Microscopic mechanism of periodical electroosmosis in reservoir rocks

doi:10.1007/s10483-012-1621-9

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (10): 1275-1286.doi: https://doi.org/10.1007/s10483-012-1621-9

Microscopic mechanism of periodical electroosmosis in reservoir rocks

陈辉, 关继腾, 房文静

Faculty of Science, China University of Petroleum, Qingdao 266555, Shandong Province, P. R. China

收稿日期:2011-11-21 修回日期:2012-04-09 出版日期:2012-10-10 发布日期:2012-10-10
通讯作者: Ji-teng GUAN, Professor, E-mail: guanjt@upc.edu.cn E-mail:guanjt@upc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 41174101) and the Natural Science Foundation of Shandong Province of China (No. ZR2011DM002)

Microscopic mechanism of periodical electroosmosis in reservoir rocks

Hui CHEN, Ji-teng GUAN, Wen-jing FANG

Faculty of Science, China University of Petroleum, Qingdao 266555, Shandong Province, P. R. China

Received:2011-11-21 Revised:2012-04-09 Online:2012-10-10 Published:2012-10-10
Supported by:
Project supported by the National Natural Science Foundation of China (No. 41174101) and the Natural Science Foundation of Shandong Province of China (No. ZR2011DM002)

摘要/Abstract

摘要： 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.

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

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

中图分类号:

O361
P631

陈辉;关继腾;房文静. Microscopic mechanism of periodical electroosmosis in reservoir rocks[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(10): 1275-1286.

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

参考文献

[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)

Microscopic mechanism of periodical electroosmosis in reservoir rocks

Microscopic mechanism of periodical electroosmosis in reservoir rocks

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Huayang DANG, Dongpei QI, Minghao ZHAO, Cuiying FAN, C.S. LU. Thermal-induced interfacial behavior of a thin one-dimensional hexagonal quasicrystal film[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 841-856.
[2]	Yansong WANG, Baolin WANG, Youjiang CUI, Kaifa WANG. Anti-plane pull-out of a rigid line inclusion from an elastic medium[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 809-822.
[3]	Chenxue JIA, Zihao WANG, Donghui ZHANG, Taihua ZHANG, Xianhong MENG. Fracture of films caused by uniaxial tensions: a numerical model[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2093-2108.
[4]	Juan PENG, Dengke LI, Zaixing HUANG, Guangjian PENG, Peijian CHEN, Shaohua CHEN. Interfacial behavior of a thermoelectric film bonded to a graded substrate[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1853-1870.
[5]	Xin ZHANG, Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Three-dimensional interfacial fracture analysis of a one-dimensional hexagonal quasicrystal coating[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1901-1920.
[6]	Minghao ZHAO, Cuiying FAN, C. S. LU, Huayang DANG. Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(11): 1633-1648.
[7]	Xing ZHAO, Zhenghua QIAN, Jinxi LIU, Cunfa GAO. Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 139-156.
[8]	M. KARIMI, A. GHASSEMI, A. ATRIAN, M. VAHABI. Compensation of stress intensity factors in hollow cylinders containing several cracks under torsion by electro-elastic coating[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(9): 1335-1360.
[9]	M. HAJIMOHAMADI, R. GHAJAR. An analytical solution for the stress field and stress intensity factor in an infinite plane containing an elliptical hole with two unequal aligned cracks[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1103-1118.
[10]	M. FAKOOR, S. M. N. GHOREISHI. Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(11): 1565-1578.
[11]	S. SINGH, K. SHARMA, R. R. BHARGAVA. Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(11): 1517-1532.
[12]	Tiemei YANG, Weiyang YANG, Junlin LI, Xuexia ZHANG. Analysis on non-oscillatory singularity behaviors of mode Ⅱ interface crack tip in orthotropic bimaterial[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(9): 1177-1192.
[13]	H. TEIMOORI, R. T. FAAL, R. DAS. Saint-Venant torsion analysis of bars with rectangular cross-section and effective coating layers[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(2): 237-252.
[14]	Hualiang WAN, Qizhi WANG, Xing ZHANG. Closed form solution of stress intensity factors for cracks emanating from surface semi-spherical cavity in finite body with energy release rate method[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1689-1706.
[15]	M. GHADIRI A. R. SHAHANI. Analysis of bonded anisotropic wedges with interface crack under anti-plane shear loading[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(5): 637-654.