Elsevier

Journal of Hydrology

Volume 342, Issues 3–4, 1 September 2007, Pages 295-304
Journal of Hydrology

Optimal planning of a dynamic pump-treat-inject groundwater remediation system

https://doi.org/10.1016/j.jhydrol.2007.05.030Get rights and content

Summary

This study integrates the genetic algorithm (GA) and constrained differential dynamic programming (CDDP) to design the pump-treat-inject system. The proposed model considers both the cost of installing wells (fixed cost) and the operating cost of pumping, injection and water treatment. To minimize the total cost while meeting the water quality constraints, the model can compute the optimal number and locations of wells, as well as the associated optimal pumping and injection schemes. Various numerical cases reveal that the requirement to balance the total volume between pumping and injection can significantly influence the final optimal design.

Introduction

Groundwater is a valuable natural resource. However, it is threatened by contaminants from industrial and waste disposal activities and the problem has become more serious in recent years. Contaminant removal to clean up the aquifer is very expensive and generally takes many years. Many approaches have been applied to this problem. The pump-and-treat (PAT) method is one of the most commonly applied methods of groundwater remediation. By pumping out contaminated groundwater, treating the water and injecting the clean water to confine the pollutant plume, the method is primary useful for decontaminating groundwater with highly soluble pollutants.

Effective design of a remediation system in groundwater requires consideration of more than just the effectiveness of the technological process involved. The first step necessary in planning is to define the goals of design. The most commonly used objective for the remediation design is to minimize costs associated with the remediation system. In recent years, optimization models have been developed to design a groundwater remediation system (Gorelick and Voss, 1984, Taghavi et al., 1994, Aly and Peralta, 1999, Culver and Shenk, 1998). Previously, the fundamental approach of an optimal design was concerned with how to operate only the pumping wells in the most contaminated area (Chang and Shoemaker, 1992, Huang and Mayer, 1997, Zheng and Wang, 1999, Chang and Hsiao, 2002). Chang and Shoemaker (1992) applied constrained differential dynamic programming (CDDP) to the optimal remediation design of time-varying pumping rates, while considering only the operation cost. Huang and Mayer (1997) used a genetic algorithm (GA) to find the optimal extraction wells and corresponding pumping rates in remediation design. Zheng and Wang (1999) used an integrated approach which used the tabu search (TS) to define well locations and linear programming for optimizing pumping rate. Although Huang and Mayer, 1997, Zheng and Wang, 1999 examine both fixed cost and operation cost, they consider only a steady pumping rate. Chang and Hsiao (2002) integrated GA and CDDP to overcome the problem of simultaneously considering both the fixed costs of well installation and the operating costs of time-varying pumping rates.

The previously reviewed studies in optimization consider only the extraction wells. However, a cost-effective remediation system for soluble pollutants should include both the withdrawal and injection wells in general. The approach has the effectiveness of creating a capture area which contains and prevents the contamination from migrating (Cohen et al., 1994, Bear and Sun, 1998, Wang et al., 1999, Cunningham and Reinhard, 2002). Such a technique is referred to as pump-treat-inject (PTI), one of the PAT, in which the contaminated water is pumped then treated, and the treated water is re-injected into the aquifer (Bear and Sun, 1998). The PTI technique has the function of hydraulic control that extraction wells locate in the dissolved plume to capture the contaminated water, and treated water is re-injected by injection wells to create a pressure ridge along the axis of the plume (Cohen et al., 1994, Wang et al., 1999). Cunningham and Reinhard (2002) demonstrated that the flow of pumping and injection acts as a hydraulic barrier, protecting potential drawdown gradient from contamination, in much the same manner as a permeable reactive barriers. More than one optimization method for the design of a PTI system has been developed. McKinney and Lin (1995) used mixed-integer programming in creating an optimal design for the air-stripping treatment process. The objective is to minimize the total cost including fixed cost and operating costs of pumping and injection at five potential wells. Bear and Sun (1998) used the two-level hierarchical optimization model to optimize the PTI design. At the basic level, well locations and pumping/injection rates are defined to maximize removal of contaminants. At the upper level, the number of wells for pumping/injection is optimized, so as to minimize the cost, taking maximum contaminant level as a constraint. Their study neglects operating cost, however, which is a large part of remediation cost. Guan and Aral (1999) used a progressive genetic algorithm to optimize the remediation design. For a specified well number, their study defines the well locations and pumping or injection rates for each well. The proposed model considers only the operating cost of steady pumping and injection. Hilton and Culver (2000) used a genetic algorithm to solve the same example as McKinney and Lin (1995). The proposed model considers the fixed and operating cost of pumping and injection. Both studies consider pumping and injection rate equilibrium, i.e. total pumping volume equals total injection volume during the planning period. However, the pumping and injection rates for each well are steady in their studies. A few researchers have considered time-varying pumping and injection rates. Minsker and Shoemaker (1998) applied SALQR to design the in situ bioremediation, which involves determining time-varying pumping and injecting rates for the extraction and injection wells, respectively. The injection wells are used to stimulate the microbial population and accelerate degradation of pollutants by injecting electron accepters, nutrients, additional carbon or electron donor sources. However, the study considered only the operating cost not the fixed cost.

