A Darcy–Cahn–Hilliard model of hydraulic fracturing with multiphase flow
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Multiphase flow in deformable porous media spans a wide range of applications, including enhanced geothermal energy, geological carbon storage, and geo-hazards. However, it presents an ongoing challenge both for experimental testing and numerical modeling, partly due to the coupling between material deformation and fluid flow. Here, we introduce a numerical model to study the case of an invading fluid pushing out a defending fluid through fracturing of the porous medium. Our model captures the coupled evolution of the fluid-fluid interface and the cracks, while controlling the relevant hydro-mechanical parameters. It is motivated by recent experimental observations of such fracturing process in synthetic porous media aiming at reproducing subsurface conditions. Through numerical simulations, we recover the two regimes of invasion, porous invasion and fracturing. We also study the effect of the injection driving force on the resulting crack pattern. Finally, our model is employed to study the regions of parameter space that are outside the capabilities of the experiments.
