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Dynamic Modeling of Cohesive Crack Propagation in Multiphase Porous Media Using the Extended Finite Element Method

Mohammadnejad, Toktam | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 42931 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In this thesis, a fully coupled numerical model is developed for the modeling of the cohesive crack propagation and hydraulic fracturing in porous media using the extended finite element method in conjunction with the cohesive crack model. The governing equations, which account for the coupling between various physical phenomena, are derived within the framework of the generalized Biot theory. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three-phase formulation. The other variables are incorporated into the model via the experimentally determined functions that specify the relationship between the hydraulic properties of the porous medium, i.e. saturation, permeability and capillary pressure.The fluid flow within the fracture is modeled using the Darcy law. By taking advantage of the cohesive crack model, the nonlinear fracture processes developing along the fracture process zone are simulated. The spatial discretization using the extended finite element method and the time domain discretization applying the generalized Newmark scheme yield the final system of fully coupled nonlinear equations, which involves the hydro-mechanical coupling between the fracture and the porous medium surrounding the fracture. The fluid leak-off and the length of fracture extension are found through the solution of the resulting system of equations, not only leading to the correct estimation of the fracture tip velocity as well as the fluid velocity within the fracture, but also allowing for the eventual formation of the fluid lag. It is illustrated that by allowing for the interaction between various processes, i.e. the solid skeleton deformation, the wetting and the non-wetting fluid flow and the cohesive crack propagation, the effect of the presence of the geomechanical discontinuity can be completely captured.Moreover, numerical convergence analysis is carried out to study the approximation error and convergence rate of several enrichment strategies for bimaterial multiphase problems exhibiting a weak discontinuity in the displacement field across the material interface.It is confirmed that the problems which arise in the blending elements can have a significant effect on the accuracy and convergence rate of the solution
  9. Keywords:
  10. Semi Saturated Porousmedia ; Multiphase Flow ; Hydraulic Fracturing ; Extended Finite Element Method ; Cohesive Crack Propagation ; Convergence Analysis

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