Optimal design of in-situ bioremediation system using the meshless element-free Galerkin method and particle swarm optimization

https://doi.org/10.1016/j.advwatres.2020.103707Get rights and content

Highlights

  • Meshless model is proposed for in-situ bioremediation simulations.

  • The proposed simulation model is validated with RT3D model.

  • Simulation-optimization (S/O) model is developed with EFGM and PSO.

  • The proposed S/O model can also explore optimal well location at positions other than the grid nodes.

  • The proposed S/O model reduces in-situ bioremediation cost and increases contaminant degradation.

Abstract

An optimal design of in-situ bioremediation system for contaminated aquifer sites mainly depends on the injection/extraction well locations and their pumping rates. Previous studies have used discretization approaches such as finite difference method (FDM) or finite element method (FEM) to solve the equations of groundwater flow and contaminant transport (GFCT) that characterize the bioremediation processes. In these numerical models, well locations can only lie at the grid nodes and therefore, the locations other than the grid nodes remain unexplored for the optimal in-situ bioremediation. To explore such locations, in this study a meshless simulation model called BIOEFGM is developed using the element-free Galerkin method (EFGM) and coupled with the particle swarm optimization (PSO). BIOEFGM model provides flexibility in adding injection/extraction wells anywhere in the computational domain during the entire optimization procedure. However, FDM/FEM requires meshing and re-meshing of the computational domain for each set of wells and it increases the computational efforts significantly for solving the optimization problem. In this paper, the proposed BIOEFGM-PSO simulation-optimization (S/O) model is first applied to a well-known bioremediation problem and then to a field type large aquifer problem. The simulation results of BIOEFGM are verified with those from the RT3D simulations. The estimated bioremediation cost from the BIOEFGM-PSO model for the first problem is found to be lesser in comparison to the same calculated with different S/O models in the previous studies. The results of this problem also show that optimized in-situ bioremediation system designed by proposed S/O model takes less remediation time and also favor effective biodegradation of contaminants. For both the problems, BIOEFGM-PSO identified optimal well locations at positions other than that of discretized nodes and it leads to efficient bioremediation. It indicates the effectiveness of the BIOEFGM-PSO model and therefore, can be applied for designing the better optimized in-situ bioremediation systems for field problems.

Introduction

Groundwater resources store large part of the world’s fresh water and act as a vital source of drinking water (Fan, 2015). Because these resources are located underneath the Earth’s top crust therefore, are poorly managed and over exploited (Zaporozec, 1981). Worldwide many groundwater sites are facing a serious problem of contamination. The contamination through petroleum products is one of the major issues. The large number of underground storage tanks (UST’s) are used to store petroleum products such as gasoline, diesel fuel, kerosene oil etc. and their leakage from UST’s result in contamination of the groundwater resources. The petroleum hydrocarbons contain toxic organic chemicals such as benzene, toluene, ethylbenzene, and xylenes (BTEX) (Bedient et al., 1994). The presence of such organic contaminants even in small amount in groundwater can deteriorate aquifer health and make it unfit for supplying drinking water to public. The natural attenuation processes can clean BTEX contaminated aquifers up to a certain limit. It includes the processes of hydrodynamic dispersion, sorption and volatilization which reduces contaminant concentration in the groundwater and biodegradation that reduces mass of contaminants (Wiedemeier et al., 1999).

