A review of hydraulic fracture models and development of an improved pseudo-3D model for stimulating tight oil/gas sand

Many injection/production wells have been hydraulically fractured to enhance injectivity/productivity. Various engineering models for fracture geometry have been developed, which define the propagation of a fracture with time and wellbore treatment pressure. These models combine with elasticity, fluid flow, material balance, and propagation criterion/in-situ stresses. When this combination describes the fracture dimensions, the fracture-geometry can be of two-dimensional (2D) and three-dimensional (3D), depending on the number of dimensional variables. For design purposes, several 2D and 3D models are already developed. But it is still a concern in the oil industry as to which model is beneficial to design optimum treatment parameters for a particular tight sand, because despite many successes, there have been many wells of poor post-fracture productivity. This article provides a review of 2D and 3D fracture models for prediction of fracture geometry. A P-3D (pseudo) model has been improved by incorporating Carter solution of material balance for the first time and was named P-3D-C model, which has predicted higher fracture conductivity. The improved model is highly potential for repetitive computation in hydraulic fracture design optimization.