倾斜及水平油水两相管流流动特性测量
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摘要
倾斜及水平油水两相流动现象广泛存在于石油工业中,流动参数测量对生产过程及工艺优化具有重要意义。由于油水两相流流动结构呈现高度随机性、不稳定性及多态性,流动过程参数难于测量。本文针对倾斜及水平油水两相流复杂流动现象,设计了环形电导传感器及阵列探针传感器。在天津大学多相流实验装置上测取倾斜及水平油水两相流宏观电导信号及局部探针信号的基础上,实验得到了两相流流型图、两相流相关速度及含水率等流动参数。采用非线性分析方法研究了倾斜油水两相流非线性动力学特性。应用双流体物理模型及数值模拟技术研究了水平油水两相流流型转化问题。采用电导与电容传感器组合测量方法研究了水平油水两相流分相流量测量问题。论文研究工作取得了如下创新性成果:
1.采用环形电导传感器与5路纵向微探针阵列传感器组合测量方法提取了倾斜油水两相流动结构信息,在此基础上测量得到了不同角度的大管径倾斜油水两相流流型图,得到管径对流型转化边界有较大影响的结论。在实验测量流型基础上,提出一种新的倾斜油水两相流混沌吸引子形态分析方法-混沌吸引子周界测度方法。考察了吸引子周界特征量随相空间嵌入参数时间延迟的变化规律,分析结果表明:吸引子面积增长率是描述吸引子形态的不变特征量,该特征量对水为连续相的拟段塞水包油(D O/W PS)和局部逆流水包油(D O/W CT)流型变化敏感,具有较好的识别效果,为从吸引子形态周界测度关系探寻流型演化的非线性动力学机制提供了一条新途径。
2.采用环形电导传感器与8路径向微探针阵列传感器组合测量方法提取了20mm水平及近水平油水两相流流动结构信息,在此基础上测得水平及近水平油水两相流全部六种流型的流型图。采用双流体模型、分散流模型以及相态逆转等物理模型计算了流型边界,研究结果表明:ST&MI与半分散流型(D O/W&W、D W/O&D O/W)的转化边界、半分散与全分散流型(D O/W、D W/O)的转化边界的物理模型与实验测量流型结果较为吻合;ST与ST&MI流型边界的物理模型与实验测量流型有较大差异,角度倾斜则会加剧物理模型与实验结果的差异。所开展的水平油水两相流数值模拟工作为从理论上认识流型演化规律提供了可行办法。
3.采用目前大庆油田使用的水平井生产测井电导与电容组合仪对水平油水两相流分相流量测量方法进行了研究。由于电导与电容传感器对水为连续相和油为连续相具有不同的敏感特性,根据其实际测量响应特性,提出了总流量在20~50方/天(低流量)及100~200方/天流量(高流量)范围内,分别采用电容及电导传感器测量分相流量的方案。对油水相间存在较大滑脱效应的低流量范围,建立了具有较高含水率预测精度的变系数漂移模型,并结合高流量分相流量统计模型可得到较好的含水率预测精度(3%以内)。最终,提供了较为可靠的基于物理模型的水平井产出剖面测井解释方法。
Inclined and horizontal oil-water two-phase flow phenomena widely exist in petroleum industry, and measurement of the flow parameters is of great significance for industrial production process and optimization. As oil-water two-phase flow structure presents highly randomness, instability and polymorphism, the flow parameters are difficult to measure. To address this complex issue, ring conductance probe and mini-conductance array probe are designed. As the conductance probe, and mini-conductance array probe signals can reflect global and local character of flow patterns in oil-water flows respectively, the dynamical experiment are carried out in Tianjin university multiphase flow loop facility. Flow parameters are measured, such as the flow pattern maps of inclined and horizontal oil-water two-phase, the cross-correlation velocity of oil-water mixtures and water volume fraction. The nonlinear dynamics characteristics of inclined oil-water flows are studied by using nonlinear analysis methods. The flow pattern transition in horizontal oil-water two phase flow are studied by using two fluid model and numerical simulation techniques. Water cut in horizontal oil-water flows are measured by combination of conductance and capacitance probe. The creative points of this study are as follows:
1. The inclined oil-water two-phase flow structure information is extracted by the combined measurement of ring conductance probe and 5-channels axial mini-conductance array probes. Based on the measured signals, the flow pattern maps in large diameter oil-water flows are proposed at different inclined angles, and it can be concluded that the pipe diameter has great influence on flow pattern transitional boundaries. A new chaotic attractor morphological analysis method, perimeter measure analysis method, is proposed, which studied the variation of perimeter measure with the embedding delay time in phase space. The analysis results show that the growth rate of attractor area is an invariant feature to describe the attractor morphological characteristic, the perimeter measure is sensitive of flow pattern transition between dispersed oil in water pseudoslug and dispersed oil in water countercurrent flow, and a good identification results have been obtained for these two water dominated flow patterns. The perimeter measure will provide a new way to study the nonlinear dynamics mechanism of flow pattern evolution.
2. The horizontal and near-horizontal oil-water two-phase flow structure information in 20 mm ID pipes is extracted by the combined measurement of ring conductance probe and 8-chanels radial mini-conductance array probes. Based on the measured signals, flow patterns maps including six kinds of typical flow patterns in horizontal oil-water flows are proposed. The flow pattern transitional boundaries are calculated by two fluid model, dispersed flow model and phase inversion model. The results show that the boundaries between ST and ST&MI flow pattern are different between experiments and physical model, while the experimental transitional boundaries between ST&MI and Semi-dispersed flow patterns (D O/W&W, D W/O&D O/W), and Semi-dispersed flow and Full-dispersed flow patterns (D O/W, D W/O) are consistent with the physical model, and the inclination angles will greatly enlarge the differences. The numerical simulation work in this study will provide a feasible method to understanding the flow pattern evolution.
3. The measurement of partial phase flow rate in horizontal oil-water flows are investigated by using the combination instrument of conductance and capacitance probe during the production well logging in horizontal wells. As the conductance probe is sensitive to water continuous flow patterns, and the capacitance probe is sensitive to oil continuous flow patterns, considering the actual experimental response character, the following measurement solutions are proposed, for the total flow rate in the range of 20~50 m3/d(low flow rate range), the capacitance probe is used to measure partial phase flow rate, and for the total flow rate in the range of 100~200 m3/d(high flow rate range), the conductance probe is used. For the low flow rate range, where exist more slip effect between oil and water phase, we establish a variable coefficient drift flux model and the proposed model has better water cut prediction precision, combination with the statistical model in high flow rate range, water cut prediction precision is less than 3%. Finally we provide a reliable well logging interpretation method of horizontal well production profile based on the physical model.
1.采用环形电导传感器与5路纵向微探针阵列传感器组合测量方法提取了倾斜油水两相流动结构信息,在此基础上测量得到了不同角度的大管径倾斜油水两相流流型图,得到管径对流型转化边界有较大影响的结论。在实验测量流型基础上,提出一种新的倾斜油水两相流混沌吸引子形态分析方法-混沌吸引子周界测度方法。考察了吸引子周界特征量随相空间嵌入参数时间延迟的变化规律,分析结果表明:吸引子面积增长率是描述吸引子形态的不变特征量,该特征量对水为连续相的拟段塞水包油(D O/W PS)和局部逆流水包油(D O/W CT)流型变化敏感,具有较好的识别效果,为从吸引子形态周界测度关系探寻流型演化的非线性动力学机制提供了一条新途径。
2.采用环形电导传感器与8路径向微探针阵列传感器组合测量方法提取了20mm水平及近水平油水两相流流动结构信息,在此基础上测得水平及近水平油水两相流全部六种流型的流型图。采用双流体模型、分散流模型以及相态逆转等物理模型计算了流型边界,研究结果表明:ST&MI与半分散流型(D O/W&W、D W/O&D O/W)的转化边界、半分散与全分散流型(D O/W、D W/O)的转化边界的物理模型与实验测量流型结果较为吻合;ST与ST&MI流型边界的物理模型与实验测量流型有较大差异,角度倾斜则会加剧物理模型与实验结果的差异。所开展的水平油水两相流数值模拟工作为从理论上认识流型演化规律提供了可行办法。
3.采用目前大庆油田使用的水平井生产测井电导与电容组合仪对水平油水两相流分相流量测量方法进行了研究。由于电导与电容传感器对水为连续相和油为连续相具有不同的敏感特性,根据其实际测量响应特性,提出了总流量在20~50方/天(低流量)及100~200方/天流量(高流量)范围内,分别采用电容及电导传感器测量分相流量的方案。对油水相间存在较大滑脱效应的低流量范围,建立了具有较高含水率预测精度的变系数漂移模型,并结合高流量分相流量统计模型可得到较好的含水率预测精度(3%以内)。最终,提供了较为可靠的基于物理模型的水平井产出剖面测井解释方法。
Inclined and horizontal oil-water two-phase flow phenomena widely exist in petroleum industry, and measurement of the flow parameters is of great significance for industrial production process and optimization. As oil-water two-phase flow structure presents highly randomness, instability and polymorphism, the flow parameters are difficult to measure. To address this complex issue, ring conductance probe and mini-conductance array probe are designed. As the conductance probe, and mini-conductance array probe signals can reflect global and local character of flow patterns in oil-water flows respectively, the dynamical experiment are carried out in Tianjin university multiphase flow loop facility. Flow parameters are measured, such as the flow pattern maps of inclined and horizontal oil-water two-phase, the cross-correlation velocity of oil-water mixtures and water volume fraction. The nonlinear dynamics characteristics of inclined oil-water flows are studied by using nonlinear analysis methods. The flow pattern transition in horizontal oil-water two phase flow are studied by using two fluid model and numerical simulation techniques. Water cut in horizontal oil-water flows are measured by combination of conductance and capacitance probe. The creative points of this study are as follows:
1. The inclined oil-water two-phase flow structure information is extracted by the combined measurement of ring conductance probe and 5-channels axial mini-conductance array probes. Based on the measured signals, the flow pattern maps in large diameter oil-water flows are proposed at different inclined angles, and it can be concluded that the pipe diameter has great influence on flow pattern transitional boundaries. A new chaotic attractor morphological analysis method, perimeter measure analysis method, is proposed, which studied the variation of perimeter measure with the embedding delay time in phase space. The analysis results show that the growth rate of attractor area is an invariant feature to describe the attractor morphological characteristic, the perimeter measure is sensitive of flow pattern transition between dispersed oil in water pseudoslug and dispersed oil in water countercurrent flow, and a good identification results have been obtained for these two water dominated flow patterns. The perimeter measure will provide a new way to study the nonlinear dynamics mechanism of flow pattern evolution.
