In-situ bioremediation of groundwater using a meshfree model and particle swarm optimization

The requirement of groundwater increases with the increase of population, industrialization, agriculture, and navigation. The groundwater quality has also become a major concern in terms of color, odor, taste, and hardness. The conservation of the quality and quantity of the groundwater requires supreme priority. Any groundwater contamination study involves identification of the source of contaminant, the movement of the pollutants in the groundwater environment once they are introduced, proper management of resource utilization, and preventive measures to ensure suitable development and remediation of polluted sites (Eldho 2001).

For the remediation of groundwater contaminated with pollutants such as trichloroethylene (TCE), dichloroethylene or phenol, conventional approaches such as pump and treat (PAT), pump and use are not effective. In such cases, in-situ bioremediation is one of the effective methods for remediation (Bedient et al. 1999).

In a typical in-situ bioremediation system, an aerobic environment is created by adding oxygenated fluid for the growth of microorganisms. Biological degradation is facilitated by oxygenated fluid. The process continues until the concentration of contaminants is reduced to the approved levels. The type of oxygenated fluid to be used is a further challenge for this method. The type of oxygenated fluid is preferably air, but pure oxygen, steam, water vapor, etc. are some other types used (Bedient et al. 1999).

The purpose of modeling bioremediation of groundwater is for the prediction of contaminant concentrations at receptor positions and the estimation of source control actions on remediation. Further, it also gives the point allocations of observation wells while the remedial study is carried out and evaluates the remedial functioning for different designs. Modeling of bioremediation of groundwater is an effective tool to predict the efficacy and clean-up time to stated levels (Bedient et al. 1999).

Numerical models are necessary for developing an efficient operative design and upkeep of an in-situ bioremediation arrangement. Simulation-optimization (S/O) models can give an efficient injection approach, suitable positions for remediation wells and time of remediation. The efficacy of S/O models for bioremediation is demonstrated by various studies (e.g., Minsker & Shoemaker 1998; Yoon & Shoemaker 2001; Prasad & Mathur 2008; Mategaonkar & Eldho 2012c).

Meshfree (MFree) methods have gained acceptance in many engineering applications owing to their mesh-free character. With the removal of grid, pre-processing time of simulation is reduced. With the ease in computing the distances in any number of spatial dimensions, working in higher dimensions does not increase the intricacy and computational cost of the method (Liu 2003, 2006; Liu & Gu 2005).

MFree methods have been applied successfully to groundwater flow and transport problems by many researchers (e.g., Li et al. 2003; Praveen Kumar & Dodagoudar 2008, 2010). Mategaonkar & Eldho (2012a; 2012b) developed a coupled flow and transport model for groundwater.

Simulation models along with optimization models for the effective remediation of groundwater pollution give the complete solution for the complex groundwater contamination problem. Shieh & Peralta (2005) presented a parallel recombinative simulated annealing (PRSA) model along with BIOPLUME II to optimize in-situ bioremediation system design with a two-stage management approach. The first-stage design goal is to minimize total system cost (pumping/treatment, well installation, and facility capital costs) and the second-stage goal is to minimize the cost of a time-varying pumping strategy using the optimal system chosen by the first-stage optimization.

Mategaonkar & Eldho (2012c) developed a S/O model for in-situ bioremediation using meshfree PCM and PSO (PCM-BIO-PSO). It is observed that the PCM-BIO-PSO model is an effective model for in-situ bioremediation of groundwater contamination. Mategaonkar & Eldho (2014) also developed a multi-objective model for PAT method for the remediation of total dissolved solids (TDS).

Luo et al. (2014) and Akbarnejad-Nesheli et al. (2016) developed a multi-objective S/O model to achieve the best in-situ bioremediation system design for groundwater with contaminated dissolved hydrocarbons and observed that the Pareto-optimal solution with low variability, high reliability is a potentially effective tool for optimizing multi-objective groundwater remediation problems under uncertainty.

Kumar et al. (2015) presented the use of a new hybrid algorithm to optimize a multi-objective function which includes the cost of remediation as the first objective and residual contaminant at the end of the remediation period as the second objective. The hybrid algorithm was formed by combining the methods of differential evolution (DE), genetic algorithms, and simulated annealing (SA). The results obtained from the hybrid algorithms were compared with DE, non-dominated sorting genetic algorithm (NSGA II) and SA. It is found that the proposed hybrid algorithm can provide the best solution. Ehsai et al. (2017) used a BIOPLUME III simulation model coupled with a NSGA-II-based model for optimal design of in-situ groundwater bioremediation system. The multi-objective optimization model tries to minimize: (1) cost; (2) sum of contaminant concentrations that violate standard; (3) contaminant plume fragmentation. The simulation period is divided into smaller time intervals for more efficient optimization aiming to minimize the contaminant plume fragmentation.

In this study, an S/O model is presented using MFree PCM for the simulation of coupled groundwater flow and transport and PSO for getting the optimal solution for efficient in-situ bioremediation. Two strategies of cost minimization with number of wells and cost minimization with time of remediation are considered with different population sizes. The proposed model is applied to a case study to demonstrate the applications of the developed model.

