Opening-dependent phase field model of hydraulic fracture evolution in porous medium under seepage-stress coupling

Abstract

In this paper, a seepage-stress coupling numerical analysis method is developed to simulate complex hydraulic fracturing in porous medium, in which the characteristics of hydraulic fracture evolution in porous medium under seepage-stress coupling are revealed. The classical Biot's poroelasticity theory is applied to couple the stress and fluid fields, and the crack propagation path of hydraulic fracturing is described by an opening-dependent phase field model. Potential energy caused by fluid pressure is also coupled into the governing equation of phase field evolution. The system of fracture opening affecting fluid flow is established. Staggered iterative scheme is applied to solve the above three-field coupled problem based on Newton–Raphson iterative algorithm. Three classical cases are presented to validate the proposed method: the first one is an analytical solution of pressure distribution in a fixed opening crack and the second one is a benchmark case of Sneddon analytical solution for a pressurized pre-crack and the third one is the KGD problem for hydraulic fracture propagation. Moreover, numerical simulations of hydraulic fracturing in shale block, multi-layer and natural fractures are also investigated. The numerical results agree well with the results in published literatures. It is indicated that hydraulic fracture evolution under seepage-stress coupling can be forecasted by the proposed method. The proposed method not only provides a powerful analytical tool for the oil or gas production, but also provides assessment tools for the stability of geotechnical engineering in water rich environments.