Transport properties of fluids of cryogenic interest

Transport properties of fluids of cryogenic interest* W.M. Haynes, D.E. Diller and H.M. Roder Thermophysics Division, National Engineering Laboratory, National Bureau of Standards, Boulder, CO 80303, USA

Received 2 February 1987 This Paper is a status report for viscosity and thermal conductivity data and correlations for pure fluids and fluid mixtures encountered in cryogenic process technology. Recommended correlations or tables of values are identified for each fluid. Specific data needs for future work are reported. Also presented are brief descriptions of the experimental techniques for viscosity and thermal conductivity measurements along with estimates of the associated experimental uncertainties. Keywords: physical properties; transport properties; measuring techniques; reviews The importance of thermophysical properties data for fluids involved in c r y o g e n i c processing is well documented ~-14. These references include studies that give estimates of the economic impact of uncertainties in values of selected properties. Although transport property data are not, in general, considered as essential as thermodynamic property data in cryogenic process calculations, transport properties are extremely important in specific applications, such as in the design of compressors, heat exchangers, flow meters, pumps, etc. or in any displacement process that involves heat, mass or momentum transfer calculations. With the ever-increasing costs of energy, materials, feedstocks and labour, and with the increased capacity of industrial plants, there has been a growing awareness of the importance of the accuracy, and sometimes even availability, of transport property data for fluids involved in industrial processes. Until recently, the primary motivations behind transport property measurements were to gain a better understanding of intermolecular forces and to understand their relationship to microscopic properties. As a result, transport property results, especially those for cryogenic fluids, have played a significant role in the development of fluid theories for a fundamental understanding of the behaviour of fluids, including mixtures. Many cryogenic fluids have extremely simple (spherical or nearly spherical) molecular structure, e.g. argon and methane; therefore, studies of these systems, including mixtures, can serve as a foundation for research on more complicated molecules encountered in evolving new technologies. The present study consists of a status report of viscosity and thermal conductivity data and correlations for pure fluids and fluid mixtures of cryogenic interest. Emphasis is p!aced on sets of wide-range data, especially for the dense fluid, and on global correlations that cover the entire fluid surface from the dilute gas to the dense liquid. Although cryogenic fluids have traditionally been defined as those

*Contribution of the National Bureau of Standards (USA), not subject to copyright in the US 0011-2275/87/070348-13$03.00 (~ 1987 Butterworth & Co (Publishers)Ltd 348

Cryogenics 1987 Vol 27 July

with normal boiling points below 123 K (-150°C), the fluids considered in this study have been expanded to include those involved in cryogenic processing with melting temperatures below ambient. The major purpose of this Paper is to serve as a primary reference or guide for the engineer who needs information (data, correlations, etc.) on the viscosity and/or thermal conductivity for fluids of cryogenic interest. This report gives recommendations for the best available correlations for each pure fluid. Data banks and compilations are identified. Since the recommendations are subjective in nature, sufficient references and sources of data are identified so that users can obtain the original data and perform their own assessments to satisfy their particular needs. The recommended correlations, in most cases, represent experimental data within the overall uncertainty of the measurements. For those cases for which a single equation is not clearly superior to others in representing the same data base, more than one correlation reference is given for that fluid. Also reported are references for new significant data that have been published since the recommended correlations were developed. This report also contains brief descriptions of the most reliable methods for thermal conductivity and viscosity measurements on fluids, with estimates of experimental uncertainty levels given. Specific data needs for future work are identified. Major sources of wide-range data (and correlations) for fluid mixtures of cryogenic interest are also compiled and discussed. Thermal conductivity

Experimental techniques Thermal conductivity is a difficult property to measure inasmuch as a temperature difference has to be applied and maintained in the fluid. Like the specific heat, the thermal conductivity is infinite at the fluid critical point. Difficulties that have to be considered for each experimental technique include heat transport by modes

