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

Abstract

Summary 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 1D 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.