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BIRS Workshop Lecture Videos

Phase field modeling for fracture propagation in porous medium Lee, Sanghyun


The computational modeling of the formation and growth of the pressurized and fluid filled fractures in poroelastic media is difficult with complex fracture topologies. Here we study the fracture propagation by approximating lower-dimensional fracture surface using the phase field function. The major advantages of using phase-field modeling for crack propagation are i) it is a fixed-topology approach in which remeshing is avoided, ii) crack propagation and joining path are automatically determined based on energy minimization, and iii) joining and branching of multiple cracks also do not require any additional techniques. Recently, the phase field approach has been widely employed to different applications and developed for various softwares. The two-field displacement phase-field system solves fully-coupled constrained minimization problem due to the crack irreversibility. Here, 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 and transport equation in order to obtain local mass conservation. Nonlinear equations are treated with Newtonâ s method. Predictor-corrector dynamic mesh refinement allows to capture more accurate interface of the fractures with reasonable number for degrees of freedom. In addition, we will discuss how to couple these phase field model to multi scale and optimization problems.

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