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An electrical conductivity model for fractal porous media
Author(s) -
Wei Wei,
Cai Jianchao,
Hu Xiangyun,
Han Qi
Publication year - 2015
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2015gl064460
Subject(s) - tortuosity , fractal , fractal dimension , porosity , porous medium , exponent , electrical resistivity and conductivity , cementation (geology) , materials science , conductivity , fractal derivative , thermodynamics , mineralogy , geotechnical engineering , geology , mathematics , physics , mathematical analysis , composite material , fractal analysis , quantum mechanics , linguistics , philosophy , cement
Archie's equation is an empirical electrical conductivity‐porosity model that has been used to predict the formation factor of porous rock for more than 70 years. However, the physical interpretation of its parameters, e.g., the cementation exponent m , remains questionable. In this study, a theoretical electrical conductivity equation is derived based on the fractal characteristics of porous media. The proposed model is expressed in terms of the tortuosity fractal dimension ( D T ), the pore fractal dimension ( D f ), the electrical conductivity of the pore liquid, and the porosity. The empirical parameter m is then determined from physically based parameters, such as D T and D f . Furthermore, a distinct interrelationship between D T and D f is obtained. We find a reasonably good match between the predicted formation factor by our model and experimental data.