (EMO) techniques have been applied successfully to monitoring of groundwater quality and to containment of contaminated groundwater, our work is a first attempt to apply EMO to the long-term (ten year) remediation of contaminated water. We apply an improved version of the Niched Pareto GA (NPGA 2) to determine the pumping rates for up to fifteen fixed-location wells. The NPGA2 uses Pareto-rank-based tournament selection and criteria-space niching to find nondominated frontiers. With 15 well locations, the niched Pareto genetic algorithm is demonstrated to outperform both a single objective genetic algorithm (SGA) and enumerated random search (ERS) by generating a better tradeoff curve.

The influence of mass transfer characteristics and porous media heterogeneity on nonaqueous phase dissolution

A two-dimensional multiphase flow and species transport model was developed and applied to the case of nonaqueous phase liquid (NAPL) emplacement and dissolution in both homogeneous and heterogeneous porous media systems. Simulations were performed to observe dissolution rate variations and the degree of NAPL-aqueous phase nonequilibrium as a function of two aqueous phase velocities and five forms of the NAPL-aqueous phase mass transfer formulation. An integrated form of the Damkohler number was introduced to analyze the degree of NAPL-aqueous phase nonequilibrium. Mass removal rates for homogeneous media were insensitive to the form of the NAPL-aqueous phase mass transfer formulation, yielding results similar to a local equilibrium approach for all but one mass transfer formulation. This latter formulation was most sensitive to NAPL saturation and yielded significant nonequilibrium behavior, which was manifested as a decrease in NAPL dissolution rates as the NAPL volume fraction decreased. Variations in mass elution rates between homogeneous and heterogeneous media were observed, with more significant variations found for variances in porous media properties than for horizontal correlation lengths. In heterogeneous media, decreases in dissolution rates were attributed to the existence of relatively immobile regions of NAPL with saturations greater than the residual saturation of the media, so-called NAPL pools. These results illustrate the importance of the statistical characteristics of heterogeneous porous media on NAPL distribution and dissolution processes.

Multi-objective optimal design of groundwater remediation systems: application of the niched Pareto genetic algorithm (NPGA)

Abstract A multiobjective optimization algorithm is applied to a groundwater quality management problem involving remediation by pump-and-treat (PAT). The multiobjective optimization framework uses the niched Pareto genetic algorithm (NPGA) and is applied to simultaneously minimize the (1) remedial design cost and (2) contaminant mass remaining at the end of the remediation horizon. Three test scenarios consider pumping rates for two-, five-, and 15 fixed-location wells as the decision variables. A single objective genetic algorithm (SGA) formulation and a random search (RS) are also applied to the three scenarios to compare performances with NPGA. With 15 decision variables, the NPGA is demonstrated to outperform both the SGA algorithm and the RS by generating a better tradeoff curve. For example, for a given cost of

Optimal design for problems involving flow and transport phenomena in saturated subsurface systems

100,000, the NPGA solution found a design with 75% less mass remaining than the corresponding RS solution. In the 15-well scenario, the NPGA generated the full span of the Pareto optimal designs, but with 30% less computational effort than that required by the SGA. The RS failed to find any Pareto optimal solutions. The optimal population size for the NPGA was found by sensitivity analysis to be approximately 100, when the total computational cost was limited to 2000 function evaluations. The NPGA was found to be robust with respect to the other algorithm parameters (tournament size and niche radius) when using an optimal population size. The inclusion of niching produced better results in terms of covering the span of the tradeoff curve. As long as some niching was included, the results were insensitive to the value of the parameter that controls niching ( σ share >0).

The influence of porous medium characteristics and measurement scale on pore-scale distributions of residual nonaqueous-phase liquids

Estimation problems arise routinely in subsurface hydrology for applications that range from water resources management to water quality protection to subsurface restoration. Interest in optimal design of such systems has increased over the last two decades and this area is considered an important and active area of research. In this work, we review the state of the art, assess important challenges that must be resolved to reach a mature level of understanding, and summarize some promising approaches that might help meet some of the challenges. While much has been accomplished to date, we conclude that more work remains before comprehensive, efficient, and robust solution methods exist to solve the most challenging applications in subsurface science. We suggest that future directions of research include the application of direct search solution methods, and developments in stochastic and multi-objective optimization. We present a set of comprehensive test problems for use in the research community as a means for benchmarking and comparing optimization approaches.

