Abstract

Pressurized and Fluid filled fracture propagation in porous media using phase field approach

Sanghyun Lee
University of Texas at Austin

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.