NUMERICAL MODELING OF HYDRAULIC FRACTURE PROPAGATION FROM HORIZONTAL WELLS IN ANISOTROPIC SHALE

摘要

The purpose of this paper is to study the growth of hydraulic fractures in anisotropic rocks such as shale. The boundary value problems of anisotropic materials often are difficult to solve due to the mathematical complexity, therefore such problems are treated numerically under the assumption of isotropy even though such assumption rarely holds in reality. This paper uses the constant element anisotropic displacement discontinuity method (ADDM) for fracture deformation with square root elements at crack tips to calculate stress intensity factors accurately. 3D correction factor G is also developed for anisotropic DDM to include height effect in 2D problems using the analytical solution for stress distribution around a line crack in orthotropic material. The crack propagation is modeled according to the normal stress ratio criterion which accounts elliptically varying fracture toughness while calculating crack trajectory. Crack extension occurs when mode-1 stress intensity factor at tips reaches a critical value K_(IC) (Φ). The fracture deformation is fully coupled with fluid flow inside the fracture by solving all the unknowns simultaneously using globally convergent Newton-Raphson method. The simulation results show significant difference in fracture geometries and apertures between isotropic and anisotropic materials. In anisotropic rock, the direction of plane of elastic symmetry w.r.t fracture influences the fracture geometry. Simulations of multi-stage single lateral fracturing, multi-lateral zipper fracturing in anisotropic shale are included.