DEVISING GROUNDWATER MITIGATION STRATEGIES FOR DIFFERENT OBJECTIVES USING ECP OPTIMIZATION

Subterranean Research, Inc.

P.O. Box 1121, Burlington, VT 05401, USA

Tel: (802) 658-8878, Fax: (802) 658-8878

E-mail:myu@subterra.com drizzo@subterra.com ddougher@subterra.com

Abstract: For groundwater remediation design problems, computational optimization techniques are being used to provide more flexible and efficient cleanup strategies. Traditionally, optimization problems are formulated to minimize accumulated costs over the lifetime of the remediation design while determining well locations and pumping rates that provide hydraulic control for concentration containment. When concentration appears in the objective or constraint functions, it is considered only at the end of the management period. We present an application of the extended cutting plane (ECP) optimization techniques to a Superfund site with a complex flow and transport scenario located in Massachusetts, U.S. In addition to capabilities provided by traditional optimization codes, ECP offers more useful functionality that can provide the stakeholder and/or decision-makers with a variety of optimal strategies from which to choose. In spatial dimensions, stakeholders may want to protect Points-Of-Compliance (POCs) or Regions-Of-Interest (ROIs). Optimal strategies have been developed in this paper to accommodate different practical groundwater remediation objectives.

 

Keywords: cutting plane method, optimization, groundwater remediation, pump and treat

Subterranean Research, Inc. (SRI) has developed comprehensive optimization tools focusing on three primary research areas: (1) A joint environmental data inversion and imaging (JEDIIÔ ) technique for subsurface environmental site characterization, (2) multiple, complementary remediation process optimization methods (SAMOAÔ , see Yu, et al., 2000), and (3) an Adaptive Long-Term Monitoring and Operations System (aLTMOsÔ , see Rizzo, et al., 2000).

In this paper, we focus on the application of an optimization method, called the extended cutting plane (ECP), to groundwater pump and treat (P&T) remediation systems with different objectives. P&T refers to the extraction and treatment of contaminated groundwater, possibly followed by reinjection of water. To design a P&T system, we need to determine well locations and flow rates, which can significantly affect the system performance and cost. Numerical simulation models for flow and transport are often used to evaluate potential P&T system designs. The simulation model is executed repeatedly to simulate different pumping scenarios. Combining an optimization method with the flow and transport simulator enables optimal pumping scenarios to be selected. Such a system design process is referred to simulation-optimization.

The authors have conducted research on the simulation-optimization approach for over a decade (e.g., Dougherty and Marryott, 1991; Marryott et al., 1993; Ahlfeld and Dougherty, 1995; Rizzo and Dougherty, 1996; Yu et al., 2000; Rizzo et al., 2000). Based on the evaluation of many different optimization methods for groundwater remediation system designs, we have developed the ECP method. ECP is an extension and improvement over the outer approximation methods that have previously been reported in the literature (e.g., Thieu et al., 1984; Horst and Tiuy, 1990; Karatzas and Pinder, 1993, 1996). In ECP, new data structures and cutting algorithms are employed to reduce the computational restrictions. ECP has been tested on a variety of published optimization results to find equivalent or improved solutions, and is substantially faster (typically factors of around 100 and greater). ECP does not require a specific flow and transport simulation model be used. It can be wrapped around any flow/transport simulation code. Some of the simulation models that we have used include MODFLOW-96 (Harbaugh and McDonald, 1996), MT3DMS (Zheng and Wang, 1999), MODFLOW-SURFACT (HydroGeoLogic, 1996), SUTRA (Voss, 1984), and PTC ( Babu et al. 1993).

For a transport simulation problem, the size of the problem refers to the number of nodes (or cells) in the model. For an optimization problem, the size of the problem refers to the number of decision variables. Due to the storage requirements and computational speed, many optimization methods can only solve medium-sized problems. Therefore, domain-specific insights may be used to select the decision variables (potential well locations) or to reduce the problem size. ECP generally can tackle linear and nonlinear optimization problems of over one hundred decision variables. When the simulated annealing method (Rizzo and Dougherty, 1996) is used with ECP in tandem (Yu et al., 2000), the combined method (SAMOA) can tackle optimization problems having thousands of decision variables.

ECP is practice-oriented optimization software. That is, we have investigated a variety of site-specific goals that affect management and design decisions for P&T systems and have built them into the objective and constraint functions. Typically, these goals include the remediation objectives, the anticipated timeframes, initial construction costs (including well, pipeline, and treatment plant construction), treatment costs, and annual operation and maintenance costs. The remediation objectives are often a compromised result of multiple stakeholders. In ECP, the remediation objectives of a P&T system might include:

• Containment: The objective is to prevent the plume from exceeding target concentrations at specified regions within specified time frames. Stakeholders specify Regions-Of-Interest (ROIs). In two dimensions, the ROI may be specified as lines (e.g., a property boundary), or areas. In three dimensions, the ROI may be specified as lines, surfaces, or volumes.
• Points-Of-Compliance: POCs are finite sets of monitoring locations at which concentration values (and perhaps other performance measures) are used to determine whether a facility is in or out of compliance with a record of decision.
• Mass removal or cleanup: The objective is to reduce the contaminant concentrations of the entire site or portions of the site (in this case, ROIs are volumes) to be below specific values (frequently the maximum contaminant level, MCL) at and/or after the specified time horizons.
• Hybrid: The objective is mixed containment and cleanup. Typically, the containment objective may be the first priority and the cleanup objective may be the second priority. Containment and cleanup objectives are often described as conflicting (or competitive) objectives, which may lead to conflicting designs. By performing optimization, it is possible to develop an integrated design in which containment and cleanup are complementary.

