水平管油—水两相和油—气—水三相流动特性研究
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摘要
油、气、水三相混合物在管内的流动是常见于石油、天然气工业中极其复杂的气液多相流动现象。深入研究油-水两相和油-气-水三相在管道内的流动规律,特别是流型和压降规律,可以为石油生产解决重要的技术难题,对完善多相流理论及实际应用具有十分重要的意义。本文在内径50mm、长为40m的水平管中,系统地研究了油-水两相和油-气-水三相的流动型态及流动特征。主要研究内容和结论如下:
     1.通过可视观察、摄影、摄像以及电导探针和压力传感器采集的信号特征分析,得到9种油水两相流型:(1)SM;(2)SW;(3)DOSW;(4)ST-MI;(5)O-DO/W-W;(6)DO/W-W;(7) O-DO/W;(8)O-DW/O;(9)DO/W。并结合静态分析手段(PDF分析),从形成机理上详尽描述了各流型的相分布及流动特征。采用无因次量关联的方法,得到了各流型转变的预测关系式。分别以油水混合速度vm和入口体积含水率φ、折算油速和折算水速为横纵坐标,绘制了油-水二相流型图,并尝试性绘制了以油相和水相的无量纲数Re、Fr、We以及体积含水率φ的乘积为横纵坐标的流型图,以强化流型图的普适性。
     2.根据油-气-水三相流动是气液流动与油水流动的耦合的特点,提出了一种新的油-气-水三相流型定义,据此识别了12种典型流型:(1)SM‖SM;(2) SW‖ST;(3) SW‖IN;(4) SW‖DW/O&DO/W;(5) IN‖ST;(6) IN‖O&DO/W;(7) IN‖DO/W&W;(8) IN‖O&DW/O;(9) IN‖DO/W; (10) AN‖O/W;(11) AN‖W/O;(12) AN‖DW/O&DO/W。从可视特征、压力信号、压差信号以及电导探针测取的信号特征入手,结合静态分析手段(PDF分析),详尽描述了各流型的相分布及流动特征。以折算气液速分别为横纵坐标,将实验数据按不同的油水比绘制了油-气-水三相流型图,从机理上分析了各流型转换的特性。并尝试性绘制了以气相和油水混合液相的无量纲数Re、Fr、We以及体积含气率β的乘积为横纵坐标的流型图,其适用性还处于探索阶段。
     3.与Mandhane和Taitel&Dukler气液两相流型图对比,发现当液相中入口体积含水率小于80%时,油气水三相波状分层流动区域上移,该区域对应为SW || IN流型范围,其油水两相呈间歇流动状态,液相含水率高于50%时该流动型态是由IN || DO/W段塞流型转变而来,液相含水率低于50%时由SW || ST流型转变而来;在低气速时,SM || SM流型向IN || ST间歇流转换的边界随着含油率的升高以及折算气速的增加而下移。
     4.对水平管中油-水两相和油-气-水三相流动平均压力梯度、截面持水率和管壁水润高度的变化规律进行了详细地研究。
     油水两相压力梯度随着油水混合液速vm的增大均单调非线性递增。而随着入口体积含水率的增加,当混合速度大于0.566m/s时,均出现了压力梯度的峰值特性,结合流型转变分析,确定油水两相流动转相对应的入口体积含水率大约为60%,并以转相点为分界点,得到了截面持水率与体积含水率和混合速度间的模拟关系式;利用双流体模型对油水分离分层流动压力梯度及截面持水率进行了预测分析,并对平面与曲面两种油水界面形态下的模拟结果与实验结果进行比较分析。
     对于油-气-水三相流动,不同液相含水率下的压力梯度均随着气液相折算速度的增加而增大。但随着入口体积含水率的增加,在一定的折算气液速的条件下,压力梯度出现了与转相相关的峰值特性,由峰值对应的液相入口体积含水率确定转相点对应的液相体积含水率为40%,明显低于油水两相流动时的转相点(入口体积含水率约为60%)。在高折算液速或者低折算液速但液相含水率高于50%工况下,随折算气速的增大,截面持水率呈指数衰减的变化趋势。定义了一个新的概念——管壁水润高度,分析了折算气液速以及入口体积含水率对该参数的影响趋势。
     5.采用互相关技术分流型研究了油-气-水三相分层流和环状流界面波速特性,结果表明:固定油水比时,SW‖ST流型气-油界面和油-水界面波速、AN‖DO/W流型和AN‖DW/O流型的气液界面波速均随折算气速和折算液速的增大而增大。固定折算液速或折算气速时,随着液相中入口体积含水率的增加,SW‖ST流型气-油界面波速逐渐减小,而油-水界面波速增大,且含水率越高,增大的幅度越大。AN‖DO/W流型和AN‖DW/O流型的气液界面波速均增大。SW‖IN流动型态其油水间歇流动的特性使气液界面波速的变化比较复杂,没有表现出比较有规律的变化趋势。而油水间歇流动的特性参数(水塞速度、水塞长度、水塞频率)随折算气液速及液相含水率的变化表现出一定的变化规律。
Oil-water two-phase flow and gas-oil-water three-phase flow are commonly encountered in the petroleum and nature gas industry. Study on the oil-water two-phase flow and oil-gas-water three-phase flow, especially the characteristics of flow patterns and pressure gradient, can solve many important technical problems for petroleum industry. It is also very important for the improvement of the theory of multi-phase flow and practical application. In this paper, characteristics are investigated systemically for oil-water two-phase flow and gas-oil-water three-phase flow in horizontal pipes with inner diameter of 50mm and length of 40m. The main contents and conclusions of the research are the following.
