Open Access

ARTICLE

Application of Euler-Poincaré Characteristic in the Prediction of Permeability of Porous Media

Yibo Zhao^1,2

1 School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2 School of Data and Computer Science, Shandong Women’s University, Jinan, Shandong, 250300, China

* Corresponding Author: Yibo Zhao,

Intelligent Automation & Soft Computing 2019, 25(4), 835-845. https://doi.org/10.31209/2019.100000087

Abstract

In this paper, a new model is proposed to predict the permeability of porous media. This model introduces the Euler-Poincaré Characteristic (Euler Number), a parameter that reflects the connectivity of porous media. Using fractal and percolation theory, we establish a permeability model as a function of critical radius, porosity and Euler number. In order to relate the result to the Euler number, we introduce the Connectivity Function to calculate the critical aperture in the percolation theory, then calculate the percolation threshold value, and establish the relationship between the percolation threshold and the Euler number. The validity of the model is verified by the structural data of 12 rock samples. For selected rock samples, the proposed model results are compared with the Daigle's method and LBM. The results show that the permeability values obtained by the model are consistent with the LBM experimental data and are higher than those predicted by the Daigle’s model.

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