Numerical modeling of CO2 fracturing by the phase field approach

We propose a phase field model to simulate CO2 fracturing under an isothermal condition. We take advantage of the ability of the phase field approach in predicting fracture initiation and branching, and also to avoid tracking the fracture path. We model the CO2 as a compressible fluid by modifying Darcy's law. In particular, we assume the permeability is correlated to the phase field value by an exponential function. The dependence of the CO2 density as a function of the pressure is captured by the Span-Wagner equation of state. The computed breakdown pressure values show good agreement with analytical solutions and experimental results.