Transport properties of fluids: W.M. Haynes et al. other than pure conduction, i.e. by convection or radiation; heat losses from the heated element to the supports; accommodation effects at low fluid pressures; and many others L~. A peculiarity of thermal conductivity is that it is impossible to measure at the exact condition of the saturated liquid, yet many results are reported where the fluid conditions are not given but saturation is implied. Selection of an effective temperature and density can then easily result in errors of several per cent. The standard technique before 1950 was the steady state hot wire, where the wire could be thin or thick and the fluid annulus was normally small to avoid convection. These systems turn out to be the least reliable with an estimated accuracy between 5 and 10%. Quite often inaccuracies were caused by the use of overly large temperature gradients, i.e. 25°C or larger. Authors that have used this method successfully include Johnston and Grilly I~ and Saxena and Saxena 17. The hot wire geometry leads directly to the method of concentric cylinders, first without, and then with, guard cylinders. The accuracy of this method is considerably better, ~ 2% for the best systems. Since the fluid annulus in these systems is small to delay the onset of convection, alignment of the cylinders is a problem, as is the thermometry between guards, the heated section and the shell. Among the authors that have obtained reliable results with this method are Needham and Ziebland 's, Guildner v~ and Le Neindre 2°. A further improvement in the accuracy of thermal conductivity measurements, to ~ 1.5%, was obtained by Michels and his co-workers 2~ by developing a parallel plate geometry with guards. Properly designed and used, this geometry reduces convection in the measurements. Sengers 22 was able to determine the dependence of the thermal conductivity on density and temperature quite near the critical point of CO2. The most recent technique to come into use for measuring the thermal conductivity of fluids is the transient hot wire method developed during the last 15 years 2"~3~. In this method a very fine vertically mounted wire is subjected to a heat pulse of short duration. Measurements are usually completed in <~ l s. A characteristic of this technique is that the onset of convection can be determined experimentally 3~'32. The accuracy of an instrument of this type can be a little better than 1%, as has been demonstrated by international comparisons on toluene, n-heptane and some of the rare gases. In fact, these fluids have been proposed as thermal conductivity standards to be used in calibrating future instruments of any design 33. In addition, this technique has been used for the most extensive measurements made on mixtures so fa r 34 .

Overview of the behaviour of the thermal conductivity of a pure fluid

Figure 1, which first appeared in Reference 35, shows the dependence of the thermal conductivity of methane on density and temperature. The measurements were made with a transient hot wire apparatus and they cover a wide range of physical states including the dilute gas, the moderately dense gas, the near critical region, the compressed liquid states and the vapour at temperatures below the critical temperature. To a first approximation what matters is the density of the fluid, i.e. how many molecules per unit volume are available to carry the heat. At high density, we have high thermal conductivity. The dependence on temperature is considerably weaker. For

p--

T v

T

E

,__-_

.0Jr4

O.111

J O.08

¢MW 0

a

1l

24

8=

o ~ a y . r ~ . L-1

Rgure 1 Overview of the thermal conductivity measurements for methane, reprinted from Reference 35. Bottom part, all measurements on a single scale. Top part, individual isotherms separated by 0.02 W m -1 K -1

fluids with a critical temperature above ambient, this dependence is often ignored; however, for cryogenic fluids, a dependence on temperature should be included in the equations used to describe thermal conductivity. Analysis of a thermal conductivity surface is normally accomplished in terms of density and temperature ~ rather than temperature and pressure because over a wide range of experimental conditions, the behaviour of thermal conductivity is dominated by its temperature dependence. The equation used is ~.(p,'/') = ),(,(T) + ~.~ ...... ( p , T ) + A),cri,ica,(p,T )

(1)

The first term on the right of Equation (1) is the dilute gas term, which is independent of density. The second is the excess thermal conductivity. The first two terms taken. together are sometimes called the 'background' thermal conductivity. The final term is the critical point enhancement. The various terms used in a correlation are shown schematically in Figure 2. The detailed behaviour of the thermal conductivity for CO2 near the critical point is shown in Figure 3, which is reprinted from Reference 22. The thermal conductivity at the critical point is infinite, and scaling laws are u ~ d to describe the thermal conductivity surface in this region 37. From a practical point of view the de~ription of a thermal conductivity surface with Equation (1) is unfortunate. Pressure is the variable used in applied problems. The user, therefore, requires an equation of state to convert pressure to density and vice versa. A unique approach, which expresses pressure as a function of thermal conductivity and temperature, is under develop.ment by a group associated with the MIDAS data b a n k ' . This approach gives great difficulty, however, when the

Cryogenics 1987 Vol 27 July

349

Transport properties of fluids: W.M. Haynes et al. O.tl.

l =

o

1

~

to

q5

~o

Figure 2 Isotherm analysis illustrated for a temperature of 197K for methane, reprinted from Reference 35. +, Experimental points; 1, dilute gas term (~); 2, background conductivity ( ~ + ;kexce,); 3, calculated thermal conductivity; inset, Akcritical

enhancement in thermal conductivity which occurs near the critical point is included.

