Special Session 108: New Developments in porous media

Phase-field modeling of proppant-filled fractures in a poroelastic medium

Mary F Wheeler
The University of Texas At Austin
USA
Co-Author(s):    Lee. S., Mikelic, A., Wick, T.
Abstract:
This work presents proppant and fluid-filled fracture with quasi-Newtonain fluid in a poroelastic medium. 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. The transport of the proppant in the fracture is modeled 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. The concentration is solved with cell-centered finite elements. 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 degree of freedoms. [1] LEE, S. AND WHEELER, M. AND WICK, T.; Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model [2] LEE, S. AND Mikelic, A. AND Wheeler, M. AND Wick, T.; Phase-field modeling of proppant-filled fractures in a poroelastic medium