     (1) By analysis of visual observation, photos, videos, the acquired signals of conductance probes and pressure transducer, integrating with static analysis (PDF analysis), it is found that oil-water two-phase flow in horizontal pipes can be classified into nine flow patterns: SM flow, SW flow, DOSW flow, ST-MI flow, O-DO/W-W flow, DO/W-W flow, O-DO/W flow, O-DW/O flow and DO/W flow. The transform boundary correlations of some flow patterns are obtained through dimensionless variable analysis, which coincide well with experimental data. Flow pattern maps are plotted with mixture velocity vs. input water cut and oil superficial velocity vs. water superficial velocity. Furthermore, another flow pattern map is also plotted with oil phase dimensionless number vs. water phase dimensionless number in order to strengthen the common suitability of the pattern map.
     (2) Gas-oil-water three-phase flow is the couple of gas-liquid flow and oil-water flow. According to this characteristic, new names of gas-oil-water three phase flow patterns are presented. Twelve flow patterns are identified, which are SM‖SM flow, SW‖ST flow, SW‖IN flow, SW‖DW/O&DO/W flow, IN‖ST flow, IN‖O&DO/W flow, IN‖DO/W&W flow, IN‖O&DW/O flow, IN‖DO/W flow, AN‖O/W flow, AN‖W/O flow and AN‖DW/O&DO/W flow. Also by analysis of visual observation, photos, videos, the acquired signals of conductance probes and pressure sensors, integrating with static analysis (PDF analysis), phase distribution and flow characteristics of these flow patterns are described in detail. Flow pattern maps are plotted with liquid superficial velocity vs. gas superficial velocity under different ratios of oil and water flowrate and the mechanism on flow patterns transition is analyzed. Another flow pattern map is also plotted with liquid phase dimensionless number vs. gas phase dimensionless number under different ratios of oil and water flowrate., but the common suitability of which need to be studied further.
     (3) Compared with Mandhane’s and Taitel&Dukler’s gas-liquid flow pattern map, it is found that the region of wavy stratified flow increases apparently for the gas-oil-water three-phase system when input water cut in liquid is less than eighty percent. The region expanded is the region of SW || IN flow pattern that oil-water two phase takes on intermittent flow regime. SW || IN flow pattern is transformed from IN || DO/W flow pattern when input water cut in liquid is higher than 50 percent and from SW || ST flow pattern when input water cut in liquid is lower than 50 percent. For low gas flowrate, the transition from SM || SM flow pattern to IN || ST flow pattern“moves”downward as oil faction and superficial gas velocity are increased.
     (4) An intensive study on characteristics of mean pressure gradient, water holdup, and height wetted by water on the pipe wall for oil-water two phase flow and gas-oil-water three-phase flow is conducted. The following regularity is obtained.
