混沌动力学方法在石油两相管流参数检测中的应用
摘要
两相流参数的测量一直是倍受关注的问题。两相流流型辨识，流量和
含率的测量对两相流系统的工业应用具有重要的意义。本文在对国内外
有关文献资料研究的基础上，提出了将混沌、分形技术应用于两相流参
数检测的新思想。主要工作及成果如下：
1 回顾了混沌理论的发展历史，在对混沌动力学方法作了比较全面
的综述之后，提出了基于混沌的两相流参数测量思路，着重研究
了混沌方法是如何应用于两相流参数检测的问题，设计出基于混
沌方法的两相流参数检测方案，为两相流参数测量开辟了一条新
的途径。
2 对大直径圆管中油水两相垂直流动时的流型重新进行了实验描
述和划分，建立了具有实用价值的流型判别标准，实现了用流量
法和持水率法对流型的辨识。通过模拟实验发现垂直管的流型具
有尺度效应，实验证明，不同实验条件下，尤其是在不同管径下
用流量或流速表示的过渡判据不能成比例地放大或缩小到其它
管径中进行流型判别。
3 建立了适用于垂直管两相流系统的两相流动非线性动力学模
型，用数值实验证明了两相流动中存在混沌现象。理论计算出两
相流系统由稳定的流动转变为混沌时的分叉值和两相流动发生
混沌现象时基本参数的范围。制作出具有推广意义的两相流动系
统的理论图版，并在油水两相流动实验中得到了验证。建立的非
线性动力学模型提供了一种研究两相流动特性的新理论工具。
4 提出了基于混沌分析方法的两相流流型辨识方法，实现了用
Poincare截面、分维数等对流型的客观辨识。通过大直径圆管中
的大量实验验证，对油泡流、分散油泡流两种流型的总体辨识成
功率都在78％以上。实验结果同时表明，关联维数对流型变化比
较敏感，可以作为判别流型的指示器。
5 提出了基于Poincare截面、关联维数分析，实现从单变量动态测
量信号中提取流量和含率信息的两相流参数检测的新方法，并通
一
过实验验证了这种方法的可行性。
Two-phase flow parameter measurement is an unresolved problem. The
identification of two-phase flow patterns, flowrate and phase fl-action
measurement are very important for the industrial applications of two-phase
flow system. This dissertation applies chaos and fractal technique to the two-
phase flow measurement. The main research results and contributions are
listed as following:
1 Based on the review of chaos techniques and its applications, a new idea
and a new scheme for flow parameter measurements of two-phase flow
are proposed.
2 Flow patterns are classified by experimental investigation of oil and
water mixture flow in large diameter vertical pipes. Practical criterion of
flow pattern identification is developed. The flow pattern can be
identified by the measurements of flow rate and water holdup. The
experimental results also show that the proposed flow pattern
identification criterion can not be applied to other pipes with different
diameter because of the scale effect of flow pattern in large diameter
vertical pipes.
3 A nonlinear dynamical model of two-phase flow is developed. The
nonlinear dynamical behavior (chaos phenomena) of two-phase flow
systems is proved by numerical experiments. Based on this model, some
bifurcation parameters are obtained, as well as the flow-parameter ranges
of two-phase flow when the chaos phenomena take place in two-phase
flow systems. Also, a theoretical graph is developed and verified by
oil/water two-phase flow experiments. The presented model provides a
new theoretical tool for the study of two-phase flow.
4 A new method for flow pattern identification is presented based on the
chaos techniques by using Poincare map and fractal dimension etc.. The
experimental results show that the total accuracy to distinguish bubble
flow and dispersed bubble flow is above 78% and the correlation
dimension can be used as flow pattern indicator because of its sensibility
to the change of flow pattern.
5 A new method for the on-line measurements of flow rate and water
iii
fraction from a time series is proposed by using Poincare map and
correlation dimension analysis. The feasibility of this method is
supported by experiments.
含率的测量对两相流系统的工业应用具有重要的意义。本文在对国内外
有关文献资料研究的基础上，提出了将混沌、分形技术应用于两相流参
数检测的新思想。主要工作及成果如下：
1 回顾了混沌理论的发展历史，在对混沌动力学方法作了比较全面
的综述之后，提出了基于混沌的两相流参数测量思路，着重研究
了混沌方法是如何应用于两相流参数检测的问题，设计出基于混
沌方法的两相流参数检测方案，为两相流参数测量开辟了一条新
的途径。
2 对大直径圆管中油水两相垂直流动时的流型重新进行了实验描
述和划分，建立了具有实用价值的流型判别标准，实现了用流量
法和持水率法对流型的辨识。通过模拟实验发现垂直管的流型具
有尺度效应，实验证明，不同实验条件下，尤其是在不同管径下
用流量或流速表示的过渡判据不能成比例地放大或缩小到其它
管径中进行流型判别。
3 建立了适用于垂直管两相流系统的两相流动非线性动力学模
型，用数值实验证明了两相流动中存在混沌现象。理论计算出两
相流系统由稳定的流动转变为混沌时的分叉值和两相流动发生
混沌现象时基本参数的范围。制作出具有推广意义的两相流动系
统的理论图版，并在油水两相流动实验中得到了验证。建立的非
线性动力学模型提供了一种研究两相流动特性的新理论工具。
4 提出了基于混沌分析方法的两相流流型辨识方法，实现了用
Poincare截面、分维数等对流型的客观辨识。通过大直径圆管中
的大量实验验证，对油泡流、分散油泡流两种流型的总体辨识成
功率都在78％以上。实验结果同时表明，关联维数对流型变化比
较敏感，可以作为判别流型的指示器。
5 提出了基于Poincare截面、关联维数分析，实现从单变量动态测
量信号中提取流量和含率信息的两相流参数检测的新方法，并通
一
过实验验证了这种方法的可行性。
Two-phase flow parameter measurement is an unresolved problem. The
identification of two-phase flow patterns, flowrate and phase fl-action
measurement are very important for the industrial applications of two-phase
flow system. This dissertation applies chaos and fractal technique to the two-
phase flow measurement. The main research results and contributions are
listed as following:
1 Based on the review of chaos techniques and its applications, a new idea
and a new scheme for flow parameter measurements of two-phase flow
are proposed.
2 Flow patterns are classified by experimental investigation of oil and
water mixture flow in large diameter vertical pipes. Practical criterion of
flow pattern identification is developed. The flow pattern can be
identified by the measurements of flow rate and water holdup. The
experimental results also show that the proposed flow pattern
identification criterion can not be applied to other pipes with different
diameter because of the scale effect of flow pattern in large diameter
vertical pipes.
3 A nonlinear dynamical model of two-phase flow is developed. The
nonlinear dynamical behavior (chaos phenomena) of two-phase flow
systems is proved by numerical experiments. Based on this model, some
bifurcation parameters are obtained, as well as the flow-parameter ranges
of two-phase flow when the chaos phenomena take place in two-phase
flow systems. Also, a theoretical graph is developed and verified by
oil/water two-phase flow experiments. The presented model provides a
new theoretical tool for the study of two-phase flow.
4 A new method for flow pattern identification is presented based on the
chaos techniques by using Poincare map and fractal dimension etc.. The
experimental results show that the total accuracy to distinguish bubble
flow and dispersed bubble flow is above 78% and the correlation
dimension can be used as flow pattern indicator because of its sensibility
to the change of flow pattern.
5 A new method for the on-line measurements of flow rate and water
iii
fraction from a time series is proposed by using Poincare map and
correlation dimension analysis. The feasibility of this method is
supported by experiments.
