PREDICTION OF LIQUID VISCOSITY FOR N-ALKANES, N-ALCOHOLS I AND N-ALKANONES By Daniel Hao phen Bachelor of Science in Engineering National Cheng Kung University Tainan, Taiwan, China 1970 Master of Science in Engineering National Taiwan University Taipei, Taiwan, China 1976 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY December, 1981 '-thesis )q$?\ D ¢~115 p t.o~ I:).- PREDICTION OF LIQUID VISCOSITY FOR N-ALKANES, N-ALCOHOLS, AND N-ALKANONES Thesis Approved: Dean of the Graduate College ii 1110766 PREFACE This study is concerned with the development of a new liquid vis- cosity prediction method. The proposed method is capable of predicting \ liquid viscosity over a wide range of temperatures and a wide range of chain lengths. The Cox equation for viscosity is used as a liquid vis- ~osity-temperature working equation. A new type of group-contribution technique, which is essential to the success of this method, is also developed. This prediction method has been tested for three homologous series, and the results indicate that the present method is better than any other currently existing method. Several extensions of the present method appear to be promising; I sincerely hope that the continuations of this study will be successful. I wish to express my deepest appreciation to my major adviser, Dr. Robert N. Maddox, for his intelligent guidance and invaluable assistance throughout this study. I am also very grateful to the other committee members, Dr. John H. Erbar, Dr. Robert L. Robinson, Jr., and Dr. Gilbert J. Mains for their assistance and advisement in the course of this work. My special thanks are due to Dr. Ruth C. Erbar for her kind help in providing pertinent literature data. Also the assistance from Dr. J.P. Chandler in the use of Marquardt's subroutine is highly appreciated. The help provided by all the faculty, staff and graduate students of the School of Chemical Engineering is acknowledged, Thanks are also extended to the University Computer Center of Oklahoma State University for the facility and computer time offered. iii Finally, I want to express my deep gratitude to my parents Chian­ Trun and Yu-Tsen Chen, my brothers, and sisters for their constant support and sacrifices during the long way of my graduate study. Above all, I wish to thank my wife Julie for her understanding, encouragement, and sustaining help. iv TABLE OF CONTENTS Chapter Page I. INTRODUCTION AND LITERATURE REVIEW • 1 Historical Background • • • • • 1 Prediction Methods in the Literature 3 Proposed Prediction Method • • • • • • 6 II. THEORETICAL DEVELOPMENTS • • • • . 8 The Cox Vapor-Pressure Equation • • • • • • • • 8 The Cox Equation for Viscosity • • • • . • • • 9 New Group-Contribution Technique . • • • • • 10 Effect of the Functional Group Position • 14 A Special Case • • . • • • • • • • • • • • 16 III • RESULTS AND COMP ARI SONS WITH OTHER METHODS • • • • • • • 18 Regression Procedure • • • • • • • • 18 Summary of the Computed Results . 18 Extrapolation Tests . • • . • 22 Comparisons with Other Methods 26 IV. CONCLUSIONS AND RECOMMENDATIONS 31 Conclusions • • • 31 Recommendations • 32 BIBLI<X;.RAPHY 33 v LIST OF TABLES Table Page I. Results of n-Alkane Liquid Viscosity Correlation and Prediction • • • . 19 II. Results of n-Alcohol Liquid Viscosity Correlation and Prediction • • • . • . 20 III. Results of n-Alkanone Liquid Viscosity Correlation and Prediction • • • • . 21 IV. Predictive Constants for the n-Alkane Series 23 V. Summary of Ext:rapolated Predictions 25 VI. Full Temperature Range Comparison of All Methods • • • • • 27 VII. Low-Temperature Range Comparison • 28 VIII. High-Tempe:rature Range Comparison 29 LIST OF FIGURES Figure Page 1. Contribution of nth Methylene (or Methyl) Group to Natu:ral Logarithm of Liquid Viscosity at T ,55 r = for n-Alkanes . 11 2. Dependence of F on the Number of Carbon Atoms n in n-Alkanes . 13 3, Illustration of the Functional Group Contribution as a Function of the Number of Carpo~ Atoms • • 15 4. Illust:ration of the Functional Group Contribution with Functional Group Position Effect and Constant Decay Ratio . , . , , , . , , , , , , , 17 vi NOMENCLATURE A constant in Equations (1-i), (1-2), (1-10), (2-3) constants in Equation (1-11) A' constant in Equation (2-1) parameters in the Cox equation for vi$cosity, Equations (1-17), (2-3)' (2-4) ao ' ' a1 ' , a2 ' parameters in Equation (2-1) ao* ' al* ,* a2 constants in Equation (2-2) a parameter in Equations (2-5), (2-6); predictive constant in n-alkane series para.meter in Equations. (2-7), (2-10) predictive constant corresponding to a functional group AAPE average absolute percent error AAPE the average of AAPE''8 defined m by Equation (3-3) B constant in Equations (1-1), (1-2), (1-3) b,B. correction term in Equation (1-9) J. constant in Equation (1-12) parameter defined by Equations (1-7), (1-8) parameter in