A Novel Method for Streamline-Based Tortuosity Calculation and Investigation of Obstacles Shape Effect on Tortuosity in Porous Media with Random Elliptical Obstacles Using Lattice Boltzmann Method

Abstract

In this research, the lattice Boltzmann method was used to simulate the fluid flow in the random elliptical porous media. Since the tortuosity is one of the most important parameters of porous media and also, the hydraulic tortuosity is more accurate and more realistic than geometric tortuosity, therefore, the hydraulic tortuosity was discussed thoroughly in this study. Contrary to many studies in which the velocity-based method has been used for calculation of tortuosity, one of the novelties in this paper is the application of streamline-based tortuosity including the detailed description of mathematical method for calculation of streamline-based tortuosity and also, the calculation of it numerically and the comparison with velocity-based tortuosity at different porosities and at various aspect ratios. Furthermore, the deviation percentage of velocity-based tortuosity from streamline-based tortuosity was surveyed and depicted. Also, the behavior of streamline-based tortuosity was illustrated as a function of porosity at different aspect ratios and the results were compared with Comiti–Renaud equation and a new equation was proposed. With the structure factor defined as the ratio of porosity to tortuosity, the variation of this quantity with respect to porosity was displayed at different aspect ratios. Also, the formation factor variation versus porosity was discussed at different aspect ratios, too. Finally, the influence of obstacles shape on the tortuosity by varying aspect ratio was investigated and it was concluded that the orientation of elliptical obstacles (vertically or horizontally) has severe effect on the tortuosity.