引文
[1] Alexei Potapov and Jurgen Kurths, Correlation Integral as a Tool for Distinguishing between Dynamics and Statistics in Times Series Data, Physica D120, 1998, 369-385．
[2] Anastasio A.Tsonis, Chaos form Theory to Application, Plenum Press, New York, 1992．
[3] Andrew M. and Harry L., Independent Coordinates for Strange Attractors from mutual Information, Physical Review A, 1986, 33(2) :1134-1140．
[4] Badii R., Broggi G., Derighetti B., and Ravani M., Dimension Increase in Filtered Chaotic Signals, Physical Review Letters, 1988, 60(11) : 979-982．
[5] Bakshi B.R., H.Zhong, Analysis of Flow in Gas-Liquid Bubble Columns Using Multi-Resolution Methods, Trans IChemE, 1995, 73(Part A, 8) : 608-614．
[6] Barenblatt G. I., Nonlinear Dynamics and Turbulence, Pitman Advanced Publishing Program, 1983．
[7] Biage, M, Delhaye, J. M, The flooding transition: An experimental appraisal of the chaostic aspect of liquid film flow before the flooding point, 26th National Heat Transfer Conf., AICHE Symp, 1989, 85(269) :274-279．
[8] Bi H.T. and Grace J.R., Regime Transitions: Analogy Between Gas-Liquid Co-Current Upward Flow and Gas-Solids Upward Transport, Int. J. Multiphase Flow 22(S1) , 1996,1-19．
[9] Brown R.A.S., The Mechanics of Large Gas Bubbles in Tubes, I. Bubbble Velocities in Stagnant Liquids, The Canadian Journal of Chemical Engineering, October, 1965, 217-223．
[10] Brown R.A.S. and Govier G.W., The Mechanics of Large Gas Bubbles in Tubes, II. The Prediction of Voidage in Vertical Gas-Liquid Flow, The Canadian Journal of Chemical Engineering, October, 1965, 224-230．
[11] Broomhead D.S. and Gregory P.King, Extracting Qualitative Dynamics from Experimental Data, Physica D 20,1986,217-236．
[12] Cai Y., Wambsganss M.W., Jendrzejczyk J.A., Application of Chaos Theory in Identification of Two-phase Flow Patterns and Transitions in a Small Horizontal Rectangular Channel,Journal of Fluids Engineer 1996,(118) :383-390．
[13] Cambel A.B., Applied Chaos Theory--Aparadigm for Complexity, Academic Press, New York, 1993．
[14] Campbell D., Eckc R. et al, Nonlinear Science: The Next Decade, the Tenth Annual Internation Conference of the Center for Nonlinear Studies Los Alamos, U.S.A., May 1990．
[15] Carlson, N.R., Barnette,J.C., New Method for Accurate Determination of Water Cut in Oil Water Well, SPWLA, Thirtieth Annual Logging Symposium, June, 1989．
[16] Celka P., A Simple Way to Compute the Existence Region of 1D Chaotic Attractor in 2D-Maps, Physica D90,1996,23 5-241．
[17] Cellucci C.J. and Albano A.M., Detecting Noise in a Time Series, Chaos, 1997, 7(3) :414-422．
[18] Cenys A. and Pyragas K., Estimation of The Number of Dergrees of Freedom, Physics Letters A, 1988,129(4) :227-230．
[19] Chen X.T. and Brill J.P.,Slug to Chum Transition in Upward Vertical Two-Phase Flow, Chemical Engineering Science, 1997,52(23) :4269-4272,.
[20] Clark N.N., VanEgmond J.W.and Nebiolo E.P., The Drift-flux Model Applied To Bubble Columns and Low Velocity Flows, Int. J. Multiphase Flow, 1990,16(2) :261-279．
[21] Costigan G. and Whalley P.B.,Slug Flow Regime Identification From Dynamic Void Fraction Measurements in Vertical Air-Water Flows, Int. J. Multiphase Flow, 1997, 23(2) :263-282．
[22] Davies M.E., Reconstructing Attractors from Filtered Time Series, Physica D 101,1997,195-206．
[23] Delnoij E., Kuipers J.A., Dynamic Simulation of Gas-Liquid Two-
Phase Flow: Effect of Column Aspect Ratio on the Flow Structure, Chemical Engineering Science,1997, 52(21-22) :3759-3772．
[24] Doyne J. Farmer and Sidorowich J., Pridicting Chaos Time Series, Physical Review Letters, 1987,59(8) :845-848．
[25] Drahos J., Bradka F. and Puncochar m.,Fractal Behavior of Pressure Fluctuations in a Bubble Column, Chemical Engineering Science, 1992,47(15-16) :4069-4075．
[26] Dvora Barnea and Neima Brauner,Holdup of the Liquid Slug in Two Phase Intermittent Flow,Int. J. Multiphase Flow, 1985,11(1) :43-49．
[27] Eckmann J.P. and Oliffson S., Lyapunov Exponents from Time Series, Physical Review A, 1986,34(6) :4971-4979．
[28] Eric Grolman and Jan M. H. Fortuin, Gas-Liquid Flow in slightly Inclined Pipes, Chemical Engineering Science, 1997, 52(24) :4461-4471．
[29] Fan, L.T., Neogi, D., Stochastic Analysis of a Three-phase Fluided Bed: Fractal Approach, AICHEJ, 1990, 36(10) : 1529-1534．
[30] Felizola H. ana Shoham O., A Unified Model for Slug Flow in Upward Inclined Pipes, Journal of Energy Resources Technology, March,1995, 117:7-12．
[31] Fernandes R.C. R, Semiat and Dukler A.E., Hydrodynamic Model for Gas-Liquid Slug Flow in Vertical Tubes, AIChE Journal, November, 1983, 29(6) :981-989．
[32] Fluctions, Bai D., Bi H.T.and Grace J.R., Chaotic behavior of Fluidized Beds Based on Pressure and Voidage, AIChE Journal, May, 1997,43(5) : 1357-1361．
[33] Foster E.A.D., A causal Bifurcation Sequence Producing A Chaotic Transient Regime, International Journal of Bifurcation and Chaos, 1997, 7(2) :319-330．
[34] Franca F., Acikgoz M., Lahet R.T., The Use of Fractal Techniques for flow Regime Identification, Int. J. Multiphase Flow ,1991, 17(4) : 545-552．
[35] Francis C.Moon, Chaotic and Fractal dynamics--An Introduction for
Applied Scientist and Engineers, John wiley & Sons, New york, 1992．
[36] Gad Hetsroni, Handbook of Multiphase Systems, Hemisphere Publishing Corporation, 1993．
[37] Gao J.B., Hwang S.K., and liu J.M., When Can Noise Induce Chaos? , Physical Review Letters, 1999, 82(6) : 1132-1135．
[38] Goichi Matsui,Identification of Flow Regimes in Vertical Gas-Liquid Two-Phase Using Differential Pressure Fluctuations, Int. J. Multiphase Flow, 1984,10(1) :711-719．
[39] Govier, G.W., Developments in the Understanding of the Vertical Flow of Two Fluid Phase, The Canadian Journal of Chemical Engineering, Ferbruary, 1965,3-10．
[40] Govier G.W., Sullivan G.A.and Wood R.K., The Upward Vertical Flow of Oil-Water Mixtures, The Canadian Journal of Chemical Engineering, April, 1961,67-75．
[41] Guanyu Wang, Dajun Chen,Xing Chen, et al, The Application of Chaotic Oscillators to Weak Signal Detection, IEEE Transaction on Industrial Electronics, April 1999．
[42] Harmathy. T. Z., A.I.Ch.E. Journal, 1960, (6) :281．
[43] Hemanta Mukherjee and Jmes P. Brill, Empirical Equations to Predict Flow Pattern n Two-Phase Inclined Flow, Int. J. Multiphase Flow, 1985,11(3) : 299-315．
[44] Henry D.I. Abarbanel, Reggie Brown, and James B.Kadtke, Prediction and System Identification in Chaotic Nonlinerar System: Time Series with Broadband Spectra, Physics Letters A, 1989,138(8) :401-408．
[45] Hewit G.F., Multiphase Measurement Challenges: Old and New, 2nd International Symposium on Measuring Technique for Multiphase flow.
[46] Hewitt G.F., In Search of Two-Phase Flow, Transaction of the ASME August 1996, 118:518-527．
[47] Hewitt G. F., Measurement of two phase flow parameters, Academic Press, London, 1978．
[48] Hill. A.D., Production Logging-Theoretical and Interpretive Elements,
SPE Henryl Doherty Series, 1990．
[49] Hill A.D.,Production logging Tool Beharior inTwo--Phase inclined Flow, JPT, Oct. 1982,2432--2440．
[50] Hubbard M.G., Dukler A.F., The characterization of flow regimes for horizontal two-phase flow, Proceedings of the Heat Transfer and Fluid Mechanics Institute, 1966, 100-121．
[51] Jan Froyland, Introduction to Chaos and Coherence, Institute of Physics Publishing Bristol, Philandelophia & NK, 1992, (Chapter 11 Time Series Analysis): 107-127．
[52] Joe Pritchard, The Chaos Cookbook--a practice programing guid, Buttenvorth-Heinemann Ltd Linacre House, Oxford, 1992．
[53] Jong Hyun Kim, John Stringer, Applied Chaos, A Wiley-Interscience Publication, John Wiley & Sons, INC.
