ORALS

SESSION: GeomechanicsThuPM3-R7	Schrefler International Symposium on Geomechanics and Applications for Sustainable Development
Thu Oct, 24 2019 / Room: Athena (105/Mezz. F)
Session Chairs: Andrew Chan; Herbert MANG; Session Monitor: TBA

17:50: [GeomechanicsThuPM313] Invited
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 Id: 328 [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.

SESSION: GeomechanicsThuPM3-R7	Schrefler International Symposium on Geomechanics and Applications for Sustainable Development
Thu Oct, 24 2019 / Room: Athena (105/Mezz. F)
Session Chairs: Andrew Chan; Herbert MANG; Session Monitor: TBA

18:15: [GeomechanicsThuPM314] Keynote
Robust Simulation of Dynamic Hydraulic Fracturing in Naturally Fractured Formations
Mohammad Vahab¹ ; Mohammadreza Hirmand² ; Katerina D. Papoulia³ ; Nasser Khalili¹ ; ¹UNSW, Sydney, Australia; ²University of Waterloo, Waterloo, Canada; ³Applied Mathematics, University of Waterloo, Waterloo, Canada;
Paper Id: 7 [Abstract]

In this study, an energy based hydro-mechanical model and computational algorithm for the problem of hydraulically driven fracture networks developing in naturally fractured impermeable media is developed. The model is based on non-differentiable energy minimization for the dynamic deformation and fracture of the body coupled with mass balance of fluid flow within the hydro-fractures. Time-discontinuity induces spurious crack-opening velocity fields which lead to nonphysical solutions for the coupled fluid pressure field defined locally along the crack faces. The use of a time-continuous fracture model, such as the present non-differentiable energy minimization approach, is crucial for the numerical soundness and stability of the hydraulic fracture propagation algorithm. A discontinuous Galerkin finite element formulation is implemented, in which every element edge in the mesh is a potential site of hydro-fracture initiation and propagation. The presence of pre-existing natural fractures, as a common challenge in nearly all geological formations, are modelled with desirable edibility by simply assigning different fracture properties to the element edges defining the natural fractures. Using the graph theory principals, a search algorithm is proposed to identify, among all, the sub-set of cracked interfaces that form the interconnected hydraulically loaded fracture network. Robustness of the proposed computational algorithm and its versatility in the study of hydraulic fracturing is shown through several numerical simulations.

References:
[1] M.R. Hirmand, K. D. Papoulia, Int. J. Numer. Meth. Eng. 115 (2018) 627-650.
[2] M. Vahab, N. Khalili, Rock. Mech. Rock. Eng. 51(2018) 3219-3239
[3] A.R. Khoei, M. Vahab, E. Haghighat, S. Moallemi, Int. J. Fract. 188 (2014) 79-108.