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

Banff International Research Station for Mathematical Innovation and Discovery

This work presents proppant and fluid-filled fracture with quasi-Newtonian 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

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Material science

video/mp4

Author affiliation: University of Texas at Austin

2017-02-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59681

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/