[54] Juanl L. Cabrera and Javier F. De La Rubia, Analysis of the Behavior of a Random Nonlinear Delay Discrete Equation, International Journal of Bifurcation and Chaos, 1996, 6(9) : 1683-1690．
[55] Karamavruc A.L.and Clark N.N.,Application of Deterministic Chaos Theory to Local Instaneous Temperature, Pressure and Heat Transfer Coefficients in a Gas Fluidized Bed, Transaction of the ASME September, 1996, 118:214-220．
[56] Kikuchi R., Yano T., Diagnosis of Chaotic Dynamic of Bubble Motion in a Column, Chemical Engineering Science, 1997, 52(21-22) :3741-3745．
[57] King horn F.C., Challenging Areas in Flow Measurement, Proceedings of 2th International Symposium on Measuring Techniques for Multiphase Flows, August 1998, Beijing, China.
[58] Kwon H. W., et al., Bubble-chord length and pressure fluctuations in three-phase fluidized beds, Ind. Eng. Chem. Res., 1994, 33(7) : 1852-1857．
[59] Lamba H. and Budd C.J., Scaling of Lyapunov Exponents at Nonsmooth Bifurcation, Physical Review E, 1994, 50(1) : 84-90．
[60] Letzel H.M., Schouten J.C.,and Kirishna R., Influence of Elevated
Pressure on the Stability of Bubbly Flows, Chemical Engineering Science, 1997,52(21-22) : 3733-3739．
[61] Liebert W., Proper Choice of The Time Delay for The Analysis of Chaotic Time Series, Physics Letters A, 1989, 142(2-3) : 107-111．
[62] Margaret Waid C., William, madigan P., Harry Smith D. Jr., A New Low-energy Gamma Ray Tool for Fullbore Measurement of Gas Holdup in a Cased Well,PWLA 37th Annual Logging Symposium, June 1996．
[63] Mcquillan K. W. and Whalley P. B.,Flow Patterns in Vertical Two-Phase Flow, Int. J. Multiphase Flow, 1985,11(2) :161-175．
[64] Michio Yamada and Koji Ohkitani, Lyapunov Spectrum of a Model of Two-Dimensional Turbulence, Physical Review Letters, 1988, 60(11) : 983-986．
[65] Minemura K. and Egashira k. itc, Simultaneous Measuring Method for Both Volumetric Flow Rates of Air-Water Mixture Using a Turbine Flowmeter, Journal of Energy Resources Technology, March, 1996,118:29-35．
[66] Mingzhou ding, Celso Grebog ,and Edward OTT, Dimensions of Strange Nonchaotic Attractors, Physics Letters A, 1989, 137(4-5) :167-172．
[67] Mishima K. and Hibiki T.,Some Characteristics of Air-Water Two-Phase Flow in Small Diameter Vertical Tubes, Int. J. Multiphase Flow, 1996,22(4) :703-712．
[68] Mohammed J.Davarzani and Allen A.Miller, Investigation of The Flow of Oil and Water Mixture in Large Diameter Vertical Pipes. SPWLA 20th Annual Logging Symposium, Jun 27-30,1983．
[69] Moore A.E. and Turley D.N.,Two-phase Flow Information from Simple Rapid Response Time Instruments, International Conference in the Physical Modeling of Multi-phase Flow Coventry, England April, 1983,315-376．
[70] Oddie,G.M, On the detection of a low-dimensional attractor in disperse principal component (oil-water) flow in a vertical pipe, Meas.
Instrum, 1991, 2(10) :225-229．
[71] Oiwa N.N., Fiedler-Ferrara N., A Fast Algorithm for Estimating Lyapunov Exponents, Physics Letters A 246,1998,117-121．
[72] Owen C. Jones, Jean-Marc Delhaye, Transient and Statistical Measurement Technique for Two-Phase Flows: A Critical Review, Int. J. Multiphase Flow , 1986, 3:89-116．
[73] Packard N.H., Crutchfield J.P., Farmer J.D., Geometry from Time Series, Physical Review Letters, 1980, 45(9) :712-716．
[74] Peter Grassberger and Itamar Procaccia, Characterization of Strange Attractors, Physical Review Letters, 1983, 50(5) :346-349．
[75] Priessler G., Hydrodynamic Calculation of a Water-air Mixture Flow in a Vertical Pipe, International Conference in the Physical Modeling of Multi-phase Flow Coventry, England April, 1983, 103-119．
[76] Rajan V.S.V. and Rafa K.G., Multiphase Flow Measurement Techniques-A review, Journal of Energy Resources Technology, September, 1993,115-151．
[77] Rasband S., Chaotic Dynamics of Nonlinear System, A Wiley Inter Science Publication, 1989:30-72．
[78] Ricardo Femat, Jose Alvarez-Ramirez, and Albert Soria, Chaotic Flow Structure in a Vertical Bubble Colume, Physics Letters A 248, 1998, 67-79．
[79] Robert M.May, review article: Simple mathematical models with very complicated dynamics, Nature, 1976, 261(10) : 459-467．
[80] Rosenberg, B., Drag and Shape of Air Bubbles Moving in Liquids. The David W. Taylor Model Basin, Report 727, Navy Dept., Washington D.C., September 1950．
[81] Salvador Pueyo, The Study of Chaotic Dynamics by Means of very Short Time Series, Physica D106, 1997, 57-65．
[82] Sano M. and sawada Y.,Measurement of the Lyapunov Spectrum Form a Chaotic Time Series, Physical Review Letters, 1985, 55(10) :1082-1085．
[83] Schleumberger, M.,Doll, H.G.,and Perebinossoff, Temperter
Measurements in Oil Well, JPT.137, 23(159) .
[84] Schleumberger, Production Logging Interpretation, 1973．
[85] Sen Choudhury D., Radhakrishnan V.R. and Mitra A.K., Gas Holdup in Vertical Concurrent Flow with Improved Gas-liquid Mixing, International Conference in the Physical Modeling of Multi-phase Flow, Coventry, England April, 1983,185-198．
[86] Song S., Jordan C., and Georgi D.,Theoretical and Experimental Studies on the Determination of the Average Fluid Velocity from Spinner Flowmeter Responses, SPWLA 37th Annual Logging Symposium, June 1996．
[87] Stanislay J.F., Kokal S. and Nicholson M. K., Intermittent Gas Liquid Flow in Upward Inclined Pies, Int. J. Multiphase Flow, 1986, 12(3) :325-335．
[88] Steve Maddox, Visualizing Production in Flowing Oil Wells, SPWLA 37th Annual Logging Symposium, June 1996．
[89] Subash S.Jayawardena and Vemuri Balakotaiah, Flow Pattern Transition Maps for Microgravity Two-Phase Flows, AIChE Journal, Junel997,43(6) :1637-1640．
[90] Tatsuo Shibata and Kunihiko Kaneko, Collective Chaos, Physical Review Letters, 1998, 81(19) :4116-4119．
[91] Tohru Ikefuchi, Lyapunov Spectral Analysis on Random Data, International Journal of Bifurcation and Chaos, 1997,(6) : 1267-1282．
[92] Toks Oshinowo and Charles M.E., Vertical Two-Phase Flow Part I. Flow Pattern Correlation, The Canadian Journal of Chemical Engineering, 52:25-35．
[93] Toks Oshinowo and Charles M.E.,Vertical Two-Phase Flow Part Ⅱ. Holdup and Pressure Drop, The Canadian Journal of Chemical Engineering, 1974, 52(8) :438-448．
[94] Troniewski L. and Ulbrich Roman, The Analysis of Flow Regime Maps of Two-Phase Gas-Liquid Flow in Pipes, Chemical Engineering Science,1984, 39(7-8) :1213-1224．
[95] Urrutia G. and Bonelli P., Cassanello M.C.and Cukierman A.L., On
Dynamic Liquid Holdup Determination by the Drainage Method, Chemical Engineering Science, 1996, 51(15): 3721-3726.
[96] Wayne D., Schnoor R., More Answers From Production Logging Than Just Flow Profiles SPWLA 37th Annual Logging Symposium, June 1996.
[97] Wilai Luewisutthichat, Chaotic Hydrodynamics of Continuous Single-Bubble Flow System.
[98] Wolf A., Jack B. Swinney and John A. Vastano, Determining Lyapunov Exponents form a Time Series, Physica 16D, 1985, 285-317.
[99] Yamada M. et al., Orthonormal wavelet expansion and its application to turbulence, Prog. Theor. Phys., 83(5): 819, 1990.
[100] Yehuda Taitel, Dvora Bornea and Dukler A.E., Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes, AIChE Journal, 1990, 26(3): 345-356.
[101] Zavareh F., Hill A.D., Flow Regimes in Vertical and Inclined Oil/Water Flow in Pipes, 1988, SPE 18215.
