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Multiscale Modelling of Non-Isothermal Multiphase Flow in Heterogeneous Porous Media with Computational Homogenization Approach

Saeedmonir, Saeed | 2022

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 55343 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. In the real engineering problems, the existing materials in the nature or human-made materials, contain different heterogeneities from the view of small scale. Reinforced composite materials and porous media containing grains or micro-cracks are some examples of these materials. Due to the large amount of these heterogeneities as well as the small size, direct modelling of these micro-structures requires extremely high computational and memorial cost. Also, the equivalent models introduced in the literature, have strong limitations and therefore, cannot capture accurate behavior of the material. Hence, multiscale methods have been proposed in order to model these heterogeneous media with impressive reduction in computational cost without loss accuracy. Among the multiscale methods, computational homogenization approach has been widely utilized by different authors. On the other side, multiphase flow in the deformable heterogeneous porous media is one of the interesting topics in the geothechnical engineering. Besides, one of the methods of the ehnahced oil recovery, is thermal shock or hot/cold water injection. Therefore, convection and conduction heat transfers through the porous media are of interesting topics.Thus, computational homogenization approach should be extended to the mentioned issues.In this dissertation, computational homogenization approach is exploited in order to model the heterogeneous porous media with different physics. In spite of the classical homogenization approach, transient terms are included in the microscopic governing equations. Therefore, RVE size should be involved in the microscopic analysis.Accordingly, this method is applied to the analysis of micro-fractured porous media. in this manner, extended finite element method has been exploited to model the micro-fractures. Next, multiphase flow in deformable porous media is studied via the computational homogenization approach. Different boundary conditions and RVE types, together with the RVE size are considered in this study. A general and novel method has been proposed for imposing the boundary conditions, in which the tangent operators and homogenizaed quantities are extracted in an automated manner from the microscopic solution. Also, thermo-hydro-mechanical analysis of heterogeneous porous media is considered in the next section. Two regimes of heat transfer, conduction and convection, are captured in the formulation. As the convection flux dominates the conduction flux, the heat is mostly transferred by the convection. It is known that the conventional finite element method cannot result in appropriate spatial temperature field. Thus, upwinding methods are utilized to overcome thid issue. Finally, several numerical examples are provided for each of the studies in order to demonstrate the efficacy and efficiency of the proposed framework
  9. Keywords:
  10. Multiscale Method ; Computational Homogenization ; Porous Media ; Heat Transfer ; Multiphase Flow ; Conductance ; Extended Finite Element Method ; Petrov-Galerkin Approach ; Convection

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