2. The horizontal and near-horizontal oil-water two-phase flow structure information in 20 mm ID pipes is extracted by the combined measurement of ring conductance probe and 8-chanels radial mini-conductance array probes. Based on the measured signals, flow patterns maps including six kinds of typical flow patterns in horizontal oil-water flows are proposed. The flow pattern transitional boundaries are calculated by two fluid model, dispersed flow model and phase inversion model. The results show that the boundaries between ST and ST&MI flow pattern are different between experiments and physical model, while the experimental transitional boundaries between ST&MI and Semi-dispersed flow patterns (D O/W&W, D W/O&D O/W), and Semi-dispersed flow and Full-dispersed flow patterns (D O/W, D W/O) are consistent with the physical model, and the inclination angles will greatly enlarge the differences. The numerical simulation work in this study will provide a feasible method to understanding the flow pattern evolution.
3. The measurement of partial phase flow rate in horizontal oil-water flows are investigated by using the combination instrument of conductance and capacitance probe during the production well logging in horizontal wells. As the conductance probe is sensitive to water continuous flow patterns, and the capacitance probe is sensitive to oil continuous flow patterns, considering the actual experimental response character, the following measurement solutions are proposed, for the total flow rate in the range of 20~50 m3/d(low flow rate range), the capacitance probe is used to measure partial phase flow rate, and for the total flow rate in the range of 100~200 m3/d(high flow rate range), the conductance probe is used. For the low flow rate range, where exist more slip effect between oil and water phase, we establish a variable coefficient drift flux model and the proposed model has better water cut prediction precision, combination with the statistical model in high flow rate range, water cut prediction precision is less than 3%. Finally we provide a reliable well logging interpretation method of horizontal well production profile based on the physical model.
引文
[1] Govier G W, Sullivan G A, Wood R K, The upward vertical flow of oil-water mixtures, J. of Chem Eng, 1961:67~75
[2] Zavareh F, Hill A D, Podio A L, Flow regimes in vertical and inclined oil/water flow in pipes, paper SPE 18215, 1988
[3] Flores J G, Chen X T, Sarica C et al, Characterization of oil-water flow patterns in vertical and deviated wells, paper SPE 38810, 1997
[4] Bannwart A C, Rodriguez O M H, Carvalho C H M et al, Flow patterns in heavy crude oil-water flow, Transactions of the ASME, 2004,126:184~189
[5] Rodriguez O M H, Bannwart A C, Experimental study on interfacial waves in vertical core flow, Journal of Petroleum Science and Engineering, 2006,54: 140~148
[6] Lin R.H., Tavlarides L.L.,. Flow patterns of n-hexadecane-CO2 liquid-liquid two-phase flow in vertical pipes under high pressure. International Journal of Multiphase flow, 2009, 35: 566～579
[7] Schlumberger, Production Looging Interpretation, 1973
[8]钟兴福,黄志尧,吕鹏举等,125mm垂直圆管中油水两相流流型辨识研究,石油学报, 2001, 22(5):89~94
[9]李明忠,王卫阳,陈听宽等,垂直管中油-两相流的持水率预测方法研究,西安交通大学学报,2002,36(3): 252~256
[10] Jin N D, Nie X B, Wang J, et al, Flow pattern identification of oil/water two phase flow based on kinematic wave theory, Flow Measurement and Instrumentation, 2003, 14: 177~182
[11] Mukherjee H, Brill J P, Beggs H D, Experimental study of oil–water flow in inclined pipes, Transactions of the ASME, 1981, 103: 56~66
[12] Hill A D, and Oolman T, Production logging tool behavior in two-phase inclined flow, Journal of Petroleum Technology, 1982, 34: 2432~2440
[13] Davarzani J, Sloan L, Roesner R E., Research on simultaneous production logging instruments in multiphase flow loop, Paper SPE 14431, presented at the 60th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers held in Las Vegas, 1985, September, 22-25
[14] Vigneaux P, Chenais P, and Hulin J P, Liquid-liquid flow in an inclined pipe, AIChE J., 1988, 34: 781-789
[15] Tabeling P, Pouliquen O, Theron B, et al, Oil-water flows in deviated pipes: Experimental study and modelling, Proceedings of the 5th International Conference on Multiphase Flow Production, Cannes, France, 1991, 19-21 June, 294-306
[16] Ding Z X, Ullah K and Huang Y, A comparison of predictive oil/water holdup models for production log interpretation in vertical and deviated wellbores, SPWLA 35th Annual Logging Symposium, Tulsa, 1994 19-22, June
[17] Hasan A R, Kabir C S, A simplified model for oil-water flow in vertical and deviated wellbores, Paper SPE 49163. SPE Annual Technical Conference and Exhibition, New Orleans,Louisiana, 1998, 27-30 September
[18] Lucas G P, and Jin N D, Investigation of a drift velocity model for predicting superficial velocities of oil and water in inclined oil-in-water pipe flows with a centre body, Meas. Sci. Technol. 2001, 12: 1546~1554
[19] Lucas G P, and Jin N D, Measurement of the homogeneous velocity of inclined oil-in-water flows using a resistance cross correlation flow meter, Meas. Sci. Technol. 2001, 12: 1529~1537
[20] Dong F, Liu X P, Deng X, et al, Identification of two-phase flow regimes in horizontal, inclined and vertical pipes, Meas. Sci. Technol., 2001, 12: 1069~1075
[21] Oddie G, Shi H, Durlofsky L J, et al, Experimental study of two and three phase flows in large diameter inclined pipes, Int. J. Multiphase Flow, 2003, 29, 527~558
[22] Lum J Y L, Al-Wahaibi T, Angeli P, Upward and downward inclination oil-water flows, Int. J. Multiphase Flow, 2006, 32: 413~435
[23]罗彦生,董福印,张晓东,斜井油水两相流动产出剖面测试技术,测井技术, 1998, 22: 168~171
[24]赵忠健,王培烈,梅继兵, JLS-25伞式集流型测试仪在斜井中的实验研究,测井技术, 2000, 24: 145~147
[25]钟兴福,李彦华,王德坤等,集流型测试仪在斜井中的响应研究,仪器仪表学报, 2001, 22: 380~380.
