Fracturing of a horizontal wellbore with axis in the direction of minimum in situ stress

Since the vertical distribution of horizontal in situ stresses is not symmetric with respect to the wellbore axis, the hydraulically induced fracture from a horizontal wellbore favors the growth of one wing and the fracture is not symmetric with respect to the wellbore as its vertical counterpart. Furthermore, if the wellbore axis is not in the direction of the maximum horizontal in situ stress, the hydraulic fracture will turn aligning its plane into the direction perpendicular to the minimum horizontal in situ stress.;A mathematical model is developed to simulate the propagation of a hydraulic fracture from the horizontal wellbores. The model employs a 3D elastic fracture equation and a 2D fluid flow equation. To simplify the problem, the shape of the hydraulic fracture in the developed plane is approximated by two ellipses which are patched together along the wellbore. Sih's (1974) strain energy density criterion is used to control the direction of the growing fracture. In order to obtain an understanding of the characteristics of fluid flow in a non-symmetric hydraulic fracture, results from the study of propagation of a non-symmetric hydraulic fracture of constant height are also presented.;The results from the study have demonstrated that: (1) The fracture tends to propagate towards the low stress zone. (2) The rate of fracture turning is largely determined by the ratio of two horizontal principal stresses and the pumping rate as well as the viscosity of the frac-fluid. The fracture plane will turn to align itself into the direction perpendicular to the minimum horizontal in situ stress. The rate of fracture turning increases with the ratio of the horizontal principal stresses, but decreases with the increase of pumping rate and the viscosity of the frac-fluid. (3) The size of a hydraulically induced fracture depends on the pumping rate and on the viscosity of the frac-fluid. A large fracture can be produced by pumping a viscous fluid at a high rate. A larger fracture has a wider opening width which guarantees the success of fracturing operation.