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Numerical Modeling of Fluid Flow in Cracked Porous Media using Phase-Field Approach

Ahmadi Olyaei, Ehsan | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57642 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. The objective of this research is to investigate fluid flow in cracked porous media. Fluid, mass, and heat transfer in porous and cracked porous media, particularly in subsurface environments characterized by complexity and uncertainty—such as hydraulic fracturing, lowـpressure groundwater flow, and more—are of great importance in the oil and geothermal energy industries. The problem domain consists of three main sections: the saturated porous medium, the crack or channel within this porous medium, and the boundary layer between the crack and the adjacent environment. The phase field method is utilized in this study to model these discontinuities. Phase field models are similar to variational approaches for modeling the growth of discontinuous domains, where the problem's unknown field and the fracture set are simultaneously determined by minimizing the total potential energy of the domain. However, this study does not focus on the growth and propagation of fractures or channels but rather on their effects. The boundary layer between the crack and the adjacent environment, with high shear stresses, significantly influences the flow profile. Fluid leakage through crack walls also affects the velocity profile. The numerical modeling of flow in fractured porous media is often based on strong simplifications that avoid the possibility of considering many significant issues happening and influencing the whole process frequently in real cases, such as the interfacial conditions between the fracture and the surrounding porous medium, or many situations deviated from the classical theories of flow inside the fractures (Poisuille Flow), like two/threeـdimensional flow inside the fracture, flow through fractures with nonـparallel walls, and flows with high Reynolds number. Despite these limitations, the developed formulation in this study provides the opportunity for accurate simulation of fluid flow through fractured porous media with complex potential conditions for cracks and discontinuities within porous media. A new version of governing equations based on the NavierـStokes equations and phase field approach is presented in this research, which ultimately leads to the continuity equations for fluid flow across the entire domain and the overall force equilibrium of the domain. The numerical solution of these equations is performed using the characteristicـbased split (CBS) method, where temporal discretization is handled by the characteristics method, and spatial discretization is carried out according to the finite element method. Using the developed relationships and the aforementioned numerical method, this research solves fluid and heat transfer problems in various scenarios of porous media, such as fractured porous media, porous media with channels of irregular geometry, and media with solidـfluid interfaces. It is illustrated that the application of the proposed formulation provides a highly accurate estimation of the flow pattern inside the tortuous channels
  9. Keywords:
  10. Fluid Flow ; Fluid Flow in Porous Media ; Porous Media ; Crack ; Finite Element Method ; Phase Field Model ; Characteristic Based Split (CBS)Method

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