[26]戴家才,郭海敏,王界益等,多相流生产测井井斜影响试验研究,石油天然气学报, 2006, 28: 69~71
[27] Mobbs S D, and Lucas G P, A turbulence model for inclined, bubbly flows. Applied Scientific Research, 1993, 51: 263~268
[28] Lucas G P, Modelling velocity profiles in inclined multiphase flow to provide a priori information for flow imaging. The Chemical Engineering Journal. 1995, 56: 167~173
[29] Brauner N, liquid-liquid two phase flow systems. in: V. Bertola (Ed.), Modeling and control of two-phase flow phenomena, CISM Center, Udine,Italy. 2002
[30] Russell T W F, Hodgson G W, Govier G W, Horizontal pipeline flow of mixtures of oil and water, Canadian Journal of Chemical Engineering, 1959, 37(1): 9~17
[31] Charles M E, Govier G W, Hodgson G W, The horizontal pipeline flow of equal density oil-water mixture, Canadian Journal of Chemical Engineering, 1961, 39(2): 27~36
[32] Hasson D, Mann U, Nir A, Annular flow of two immiscible liquids, The Canadian Journal of Chemical Engineering, 1970, 48: 514~520
[33] Guzhov A I,Girsin A D,Medvedev V F, et a1, Emulsion Formation During the Flow of Two Liquids in a Pipe, Neft Khoz, 1973, 8(8): 58~61
[34] Malinowsky M S, An experimental study of oil-water and air-oil-water flowing mixtures in horizontal pipes, MS Thesis, U. of Tulsa, 1975
[35] Oglesby K D, An experimental study on the effect of oil viscosity,mixture velocity and water fraction on horizontal oil-water flow, MS Thesis, U. of Tulsa, 1979
[36] Arirachakaran S, Oglesby K D, Malinowski M S, An analysis of oil/water phenomena in horizontal pipes, SPE Productions Operations Symp, SPE 18836, 1989
[37] Trallero J L, Brill J P, A study of oil-water flow patterns in horizontal pipes, SPE 36609, 1996
[38] Nadler M, Mewes D, Flow induced emulsification in the flow of two immiscible liquids in horizontal pipes, International Journal of Multiphase Flow, 1997,23(1): 55~68
[39] Angeli P, Hewitt G F, Pressure gradient in horizontal liquid-liquid flows, International Journal of Multiphase Flow, 1998, 24: 1183~1203
[40] Angeli P, Hewitt G F, Flow structure in horizontal oil-water flow, International Journal of Multiphase Flow, 2000, 26: 1117~1140
[41] Brauner N, Maron D M, Flow pattern transitions in two-phase liquid-liquid flow in horizontal tubes, International Journal of Multiphase Flow, 1992, 18: 123~140
[42] Brauner N, Rovinsky J, Moalem Maron, Determination of the interface curvature in stratified two-phase systems by energy considerations, International Journal of Multiphase Flow, 1996, 22: 1167~1185
[43] Brauner N, Maron D M, Rovinsky J, A two-fluid model for stratified flows with curved interfaces, International Journal of Multiphase Flow, 1998, 24: 975~1004
[44] Gorelik D, Brauner N, The interface configuration in two-phase stratified pipe flow, International Journal of Multiphase Flow, 1999, 25: 977~1007
[45] Shi H, Jepson W P, The effect of surfactants on flow characteristics in oil-water flows in large diameter horizontal pipelines, BHRA, 1997
[46] Elseth G, An Experimental study of oil-water flow in horizontal pipes, PhD Dissertation, The Norwegian University of Science and Technology, 2001
[47] Shi H, Cai J, Jepson W P, Oil-water two-phase flows in large-diameter pipelines, Transactions of the ASME, 2001, 123(12):270~276
[48] Brauner N, The prediction of dispersed flows boundaries in liquid-liquid and gas-liquid systems, International Journal of Multiphase Flow, 2001, 27: 885~910
[49] Brauner N, Ullmann A, Modelling of phase inversion phenomenon in two-phase pipe flow, International Journal of Multiphase Flow, 2002, 28: 1177~1204
[50] Ng T S, Lawrence C J, Hewitt G F, Interface shaped for two-phase laminar stratified flow in a circular pipe, International Journal of Multiphase Flow, 2001, 27: 1301~1311
[51] Ng T S, Lawrence C J, Hewitt G F, Laminar stratified pipe flow, International Journal of Multiphase Flow, 2002, 28: 963~996
[52] Lum J Y L, Lovick J, Angeli P, Dual continuous horizontal and low inclination two-phase liquid flows, The Canadian Journal of Chemical Engineering, 2004, 83(2):303~315
[53] Lovick J, Angeli P, Droplet size and velocity profiles in liquid–liquid horizontal flows, Chem. Eng. Sci., 2004, 59(15): 3105~3115
[54] Soleimani A, Lawrence C J, Hewitt G F, Spatial distribution of oil and water horizontal pipe flow, SPE 56524. SPE Annual Technical Conference and Exhibition, Houston, USA, 1999
[55] Kvandal H K, Elseth G, Melaaen M C, Measurement of velocity and phase fraction in dispersed two-phase flow, Int. Symp. on Liquid-Liquid Two-Phase Flow and Transport Phenomena. Antalya, Turkey, 2000
[56] Ioannou K, Nydal O J, Angeli P, Phase inversion in dispersed liquid–liquid flows, Experimental Thermal and Fluid Science, 2005, 29: 331~339
[57] Calos F T M, Modeling of oil-water flow in horizontal and near horizontal pipes, PhD Dissertation, University of Tulsa, 2006
[58] Al-Wahaibi T, Angeli P, Transition between stratified and non-stratified horizontal oil-water flow, PartⅠ: Stability analysis. Chemical Engineering Science. .2007, 62: 2915~2928
[59] Al-Wahaibi T, Smith M, Angeli P, Transition between stratified and non-stratified horizontal oil-water flow. PartⅡ: Mechanism of drop formation. Chemical Engineering Science. 2007, 62: 2929~2940
[60]蔡继勇,陈听宽,汤为等,水平管内油水乳状液流动特性研究,化学工程,1999,27(3): 32~35
[61]陈杰,孙红彦,梁志鹏等,水平管内油水两相流流型的实验研究,油气储运,2000,19 (12):27~31
[62]陈杰,于达,严大凡,水平管内油-水两相流动压降规律的实验研究,实验力学, 2001, 16 (4): 402~408
[63]陈杰,于达,严大凡,油-水两相流流型转换研究,水动力学研究与进展,2003, 18 (3): 355~364
[64]姚海元,宫敬,水平管内油水两相流流型转换特性,化工学报,2005,56(9):1649~1653
[65]窦丹,于达,宫敬,原油/水管流压降规律实验,石油化工高等学校学报, 2006,19(2): 60～63
[66]宫敬,王玮,于达,稠油-水两相水平管流流型实验研究,石油学报,2007,28 (2): 140~143
[67]徐孝轩,宫敬,水平管中油水两相流动研究进展,化工机械,2006,33 (1):59~65
[68] Xu X X, Study on oil-water two-phase flow in horizontal pipelines, Journal of Petroleum Science and Engineering, 2007, 59(1-2): 43~58
[69]吴铁军,郭烈锦,刘文红等,水平管内油水两相流流型及其转换规律研究,工程热物理学报,2002,23 (4):491~494
[70] Liu W H, Guo L J, Wu T J, et al, An experimental study on the flow characteristics of oil-water two-phase flow in horizontal straight pipes, Chinese J. Chem. Eng., 2003, 11(5): 491~496
[71]顾汉洋,高晖,郭烈锦,水平管油水两相分层紊流流动的数值研究,工程热物理学报,2003, 24(5): 810~812
[72] Gao H, Gu H Y, Guo L J, Numerical study of stratified oil-water two-phase turbulent flow in a horizontal tube, International Journal of Heat and Mass Transfer, 2003, 46: 749~754
[73] Vallée C, H?hne T, Prasser H M, et al, Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena, Nuclear Engineering and Design, 2008, 238(3): 637~646
[74]张修刚,牛冬梅,苏新军等,水平管内油水两相流动摩擦压降的试验研究,油气储运,2003,22(2): 47~50
[75]王树众,牛冬梅,林宗虎等,油水混合物在水平管众的二相流动特性研究,化学工程,2005,33(2): 26~29
[76]张丽娜,王小尚,张荷玲等,新型油水两相水平管流流型分类方法,油气储运,2006,25(10):49~51
[77]康万利,刘忠和,刘国权,国外水平管内油水两相流压降模型研究进展,大庆石油学院学报,2006,30(5): 20~23
[78]马龙博,张宏建,周洪亮等,基于Hilbert-Huang变换和支持向量机的油水两相流流型识别,化工学报,2007,58(3):617~622
[79] Piela K, Delfos R, Ooms G, et al, Experimental investigation of phase inversion in an oil-water flow through a horizontal pipe loop, International Journal of Multiphase Flow, 2006, 32: 1087~1099
[80] Piela K, Delfos R, Ooms G, et al, On the phase inversion process in an oil-water pipe flow, International Journal of Multiphase Flow, 2008, 34: 665~677
[81] Piela K, Delfos R, Ooms G, et al, phase inversion in the mixing zone between a water flow and an oil flow through a pipe, International Journal of Multiphase Flow, 2009, 35: 91~95
[82] Grassi B, Strazza D, Poesio P, Experimental validation of theoretical models in two-phase high-viscosity ratio liquid-liquid flows in horizontal and slightly inclined pipes, International Journal of Multiphase Flow, 2008, 34: 950~965
[83] Xu J Y, Wu Y X, Feng F F, et al, Experimental investigation on the slip between oil and water in horizontal pipes, Experimental Thermal and Fluid Science, 2008, 33: 178~183
[84] Farrar B, Bruun H H, A computer based hot-film technique used for flow measurements in a vertical kerosene-water pipe flow, International Journal of Multiphase Flow, 1996, 22: 733~751
[85] Jana A K, Das G, Das P K, A novel technique to identify flow patterns during liquid-liquid two-phase upflow through a vertical pipe, Ind. Eng. Chem. Res., 2006, 45:2381~2393
[86] Jana A K, Das G, Das P K, Flow regime identification of two-phase liquid-liquid upflow through vertical pipe, Chemical Engineering Science, 2006, 61: 1500~1515
[87] Augier F, Guiraud P, Masbernat O, Velocity fluctuations in a homogeneous dispersed liquid-liquid flow at high phase fraction. ICMF04, Yokohama, Japan, 2004
