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Description
The petrophysical properties of rocks, such as thermal conductivity, electrical conductivity, and fluid transport, have been studied based on fractal geometry theory in many areas over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal tortuous capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for 8 sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. The proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by other algorithm. There is a self-similar fractal range in sandstone when excluding smaller pores and the fractal dimensions are intimate related to the microstructures of porous media.
References
- Yu, B. and J. Li, Some fractal characters of porous media. Fractals, 2001. 9(3): p. 365-372.
- Cai, J. and B. Yu, A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media. Transport in Porous Media, 2011. 89(2): p. 251-263.
- Pia, G. and U. Sanna, An intermingled fractal units model and method to predict permeability in porous rock. International Journal of Engineering Science, 2014. 75: p. 31-39.
- Cai, J., et al., Electrical conductivity models in saturated porous media: A review. Earth-Science Reviews, 2017. 171: p. 419-433.
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