     The pressure gradient for oil-water flow increases nonlinearly with the increase of mixture velocity. While mixture velocity is higher than 0.566m/s, corresponding to the phase inversion point, a sharp peak in pressure gradient appears. Combining with the analysis of flow pattern transition, the input water cut at phase inversion point is around 60%. The relational equations that water holdup is influenced by input water cut and mixture velocity are obtained before and after phase inversion point. Two fluid model is used to predict the pressure gradient and water holdup for oil-water separated stratified flow under the condition of curve interface and plane interface, and the predicted data is compared with the experiment data.
     For the gas-oil-water three phase flow, the pressure gradient under different input water cuts in liquid increases with the increase of gas and liquid superficial velocities. Corresponding to the phase inversion point, a sharp peak in pressure gradient also appears at some gas and liquid superficial velocities. It is found that the input water cut of the phase inversion point for three phase flow which is around 40%, is obviously lower than that for two phase flow, which is around 60%. At high liquid superficial velocity or at low liquid superficial velocity with higher input water cut in liquid over 50%, the water holdup takes on the trend to damped exponentially. A new term, height wetted by water on the pipe wall, is put forward.. Influences of gas and liquid superficial velocities and input water cut in liquid on it are analyzed.
     (5) Cross-correlation technology is used for the study of the characteristics of the interfacial wave velocity about stratified flow regime and annual flow regimes for gas-oil-water three phase flow. The results show that the wave velocity of the gas-oil interface and oil-water interface of SW‖ST flow pattern, the gas-liquid interface of AN‖DO/W flow pattern and AN‖DW/O flow pattern increase with the increase of gas superficial velocity and liquid superficial velocity on the condition of fixed ratio of oil and water flow rates. When liquid superficial velocity or gas superficial velocity is fixed, the velocity of gas-oil interface of SW‖ST flow pattern decreases while the velocity of oil-water interface of SW‖ST flow pattern increases with the increase of input water cut in liquid, and the higher the input water cut, the bigger the increase amplitude. For AN‖DO/W flow pattern and AN‖DW/O flow pattern, the wave velocity of gas- liquid interface also increases. No regularity is obtained for the wave velocity on gas-liquid interface for SW‖IN flow pattern due to the intermittent flow between oil and water, but the characteristic parameters of oil-water intermittent flow, such as the water slug velocity, the water slug length and the water slug frequency, are of regular variation with liquid superficial velocity, gas superficial velocity and input water cut in liquid.
引文
[1] Acikgoz M , Franca F , Lahey R. T.. An experimental study of three-phase flow regimes[J]. Int J Multiphase Flow, 1992, 18(3): 327-336
    [2]郭烈锦,李广军,陈学俊.卧式螺旋管内油-气-水三相流流型的实验研究[J].西安交通大学学报, 1997, 31 (4) : 54-60
    [3] Hewitt G F , Khor S K, Pan L.. Three-phase gas-liquid-liquid flow : flow pattern , holdups and pressure drop. Proc of Int Symp on Multiphase Flow[C]. Beijing : International Academic Publishers , 1997: 1-19
    [4]于立军.水平管内油气水三相流动特性研究[D].西安:西安交通大学, 1997
    [5]郭烈锦,李广军,陈学俊等.卧式螺旋管内油-气两相流流型的研究[J].工程热物理学报, 1996, 17 (4): 472-476
    [6] Nadler M., Mewes D.. Flow Induced Emulsification in the Flow of Two Immiscible Liquids in Horizontal Pipes[J]. Int. J. Multiphase Flow, 1997, 23(1): 55-68
    [7] Trallero J. L., et al.. A study of oil-water flow patterns in horizontal pipes, SPE 36609, 1996
    [8] Hewitt G.F.. From gas-liquid to liquid-liquid two-phase flow: a difficult journey. Int.Symposium on Liquid-Liquid Two-Phase Flow and Transport Phenomena[C]. Antalya, 1997: 3-7
    [9] Angeli P., Hewitt G F.. Flow Structure in horizontal oil-water flow [J]. Int J Multiphase Flow, 2000, 26: 1117-1140
    [12]于立军.油气水三相流动不同流型摩擦阻力的实验研究[J].上海交通大学学报, 1999, 33(3): 259-261
    [13] Simpson H. C., Rooney D. H., Gilchrist A., et al.. An assessment of some two-phase flow pressure gradient, hold-up, and flow pattern prediction methods in current use [A]. Fairhurst P. Proceedings of the 3rd International Conference on Multi-phase Flow[C]. BHRA, 1987: 22-36
    [14] Bacharov A. I., Andriasov R. S., Sakkarov V. A..Investigation of the motion of gas-water-oil mixtures in horizontal pipes[J]. Neftepromyslovoe delo, 1972, 6: 27-30
    [15] Guzhov A. I., Medvedev V. F., Savelev V. A.. Movement of gas-water-oil mixture through pipelines [J]. Int. Chemical Engineering, 1979, 14: 713-714.
