A GENERAL VISCOSITY CORRELATION FOR LIQUID MIXTURES by BARRY ALLEN WHITE 1t Bachelor of Science Oklahoma State University Stillwater, Oklahoma 1968 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE August , 1969 w.\ft Y NOV o 1969 A GENERAL VISCOSITY CORRELATION FOR LIQUID MIXTURES Thesis Approved:. 730170 ii PREFACE This study is concerned with evaluating existing and formulating new correlations for the viscosity of binary mixtures of paraffin hydro- carbons. Viscosity of the n-butane-n-decane system was measured over a 25 to 85 mole fraction range to evaluate a correlation using logarithm of surface tension and reciprocal viscosity. The surface tension correlation was judged invalid and other cor- relations from the literature were tested with experimental and liter- ature viscosity data.
A new correlation was devise.cl using an experi- mentally-determined interaction parameter. I wish to thank my major adviser, Dr. ~addox, for his patience and concern during my research. Several other graduate stu- dents helped me considerably and I would like to thank them: Stuart E.
Bennett, for designing and constructing the apparatus and for drawing details of it; James R. Dea:m, for his surface tension data and correlation, and his density data; WilUam R. OWens, for his assistance in writing computer programs; and Harry G. Rackett, for his density and other equations.
Much gratitude must go the sponsoring organizations,· the Natural Gas Processors Association, who funded the research, and the National Aeronautics and Space Administration, who provided for my subsistence. Last, but not least, I thank my wife~ Jan, for. helping me prepare this thesis and giving moral support during graduate school. iii TABLE OF CONTENTS Chapter Page I.
LITERATURE SURVEY 4 Viscosity Corr~lations Viscosity and Density Data. 4 9 Sources of Other Data • • • •. 14 Pressure Cell • • • • • • Liquid Injection. 20 20 ~ Temperature Controls The Pressure Distribution Sys:t~ •• Materials· Tested • • • •.
DISCUSSION OF DATA ••. DISCUSSION OF CORRELATION • • • • • • • • • • • • • 0 • • 34 Definition of Error Reporting • • • • • • • • • • • • 34 .· Surface Tension~Viscosity • • • • • ' .Mixture Viscosity Correlations 36 Mixing-Rule Correlations • , • • • • , • • • • • • • • 39 Grunberg.;Nissan Correlation • • • Corresponding States Correlation • • • • • • •. 42 39 Free Energy,Correlatibn • • • • 44 Reduced Viscosity Correlation ••. CONCLUSIONS AND RECOMMENDATIONS 53 Recommendations.
II e 8 8 54 A SELECTED BIBLIOGRAPHY NOMENCLATURE iv LIST OF FIGURES Figure Page 1. D_iagram of the Zeitfuchs Cross-Arm Viscometer •• 15 2. Schematic Diagram of the Experimental Apparatus ••. Detail of the Pressure Cell •• • 0 • 18 4.
Detail of the Observation Ports Assembly • • • e a • • • • 19 5. Detail of the Liquid Injectiqn Assembly. Density of n-Butane-n-Decane Mixtures • • • • • • • • • • • 28 7.ane-n-Decane Viscosity-Composition Chart •. n-Butane-n-Decane Viscosity-Temperature Chart •.
n-Butane-n-Decane Pressure-Composition Chart. Bennett Correlation for Methane-n-Nonane. Bennett Correlation for Methane-n-Decane 37 12. Bennett Correlation for n-Butane-n-Decane.
Stiel Acentric Factor Correlation for Methane-n-Oecane. Stiel Acentric Factor Correlation for n-Buta,ne-n-Decane. Stiel Reduced Temperature Correlation for Methane-n-Decane. Stiel Reduced Temperature Correlation for n-Butane-n- De cane.
52 v LIST OF TABLES Table Page I. SUMMARY OF EXPERIMENTAL DATA FOR N-BUTANE-N-DECANE •. SUMMARY OF GRUNBERG-NISSAN CORRELATION • • • • • • 41 III. SUMMARY OF PRESTON, CHAPMAN, AND PRAUSNITZ CORRELATION FOR BUTANE-DECANE • • • • , • • • • • • • • 43 IV.