[102] 布朗著，张朝琛译，升举法采油工艺，石油工业出版社，1987．
[103] 蔡继勇，陈听宽，垂直上升管内油水乳状液流动特性的研究，石油学报，1998，19(4)：95-98．
[104] 陈家琅，石油气液两相管流，石油工业出版社，1989．
[105] 陈甘棠、王樟茂，流态化技术的理论和应用，北京，中国石化出版社，1996．
[106] 陈珙，小波分析技术及其在两相流流型检测中的应用，浙江大学博士学位论文，1999．
[107] 陈关荣，控制非线性动力系统的混沌现象，控制理论与应用，1997年，第1期，1-6．
[108] 陈维翰，线性关系及其应用，重庆大学出版社，1989．
[109] 陈予恕，陈启韶，一般力学中动力系统的非线性和混沌的最新进展和展望，非线性动力学学报，1994，(2)：97-109．
[110] 程易，魏飞，王振宇等，高速气固流化床局部瞬态行为混沌分析，第九届全国化学工程科技报告会论文集，青岛，1998，643-648．
[111] 董峰，赵国勋，徐苓安，应用电阻电层析成像技术测定两相流中气含率的研究，东北大学学报，2000，21(S1)：169-172．
[112] 龚云帆，徐健学，混沌信号与噪声，信号处理，1997，13(2)：112-125．
[113] Govier著，权忠舆等译，复杂混和物在管道中的流动，石油工业出版社，1984．
[114] 顾凡及，神经系统中非线性动力学问题，国外医学生物医学工程分册，1995，18(4)：187-1194．
[115] 郭海敏，生产测井油气水三相流动油井动态监测解释方法研究，石油工业部石油勘探开发科学研究院博士学位论文，1991．
[116] 郭爱克，孙海坚，生命与思维——在混沌的边缘演化，科技导报，1998，(1)：13-17．
[117] Hermann Haken，协同学-自然成功的奥秘，戴鸣钟译，上海科学普及出版社，1988．
[118] 郝柏林，从抛物线谈起，上海科技教育出版社，1993．
[119] 黄俊钦，测试误差分析与数学模型，国防工业出版社，1985．
[120] 黄铁伦，郑燕萍，黄海，流化床检测技术研究现状及趋势，第九届全国化学工程科技报告会论文集，青岛，1998，1022-1027．
[121] 黄志尧，分形技术与小波分析在气固流化床中的应用，东北大学学报，2000，21(S1)：194-197，2000．
[122] 黄志尧，陈珙，王保良，流动成像在两相流流型辨识中的应用，多相流检测技术进展，石油工业出版社，1992，65-69．
[123] 姜文达，生产测井现状和展望，生产测井技术应用与进展，石油工业出版社，1998，7-11．
[124] 金宁德，钟兴福，油、气、水三相流流型的分形及混沌特征分析，多相流检测技术进展，北京，石油工业出版社，1996，85-93．
[125] 金宁德，油井多相流测量系统模型建立及分析方法研究，浙江大学博士学位论文，1997．
[126] 金宁德，王微微，任英玉等，油水两相流流型的分形表征，东北大学学报，2000，21(S1)：128-130．
[127] 贾复，柳绮年，陈学武，上升气泡群引起的湍流特性，中国科学(A辑)，1991，(5)：486-495．
[128] 劳力云，郑之初，吴应湘等，气液两相管流的压力波动特性与流态之间的关系，东北大学学报，2000，21(S1)：9-11．
[129] 李凡华，刘慈群，宋付权，分形在油气田开发中的应用，力学进展，1998，28(1)：101-110．
[130] 李海青，两相流参数检测及应用，杭州，浙江大学出版社，1991：1～8．
[131] 李海青，多相流测试技术现状及趋势，多相流检测技术进展，石油工业出版社，1996：33～42．
[132] 李海青，黄志尧主编，特种检测技术及应用，浙江大学出版社，2000．
[133] 李海青，黄志尧主编，软测量技术原理及应用，化学工业出版社，2000．
[134] 李后强，汪富泉，分形理论及其在分子科学中的应用，北京，科学出版社，1997．
[135] 李神，汪克林，非线性科学选讲，中国科技大学出版社，1994。
[136] 李希文，大直径垂直管道中油和水混合流动的研究，第24届测井分析家年会论文集，1994．
[137] 李颖川，含液气井两相管流综合模型及其应用，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，191-196．
[138] 李诩神，汪克林，非线性科学选讲，中国科技大学出版社，1994，pp．35-40．
[139] 林家瑞，朱凡三，陈瑞红，强背景噪声下微弱胜利电信号的检测与处理，华中理工大学学报，1994，22(9)：119-123．
[140] 林家瑞，朱帆三，陈瑞红，生物医学弱电信号的检测与处理技术，国外医学生物医学工程分册，1994，17(1)：8—13．
[141] 凌夏华，非线性动力学系统的数值研究，上海交通大学出版社，1989：73～82．
[142] 林宗虎，气液固多相流测量，中国计量出版社，1988．
[143] 林宗虎著，管路内气液两相流特性及其工程应用，西安交通大学出版社，1992．
[144] 廖望才，心率变异性非线性信息处理的现状与展望，国外医学生物医学工程分册，1995，18(3)：311-1316．
[145] 鲁宏伟，吴雅，杨叔子，基于时序的李亚普诺夫指数的计算，华中理工大学学报，1995，23(9)：109-112．
[146] 陆启韶，分岔与奇异性，上海科技教育出版社，1995．
[147] 刘大有，描写混合物运动的双流体模型与扩散模型，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，21-26．
[148] 刘芳 译，心率变异自回归谱模型，国外医学生物医学工程分册，1994，17(5)：293-296．
[149] 刘芳译，控制心脏的混沌，国外医学生物医学工程分册，1994，17(3)：157-159．
[150] 刘芳译，心脏中的混沌现象，国外医学生物医学工程分册，1998，21(2)：100-310．
[151] 刘心东，混沌及其在生物医学工程中的应用，国外医学生物医学工程分册，1993，16(2)：63-70．
[152] 刘心东，蒋江民，蒋大宗，利用Lyapunov指数提取心电动态生理及病理信息的研究，生物医学工程学杂志，1995，12(3)：249-253．
[153] 刘兴斌，熊江红，吴世旗等，电容含水率计测油水两相流含水率，多相流检测技术进展，石油工业出版社，1992，143-147．
[154] 刘兴斌，井下油水两相流测量，哈尔滨工业大学博士学位论文，1996．
[155] 陆风根等，生产测井解释及其流体参数换算，石油工业出版社，1984．
[156] 苗东升，混沌学纵横谈，中国人民大学出版社，1993．
[157] 潘涛译，给生物医学工程学家的混沌理论，国外医学生物医学工程分册，1990，13(2)：97-102．
[158] 乔贺堂主编，生产测井原理及资料解释，石油工业出版社，1982．
[159] 乔贺堂，王宝春，刘兴斌，油井多相流测量技术，多相流检测技术进展，石油工业出版社，1992，25-32．
[160] 乔贺堂主编，生产测井技术论文集，石油工业出版社，1997．
[161] 生产测井技术，大庆生产测井研究所，1980．
[162] 沈强，混沌的数值分析方法及其在生物医学工程中的应用，国外医学生物医学工程分册，1994，17(6)：311-316．
[163] 沈强，非线性动力学现代理论在生物医学工程中的应用，国外医学生物医学工程分册，1996，19(2)：68-75．
[164] 孙淘，张宏建，徐贯东等，水平管气液两相流压差波动信号的统计分析，东北大学学报，2000，21(S1)：22-24．
[165] 谭廷栋，油气测井技术发展趋势，生产测井技术应用与进展，石油工业出版社，1998，1-5．
[166] 童勤业，刘刚强，刘加友，EEG的信息熵分析，生物物理学报，1993，9(4)：645-650．
[167] 童勤业，精神分裂症病人脑电图的非线性动力学分析，浙江医科大学学报，1997，26(5)：209-211．
[168] 王宝春，利用压差式密度计确定含水率的方法，大庆石油地质与开发，1984，3(6)：285-291。
[169] 王保良，电容层析成象技术及其在两相流参数检测中的应用研究，浙江大学博士学位论文，1998．
[170] 王北翔译，瞬态两相流的流型研究和简化解法，油气储运，1998，17(5)：57-61．
[171] 王栋，林宗虎，分流分相式气液两相流流量计，东北大学学报，2000，21(S1)：36-39．
[172] 王东生，曹磊，混沌、分形及其应用，中国科技大学出版社，1995：129～141．
[173] 王冠宇，混沌振子微弱信号检测的理论研究与实践，浙江大学博士学位论文，1998．
[174] 王经，蒋安众，两相流的非线性动力特性及混沌时间序列分析方法的研究，多相流检测技术进展，北京，石油工业出版社，1996，79-84．
[175] 王亮，刘豹，单变量时间序列预测：综述与评价，天津大学学报，1991，(2)：70-78．
[176] 王玉涛，刘克显，王师，软测量技术及其在过程检测与控制系统中的应用，东北大学学报，2000，21(S1)：124-126．
[177] 王进旗，柳建涛，电磁波传播原油含水分析仪的实验研究，多相流检测技术进展，石油工业出版社，1992，153-155．
[178] 王金钟，李振芳，一种新型的油井产出剖面测井仪，多相流检测技术进展，石油工业出版社，1992，117-123．
