A three-dimensional solution of hydraulic fracture width for wellbore strengthening applications

• Main Authors: Jincai Zhang, Shangxian Yin
• Format: Article
• Language: English
• Published: SpringerOpen 2019-05-01
• Series: Petroleum Science
• Subjects: Hydraulic fracture; Fracture width; Wellbore strengthening; Fracture propagation; 3-D modeling
• Online Access: http://link.springer.com/article/10.1007/s12182-019-0317-7

Abstract Determining the width of an induced hydraulic fracture is the first step for applying wellbore strengthening and hydraulic fracturing techniques. However, current 2-D analytical solutions obtained from the plane strain assumption may have large uncertainties when the fracture height is small. To solve this problem, a 3-D finite element method (FEM) is used to model wellbore strengthening and calculate the fracture width. Comparisons show that the 2-D plane strain solution is the asymptote of the 3-D FEM solution. Therefore, the 2-D solution may overestimate the fracture width. This indicates that the 2-D solution may not be applicable in 3-D conditions. Based on the FEM modeling, a new 3-D semi-analytical solution for determining the fracture width is proposed, which accounts for the effects of 3-D fracture dimensions, stress anisotropy and borehole inclination. Compared to the 2-D solution, this new 3-D semi-analytical solution predicts a smaller fracture width. This implies that the 2-D-based old design for wellbore strengthening may overestimate the fracture width, which can be reduced using the proposed 3-D solution. It also allows an easy way to calculate the fracture width in complex geometrical and geological conditions. This solution has been verified against 3-D finite element calculations for field applications.