ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
Prev
Next
|
|
|
A fractal approach to low velocity non-Darcy flow in a low permeability porous medium |
Cai Jian-Chao (蔡建超) |
Institute of Geophysics and Geomatics, Key Laboratory of Tectonics and Petroleum Resources of Ministryof Education, China University of Geosciences, Wuhan 430074, China |
|
|
Abstract In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient (TPG) is also obtained. It is notable that the TPG (J) and permeability (K) of the porous medium analytically exhibit the scaling behavior J ~ K-DT/(1 + DT), where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.
|
Received: 11 June 2013
Revised: 05 September 2013
Accepted manuscript online:
|
PACS:
|
47.50.-d
|
(Non-Newtonian fluid flows)
|
|
05.45.Df
|
(Fractals)
|
|
47.15.-x
|
(Laminar flows)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 41102080), the Fundamental Research Funds for the Central Universities, China (Grant Nos. CUG130404 and CUG130103), the Fund from the Key Laboratory of Tectonics and Petroleum Resources of Ministry of Education, China University of Geosciences (Wuhan), China (Grant No. TPR-2013-18). |
Corresponding Authors:
Cai Jian-Chao
E-mail: caijc@cug.edu.cn
|
About author: 47.50.-d; 05.45.Df; 47.15.-x |
Cite this article:
Cai Jian-Chao (蔡建超) A fractal approach to low velocity non-Darcy flow in a low permeability porous medium 2014 Chin. Phys. B 23 044701
|
[1] |
Wang X H, Liu Z F, Wu Q S and Li B 2002 Physica A 311 320
|
[2] |
Dehghanpour H, Aminzadeh B, Mirzaei M and DiCarlo D A 2011 Phys. Rev. E 83 065302
|
[3] |
Mirzaei-Paiaman A, Masihi M and Standnes D C 2011 Transp. Porous Media 89 49
|
[4] |
Cheng C L, Kang M, Perfect E, Voisin S, Horita J, Bilheux H Z, Warren J M, Jacobson D L and Hussey D S 2012 Soil Sci. Soc. Am. J. 76 1184
|
[5] |
Xiao B Q, Fan J T and Ding F 2012 Energy Fuels 26 6971
|
[6] |
Masoodi R and Pillai K M 2012 J. Porous Media 15 775
|
[7] |
Dou Z and Zhou Z F 2013 Int. J. Heat Fluid Flow 42 23
|
[8] |
Cheng C L, Gragg M J, Perfect E, White M D, Lemiszki P J and McKay L D 2013 Int. J. Greenh. Gas Con. 18 277
|
[9] |
Kececioglu I and Jiang Y 1994 J. Fluids Eng. 116 164
|
[10] |
He N, Reynolds A C and Oliver D S 1997 SPE J. 2 312
|
[11] |
Prada A and Civan F 1999 J. Pet. Sci. Eng. 22 237
|
[12] |
Zhu W, Song H, Huang X, Liu X, He D and Ran Q 2011 Energy Fuels 25 1111
|
[13] |
Zeng Z and Grigg R 2006 Transp. Porous Media 63 57
|
[14] |
Wang S, Huang Y and Civan F 2006 J. Pet. Sci. Eng. 50 83
|
[15] |
Swartzendruber D 1962 J. Geophys. Res. 67 5205
|
[16] |
Derjaguin B and Churayev N 1971 J. Colloid Interface Sci. 36 415
|
[17] |
Chai Z, Shi B, Guo Z and Rong F 2011 J. Non-Newt. Fluid Mech. 166 332
|
[18] |
Liu W, Yao J and Wang Y 2012 Int. J. Heat Mass Transfer 55 6017
|
[19] |
Wang X, Thauvin F and Mohanty K 1999 Chem. Eng. Sci. 54 1859
|
[20] |
Song F Q, Jiang R J and Li B S 2007 Chin. Phys. Lett. 24 1995
|
[21] |
Horn R, Smith D and Haller W 1989 Chem. Phys. Lett. 162 404