[179] 吴祥兴，陈忠，混沌学导论，上海科学技术文献出版社，1997．
[180] 谢荣华主编，生产测井技术应用与进展，石油工业出版社，1998．
[181] 徐立军，韩永涛，徐苓安，超声成像用于气、液两相流流型识别及截面含气率的测量，多相流检测技术进展，石油工业出版社，1992，317-324．
[182] 徐苓安，邓湘，董峰，电层析成像技术在生产过程中的应用，，东北大学学报，2000，21(S1)：1-5．
[183] 许晓红、正常人心动周期变化信号的混沌特征随年龄的变化，生物医学工程学杂志，1996，13(1)：26-28．
[184] 张作生，彭虎，公佩祥，时间序列分维数提取算法的研究，中国科学技术大学学报，1997，27(2)：221-224．
[185] 张宝群，油井四参数综合测试仪，石油钻采工艺，1979，6．
[186] 张宝群，油水两相滑动实验，测井技术，1981，(2)．
[187] 张伟，陈予恕，含有参数激励非线性动力系统的现代理论的发展，力学进展，1998，28(1)：1-16．
[188] 张远君，王慧玉，张振鹏，两相流体动动力学基础理论及工程应用，北京航空学院出版社，1987．
[189] 张永安，湛艮华，汪应洛，汇率波动的奇异吸引子测定及其应用分析，西安交通大学学报，1998，32(8)：92-95．
[190] 赵松年，非线性科学-它的内容、方法和意义，科学出版社，1994
[191] 赵似兰，彭伟，段鲲，睡眠脑电的分形维数分析，生物物理学报，1995，11(2)：226-232．
[192] 赵玉成，许庆余，时间序列分维数用于分岔参数的识别，西安交通大学学报，1998，32(8)：106-107．
[193] 郑会永，刘华强，戴冠中，非线性动力系统中的分形、混沌及其应用，非线性动力学学报，1996，(2)：182-189．
[194] 郑之初，海洋高技术与单相流检测技术，多相流检测技术进展，石油工业出版社，1992，1-6．
[195] 钟兴福，李海青等，油水两相持水率非线性模型及其数值解，测井技术，1998，22(6)：404-406．
[196] 钟兴福，李海青，单变量动态信号中含水率和流量信息的提取．东北大学学报，2000，21(S1)：33-35．
[197] 周纪卿，朱因远，非线性振动，西安交通大学出版社，1998．
[198] 周礼杲，分形几何在生物医学中的应用，国外医学生物医学工程分册，1991，14(5)：249-256．
[199] 周力行，湍流气粒多相流数值模拟理论的最新进展，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，4-11．
[200] 周凌云，王瑞丽，吴光敏，非线性物理理论及应用，科学出版社，2000．
[201] 周曙，余英林，脑干内的混沌，生物物理学报，1995，11(3)：433-438．
[202] 周云波，心率和呼吸动力学的非线性分析方法，国外医学生物医学工程分册，1997，20(5)：296-300．
[203] 周云龙，陈听宽，陈学俊，蒸发管内汽-液两相流不稳定性线性分相模型，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，203-208．
[204] 庄海军，刘兴斌，一种用于测量油水两相流持水率的电阻抗传感器，东北大学学报，2000，21(S1)：110-112．
[2] Anastasio A.Tsonis, Chaos form Theory to Application, Plenum Press, New York, 1992．
[3] Andrew M. and Harry L., Independent Coordinates for Strange Attractors from mutual Information, Physical Review A, 1986, 33(2) :1134-1140．
[4] Badii R., Broggi G., Derighetti B., and Ravani M., Dimension Increase in Filtered Chaotic Signals, Physical Review Letters, 1988, 60(11) : 979-982．
[5] Bakshi B.R., H.Zhong, Analysis of Flow in Gas-Liquid Bubble Columns Using Multi-Resolution Methods, Trans IChemE, 1995, 73(Part A, 8) : 608-614．
[6] Barenblatt G. I., Nonlinear Dynamics and Turbulence, Pitman Advanced Publishing Program, 1983．
[7] Biage, M, Delhaye, J. M, The flooding transition: An experimental appraisal of the chaostic aspect of liquid film flow before the flooding point, 26th National Heat Transfer Conf., AICHE Symp, 1989, 85(269) :274-279．
[8] Bi H.T. and Grace J.R., Regime Transitions: Analogy Between Gas-Liquid Co-Current Upward Flow and Gas-Solids Upward Transport, Int. J. Multiphase Flow 22(S1) , 1996,1-19．
[9] Brown R.A.S., The Mechanics of Large Gas Bubbles in Tubes, I. Bubbble Velocities in Stagnant Liquids, The Canadian Journal of Chemical Engineering, October, 1965, 217-223．
[10] Brown R.A.S. and Govier G.W., The Mechanics of Large Gas Bubbles in Tubes, II. The Prediction of Voidage in Vertical Gas-Liquid Flow, The Canadian Journal of Chemical Engineering, October, 1965, 224-230．
[11] Broomhead D.S. and Gregory P.King, Extracting Qualitative Dynamics from Experimental Data, Physica D 20,1986,217-236．
[12] Cai Y., Wambsganss M.W., Jendrzejczyk J.A., Application of Chaos Theory in Identification of Two-phase Flow Patterns and Transitions in a Small Horizontal Rectangular Channel,Journal of Fluids Engineer 1996,(118) :383-390．
[13] Cambel A.B., Applied Chaos Theory--Aparadigm for Complexity, Academic Press, New York, 1993．
[14] Campbell D., Eckc R. et al, Nonlinear Science: The Next Decade, the Tenth Annual Internation Conference of the Center for Nonlinear Studies Los Alamos, U.S.A., May 1990．
[15] Carlson, N.R., Barnette,J.C., New Method for Accurate Determination of Water Cut in Oil Water Well, SPWLA, Thirtieth Annual Logging Symposium, June, 1989．
[16] Celka P., A Simple Way to Compute the Existence Region of 1D Chaotic Attractor in 2D-Maps, Physica D90,1996,23 5-241．
[17] Cellucci C.J. and Albano A.M., Detecting Noise in a Time Series, Chaos, 1997, 7(3) :414-422．
[18] Cenys A. and Pyragas K., Estimation of The Number of Dergrees of Freedom, Physics Letters A, 1988,129(4) :227-230．
[19] Chen X.T. and Brill J.P.,Slug to Chum Transition in Upward Vertical Two-Phase Flow, Chemical Engineering Science, 1997,52(23) :4269-4272,.