    [16] Lunde K., Nuland S., Lingelem, M.. Aspects of three-phase flow in gas condensate pipeline. 30th European two-phase Flow Group Meeting[C]. Hannover,1993, Paper 11
    [17] Nadler M., Mewes D.. Multiphase slug flow in horizontal pipes. 30th European Two-phase Flow Group Meeting[C]. Hannover, 1993, Paper 12
    [18] Pan L., Tayanti S., Hewitt G. F.. Flow pattern, phase inversion and pressure gradient in air-oil-water flow in a horizontal pipe. Proceeding of the 2nd International Conference on Multiphase Flow[C]. Kyoto, 1995, Paper FT2-1
    [19]王跃社,鹿院卫,周芳德.垂直上升管内气体扰动油水两相乳化液流动特性[J].化工学报, 2000, 51(5): 676-681.
    [20] Nadler M., Mewes D.. The pressure drop of the three-phase of oil, water, and gas in horizontal pipes. Proceeding of the 2nd International Conference on Multiphase Flow[C]. Kyoto, 1995, Paper FT2-9
    [21] Nuland S., et al. Phase fraction in three-phase gas/oil/water flow. Proc.5th Int. Conf. on Multiphase Prod[C]. Cannes ,1991: 3-30
    [22] Acikgoz M., et al. An experiment study of three-phase flow regimes[J]. Int. J. Multiphase Flow, 1992(3): 327-336
    [23] Lahey R. T., et al. Global Volumetric phase fractions in horizontal three-phase flows[J]. AIChEJ, 1992, 7: 1049-1058
    [24] Stapelberg H. H., et al. The pressure loss and slug frequency of liquid-liquid-gas slug in horizontal pipes[J]. Int. J. Multiphase Flow, 1994, 20 (2): 285-303
    [25] Lee A. H., et al. Study of flow regime of transition oil/water/gas mixtures in horizontal pipelines. Proc. 3th Int. Offshore and Polar Eng. Conf[C]. Singapore, 1993: 159-164
    [26] Neogi S., et al.. A model for multiphase(gas/oil/water)stratified flow in horizontal pipelines, SPE 28799, 1994
    [27] Wilkens R., Jepson W.P.. Studies of multiphase flow in high pressure horizontal and +5 degree inclined pipelines. Proc. 6th Offshore and Polar Eng. Conf.[C]. Los Angeles, 1996: 139-147
    [28] Taitel Y., et al.. Stratified three phase flow in pipes[J]. Int. J. Multiphase Flow, 1995, 3: 53-60
    [29] Pan L.. High pressure three-phase (gas/liquid/liquid) flow[D]. London: Imperial College, 1996
    [30]吴浩江,李斌,周芳德.水平管内油气水三相流流型的实验研究[J].油气储运, 1999, 18(7): 30-34
    [31]于立军,蒋安众等.水平管内油气水三相流动特性研究[J].上海交通大学学报, 2000, 34(9): 1171-1174
    [32]周云龙,蔡辉等.水平管内油-气-水三相流流型特性研究[J].东北电力学院学报, 2000, 20(2): 1-5
    [33]胡志华,钱焕群等.水平管内油-气-水三相流流型的研究[J].西安交通大学学报, 2001, 35(9):899-913
    [34] Oddie G., Shi H., Durlofsky L. T., et al.. Experimental Study of Two and Three Phase Flows in Large Diameter Inclined Pipes[J]. Int. J. Multiphase Flow, 2003, 29: 527-558
    [35] Hall A.R.W., et al.. An experimental investigation of the water phase in the multiphase flow of oil water and gas, Proc. 6th Int. Conf. on Multiphase Prod[C]. Cannes, 1993: 251-272
    [36] Lin P. H., et al. Prediction of the initiation of slugs with linear-stability theory[J]. Int. J. Multiphase Flow, 1986, 1: 79-98
    [37] Wilkens R.J.. Prediction of the flow regime transitions in high pressure, large diameter inclined multiphase pipelines[D]. OH: Ohio University, 1997
    [38] Taitel Y., Bornea D., Dukler A. E.. Modeling flow pattern transitions for steady upward gas-liquid flow in vertical tubes[J]. AIChE, 1980, 26(3): 345-354
    [39] Mishima K., Ishii M.. Flow regime transition criteria for upward two-phase flow in vertical tubes[J]. Int J Heat Mass Transfer, 1984, 27(5): 723-737
    [40] Roumy R.. Structure of air-water two phase flow: Study of void fraction and flow configuration[R]. Rept. CEAR-3892, Centre d’Etudes Neclears de Grenoble, France.
