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

Systematic 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, CfD. Once the latter is determined, the optimum fracture dimensions, i.e., fracture length and width, are set. However, UFD in its original form needs the ability to calculate the Proppant Number and that is possible only if fracture height is an input parameter and hence fraction of proppant ending up in the pay can be determined before the optimization. PKN or KGD fracture propagation models in design mode provide basic treatment parameters to achieve a known target length and also associated net pressure. Linear Elastic Fracture Mechanics (LEFM) relationship can be used to obtain fracture height associated to a given vertical pressure distribution via vertical stress profile and fracture toughness profile. This study considers the contributions of all layers to the stress intensity factor at the fracture tips to find the potential equilibrium height defined by the condition where the stress intensity factor minus fracture toughness difference changes sign (but not necessary becomes zero.) After an equilibrium height and the corresponding net pressure are found, an optimization is carried out to find target length and a 2D design model is used to calculate treatment parameters, first of all net pressure. The ultimate goal is to find a consistent pair of these two different sub-models; when the assumed pressure condition in the LEFM part coincides with the resulting pressure condition from the UFD/2D part. Parts of this work also allows for determining conditions to avoid propagating into unintended layers (i.e. gas cap and/or aquifer) or to assure coverage of intended layers (such as a non-perforated layer with recoverable hydrocarbon.)