  A Darcy-Cahn-Hilliard model coupled with damage is developed to describe
multiphase-flow and fluid-driven fracturing in porous media. The model is
motivated by recent experimental observations in Hele-Shaw cells of the
fluid-driven fracturing of a synthetic porous medium with tunable fracture
resistance. The model is derived from continuum thermodynamics and employs
several simplifying assumptions, such as linear poroelasticity and
viscous-dominated flow. Two distinct phase fields are used to regularize the
interface between an invading and a defending fluid, as well as the ensuing
damage. The damage model is a cohesive version of a phase-field model for
fracture, in which model parameters allow for control over both nucleation and
crack growth. Model-based simulations with finite elements are then performed
to calibrate the model against recent experimental results. In particular, an
experimentally-inferred phase diagram differentiating two flow regimes of
porous invasion and fracturing is recovered. Finally, the model is employed to
explore the parameter space beyond experimental capabilities, giving rise to
the construction of an expanded phase diagram that suggests a new flow regime.