[20] Clark N.N., VanEgmond J.W.and Nebiolo E.P., The Drift-flux Model Applied To Bubble Columns and Low Velocity Flows, Int. J. Multiphase Flow, 1990,16(2) :261-279．
[21] Costigan G. and Whalley P.B.,Slug Flow Regime Identification From Dynamic Void Fraction Measurements in Vertical Air-Water Flows, Int. J. Multiphase Flow, 1997, 23(2) :263-282．
[22] Davies M.E., Reconstructing Attractors from Filtered Time Series, Physica D 101,1997,195-206．
[23] Delnoij E., Kuipers J.A., Dynamic Simulation of Gas-Liquid Two-
Phase Flow: Effect of Column Aspect Ratio on the Flow Structure, Chemical Engineering Science,1997, 52(21-22) :3759-3772．
[24] Doyne J. Farmer and Sidorowich J., Pridicting Chaos Time Series, Physical Review Letters, 1987,59(8) :845-848．
[25] Drahos J., Bradka F. and Puncochar m.,Fractal Behavior of Pressure Fluctuations in a Bubble Column, Chemical Engineering Science, 1992,47(15-16) :4069-4075．
[26] Dvora Barnea and Neima Brauner,Holdup of the Liquid Slug in Two Phase Intermittent Flow,Int. J. Multiphase Flow, 1985,11(1) :43-49．
[27] Eckmann J.P. and Oliffson S., Lyapunov Exponents from Time Series, Physical Review A, 1986,34(6) :4971-4979．
[28] Eric Grolman and Jan M. H. Fortuin, Gas-Liquid Flow in slightly Inclined Pipes, Chemical Engineering Science, 1997, 52(24) :4461-4471．
[29] Fan, L.T., Neogi, D., Stochastic Analysis of a Three-phase Fluided Bed: Fractal Approach, AICHEJ, 1990, 36(10) : 1529-1534．
[30] Felizola H. ana Shoham O., A Unified Model for Slug Flow in Upward Inclined Pipes, Journal of Energy Resources Technology, March,1995, 117:7-12．
[31] Fernandes R.C. R, Semiat and Dukler A.E., Hydrodynamic Model for Gas-Liquid Slug Flow in Vertical Tubes, AIChE Journal, November, 1983, 29(6) :981-989．
[32] Fluctions, Bai D., Bi H.T.and Grace J.R., Chaotic behavior of Fluidized Beds Based on Pressure and Voidage, AIChE Journal, May, 1997,43(5) : 1357-1361．
[33] Foster E.A.D., A causal Bifurcation Sequence Producing A Chaotic Transient Regime, International Journal of Bifurcation and Chaos, 1997, 7(2) :319-330．
[34] Franca F., Acikgoz M., Lahet R.T., The Use of Fractal Techniques for flow Regime Identification, Int. J. Multiphase Flow ,1991, 17(4) : 545-552．
[35] Francis C.Moon, Chaotic and Fractal dynamics--An Introduction for
Applied Scientist and Engineers, John wiley & Sons, New york, 1992．
[36] Gad Hetsroni, Handbook of Multiphase Systems, Hemisphere Publishing Corporation, 1993．
[37] Gao J.B., Hwang S.K., and liu J.M., When Can Noise Induce Chaos? , Physical Review Letters, 1999, 82(6) : 1132-1135．
[38] Goichi Matsui,Identification of Flow Regimes in Vertical Gas-Liquid Two-Phase Using Differential Pressure Fluctuations, Int. J. Multiphase Flow, 1984,10(1) :711-719．
[39] Govier, G.W., Developments in the Understanding of the Vertical Flow of Two Fluid Phase, The Canadian Journal of Chemical Engineering, Ferbruary, 1965,3-10．
[40] Govier G.W., Sullivan G.A.and Wood R.K., The Upward Vertical Flow of Oil-Water Mixtures, The Canadian Journal of Chemical Engineering, April, 1961,67-75．
[41] Guanyu Wang, Dajun Chen,Xing Chen, et al, The Application of Chaotic Oscillators to Weak Signal Detection, IEEE Transaction on Industrial Electronics, April 1999．
[42] Harmathy. T. Z., A.I.Ch.E. Journal, 1960, (6) :281．
[43] Hemanta Mukherjee and Jmes P. Brill, Empirical Equations to Predict Flow Pattern n Two-Phase Inclined Flow, Int. J. Multiphase Flow, 1985,11(3) : 299-315．
[44] Henry D.I. Abarbanel, Reggie Brown, and James B.Kadtke, Prediction and System Identification in Chaotic Nonlinerar System: Time Series with Broadband Spectra, Physics Letters A, 1989,138(8) :401-408．
[45] Hewit G.F., Multiphase Measurement Challenges: Old and New, 2nd International Symposium on Measuring Technique for Multiphase flow.
[46] Hewitt G.F., In Search of Two-Phase Flow, Transaction of the ASME August 1996, 118:518-527．
[47] Hewitt G. F., Measurement of two phase flow parameters, Academic Press, London, 1978．
[48] Hill. A.D., Production Logging-Theoretical and Interpretive Elements,
SPE Henryl Doherty Series, 1990．
[49] Hill A.D.,Production logging Tool Beharior inTwo--Phase inclined Flow, JPT, Oct. 1982,2432--2440．
[50] Hubbard M.G., Dukler A.F., The characterization of flow regimes for horizontal two-phase flow, Proceedings of the Heat Transfer and Fluid Mechanics Institute, 1966, 100-121．
[51] Jan Froyland, Introduction to Chaos and Coherence, Institute of Physics Publishing Bristol, Philandelophia & NK, 1992, (Chapter 11 Time Series Analysis): 107-127．
[52] Joe Pritchard, The Chaos Cookbook--a practice programing guid, Buttenvorth-Heinemann Ltd Linacre House, Oxford, 1992．
[53] Jong Hyun Kim, John Stringer, Applied Chaos, A Wiley-Interscience Publication, John Wiley & Sons, INC.
[54] Juanl L. Cabrera and Javier F. De La Rubia, Analysis of the Behavior of a Random Nonlinear Delay Discrete Equation, International Journal of Bifurcation and Chaos, 1996, 6(9) : 1683-1690．
[55] Karamavruc A.L.and Clark N.N.,Application of Deterministic Chaos Theory to Local Instaneous Temperature, Pressure and Heat Transfer Coefficients in a Gas Fluidized Bed, Transaction of the ASME September, 1996, 118:214-220．
[56] Kikuchi R., Yano T., Diagnosis of Chaotic Dynamic of Bubble Motion in a Column, Chemical Engineering Science, 1997, 52(21-22) :3741-3745．
[57] King horn F.C., Challenging Areas in Flow Measurement, Proceedings of 2th International Symposium on Measuring Techniques for Multiphase Flows, August 1998, Beijing, China.
[58] Kwon H. W., et al., Bubble-chord length and pressure fluctuations in three-phase fluidized beds, Ind. Eng. Chem. Res., 1994, 33(7) : 1852-1857．
[59] Lamba H. and Budd C.J., Scaling of Lyapunov Exponents at Nonsmooth Bifurcation, Physical Review E, 1994, 50(1) : 84-90．
[60] Letzel H.M., Schouten J.C.,and Kirishna R., Influence of Elevated
Pressure on the Stability of Bubbly Flows, Chemical Engineering Science, 1997,52(21-22) : 3733-3739．
[61] Liebert W., Proper Choice of The Time Delay for The Analysis of Chaotic Time Series, Physics Letters A, 1989, 142(2-3) : 107-111．
[62] Margaret Waid C., William, madigan P., Harry Smith D. Jr., A New Low-energy Gamma Ray Tool for Fullbore Measurement of Gas Holdup in a Cased Well,PWLA 37th Annual Logging Symposium, June 1996．
[63] Mcquillan K. W. and Whalley P. B.,Flow Patterns in Vertical Two-Phase Flow, Int. J. Multiphase Flow, 1985,11(2) :161-175．
[64] Michio Yamada and Koji Ohkitani, Lyapunov Spectrum of a Model of Two-Dimensional Turbulence, Physical Review Letters, 1988, 60(11) : 983-986．
[65] Minemura K. and Egashira k. itc, Simultaneous Measuring Method for Both Volumetric Flow Rates of Air-Water Mixture Using a Turbine Flowmeter, Journal of Energy Resources Technology, March, 1996,118:29-35．
[66] Mingzhou ding, Celso Grebog ,and Edward OTT, Dimensions of Strange Nonchaotic Attractors, Physics Letters A, 1989, 137(4-5) :167-172．
[67] Mishima K. and Hibiki T.,Some Characteristics of Air-Water Two-Phase Flow in Small Diameter Vertical Tubes, Int. J. Multiphase Flow, 1996,22(4) :703-712．
[68] Mohammed J.Davarzani and Allen A.Miller, Investigation of The Flow of Oil and Water Mixture in Large Diameter Vertical Pipes. SPWLA 20th Annual Logging Symposium, Jun 27-30,1983．
[69] Moore A.E. and Turley D.N.,Two-phase Flow Information from Simple Rapid Response Time Instruments, International Conference in the Physical Modeling of Multi-phase Flow Coventry, England April, 1983,315-376．
[70] Oddie,G.M, On the detection of a low-dimensional attractor in disperse principal component (oil-water) flow in a vertical pipe, Meas.