In this paper, ECP is applied to a P&T design problem in Massachusetts. In 1994, The site was added to the Superfund National Priorities List (NPL) due to the discovery of groundwater contamination at the site (see Figure 1). The primary contaminants of concern are solvents (TCE and PCE) found at depths between 30 and 60 feet below the ground surface. Groundwater flows from the site toward several municipal well fields and to a lake that borders the site on the south. TCE is the contaminant being modeled in this study.

Fig.1  Site map and predicted TCP plume (maximum over all layers) after 10 years of remediation using the existing well configuration.

A three-dimensional MODFLOW-SURFACT model of the site was prepared and provided by HydroGeoLogic, Inc. The model has 70,644 cells with 116 rows, 87 columns, and 7 layers. The initial plume concentration was for the year circa 1998 and flow is steady state (except for the remediation-induced flow). The initial maximum concentration at the site was 750 ppb. A dual domain approach is used in the model to represent the retarding mechanisms involving both equilibrium and kinetic adsorption processes (Feehley and Zheng, 2000). The management time horizon at the site was limited to 27 years, of which the active cleanup time horizon was limited to the first 10 years, followed by 17 years of monitored natural attenuation. Two existing (as-built) wells are pumping with total flow rates of 12902 cubic feet per day (cfd) or 67 gallons per minutes (gpm).

Mathematical optimization was applied to find well locations and extraction flow rates that achieve the given remediation objectives while minimizing the total accumulated cost. The target TCE concentrations are 5 ppb. Two ROIs and a set of POCs were specified:

• ROI A is described by two line segments at the northwest property boundary shown in Fig. 1 and 2. For this 3-D model, ROI A is formed by two planes and has 371 grid points.
• ROI B is a volume formed by extending the area shown in Fig. 2, Case 3 vertically through all layers. It has 3969 grid points.
• The set of POCs consists of 9 points of compliance (see Fig. 2, Cases 2 and 4). The TCE concentration at a POC is the maximum value along the vertical direction over all model layers.

We apply the ECP optimization method to the P&T system design problem using four different remediation objectives. Due to the budget and treatment capacity constraints, the maximum number of remediation wells at the site cannot exceed 4. This constraint applies to all design cases. These 4 optimization cases are listed below:

• Case 0 – As-built design consisting of 2 existing remediation wells is shown for comparison purposes.
• Case 1 – The objective is containment at the northwest property line (ROI A).
• Case 2 – The objective is maximizing the mass removal over the site (actually over the entire modeled volume) and achieving compliance at the 9 POCs. In this Case, we required that the 2 as-built remediation wells be used.
• Case 3 – The objective is containment at the northwest property line (ROI A) and mass removal over the area shown in Fig. 2, Case 3 (ROI B).
• Case 4 – The objective is containment at ROI A and compliance at POCs. In this Case, we required that the two as-built remediation wells be used.

Optimization may introduce new actions or modify existing designs to reduce risks to human health and the environment, reduce operating costs, and/or shorten cleanup time associated with the remediation. Optimization may also suggest feasible remediation objectives within a given time horizon. We applied the ECP optimization technique to the four case problems stated in previous section. The results of the as-built well configuration and the optimization for the four different remediation objectives are summarized in Table 1. The plumes at the end of 10 years are shown in Figures 1 and 2. The transport simulation shows that the as-built design does not achieve the desired remediation objectives.

In Case 1, two wells are selected out of 50 candidate well locations and pump at a total flow rate of 45.2 gpm. While these two wells successfully achieve the target containment at ROI A, the contaminant mass is not effectively removed. For this case, it may not be possible to close the site at the end of remediation period due to the residual contaminant mass.

Case 2 removes as much contaminant mass as possible from the site while attaining the target concentration values at the POCs. Recall the added constraint that the two existing wells must be used. Table 1 shows that this solution yields the highest contaminant mass removal.

Cases 3 and 4 are hybrids involving containment at ROI A together with mass removal over ROI B (Case 3) and with POCs (Case 4). Both Cases accomplish their objectives. Note, however, that a greater amount of contaminant mass remains in the subsurface in Case 4, even though it pumps significantly more that the Case 3 solution. This difference is caused by two factors: (1) Case 3 used mass removal over ROI B while Case 4 used compliance at POCs, and (2) Case 4 also required that the two existing wells be used. Table 1 shows that, as a side-effect, Case 3 also satisfies all the POCs.

                  Table 1  Description of optimization cases for different remediation objectives.

Fig. 2  Predicted TCE concentrations in the mobile domain after pumping for 10 years. Maximum concentration over all layers is shown. The red circles indicate pumping wells. POCs are indicated by the green triangles.

 

The authors are grateful to Steve Young and John for their support of this project.

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