Using a Mixed Integer Linear Programming Technique to Optimize a Fracture Treatment Design

Abstract

IN1RODUCTION Well stimulation procedures are designed to reduce the restrictions to flow from the reservoir into the wellbore and increase productivity.1 Hydraulic fracturing in low permeability reservoirs is an important and successful stimulation methodology widely used by the petroleum industry. The design of the optimum fracture treatment has three basic steps. The first step involves calculating fracture dimensions and conductivity for various fracture fluid pumping schedules. The second step is determining the oil and gas production rates and recoveries using the values of propped fracture length obtained from the fracture treatment design. The third step requires one to determine the optimum fracture treatment design by maximizing the economic benefit of the treatment. Since a fracture treatment design involves selection of fracturing fluids, additives, proppant materials, injection rate, pump schedule, and fracture dimensions, the determination of the optimum combination of all variables can be quite complicated. In this research, we have developed two methods to investigate reasonable combinations of design and treatment parameters to determine the most profitable fracture treatment design. Depending upon the post-fracture treatment production rates, the related expenses, and the economic constraints, the optimum treatment can be easily determined. The first optimization method is based on a mathematical technique called Mixed Integer Linear Programming (MILP).2 This method can be used to minimize or maximize a desired objective function subject to certain constraints. For this work, we have chosen the objective function to be the discounted net present value due to a fracture treatment. The constraints are related to the fracture dimensions and other items necessary to linearize the fracture design problem.3

Hydraulic Fracturing Treatment Optimization for Low Permeability Reservoirs Based on Unified Fracture Design

“…From large number of simulations, the optimal treatment parameters are determined to maximize the net present values. To obtain the global optimization solution [25][26][27], several optimization methods are used such as genetic algorithm [28][29][30][31][32], neural networks [31][32][33], integer programming [34,35], surrogate-based approach [23,36].…”

Surrogate-based optimization of hydraulic fracturing in pre-existing fracture networks

“…Nevertheless, this procedure, requiring brute-force parameter-sensitivity analysis,is tedious and incapable of exploring parameter space globally, which could potentially 70 lead to the problem of converging to a local minimum of the objective function. 71 Rueda et al (1994) optimized fracturing variables, including the injected fluid 72 volume, pumping rate, fluid and proppant type, by applying a mixed integer linear 73 programming (MILP) approach, which also lacks a global optimization capability. 74 Mohaghegh et al (1999) proposed a surrogate-based optimization approach by using a 75 genetic algorithm to fit the dataset generated from a fracturing simulator that models both 76 fracture propagation and proppant transport.…”

A multiperiod planning model for gas production system

“…Mixed-integer linear programming (MILP) models have been proposed to address some production operations such as hydraulic fracturing (Queipo et al, 2002;Rueda and Holditch, 1994) and development plans of gas and oil fields (Barker et al, 1994). A multiperiod model was developed for the planning and scheduling of oil investment and operation of offshore facilities where piecewise linear approximations are used to model the nonlinear equations (Iyer et al, 1998).…”