Total cost of a PTI system should include the installation and operation cost, and, to be cost-effective, the operation policy should be time-varying because the dynamic policies are allowed to change as the contaminant plume moves. However, optimal design for the PTI system is a highly complex problem and none of the previous works has examined this problem. Therefore, this study develops a hybrid algorithm by integrating the genetic algorithm (GA) and constrained differential dynamic programming (CDDP) to solve the dynamic PTI design problem. The optimal wells network and the optimal pumping or injection rates for each well are all computed by the proposed algorithm. The algorithm incorporates the time-varying policies of PTI system and also considers pumping and injection rate equilibrium for each time step.

Section snippets

Formulation of the planning model

The formulation to minimize both the fixed and operating costs of the system while determining the extraction or injection well network and pumping/injection rate is as follows:minWΩut,j,jPut,i,iIt=1,,NJ(W)=ja1yj(P)+t=1Nja2ut,j(P)[Lj(P)-ht+1,j(P)]+a3ut,j(P)+ia1yi(I)+t=1Ni[a4ut,i(I)]subject to{xt+1}=T(xt,ut(W),t,W),t=1,2,,NcN,lcmax,lΦjut,j(P)Tumax,t=1,2,,N,jP,PΩumin(p)ut,j(P)umax(p),t=1,2,,N,jP,PΩumin(in)ut,i(I)umax(in),t=1,2,,N,iI,IΩhminht,ihmax,t=1,2,,N,iWjut,j(

The algorithm of GCDDP: integration of a GA and CDDP

As previous stated, this investigation integrates GA and CDDP to solve the problem defined by Eqs. (1), (2), (3), (4), (5), (6), (7), (8). The problem is a mixed-integer nonlinear time-varying problem and includes discontinuous variables (pumping/injection well locations) and continuous variables (time-varying pumping/injection rates), and cannot be solved by a single conventional optimization scheme. Therefore, this study further explores the problem structure and reformulates the problem into

Results and discussion

This study presents the solutions obtained for a hypothetical, isotropic confined aquifer with dimensions of 600 m by 1200 m to demonstrate the performance of the algorithm described above. Fig. 3 indicates the finite element mesh which has 91 finite element nodes, along with 24 candidate well sites, and 17 observation wells. The boundary conditions on the north and south sides are no-flow boundaries for head and concentration. Constant-head boundaries with 22 and 10 m are located on the west and

Conclusions

This study proposes an optimal planning model for groundwater remediation system based on the pump-treat-inject technique (PTI). The optimization model integrated CDDP and GA to design a pumping and injecting network system and the associated operation policy with a minimum total cost while simultaneously considering the fixed costs and time-varying operating costs. A PTI system using only injecting wells may have the lowest cost but is not a practical design, since an injection well can only

Acknowledgements

The work was supported by the National Science Council of the Republic of China for financially under Contract No. NSC 94-2211-E-235-002. The authors would like to thank Prof. Shan, H.-Y, Prof. M.A. Goodwin, anonymous reviewers and helpers.

References (24)

  • J.A. Cunningham et al.

    Injection–extraction treatment well pairs: an alternative to permeable reactive barriers

    Ground Water

    (2002)
  • David E. Goldberg

    Genetic Algorithms in Search, Optimization, and Machine Learning

    (1989)
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