Hydraulic Fracture Production Optimization With a Pseudo-3D Model in Multi-layered Lithology

Abstract

AbstractSystematic design and optimization procedures for hydraulic fracturing are available using two-dimensional (2D) (with constant fracture height) and pseudo three dimensional (p-3D) models to maximize well production by optimizing fracture geometry, including fracture height, half-length and width.A multi-layered p-3D approach to design is proposed integrating Unified Fracture Design (UFD), fracture propagation models and Linear Elastic Fracture Mechanics (LEFM) relationship to generate optimized fracture geometry, including fracture height, width and half-length to achieve the maximized production. Containment layers are discretized to allow for plausible fracture heights when seeking convergence of fracture height and net pressure.UFD sizes the fracture geometry to physically optimize the hydraulically fractured well performance. The Proppant Number is a correlating parameter, which in turn provides the maximum dimensionless productivity index (JD) corresponding to the optimum dimensionless fracture conductivity, CjD. Once the latter is determined, the fracture dimensions, i.e., fracture length and width, are set. However, UFD in its original form needs fracture height as an input parameter.PKN or KGD fracture propagation models predict hydraulic fracture geometry and the associated net pressure. Linear Elastic Fracture Mechanics (LEFM) relationship calculates fracture height by finding the net pressure distribution at layers, which plays an important role when the fracture is propagating in the reservoir. In multi-layered reservoirs, the net pressure of each layer varies as a result of different rock properties. This study considers the contributions of all layers to the stress intensity factor at the fracture tips to find the final equilibrium height defined by the condition where the fracture toughness equals the calculated stress intensity factor based on LEFM. After an equilibrium height and the corresponding net pressure at the center of perforation are obtained, PKN/KGD models are used again, to calculate fracture width and half-length at each layer. This work also allows for a calculation of the fracture height that would not propagate into unintended layers (i.e. gas cap and/or aquifer)