Data and r e s o u r c e s We do not reproduce actual data here but rather indicate sources the user might consult. Centres active in research and evaluation of thermal conductivity data include among others: the Transport Properties Project Center of IUPAC 39 located at the Imperial College (London, UK), the MIDAS d , ~ bank 3s at the Universities of Stuttgart ¢01 crnxc°C

~o I O 4 /IX

and Siegen (FRG), CINDAS at Purdue University (USA) ~' and the Thermophysics Division of the National Bureau of Standards (USA). A list of evaluated thermal conductivity data sets in MIDAS a' is given in Table A1 of the Appendix. A list of fluids selected for numerical data analysis at CINDAS 4° is given in Table A2 of the Appendix. CINDAS has also completed an exhaustive compilation and assessment of thermal conductivity, thermal diffusivity and viscosity data for 25 pure substances and their binary combinations that are of interest to the gas industry 42. A list of the fluids included in this report 4z is given in Table A3 of the Appendix. References recommended for thermal conductivity surfaces are presented in Table 1 for pure fluids 35"4~3 and in Table 2 for mixtures 32"34"4~-51•64"84-88.In Table 1, emphasis is placed on correlations and new data that cover large ranges in pressure, density and temperature. The journals Physica and the International Journal of Thermophysics are two of the most likely to carry thermal conductivity data for fluids. Wide-range correlations currently in progress for the thermal conductivity of pure fluids considered in this study should be noted. New correlations for CO,, NH3, N2 and some refrigerants are being carried out through the IUPAC Subcommittee on Transport Properties s~. New correlations for CH 4, C2H6, C3H8, iC4Hlo and nC4Hl, are being developed in the Thermophysics Division of the National Bureau of Standards'~( In Table 2 we concentrate again on correlations and data sets that cover a major portion of the phase diagram including the variation in composition. Mixtures exhibit a critical enhancement 32"3a quite similar to that of the pure fluids. Thermal conductivity data for a complete surface of a mixture are rare. For example, the MIDAS data bank contains 257 articles on binary mixtures, yet it stores • 41 • evaluated data for only 26 mixtures . Cons=der also the global model TRAPP 7R,"7 9 which was specifically designed to predict the transport properties of hydrocarbon mixtures. To validate TRAPP the authors found only 24 binary mixtures and used a total of 159 experimental points. A final example is the report on transport properties of selected chemical compounds by CINDAS prepared for the Gas Research Institute 42. At first glance_ it looks as if there is a lot of data. Closer inspection discloses that much of the data is for the gas phase a t apressure of 1 atm*. There are very little liquid state data and no data for liquid mixtures.

31.2 °

Recommendations

!

30 °

4 i

Oo

IO0

200

300

400

.500

&OOA m

Figure 3 Thermal conductivity coefficient of CO2 v e r s u s density, reprinted with permission from thesis of Sengers 22. (1 Am -0.045moldm-3; l c a l c m - l s - l ° C -~ = 4 1 8 . 4 W m ~K 1)

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Cryogenics

1 9 8 7 V o l 27 J u l y

A purely experimental approach to mixture properties suggests an infinite data requirement• It is imperative that experimental measurements be made on judiciously selected systems that represent classes of systems encountered in cryogenic processing. Maximum information will be gained from data on mixtures whose components exhibit large disparities in such parameters as size (e.g. methane with C4"s and higher), shape and/or polarity (e.g. CH 4 + NH3). Measurement programmes will be guided by developments in predictive models. Because of the vast scope of mixture properties, it is also extremely important that the development of accurate predictive models is a prime consideration in the selection of systems for experimental measurements. For the future it is recommended that measurements on the thermal conductivity of pure fluids should be carried "1 atm = 101 kPa