    [41] Whalley P. B., Hewitt G. F. & Terry J. W.. Photographic studies of two-phase flow using a parallel light technique[R]. Rept. AERE-R9389, UKAEA, Harwell, 1979
    [42] Kumar S. B., Moslemian D., Dudukovic M. P.. Aγ-ray tomographic scanners for imaging voidage distribution in two-phase flow systems[J]. Flow Measurement & Instrumentation, 1995, 6: 61~73
    [43] Bergles A. E.. Electrical probes for study of two phase flows. 11th Nat. ASME/AIChE Heat Transfer Conference[C]. Minneapolis, 1969: 70-81
    [44] Jones O. C., Zuber N.. Statistical methods for measurement and analysis in two-phase flow. 5th International Heat Transfer Conference Science[C]. Council, Japan, 1974
    [45] Franca F., Acikgoz M., Lahey R. T.. The use of fractal techniques for flow regime identification[J]. Int. J. Multiphase Flow, 1991, 17: 545-552
    [46] Hagiwara Y.. Experimental studies on chaotic behavior of liquid film flow in annular two phase flows[J] . Physico-chemical Hydrodynamics , 1988 ,10(1) : 135-147
    [47]郑君里,杨行俊.人工神经网络[M].北京:高等教育出版社, 1992
    [48]吴浩江,胡志华,周芳德.改进BP神经网络在流型智能识别中的应用[J].西安交通大学学报, 2000, 34(1): 22-25
    [49]康耀红.数据融合理论与应用[M].西安:西安电子科技大学出版社, 1997
    [50] Stapelberg H.H., Mewes D.. Pressure drop calculation in three-phase slug flow of water , oil , and air[J]. International Chemical Engineering, 1994, 34 (3) : 295-314
    [51] Taitel Y., Barnea D., Brill J. P.. Stratified three phase flow in pipes[J]. Int. J. Multiphase Flow, 1995, 21(1): 53-60
    [52] Odozi U.A.. Three-phase gas/liquid/liquid slug flow[D]. London: Imperial College, 2000
    [53] Odozi U.A., Mendes-Tatsis M.A., Hewitt G.F.. Pressure drop and liquid holdup in three-phase air-oil-water slug flow. In: 3rd International Conference Multiphase Flow[C]. Lyon, 1998
    [54]张西民等.水平圆管内油气水三相流摩擦阻力的模型与结构关系式[J].西安交通大学学报, 1999, 33(1): 59-63
    [55]李广军.管道内气液两相流界面波特性研究[D].西安:西安交通大学, 1996
    [56] Kang H.C., Kim M.H.. The development of a flush wire probes and calibration method for measuring liquid film thickness[J]. Int.J. Multiphase Flow, 1992, 18: 423-437
    [57] Charles M. E., Govier G. W., Hodgson G. W.. The horizontal pipeline flow of equal density oil-water mixture[J]. Can. J. Chem. Eng., 1961, 39(17): 27-36
    [58] Russell T.W.F., Hodgson G. W., Govier G. W.. Horizontal pipeline flow mixtures of oil and water[J]. Can J. Chem. Eng., 1959, 37: 9-17
    [59] Brauner N., Maron D M.. Stability analysis of stratified liquid-liquid flow[J]. Int. J. Multiphase Flow, 1992, 18 (1): 103-121
    [60] Malinowsky M. S.. An experimental study oil-water and air-oil-water flowing mixtures in horizontal pipes[D]. Tulsa: The University of Tulsa, 1995
    [61] Trallero J. L.. Oil-Water Flow Patterns in Horizontal Pipes[D]. Tulsa: The University of Tulsa, 1995
    [62] Beretta A., Ferrari P., Galbiati L., et al.. Horizontal oil-water flow in small diameter tubes: Flow patterns[J]. Int. Comm. Heat Mass Transfer, 1997, 24 (2): 223-229
    [63] Oglesby K.D.. An Experimental Study on the Effects of Oil Viscosity, Mixture Velocity, and Water Fraction on Horizontal Oil/Water Flow[D]. Tulsa: The University of Tulsa, 1979