SUMMARY OF THE PROPOSED CORRELATION 45 vi CHAPTER I INTRODUCTION The Natural Gas Processors Association (NGPA) of Tulsa, Oklahoma, is sponsoring research on absorbers to determine causes for low effi- ciency and ways to improve this efficiency. The research at the Oklahoma State University School of Chemical Engineering is in two phases - static and dynamic. Included in the static phase are the study of viscosity and surface tension of paraffin hydrocarbon mixtures. The dynamic phase is concerned with evaluating absorption factors, A, from operating absorbers.
A= L/KV (1-1) where L = liquid flow rate, moles/hr V = vapor flow rate, moles/hr K = vapor-liquid equilibrium constant Deam (6) has measured surface tension of pure components and liquid mixtures using a pendant drop apparatus. He has correlated these data with a parachor and an excess surface tension equation. For densities outside the range of literature data, he used the Rackett equation (30). Bennett (2) designed and constructed a viscometer apparatus for use over a wide temperature and pressure range.
Using a capillary 1 2 viscometer, he measured the viscosity of liquid ·methane-n-nonane mix- tures. He observed that plots of the logarithm of surface tension ver- sus reciprocal viscosity generated a 'family of parallel straight lines of constant composition. This follows the work of Pelofsky (27) and Schonhorn (34), who used similar coordinate systems to correlate pure component viscosities. }lowever, Bennett could not get a wide enough composition range using the methane-nonane system to fully test his hypothesis.
This author used B,~nnett 1 s apparatus to measure the viscosity of the n-butane-n-decane ·.s,i'~:l~em over a 25 to 85 mole per cent butane composition range. He also used literature viscosities of the methane- n-decane (24), n-hexane-n-hexa4ecane (17), n-hexane~n-tetradecane (17), and n-hexadecane-n-tetradecane systems to test the Bennett and other correlations. Even though the log surface tension-recipl;"ocal vi,scosity plots do yield parallel straight lines of constant composition (Figures 10, 11, 12), these lines do not lie between the pure component lines as they would if mixture surface tension were a simple function of composition and pure component viscosity. Therefore, this type of correlation was· discarded and other types were applied.
The most successful type of correlation attempted was (1-2) where f ·is an experimentally determined function of composition, tern- perature, and the excess Gibbs free energy. This approach is from Grunberg and Nissan (15) and Gambill (12), who suggest that the devia- tion from Arrhenius'' prediction 3 (1-3) is a function of exponential reciprocal temperature, composition, and constants in the Margules free energy equation. This type of correla~ tion gives a predicted viscosity within five per cent of the experi- mentally determined value. CHAPTER II LITERA.TURE SURVEY Several different topics were surveyed in the literature.
Rather than confuse the reader by presenting.the survey in one mass, the author attempted to group the results according to these topics. Viscosity Correlations In addition to the Bennett correlation, other methods of pre- dieting mixture viscodty were sought. The main type of correlations published were corresponding states, empirical, surface tension, three-. body model, and residual viscosity.
Stiel (36) presents a plot o f ~ vs. uJ for saturated pure liquids at Tr= 0.7 and one ofj-(jvs. Tr for a gaseous mixture of nitrogen-ethylene. Each curve suggests that the reduced visGosity is a function of the independent variable, acentric factor and reduced temperature, respectively.
Stiel attributes the following rules to Prausnitz and Gunn (36). xiz c i) Stiel (36) also mentioned the work of Preston, Chapman, and 4 5 Prausnitz (29), who have worked with the corresponding states principle in correlating the transport properties of cryogenic mixtures. They show that the reduced viscosity,,*, is a function of reciprocal re- duced temperature, 1/T*, alone, where log 10 1* = + A B/!* (2-4.,'6') Preston, et 'al. suggest mixing rules, '(2-7) (2-8) (2-9.L_xiVCi (2·-11) i to use.in reducing mixture data to a form suitable for the original correlation.