Transport properties of fluids: W.M. Haynes et al. Table 1 Thermal conductivity sources for pure fluids Substance

Surface correlation

New data

H2 He Ne Kr Xe Ar

McCarty e t aL 43 Hands and Arp ~ Vargaftik s2 Hanley et aL s3 Hanley et al. 53 Younglove and Hanleys5 Younglove ss

Roder¢4-4~ Cohen et al. ~ - s l

N2

F2 CI2 CO C02 NO N20 S02 NH3 CH4

Younglove ss Hanley e t al. s3 Stephan and Laeseckee~ Younglove ss Roders2 Hanley and Prydz63 Vargaftik s2 Barua e t aL s4 Vargaftik s2 Barua e t aL ~ Hanleys5 Vargaftik s2 Vargaftik s2 Hanley et aL ss

C2He

Hanley et aL es

C3H8

Holland et al. 73

iC4Hm nC4Hm C2H4 C3H6 H20 Refrigerants

Nieuwoudt et al. 77 Ely and Hanley 7a'Ta Holland et al. a~ Vargaftik s2 Sengers et aL a2 ASHRAE s3

02

out on He, Ci2, NO, N20, SO2, and NF 3. Measurements on mixtures should include a large range of the property surface and be especially selected to emphasize size and polarity differences in the components. For a proper analysis of transport property measurements, it is extremely important that a knowledge of the PVT surface of the system under study is available. From Table 1, it is evident that a considerable amount of data has been added to the data base during the past few years. While several new correlation methods have been introduced primarily for the liquid state 9~'92, what is really needed are new or revised global correlations which cover all physical states. For mixtures, the global correlation T R A P P needs to be revised to improve or change the reference fluid and to include a critical enhancement sa.

Thermal diffusivity We define thermal diffusivity by Equation (2) o~ = x J o C p

(2)

Trappenierss4 Trappenierss4 Nieto de Castro and Roder$7 Mardolcar et al. sa Calado e t al. sa Roder e t a l e °

Needham and Ziebland TM RodePS.'~ Prasad e t aL 67 Mardolcar and Nieto de Castro= Roder and Nieto de Castro 7° Prasad and Venart 7t'72 Roder and Nieto de Castro TM Le Neindre e t aL 7s Prasad and Venart ~e Nieto de Castro e t aL e° Prasad and Venart 72 Tables A 1 and A 2 of Appendix

where: ct is the thermal diffusivity; ~. the thermal conductivity; p the density; and Cp the specific heat at constant pressure. For the present, we feel that the user is advised to calculate the thermal diffusivity from Equation (2) using experimental and correlated values for ~. and an equation of state that will allow the calculation of the specific heat. In the future it may be possible to obtain the thermal diffusivity directly from the transient hot wire thermal conductivity experiments. Some preliminary results for toluene have already been reported 9"~'94.

Viscosity Experimental techniques Many different methods have been used to obtain accurate viscosity results for cryogenic fluids. Here, a brief survey of these techniques will be presented, with emphasis on those instruments that can be used for the entire fluid surface; i.e. for the dilute gas, compressed gas, saturated and compressed liquid, near-critical region, and

Table 2 Thermal conductivity sources for mixtures Components

Surface correlation

Data sources

3He-4He Methane-ethane

Cohen e t al. 4a Friend and Roder~

Cohen e t al. 4s-sl

Air (N2-02)