    [64] Lafin G.C., Oglesby K.D.. An Experimental Study on the Effects of Flow Rate, Water Fraction and Gas-Liquid Ratio on Air-Oil/Water Flow in Horizontal Pipes[D]. Tulsa: The University of Tulsa, 1976
    [65] Valle A., Kvandal H.. Pressure Drop and Dispersions Characteristics of Separated Oil/Water Flow. Int. Symp. On Two-phase Flow Modelling and Experimentation[C]. Rome, 1995
    [66] Guzhov A.I., et al.. Emulsion Formation During the Flow of Two Immiscible Liquids in a pipe. Neft[C] Russian: 1973, 58-61
    [67] Cox A.L.. A Study of Horizontal and Downhill Two-Phase Oil/Water Flow[D]. Texas : The University of Texas, 1985
    [68] Scott G. M.. A Study of Two-Phase Liquid-Liquid Flow at Variable Inclinations[D]. Texas: The University of Texas, 1985
    [69] Soleimani A.. Phase Distribution and Associated Phenomena in Oil-Water Flows in Horizontal Tubes[D]. London: Imperial College, 1999
    [70] Alkaya B., Jayawardena S. S., Brill J. P.. Oil-Water Flow Patterns in Slightly Inclined Pipes[A]. Proc. ETCE/OMAE Joint Conf.[C]. New Orleans: 2000
    [71] Angeli P., Hewitt G. F.. Drop Size Distribution in Horizontal Oil-Water Dispersed Flows[J]. Chem. Eng. Sci., 2000, 55: 3133-3143
    [72] Elseth G.. An Experimental Study of Oil-Water Flow in Horizontal Pipes[D]. Norway: Norwegian University of Science and Technology, 2001
    [73] Simmons M. J. H., Azzopardi B. J.. Drop Size Distribution in Dispersed Liquid-Liquid Pipe Flow[J]. Int. J. Multiphase Flow, 2001, 27: 843-859
    [74] Lovick J., Angeli P.. Experimental Studies on the Dual Continuous Flow Pattern in Oil-Water Flows[J]. Int. J. Multiphase Flow, 2004, 30: 139-157
    [75] Jana A.K., Das G., Das P.K.. Flow regime identification of two-phase liquid–liquid upflow through vertical pipe[J]. Chemical Engineering Science, 2006, 61(5): 1500-1515
    [76] Yih C.S.. Instability Due to Viscosity Stratification[J]. J. Fluid Mech, 1967, 27: 337-352
    [77]吴铁军,郭烈锦等.水平管内油水两相流流型及其转换规律研究[J].工程热物理学报, 2002, 23(4): 491-494
    [78] Charles M. E., Govier G. W., et al.. The Horizontal Pipeline Flow of Equal Density Oil/Water Mixtures[J]. Can. J. Chem. Eng, 1969, 39(17): 27-36
    [79] Arirachakaran S., et al.. An Analysis of Oil/Water Flow Phenomena in Horizontal Pipes. SPE 18836, 1989: 155-167
    [80] Hinze O.J.. Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes[J]. A.I.Ch.E. Journal, 1955, 1(3): 289-295
    [81] Collins S.B., Knudsen J.G.. Drop-size Distributions Produced by Turbulent Pipe Flow of ImmiscibleLiquids[J]. A.I.Ch.E. Journal, 1972, 16(6): 1072-1080
    [82] Sevik M., Park S. H.. The Splitting of Drops and Bubbles by Turbulent Fluid Flow[J]. J. Fluid Eng. Transactions of the ASME, 1973, 3: 54-59
    [83] Karabelas A. J.. Droplet Size Spectra Generated in Turbulent Pipe Flow of Dilute Liquid-liquid Dispersions[J]. A.I.Ch.E. Journal, 1978, 24(2): 170-180
    [84] Hanzevak E. I., Demetriou G.D.. Effect of Velocity and Pipeline Configuration on Dispersion in Turbulent Hydrocarbon-Water Flow Using Laser Image Processing[J]. Int. J. Multiphase Flow, 1989, 15(6): 985-996
    [85] Pacek A.W., Nienow A.W.. A Problem for the Description of Turbulent Dispersed Liquid-liquid Systems[J]. Int. J. Multiphase Flow, 1995, 21 (2): 323-328
