Journal
GEOPHYSICAL RESEARCH LETTERS
Volume 42, Issue 12, Pages 4833-4840Publisher
AMER GEOPHYSICAL UNION
DOI: 10.1002/2015GL064460
Keywords
electrical conductivity; Archie's equation; cementation; fractal; tortuosity
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Funding
- National Natural Science Foundation of China [41102080, 41274077, 41474055]
- Natural Science Foundation of Hubei Province [2015CFA019]
- Fundamental Research Funds for the Central Universities [CUG130404, CUG130103]
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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 70years. 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.
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