David P. Ahlfeld

Optimal groundwater remediation with well location as a decision variable: Model development

A new formulation for the optimal design of aquifer remediation strategies is presented in which the well location problem is solved by explicitly incorporating the spatial coordinates and pumping rates of wells as decision variables. The Hermite interpolation function is used to represent the well location as a continuous function of space and to facilitate the incorporation of a barrier function for containing the well location within the model domain. The management model combines the numerical simulation of groundwater flow and contaminant transport with optimization methods to select the optimal location and pump rate by moving each well within the problem domain unrestricted by nodal location. The details of the numerical implementation required to incorporate well locations as decision variables in a two-dimensional Galerkin finite element discretization of the groundwater flow and contaminant transport equations are presented. The approach is contrasted with an optimization model for groundwater quality management in which optimal well locations are chosen from a number of preselected candidate locations. A simple hypothetical problem is solved to compare these two approaches and examine the numerical behavior of the new formulation. The results indicate that a formulation in which well location is a decision variable can be implemented and that improved solutions are possible. The results are also used to demonstrate how this approach can be used to solve problems in which the initial costs of well installation are included.

Nonlinear programming on generalized networks

We describe a specialization of the primal truncated Newton algorithm for solving nonlinear optimization problems on networks with gains. The algorithm and its implementation are able to capitalize on the special structure of the constraints. Extensive computational tests show that the algorithm is capable of solving very large problems. Testing of numerous tactical issues are described, including maximal basis, projected line search, and pivot strategies. Comparisons with NLPNET, a nonlinear network code, and MINOS, a general-purpose nonlinear programming code, are also included.

Designing optimal strategies for contaminated groundwater remediation

Abstract The problem of locating pumps and setting pump rates to most effectively stabilize and remove a plume of contaminated groundwater at a hazardous waste site is examined. Nonlinear optimization methods are combined with convective-disperisve transport simulation in a unit response matrix type of optimization formulation. Constraints are used which guarantee that the contaminant plume is removed by limiting the concentrations at nodal points in the domain at a future time. Additional constraints explicitly require that concentrations not increase in the area outside the initial plume boundary. The effectiveness of alternative formulations are examined by performing numerical experiments using a hypothetical aquifer. The experiments show that computational costs are dominated by the repeated simulations required for computation of constraint gradients and are proportional to the number of pump sites under consideration. This characteristic of the formulation and algorithm used, limits the use of the approach to problems where the number of potential pump sites is relatively small.

Respirometric assay for biofilm kinetics estimation: Parameter identifiability and retrievability

Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (insertion markμ) and the half-saturation coefficient (Ks)-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for insertion markμ estimates than for Ks estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters. Copyright 1998 John Wiley & Sons, Inc.

Assessing groundwater policy with coupled economic-groundwater hydrologic modeling

This study explores groundwater management policies and the effect of modeling assumptions on the projected performance of those policies. The study compares an optimal economic allocation for groundwater use subject to streamflow constraints, achieved by a central planner with perfect foresight, with a uniform tax on groundwater use and a uniform quota on groundwater use. The policies are compared with two modeling approaches, the Optimal Control Model (OCM) and the Multi-Agent System Simulation (MASS). The economic decision models are coupled with a physically based representation of the aquifer using a calibrated MODFLOW groundwater model. The results indicate that uniformly applied policies perform poorly when simulated with more realistic, heterogeneous, myopic, and self-interested agents. In particular, the effects of the physical heterogeneity of the basin and the agents undercut the perceived benefits of policy instruments assessed with simple, single-cell groundwater modeling. This study demonstrates the results of coupling realistic hydrogeology and human behavior models to assess groundwater management policies. The Republican River Basin, which overlies a portion of the Ogallala aquifer in the High Plains of the United States, is used as a case study for this analysis.