    [86] Postman F. H., Carpenter P.G.. The multiphase flow of gas, oil, and water through vertical flow strings with application to the design of gas lift installation[J]. Drill and Prod. Parch., 1952: 257
    [87] Sobocinski D. P.. oil-gas-water mixture in pipeline[D]. Tulsa: University of Tulsa, 1955
    [88] Anderson R. J., Russell T. W. F.. Film formation in two-phase annular flow[J]. AICHE, 1970, 16: 626-633
    [89] Wilkes N. S., Conkie W., et al.. A model for the droplet deposition rate in horizontal two-phase annular flow[R]. UKAEA Report NO. AERE-R9691, 1980
    [90] Brauner N., Rovinsky J., Moalem Maron D.. Analytical solution for Laminar-Laminar two-phase flow in circular conduits(1996a)[J]. Chem. Eng., 1996: 141-142
    [91] Brauner N., Moalem Maron D., Rovinsky J.. A two-fluid model for stratified flows with curved interfaces[J]. Int. J. Multiphase Flow, 1998, 24(6): 975-1004
    [92] Taitel Y., Dukler A. E.. A model for predicting flow regime transactions in horizontal and near horizontal gas–liquid flow[J]. AIChEJ, 1976, 22: 47-55
    [93] Ferguson M. E. G., Spedding P. L.. Measurement and prediction of pressure drop in two phase flow[J]. J. Chem. Technol. Biotechnol, 1995, 62 : 262-278
    [94] Fayed A. S., Otten L.. Comparing measured and calculated multiphase flow pressure drop[J]. Oil Gas J., 1983, 8: 136-144.
    [95] Pleshko A., Sharma M. P.. An experimental study of vertical three phase (oil–water–air) upward flow, Proc. ASME. Conf. Advances in Gas–Liquid Flows[C]. FED 99, HTD 155, 1990: 97-108
    [96] Gregory G. A., Frogassi M.. A critical evaluation of multiphase gas liquid pipeline calculationmethods. Int. Conf. Multiphase Flow[C]. London, 1995: 93-108
    [97] Spedding P. L., Benard E., Donnelly G. F.. Prediction of pressure drop in multiphase horizontal pipe flow[J]. International Communications in Heat and Mass Transfer, 2006, 33 (9): 1053-1062
    [98] Stapelberg, Mewes D.. The flow of two immiscible liquids and air in a horizontal pipe. Proc. ASME Conf. Advances in Gas–Liquid Flows[C]. FED 99, HTD 155, 1990: 89-96
    [99] Brinkman H. C.. The viscosity of concentrated suspensions and solutions[J]. J. Chem. Phys., 1975, 20: 571-594
    [100] Paglianti A., Giona M., Soldati A.. Characterization of subregimes in two-phase slug flow[J]. Int. J. Multiphase Flow, 1996, 22(4): 781-796
    [101] Kang. H. C., Kim M.H.. The relation between the interfacial shear stress and the wave motion in a stratified flow[J]. Int. J. Multiphase Flow, 1993, 19(1): 35-49
    [102] Ohba K., Nagae K..Characteristics and behavior of the interfacial wave on the liquid film in a vertically upward air-water two-phase annular flow[J]. Nuclear Engineering and Design, 1993, 14 (1): 119-127
    [103] Karapantsios T. D., Karabelas A. J.. Longgitudinal characteristics of wavy falling films[J]. Int. J. Multiphase Flow, 1993, 21(1): 119-127
    [104] Shi T., Kocamustu G.. Interfacial measurements in horizontal stratified flow patterns[J]. Nuclear Engineering and Design, 1994, 14 (9): 81-96
    [105]徐苓安.相关流量测量方法.天津:天津大学出版社, 1988