Optimization Models for Planning Shale Gas Well Refracture Treatments

Abstract

Refracturing is a promising option for addressing the characteristically steep decline curves of shale gas wells. In this work we propose two optimization models to address the refracturing planning problem. First, we present a continuous time nonlinear programming model based on a novel forecast function that predicts pre- and post-treatment productivity declines. Next, we propose a discrete-time, multi-period mixed-integer linear programming (MILP) model that explicitly accounts for the possibility of multiple refracture treatments over the lifespan of a well. In an attempt to reduce solution times to a minimum, we compare three alternative formulations against each other (big-M formulation, disjunctive formulation using Standard and Compact Hull-Reformulations) and find that the disjunctive models yield the best computational performance. Finally, we apply the proposed MILP model to two case studies to demonstrate how refracturing can increase the expected recovery of a well and improve its profitability by several hundred thousand USD.