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Detecting unstable periodic orbits from oil-gas-water three-phase slug flows

Zhao Jun-Ying Jin Ning-De Gao Zhong-Ke

Detecting unstable periodic orbits from oil-gas-water three-phase slug flows

Zhao Jun-Ying, Jin Ning-De, Gao Zhong-Ke
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  • We use the close return method combined with adaptive threshold selection to detect the unstable periodic orbits from the signals measured from experimental oil-gas-water three-phase slug flows, and find that the period of the emulsion type slug flow is longer than that of oil in water type slug flow. Especially, the orbit of oil in water type slug flow is basically composed of one big loop and one small loop, and the emulsion type slug flow orbit is composed of two big smooth loops. In addition, we employ the method of adaptive optimal kernel time-frequency representation to investigate the flow behaviors of two typical oil-gas-water three-phase slug flows and indicate that the energy of the oil in water slug flow exhibits a dispersed distribution and its frequency spectrum consists of various components distributes in a wide range. In contrast, the energy of emulsion type slug flow is distributed in a rather concentrated region and the high frequency component in its frequency spectrum is much less than that of the oil in water slug flow. These results are well consistent with the detected structure of unstable periodic orbit, further suggesting that the fluid mechanism underlying oil in water type slug flow is more complicated than that of the emulsion type slug flow.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41174109, 50974095, 61104148) and the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2011ZX05020-006).
    [1]

    Tek M R 1961 J. Pet. Tech. 13 1029

    [2]

    Shean A R 1976 M. S. Thesis (Cambridge:Massachusetts Institute of Technology)

    [3]

    Thorn R, Johansen G A, Hammer E A 1997 Meas. Sci. Technol. 8 691

    [4]

    Woods G S, Spedding P L, Watterson J K, Raghunathan R S 1998 Chem. Eng. Res. 76 571

    [5]

    Farrar B, Bruun H H 1996 Int. J. Multiphase Flow 22 733

    [6]

    Sun B, Wang E P, Zheng Y J 2011 Acta Phys. Sin. 60 014701 (in Chinese) [孙斌, 王二朋, 郑永军 2011 物理学报 60 014701]

    [7]

    Wu H J, Zhou F D, Wu Y Y 2001 Int. J. Multiphase Flow 27 459

    [8]

    Daw C S, Finney C E A, Vasudevan M, van Goor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308

    [9]

    Zhou Y L, Li H W, He Q Y 2008 Chin. Soc. Elec. Eng. 28 49 (in Chinese) [周云龙, 李洪伟, 何强勇 2008 中国电机工程学报 28 49]

    [10]

    Fan L T, Neogi D, Yashima M, Nassar R 1990 Aiche J. 36 1529

    [11]

    Wang Z Y, Jin N D, Gao Z K, Zong Y B, Wang T 2010 Chem. Eng. Sci. 65 5226

    [12]

    Dukler A E, Hubbard M G 1975 Ind. Eng. Chem. Fundam. 14 337

    [13]

    Taitel Y, Dukler A E 1977 Int. J. Multiphase Flow 3 585

    [14]

    Guet S, Decarre S, Henriot V, Liné A 2006 Chem. Eng. Sci. 61 7336

    [15]

    Wang X, Guo L J, Zhang X M 2006 Chin. J. Chem. Eng. 14 626

    [16]

    Taitel Y, Barnea D 1990 Chem. Eng. Sci. 45 1199

    [17]

    van Hout R, Barnea D, Shemer L 2001 Int. J. Multiphase Flow 27 1579

    [18]

    Yun J X, Lei Q, Zhang S H, Shen S C, Yao K J 2010 Chem. Eng. Sci. 65 5256

    [19]

    Liu Y P, Zhang H, Wang J 2008 J. Shanghai Jiaotong Univ. 42 1247 (in Chinese) [刘夷平, 张华, 王经 2008 上海交通大学学报 42 1247]

    [20]

    Taha T, Cui Z F 2006 Chem. Eng. Sci. 61 665

    [21]

    Gao S, Li W, You Y X, Hu T Q 2012 Acta Phys. Sin. 61 104701 (in Chinese) [高嵩, 李巍, 尤云祥, 胡天群 2012 物理学报 61 104701]

    [22]

