Modeling and optimization of shale gas water management systems

Resumen

Shale gas has emerged as a potential resource to transform the global energy market. Nevertheless, gas extraction from tight shale formations is only possible after horizontal drilling and hydraulic fracturing, which generally demand large amounts of water. Part of the ejected fracturing fluid returns to the surface as flowback water, containing a variety of pollutants. Thus, water reuse and water recycling technologies have received further interest for enhancing overall shale gas process efficiency and sustainability. Thereby, the objectives of this thesis are: - Develop mathematical models to treat flowback and produced water at various salinities and flow rates, decreasing the high environmental impact due to the freshwater withdrawal and wastewater generated during shale gas production at minimum cost. - Develop mathematical programming models for planning shale gas water management through the first stage of the well's life to promote the reuse of flowback water by optimizing simultaneously all operations belonging several wellpads. Within the first objective, we developed medium size generalized disjunctive-programming (GDP) models reformulated as mixed integer non-linear programming problems (MINLPs). First, we focused on flowback water pretreatment and later, in wastewater desalination treatment. Particularly, an emergent desalination technology, Membrane Distillation, has been studied. All mathematical models have been implemented using GAMS® software. First, we introduce a new optimization model for wastewater from shale gas production including a superstructure with several water pretreatment alternatives. The mathematical model is formulated via GDP to minimize the total annualized cost. Hence, the superstructure developed allows identifying the optimal pretreatment sequence with minimum cost, according to inlet water composition and wastewater desired destination (i.e., water reuse as fracking fluid or desalination in thermal or membrane techonologies). As each destination requires specific composition constraints, three case studies illustrate the applicability of the proposed approach. Additionally, four distinct flowback water compositions are evaluated for the different target conditions. The results highlight the ability of the developed model for the cost-effective water pretreatment system synthesis, by reaching the required water compositions for each specified destination. Regarding desalination technologies, a rigorous optimization model with energy recovery for the synthesis of multistage direct contact membrane distillation (DCMD) system has been developed. The mathematical model is focused on maximizing the total amount of water recovered. The outflow brine is fixed close to salt saturation conditions (300 g·kg-1) approaching zero liquid discharge (ZLD). A sensitivity analysis is performed to evaluate the system’s behavior under different uncertainty sources such as the heat source availability and inlet salinity conditions. The results emphasize the applicability of this promising technology, especially with low steam cost or waste heat, and reveal variable costs and system configurations depending on inlet conditions. Within the second objective, large-scale multi-period water management problems, and collaborative water management models have been studied. Thus, to address water planning decisions in shale gas operations, in a first stage a new non-convex MINLP optimization model is presented that explicitly takes into account the effect of high concentration of total dissolved solids (TDS) and its temporal variations in the impaired water. The model comprises different water management strategies: direct reuse, treatment or send to Class II disposal wells. The objective is to maximize the “sustainability profit” to find a compromise solution among the three pillars of sustainability: economic, environmental and social criteria. The solution determines freshwater consumption, flowback destination, the fracturing schedule, fracturing fluid composition and the number of tanks leased at each time period. Because of the rigorous determination of TDS in all water streams, the model is a nonconvex MINLP model that is tackled in two steps: first, an MILP model is solved on the basis of McCormick relaxations for the bilinear terms; next, the binary variables that determine the fracturing schedule are fixed, and a smaller MINLP is solved. Finally, several case studies based on Marcellus Shale Play are optimized to illustrate the effectiveness of the proposed formulation. Later, a simplified version of the shale gas water management model developed in the previous work has been used to study possible cooperative strategies among companies. This model allows increasing benefits and reduces costs and environmental impacts of water management in shale gas production. If different companies are working in the same shale zone and their shale pads are relatively close (under 50 km), they might adopt a cooperative strategy, which can offer economic and environmental advantages. The objective is to compute a distribution of whatever quantifiable unit among the stakeholders to achieve a stable agreement on cooperation among them. To allocate the cost, profit and/or environmental impact among stakeholders, the Core and Shapley value are applied. Finally, the impact of cooperation among companies is shown by two examples involving three and eight players, respectively. The results show that adopting cooperative strategies in shale water management, companies are allowed to improve their benefits and to enhance the sustainability of their operations. The results obtained in this thesis should help to make cost-effective and environmentally-friendly water management decisions in the eventual development of shale gas wells.