Here, h is the piezometric head; is the specific yield; t is time; and are the velocities in the x and y directions, respectively; and are the hydraulic conductivities in the x and y directions. respectively; Q_w is flow rate from the well and q_s is the volume rate of steady uniform recharge per unit area per unit thickness of the aquifer. Actual velocity is obtained as and ⁠; is the porosity; c is contaminant concentration; is the total microbial concentration; is maximum contaminant utilization rate per unit mass of microorganisms; is the contaminant half saturation constant; O is oxygen concentration; is oxygen half saturation constant; is the concentration of microbes; is the time interval being considered; F is the ratio of oxygen to contaminant consumed; is the retardation coefficient for the contaminant; are dispersion coefficient [L²T⁻¹] in x and directions, respectively.

Here, is the area of support domain in which the pumping well or recharge well lies and is the global matrix of the entire source and sink terms. The basis function and its derivatives are calculated for each support domain following the Kronecker delta property and are assimilated in the global matrix for whole problem domain.

Based on the above formulation, a two-dimensional meshfree model for flow, transport, and bioremediation has been developed. The developed flow, transport, and bioremediation equations were verified using available analytical and numerical solutions (Mategaonkar & Eldho 2012a; 2012b; 2012c). Further, the flow models are coupled to get an efficient model with PCM-BIO model for bioremediation simulation. To simulate the transport of pollutant and oxygen in the subsurface in aerobic bioremediation, Equations (7b) and (7c) are solved simultaneously.

The purpose of the present study is to get optimal injection rates for the wells for minimization of the total cost of remediation along with remediation time and number of wells. Concentration distribution is analyzed for different strategies for the entire remediation period.

Here, two scenarios of optimization are considered: cost minimization with number of wells and cost minimization with time of remediation.

The aim of optimization for this scenario is to identify bioremediation designs that minimize cost of remediation and the number of injection wells by fulfilling the limitations on the specified contaminant concentration. The result causes the least number of wells for clean-up with the consideration of the plume position. Thus, the objective function contains the oxygen injection rate and number of wells to optimize.

The purpose of optimization for this scenario, is to identify bioremediation designs which reduce cost and time of remediation on the selected pollutant concentration. The solution gives the minimum time of remediation for different population sizes and thereby the remediation cost is reduced.

The objective function comprises the injection rate of water containing oxygen, time of remediation, and the number of wells. Here, the cost of setting up of the injection well is considered as fixed and hence it is not considered in the objective function. Based on the above formulation, a multi-objective model PCM-BIO-PSO-MO is developed.

The oxygen content in injected water is fixed and hence cannot be considered as a decision variable. In this study, aerated oxygen containing 8 mg/L of oxygen concentration is considered (Hinchee et al. 1987; Minsker & Shoemaker 1998). Further, it is assumed by the model that the microorganisms are present in substantial amounts in the aquifer for bioremediation (Minsker & Shoemaker 1998). The rate of decay is assumed to be equal to the rate of biomass growth ensuring the indigenous nature of biomass.

A step-by-step procedure for the PCM-BIO-PSO-MO model is given below (Figure 1):

• 1.

  Input all physiological and hydrological parameters.

• 2.

  Discretize the aquifer into equidistant nodes in x and y directions. Consider a rectangular support domain for each node.

• 3.

  Apply PCM-BIO-PSO-MO model for three different cases:

  • a.

    cost optimization with number of wells;

  • b.

    cost optimization with time of remediation;

  • c.

    cost optimization with number of wells and time of remediation.

• 4.

  The model is run to reach the contamination level to 5 ppb or less.

The developed PCM-BIO-PSO-MO has been applied to a hypothetical problem and verified as a single-objective model and found to be satisfactory (Mategaonkar & Eldho 2012c).

The application of the PCM-BIO-PSO model is investigated by considering a case study which is like a field problem (Figure 2). The primary components of the contamination are identified as TCE, originating from a nearby laundry. From the pumping and flow rate, the aquifer parameters are determined, and the location of contaminant plume is identified. The average groundwater velocity in the area is about 0.1 m/day. The aquifer is spread over approximately 1,350 m × 1,000 m with a thickness of 100 m (Figure 2). The maximum contamination concentration at the hotspot is about 70 μg/L. The adopted method should remediate the plume to a drinking water standard of 5 ppb (Hazen & Fliermans 1995). The hydrogeological and physical parameters for this case study are given in Table 1 (Minsker & Shoemaker 1998).

A specific quantity of oxygen is infused into the aquifer to start bioremediation. Decision variables do not influence the oxygen concentration in the injection of water. It is determined by the user quantified values. For the aquifer considered, 9 m and 4.5 m are the dispersivity values in longitudinal and transverse directions. The southern and northern boundaries are not flux boundaries. Constant head at the western boundary is 92.5 m and at the eastern boundary is 90.00 m.

