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. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4297–4307, 2016

Stochastic programming models for optimal shale well development and refracturing planning under uncertainty

“…As suggested by Cafaro et al (2016), 13 the gas production of an unconventional well can be represented adequately by a decreasing power function. This power function is defined by an expected initial production peak parameter k p and an expected initial production decline parameter a p , both of which are assumed to be scenario-dependent.…”

“…Last, Cafaro et al (2016) 13 present an optimization framework to plan shale gas well refracture treatments. In their work, the authors assume that the decision to drill, fracture and complete a prospective shale well has already been made.…”

“…In their work, the authors assume that the decision to drill, fracture and complete a prospective shale well has already been made. To determine if, when and how often the well should be restimulated over its lifespan, Cafaro et al (2016) 13 propose two optimization models: a continuous-time nonlinear programming (NLP) model and a discrete-time mixed-integer linear programming (MILP) model. Whereas the NLP model is primarily designed to identify the optimal time to refracture a [Color figure can be viewed at wileyonlinelibrary.com] Figure 2.…”

“…In this publication, we present an important extension of the work by Cafaro et al (2016). 13 Our primary objective is to explicitly account for two major sources of uncertainty: price developments over time, and production performance before and after restimulations.…”

“…In this publication, we present an important extension of the work by Cafaro et al (2016). 13 Our primary objective is to explicitly account for two major sources of uncertainty: price developments over time, and production performance before and after restimulations. In addition, we present a generalized production estimate function, and a moving horizon framework that enables upstream operators to schedule refracture treatments as true recourse actions after uncertainty realizations and/or potential disruptions.…”