For BTEX contaminated aquifers, biodegradation is the most suitable attenuation process since it reduces actual mass of BTEX compounds by consuming the available oxygen in the groundwater (USEPA, 2004). In groundwater sites with large BTEX concentration, biodegradation process results in depletion of oxygen in the core of the plume and thereby it stops further degradation of BTEX compounds. To stimulate the biodegradation of these petroleum hydrocarbons, in-situ bioremediation is the most preferred cleaning technique. In-situ groundwater bioremediation is a technique that promotes the growth and reproduction of indigenous microorganisms to increase the biodegradation rate of organic compounds in the saturated region (USEPA, 2004). This is achieved by supplying electron acceptors such as oxygen and nitrate, and nutrients such as nitrogen and phosphorus to the microorganisms in the contaminated region. In-situ bioremediation employs the use of both injection and extraction wells in the polluted groundwater site. The injection wells are used to transport electron acceptors and nutrients to the microorganisms. The extraction wells are used to increase the hydraulic gradient, control the plume movement and remove the contaminants from the aquifer system. This remediation approach can effectively degrade dissolved and adsorbed organic compounds in the groundwater and soil respectively (Schreiber and Bahr, 2002).

Designing an optimal in-situ bioremediation system is an important exercise for groundwater scientists and is mainly dependent on the wells location and their injection/extraction rates. It can be designed using the different S/O models which couple GFCT based bioremediation simulations with the optimization algorithms. Over the last few decades, several studies on in-situ groundwater bioremediation have been reported. Yoon and Shoemaker (1999) used the BIO2D model, proposed by Taylor (1993), for bioremediation simulations and applied different optimization algorithms to find out the fastest algorithm for designing the optimized in-situ bioremediation system. Later, Yoon and Shoemaker (2001) used a real coded genetic algorithm (RGA) for the optimal in-situ bioremediation. Shieh and Peralta (2005) coupled the BIOPLUME II model, proposed by Rifai et al. (1987), with a hybrid algorithm combining genetic algorithm (GA) and simulated annealing (SA) for the optimal design of in-situ bioremediation system. Prasad and Mathur (2008) used the artificial neural network (ANN) as a proxy simulator of BIOPLUME III (Rifai et al., 1997) and presented a technique based on ANN and Monte Carlo approach for identifying the potential well locations for an optimal in-situ bioremediation. Sudheer et al. (2013) trained the support vector machine (SVM) with BIOFDM simulations and combined it with the PSO for scheduling the optimum pumping policy for in-situ bioremediation. Yadav et al. (2016) used the extreme learning machine (ELM) as a proxy simulator of BIOPLUME II and combined it with PSO for finding the optimal strategy for in-situ groundwater bioremediation. In most of the aforementioned studies, the case study of Shieh and Peralta (2005) is solved using different S/O models and the optimal well locations were determined from the limited preselected locations (Prasad, Mathur, 2008, Sudheer, Kumar, Prasad, Mathur, 2013, Yadav, Ch, Mathur, Adamowski, 2016). However, Raei et al. (2017) used all the grid nodes in the same study area as a search space to find out the optimal well locations. Using this approach and calling BIOPLUME III simulations within NSGA-II, they found that bioremediation cost decreases by 20 to 40 % of costs estimated in studies with predefined well locations.

In the optimal design of groundwater bioremediation system, well locations are the important decision variables. In the past several studies, the mesh based methods (FDM/FEM) have been mostly used for running the GFCT simulations of the bioremediation mechanism (Yoon, Shoemaker, 1999, Yoon, Shoemaker, 2001, Shieh, Peralta, 2005, Prasad, Mathur, 2008, Sudheer, Kumar, Prasad, Mathur, 2013, Yadav, Ch, Mathur, Adamowski, 2016, Raei, Nikoo, Pourshahabi, 2017). The mesh based simulation models provide optimal well locations only at the grid nodes in the optimized bioremediation system, however, optimal well locations can also lie at the locations other than the grid nodes. In such cases, meshless methods provide advantages over the mesh based methods and can be used to locate optimal well coordinates anywhere inside the problem domain. These methods are recently emerged as better alternative of FEM/FDM and are independent of remeshing procedure unlike FDM/FEM.