Equations (2-5), (2-6) parameter in Equations (2-?), (2-10) predictive constant corresponding to a functional group c constant in Equation (1-2) calc. calculated liquid viscosity d liquid density at 20° C, g/cm3 vii E percent error defined by Equation (J-1) the absolute value of percent error exp. experimental liquid viscosity EXPD AAPE for a compound outside the range of regression percent error caused by each additional carbon atom beyond m AAPE for compounds inside the range of fitting F fitted value for a certain parameter, a function of n n M molecular weight m number of carbon atoms of a compound member up to which the regression is perfonned MC number of carbon atoms in the carbon chain n, N number of carbon atoms in a.compound. n used in _gth methylene (or methyl) group N* equivalent chain length defined by Equation (1-4) structural or functional group correction in Equation (1-4) upper and lower bound of the n range NCPD number of compounds in a certain sample NPT number of data points for a certain compound p vapor pressure in Equations (2-1), (2-2), atm p critical pressure c position where the functional group occurs r decay ratio parameter in Equation (2-7) temperature, K relative temperature defined in Equation (1-17) viii T* parameter in Equation (1-3), defined by Equation (1-5), (1-6) T critical temperature, K c TMPE temperature where maximum percent error occurs T reduced temperature r Tb nor.mal boiling point, K TO reference temperature, K Y'/L liquid viscosity, cP A. predictive constant for functional group position effect /Ao reference viscosity, mPa s f- liquid viscosity, mPa s 5 parameter defined by Equation (1-13) 5f relative position of a functional group <f ~ )(0) a quantity defined by Equation (1-15) <J1- 5) (1) a quantity defined by Equation (1-16) UJ acentric factor Alnf difference of natural logarithmic liquid viscosity between two neighboring members of the n-alkane series ix CHAPTER I INTRODUCTION AND LITERATURE REVIEW A new method for predicting liquid dynamic (absolute) viscosity of nonnal alkanes, nonnal alcohols, and nonnal alkanones over a wide range of temperatures and a wide range of carbon chain lengths has been deve­ loped. Also a new type of group-contribution technique which involves the use of the geometric series is proposed to generate the predictive parameters in the working equation. No other physical properties are required in this prediction method. The only information needed is the structure of that compound. The new method can predict (also correlate) liquid viscosity more accurately than any other existing method for all three compound series. Historical Background While the mechanism or theory of gas viscosity has met with some success by the application of the kinetic theory of gases, the develop­ ment of the theoretical foundation of liquid viscosity is still in the primitive stage. So far there is no theory which can reduce to a simple function fonn and allow liquid viscosities to be estimated adequately with resonable effort. Therefore, empirical methods are used in all practical situations. These methods allow parameters or certain theore­ tical constants to be approximated from structure or other physical pro­ perties through study of experimental data. The best known correlation for showing the effect of temperature 1 2 _ on liquid viscosity is the De Guzman-Andrade equation r = A eXJ?(B/T) (1-1) where A and B are positive constants. This equation was proposed by De Guzman (1913) and then suggested by Andra.de (1930) from an analysis of the theory of liquid viscosity. It holds fairly well over a temperature range from somewhat above the normal boiling point to near the freezing point. Because of its simplicity, this equation has been the basis of many empirical prediction methods. However, it often fails at low tern- peratures as the freezing point is approached; also, it is not suitable for reduced temperatures above 0.75. One variation of equation (1-1), which resembles the Antoine equation, was proposed by Gutman and Simmons (1952) .. ln µ = A + B/( T + C) (1-2) where A, B, Care constants. Although this modification has been shown to be quite accurate at low temperatures, it is not particularly good for the high temperature region (Reid et al., 1977). Above the normal boiling point, the correlations commonly used are no longer liquid viscosity-temperature equations. The correlations of Letsou and Stiel (1973), for example, are of a corresponding-states type. The prediction methods for low temperatures based on the viscosity- temperature equation are mainly structural in nature, whereas the predic- tion methods for high temperatures are not. Because of this difference in approaches, one can hardly eXJ?ect good matches from these two different types of estimation methods in the connection region (around reduced tem-- perature Tr = .75).