Modified Approach to Incorporating Hydraulic Fracture Width Profile in Unified Fracture Design Model

Abstract

Abstract Hydraulic fracturing is one of the most effective ways to stimulate oil production. To this end, our study suggests an algorithm of calculating the optimal hydraulic fracturing design based on a modified approach to incorporating hydraulic fracture width profile in the context of unified fracture design (UFD) concept. Vertical propagation of fracture is controlled by the plane-strain problem of brittle fracture mechanics. To determine equilibrium height of hydraulic fracture, we suggest using the Irwin criterion, which implies that stress intensity factor equals the value of fracture toughness in a multi-layered structure. Fracture growth profile is calculated by solving a 2D elasticity problem in the context of three-layer approximation. Calculation of hydraulic fracture length is based on PKN model for power-law rheology fluid and specified proppant concentration schedule based on Nolte model. Injected volume, pumping time and fluid efficiency are determined by iterative solution of material balance equation. Hydraulic fracturing optimization involves selection of parameters of fracturing operation, including injection rate and rheology of fracturing fluid for maximization of dimensionless productivity index. The proposed model was used to formulate a numerical algorithm for hydraulic fracturing design calculation and its optimization in the context of the above presumptions. This optimization approach further develops the unified fracture design concept and adds to it the advanced model of fracture width profile calculation. The presented algorithm of design calculation and optimization helped to significantly increase the accuracy of hydraulic fracture geometry and net pressure calculations, which is confirmed by comparison with commercial software.