Shale gas production is associated with significant usage of fresh water and discharge of wastewater. Consequently, there is a necessity to create proper management strategies for water resources in shale gas production and to integrate conventional energy sources (e.g., shale gas) with renewables (e.g., solar energy). The objective of this study is to develop a design framework for integrating water and energy systems including multiple energy sources, the cogeneration process and desalination

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... technologies in treating wastewater and providing fresh water for shale gas production. Solar energy is included to provide thermal power directly to a multi-effect distillation plant (MED) exclusively (to be more feasible economically) or indirect supply through a thermal energy storage system. Thus, MED is driven by direct or indirect solar energy and excess or direct cogeneration process heat. The proposed thermal energy storage along with the fossil fuel boiler will allow for the dual-purpose system to operate at steady-state by managing the dynamic variability of solar energy. Additionally, electric production is considered to supply a reverse osmosis plant (RO) without connecting to the local electric grid. A multi-period mixed integer nonlinear program (MINLP) is developed and applied to discretize the operation period to track the diurnal fluctuations of solar energy. The solution of the optimization program determines the optimal mix of solar energy, thermal storage and fossil fuel to attain the maximum annual profit of the entire system. A case study is solved for water treatment and energy management for Eagle Ford Basin in Texas. Processes 2018, 6, 52 2 of 26 for hydraulic fracturing ranges between 1000 and 30,000 m 3 , leading to substantial amounts of water usage. For instance, the annual water usage in shale gas production is estimated to be about 120 MM m 3 . In the Eagle Ford Shale Play, the annual water use is 18 MM m 3 for 1040 wells [15] . Wastewater associated with shale gas production is discharged in two forms: flowback water (which is released over several weeks following production) and produced water (which is the long-term wastewater) [14, 16] . Treatment of shale gas wastewater followed by recycling and reuse can provide major economic and environmental benefits [12] [13] [14] [15] [16] [17] . Regrettably, a small fraction of the shale-gas wastewater is recycled. A recent study [18] reported that in 2014, less than 10% of the roughly 80,000 wells in the U.S. used recycled water after proper treatment. Lira-Barragán et al. [18] developed a mathematical programming model for the combination of water networks in the shale gas site by taking into consideration the requirement of water, the uncertainty of used and flowback water, and the optimal size of treatment units, storage systems and disposals. Gao and You [12] addressed the shale-gas water problem as a mixed integer linear fractional programming (MILFP) problem to maximize the profit per unit of freshwater consumption. Yang et al. [14] developed a two-stage mixed integer nonlinear programming (MINLP) model for shale gas formations with the uncertainty of water availability. Several approaches may be used for treatment and management of shale gas wastewater [13] [14] [15] [16] [17] [18] [19] [20] . These approaches include conventional technologies such as multi-effect distillation and reverse osmosis. Additionally, emerging technologies such as membrane distillation may be used to exploit excess heat from flared gases, compression stations and other on-site sources and to provide a modular system with high levels of salt rejection [16, [21] [22] [23] [24] [25] [26] [27] [28] [29] . Additionally, renewable energy (such as solar) may be utilized to enhance the sustainability of the system. Therefore, it is important to consider the water management problem for shale gas production via a water-energy nexus framework. This work is aimed at developing a new systematic approach to the design, operation, integration and optimization of a dual-purpose system, which integrates solar energy and fossil fuels to produce electricity and desalinated water while treating shale-gas wastewater. In addition to fossil fuels, a concentrated solar power field, a thermal storage system, conventional steam generators and the cogeneration process are coupled with two water treatment plants: reverse osmosis (RO) and multiple-effect distillation (MED). A multi-period mixed integer nonlinear program (MINLP) formulation is developed to account for the diurnal fluctuations of solar energy. The solution of the mixed integer nonlinear program (MINLP) determines the optimal mix of solar energy, thermal storage and fossil fuel and the details of wastewater treatment and water recycling. Problem Statement Consider a shale-gas production site with the following known information: