Multi-period reverse logistics network design for water resource management in hydraulic fracturing

This paper addresses the effective management of water resources during the hydraulic fracturing process used for natural gas extraction. With increasing demand and scrutiny on shale gas production due to economic, environmental, and social factors, effective water management strategies are needed to address the challenges of flow -back water usage during hydraulic fracturing. This research contributes to the existing literature from a multi -period reverse logistics network design perspective with realistic modeling approaches. A mathematical formulation is developed for optimizing the design of a multi -period reverse logistics network for effective water resource management that incorporates production scheduling of a hydraulic fracturing process. This mixed integer programming model determines the optimal locations and capacities of impoundments, treatment facilities, and disposal sites while minimizing fixed and operational costs under constraints such as freshwater withdrawal limits, production schedules, inventory balance, and treatment and disposal options. A two -stage stochastic programming formulation is further developed as a means to address the uncertainty associated with water flows during the fracturing operation. The strategic location and capacity decisions are given in the first stage of this formulation, whereas operational decisions such as water flows are handled in the second stage under independently sampled scenarios. A sample average approximation algorithm is proposed to solve the stochastic formulation. The model is tested on a case study from the United States that explores potential impacts on water resource management due to cost variations, changes in operational parameters, and uncertainty in demands and supplies. The base case setup delivers a 12.8% reduction in freshwater usage. The benefit of multi -period reverse logistics network design is further demonstrated through variations in water demand and equipment degradation. The managerial insights derived through sensitivity analysis highlight the values of the proposed multi -period formulation, capacity expansions, and parameter estimations.