[88] Jin N D, Zhao X, Wang J et al, Design and geometry optimization of a conductive probe with a vertical multiple electrode array for measuring volume fraction and axial velocity of two-phase flow. Meas. Sci. Technol. 2008,19, 045403
[89]胡金海,刘兴斌,黄春辉等,一种同时测量流量和含水率的电导式传感器,测井技术,2002,26(2):154~157
[90] Jones Jr, Zuber N, The interrelation between void fraction fluctuation and flow pattern in two-phase flow, Int. J. Multiphase Flow, 1975, 2(2): 273~306
[91] Lee J Y, Kim N S, Ishii M, Flow regime identification using chaotic characteristics of two-phase flow, Nuclear Engineering and Design, 2008, 238: 945~957
[92] Hubbard M G, Dukler A E, The characterization of flow regimes for horizontal two-phase flow, Proc. Heat Transfer &Fluid Mechanics Inst, 1966: 100~121
[93] Albrecht R W et al, Measurement of two-phase flow properties using the nuclear reactor instrument, Prog. Nucl. Energy, 1982, 37~50
[94]黄志尧,王保良,李海青等,软测量技术在多相流检测中的应用,仪器仪表学报,2001,22(3):421～424
[95] Wu H J, Zhou F D, Wu Y Y, Intelligent identification system of flow regime of oil/gas/water, Int. J. Multiphase Flow, 2001,27: 459~475
[96]赵鑫,金宁德,李伟波,油水两相流相含率的软测量方法。化工学报,2005,56(10):1875~1879
[97] Oddie G M, On the detection of a low-dimensional attractor in disperse two-component (oil-water) flow in a vertical pipe, Flow. Meas. Instrum. 1991, 2: 225~229
[98]金宁德,宁英男,王微微等,垂直上升管中油水两相流流型表征,化工学报,2001,52(10):907~915
[99]郑桂波,金宁德,两相流流型多尺度熵及动力学特性分析,物理学报,2009,58(7): 4485~4492
[100]金宁德,李伟波,赵鑫,利用符号时间序列分析方法表征垂直上升管中油水两相流流型,化工学报,2005,56(1):116~120
[101] Maxwell J C, A Treatise on Electricity and Magnetism,Clarendon Press, Oxford, 1882
[102] De La Rue R E, Tobias C W, On the conductivity of dispersions, Journal of the Electrochemical Society, 1959,106(9): 827~832
[103] Nasr-EI-Din H, Shook C A, Ccowell J, A conductivity probe for measuring local concentrations in slurry systems. Int. J. Multiphase Flow., 1987, 13(3): 365~378
[104] Turner J C R, Electrical conductivity of liquid-fluidised beds, AIChE Symposium Series, 1973, 69(128): 115~122
[105] Bruggeman D A G, Calculation of different physical constants of heterogeneous substances. Annalen Physica, 1935,(24): 636~679
[106] Lemlich R, A theory for the limiting conductivity of polyhedral foam at low density, J. Colloids Interface Sci., 1978, 64(1): 107~110
[107] Feitosa K, Marze S, Saint-Jalmes A, et al, Electrical conductivity of dispersions: from dry foams to dilute suspensions, J. Phys. Condens., 2005, 17: 6301~6305
[108] Coney M W E, The theory and application of conductance probes for the measurement of liquid film thickness in two phase flow, J. Phys. E: Scient Instrum, 1973, 6: 903~910
[109] Andreussi P, Donfrancesco A D, Messia M, An impedance method for the measurement of liquid hold-up in two phase flow, Int. J. Multiphase Flow, 1988, 14 (6): 777~785
[110] Zhao D J, Guo L J, Hu X W, et al, Experimental study on local characterisicts of oil-water dispersed flow in vertical pipe, Int. J. Multiph. Flow., 2006, 32: 1254~1268
[111] Lucas G P, Panagiotopoulos N, Oil volume fraction and velocity profiles in vertical, bubbly oil-in-water flows, Flow. Meas. Instrum. 2009, 20(3): 127~135
[112] Wu Q, Ishii M, Sensitivity study on double-sensor conductivity probe for the measurement of interfacial area concentration in bubbly flow, Int. J. Multiphase Flow, 1999, 25: 155~173
[113] Fairuzov Y V, Arenas-Medina P, Verdejo-Fierro J,et al, Flow pattern transitions in horizontal pipelines carrying oil-water mixtures: full-scale experiments, Journal of Energy Resources Technology, 2000, 122: 169~176
[114] Evans J T, Forgang S, Itskovich G B, Downhole multiphase flow sensor, United States Patent, No. 5736637. Apr. 7, 1998.
[115] Chace D, Trcka D, Georgi D, et al, New instrument and methods for production logging in multiphase horizontal wells, paper SPE 53320, 1999.
[116] Maxit J O, Reittinger P W, Wang J, et al, Downhole instrumentation for the measurement of three-phase volume fractions and phase velocities in horizontal wells. Transactions of the ASME, 2000, Vol.122: 56~60.
[117] Maxit J O, Chace D, Wang J, et al, Multi-phase compensated spinner flow meter, United States Patent, No. US6601461B2. Aug. 5, 2003.
[118] Kelder O, Chatriwala S A, Ma S, et al, Expanding advanced production logging operations to short radius horizontal wells. paper SPE 93526, 2005.
[119] Morris C W, Lenn C P, Albertin I J, Water production logging in horizontal wells, Journal of Petroleum Science and Engineering. 1999, 22: 217~227.
[120] Young A R and Johnson S A, A new production logging tool for determining holdups, paper SPE 38652, 1997.
[121] Baldauff J, Runge T, Cadenhead J Faur M, Marcus R, Mas C, North R, Oddie G, Profiling and quantifying complex multiphase flow, Schlumberger Oilfield Review, 2004,16:4~13.
[122]吴世旗,侯连弟,于跃等大庆低渗透油田水平井生产测井技术研究,“八五”国家重点科技攻关项目专题技术总结报告,1996
[123]吴世旗,钟兴福,刘兴斌等,水平井产出剖面测井技术及应用,油气井测试,2005,14(2): 57~59
[124]谢荣华,创新检测技术服务油田开发为创建百年油田提供可靠技术保障,大庆石油地质与开发,2006,25(1): 28~32
[125]崔庆保,高臣,郭忠懿,大庆油田产出剖面测井技术研究与进展,测井技术,2007,31(1): 30~34
[126]吴锡令,景永奇,吴世旗,多相管流电磁成像测井方法研究,地球物理学报,1999,42(4): 557~563
[127]吴锡令,流动成像测井研究进展,地球物理学进展,2002,17(2): 272~276
[128]赵彦伟,吴锡令,王晓星,油井多相流电磁成像测量敏感场仿真,地球物理学报,2007,50(3): 946~950
[129]吴锡令,王晓星,赵彦伟,杨梅,油井流动成像电磁测量方法研究,中国科学D辑:地球科学,2008,38(S1):161~165
[130]杨梅,吴锡令,王志磊等仪器插入情况下倾斜井内油水两相流流型测量实验,科技导报,2008,26(15):73~78
[131]戴家才,郭海敏,和亿成等,水平井、斜井集流式生产测井实验研究,测井技术,2005,29(6):493~495
[132]戴家才,郭海敏,王界益等,多相流生产测井井斜影响试验研究,石油天然气学报,2006,28(3):69~71
[133]侯月明,郭海敏,戴家才等,水平井生产测井解释方法研,测井技术,2004,28(1): 24~26
[134]邹存友,郭海敏,水平井生产测井数据解释模型与实例分析,江汉石油学院学报,2004,26(4):90~91
[135]刘军峰,郭海敏,戴家才,水平井油水两相产液剖面解释方法探讨,石油地质与工程,2006,20(5):43~45
[136]郭海敏,刘军峰,戴家才等,水平井产出剖面解释模型及图版,中国科学D辑:地球科学,2008,38(S2): 146~150
[137]张修刚,王栋,林宗虎,近期多相流过程层析成像技术的发展,热能动力工程,2004,19(3): 221~226
[138]陈德运,张华,朱波等,油水两相流电阻层析成像系统流型的辨识,电机与控制学报,2007,11(6): 639~643
[139] Ismail I, Gamio J C, Bukhari S F A, et al, Tomography for multi-phase flow measurement in the oil industry, Flow. Meas. Instrum. 2005, 16: 145~155
[140] Prasser H M, B?ttger A, Zschau J, A new electrode-mesh tomograph for gas-liquid flows, Flow. Meas. Instrum. 1998, 9: 111~119
[141] Silva M J D, Schleicher E, Hampel U, Capacitance wire-mesh sensor for fast measurement of phase fraction distributions, Meas. Sci. Technol, 2007, 18: 2245~2251
[142] Hogsett S, Ishii M, Local two-phase flow measurements using sensor techniques. Nuclear Engineering and Design, 1997, 175: 15~24
[143] Hibiki T, Ishii M, Experimental study on interfacial area transport in bubbly two-phase flow, Int. J. Heat Mass Transfer, 1999, 4: 3019~3035
[144] Hibiki T, Situ R, Mi Y et al, Local flow measurement of vertical upward bubbly flow in an annulus, Int. J. Heat Mass Transfer, 2003, 46: 1479~1496
[145] Lucas G P, Mishra R, Measurement of bubble velocity components in a swirling gas-liquid pipe flow using a local four-sensor conductance probe, Meas. Sci. Technol, 2005, 16: 749~758
[146] Franca F, Acikgoz M, Lahey R T et al, The use of fractal techniques for flow regime identification. Int. J. Multiphase Flow, 1991, 17: 545~552
[147] Johnsson F, Zijerveld R C, Schouten J C et al, Characterization of fluidization regimes by time-series analysis of pressure fluctuations, Int. J. Multiphase Flow, 2000, 26: 663~715
[148] Jin N D, Nie X B, Ren Y Y et al, Characterization of oil water two phase flow patterns based on nonlinear time series analysis, Flow. Meas. Instrum, 2003, 14: 169~175
[149] Echmann J P, Kamphorst S O, Ruelle D, Recurrence plots of dynamical systems, Europhysics Letters, 1987, 5: 973~977
[150] Zbilut J P, Webber Jr C L, Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A, 1992, 171: 199~203
[151] Jin N D, Zheng G B, Dong F et al, Application of Chaotic Recurrence Plot Analysis to Identification of Oil/Water Two-Phase Flow Patterns, 3rd International Conference on Fuzzy Systems and Knowledge Discovery, Xi’an, P.R. China. 2006, 4223: 1213~1216
[152] Zong Y B, Jin N D, Multi-scale recurrence plot analysis of inclined oil-water two phase flow structure based on conductance fluctuation signals. Eur. Phys. J. Specical Topics. 2008, 164: 165~177
[153] Gandhi A B, Joshi J B, Kulkarni A A et al, SVR-based prediction of point gas hold-up for bubble column reactor through recurrence quantification analysis of LDA time-series, Int. J. Multiphase Flow, 2008, 34: 1099~1107
[154] Takens F, Dynamical system and turbulence, Lectrure Notes in Mathematics. Berlin: Springer-Verlag, 1981, 898: 366~381
[155] Abarbanel H D I, Brown R, Sidorowich J J et al, The analysis of observed chaotic data in physical systems, Reviews of Modern Physicas. 1993, 65: 1331~1392.