Instrum, 1991, 2(10) :225-229．
[71] Oiwa N.N., Fiedler-Ferrara N., A Fast Algorithm for Estimating Lyapunov Exponents, Physics Letters A 246,1998,117-121．
[72] Owen C. Jones, Jean-Marc Delhaye, Transient and Statistical Measurement Technique for Two-Phase Flows: A Critical Review, Int. J. Multiphase Flow , 1986, 3:89-116．
[73] Packard N.H., Crutchfield J.P., Farmer J.D., Geometry from Time Series, Physical Review Letters, 1980, 45(9) :712-716．
[74] Peter Grassberger and Itamar Procaccia, Characterization of Strange Attractors, Physical Review Letters, 1983, 50(5) :346-349．
[75] Priessler G., Hydrodynamic Calculation of a Water-air Mixture Flow in a Vertical Pipe, International Conference in the Physical Modeling of Multi-phase Flow Coventry, England April, 1983, 103-119．
[76] Rajan V.S.V. and Rafa K.G., Multiphase Flow Measurement Techniques-A review, Journal of Energy Resources Technology, September, 1993,115-151．
[77] Rasband S., Chaotic Dynamics of Nonlinear System, A Wiley Inter Science Publication, 1989:30-72．
[78] Ricardo Femat, Jose Alvarez-Ramirez, and Albert Soria, Chaotic Flow Structure in a Vertical Bubble Colume, Physics Letters A 248, 1998, 67-79．
[79] Robert M.May, review article: Simple mathematical models with very complicated dynamics, Nature, 1976, 261(10) : 459-467．
[80] Rosenberg, B., Drag and Shape of Air Bubbles Moving in Liquids. The David W. Taylor Model Basin, Report 727, Navy Dept., Washington D.C., September 1950．
[81] Salvador Pueyo, The Study of Chaotic Dynamics by Means of very Short Time Series, Physica D106, 1997, 57-65．
[82] Sano M. and sawada Y.,Measurement of the Lyapunov Spectrum Form a Chaotic Time Series, Physical Review Letters, 1985, 55(10) :1082-1085．
[83] Schleumberger, M.,Doll, H.G.,and Perebinossoff, Temperter
Measurements in Oil Well, JPT.137, 23(159) .
[84] Schleumberger, Production Logging Interpretation, 1973．
[85] Sen Choudhury D., Radhakrishnan V.R. and Mitra A.K., Gas Holdup in Vertical Concurrent Flow with Improved Gas-liquid Mixing, International Conference in the Physical Modeling of Multi-phase Flow, Coventry, England April, 1983,185-198．
[86] Song S., Jordan C., and Georgi D.,Theoretical and Experimental Studies on the Determination of the Average Fluid Velocity from Spinner Flowmeter Responses, SPWLA 37th Annual Logging Symposium, June 1996．
[87] Stanislay J.F., Kokal S. and Nicholson M. K., Intermittent Gas Liquid Flow in Upward Inclined Pies, Int. J. Multiphase Flow, 1986, 12(3) :325-335．
[88] Steve Maddox, Visualizing Production in Flowing Oil Wells, SPWLA 37th Annual Logging Symposium, June 1996．
[89] Subash S.Jayawardena and Vemuri Balakotaiah, Flow Pattern Transition Maps for Microgravity Two-Phase Flows, AIChE Journal, Junel997,43(6) :1637-1640．
[90] Tatsuo Shibata and Kunihiko Kaneko, Collective Chaos, Physical Review Letters, 1998, 81(19) :4116-4119．
[91] Tohru Ikefuchi, Lyapunov Spectral Analysis on Random Data, International Journal of Bifurcation and Chaos, 1997,(6) : 1267-1282．
[92] Toks Oshinowo and Charles M.E., Vertical Two-Phase Flow Part I. Flow Pattern Correlation, The Canadian Journal of Chemical Engineering, 52:25-35．
[93] Toks Oshinowo and Charles M.E.,Vertical Two-Phase Flow Part Ⅱ. Holdup and Pressure Drop, The Canadian Journal of Chemical Engineering, 1974, 52(8) :438-448．
[94] Troniewski L. and Ulbrich Roman, The Analysis of Flow Regime Maps of Two-Phase Gas-Liquid Flow in Pipes, Chemical Engineering Science,1984, 39(7-8) :1213-1224．
[95] Urrutia G. and Bonelli P., Cassanello M.C.and Cukierman A.L., On
Dynamic Liquid Holdup Determination by the Drainage Method, Chemical Engineering Science, 1996, 51(15): 3721-3726.
[96] Wayne D., Schnoor R., More Answers From Production Logging Than Just Flow Profiles SPWLA 37th Annual Logging Symposium, June 1996.
[97] Wilai Luewisutthichat, Chaotic Hydrodynamics of Continuous Single-Bubble Flow System.
[98] Wolf A., Jack B. Swinney and John A. Vastano, Determining Lyapunov Exponents form a Time Series, Physica 16D, 1985, 285-317.
[99] Yamada M. et al., Orthonormal wavelet expansion and its application to turbulence, Prog. Theor. Phys., 83(5): 819, 1990.
[100] Yehuda Taitel, Dvora Bornea and Dukler A.E., Modeling Flow Pattern Transitions for Steady Upward Gas-Liquid Flow in Vertical Tubes, AIChE Journal, 1990, 26(3): 345-356.
[101] Zavareh F., Hill A.D., Flow Regimes in Vertical and Inclined Oil/Water Flow in Pipes, 1988, SPE 18215.
[102] 布朗著，张朝琛译，升举法采油工艺，石油工业出版社，1987．
[103] 蔡继勇，陈听宽，垂直上升管内油水乳状液流动特性的研究，石油学报，1998，19(4)：95-98．
[104] 陈家琅，石油气液两相管流，石油工业出版社，1989．
[105] 陈甘棠、王樟茂，流态化技术的理论和应用，北京，中国石化出版社，1996．
[106] 陈珙，小波分析技术及其在两相流流型检测中的应用，浙江大学博士学位论文，1999．
[107] 陈关荣，控制非线性动力系统的混沌现象，控制理论与应用，1997年，第1期，1-6．
[108] 陈维翰，线性关系及其应用，重庆大学出版社，1989．
[109] 陈予恕，陈启韶，一般力学中动力系统的非线性和混沌的最新进展和展望，非线性动力学学报，1994，(2)：97-109．
[110] 程易，魏飞，王振宇等，高速气固流化床局部瞬态行为混沌分析，第九届全国化学工程科技报告会论文集，青岛，1998，643-648．
[111] 董峰，赵国勋，徐苓安，应用电阻电层析成像技术测定两相流中气含率的研究，东北大学学报，2000，21(S1)：169-172．
[112] 龚云帆，徐健学，混沌信号与噪声，信号处理，1997，13(2)：112-125．