Development and application of a coupled-process parameter inversion model based on the maximum likelihood estimation method

Abstract A series of experiments was performed to characterize the morphologic distribution of nonaqueous-phase liquids (NAPLs) at residual saturation, as a function of porous medium size. Morphologic characterization of NAPL distributions was accomplished using a novel in situ polymerization technique. The porous medium consisted of glass beads. Blob length, volume and shape characteristics were determined for each experiment, and pore size distributions were determined through capillary pressure-saturation experiments. Both the blob lenght and pore size distributions were fitted to a van Genuchten function. Both blob lenght and pressure-saturation data could be scaled with the same averaged porous medium characteristics. The blob length distributions were found to be wider than the pore size distributions. Estimates of representative elementary volumes (REVs) were generated from statistical analysis using a van Genuchten cumulative frequency distribution function for blob lenght and an empirical function for blob volume as a function of blob length. Simulations were also performed using a Monte Carlo method. The size of the REV needed for a given level of prediction of the residual saturation level was found to increase as a function of mean particle volume for the similar used in this study. Extrapolation of the REV analysis suggests that the size of an REV will increase rapidly as uniformity of the medium decreases. If this extrapolation holds true, significant uncertainty would exist in most determination of residual saturation for poorly sorted media that have been reported to date.

The effects of surfactant formulation on nonequilibrium NAPL solubilization

The coupled flow-mass transport inverse problem is formulated using the maximum likelihood estimation concept. An evolutionary computational algorithm, the genetic algorithm, is applied to search for a global or near-global solution. The resulting inverse model allows for flow and transport parameter estimation, based on inversion of spatial and temporal distributions of head and concentration measurements. Numerical experiments using a subset of the three-dimensional tracer tests conducted at the Columbus, Mississippi site are presented to test the models ability to identify a wide range of parameters and parametrization schemes. The results indicate that the model can be applied to identify zoned parameters of hydraulic conductivity, geostatistical parameters of the hydraulic conductivity field, angle of hydraulic conductivity anisotropy, solute hydrodynamic dispersivity, and sorption parameters. The identification criterion, or objective function residual, is shown to decrease significantly as the complexity of the hydraulic conductivity parametrization is increased. Predictive modeling using the estimated parameters indicated that the geostatistical hydraulic conductivity distribution scheme produced good agreement between simulated and observed heads and concentrations. The genetic algorithm, while providing apparently robust solutions, is found to be considerably less efficient computationally than a quasi-Newton algorithm.

Optimal design of pump-and-treat systems under uncertain hydraulic conductivity and plume distribution.

Surfactant-enhanced aquifer remediation (SEAR) involves the injection of surfactant solutions into aquifers contaminated with nonaqueous phase liquids (NAPL). Batch and column experiments were used to assess the effect of surfactant formulation on the rate of NAPL solubilization. The experimental variables were surfactant type, surfactant concentration, electrolyte concentration, and cosolvent concentration. Model equations were proposed and solved to describe solubilization under the conditions of each type of experiment. Using these models, a solubilization rate constant, kappa(b), and an overall mass transfer rate coefficient, kappa, were estimated from the batch and column experiments, respectively. The solubilization rate constant was consistently sensitive to surfactant type, surfactant concentration, and electrolyte concentration. The estimated solubilization rate constants varied over two orders of magnitude. The results of the column experiments also were sensitive to the surfactant formulation. Variations in the fitted mass transfer rate coefficient parameter, beta(0), were related to variations in the surfactant formulations. A comparison between the results of the batch and column experiments yields an apparent relationship between beta(0) and kappa(b). This relationship suggests that the mass transfer rate coefficient is directly related to the formulation of the surfactant solution.

Visualization of surfactant-enhanced nonaqueous phase liquid mobilization and solubilization in a two-dimensional micromodel

In this work, we present a stochastic optimal control framework for assisting the management of the cleanup by pump-and-treat of polluted shallow aquifers. In the problem being investigated, hydraulic conductivity distribution and dissolved contaminant plume location are considered as the uncertain variables. The framework considers the subdivision of the cleanup horizon in a number of stress periods over which the pumping policy implemented until that stage is dynamically adjusted based upon new information that has become available in the previous stages. In particular, by following a geostatistical approach, we study the idea of monitoring the cumulative contaminant mass extracted from the installed recovery wells, and using these measurements to generate conditional realizations of the hydraulic conductivity field. These realizations are thus used to obtain a more accurate evaluation of the initial plume distribution, and modify accordingly the design of the pump-and-treat system for the remainder of the remedial process. The study indicates that measurements of contaminant mass extracted from pumping wells retain valuable information about the plume location and the spatial heterogeneity characterizing the hydraulic conductivity field. However, such an information may prove quite soft, particularly in the instances where recovery wells are installed in regions where contaminant concentration is low or zero. On the other hand, integrated solute mass measurements may effectively allow for reducing parameter uncertainty and identifying the plume distribution if more recovery wells are available, in particular in the early stages of the cleanup process.