Stephan and Laeseckeas Kadoya e t aL es Barua e t aL s4

CO-NO

Friend and Roder32 Roder and Friend 34'as Hemmingers7

Cryogenics 1987 Vol 27 July

351

Transport properties of fluids: W.M. Haynes et al. for the vapour below the critical temperature. Viscometers can be grouped into two major categories, moving fluid and moving body viscometers. Examples from these two categories are the capillary flow and oscillating body viscometers, which are the two primary instruments for making absolute viscosity measurements, and which are characterized by uncertainties of < + 0.5%. The capillary flow technique has probably been the most widely used and most reliable instrument for absolute viscosity measurements for more than fifty years. The viscosity is calculated from the Poiseuille equation from a measurement of the flow rate produced by a pressure difference along a uniform tube of known diameter. Accuracies and precisions of + 0.1% have been attained. The capillary flow viscometer has been used over wide temperature ranges primarily for gas measurements; liquid measurements under pressure present special problems. Descriptions of reliable capillary flow viscometers are presented in References 95-101. The oscillating disc viscometer has been developed, primarily by Kestin and co-workers ")a-"~5, during the past 40 years into a state-of-the-art instrument. Like the capillary flow viscometer, an exact working equation is available. The viscosity of a gas is determined from the observed damping of the disc; an oscillating cup or ball is used for liquids. This instrument is capable of precisions and accuracies of + 0.1%. Its simplicity and compactness in design have facilitated measurements to extreme pressures. However, it has been primarily used for measurements at room temperature and above. Although viscosity data of high precision and accuracy ( = 0.1%) are often needed to make advances in the development of the microscopic theory of fluids, there are many practical engineering applications where a more modest accuracy (+ 2%) is sufficient. Viscometers, which are characterized by uncertainties at this level, include the falling body, rotating coaxial cylinders, rolling ball, torsionally oscillating piezoelectric crystal and the vibrating wire. The last two techniques, which have been used over wide pressure and temperature ranges for both gas and liquid measurements, will be discussed next. The torsional piezoelectric crystal method "~5-"~s makes use of measurements of the electrical properties of a piezoelectric cylinder (usually crystalline quartz), vibrating near its resonant frequency, to obtain the viscosity of the surrounding fluid. A description of its use for measurements on compressed gases and liquids is found in Reference 108. The main advantages of this method are that the device can be very compact, it requires only a very small quantity of fluid, and it can be conveniently used over wide ranges of temperature, pressure, and viscosity. The precision of this method, which depends on the range of the viscosity-density product being measured, is typically + 0.5%. The accuracy of the torsional crystal method is estimated to be ~ + 2%, based mostly on comparisons with accurate data obtained with other methods. This technique has been used more than any other for obtaining wide-range viscosity data for cryogenic fluids, including mixtures. The vibrating wire viscometer "~-Ill has been developed during the past 20 years and could well become one of the most convenient methods for wide-range measurements. It has been used for both gas l~''l ") and liquid Ill measurements, and for obtaining data in the critical region. Because of its simplicity and the compactness of its measurement cell, the vibrating wire viscometer is an excellent instrument for use at extreme conditions, suchas at low or high temperatures, at high pressures or in corrosive atmospheres. The viscosity is computed, using

352

Cryogenics 1987 Vol 27 July

Stokes' theory, by determining the damping of transverse oscillations of a taut wire in a fluid. This technique minimizes hydrodynamic correction terms, which are prevalent in many methods. The accuracy and precision of measurements with the vibrating wire viscometer are comparable to those of the torsional crystal method. However, it should be noted that while the torsional crystal method is best for dense liquid measurements, the vibrating wire technique is easier and more reliable to use for gas measurements.

Dependences of viscosity on density and temperature The dependences of the viscosity on density and temperature are illustrated in Figure 4, reprinted from Reference 112, using methane data obtained with a torsional crystal viscometer ~2. The critical point parameters for methane are Tc = 190.5 K and Pc = 10.2 mol dm -3. The temperature range covered in Figure 4 is 0.52-1.57 Tc and the density range is 0-2.8 Pc. At densities smaller than 2po the viscosity increases weakly with both density and temperature. At densities larger than 2p¢, however, the viscosity increases strongly with density and decreases weakly with temperature at fixed density. Analogous to Equation (1) for the thermal conductivity, these dependences can be described by an equation of the form tl(p,T) = ~lo(T) + rl ...... (p,T) + Atlcr,t,c,,(p,T )

(3)

where: 11o is the viscosity of the dilute gas and depends only on temperature; !1...... (p,T) is the difference [rl(p,T) - Vlo(T)] away from the critical point; and Al%ri,ical(p,T ) is the viscosity enhancement near the critical point. This last term can usually be neglected except when very close to the critical temperature and density. Additional information about the behaviour of the viscosity near the critical point can be found in References 37 and 113. I

I

I

i

i 100 K

180(

Saturated ¢)

1400

120K,

OD

=L

1200

>I-

1000

0 to u) >

140K~,

800

600[~-

180 K

400~-

2 0 0 K ,~

,#

250

0

10

20

30

OENSITY, mol/L Rgure 4 Viscosity of compressed gaseous and liquid methane as a function of density along isotherms, reprinted from Reference 112

Transport properties o f fluids: W.M. Haynes et al.

