(570o) Optimization of Water Supply Chain Design and Long-Term Planning for Shale Gas Production: Milfp Model and Algorithms
Natural gas is playing a significant role in meeting the global energy demand as well as behaving as a bridge fuel as the U.S. develops more sustainable and renewable fuel options . Shale gas, as the unconventional natural gas extracted from shale rock, has emerged as one of the most promising energy source within the past decade . The large-scale production of shale gas is not possible until the hydraulic fracturing and horizontal drilling technologies are developed [3, 4], and the combination of these two technologies resulted in exponential increase in gas production . However, accompanying the benefits of the shale gas production are environmental concerns. Issues regarding water usage and environmental impacts have brought the shale gas extraction into a highly controversial situation [6, 7]. Many works have been done on the optimization problem regarding shale gas and water [8, 9]. In this work, we propose an optimization model for the design and operation of the water management systems and supply chain in shale gas production process. Distinct from most of the existing works in this field, to take both economic and environmental impacts into account, we present a novel fractional objective function defined as the net profit per unit freshwater consumption. In this way, we are able to maximize the profit by consuming the least freshwater, thus leading to a more profitable and sustainable water management system.
Due to the fractional form objective function, the resulting problem is a mixed-integer linear fractional programming (MILFP), which can be computationally intractable for large-scale problems due to its combinatorial nature and pseudo-convexity. Therefore, we presented tailored algorithms to facilitate the solution process: parametric algorithm based on exact Newton’s method and reformulation-linearization method to globally optimize the MILFP problem [10-12].
To illustrate the application of the proposed supply chain model and solution approaches, we investigate two case studies with different scales, a smaller case study to demonstrate the optimal water management strategy and a larger case to compare the computation performance of proposed algorithms. In this model we consider a set of freshwater sources, shale sites with multiple wells in each one and three different water treatment options, including disposal wells, centralized wastewater treatment (CWT) facility and onsite treatment methods. Water is classified into three levels with different total dissolved solids (TDS) concentration. The total time span is set to 10 years, divided into 520 periods. As the optimization result shows, almost all the freshwater are transported by pipelines. For level 1 water, CWT facilities and onsite treatment methods are applied; for level 2 water, all the water is treated by CWT facilities; for level 3 water, CWT facilities and disposal wells are applied to treat the produced water. In all, CWT facilities treat more than half of the produced water, and the rest is treated by disposal well s and onsite treatment. The optimal objective value is $36.4 per thousand barrels freshwater consumption for the small case, and for both cases, the proposed parametric algorithm based on exact Newton’s method is proven the most efficient solution approach in solving such MILFP problem.
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