A meshless method uses scattered field nodes to represent problem domain and its boundaries. The governing equations are then discretized using the field variable values at the scattered nodes. In the recent decade, different meshless models namely, element-free Galerkin method (EFGM), point collocation method (PCM), meshless local Petrov-Galerkin method (MLPG) have been successfully applied over the real field GFCT problems. Meenal and Eldho (2011) first developed a meshless PCM based groundwater flow model, and subsequently they also developed a PCM based contaminant transport model for the unconfined flow (Meenal and Eldho, 2012). Swathi and Eldho (2014) presented a MLPG based model for the unconfined groundwater flow problems, and later on they developed the MLPG based model for the contaminant transport problems (Boddula and Eldho, 2017). Pathania et al. (2019) proposed a EFGM based groundwater model for the unconfined aquifers and demonstrated its suitability to field aquifers with surface water groundwater interactions. Among the meshless GFCT models, PCM has also been used for the in-situ bioremediation simulations by Mategaonkar and Eldho (2012). They coupled the PCM simulations with the PSO algorithm for proposing an optimized bioremediation strategy. Recently, Seyedpour et al. (2019) used the meshless RPCM based GFCT simulations and GA for the optimal design of groundwater remediation.

EFGM is a robust meshless method and therefore, it has been applied in many practical engineering problems (Liu and Gu, 2005). EFGM uses moving least squares (MLS) approximation in the Galerkin weak-form to produce a set of algebraic equations (Belytschko et al., 1994). In EFGM, MLS approximation provides stability in function approximation and the Galerkin approach construct a discretized global system equations that gives a stable solution (Liu and Gu, 2005). The integral operator in EFGM helps to smooth the error due to function approximations, however, differential operator in meshless collocation methods tend to increase this error (Liu and Gu, 2005). EFGM possess high accuracy and convergence rate than the FEM/FDM since it uses more support nodes for constructing the shape functions (Liu and Gu, 2005). The irregular arrangement of the nodes also does not influence EFGM performance (Belytschko et al., 1994). Moreover, the meshless feature of the EFGM offers convenience to add/remove well at any location during the entire optimization process and thus, provides more search space to explore the optimal well locations within the problem domain. Therefore, this study first develops the EFGM based new simulation model called BIOEFGM for the bioremediation simulations. In the recent years, PSO has been successfully applied with different simulation models for the optimal in-situ groundwater bioremediation of aquifers (Mategaonkar, Eldho, 2012, Sudheer, Kumar, Prasad, Mathur, 2013, Yadav, Ch, Mathur, Adamowski, 2016). Therefore, in this study, PSO algorithm is used to design the optimal bioremediation system.

In the present study, we propose BIOEFGM-PSO based a new S/O model for the optimal design of in-situ groundwater bioremediation system. The proposed model finds optimal well locations and pumping rates by coupling the EFGM based bioremediation simulations with the PSO. BIOEFGM is free from meshing and remeshing procedure unlike FDM/FEM and therefore, can easily accommodate a set of new wells in the simulation domain at each iteration of an optimizer. It also reduces a lot of computational efforts required in solving optimization problems. In this study, the proposed S/O model is first applied to a well known bioremediation problem of Shieh and Peralta (2005) and it has also been solved using different S/O models in the similar previous studies (Sudheer, Kumar, Prasad, Mathur, 2013, Yadav, Ch, Mathur, Adamowski, 2016, Raei, Nikoo, Pourshahabi, 2017). Further, the proposed S/O model is used to design an optimized bioremediation system for a hypothetical field type large aquifer system. In the past, only simple hypothetical aquifers have been considered and the present study also considers a hypothetical field type large aquifer with irregular boundaries. The proposed S/O model is very useful and can save costs associated with highly expensive bioremediation technique by finding optimal injection/extraction locations at those points otherwise remains unexplored locations with mesh based methods for the similar nodal configuration of the problem domain.