|
[22] |
Derjaguin B, Zorin Z, Rabinovich Y I and Churaev N 1974 J. Colloid Interface Sci. 46 437
|
[23] |
Wu Y S, Pruess K and Witherspoon P 1991 Transp. Porous Media 6 115
|
[24] |
Hammad K J and Vradis G C 1996 Int. J. Heat Mass Transfer 39 1555
|
[25] |
Yun M J, Yu B M and Cai J C 2008 Int. J. Heat Mass Transfer 51 1402
|
[26] |
Mirzaei-Paiaman A, Masihi M and Standnes D C 2011 Energy Fuels 25 3053
|
[27] |
van Engelen G P, Kaul C L, Vos B and Aranha H P 1981 J. Pet. Technol. 33 2539
|
[28] |
Masoodi R, Tan H and Pillai K M 2012 AIChE J. 58 2536
|
[29] |
Wang X H and Liu Z F 2004 Physica A 337 384
|
[30] |
Wen Z, Huang G H and Zhan H B 2008 Adv. Water Res. 31 1754
|
[31] |
Wen Z, Liu K and Chen X 2013 J. Hydrol. 498 124
|
[32] |
Mandelbrot B B 1982 The Fractal Geometry of Nature (New York: W. H. Freeman)
|
[33] |
Perfect E and Blevins R L 1997 Soil. Sci. Soc. Am. J. 61 896
|
[34] |
Xiao B Q, Yu B M, Wang Z C and Chen L X 2009 Phys. Lett. A 373 4178
|
[35] |
Atzeni C, Pia G and Sanna U 2010 Constr. Build. Mater. 24 1843
|
[36] |
Cai J C, Yu B M, Zou M Q and Luo L 2010 Energy Fuels 24 1860
|
[37] |
Xiao B Q 2013 Chin. Phys. B 22 014402
|
[38] |
Yu B M and Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
|
[39] |
Jiang X B, Hou B H, Wang J K, Yin Q X and Zhang M J 2011 Ind. Eng. Chem. Res. 50 10229
|
[40] |
Jiang X B, Wang J K, Hou B H and He H G 2013 Ind. Eng. Chem. Res. 52 15685
|
[41] |
Cai J C, Hu X Y, Standnes D C and You L J 2012 Colloids Surf. A 414 228
|
[42] |
Xiao B Q, Yang Y and Chen L X 2013 Powder Technol. 239 409
|
[43] |
Yu B M and Li J H 2001 Fractals 9 365
|
[44] |
Feng Y J, Yu B M, Zou M Q and Zhang D M 2004 J. Phys. D: Appl. Phys. 37 3030
|
[45] |
Cai J C, Yu B M, Zou M Q and Mei M F 2010 Chem. Eng. Sci. 65 5178
|
[46] |
Xiao B Q, Gao S H and Chen L X 2010 Fractals 18 409
|
[47] |
Cai J C and Yu B M 2010 Fractals 18 417
|
[48] |
Cai J C and Yu B M 2011 Transp. Porous Media 89 251
|
[49] |
Bird R B, Stewart W E and Lightfoot E N 1960 Transport Phenomena (New York: Wiley)
|
[50] |
Wang Y M, Pang Y M, Yang S F and Chen H L 2005 Geological J. China Universities 11 617 (in Chinese)
|
[51] |
Yu B M 2005 Chin. Phys. Lett. 22 158
|
[52] |
Yun M J, Yu B M, Zhang B and Huang M T 2005 Chin. Phys. Lett. 22 1464
|
[53] |
Kou J L, Tang X M, Zhang H Y, Lu H J, Wu F M, Xu Y S and Dong Y S 2012 Chin. Phys. B 21 044701
|
[54] |
Li Z X, Han H B, Cheng L S, Zhang M L and Shi C E 2004 Pet. Explor. Dev. 30 109 (in Chinese)
|
[55] |
He X K 2007 Pet. Geology Eng. 21 80 (in Chinese)
|
[56] |
Kang M, Perfect E, Cheng C, Bilheux H, Gragg M, Wright D, Lamanna J, Horita J and Warren J 2013 Vadose Zone J. 12 No. 3
|
[57] |
Cai J C and Sun S Y 2013 Int. J. Mod. Phys. C 24 1350056
|
[58] |
Dehghanpour H, Lan Q, Saeed Y, Fei H and Qi Z 2013 Energy Fuels 27 3039
|
[59] |
Mirzaei-Paiaman A and Masihi M 2013 Energy Fuels 27 4662
|
[60] |
Mirzaei M and DiCarlo D 2013 Transp. Porous Media 99 37
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|