Phase field model for simulating hydraulic fracture propagation and oil–water two-phase flow in reservoir

Abstract

A novel phase field model of two-phase fluid flow based on the interaction between solid and pore fluids for modelling hydraulic fracture propagation in poro-elastic media is proposed. In this model, the two-phase fluid flow in the matrix obeys Darcy’s law. Moreover, the capillary pressure in the flow process is considered, and the anisotropic relative permeability model of the two-phase flow, which is related to fluid saturation, is introduced. The driving force of the phase field and Biot’s modulus of the two-phase fluid flow vary with the phase field and fluid saturation. Displacement, pressure, and saturation are solved in a staggered manner. The corresponding numerical solution iterative format is established using the finite element numerical discretisation and Newton–Raphson iterative methods. The correctness of the model is verified, and the limitations of the single-phase flow model are revealed. In addition, the influence of different matrix permeabilities on fracture propagation in porous media, the propagation law of hydraulic fractures under different matrix water saturations, and the effect of different stress differences on hydraulic fracture propagation in multi-layer superimposed formations are studied.