Advective control of groundwater contaminant plumes: Model development and comparison to hydraulic control

A new optimization formulation for designing groundwater plume control systems is presented. The new formulation uses particle-tracking techniques in a two-step solution process. The two-step procedure is motivated by numerical and computational considerations; particle representation is defined to take advantage of specific properties and improve model convergence. The optimization formulation seeks the least cost control system that satisfies the two equivalent requirements that the contaminant plume be located within the capture zone (step 1) and that all particles representing contaminant solute travel to an extraction well (step 2). To date, optimization formulations for plume capture design have emphasized either hydraulic or concentration control; however, these formulations provide indirect representation of the plume control and containment problem. The model presented here explicitly represents the capture zone design problem using particle tracking and formalizes the design procedures used by many practitioners. Two example problems representing two- and three-dimensional flow systems are used to demonstrate the new advective control model. Hydraulic control formulations for the two problems are also developed, and designs are compared with those of the advective control model. Control systems resulting from the hydraulic control model are sensitive to constraint magnitude and location, highlighting the need for constraint calibration in order to best achieve design goals. Conversely, constraints in the new model directly represent the plume capture problem, and the model provides more efficient capture zone designs than the hydraulic control formulation.

Comparing artificial neural networks and regression models for predicting faecal coliform concentrations

Abstract This paper compares the performance of ordinary least squares (OLS) and binary logistic regression methods, and artificial neural networks (ANNs) for the prediction of surface water faecal coliform concentrations in a 8.2 km2 mixed land-use watershed. Model inputs consist of precipitation and temperature data, as well as instantaneous measurements of streamflow and conductivity. The ANNs are able to correctly classify 69% and 85% of faecal coliform concentrations relative to 20 and 200 cfu/100 mL water quality standards, respectively, results moderately better than those observed for the regression models. The ANN models using only meteorological inputs were able to correctly classify 72% and 81% of the observations relative to the 20 and 200 cfu/100 mL standards, respectively. The ANN models are notably better at predicting when the 200 cfu/100 mL standard is violated. In addition, the ANN models have lower percentages of false negatives, a characteristic desirable for protection of public health.

Groundwater Remediation Design Using a Three-Dimensional Simulation Model and Mixed-Integer Programming

A three-dimensional groundwater flow management model for making decisions on the design of hydrodynamic control of a groundwater flow system using a combination of extraction and/or injection wells is developed. The model takes into account constraints imposed on the system to stop the horizontal spread of contaminants and to ensure a net upward flow in areas where downward vertical gradients exist. The mathematical formulation of the groundwater remediation problem as a mixed-integer model and the strategy for solving the model are presented. Numerical results are presented for the Toms River Plant site, which is modeled as a five-layer aquifer system with interconnecting aquitards. A sensitivity analysis on the relative magnitude of the continuous operating costs and the fixed-charge costs is also presented.

Simplicial Decomposition for Convex Generalized Networks

Abstract The simplicial decomposition algorithm is specialized to solve nonlinear programs with generalized network constraints. Large scale problems can be solved efficiently by capitalizing on the intrinsic structure of the generalized network basis in the subproblem steps. The performace of the master problem is improved using a forcing sequence strategy to solve the master inexactly in a controlled fashion. The resulting software system (GNSD) is capable of solving large problems from a wide variety of applications. We investigate tactics that affect its performance and compare GNSD with other nonlinear programming codes.

GWM-2005 - A Groundwater-Management Process for MODFLOW-2005 with Local Grid Refinement (LGR) Capability

This report describes the Groundwater-Management (GWM) Process for MODFLOW-2005, the 2005 version of the U.S. Geological Survey modular three-dimensional groundwater model. GWM can solve a broad range of groundwater-management problems by combined use of simulationand optimization-modeling techniques. These problems include limiting groundwater-level declines or streamflow depletions, managing groundwater withdrawals, and conjunctively using groundwater and surface-water resources. GWM was initially released for the 2000 version of MODFLOW. Several modifications and enhancements have been made to GWM since its initial release to increase the scope of the program’s capabilities and to improve its operation and reporting of results. The new code, which is called GWM-2005, also was designed to support the local grid refinement capability of MODFLOW-2005. Local grid refinement allows for the simulation of one or more higher resolution local grids (referred to as child models) within a coarser grid parent model. Local grid refinement is often needed to improve simulation accuracy in regions where hydraulic gradients change substantially over short distances or in areas requiring detailed representation of aquifer heterogeneity. GWM-2005 can be used to formulate and solve groundwatermanagement problems that include components in both parent and child models. Although local grid refinement increases simulation accuracy, it can also substantially increase simulation run times.