| Convergence in Dynamic Hydraulic Fracturing Modeling: Step-Wise Crack Advancement and Pressure Oscillations in Saturated Porous Media Mohammadreza Hirmand1; Mohammad Vahab2; Katerina D. Papoulia3; Nasser Khalili2; 1UNIVERSITY OF WATERLOO, Waterloo, Canada; 2UNSW, Sydney, Australia; 3APPLIED MATHEMATICS, UNIVERSITY OF WATERLOO, Waterloo, Canada; PAPER: 328/Geomechanics/Invited (Oral) SCHEDULED: 17:50/Thu. 24 Oct. 2019/Athena (105/Mezz. F) ABSTRACT: Crack propagation is most frequently implemented on the basis of so-called extrinsic models in which discontinuity surfaces (cracks) are introduced upon satisfaction of an external stress criterion. Often, an implicit time marching scheme is employed in which the crack is kept fixed within the computations of the iterative solver. The crack is advanced to a pre-determined length on the basis of a pre-determined propagation law at the end of the load step. This approach has been shown to lack mathematical soundness and is especially problematic in the context of hydraulic fracturing. The sequential solution of the displacement and crack surface in unknown fields leads to crack propagation velocities that do not converge with time step and mesh size refinement. A consequence of this issue is that the hydraulic fracturing model cannot properly capture the step-wise crack advancement and pressure oscillations in saturated porous media. This is not a coincidence but a manifestation of robustness issues with extrinsic crack propagation algorithms. We propose a hydraulic fracturing model with non-differentiable energy minimization for cohesive fracture in which formation and propagation of cracks are direct outcomes of the computations within the time step. The method allows advancement for any length of crack within a time step given the applied loads without need to introduce crack nucleation and crack increment length criteria. Numerical results show step-wise behavior which also exhibit convergence with time step and mesh size refinement. References: [1] K. D. Papoulia, C.-H. Sam, S. A. Vavasis, Time continuity in cohesive finite element modeling, International Journal for Numerical Methods in Engineering 58 (2003) 679-701. [2] K. D. Papoulia, Non-differentiable energy minimization for cohesive fracture, International Journal of Fracture 204 (2017) 593 143-158. [3] M. R. Hirmand, K. D. Papoulia, A continuation method for rigid-cohesive fracture in a discontinuous Galerkin finite element setting, International Journal for Numerical Methods in Engineering 115 (2018) 627-650. [4] M. R. Hirmand, K. D. Papoulia, Block coordinate descent energy minimization for dynamic cohesive fracture, Computer Methods in Applied Mechanics and Engineering (2019). https://doi.org/10.1016/j.cma.2019.05.051. [5] C. Peruzzo, T. D. Cao, E. Milanese, P. Favia, F. Pesavento, F. Hussain, B. A. Schrefler, Dynamics of fracturing saturated porous media and self-organization of rupture, Journal of the Mechanics and Physics of Solids 111 (2018) 113-133. [6] A. Khoei, M. Vahab, M. Hirmand, An enriched FEM technique for numerical simulation of interacting discontinuities in naturally fractured porous media, Computer Methods in Applied Mechanics and Engineering 331 (2018) 197-231. |
