Neutrosophic Optimization Model and Computational Algorithm for Optimal Shale Gas Water Management under Uncertainty

Shale gas energy is the most prominent and dominating source of power across the globe. The processes for the extraction of shale gas from shale rocks are very complex. In this study, a multiobjective optimization framework is presented for an overall water management system that includes the allocation of freshwater for hydraulic fracturing and optimal management of the resulting wastewater with different techniques. The generated wastewater from the shale fracking process contains highly toxic chemicals. The optimal control of a massive amount of contaminated water is quite a challenging task. Therefore, an on-site treatment plant, underground disposal facility, and treatment plant with expansion capacity were designed to overcome environmental issues. A multiobjective trade-off between socio-economic and environmental concerns was established under a set of conflicting constraints. A solution method—the neutrosophic goal programming approach—is suggested, inspired by independent, neutral/indeterminacy thoughts of the decision-maker(s). A theoretical computational study is presented to show the validity and applicability of the proposed multiobjective shale gas water management optimization model and solution procedure. The obtained results and conclusions, along with the significant contributions, are discussed in the context of shale gas supply chain planning policies over different time horizons.

Cost Optimization of Osmotically Assisted Reverse Osmosis

We develop a nonlinear optimization model to identify minimum cost designs for osmotically assisted reverse osmosis (OARO), a multistaged membrane-based process for desalinating high-salinity brines. The optimization model enables comprehensive evaluation of a complex process configuration and operational decision space that includes nonlinear process performance and implicit relationships among membrane stages, saline sweep cycles, and makeup, purge, and recycle streams. The objective function minimizes cost, rather than energy or capital expenditures, to accurately account for the trade-offs in capital and operational expenses inherent in multistaged membrane processes. Generally, we find that cost-optimal OARO processes minimize the number of stages, eliminate the use of saline makeup streams, purge from the first sweep cycle, and successively decrease stage membrane area and sweep flow rates. The optimal OARO configuration for treating feed salinities of 50-125 g/L total dissolved solids with water recoveries between 30-70% results in costs less than or equal to $6 per m³ of product water. Sensitivity analysis suggests that future research to minimize OARO costs should focus on minimizing the membrane structural parameter while maximizing the membrane burst pressure and reducing the membrane unit cost.

Game-based analysis of energy-water nexus for identifying environmental impacts during Shale gas operations under stochastic input

Environmental issues have become some of the greatest challenges encountered across the life cycle Shale gas operations, and mostly involve the management, disposal, and spill of flowback and produced (FP) waters during the process of hydraulic fracturing. This study evaluates Shale gas resources, addresses water resource management problems, and identifies the corresponding environmental implications of FP waters under uncertainty. Multiple tools, including structural optimization, process design, cost analysis, environmental assessment, and stochastic technology, are integrated into a general modeling framework based on game theory. This mathematic framework corresponds to a dominant-subordinate-interactive problem, where two major participants are identified as the downstream decision maker at the dominant level (e.g., power generation sector) and the upstream decision maker at the subordinate level (e.g., Shale gas producer). The Monte Carlo technique is used for simulating the estimated ultimate recovery (EUR) of a single well. Thereafter, the developed model is applied to a special case study of the Marcellus Shale play in Beaver County, Pennsylvania. Multiple decisions regarding gas production, processing, water management, as well as electricity generation would been examined under different probability levels. Results indicate that the changes in violation levels would lead to distinct environmental and economic performances of the supply chain. A lower probability level of the EUR value would correspond to an increased reliability on fulfilling the system demands, and then to higher economic benefits and freshwater supply; conversely, a higher probability level of the EUR value would result in lower economic benefits and lower freshwater supply, and the risk of violating the EUR value would also increase.