单毛细管中赫切尔-巴尔克莱流体的分形分析

员美娟; 郑伟; 李云宝; 李钰

doi:10.7498/aps.61.164701

摘要

运用分形理论给出了非牛顿流体中的赫切尔-巴尔克莱流体在单毛细管中的渗流分形模型. 此模型将赫切尔-巴尔克莱流体的流量、流速、启动压力梯度和有效渗透率与流体的流变特性、毛细管的结构参数联系起来, 并且不含经验常数, 每个参数都具有明确的物理意义, 所得分形模型更能体现出赫切尔-巴尔克莱流体流动的内在物理机理.

关键词:

A fractal model for Herschel-Bulkley fluid in a capillary is proposed based on the fractal theory. The proposed model relates flow rate, velocity, starting pressure gradient and effective permeability to the rheological characteristics of fluid and the structural parameters of capillary, and all parameters in the proposed expressions have clear physical meanings. The analytical expressions reveal the physical principle for Herschel-Bulkley fluid flow in a capillary.

Keywords:

作者及机构信息

1.
武汉科技大学冶金工业过程系统科学湖北省重点实验室, 武汉 430081;

2.
西南石油大学油气藏地质及开发工程国家重点实验室, 成都 610500;

3.
中国科学院测量与地球物理研究所大地测量与地球动力学国家重点实验室, 武汉 430077

基金项目: 中国石油大学油气资源与探测国家重点实验室开放课题基金(批准号：PRP/open-1206); 西南石油大学油气藏地质及开发工程国家重点实验室开放基金(批准号：PLN1113); 冶金矿产资源高效利用与造块湖北省重点实验室开放基金、国家自然科学基金(批准号：41102080)和武汉科技大学绿色制造与节能减排科技研究中心开放基金 (批准号：B1219)资助的课题.

Authors and contacts

1.
Key Laboratory of Systems Science in Metallurgical Process of Hubei Province, Wuhan University of Science and Technology, Wuhan 430081, China;

2.
State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China;

3.
State Key Laboratory of Geodesy and Earth's Dynamics, Institute of Geodesy and Geophysics, Chinese Academy of Sciences, Wuhan 430077, China

Funds: Project supported by the Foundation of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, China (Grant No. PRP/open-1206), the Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, China (Grant No. PLN1113), the Foundation of Hubei Key Laboratory for Efficient Utilization and Agglomeration of Metallurgic Mineral Resources, the National Natural Science Foundation of China (Grant No. 41102080), and the Open Fund of Research Center of Green Manufacturing and Energy-Saving and Emission Reduction Technology in Wuhan University of Science and Technology, China (Grant No. B1219).

参考文献

[1]	Herschel W H, Bulkley R 1926 Colloid. Polym. Sci. 39 291
[2]	Govier G W, Aziz K 1972 The Flow of Complex Mixtures in Pipes (New York: Litton) p143
[3]	Balhoff M T, Thompson K E 2004 AICHE J. 50 3034
[4]	Balhoff M T, Thompson K E 2006 Chem. Eng. Sci. 61 698
[5]	Xu Y S, Wu F M, Chen Y Y, Xu X Z 2003 Chin. Phys. 12 621
[6]	Yuan Y, Shi S H, Luo M K 2011 Chin. Phys. B 20 040509
[7]	Xu Y S, Xu X Z 2002 Chin. Phys. 11 583
[8]	Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[9]	Cai J C, Yu B M, Zou M Q, Mei M F 2010 Chem. Eng. Sci. 65 5178
[10]	Zhang C B, Chen Y P, Shi M H, Fu P P, Wu J F 2009 Acta Phys. Sin. 58 7050 (in Chinese) [张程宾, 陈永平, 施明恒, 付盼盼, 吴嘉峰 2009 58 7050]
[11]	Cai J C, Yu B M, Zou M Q, Luo L 2010 Energy Fuels 24 1860
[12]	Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese) [姜泽辉, 赵海发, 郑瑞华 2009 58 7579]
[13]	Hua S C, Wang H G, Wang L Y, Zhang W, Liu G 2008 Acta Phys. Sin. 57 1241 (in Chinese) [华邵春, 王汉功, 汪刘应, 张武, 刘顾 2008 57 1241]
[14]	Cai J C, Yu B M 2010 Fractals 18 417
[15]	Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[16]	Shen J, Wang Y, Wu X 1996 Acta Phys. Sin. 45 1501 (in Chinese) [沈军, 王钰, 吴翔1996 451501]
[17]	Yu B M, Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
[18]	Yun M J, Yu B M, Zheng W, Yuan J 2011 Acta Phys. Sin. 60 024703 (in Chinese) [员美娟, 郁伯铭, 郑伟, 袁洁 2011 60 024703]
[19]	Wheatcraft S W, Tyler S W 1988 Water Res. Researches 24 566
[20]	Yu B M 2005 Chin. Phys. Lett. 22 158
[21]	Cai J C, Yu B M, Mei M F, Luo L 2010 Chin. Phys. Lett. 27 054701
[22]	Yun M J, Yu B M, Xu P, Cai J C 2008 Chin. Phys. Lett. 25 616
[23]	Cai J C, Yu B M 2011 Transp. Porous Media 89 251
[24]	Borghesani A F 1988 Encyclopedia of Fluid Mechanics (Houston: Gulf) p89
[25]	Deshpande N S, Barigou M 2001 Chem. Eng. Sci. 56 3845
[26]	Cavatorta O N, Tonini R D 1987 Int. Commun. Heat Mass 14 359
[27]	Yu B M, Li J H 2004 Chin. Phys. Lett. 21 1569