[113] Govier著，权忠舆等译，复杂混和物在管道中的流动，石油工业出版社，1984．
[114] 顾凡及，神经系统中非线性动力学问题，国外医学生物医学工程分册，1995，18(4)：187-1194．
[115] 郭海敏，生产测井油气水三相流动油井动态监测解释方法研究，石油工业部石油勘探开发科学研究院博士学位论文，1991．
[116] 郭爱克，孙海坚，生命与思维——在混沌的边缘演化，科技导报，1998，(1)：13-17．
[117] Hermann Haken，协同学-自然成功的奥秘，戴鸣钟译，上海科学普及出版社，1988．
[118] 郝柏林，从抛物线谈起，上海科技教育出版社，1993．
[119] 黄俊钦，测试误差分析与数学模型，国防工业出版社，1985．
[120] 黄铁伦，郑燕萍，黄海，流化床检测技术研究现状及趋势，第九届全国化学工程科技报告会论文集，青岛，1998，1022-1027．
[121] 黄志尧，分形技术与小波分析在气固流化床中的应用，东北大学学报，2000，21(S1)：194-197，2000．
[122] 黄志尧，陈珙，王保良，流动成像在两相流流型辨识中的应用，多相流检测技术进展，石油工业出版社，1992，65-69．
[123] 姜文达，生产测井现状和展望，生产测井技术应用与进展，石油工业出版社，1998，7-11．
[124] 金宁德，钟兴福，油、气、水三相流流型的分形及混沌特征分析，多相流检测技术进展，北京，石油工业出版社，1996，85-93．
[125] 金宁德，油井多相流测量系统模型建立及分析方法研究，浙江大学博士学位论文，1997．
[126] 金宁德，王微微，任英玉等，油水两相流流型的分形表征，东北大学学报，2000，21(S1)：128-130．
[127] 贾复，柳绮年，陈学武，上升气泡群引起的湍流特性，中国科学(A辑)，1991，(5)：486-495．
[128] 劳力云，郑之初，吴应湘等，气液两相管流的压力波动特性与流态之间的关系，东北大学学报，2000，21(S1)：9-11．
[129] 李凡华，刘慈群，宋付权，分形在油气田开发中的应用，力学进展，1998，28(1)：101-110．
[130] 李海青，两相流参数检测及应用，杭州，浙江大学出版社，1991：1～8．
[131] 李海青，多相流测试技术现状及趋势，多相流检测技术进展，石油工业出版社，1996：33～42．
[132] 李海青，黄志尧主编，特种检测技术及应用，浙江大学出版社，2000．
[133] 李海青，黄志尧主编，软测量技术原理及应用，化学工业出版社，2000．
[134] 李后强，汪富泉，分形理论及其在分子科学中的应用，北京，科学出版社，1997．
[135] 李神，汪克林，非线性科学选讲，中国科技大学出版社，1994。
[136] 李希文，大直径垂直管道中油和水混合流动的研究，第24届测井分析家年会论文集，1994．
[137] 李颖川，含液气井两相管流综合模型及其应用，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，191-196．
[138] 李诩神，汪克林，非线性科学选讲，中国科技大学出版社，1994，pp．35-40．
[139] 林家瑞，朱凡三，陈瑞红，强背景噪声下微弱胜利电信号的检测与处理，华中理工大学学报，1994，22(9)：119-123．
[140] 林家瑞，朱帆三，陈瑞红，生物医学弱电信号的检测与处理技术，国外医学生物医学工程分册，1994，17(1)：8—13．
[141] 凌夏华，非线性动力学系统的数值研究，上海交通大学出版社，1989：73～82．
[142] 林宗虎，气液固多相流测量，中国计量出版社，1988．
[143] 林宗虎著，管路内气液两相流特性及其工程应用，西安交通大学出版社，1992．
[144] 廖望才，心率变异性非线性信息处理的现状与展望，国外医学生物医学工程分册，1995，18(3)：311-1316．
[145] 鲁宏伟，吴雅，杨叔子，基于时序的李亚普诺夫指数的计算，华中理工大学学报，1995，23(9)：109-112．
[146] 陆启韶，分岔与奇异性，上海科技教育出版社，1995．
[147] 刘大有，描写混合物运动的双流体模型与扩散模型，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，21-26．
[148] 刘芳 译，心率变异自回归谱模型，国外医学生物医学工程分册，1994，17(5)：293-296．
[149] 刘芳译，控制心脏的混沌，国外医学生物医学工程分册，1994，17(3)：157-159．
[150] 刘芳译，心脏中的混沌现象，国外医学生物医学工程分册，1998，21(2)：100-310．
[151] 刘心东，混沌及其在生物医学工程中的应用，国外医学生物医学工程分册，1993，16(2)：63-70．
[152] 刘心东，蒋江民，蒋大宗，利用Lyapunov指数提取心电动态生理及病理信息的研究，生物医学工程学杂志，1995，12(3)：249-253．
[153] 刘兴斌，熊江红，吴世旗等，电容含水率计测油水两相流含水率，多相流检测技术进展，石油工业出版社，1992，143-147．
[154] 刘兴斌，井下油水两相流测量，哈尔滨工业大学博士学位论文，1996．
[155] 陆风根等，生产测井解释及其流体参数换算，石油工业出版社，1984．
[156] 苗东升，混沌学纵横谈，中国人民大学出版社，1993．
[157] 潘涛译，给生物医学工程学家的混沌理论，国外医学生物医学工程分册，1990，13(2)：97-102．
[158] 乔贺堂主编，生产测井原理及资料解释，石油工业出版社，1982．
[159] 乔贺堂，王宝春，刘兴斌，油井多相流测量技术，多相流检测技术进展，石油工业出版社，1992，25-32．
[160] 乔贺堂主编，生产测井技术论文集，石油工业出版社，1997．
[161] 生产测井技术，大庆生产测井研究所，1980．
[162] 沈强，混沌的数值分析方法及其在生物医学工程中的应用，国外医学生物医学工程分册，1994，17(6)：311-316．
[163] 沈强，非线性动力学现代理论在生物医学工程中的应用，国外医学生物医学工程分册，1996，19(2)：68-75．
[164] 孙淘，张宏建，徐贯东等，水平管气液两相流压差波动信号的统计分析，东北大学学报，2000，21(S1)：22-24．
[165] 谭廷栋，油气测井技术发展趋势，生产测井技术应用与进展，石油工业出版社，1998，1-5．
[166] 童勤业，刘刚强，刘加友，EEG的信息熵分析，生物物理学报，1993，9(4)：645-650．
[167] 童勤业，精神分裂症病人脑电图的非线性动力学分析，浙江医科大学学报，1997，26(5)：209-211．
[168] 王宝春，利用压差式密度计确定含水率的方法，大庆石油地质与开发，1984，3(6)：285-291。
[169] 王保良，电容层析成象技术及其在两相流参数检测中的应用研究，浙江大学博士学位论文，1998．
[170] 王北翔译，瞬态两相流的流型研究和简化解法，油气储运，1998，17(5)：57-61．
[171] 王栋，林宗虎，分流分相式气液两相流流量计，东北大学学报，2000，21(S1)：36-39．
[172] 王东生，曹磊，混沌、分形及其应用，中国科技大学出版社，1995：129～141．
[173] 王冠宇，混沌振子微弱信号检测的理论研究与实践，浙江大学博士学位论文，1998．
[174] 王经，蒋安众，两相流的非线性动力特性及混沌时间序列分析方法的研究，多相流检测技术进展，北京，石油工业出版社，1996，79-84．
[175] 王亮，刘豹，单变量时间序列预测：综述与评价，天津大学学报，1991，(2)：70-78．
[176] 王玉涛，刘克显，王师，软测量技术及其在过程检测与控制系统中的应用，东北大学学报，2000，21(S1)：124-126．
[177] 王进旗，柳建涛，电磁波传播原油含水分析仪的实验研究，多相流检测技术进展，石油工业出版社，1992，153-155．
[178] 王金钟，李振芳，一种新型的油井产出剖面测井仪，多相流检测技术进展，石油工业出版社，1992，117-123．
[179] 吴祥兴，陈忠，混沌学导论，上海科学技术文献出版社，1997．
[180] 谢荣华主编，生产测井技术应用与进展，石油工业出版社，1998．
[181] 徐立军，韩永涛，徐苓安，超声成像用于气、液两相流流型识别及截面含气率的测量，多相流检测技术进展，石油工业出版社，1992，317-324．
[182] 徐苓安，邓湘，董峰，电层析成像技术在生产过程中的应用，，东北大学学报，2000，21(S1)：1-5．
[183] 许晓红、正常人心动周期变化信号的混沌特征随年龄的变化，生物医学工程学杂志，1996，13(1)：26-28．
[184] 张作生，彭虎，公佩祥，时间序列分维数提取算法的研究，中国科学技术大学学报，1997，27(2)：221-224．
[185] 张宝群，油井四参数综合测试仪，石油钻采工艺，1979，6．
[186] 张宝群，油水两相滑动实验，测井技术，1981，(2)．
[187] 张伟，陈予恕，含有参数激励非线性动力系统的现代理论的发展，力学进展，1998，28(1)：1-16．
[188] 张远君，王慧玉，张振鹏，两相流体动动力学基础理论及工程应用，北京航空学院出版社，1987．
[189] 张永安，湛艮华，汪应洛，汇率波动的奇异吸引子测定及其应用分析，西安交通大学学报，1998，32(8)：92-95．
[190] 赵松年，非线性科学-它的内容、方法和意义，科学出版社，1994
[191] 赵似兰，彭伟，段鲲，睡眠脑电的分形维数分析，生物物理学报，1995，11(2)：226-232．
[192] 赵玉成，许庆余，时间序列分维数用于分岔参数的识别，西安交通大学学报，1998，32(8)：106-107．
[193] 郑会永，刘华强，戴冠中，非线性动力系统中的分形、混沌及其应用，非线性动力学学报，1996，(2)：182-189．
[194] 郑之初，海洋高技术与单相流检测技术，多相流检测技术进展，石油工业出版社，1992，1-6．
[195] 钟兴福，李海青等，油水两相持水率非线性模型及其数值解，测井技术，1998，22(6)：404-406．
[196] 钟兴福，李海青，单变量动态信号中含水率和流量信息的提取．东北大学学报，2000，21(S1)：33-35．
[197] 周纪卿，朱因远，非线性振动，西安交通大学出版社，1998．
[198] 周礼杲，分形几何在生物医学中的应用，国外医学生物医学工程分册，1991，14(5)：249-256．
[199] 周力行，湍流气粒多相流数值模拟理论的最新进展，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，4-11．
[200] 周凌云，王瑞丽，吴光敏，非线性物理理论及应用，科学出版社，2000．
[201] 周曙，余英林，脑干内的混沌，生物物理学报，1995，11(3)：433-438．
[202] 周云波，心率和呼吸动力学的非线性分析方法，国外医学生物医学工程分册，1997，20(5)：296-300．
[203] 周云龙，陈听宽，陈学俊，蒸发管内汽-液两相流不稳定性线性分相模型，第四届多相流、非牛顿流、物理化学流学术会议论文集，西安，1993，203-208．
[204] 庄海军，刘兴斌，一种用于测量油水两相流持水率的电阻抗传感器，东北大学学报，2000，21(S1)：110-112．