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Dual Porosity Method for Modeling Two-Phase Fluid Flow in Deformable Porous Media Applying the Improved Shape Factors

Khorshidi, Mohammad | 2025

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 58592 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khoei, Amir Reza
  7. Abstract:
  8. Natural reservoirs, in addition to having pores and voids, contain fractures and microfractures in which the flow of one or more fluids occurs simultaneously. Resource extraction from these reservoirs usually requires the injection of a second fluid. Therefore, the analysis of two-phase flow is important in the fields of reservoir, water, and geomechanics engineering. Since the 1960s, the dual-porosity method has been developed as an efficient tool for modeling fractured porous media (fractured formation), and numerous studies have been conducted to enhance this method. The dual-porosity method is an approximate approach that offers significant advantages due to its low computational cost and simplicity of implementation in simulations. In this method, the medium is divided into two overlapping but distinct subdomains: the matrix and the fractures. These subdomains are coupled through a transfer function that governs the rate of fluid exchange between the matrix and the fracture system. The key parameter in this function is the shape factor, which has a significant impact on the accuracy of the results, particularly at early times. In recent decades, various formulations for the shape factor have been proposed. However, in most research and industrial modeling, this factor is treated as a constant, dependent on the geometry of the medium or based on specific boundary conditions. Numerous studies have shown that the shape factor has a transient nature, and this characteristic is observable in both single-phase and two-phase fluid flow within rigid and deformable porous media. Nevertheless, few studies have addressed the impact of the transient shape factor on two-phase fluid flow in these media. In the present study, two-phase fluid flow in rigid and deformable porous media is investigated. For each fluid phase (wetting and non-wetting), time-dependent shape factors, corresponding to the medium's properties and boundary conditions, have been derived and applied. For the numerical implementation of the dual-porosity method and the proposed shape factors, the Finite Element Method has been used for spatial discretization of the governing equations, and the Generalized Newmark method has been used for temporal discretization. The shape factors introduced in this research provide an accurate estimation of the fluid volume exchanged between the matrix and fractures. Consequently, they have significantly improved the accuracy of the dual-porosity method in both the transient and steady-state stages. The proposed numerical framework demonstrates a high capability for simulating problems with various boundary conditions and geometries and shows high numerical stability. In this study, both the transient and steady-state forms of the dual-porosity method have been investigated, and its results have shown acceptable performance compared to dual-porosity methods with constant shape factors. Depending on the problem type and the required accuracy in modeling, the proposed dual-porosity method can be used in either its transient or steady-state form.
  9. Keywords:
  10. Two Phase Fluid Flow ; Dual Porosity Model ; Finite Element Method ; Porous Media ; Time-Varying Shape Factor ; Naturally Fractured Reservoir

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