Miehe Numerical study of multiple hydraulic fractures propagation in poroelastic media based on energy decomposition phase field methods

Abstract

This paper proposes a novel phase-filed model for simulating hydraulic fracturing in poroelastic media under complex stress conditions. The main theoretical contribution lies in the fact that a generalized strain energy density decomposition is incorporated to hydraulic fracturing phase field model, which unifies hydrostatic-deviatoric and spectral decompositions and predicts material failure through classical Mohr-Coulomb failure criterion. Based on Biot’s poroelastic theory, an indicator function is used to distinguish between fluid flow in fractures and in pores. The fully coupled equations are solved by combining staggered schemes with Newton-Raphson methods. The proposed model is validated by comparing laboratory experimental results with numerical results. In order to demonstrate the influence of introducing hydrostatic-deviatoric and spectral energy decompositions, we simulated propagation of multiple hydraulic fractures and coalescence of hydraulic fractures with natural fractures. Finally, the effects of stress ratios (σx/σy) on multiple hydraulic fractures are analysed. It is found that when the stress ratio is 2, a more complex hydraulic fracture network is formed in the porous media.