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Simulation of Two-phase Flow through Rock Fractures using Multi-block Lattice Boltzmann Method

Foroughi, Sajad | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51384 (06)
  4. University: Sharif University of Technology
  5. Department: Chemical and Petroleum Engineering
  6. Advisor(s): Pishvaie, Mahmoud Reza; Jamshidi, Saeid
  7. Abstract:
  8. Determining the parameters of the porous media and fractures in order to properly understand the processes governing these environments is very important. Traditionally, these parameters are determined in the laboratory. In recent years, with the advancement of computational capabilities, numerical methods have been considered to determine the parameters of the porous media. In the last few decades, the lattice Boltzmann method has been considered by the researchers as a class of computational fluid dynamic methods for simulating fluid flow. The advantages of the lattice Boltzmann method include simplicity in applying to complex media and the ability to simulate different phenomena. In this study, at first, fluid flow in a set of percolation porous media with the help of the lattice Boltzmann method is simulated. The parameters of these structures including permeability and tortuosity coefficient were obtained from simulation results. Then based on the obtained results, a relationship between static and dynamic parameters has been proposed. The proposed relationship has been validated by experimental data. Afterwards, in order to study the fracture parameters by implementation of an algorithm which is based on fractal theory, a set of rough fractures have been constructed. Simulation of fluid flow using the lattice Boltzmann method through these fracture structures allows the calculation of the fracture parameters. At low velocities, the permeability parameter and at higher velocities the inertial resistance coefficient is calculated for the fracture. With the help of the obtained results, two models are proposed for the permeability and inertial resistance coefficient of the fracture. The performance of these two models is validated by experimental data. After that, with the implementation of a multi-relaxation time lattice Boltzmann method, a slip flow simulator has been developed using slip boundary condition that is able to simulate slippage in a porous medium. The presented approach is validated with the available analytical solution and with the simulation in the converging/diverging tubes, it is shown that increasing pore aspect ratio leads to a reduction of the slippage effects.
    Subsequently, the two-phase lattice Boltzmann method has been implemented and verified with the help of the existing test cases. Then, by simulating the two-phase flow in the constructed rough fractures, the effect of different parameters on the relative permeability of fracture is investigated. The results show that the viscosity ratio, fracture wall roughness and wettability affect the behavior of relative permeability. In addition, the developed code allows the simulation of the viscous coupling effect. Finally, considering that the simulation of fluid flow in porous media and fractures require a high resolution images, besides the traditional lattice Boltzmann method is applied on uniform blocks. The development of multi-block lattice Boltzmann method became necessary. In this study, a multi-block lattice Boltzmann approach is presented that is able to simulate single-phase and two-phase flows. The developed algorithm is validated with the help of simulating available benchmarks for single-phase and two-phase flows. Next, this approach is used to simulate flow in a fracture. For this purpose, with the help of a certain algorithm and using quad-tree grids, the structure of a rough fracture with its present phases is reconstructed. The reconstruction is performed in a way that on the solid boundary and on the boundary of the phases, fine blocks are placed and the coarse blocks are applied to the rest of the flow domain. The obtained results show that the developed algorithm is capable of reconstructing the fracture with a smaller number of blocks comparing with the uniform fine blocks. As a result, the computational time required for simulation is significantly reduced, while the calculated effective permeability parameters have little difference with the calculated results of simulation by the traditional lattice Boltzmann method
  9. Keywords:
  10. Lattice Boltzmann Method ; Porous Media ; Relative Permeability ; Slip Flow ; Fracture Permeability ; Inertial Resistance Coefficient

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