The case study, as mentioned above, is analyzed with the model. For the PCM-BIO-PSO model, 588 nodes are considered (Figure 3) with value as 3 and ⁠. The value of is taken as 150, day and for every square support domain nine nodes are considered. The nodal assembly for the PCM-BIO-PSO-MO model and the position of injection wells are shown in Figure 3.

The injection wells are provided at nodes 144, 183, 198, 227, and 239. The injection rates vary from 200 to 2,000 m³/d for the simulation. Further parameters applied are and . For the S/O model, the hydraulic heads of every node ought to be fewer than and more than (Table 1). is selected to guarantee that the rise in the hydraulic head is equivalent to the most possible hydraulic head.

Original contaminant strength in the plume ranges from 0.5 to 70 μg/L with the peak concentration (>50 μg/L) at nodes 144, 183, 198, 227, and 239 (Figure 3). The primary biomass concentration at every node is assumed to be 0.005 mg/L. The plume is assumed to be enclosed in the oxygen concentration of 3 mg/L while at the center oxygen strength is assumed to be exhausted. The adopted method should remediate the plume to a drinking water standard of 5 ppb. The concentration levels in the 16 investigated observation wells are given in Table 2.

The PCM-BIO-PSO model is applied to remediate the groundwater by in-situ bioremediation. Three different cases are considered by applying the PCM-BIO-PSO with the cost and number of injection wells, cost and time of remediation, and cost and both number of wells and time of remediation. In all the cases, the three population sizes for PSO considered are 50, 75, and 100.

The purpose of the bioremediation is to decrease the contaminant plume up to 5 ppb; hydraulic heads at every node ought to be lower than and higher than ⁠. The assumed quantities of and are shown in Table 1. is selected in such a manner that it does not rise above the top of the aquifer whereas is selected to make sure that the rise in the hydraulic head is equivalent to the maximum possible injected hydraulic head (Minsker & Shoemaker 1998).

With the temporal interval of 1 day, the model is run for 100 days. The rate of aerated oxygen is taken as $0.56 (INR 28 approx.) and the rate of injection/extraction is taken as $14.41 (INR 720 approx.) per per month (Minsker & Shoemaker 1998).

For the first case, three (at nodes 144, 183, and 198), four (at nodes 144, 183, 198, and 227), and five injection wells (at nodes 144, 183, 198, 227, and 239) are considered for remediation.

For this case, three population sizes of 50, 75, and 100 are considered. It is observed that the optimal solution for all the cases is achieved for a four wells' scenario. The cost variation with number of wells is shown in Table 3. The total cost ranges from Rs. 5.59 × 10⁷ to Rs. 9.24 × 10⁷ for a population size of 100 and 100 days.

For the second case, three different periods of remediation of 70, 100, and 200 days are considered. For this case, also three population sizes (50, 75, and 100) are considered. Cost variation with time for all the population sizes is shown in Figure 4. From Table 3 it is observed that the optimal solution is obtained for 100 days. The total cost for all scenarios range from Rs. 5.59 × 10⁷ to Rs. 1.35 × 10⁸ for all time periods.

For the third case, both the number of wells and time of remediation were optimization functions along with cost. The results are shown in Table 4. It is observed that even if the number of injection wells is reduced, the cost is not reduced because of high injection rate, and cost is not reduced even if the time of remediation is reduced.

The simulation-optimization models help to design optimal remediation of groundwater. In this study, a PCM-based meshfree model is developed for bioremediation simulation. Also, a PSO-based optimization model is developed for optimization. PCM is a very simple method to work with and apply. With the appropriate selection of shape parameters, the model provides efficient results. The PCM models are further coupled with PSO-based optimization techniques (PCM-BIO-PSO) for in-situ bioremediation of groundwater contamination to get an efficient and optimal solution to the bioremediation problem.

In this study, the PCM-BIO-PSO model is applied to a case study similar to a field problem for in-situ bioremediation with three scenarios, namely, cost and number of injection wells, cost and time of remediation, cost and number of wells and time of remediation together.

The total cost for three wells for 70 days, 100 days, and 200 days is Rs. 6.87 × 10⁷, Rs. 6.78 × 10⁷, and Rs. 1.57 × 10⁸, respectively. The total cost for four wells for 70 days, 100 days, and 200 days is Rs. 6.35 × 10⁷, Rs. 5.59 × 10⁷, and Rs. 1.19 × 10⁸ respectively. The total cost for five wells for 70 days, 100 days, and 200 days is Rs. 1.35 × 10⁸, Rs. 9.24 × 10⁷, and Rs. 1.85 × 10⁸, respectively. In all the cases, it is observed that the PCM-BIO-PSO-MO model gives the optimal cost of Rs. 5.59 × 10⁷ for four wells, 100 days, and 100 population size for four wells' scenario.

It is observed that as the number of injection wells increases the cost is increased, but at the same time, the remediation time is reduced. The injection rate increases for less time of remediation. Also, the problem solution is optimized with the increasing population size. The proposed methodology can be effectively used in the in-situ bioremediation of contaminated sites.

The authors are grateful to Dr Ulf Mohrlok, Karlsruhe Institute of Technology for his support.