For compressed liquids, it is also useful to examine the dependence of the fluidity (reciprocal of viscosity), on specific volume 114H~. At high densities, the fluidity increases linearly with volume and weakly with temperature over considerable volume and temperature ranges. This behaviour can be described by a relatively simple equation, limited only by the density range where 1/tI versus V is linear. Survey o f data and correlations

Centres active in the critical evaluation and correlation of viscosity data are essentially the same as those for the thermal conductivity. They include the IUPAC Transport P r o p e r t i e s Project 39, the M I D A S Data Bank TM, CINDAS 41) and the National Bureau of Standards Thermophysics Division. A list of evaluated data sets for viscosity in the MIDAS Data Bank System 4~ is given in Table A4 of the Appendix. Fluids selected for numerical data analysis at C1NDAS 4°'4-~ are listed in Tables A2 and A3 in the Appendix. Stephan and Lucas have published a comprehensive compilation and critical evaluation of viscosity data for compressed gases and liquids entitled 'Viscosity of Dense Fluids 'j~6. This book presents tables and figures of recommended viscosity values as a function of pressure and temperature for 50 fluids. A list of fluids from the study of Stephan and Lucas is given in Table A5 of the Appendix. For some of the fluids considered in the present study, tables in the book of Stephan and Lucas represent the best correlated sets of critically evaluated values available. Although a summary of theoretical and correlation techniques for analysing viscosity data are presented in this book, neither the equations that are used

to produce the tables and figures nor the criteria used for development of the correlations and tables are included.

In Table 3, recommended references to correlations 43"53"55"56"62"65"66"69"73"77"81"s3"116"118']23 for the viscosity of pure fluids of cryogenic interest are presented. Also listed in this table are references ~2H7"~-~22 to data that were published after the relevant correlation was developed. Correlations and accurate data that cover large ranges of temperature, pressure and density have been emphasized in this table. For many of the fluids considered here, alternative viscosity correlations are offered since there is not a single correlation that is clearly superior to all others. As for thermal conductivity, there are viscosity correlations in progress that should be mentioned. New equations are being developed for CO2, NH 3 and N 2 through the IUPAC Subcommittee on Transport Properties~L The Thermophysics Division of the National Bureau of Standards has work in progress on the low molecular weight alkanes ~. There are few correlations and wide-range data available for the viscosities of mixtures. In Table 4 are presented references 8~'~6"~24-128 to the sets of viscosity data that are expected to be most useful in the development of global equations for mixtures. A very useful global predictive model, based on the extended corresponding states model and available as a computer program called T R A P P 7s'129, has been tested with data for many pure fluids and for a few binary mixtures. While not as accurate as the correlating equations referenced in Table 3, this model is especially useful at densities smaller than twice critical density and for those pure fluids and mixtures for which few data are available.

Table 3 Viscosity sources for pure fluids Substance

Surface correlation

H2

McCarty et al.~ Stephan and Lucas11° Stephan and Lucas11s Stephan and Lucas118 Younglove and Hanleyss Younglove~ Stephan and Lucas116 Hanley et aL 53 Stephan and Lucas118 Hanley et aL s3 Stephan and Lucas T M Younglove~s Stephan and Lucas11e Youngloves~ Roders2 Stephan and Lucas11e Haynes 1is

He Ne Ar Kr Xe N2 02 F2 CI2 CO C02 NO NzO NHz CH4 C2H6 C3He iC4Hlo nC4H10 C2H4

C3Hs HzO Refrigerants

Stephan and Lucas1~8 Stephan and Lucas "s Hanley 6s Stephan and Lucas T M Hanley et aL es Hanley et al. 69 Holland et aL73 Nieuwoudt et aL77 Stephan and Lucas11s Holland et aLel Stephan and Lucas 11e Watson et aL lz3 Stephan and Lucas 11s ASHRAE aa