[156] Marwan N, Wessel N, Meyerfeldt U et al, Recurrence plot based measures of complexity and its application to heart rate variability data, Physical Review E. 2002, 66(2): 26702.
[157] Annunziato M, Bertini I, Piacentini M, et al, Flame dynamics charaterisation by chaotic analysis of image sequences, 36 Int. Heat Transfer and Fluid Mechanics Institute, Sacramento, USA, 1999
[158] Annunziato M, Abarbanel H D I, Non linear dynamics for classification of multiphase flow regimes. In: Proceedings of International Conference on Soft Computing, Genova, Italy, 1999
[159] LlauróF X, Llop M F, Characterization and classification of fluidization regimes by non-linear analysis of pressure fluctuations, Int. J. Multiphase Flow, 2006, 32: 1397~1404.
[160] Xiao N, Jin N D, Research on flow pattern classification method of two phase flow based on chaotic attractor morphological characteristic, Acta Physica Sinica, 2007, 56(9): 5149~5157
[161] Zheng G B, Jin N D, Jia X H et al, Gas–liquid two phase flow measurement method based on combination instrument of turbine flowmeter and conductance sensor, Int. J. Multiphase Flow, 2008, 34: 1031~1047.
[162]尹左廷,水平井产出剖面测井电导传感器几何结构优化,硕士学位论文,天津大学,2008
[163] van Der Welle R, Void fraction, bubble velocity and bubble size in two-phase flow. Int. J. Multiphase Flow, 1985, 11: 317~345
[164] Vedapuri D, Bessette D, Jepson W P, A segregated flow model to predict water layer thickness in oil-water flows in horizontal and Sligh t ly Inclined P ipelines, BHR Group Conference Series Publication, 1997
[165] Barnea D, Taitel Y, Kelvin-Helmholtz stability criteria for stratified flow:viscous versus non-viscous(inviscid) approaches, Int. J. Multiphase Flow, 1993, 19: 639~649
[166] Kolmogorov A N, On the breaking of drops in turbulent flow, Doklady Akad. Nuuk, 1949, 66: 825~828
[167] Hinze J, Fundamentals of the hydrodynamic mechanism of splitting in dispersion process, AIChE J, 1955, 1: 289~295
[168] Hutchinson P, Hewitt G F and Dukler A E, Deposition of liquid or solid dispersions flow turbulent gas streams; A stochastic model, Chem. Eng.Sci, 1971, 26: 419~439
[169] Taitel Y, Barnea D and Dukler A E, Modeling flow pattern transition for steady upward gas-liquid flow in vertical tubes, AIChE J, 1980, 26: 345~354
[170] Chen X T, Cai X D and Brill J P, A general model for transition to dispersed-bubble flow, Chem. Eng. Sci, 1997, 52: 4373~4370
[171] Yeh G, Haynie Jr F H, Moses R E, Phase-volume relationship at the point of phase inversion in liquid dispersions, AIChE J, 1964, 10(2): 260~265
[172] Decarre S, Fabre J, Phase inversion prediction study, Journal of L’Institute Francais du Prtrole, 1997, 52: 415~424
[173]王福军,计算流体动力学分析:CFD软件原理与应用,北京:清华大学出版社,2004
[174] Launder B E, Spalding D B, Lectures in Mathematical Models of Turbulence. London: Academic Press, 1972
[175] K?rner St, Friedel L, Phase distribution and bubble velocity in two-phase slit flow, Int. J. Multiphase Flow, 1999, 25: 1181~1194
[176] Krishna R, van Baten J M, Simulating the motion of gas bubbles in a liquid, Nature, 1999, 398: 208~208
[177] van Wachem B G and Schouten J C, Experimental validation of 3-D lagrangian VOF model: bubble shape and rise velocity, AIChE J, 2002, 48(12): 2744~2753
[178] L?rstad D, Fuchs L, High-order surface tension VOF-model for 3D bubble flows with high density ratio, Journal of Computational Physics, 2004, 200: 153~176
[179] Beck M S, Correlation in instruments: cross correlation flowmeters, Journal of Physics E (Scientific Instruments), 1981, 14(1): 7~19
[180] Thorn R, Beck M S, Green R G, Non-intrusive methods of velocity measurement in pneumatic conveying, Journal of Physics E (Scientific Instruments), 1982, 15(11): 1131~1139
[181]赵鑫,金宁德,王化祥,相关流量测量技术发展,化工自动化及仪表,2005,32(1):1~6
[182]刘兴斌,胡金海,周家强等,电导式相关流量测井仪在产出剖面测井中的应用,测井技术,2004,28(02):138~140,144
[183]胡金海,刘兴斌,黄春辉等,相关流量计水平条件下两相流实验效果分析,测井技术,2006,30(01):54~56
[184]刘兴斌,强锡富,庄海军等,集流型流体电容仪测量井下油水两相流的含水率,传感器技术,1995,4:50~53
[185] Schlumberger, Production Logging Interpretation, 1970
[186]董芳,金宁德,宗艳波等,两相流流型动力学特征多尺度递归定量分析,物理学报, 2008, 57(10): 6145~6154
[187]肖楠,金宁德,基于混沌吸引子形态特性的两相流流型分类方法研究,物理学报,2007, 56(9): 5149~5156
[188] Gao Z K, Jin N D, Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks, Physcial Review E, 2009, 79, 066303
[189]徐苓安,相关流量计的设计与应用,天津:天津大学出版社,1992
[2] Zavareh F, Hill A D, Podio A L, Flow regimes in vertical and inclined oil/water flow in pipes, paper SPE 18215, 1988
[3] Flores J G, Chen X T, Sarica C et al, Characterization of oil-water flow patterns in vertical and deviated wells, paper SPE 38810, 1997
[4] Bannwart A C, Rodriguez O M H, Carvalho C H M et al, Flow patterns in heavy crude oil-water flow, Transactions of the ASME, 2004,126:184~189
[5] Rodriguez O M H, Bannwart A C, Experimental study on interfacial waves in vertical core flow, Journal of Petroleum Science and Engineering, 2006,54: 140~148
[6] Lin R.H., Tavlarides L.L.,. Flow patterns of n-hexadecane-CO2 liquid-liquid two-phase flow in vertical pipes under high pressure. International Journal of Multiphase flow, 2009, 35: 566～579
[7] Schlumberger, Production Looging Interpretation, 1973
[8]钟兴福,黄志尧,吕鹏举等,125mm垂直圆管中油水两相流流型辨识研究,石油学报, 2001, 22(5):89~94
[9]李明忠,王卫阳,陈听宽等,垂直管中油-两相流的持水率预测方法研究,西安交通大学学报,2002,36(3): 252~256
[10] Jin N D, Nie X B, Wang J, et al, Flow pattern identification of oil/water two phase flow based on kinematic wave theory, Flow Measurement and Instrumentation, 2003, 14: 177~182
[11] Mukherjee H, Brill J P, Beggs H D, Experimental study of oil–water flow in inclined pipes, Transactions of the ASME, 1981, 103: 56~66
[12] Hill A D, and Oolman T, Production logging tool behavior in two-phase inclined flow, Journal of Petroleum Technology, 1982, 34: 2432~2440
[13] Davarzani J, Sloan L, Roesner R E., Research on simultaneous production logging instruments in multiphase flow loop, Paper SPE 14431, presented at the 60th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers held in Las Vegas, 1985, September, 22-25
[14] Vigneaux P, Chenais P, and Hulin J P, Liquid-liquid flow in an inclined pipe, AIChE J., 1988, 34: 781-789
[15] Tabeling P, Pouliquen O, Theron B, et al, Oil-water flows in deviated pipes: Experimental study and modelling, Proceedings of the 5th International Conference on Multiphase Flow Production, Cannes, France, 1991, 19-21 June, 294-306
[16] Ding Z X, Ullah K and Huang Y, A comparison of predictive oil/water holdup models for production log interpretation in vertical and deviated wellbores, SPWLA 35th Annual Logging Symposium, Tulsa, 1994 19-22, June
[17] Hasan A R, Kabir C S, A simplified model for oil-water flow in vertical and deviated wellbores, Paper SPE 49163. SPE Annual Technical Conference and Exhibition, New Orleans,Louisiana, 1998, 27-30 September
[18] Lucas G P, and Jin N D, Investigation of a drift velocity model for predicting superficial velocities of oil and water in inclined oil-in-water pipe flows with a centre body, Meas. Sci. Technol. 2001, 12: 1546~1554
[19] Lucas G P, and Jin N D, Measurement of the homogeneous velocity of inclined oil-in-water flows using a resistance cross correlation flow meter, Meas. Sci. Technol. 2001, 12: 1529~1537
[20] Dong F, Liu X P, Deng X, et al, Identification of two-phase flow regimes in horizontal, inclined and vertical pipes, Meas. Sci. Technol., 2001, 12: 1069~1075
[21] Oddie G, Shi H, Durlofsky L J, et al, Experimental study of two and three phase flows in large diameter inclined pipes, Int. J. Multiphase Flow, 2003, 29, 527~558
[22] Lum J Y L, Al-Wahaibi T, Angeli P, Upward and downward inclination oil-water flows, Int. J. Multiphase Flow, 2006, 32: 413~435
[23]罗彦生,董福印,张晓东,斜井油水两相流动产出剖面测试技术,测井技术, 1998, 22: 168~171
[24]赵忠健,王培烈,梅继兵, JLS-25伞式集流型测试仪在斜井中的实验研究,测井技术, 2000, 24: 145~147
[25]钟兴福,李彦华,王德坤等,集流型测试仪在斜井中的响应研究,仪器仪表学报, 2001, 22: 380~380.