Section snippets

BIOEFGM Simulation model development

In this section, a two-dimensional EFGM model called BIOEFGM is presented for the simulation of biodegradation of organic contaminants within the groundwater. In BIOEFGM, EFGM technique is used to discretize the governing GFCT equations which represent the bioremediation process. In EFGM, the weak integral of the governing equation weighted with MLS based shape functions is made zero. EFGM shape functions are derived using the MLS approximation and details are given in Park and Leap (2000). In

Particle swarm optimization

The particle swarm optimization (PSO) is a well known metaheuristic optimizer proposed by Kennedy and Eberhart (1995) and mimics the social behavior of birds flocking. The PSO initially assume a population of random possible solutions termed as particles and assign each particle both the random location and velocity. The particle location represents the possible value of decision variables in one-dimensional array and the velocity component drives a particle to move and search the optimal

Mathematical model for optimal in-situ bioremediation cost

The mathematical expression for the objective function used to determine optimal in-situ bioremediation cost is given by Shieh and Peralta (2005). This objective function includes well installation cost, pumping/treatment cost and facility capital cost and mathematically expressed asMinimizeR=t=1Tp(1(1+dr)tlpw=1WCf(w)Q(w,t))+w=1WCs(w)I(w)+Max{Ci(w=1WiQ(w,t))}t=1Tp+Max{Ct(w=1WeQ(w,t))}t=1Tp

The Eq.  (24) is subjected to the following constraints

1. The residual contamination in the study

BIOEFGM-PSO Model development

In the proposed BIOEFGM-PSO model, the BIOEFGM model developed in the Section 2 is coupled with the PSO for designing the optimized in-situ bioremediation systems. In this study, BIOEFGM code is written in MATLAB and coupled with its PSO solver. In BIOEFGM, head values are calculated first from the EFGM flow model and then these values are used to compute the groundwater velocities using the Darcy law. Thereafter, these velocities are supplied to the EFGM based transport models for oxygen and

Case study 1

In this case study, a hypothetical confined groundwater site of 701.5 m  ×  518.5 m size with initial concentration distribution of BTEX contaminant similar to the study given by Shieh and Peralta (2005) is selected for designing the optimal in-situ bioremediation system using proposed S/O model (Fig. 2a). Here, no constant concentrations are imposed to generate the BTEX plume. This problem is also investigated by other researchers (Sudheer, Kumar, Prasad, Mathur, 2013, Yadav, Ch, Mathur,

Case study 2

This case study deals with the designing of an optimal in-situ bioremediation system for a field type hypothetical large aquifer system contaminated with BTEX hydrocarbons. Most of the previous studies have considered small aquifer systems with regular boundaries. Here, a hypothetical large aquifer with initial BTEX plume as shown in Fig. 10a is considered for finding an optimal strategy for in-situ bioremediation using the BIOEFGM-PSO model. The aquifer is a confined aquifer and of 6.93 Km2

Discussion

In the present study, EFGM based BIOEFGM model is presented first to solve the governing GFCT equations in the bioremediation model. In the past studies, FDM/FEM based numerical models were used for running the bioremediation simulations in the optimal design of in-situ bioremediation system which can provide optimal well locations only at the grid nodes. However, in the proposed BIOEFGM-PSO model, BIOEFGM allows PSO to check anywhere in the flow domain for the optimality of the well locations

Conclusions

In this study, a new S/O model called BIOEFGM-PSO is developed for the optimal design of in-situ bioremediation system. In the proposed S/O model, meshless BIOEFGM allows PSO to search all the possible locations including both discretized nodes as well as remaining area for the optimal well locations in the aquifer system. For the studied problems, BIOEFGM model results are found closer to RT3D results and hence, it can be used as an alternate numerical model for bioremediation simulations. The

Author Contributions

1. Tinesh Pathania conceived the idea and developed a simulation-optimization model (S/O) for the optimal design of an in-situ bioremediation system.

2. T.I. Eldho provided the important feedbacks in developing the S/O model and helped in applying it to the aquifer problems.

3. Tinesh Pathania and T.I. Eldho prepared the draft paper and finally, Andrea Bottacin-Busolin revised the manuscript critically for intellectual content.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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