Optimal Well Locations using Genetic Algorithm for Tushki Project, Western Desert, Egypt
Abstract
The well location problem is challenging due to the non-linear, discrete and often multi-modal objective function. The optimal distribution of productive well locations mitigates the groundwater productivity problem that threats the national projects in arid countries like Egypt. In this paper, a trial to mitigate this problem in Tushki National Project, south western desert, Egypt is supposed via delineating the optimal well locations and optimal pumping rates. The methodology of combination between simulation and optimization techniques is applied. The simulation outputs of groundwater flow system by Visual MODFLOW model is linked by the constructed Fortran Code for Optimal well Location using Genetic Algorithm (OLGA Code) for obtaining the optimum management of groundwater resources in this project. Two management cases are considered by running the model domain with adopted steady and transit calibrated parameters. The first management case deals with the present well locations and predicts the optimal value of the objective function (maximum pumping rate). In the second case, the optimal new well locations resulted from the OLGA Code is predicted from flexible well location with the moving well option. Also, the prediction of the future changes in both head and flow are studied in steady and transient states.
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Introduction
Selecting optimal well sites is a valuable problem to solve; maximizing groundwater recovery increases oil reserves and minimizing costs improves profitability. One of the best methods of selecting optimal sites is the combined use of simulation and optimization (S/O) models. While simulation models basically provide solutions of the governing equations of groundwater flow, optimization models identify an optimal management and planning strategy from a set of feasible alternative strategies. The genetic algorithm (GA) is widely used to modify the parameters of groundwater flow models (Yan et al., 2003; Yao et al., 2003) and to solve the management models of groundwater resources (Mckinney and Lin, 1994; Liu et al., 2002; Zhu et al., 2003). Rana et al, (2008) conducted a study on a spatio-temporal optimization of agricultural drainage, using groundwater model and GA. Guan et al. (2008) proposed an improved genetic algorithm (IGA) to solve optimization problems with equality and inequality constraints. Hamid et al. (2009) presented a paper focusing on the S/O for conjunctive use of surface water and groundwater on a basin-wide scale, the Najafabad plain in west-central Iran. Gad et al., (2011), and Moharram et al., (2012) used an optimization model based on the combination of MODFLOW simulation with GA to maximize the total pumping rate from the Nubian sandstone aquifer in El-Dakhla and El-Farafra depressions, Egypt. Saafan et al., (2011) applied multi-objective genetic algorithm (MOGA) Code in El-Farafra depression, Egypt to study the maximum pumping rate and minimum operation cost. Gad and Khalaf, (2013) used MOGA model to develop the maximum pumping rate and minimum operation cost in the Miocene aquifer of Wadi El-Farigh, West Delta, Egypt.
In the other side, there are limited studies for the determination of optimal operating strategy, including unknown well locations and pumping rates, for groundwater systems to the best of our knowledge (Wang and Ahlfeld, 1994, Karahan and Ayvaz, 2005, and Ayvaz and Karahan, 2008). Saffi and Cheddadi (2007) developed an algebraic expression which gave the matrix of transient influence coefficients for one-dimensional semi-confined aquifer model and solved the governing equation by using a mixed compartment model. Tung and Chou (2004) integrated pattern classification and tabu search to optimize the average zonal groundwater pumping for an aquifer. As a general, the research conducted in this field dealt with the identification of locations and released histories of unknown groundwater pollution sources (Mahar and Datta, 2000, 2001; Aral et al., 2001; Ruperti, 2002; Singh et al., 2004; Sun et al., 2006), pumping well optimization for optimum remediation design (Wang and Ahlfeld, 1994; Huang and Mayer, 1997; Guan and Aral, 1999; Zheng and Wang, 1999; Mantoglou and Kourakos, 2007; Chang et al., 2007), and optimum well locations and pumping rates in the coastal sides (Park and Aral, 2004; Ferreira da Silva and Haie, 2007).
Conclusion
This paper is devoted to propose an assisted methodology to identify representative models for optimal well locations. To do so, first a mathematical equations were developed to model the representativeness of a subset of constrains with respect to the full set that characterizes the well location problem. Then, an optimization tool was implemented to identify the representative constrains of any problem, considering not only the main output variables, but also the probability distribution of the attribute-levels of the problem. Accordingly, OLGA Code was linked MODFLOW with genetic algorithm technique to establish a simulation optimization groundwater model. This model was applied for NSAASA to develop the optimal location of the groundwater productive wells with maximum pumping rate. Three scenarios were tested to choose the proper water exploitation policy. For the first scenario, the predicted groundwater drawdown after simulation period of 50 years ranged from 3.42 to 13.73 m while the corresponding optimal pumping rates ranged from 57585 to 50144 m3 /day. Under the second proposed scenario, the predicted drawdown (r) and the corresponding total optimal pumping rate for all wells (Qopt) ranged from 2.22 to 12.13 m and between 102038 and 100773 m3 /day, respectively. Moreover, the predicted value of (r) based on the 3rd scenario was more or less similar to the results of the other two scenarios although the number of the operating wells was increased by 19%. Computational restrictions were common and likely the cause of the systemic lack of algorithm benchmarking for well location optimization. Still, some valuable insight can be gained from these results that could guide further investigation.
Based on the results of the OLGA model, it is highly recommended to choose the new productive well locations in staggered system parallel to the western side of the Khour Tushki area. More applied studies are needed for verification the results of this optimal well location model. Also, this study should be extended to contain more test cases and more comprehensive selection of algorithms including interpolation methods, ad joint methods and hybrid methods.