The main value of this correlation is to calculate point values of viscosity and not a general line. One drawback of this system is the necessity of having experimental viscosity to determine ">112 • Gambill (12) lists several empirical equations proposed by others .and makes comments a.bout their applications. For miscible liquid- liquid mixtures, he separates the equations into two types, those with 6 and those without an interaction parameter. Equations with this para- meter will predict experimental results more accurately than equations without, but generally this parameter must be detel'mined using experi- mental results.
Gambill says this parameter will vary with absolute temperature as exp(B/T), and will also be proportional with real-non- ideal mixtures to the energy of mixing. Gambill (12) recommends equations by Kendall and Monroe (21) as the best equation withQut an interaction paramet~r (2. 12) and Grunberg and Nissan (15) as the best with a pa:i:-ameter. (2-13) Grunberg and Nissan (15) attached theoretical importance to their parameter by defining d as d = c b (2-14) where C is the ratio of the logarithm of the viscosity to the logarithm of the vapor pressure and bis the constant in the shortened form of the Margules equation: (2-15) In this way the interaction parameter can be calculated using the Van Laar equation with constants evaluated from van der Waal's equation.) (2-20) Assume for a first estimate, the Arrhenius equation for mixture vis- cosity, 'Equation (1-3), the Antoine equation for pure component vapor pressure, log 10 P = A - B/(C + t) (2-21) where tis temperature in degrees Fahrenheit, and that vapor pressure of a mixture can be averaged by mole fraction, and the final equation for the Grunberg-Nissan interaction parameter is (2-22) An empirical equation using diffusivity was proposed by Budden- berg and Wilke (4) for the viscosity of gas mixtures.38~ 2 1 + - 1+ - xl 0 12e1 x2 °12€>2 (2-23) Herning and Zipperer are attributed by Dean and Stiel (7) to have presented a correlation using molecular weight.
m = (2-24) 8 Silverman and Roseveare (35) proposed a viscosity correlation based on surface tension with two empirical constants. (2-25) Pelofsky (27) surveyed the field of surface tension-viscosity correlations and proposed (j' = A exp (B/>'t) (2 -26) Written in logarithmic form, lnO' = ln A+ B/'1 (.2-2(7) Equation (2-27) states that a straight line with slope B can be drawn intersecting the point where the viscosity becomes infinite at a sur- face tension value of A using natural logarithm of the surface tension and reciprocal viscosity as coordinates. This idea, using lnCT ,!ilnd 1/~ as coordinates, is the basis of Bennett's correlation. Bennett (2) proposed that lines of constant"c.omposition plotted on this coordinate system would be straight and parallel, and distri- buted between the pure component lines according to a function of the composition.
Schonhorn (34) modified Pelofsky's equation to extend it over the entire range of the liquid phase. This is done by introducing 'f\v' the viscosity of the vapor in equilibrium with the liquid so that the final equation is (2. Residual viscosity is one correlation used by most publishers of viscosity data to show the accuracy of the data. This is defined as the viscosity at a given temperature and pressure minus the viscosity of the gas at the given temperature anµ a standard pressure, usually atmospheric.
Plotting residual viscosity as a function of density generally gives a single curve independent of temperature. The shape of the curve is a function of the molecular weight of the fluid studied. Giddings and Kobayashi (13) have published a family of curves of different molecular weight mixtures using residual viscosity and reduced density as coordinates. They also show a chart of dilute gas viscosity as a function of temperature and molecular weight.
Several workers have published equations for dilute gas viscosity, including Lee and Eakiri (22) (7.J-'l = B T3 / 2 / (T + S) (2-31) Viscosity and Density Data The Zeitfuchs-type capillary viscometer used in this study measures kinematic viscosity. The Bennett <;:orrelation (2) uses absolute viscosity, which is the product of kinematic viscosity and density. Therefore, the density of the butane-decane system must be 10 known at the experimental points.
