This work presents phase field modeling of pressurized and fluid-filled fracture propagation in a poroe-elastic medium.
Here lower-dimensional fracture surface is approximated by using the phase field function.
The two-field displacement-phase-field system solves fully-coupled
constrained minimization problem due to the crack irreversibility.
This constrained optimization problem is handled by using active set strategy.
The pressure is obtained by using a diffraction equation where the phase-field variable serves as an indicator
function that distinguishes between the fracture and the reservoir.
Then the above system is coupled via a fixed-stress iteration.
In addition, we couple with transport system for proppant filled fracture by using a power-law fluid system.
The numerical discretization in space is based on Galerkin finite elements for displacements and phase-field,
and an Enriched Galerkin method is applied for the pressure equation in order to obtain local mass conservation.
Nonlinear equations are treated with Newton’s method. Predictor-corrector dynamic mesh refinement allows to capture more accurate
interface of the fractures with reasonable number for degrees of freedom.