    Sæther G, Bendiksen K, Mller J, Froland E 1990 Int. J. Multiphase Flow 16 1117

    [23]

    He L M, Zhao Q J, Chen Z Y 2003 Proceeding of the CSEE 23 189 (in Chinese) [何利民, 赵庆军, 陆振瑜 2003 中国电机工程学报 23 189]

    [24]

    Auerbach D, Cvitanovic P, Eckmann J P, Gunaratne G, Procaccia I 1987 Phys. Rev. Lett. 58 2387

    [25]

    Cvitanović P 1988 Phys. Rev. Lett. 61 2729

    [26]

    Badii R, Brun E, Finardi M, Flepp L, Holzner R, Parisi J, Reyl C, Simonet J 1994 Rev. Mod. Phys. 66 1389

    [27]

    Jin J X, Qiu S S, Xie L Y, Feng M K 2008 Acta Phys. Sin. 57 2743 (in Chinese) [晋建秀, 丘水生, 谢丽英, 冯明库 2008 物理学报 57 2743]

    [28]

    Grebogi C, Ott E, Yorke J A 1988 Phys. Rev. A 37 1711

    [29]

    Pei X, Moss F 1996 Nature 379 618

    [30]

    So P, Francis J T, Netoff T I, Gluckman B J, Schiff S J 1998 Biophys. J. 74 2776

    [31]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese) [谢勇, 徐健学, 康艳梅, 胡三觉, 段玉斌 2003 物理学报 52 1112]

    [32]

    Narayannan K, Govindan R B, Gopinathan M S 1998 Phys. Rev. E 57 4594

    [33]

    Zhang J, Luo X D, Nakamura T, Sun J F, Small M 2007 Phys. Rev. E 75 016218

    [34]

    Lathrop D P, Kostelich E J 1989 Phys. Rev. A 40 4028

    [35]

    Mindlin G B, Solari H G, Natiello M A, Gilmore R, Hou X J 1991 J. Nonlinear Sci. 1 147

    [36]

    Bi Q S 2010 Sci. China Tech. Sci. 53 748

    [37]

    Kazantsev E 1998 Nonlin. Processes Geophys. 5 193

    [38]

    Kazantsev E 2001 Nonlin. Processes Geophys. 8 281

    [39]

    Heagy J F, Carroll T L, Pecora L M 1995 Phys. Rev. E 52 1253

    [40]

    Long M, Qiu S S 2007 Chin. Phys. 16 2254

    [41]

    Socolar J E S, Sukow D W, Gauthier D J 1994 Phys. Rev. E 50 3245

    [42]

    Wu S H, Hao J H, Xu H B 2010 Chin. Phys. B 19 020509

    [43]

    Pei X, Dolan K, Moss F 1998 Chaos 8 853

    [44]

    Mindlin G, Gilmore R 1992 Physica D 58 229

    [45]

    Pierson D, Moss F 1995 Phys. Rev. Lett. 75 2124

    [46]

    So P, Ott E, Schiff S, Kaplan D T, Sauer T, Grebogi C 1996 Phys. Rev. Lett. 76 4705

    [47]

    So P, Ott E, Sauer T, Gluckman B J, Grebogi C, Schiff S 1997 Phys. Rev. E 55 5398

    [48]

    Buhl M, Kennel M B 2007 Chaos 17 033102

    [49]

    Gao Z K, Jin N D 2012 Nonlin. Anal.:Real World Appl. 13 947

    [50]

    Takens F 1981 Dynamical Systems and Turbulence (Berlin:Spring Verlag) 366

    [51]

    Dhamala M, Lai Y C, Kostelich E J 2000 Phys. Rev. E 61 6485

    [52]

    Hunt B R, Ott E 1996 Phys. Rev. E 54 328

    [53]

    Gao Z K, Jin N D 2012 Physica A 391 3005

    [54]

    Hervieua E, Seleghimb P 1998 Nucl. Eng. Design 184 421

    [55]

    Jana A K, Das G, Das P K 2006 Chem. Eng. Sci. 61 1500

    [56]

    Jones D L, Baraniuk R G 1995 IEEE Trans. Sign. Proc. 43 2361

    [57]

    Du M, Jin N D, Gao Z K, Wang Z Y, Zhai L S 2012 Int. J. Multiphase Flow 41 91

  • [1]

