Incorporation of 2D Fluid Flow into a Pseudo-3D Hydraulic Fracturing Simulator

Weng, Xiaowei (Arco E&P Technology)



Pseudo 3D (P3D) hydraulic fracturing models often overpredict fracture height for a poorly contained fracture. This is caused partly by either the neglect of the fluid flow component in the vertical direction or a crude treatment of the 2D fluid flow in the fracture as ID flow in the vertical direction in the fracture-height calculation. This paper presents a height-growth model that adopts a flow field more representative of the actual 2D flow in a fracture. In this model, the fracture is divided into two regions: an inner region where the flow direction is nearly horizontal, and an outer region where the flow field is approximated by a radial flow from an imaginary source. The governing equations for determining height growth rate and the numerical method for solving these equations are described. A commercial P3D simulator was modified by replacing its original height-growth model with this 2D flow-height model. The modified simulator was tested against the original simulator and the Terra Tek and U. of Texas fully 3D simulators. The modified P3D simulator incorporating the new height model showed significant improvement over the original model in height calculations and good agreement with the fully 3D models.


Over the past decade, numerous 3D hydraulic-fracturing models have been developed. These models can predict fracture geometry, including height, with known reservoir parameters. The 3D models can be divided into two categories. The first type of models, often called P3D models, evolves from the 2D Perkins-Kern-Nordgren (PKN) model. Unlike the constant fracture height assumed in the PKN model, the height in a P3D model grows with time and varies along the pay-zone direction. The fluid flow in the fracture is assumed to be predominantly ID. The plane-strain condition is assumed on the deformation of each vertical fracture cross section. The other type of models, called fully 3D models, solves a set of coupled equations governing the deformation of a 3D fracture and the 2D fluid flow in the fracture. The fully 3D models are mathematically more rigorous but very complex and difficult to run.

Different P3D models use different approaches to calculate fracture height and vary significantly in degree of complexity. The simplest approach is to determine height from the local net pressure, stress profile, and rock toughness by satisfying the static equilibrium of the fracture. The height thus obtained is the equilibrium fracture height. Fluid pressure is assumed constant over each vertical cross section, and the fluid flow is assumed to be in the pay-zone direction only.