Three-Dimensional Hydraulic Fracture Propagation in the Presence of Stress Variations

Abstract

Abstract Models of three-dimensional (3D) fracture propagation are being developed to study the effect of variations of stress and rock properties on fracture height and bottomhole pressure (BHP). Initially a blanket sand bounded by zones of higher minimum in-situ stress is considered, with stresses symmetrical about both the pay-zone axis and the wellbore. An elliptical fracture perimeter is assumed. Fluid flows are one-dimensional (ID) Newtonian in the direction of the pay zone. Two models, FL1 and FL2, are developed. In FL1, a discontinuous stress variation is approximated by ar variation in the vertical coordinate, and the fracture criterion, Ki =Ke, is satisfied at both major and minor axes. The net pressure at the tip, Lf, of the long axis required by the boundary condition Ki =Kc does not seem crucial in determining fracture height or BHP (compare with one group of published models8,9 that assumes p = 0 at Lf). Model FL2 properly represents the discontinuous stresses, and satisfies Ki=Ke. at the wellbore but not at the tip of the long axis. A parametric study is made, with both models, of the comparative effects of stress contrast, σ2-σ1, Ke, pay-zone height, h, and Young's modulus, E, on fracture height and BHP. Results indicate that Kc does not have as much effect as either for σ2- σ1, at least for large stress contrasts. Model FL2 suggests the possibility of a rapid growth in fracture height as σ2−σ1 is reduced. Such modeling may be able to give an upper or "safe" limit on the pumping parameters (q and μ) to ensure good containment. When the stress contrast is high, σ2−σ1, ≥700 psi [4826 kPa], an analytic derivation of BHP appears to be a good approximation for the parameters we use, if everywhere the fracture height is assumed equal to the pay zone height. Although leakoff is neglected here, subsequent modeling results show that, for leakoff coefficients C≲0.001 ft-min−½ [3.9×10−5 m·s−½], the results herein are a good approximation to the case when leakoff is included.