    Tek M R 1961 J. Pet. Tech. 13 1029

    [2]

    Shean A R 1976 M. S. Thesis (Cambridge:Massachusetts Institute of Technology)

    [3]

    Thorn R, Johansen G A, Hammer E A 1997 Meas. Sci. Technol. 8 691

    [4]

    Woods G S, Spedding P L, Watterson J K, Raghunathan R S 1998 Chem. Eng. Res. 76 571

    [5]

    Farrar B, Bruun H H 1996 Int. J. Multiphase Flow 22 733

    [6]

    Sun B, Wang E P, Zheng Y J 2011 Acta Phys. Sin. 60 014701 (in Chinese) [孙斌, 王二朋, 郑永军 2011 物理学报 60 014701]

    [7]

    Wu H J, Zhou F D, Wu Y Y 2001 Int. J. Multiphase Flow 27 459

    [8]

    Daw C S, Finney C E A, Vasudevan M, van Goor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308

    [9]

    Zhou Y L, Li H W, He Q Y 2008 Chin. Soc. Elec. Eng. 28 49 (in Chinese) [周云龙, 李洪伟, 何强勇 2008 中国电机工程学报 28 49]

    [10]

    Fan L T, Neogi D, Yashima M, Nassar R 1990 Aiche J. 36 1529

    [11]

    Wang Z Y, Jin N D, Gao Z K, Zong Y B, Wang T 2010 Chem. Eng. Sci. 65 5226

    [12]

    Dukler A E, Hubbard M G 1975 Ind. Eng. Chem. Fundam. 14 337

    [13]

    Taitel Y, Dukler A E 1977 Int. J. Multiphase Flow 3 585

    [14]

    Guet S, Decarre S, Henriot V, Liné A 2006 Chem. Eng. Sci. 61 7336

    [15]

    Wang X, Guo L J, Zhang X M 2006 Chin. J. Chem. Eng. 14 626

    [16]

    Taitel Y, Barnea D 1990 Chem. Eng. Sci. 45 1199

    [17]

    van Hout R, Barnea D, Shemer L 2001 Int. J. Multiphase Flow 27 1579

    [18]

    Yun J X, Lei Q, Zhang S H, Shen S C, Yao K J 2010 Chem. Eng. Sci. 65 5256

    [19]

    Liu Y P, Zhang H, Wang J 2008 J. Shanghai Jiaotong Univ. 42 1247 (in Chinese) [刘夷平, 张华, 王经 2008 上海交通大学学报 42 1247]

    [20]

    Taha T, Cui Z F 2006 Chem. Eng. Sci. 61 665

    [21]

    Gao S, Li W, You Y X, Hu T Q 2012 Acta Phys. Sin. 61 104701 (in Chinese) [高嵩, 李巍, 尤云祥, 胡天群 2012 物理学报 61 104701]

    [22]

    Sæther G, Bendiksen K, Mller J, Froland E 1990 Int. J. Multiphase Flow 16 1117

    [23]

    He L M, Zhao Q J, Chen Z Y 2003 Proceeding of the CSEE 23 189 (in Chinese) [何利民, 赵庆军, 陆振瑜 2003 中国电机工程学报 23 189]

    [24]

    Auerbach D, Cvitanovic P, Eckmann J P, Gunaratne G, Procaccia I 1987 Phys. Rev. Lett. 58 2387

    [25]

    Cvitanović P 1988 Phys. Rev. Lett. 61 2729

    [26]

    Badii R, Brun E, Finardi M, Flepp L, Holzner R, Parisi J, Reyl C, Simonet J 1994 Rev. Mod. Phys. 66 1389

    [27]

    Jin J X, Qiu S S, Xie L Y, Feng M K 2008 Acta Phys. Sin. 57 2743 (in Chinese) [晋建秀, 丘水生, 谢丽英, 冯明库 2008 物理学报 57 2743]

    [28]

    Grebogi C, Ott E, Yorke J A 1988 Phys. Rev. A 37 1711

    [29]

    Pei X, Moss F 1996 Nature 379 618

    [30]

    So P, Francis J T, Netoff T I, Gluckman B J, Schiff S J 1998 Biophys. J. 74 2776

    [31]

