Microscopic mechanism of periodical electroosmosis in reservoir rocks

doi:10.1007/s10483-012-1621-9

Abstract

Abstract: Based on the electric double layer (EDL) theory and the momentum equation governing the electroosmosis flow, this paper presents an analytical solution to the peri- odical electroosmosis with a parallel straight capillary bundle model of reservoir rocks to reveal the microscopic mechanism of the electroosmotic flows in rocks. The theory shows that both the frequency dispersion characteristics of the macroscopic electroosmotic Darcy velocity in unsealed rocks and the electroosmotic pressure coefficient in sealed rocks de- pend on the porosity and electrochemical properties of reservoir rocks. The mathematical simulation indicates that the distribution of the periodical electroosmotic velocity is wave- like in the rock pore. The greater the porosity is, the greater electroosmotic the Darcy velocity and the smaller electroosmotic pressure coefficient are generated. The module values of the electroosmotic Darcy velocity and the electroosmotic pressure coefficient increase with the decreasing solution concentration or the increasing cation exchange ca- pacity without affecting the phase of the electroosmotic Darcy velocity.

Key words: reservoir rock, periodical electroosmosis, microscopic mechanism, frequency dispersion characteristic, mathematical simulation, torsion of cracked cylinder, strongly singular integral equation, star-type crack, torsional rigidity, stress intensity factor

2010 MSC Number:

O361
P631

Hui CHEN;Ji-teng GUAN;Wen-jing FANG . Microscopic mechanism of periodical electroosmosis in reservoir rocks. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1275-1286.

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References

[1] Lin, J. Z., Bao, F. B., Zhang, K., and Wang, R. J. The Theory and Application of Microflows andNanoflows (in Chinese), Science Press, Beijing, 193-196 (2010)
[2] You, H. Y. The Electroosmosis and Application in Chromatography (in Chinese), Science Press,Beijing, 1-5 (2010)
[3] Wu, J. K., Gong, L., Chen, B., and Cao, K. Advances in the research of electroosmotic flows inmicro/nanofluidic systems. Advance in Mechanics, 39(5), 555-565 (2009)
[4] Hayat, T., Afzal, S., and Hendi, A. Exact solution of electroosmotic flow in generalized Burg-ers fluid. Applied Mathematics and Mechanics (English Edition), 32(9), 1119-1126 (2011) DOI10.1007/s10483-011-1486-6
[5] Philip, M. R. and Frank, D. M. Frequency-dependent electroosmosis. Journal of Colloid andInterface Science, 254(2), 372-383 (2002)
[6] James, G. B. Electrokinetic effects and fluid permeability. Physica B, 338, 270-273 (2003)
[7] David, B. P. and Po-Zen, W. Low-frequency AC electrokinetics. Colloid and Surfaces A: Physic-ochemical and Engineering Aspects, 159, 283-292 (1999)
[8] Reuss, F. F. Charge-induced flow. Proceedings of the Imperial Society of Naturalists of Moscow,3, 327-340 (1809)
[9] Rice, C. L. and Whitehead, R. Electrokinetic flow in a narrow cylindrical capillary. The Journalof Physical Chemistry, 69(11), 4017-4023 (1965)
[10] Pride, S. R. Governing equations for the coupled electromagnetics and acoustics of porous media.Physical Review B, 50(21), 15678-15696 (1994)
[11] Dutta, P. and Beskok, A. Analytical solution of time periodic electroosmotic flows: analogies toStokes second problem. Analytical Chemistry, 73(21), 5097-5102 (2001)
[12] James, P. G. Electroosmotic flows with random zeta potential. Journal of Colloid and InterfaceScience, 249, 217-226 (2002)
[13] Kang, Y., Yang, C., and Huang, X. Y. AC electroosmosis in microchannels packed with a porousmedium. Journal of Micromechanics and Microengineering, 14, 1249-1257 (2004)
[14] Wang, R. J., Lin, J. Z., and Li, Z. H. Study on the impacting factors of transverse diffusion in themicro-channels of T-sensors. Journal of Nanoscience and Nanotechnology, 5(8), 1281-1286 (2005)
[15] Wang, R. J. and Lin, J. Z. Numerical analysis on a passive chaotic micromixer with helicalmicrochannel. Journal of Nanoscience and Nanotechnology, 6(1), 190-194 (2006)
[16] Zhang, K., Lin, J. Z., and Li, Z. H. Research on diffusion in the microchannel flow driven byelectroosmosis. Applied Mathematics and Mechanics (English Edition), 27(5), 575-582 (2006)DOI 10.1007/s10483-006-0502-1
[17] Wang, R. J., Lin, J. Z., and Li, Z. H. Analysis of electroosmotic flow characteristics at joint ofcapillaries with step change in -potential and dimension. Biomedical Microdevices, 7(2), 131-135(2005)
[18] Li, Z. H., Lin, J. Z., and Nie, D. M. New approach to minimize dispersion induced by turnin capillary electrophersis channel flows. Applied Mathematics and Mechanics (English Edition),26(6), 685-690 (2005) DOI 10.1007/BF02465417
[19] Wu, J. K. andWang, X. M. Flow behavior of periodical electroosmosis in microchannel for biochips(in Chinese). Chinese Journal of Theoretical Applied Mechanics, 38(3), 309-315 (2006)
[20] Gong, L., Wu, J. K., Wang, L., and Chao, K. Periodical streaming potential and electro-viscouseffects in microchannel flow. Applied Mathematics and Mechanics (English Edition), 29(6), 715-724 (2008) DOI 10.1007/s10438-008-0603-7
[21] Qin, J. S. and Li, A. F. Physical Properties of Petroleum Reservoir (in Chinese), China Universityof Petroleum Press, Dongying, 181 (2006)
[22] Guan, J. T. and Fang, W. J. Coupling relationship for electrochemical hydrodynamics in water-saturated sandy soil and clay soil (in Chinese). Chinese Journal of Geotechnical Engineering,22(6), 664-667 (2000)
[23] Shaliro, A. Rock’s Physicochemical Property and Its Practical Application to Geophysics in OilField (in Chinese) (translated by Jiang, E. C.), Petroleum Industry Press, Beijing, 3-10 (1987)
[24] Guan, J. T., Wang, Q., Fan, Y. H., Fang, W. J., and Yu, H. Study on the mechanisms of elec-trochemical logging response in shaly sandstone based on capillary model (in Chinese). ChineseJournal of Geophysics, 53(1), 214-223 (2010)