[26]戴家才,郭海敏,王界益等,多相流生产测井井斜影响试验研究,石油天然气学报, 2006, 28: 69~71
[27] Mobbs S D, and Lucas G P, A turbulence model for inclined, bubbly flows. Applied Scientific Research, 1993, 51: 263~268
[28] Lucas G P, Modelling velocity profiles in inclined multiphase flow to provide a priori information for flow imaging. The Chemical Engineering Journal. 1995, 56: 167~173
[29] Brauner N, liquid-liquid two phase flow systems. in: V. Bertola (Ed.), Modeling and control of two-phase flow phenomena, CISM Center, Udine,Italy. 2002
[30] Russell T W F, Hodgson G W, Govier G W, Horizontal pipeline flow of mixtures of oil and water, Canadian Journal of Chemical Engineering, 1959, 37(1): 9~17
[31] Charles M E, Govier G W, Hodgson G W, The horizontal pipeline flow of equal density oil-water mixture, Canadian Journal of Chemical Engineering, 1961, 39(2): 27~36
[32] Hasson D, Mann U, Nir A, Annular flow of two immiscible liquids, The Canadian Journal of Chemical Engineering, 1970, 48: 514~520
[33] Guzhov A I,Girsin A D,Medvedev V F, et a1, Emulsion Formation During the Flow of Two Liquids in a Pipe, Neft Khoz, 1973, 8(8): 58~61
[34] Malinowsky M S, An experimental study of oil-water and air-oil-water flowing mixtures in horizontal pipes, MS Thesis, U. of Tulsa, 1975
[35] Oglesby K D, An experimental study on the effect of oil viscosity,mixture velocity and water fraction on horizontal oil-water flow, MS Thesis, U. of Tulsa, 1979
[36] Arirachakaran S, Oglesby K D, Malinowski M S, An analysis of oil/water phenomena in horizontal pipes, SPE Productions Operations Symp, SPE 18836, 1989
[37] Trallero J L, Brill J P, A study of oil-water flow patterns in horizontal pipes, SPE 36609, 1996
[38] Nadler M, Mewes D, Flow induced emulsification in the flow of two immiscible liquids in horizontal pipes, International Journal of Multiphase Flow, 1997,23(1): 55~68
[39] Angeli P, Hewitt G F, Pressure gradient in horizontal liquid-liquid flows, International Journal of Multiphase Flow, 1998, 24: 1183~1203
[40] Angeli P, Hewitt G F, Flow structure in horizontal oil-water flow, International Journal of Multiphase Flow, 2000, 26: 1117~1140
[41] Brauner N, Maron D M, Flow pattern transitions in two-phase liquid-liquid flow in horizontal tubes, International Journal of Multiphase Flow, 1992, 18: 123~140
[42] Brauner N, Rovinsky J, Moalem Maron, Determination of the interface curvature in stratified two-phase systems by energy considerations, International Journal of Multiphase Flow, 1996, 22: 1167~1185
[43] Brauner N, Maron D M, Rovinsky J, A two-fluid model for stratified flows with curved interfaces, International Journal of Multiphase Flow, 1998, 24: 975~1004
[44] Gorelik D, Brauner N, The interface configuration in two-phase stratified pipe flow, International Journal of Multiphase Flow, 1999, 25: 977~1007
[45] Shi H, Jepson W P, The effect of surfactants on flow characteristics in oil-water flows in large diameter horizontal pipelines, BHRA, 1997
[46] Elseth G, An Experimental study of oil-water flow in horizontal pipes, PhD Dissertation, The Norwegian University of Science and Technology, 2001
[47] Shi H, Cai J, Jepson W P, Oil-water two-phase flows in large-diameter pipelines, Transactions of the ASME, 2001, 123(12):270~276
[48] Brauner N, The prediction of dispersed flows boundaries in liquid-liquid and gas-liquid systems, International Journal of Multiphase Flow, 2001, 27: 885~910
[49] Brauner N, Ullmann A, Modelling of phase inversion phenomenon in two-phase pipe flow, International Journal of Multiphase Flow, 2002, 28: 1177~1204
[50] Ng T S, Lawrence C J, Hewitt G F, Interface shaped for two-phase laminar stratified flow in a circular pipe, International Journal of Multiphase Flow, 2001, 27: 1301~1311
[51] Ng T S, Lawrence C J, Hewitt G F, Laminar stratified pipe flow, International Journal of Multiphase Flow, 2002, 28: 963~996
[52] Lum J Y L, Lovick J, Angeli P, Dual continuous horizontal and low inclination two-phase liquid flows, The Canadian Journal of Chemical Engineering, 2004, 83(2):303~315
[53] Lovick J, Angeli P, Droplet size and velocity profiles in liquid–liquid horizontal flows, Chem. Eng. Sci., 2004, 59(15): 3105~3115
[54] Soleimani A, Lawrence C J, Hewitt G F, Spatial distribution of oil and water horizontal pipe flow, SPE 56524. SPE Annual Technical Conference and Exhibition, Houston, USA, 1999
[55] Kvandal H K, Elseth G, Melaaen M C, Measurement of velocity and phase fraction in dispersed two-phase flow, Int. Symp. on Liquid-Liquid Two-Phase Flow and Transport Phenomena. Antalya, Turkey, 2000
[56] Ioannou K, Nydal O J, Angeli P, Phase inversion in dispersed liquid–liquid flows, Experimental Thermal and Fluid Science, 2005, 29: 331~339
[57] Calos F T M, Modeling of oil-water flow in horizontal and near horizontal pipes, PhD Dissertation, University of Tulsa, 2006
[58] Al-Wahaibi T, Angeli P, Transition between stratified and non-stratified horizontal oil-water flow, PartⅠ: Stability analysis. Chemical Engineering Science. .2007, 62: 2915~2928
[59] Al-Wahaibi T, Smith M, Angeli P, Transition between stratified and non-stratified horizontal oil-water flow. PartⅡ: Mechanism of drop formation. Chemical Engineering Science. 2007, 62: 2929~2940
[60]蔡继勇,陈听宽,汤为等,水平管内油水乳状液流动特性研究,化学工程,1999,27(3): 32~35
[61]陈杰,孙红彦,梁志鹏等,水平管内油水两相流流型的实验研究,油气储运,2000,19 (12):27~31
[62]陈杰,于达,严大凡,水平管内油-水两相流动压降规律的实验研究,实验力学, 2001, 16 (4): 402~408
[63]陈杰,于达,严大凡,油-水两相流流型转换研究,水动力学研究与进展,2003, 18 (3): 355~364
[64]姚海元,宫敬,水平管内油水两相流流型转换特性,化工学报,2005,56(9):1649~1653
[65]窦丹,于达,宫敬,原油/水管流压降规律实验,石油化工高等学校学报, 2006,19(2): 60～63
[66]宫敬,王玮,于达,稠油-水两相水平管流流型实验研究,石油学报,2007,28 (2): 140~143
[67]徐孝轩,宫敬,水平管中油水两相流动研究进展,化工机械,2006,33 (1):59~65
[68] Xu X X, Study on oil-water two-phase flow in horizontal pipelines, Journal of Petroleum Science and Engineering, 2007, 59(1-2): 43~58
[69]吴铁军,郭烈锦,刘文红等,水平管内油水两相流流型及其转换规律研究,工程热物理学报,2002,23 (4):491~494
[70] Liu W H, Guo L J, Wu T J, et al, An experimental study on the flow characteristics of oil-water two-phase flow in horizontal straight pipes, Chinese J. Chem. Eng., 2003, 11(5): 491~496
[71]顾汉洋,高晖,郭烈锦,水平管油水两相分层紊流流动的数值研究,工程热物理学报,2003, 24(5): 810~812
[72] Gao H, Gu H Y, Guo L J, Numerical study of stratified oil-water two-phase turbulent flow in a horizontal tube, International Journal of Heat and Mass Transfer, 2003, 46: 749~754
[73] Vallée C, H?hne T, Prasser H M, et al, Experimental investigation and CFD simulation of horizontal stratified two-phase flow phenomena, Nuclear Engineering and Design, 2008, 238(3): 637~646
[74]张修刚,牛冬梅,苏新军等,水平管内油水两相流动摩擦压降的试验研究,油气储运,2003,22(2): 47~50
[75]王树众,牛冬梅,林宗虎等,油水混合物在水平管众的二相流动特性研究,化学工程,2005,33(2): 26~29
