Incorporation of 2D fluid flow into a pseudo-3D hydraulic fracturing simulator

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.