A Semianalytical Solution for a Griffith Crack Nonuniformly Pressurized By Internal Fluid

Unintentional variations of fluid pressure within a hydraulic fracture will disturb the surrounding stress state, affect the stability of fracture propagation and complicate the fracture intersections during the process of hydraulic fracturing. However, little attention has been paid to the effect of nonuniform fluid pressure inside the hydraulic fracture. This paper presents a semianalytical solution for a Griffith crack nonuniformly pressurized by internal fluid in an impermeable elastic plane. The fluid pressure is hypothetically designated as a general polynomial with respect to the location of the fluid, such that the effect of an arbitrary form of fluid pressure distribution can be explored by polynomial fitting. The semianalytical solution is capable of being degenerated into constant pressure forms which confirms that the solution is an extension of classic constant pressure. In addition, the critical propagation conditions and stress distributions (e.g., σ_xx) under constant and nonuniform pressures are compared and discussed. The comparison results indicate that the effect of nonuniform fluid pressure accumulated by the number of polynomial terms increases the magnitude of stress (or displacement) but does not change its distribution. Subsequently, the semianalytical solution is validated by comparing the fracture intersection predicted by the semianalytical solution with the laboratory experimental observations and published predictions under constant fluid pressure. Good agreement with the experiments and sufficient advantages over previous predictions are observed. Finally, a sensitivity analysis of existing parameters in the semianalytical solution, including crack length, initial pressure, number of terms and number of subintervals, is conducted to evaluate their influence on surrounding stresses and critical propagation conditions, which further demonstrates the applicability and reliability of the presented semianalytical solution. The new solution enriches hydraulic fracturing theory by considering the nonuniform fluid pressure effect and provides important reference for fracture network design during hydraulic fracturing.