    Xie Y, Xu J X, Kang Y M, Hu S J, Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese) [谢勇, 徐健学, 康艳梅, 胡三觉, 段玉斌 2003 物理学报 52 1112]

    [32]

    Narayannan K, Govindan R B, Gopinathan M S 1998 Phys. Rev. E 57 4594

    [33]

    Zhang J, Luo X D, Nakamura T, Sun J F, Small M 2007 Phys. Rev. E 75 016218

    [34]

    Lathrop D P, Kostelich E J 1989 Phys. Rev. A 40 4028

    [35]

    Mindlin G B, Solari H G, Natiello M A, Gilmore R, Hou X J 1991 J. Nonlinear Sci. 1 147

    [36]

    Bi Q S 2010 Sci. China Tech. Sci. 53 748

    [37]

    Kazantsev E 1998 Nonlin. Processes Geophys. 5 193

    [38]

    Kazantsev E 2001 Nonlin. Processes Geophys. 8 281

    [39]

    Heagy J F, Carroll T L, Pecora L M 1995 Phys. Rev. E 52 1253

    [40]

    Long M, Qiu S S 2007 Chin. Phys. 16 2254

    [41]

    Socolar J E S, Sukow D W, Gauthier D J 1994 Phys. Rev. E 50 3245

    [42]

    Wu S H, Hao J H, Xu H B 2010 Chin. Phys. B 19 020509

    [43]

    Pei X, Dolan K, Moss F 1998 Chaos 8 853

    [44]

    Mindlin G, Gilmore R 1992 Physica D 58 229

    [45]

    Pierson D, Moss F 1995 Phys. Rev. Lett. 75 2124

    [46]

    So P, Ott E, Schiff S, Kaplan D T, Sauer T, Grebogi C 1996 Phys. Rev. Lett. 76 4705

    [47]

    So P, Ott E, Sauer T, Gluckman B J, Grebogi C, Schiff S 1997 Phys. Rev. E 55 5398

    [48]

    Buhl M, Kennel M B 2007 Chaos 17 033102

    [49]

    Gao Z K, Jin N D 2012 Nonlin. Anal.:Real World Appl. 13 947

    [50]

    Takens F 1981 Dynamical Systems and Turbulence (Berlin:Spring Verlag) 366

    [51]

    Dhamala M, Lai Y C, Kostelich E J 2000 Phys. Rev. E 61 6485

    [52]

    Hunt B R, Ott E 1996 Phys. Rev. E 54 328

    [53]

    Gao Z K, Jin N D 2012 Physica A 391 3005

    [54]

    Hervieua E, Seleghimb P 1998 Nucl. Eng. Design 184 421

    [55]

    Jana A K, Das G, Das P K 2006 Chem. Eng. Sci. 61 1500

    [56]

    Jones D L, Baraniuk R G 1995 IEEE Trans. Sign. Proc. 43 2361

    [57]

    Du M, Jin N D, Gao Z K, Wang Z Y, Zhai L S 2012 Int. J. Multiphase Flow 41 91

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  • Received Date:  16 August 2012
  • Accepted Date:  12 November 2012
  • Published Online:  20 April 2013

Detecting unstable periodic orbits from oil-gas-water three-phase slug flows

  • 1. School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 41174109, 50974095, 61104148) and the National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2011ZX05020-006).

Abstract: We use the close return method combined with adaptive threshold selection to detect the unstable periodic orbits from the signals measured from experimental oil-gas-water three-phase slug flows, and find that the period of the emulsion type slug flow is longer than that of oil in water type slug flow. Especially, the orbit of oil in water type slug flow is basically composed of one big loop and one small loop, and the emulsion type slug flow orbit is composed of two big smooth loops. In addition, we employ the method of adaptive optimal kernel time-frequency representation to investigate the flow behaviors of two typical oil-gas-water three-phase slug flows and indicate that the energy of the oil in water slug flow exhibits a dispersed distribution and its frequency spectrum consists of various components distributes in a wide range. In contrast, the energy of emulsion type slug flow is distributed in a rather concentrated region and the high frequency component in its frequency spectrum is much less than that of the oil in water slug flow. These results are well consistent with the detected structure of unstable periodic orbit, further suggesting that the fluid mechanism underlying oil in water type slug flow is more complicated than that of the emulsion type slug flow.

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