Fair Shale Gas Water Cost Distribution Using Nash Bargaining Game

Abstract In this work, we address the optimal water management strategies and fair cost distribution among various shale gas companies placed in the same play. A mixed integer non-linear programming (MINLP) formulation with the objective of maximizing the Nash product is presented including the analysis of different policies to determine the most appropriate transportation cost distribution. As a result of Nash product maximization and transfer cost designation formulation, the problem includes non-linearities in the objective function which hinders its resolution. Therefore, to solve the model effectively, we apply logarithmic operation and separable programming approach to reformulate the Nash product and Glover's linearization to reformulate the bilinear terms appearing in the transfer cost designation. Finally, the applicability of the proposed approach is illustrated in a case study comprising 4 companies. Then, an example comprising 10 shale gas companies is performed to analyse the behaviour of the proposed formulation considering a larger problem.