Examination of the Fractal Model for Streaming Potential Coefficient in Porous Media
Main Article Content
Abstract
Abstract: In this work, the fractal model for the streaming potential coefficient in porous media recently published has been examined by calculating the zeta potential from the measured streaming potential coefficient. Obtained values of the zeta potential are then compared with experimental data. Additionally, the variation of the streaming potential coefficient with fluid electrical conductivity is predicted from the model. The results show that the model predictions are in good agreement with the experimental data available in literature. The comparison between the proposed model and the Helmholtz-Smoluchowski (HS) equation is also carried out. It is seen that the prediction from the proposed model is quite close to what is expected from the HS equation, in particularly at the high fluid conductivity or large grain diameters. Therefore, the model can be an alternative approach to obtain the zeta potential from the streaming potential measurements.
Keywords: Streaming potential, zeta potential, fractal, porous media.
Keywords:
Streaming potential; zeta potential; Fractal; Porous media
References
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[3] M. Haartsen, S. R. Pride, Journal of Geophysical Research 102 (1997) 24745–24769.
[4] S. Garambois, M. Dietrich, Journal of Geophysical Research: Solid Earth 107 (2002).
[5] W. Guan, H. Hu, Journal of Computational Physics 227 (2008) 5633–5648.
[6] B. Wurmstich, F. D. Morgan, Geophysics 59 (1994) 46–56.
[7] K. Titov, A. Revil, P. Konosavsky, S. Straface, S. Troisi, Geophysical Journal International 162 (2005) 641–650.
[8] R. F. Corwin, D. B. Hoover, Geophysics 44 (1979) 226–245.
[9] G. Mauri, G. Williams-Jones, G. Saracco, Journal of Volcanology and Geothermal Research 191 (2010) 233–244.
[10] P. Martinez-Pagan, A. Jardani, A. Revil, A. Haas, GEOPHYSICS 75 (2010) WA17–WA25.
[11] V. Naudet, A. Revil, J.-Y. Bottero, P. Bgassat, Geophysical Research Letters 30 (2003).
[12] J. H. Saunders, M. D. Jackson, C. C. Pain, Geophysics 73(5) (2008) E165–E180.
[13] H. Mizutani, T. Ishido, T. Yokokura, S. Ohnishi, Geophys. Res. Lett. 3 (1976).
[14] M. Trique, P. Richon, F. Perrier, J. Avouac, J.C.Sabroux, Nature (1999) 137–141.
[15] B. B. Mandelbrot, The Fractal Geometry of Nature, W.H. Freeman, New York, 1982.
[16] J. Feder, A. Aharony, Fractals in Physics, North Holland, Amsterdam, 1989.
[17] P. Xu, Fractals 23 (2015) 1530001 (11 pages).
[18] B. Yu, P. Cheng, International Journal of Heat and Mass Transfer 45 (2002) 2983–2993.
[19] J. C. Cai, X. Y. Hu, D. C. Standnes, L. J. You, Colloids and Surfaces, A: Physicocemical and Engineering Aspects 414 (2012) 228–233.
[20] J. C. Cai, L. J. You, X. Y. Hu, J. Wang, R. H. Peng, International Journal of Modern Physics C 23 (2012) DOI: 10.1142/S0129183112500544.
[21] M. Liang, S. Yang, B. Yu, Journal of Electrostatics 72 (2014).
[22] M. Liang, S. Yang, T. Miao, B. Yu, Chemical Engineering Science 127 (2015).
[23] L. D. Thanh, P. V. Do, N. V. Nghia, N. X. Ca, Geophysical Prospecting 66 (2018) 753–766.
[24] W. R. Sill, Geophysics 48 (1983) 76–86.
[25] F. D. Morgan, E. R. Williams, T. R. Madden, Journal of Geophysical Research 94 (1989) 12.449–12.461.
[26] L. Jouniaux, T. Ishido, International Journal of Geophysics 2012, Article ID 286107 (2012) 16 pages, doi:10.1155/2012/286107.
[27] P. W. J. Glover, N. Dery, Geophysics 75 (2010) F225–F241.
[28] T. Ishido, H. Mizutani, Journal of Geophysical Research 86 (1981) 1763–1775.
[29] A. Revil, L. M. Cathles III, P. D. Manhardt, Water Resources Research 3 (1999) 651–662.
[30] L. Guarracino, D. Jougnot, Journal of Geophysical Research: Solid Earth 123 (2018) 52–65.
[31] C. Rice, R. Whitehead, J. Phys. Chem. 69 (1965) 4017–4024.
[32] T. Paillat, E. Moreau, P.O.Grimaud, G. Touchard, IEEE Transactions on Dielectrics and Electrical Insulation 7 (2000) 693–704.
[33] R. J. Hunter, Zeta Potential in Colloid Science, Academic, New York, 1981.
[34] J. Israelachvili, Intermolecular and Surface Forces, Academic Press, 1992.
[35] X. Hu, S. Hu, F. Jin, S. Huang, Physics of Petroleum Reservoirs, Springer-Verlag Berlin Heidelberg, 2017.
[36] Z. Bassiouni, Theory, Measurement, and Interpretation of Well Logs, Henry L. Doherty Memorial Fund of AIME, Society of Petroleum Engineers, 1994.
[37] M. M. I. Abaza, Streaming Current and Streaming Potential Induced by Water Flow Through Porous Media, Ph.D. thesis, Utah State University, 1996.
[38] K. S. Birdi, Handbook of Surface and Colloid Chemistry, Third Edition, CRC Press, 2008.
[39] J. Wang, H. Hu, W. Guan, H. Li, Geophysical Journal International 201 (2015) 869–877.
[40] D. R. Lide, CRC Handbook of Chemistry and Physics, CRC Press, 2004.
[41] P. N. Sen, P. A. Goode, Geophysics 57 (1992) 89–96.
[42] E. Walker, P. W. J. Glover, J. Ruel, Journal of Geophysical Research. Solid Earth 119 (2014) 957–970.
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[44] A. Revil, P. W. J. Glover, Geophysical Research Letters 25 (1998) 691–694.
[45] L. Jouniaux, J. Pozzi, Geophysical Research Letters 22 (1995) 485–488.
[46] K. Bjorlykke, Petroleum Geoscience From Sedimentary Environments to Rock Physics, Springer, Berlin, Heidelberg, 2010.
[47] D. L. Johnson, J. Koplik, L. M. Schwartz, Phys. Rev. Lett. 57 (1986) 2564–2567.
[48] A. Boleve, A. Crespy, A. Revil, F. Janod, J. L. Mattiuzzo, Journal of Geophysical Research B08204 (2007).
[49] P. Sen, C. Scala, M. H. Cohen, Journal of the Soil Mechanics and foundations Division 46 (1981) 781–795.