A Model for Electrical Conductivity of Porous Materials under Saturated Conditions
Main Article Content
Abstract
Measurements of electrical conductivity have been used for the geological material characterizations due to their sensitivity to various parameters of porous materials. It is one of the most used geophysical methods in geological, geotechnical, and environmental issues. In this study, we develop a theoretical model for predicting the electrical conductivity of porous media under water-saturated conditions using a similarly skewed pore size distribution. The proposed model is related to the electrical conductivity of the pore fluid, the specific electrical conductance and the microstructural parameters of a porous medium. The model predictions are successfully compared with published experimental data as well as another model available in literature. The model opens up new possibilities for prediction of the electrical conductivity of porous materials.
Keywords:
Electrical properties, electrical conductivity, porous media, fluid.
References
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[3] A. Revil, P. W. J. Glover, Theory of Ionic-Surface Electrical Conduction in Porous Media, Phys. Rev. B, Vol. 55 No. 3, 1997, pp. 1757–1773, https://doi.org/10.1103/PhysRevB.55.1757.
[4] G. E. Archie, The Electrical Resistivity Log as an Aid in Determining some Reservoir Characteristics, Petrol. Trans. AIME, Vol. 146, No. 1, 1942, pp. 54-62, https://doi.org/10.2118/942054-G.
[5] J. Cai, W. Wei, X. Hu, D. A. Wood, Electrical Conductivity Models in Saturated Porous Media: A Review, Earth Sci. Rev., Vol. 171, 2017, pp. 419-433, https://doi.org/10.1016/j.earscirev.2017.06.013.
[6] D. C. Herrick, W. D. Kennedy, Electrical Efficiency a Pore Geometric Theory for Interpreting the Electrical Properties of Reservoir Rocks, Geophysics, Vol. 59, No. 6, 1994, pp. 918-927, https://doi.org/10.1190/1.1443651.
[7] W. Wei, J. Cai, X. Hu, Q. Han, An Electrical Conductivity Model for Fractal Porous Media, Geophys. Res. Lett., Vol. 42, No. 12, 2015, pp. 4833-4840, https://doi.org/10.1002/2015GL064460.
[8] L. D. Thanh, D. Jougnot, P. V. Do, N. V. Nghia, A Physically Based Model for the Electrical Conductivity of Water-Saturated Porous Media, Geophys. J. Int, Vol. 219, No. 2, 2019, pp. 866-876, https://doi.org/10.1093/gji/ggz328.
[9] D. Jougnot, A. Mendieta, P. Leroy, A. Maineult, Exploring the Effect of the Pore Size Distribution on the Streaming Potential Generation in Saturated Porous Media, Insight From Pore Network Simulations. J. Geophys. Res.: Solid Earth, Vol. 124, No. 6, 2019, 5315-5335, https://doi.org/10.1029/2018JB017240.
[10] M. D. Jackson, Characterization of Multiphase Electrokinetic Coupling Using a Bundle of Capillary Tubes Model, J. Geophys. Res.: Solid Earth, Vol. 113, No. B4, 2008, pp. 1-13, https://doi:10.1029/2007JB005490.
[11] M. D. Jackson, Multiphase Electrokinetic Coupling: Insights into the Impact of Fluid and Charge Distribution at the Pore Scale from a Bundle of Capillary Tubes Model, J. Geophys. Res.: Solid Earth, Vol. 115, No. B7, 2010, pp. 1-17, https://doi:10.1029/2009JB007092.
[12] L. D. Thanh, P. V. Do, N. V. Nghia, N. X. Ca, A Fractal Model for Streaming Potential Coefficient in Porous Media, Geophys. Pro., Vol. 66, No. 4, 2018, pp. 753-766, https://doi.org/10.1111/1365-2478.12592.
[13] H. O. Pfannkuch, On the Correlation of Electrical Conductivity Properties of Porous Systems with Viscous Flow Transport Coefficients, Develop. Soil Sci., Vol. 2, 1972, pp. 42-54, https://doi.org/10.1016/S0166-2481(08)70527-0.
[14] Z. Bassiouni, Theory, Measurement, and Interpretation of Well Logs. Henry L. Doherty Memorial Fund of AIME, Soc. Petroleum Engineers, 1994.
[15] J. Cai, X. Hu, D. C. Standnes, L. You, An Analytical Model for Spontaneous Imbibition in Fractal Porous Media Including Gravity, Colloids Surf., A: Physicochem. Eng. Aspects, Vol. 414, 2012, pp. 228-233, https://doi.org/10.1016/j.colsurfa.2012.08.047.
[16] B. Ghanbarian, A. G. Hunt, R. P. Ewing, M. Sahimi, Tortuosity in Porous Media: A Critical Review, Soil Sci. Soc. America J., Vol. 77, No. 5, 2013, pp. 1461-1477, https://doi.org/10.2136/sssaj2012.0435.
[17] A. Bole`ve, A. Crespy, A. Revil, F. Janod, J. L. Mattiuzzo, Streaming Potentials of Granular Media: Influence of the Dukhin and Reynolds Numbers, J. Geophys. Res.: Solid Earth, Vol. 112, No. B8, 2007, pp. 1-14, https://doi:10.1029/2006JB004673.
[18] P. N. Sen, C. Scala, M. H. Cohen, A Self-Similar Model for Sedimentary Rocks with Application to the Dielectric Constant of Fused Glass Beads, Geophysics, Vol. 46, No. 5, 1981, pp. 781-795, https://doi.org/10.1190/1.1441215.
[19] D. Wildenschild, J. J. Roberts, E. D. Carlberg, On the Relationship between Microstructure and Electrical and Hydraulic Properties of Sandclay Mixtures, Geophys. Res. Lett., Vol. 27, No. 19, 2000, pp. 3085-3088, https://doi.org/10.1029/2000GL011553.
[20] P. W. Glover, E. Walker, Grain-size to Effective Pore-size Transformation Derived from Electrokinetic Theory, Geophysics, Vol. 74, No. 1, 2009, pp. 17-29, https://doi.org/10.1190/1.3033217.