[76]张丽娜,王小尚,张荷玲等,新型油水两相水平管流流型分类方法,油气储运,2006,25(10):49~51
[77]康万利,刘忠和,刘国权,国外水平管内油水两相流压降模型研究进展,大庆石油学院学报,2006,30(5): 20~23
[78]马龙博,张宏建,周洪亮等,基于Hilbert-Huang变换和支持向量机的油水两相流流型识别,化工学报,2007,58(3):617~622
[79] Piela K, Delfos R, Ooms G, et al, Experimental investigation of phase inversion in an oil-water flow through a horizontal pipe loop, International Journal of Multiphase Flow, 2006, 32: 1087~1099
[80] Piela K, Delfos R, Ooms G, et al, On the phase inversion process in an oil-water pipe flow, International Journal of Multiphase Flow, 2008, 34: 665~677
[81] Piela K, Delfos R, Ooms G, et al, phase inversion in the mixing zone between a water flow and an oil flow through a pipe, International Journal of Multiphase Flow, 2009, 35: 91~95
[82] Grassi B, Strazza D, Poesio P, Experimental validation of theoretical models in two-phase high-viscosity ratio liquid-liquid flows in horizontal and slightly inclined pipes, International Journal of Multiphase Flow, 2008, 34: 950~965
[83] Xu J Y, Wu Y X, Feng F F, et al, Experimental investigation on the slip between oil and water in horizontal pipes, Experimental Thermal and Fluid Science, 2008, 33: 178~183
[84] Farrar B, Bruun H H, A computer based hot-film technique used for flow measurements in a vertical kerosene-water pipe flow, International Journal of Multiphase Flow, 1996, 22: 733~751
[85] Jana A K, Das G, Das P K, A novel technique to identify flow patterns during liquid-liquid two-phase upflow through a vertical pipe, Ind. Eng. Chem. Res., 2006, 45:2381~2393
[86] Jana A K, Das G, Das P K, Flow regime identification of two-phase liquid-liquid upflow through vertical pipe, Chemical Engineering Science, 2006, 61: 1500~1515
[87] Augier F, Guiraud P, Masbernat O, Velocity fluctuations in a homogeneous dispersed liquid-liquid flow at high phase fraction. ICMF04, Yokohama, Japan, 2004
[88] Jin N D, Zhao X, Wang J et al, Design and geometry optimization of a conductive probe with a vertical multiple electrode array for measuring volume fraction and axial velocity of two-phase flow. Meas. Sci. Technol. 2008,19, 045403
[89]胡金海,刘兴斌,黄春辉等,一种同时测量流量和含水率的电导式传感器,测井技术,2002,26(2):154~157
[90] Jones Jr, Zuber N, The interrelation between void fraction fluctuation and flow pattern in two-phase flow, Int. J. Multiphase Flow, 1975, 2(2): 273~306
[91] Lee J Y, Kim N S, Ishii M, Flow regime identification using chaotic characteristics of two-phase flow, Nuclear Engineering and Design, 2008, 238: 945~957
[92] Hubbard M G, Dukler A E, The characterization of flow regimes for horizontal two-phase flow, Proc. Heat Transfer &Fluid Mechanics Inst, 1966: 100~121
[93] Albrecht R W et al, Measurement of two-phase flow properties using the nuclear reactor instrument, Prog. Nucl. Energy, 1982, 37~50
[94]黄志尧,王保良,李海青等,软测量技术在多相流检测中的应用,仪器仪表学报,2001,22(3):421～424
[95] Wu H J, Zhou F D, Wu Y Y, Intelligent identification system of flow regime of oil/gas/water, Int. J. Multiphase Flow, 2001,27: 459~475
[96]赵鑫,金宁德,李伟波,油水两相流相含率的软测量方法。化工学报,2005,56(10):1875~1879
[97] Oddie G M, On the detection of a low-dimensional attractor in disperse two-component (oil-water) flow in a vertical pipe, Flow. Meas. Instrum. 1991, 2: 225~229
[98]金宁德,宁英男,王微微等,垂直上升管中油水两相流流型表征,化工学报,2001,52(10):907~915
[99]郑桂波,金宁德,两相流流型多尺度熵及动力学特性分析,物理学报,2009,58(7): 4485~4492
[100]金宁德,李伟波,赵鑫,利用符号时间序列分析方法表征垂直上升管中油水两相流流型,化工学报,2005,56(1):116~120
[101] Maxwell J C, A Treatise on Electricity and Magnetism,Clarendon Press, Oxford, 1882
[102] De La Rue R E, Tobias C W, On the conductivity of dispersions, Journal of the Electrochemical Society, 1959,106(9): 827~832
[103] Nasr-EI-Din H, Shook C A, Ccowell J, A conductivity probe for measuring local concentrations in slurry systems. Int. J. Multiphase Flow., 1987, 13(3): 365~378
[104] Turner J C R, Electrical conductivity of liquid-fluidised beds, AIChE Symposium Series, 1973, 69(128): 115~122
[105] Bruggeman D A G, Calculation of different physical constants of heterogeneous substances. Annalen Physica, 1935,(24): 636~679
[106] Lemlich R, A theory for the limiting conductivity of polyhedral foam at low density, J. Colloids Interface Sci., 1978, 64(1): 107~110
[107] Feitosa K, Marze S, Saint-Jalmes A, et al, Electrical conductivity of dispersions: from dry foams to dilute suspensions, J. Phys. Condens., 2005, 17: 6301~6305
[108] Coney M W E, The theory and application of conductance probes for the measurement of liquid film thickness in two phase flow, J. Phys. E: Scient Instrum, 1973, 6: 903~910
[109] Andreussi P, Donfrancesco A D, Messia M, An impedance method for the measurement of liquid hold-up in two phase flow, Int. J. Multiphase Flow, 1988, 14 (6): 777~785
[110] Zhao D J, Guo L J, Hu X W, et al, Experimental study on local characterisicts of oil-water dispersed flow in vertical pipe, Int. J. Multiph. Flow., 2006, 32: 1254~1268
[111] Lucas G P, Panagiotopoulos N, Oil volume fraction and velocity profiles in vertical, bubbly oil-in-water flows, Flow. Meas. Instrum. 2009, 20(3): 127~135
[112] Wu Q, Ishii M, Sensitivity study on double-sensor conductivity probe for the measurement of interfacial area concentration in bubbly flow, Int. J. Multiphase Flow, 1999, 25: 155~173
[113] Fairuzov Y V, Arenas-Medina P, Verdejo-Fierro J,et al, Flow pattern transitions in horizontal pipelines carrying oil-water mixtures: full-scale experiments, Journal of Energy Resources Technology, 2000, 122: 169~176
[114] Evans J T, Forgang S, Itskovich G B, Downhole multiphase flow sensor, United States Patent, No. 5736637. Apr. 7, 1998.
[115] Chace D, Trcka D, Georgi D, et al, New instrument and methods for production logging in multiphase horizontal wells, paper SPE 53320, 1999.
[116] Maxit J O, Reittinger P W, Wang J, et al, Downhole instrumentation for the measurement of three-phase volume fractions and phase velocities in horizontal wells. Transactions of the ASME, 2000, Vol.122: 56~60.
[117] Maxit J O, Chace D, Wang J, et al, Multi-phase compensated spinner flow meter, United States Patent, No. US6601461B2. Aug. 5, 2003.
[118] Kelder O, Chatriwala S A, Ma S, et al, Expanding advanced production logging operations to short radius horizontal wells. paper SPE 93526, 2005.
[119] Morris C W, Lenn C P, Albertin I J, Water production logging in horizontal wells, Journal of Petroleum Science and Engineering. 1999, 22: 217~227.
[120] Young A R and Johnson S A, A new production logging tool for determining holdups, paper SPE 38652, 1997.
[121] Baldauff J, Runge T, Cadenhead J Faur M, Marcus R, Mas C, North R, Oddie G, Profiling and quantifying complex multiphase flow, Schlumberger Oilfield Review, 2004,16:4~13.