施引文献

[1]	Herschel W H, Bulkley R 1926 Colloid. Polym. Sci. 39 291
[2]	Govier G W, Aziz K 1972 The Flow of Complex Mixtures in Pipes (New York: Litton) p143
[3]	Balhoff M T, Thompson K E 2004 AICHE J. 50 3034
[4]	Balhoff M T, Thompson K E 2006 Chem. Eng. Sci. 61 698
[5]	Xu Y S, Wu F M, Chen Y Y, Xu X Z 2003 Chin. Phys. 12 621
[6]	Yuan Y, Shi S H, Luo M K 2011 Chin. Phys. B 20 040509
[7]	Xu Y S, Xu X Z 2002 Chin. Phys. 11 583
[8]	Wu B Z, Xu Y S, Liu Y, Huang G X 2005 Chin. Phys. 14 2046
[9]	Cai J C, Yu B M, Zou M Q, Mei M F 2010 Chem. Eng. Sci. 65 5178
[10]	Zhang C B, Chen Y P, Shi M H, Fu P P, Wu J F 2009 Acta Phys. Sin. 58 7050 (in Chinese) [张程宾, 陈永平, 施明恒, 付盼盼, 吴嘉峰 2009 58 7050]
[11]	Cai J C, Yu B M, Zou M Q, Luo L 2010 Energy Fuels 24 1860
[12]	Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese) [姜泽辉, 赵海发, 郑瑞华 2009 58 7579]
[13]	Hua S C, Wang H G, Wang L Y, Zhang W, Liu G 2008 Acta Phys. Sin. 57 1241 (in Chinese) [华邵春, 王汉功, 汪刘应, 张武, 刘顾 2008 57 1241]
[14]	Cai J C, Yu B M 2010 Fractals 18 417
[15]	Katz A J, Thompson A H 1985 Phys. Rev. Lett. 54 1325
[16]	Shen J, Wang Y, Wu X 1996 Acta Phys. Sin. 45 1501 (in Chinese) [沈军, 王钰, 吴翔1996 451501]
[17]	Yu B M, Cheng P 2002 Int. J. Heat Mass Transfer 45 2983
[18]	Yun M J, Yu B M, Zheng W, Yuan J 2011 Acta Phys. Sin. 60 024703 (in Chinese) [员美娟, 郁伯铭, 郑伟, 袁洁 2011 60 024703]
[19]	Wheatcraft S W, Tyler S W 1988 Water Res. Researches 24 566
[20]	Yu B M 2005 Chin. Phys. Lett. 22 158
[21]	Cai J C, Yu B M, Mei M F, Luo L 2010 Chin. Phys. Lett. 27 054701
[22]	Yun M J, Yu B M, Xu P, Cai J C 2008 Chin. Phys. Lett. 25 616
[23]	Cai J C, Yu B M 2011 Transp. Porous Media 89 251
[24]	Borghesani A F 1988 Encyclopedia of Fluid Mechanics (Houston: Gulf) p89
[25]	Deshpande N S, Barigou M 2001 Chem. Eng. Sci. 56 3845
[26]	Cavatorta O N, Tonini R D 1987 Int. Commun. Heat Mass 14 359
[27]	Yu B M, Li J H 2004 Chin. Phys. Lett. 21 1569

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