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, Volume 78, Issue 1, pp 1165–1180 | Cite as

Estimating critical path analysis on digital topology of the connectivity of pore media

  • Yibo ZhaoEmail author


The relationship between pore media microstructure and permeability has been a hot topic in the field of geosciences. However, there are still significant technical challenges in accurately estimating permeability, especially in spatially complex pore media. Here we introduce morphological of porous media, expressed by Euler-Poincaré Characteristic (Euler Number) which is a key parameter in the digital topology that describes the connectivity of pore media. In this short communication, the connectivity function of porous media is established by Euler number and used to determine the critical pore size in the theory of percolation. Then the critical path analysis (CPA) and percolation theory are combined to study the relationship between the Euler number and the permeability of porous media. Using twelve digital core samples, the empirical formula and the theoretical estimations of CPA-based model (Friedman and Seaton, 1998) are compared respectively with the experimental measurement data. The results show that the permeability estimation under the Euler number factor model is more accurate than the CPA-based model. Some possible sources of uncertainty are also discussed. The relationship between permeability and morphological (Euler Number) of porous media makes it possible to predict permeability of porous media accurately and reasonably.


Permeability Euler number Percolation theory Critical path analysis 



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Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduChina
  2. 2.School of Data and Computer ScienceShandong Women’s UniversityJinanChina

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