[122]吴世旗,侯连弟,于跃等大庆低渗透油田水平井生产测井技术研究,“八五”国家重点科技攻关项目专题技术总结报告,1996
[123]吴世旗,钟兴福,刘兴斌等,水平井产出剖面测井技术及应用,油气井测试,2005,14(2): 57~59
[124]谢荣华,创新检测技术服务油田开发为创建百年油田提供可靠技术保障,大庆石油地质与开发,2006,25(1): 28~32
[125]崔庆保,高臣,郭忠懿,大庆油田产出剖面测井技术研究与进展,测井技术,2007,31(1): 30~34
[126]吴锡令,景永奇,吴世旗,多相管流电磁成像测井方法研究,地球物理学报,1999,42(4): 557~563
[127]吴锡令,流动成像测井研究进展,地球物理学进展,2002,17(2): 272~276
[128]赵彦伟,吴锡令,王晓星,油井多相流电磁成像测量敏感场仿真,地球物理学报,2007,50(3): 946~950
[129]吴锡令,王晓星,赵彦伟,杨梅,油井流动成像电磁测量方法研究,中国科学D辑:地球科学,2008,38(S1):161~165
[130]杨梅,吴锡令,王志磊等仪器插入情况下倾斜井内油水两相流流型测量实验,科技导报,2008,26(15):73~78
[131]戴家才,郭海敏,和亿成等,水平井、斜井集流式生产测井实验研究,测井技术,2005,29(6):493~495
[132]戴家才,郭海敏,王界益等,多相流生产测井井斜影响试验研究,石油天然气学报,2006,28(3):69~71
[133]侯月明,郭海敏,戴家才等,水平井生产测井解释方法研,测井技术,2004,28(1): 24~26
[134]邹存友,郭海敏,水平井生产测井数据解释模型与实例分析,江汉石油学院学报,2004,26(4):90~91
[135]刘军峰,郭海敏,戴家才,水平井油水两相产液剖面解释方法探讨,石油地质与工程,2006,20(5):43~45
[136]郭海敏,刘军峰,戴家才等,水平井产出剖面解释模型及图版,中国科学D辑:地球科学,2008,38(S2): 146~150
[137]张修刚,王栋,林宗虎,近期多相流过程层析成像技术的发展,热能动力工程,2004,19(3): 221~226
[138]陈德运,张华,朱波等,油水两相流电阻层析成像系统流型的辨识,电机与控制学报,2007,11(6): 639~643
[139] Ismail I, Gamio J C, Bukhari S F A, et al, Tomography for multi-phase flow measurement in the oil industry, Flow. Meas. Instrum. 2005, 16: 145~155
[140] Prasser H M, B?ttger A, Zschau J, A new electrode-mesh tomograph for gas-liquid flows, Flow. Meas. Instrum. 1998, 9: 111~119
[141] Silva M J D, Schleicher E, Hampel U, Capacitance wire-mesh sensor for fast measurement of phase fraction distributions, Meas. Sci. Technol, 2007, 18: 2245~2251
[142] Hogsett S, Ishii M, Local two-phase flow measurements using sensor techniques. Nuclear Engineering and Design, 1997, 175: 15~24
[143] Hibiki T, Ishii M, Experimental study on interfacial area transport in bubbly two-phase flow, Int. J. Heat Mass Transfer, 1999, 4: 3019~3035
[144] Hibiki T, Situ R, Mi Y et al, Local flow measurement of vertical upward bubbly flow in an annulus, Int. J. Heat Mass Transfer, 2003, 46: 1479~1496
[145] Lucas G P, Mishra R, Measurement of bubble velocity components in a swirling gas-liquid pipe flow using a local four-sensor conductance probe, Meas. Sci. Technol, 2005, 16: 749~758
[146] Franca F, Acikgoz M, Lahey R T et al, The use of fractal techniques for flow regime identification. Int. J. Multiphase Flow, 1991, 17: 545~552
[147] Johnsson F, Zijerveld R C, Schouten J C et al, Characterization of fluidization regimes by time-series analysis of pressure fluctuations, Int. J. Multiphase Flow, 2000, 26: 663~715
[148] Jin N D, Nie X B, Ren Y Y et al, Characterization of oil water two phase flow patterns based on nonlinear time series analysis, Flow. Meas. Instrum, 2003, 14: 169~175
[149] Echmann J P, Kamphorst S O, Ruelle D, Recurrence plots of dynamical systems, Europhysics Letters, 1987, 5: 973~977
[150] Zbilut J P, Webber Jr C L, Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A, 1992, 171: 199~203
[151] Jin N D, Zheng G B, Dong F et al, Application of Chaotic Recurrence Plot Analysis to Identification of Oil/Water Two-Phase Flow Patterns, 3rd International Conference on Fuzzy Systems and Knowledge Discovery, Xi’an, P.R. China. 2006, 4223: 1213~1216
[152] Zong Y B, Jin N D, Multi-scale recurrence plot analysis of inclined oil-water two phase flow structure based on conductance fluctuation signals. Eur. Phys. J. Specical Topics. 2008, 164: 165~177
[153] Gandhi A B, Joshi J B, Kulkarni A A et al, SVR-based prediction of point gas hold-up for bubble column reactor through recurrence quantification analysis of LDA time-series, Int. J. Multiphase Flow, 2008, 34: 1099~1107
[154] Takens F, Dynamical system and turbulence, Lectrure Notes in Mathematics. Berlin: Springer-Verlag, 1981, 898: 366~381
[155] Abarbanel H D I, Brown R, Sidorowich J J et al, The analysis of observed chaotic data in physical systems, Reviews of Modern Physicas. 1993, 65: 1331~1392.
[156] Marwan N, Wessel N, Meyerfeldt U et al, Recurrence plot based measures of complexity and its application to heart rate variability data, Physical Review E. 2002, 66(2): 26702.
[157] Annunziato M, Bertini I, Piacentini M, et al, Flame dynamics charaterisation by chaotic analysis of image sequences, 36 Int. Heat Transfer and Fluid Mechanics Institute, Sacramento, USA, 1999
[158] Annunziato M, Abarbanel H D I, Non linear dynamics for classification of multiphase flow regimes. In: Proceedings of International Conference on Soft Computing, Genova, Italy, 1999
[159] LlauróF X, Llop M F, Characterization and classification of fluidization regimes by non-linear analysis of pressure fluctuations, Int. J. Multiphase Flow, 2006, 32: 1397~1404.
[160] Xiao N, Jin N D, Research on flow pattern classification method of two phase flow based on chaotic attractor morphological characteristic, Acta Physica Sinica, 2007, 56(9): 5149~5157
[161] Zheng G B, Jin N D, Jia X H et al, Gas–liquid two phase flow measurement method based on combination instrument of turbine flowmeter and conductance sensor, Int. J. Multiphase Flow, 2008, 34: 1031~1047.
[162]尹左廷,水平井产出剖面测井电导传感器几何结构优化,硕士学位论文,天津大学,2008
[163] van Der Welle R, Void fraction, bubble velocity and bubble size in two-phase flow. Int. J. Multiphase Flow, 1985, 11: 317~345
[164] Vedapuri D, Bessette D, Jepson W P, A segregated flow model to predict water layer thickness in oil-water flows in horizontal and Sligh t ly Inclined P ipelines, BHR Group Conference Series Publication, 1997
[165] Barnea D, Taitel Y, Kelvin-Helmholtz stability criteria for stratified flow:viscous versus non-viscous(inviscid) approaches, Int. J. Multiphase Flow, 1993, 19: 639~649
[166] Kolmogorov A N, On the breaking of drops in turbulent flow, Doklady Akad. Nuuk, 1949, 66: 825~828
[167] Hinze J, Fundamentals of the hydrodynamic mechanism of splitting in dispersion process, AIChE J, 1955, 1: 289~295
[168] Hutchinson P, Hewitt G F and Dukler A E, Deposition of liquid or solid dispersions flow turbulent gas streams; A stochastic model, Chem. Eng.Sci, 1971, 26: 419~439
[169] Taitel Y, Barnea D and Dukler A E, Modeling flow pattern transition for steady upward gas-liquid flow in vertical tubes, AIChE J, 1980, 26: 345~354
[170] Chen X T, Cai X D and Brill J P, A general model for transition to dispersed-bubble flow, Chem. Eng. Sci, 1997, 52: 4373~4370
[171] Yeh G, Haynie Jr F H, Moses R E, Phase-volume relationship at the point of phase inversion in liquid dispersions, AIChE J, 1964, 10(2): 260~265
[172] Decarre S, Fabre J, Phase inversion prediction study, Journal of L’Institute Francais du Prtrole, 1997, 52: 415~424
[173]王福军,计算流体动力学分析:CFD软件原理与应用,北京:清华大学出版社,2004
[174] Launder B E, Spalding D B, Lectures in Mathematical Models of Turbulence. London: Academic Press, 1972
[175] K?rner St, Friedel L, Phase distribution and bubble velocity in two-phase slit flow, Int. J. Multiphase Flow, 1999, 25: 1181~1194
[176] Krishna R, van Baten J M, Simulating the motion of gas bubbles in a liquid, Nature, 1999, 398: 208~208
[177] van Wachem B G and Schouten J C, Experimental validation of 3-D lagrangian VOF model: bubble shape and rise velocity, AIChE J, 2002, 48(12): 2744~2753
[178] L?rstad D, Fuchs L, High-order surface tension VOF-model for 3D bubble flows with high density ratio, Journal of Computational Physics, 2004, 200: 153~176
[179] Beck M S, Correlation in instruments: cross correlation flowmeters, Journal of Physics E (Scientific Instruments), 1981, 14(1): 7~19
[180] Thorn R, Beck M S, Green R G, Non-intrusive methods of velocity measurement in pneumatic conveying, Journal of Physics E (Scientific Instruments), 1982, 15(11): 1131~1139
[181]赵鑫,金宁德,王化祥,相关流量测量技术发展,化工自动化及仪表,2005,32(1):1~6
[182]刘兴斌,胡金海,周家强等,电导式相关流量测井仪在产出剖面测井中的应用,测井技术,2004,28(02):138~140,144
[183]胡金海,刘兴斌,黄春辉等,相关流量计水平条件下两相流实验效果分析,测井技术,2006,30(01):54~56
[184]刘兴斌,强锡富,庄海军等,集流型流体电容仪测量井下油水两相流的含水率,传感器技术,1995,4:50~53
[185] Schlumberger, Production Logging Interpretation, 1970
[186]董芳,金宁德,宗艳波等,两相流流型动力学特征多尺度递归定量分析,物理学报, 2008, 57(10): 6145~6154
[187]肖楠,金宁德,基于混沌吸引子形态特性的两相流流型分类方法研究,物理学报,2007, 56(9): 5149~5156
[188] Gao Z K, Jin N D, Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks, Physcial Review E, 2009, 79, 066303
[189]徐苓安,相关流量计的设计与应用,天津:天津大学出版社,1992