New data

Diller 117

Oilier and Ball !19

Diller 112 Diller and Saber 12° Diller 121 Oilier t22

Tables A 1

and ,42 of Appendix

C r y o g e n i c s 1987 V o l 27 J u l y

353

Transport properties of fluids: W.M. Haynes et el. Table 4 Viscosity sources for mixtures

Components N2-CH4 CH4-C2H6 C02-C2H6 CH4-C3He C02-nCloH22 Air (Nz-02)

Diller124 Dillerlzs Diller et aL 12e Huang et aL 127 Cullick and Mathis 12e Stephan and Lucas116 Kadoya et aL es

Suggestions for future work The goal of thermophysical properties research is to develop validated, global predictive mathematical models for the thermophysical properties of the fluids of interest. This goal is seldom realized completely. There is as yet no global (e.g. gas and liquid) molecular theory of fluids for the viscosities of pure fluids and their mixtures. Hence, the need for theoretical improvements is very great. Experimental work on carefully selected fluids and binary mixtures, representative of classes of fluids, is also important. Current examples are carbon dioxide + hydrocarbon mixtures and refrigerant mixtures. Although the viscosity data for some of the cryogenic fluids considered in the present study represent the most comprehensive, accurate and consistent sets available for any fluid, there are some fluids considered here for which viscosity data are essentially non-existent. These include the fluids C!2, NO, N20, SO2 and some of the refrigerants. For almost any cryogenic fluid, there are gaps in the data base. Since relative viscosity measurements are much easier to obtain than absolute results, viscosity data of standard reference quality for selected fluids, such as argon, would be extremely useful. For thermal conductivities, standard reference data have been proposed, as discussed in an earlier section.

Conclusions This Paper has presented a discussion of the importance, availability and deficiencies of existing data bases and correlations for the viscosity and thermal conductivity of cryogenic fluids, including mixtures, considering both academic and industrial viewpoints. The transport properties for many of the traditional pure cryogens are in relatively good shape. In fact, some of these data sets represent the most comprehensive, accurate and consistent sets of transport property data in existence. Comprehensive correlations, which represent the state-of-the-art data within experimental uncertainty, are available for most of these fluids. However, for almost any cryogenic fluid, there is usually some gap in the data coverage or a question about the quality of the available data for at least one of the properties considered in this Paper. For some pure fluids considered in this study, wide-range comprehensive sets of transport property data are still needed. Many of the cryogenic fluids are relatively simple in molecular structure. Cryogenic fluids can be grouped into a wide array of molecular species, such as quantum fluids, rare gases, monatomic and diatomic molecules, polar fluids, hydrocarbons, and simple inorganics. Thus, it is possible to select cryogenic systems for which there is an adequate data base for the pure components and for which the components are simple enough for unambiguous theoretical and experimental analysis that are representative of important mixtures in new technologies. Since the major thrust of future studies of the transport properties of cryogenic fluids will almost certainly involve

354

Cryogenics 1987 Vol 27 July

Data sources

Surface correlation

mixtures, and since it is impossible to satisfy industrial needs with measurements only, it is extremely important that the overall approach in the development of predictive models be as general and flexible as possible. This signifies an integrated approach where efforts in experiment, theory and correlation complement and support each other with both scientific and industrial objectives in mind. Specific needs can be satisfied with appropriate emphasis. An ultimate goal of providing accurate, theoretically based predictive models relies heavily on the availability of data of the highest quality. At the same time, measurement programmes should be guided by development of predictive models. Empirical data fits are probably being pushed to their limits. More advances in theory are needed; contrary to the situation for that of a monatomic dilute gas, no complete and rigorous theory of the dense fluid has been developed. In the development of predictive models for mixtures, systems which contain species that exhibit large differences in size, polarity, shape, etc. represent the areas where significant improvement is most needed. This means that maximum benefits will be derived from a judicious selection of systems that fit the above criteria. However, there are other factors that should be considered in the selection of mixtures that will provide maximum gains. Accurate, wide-range transport property data for the pure components are needed. In addition, accurate PVT information for the selected mixtures and their components are required for an analysis of the experimental transport property data and for development of predictive transport property models.

Acknowledgements We are grateful to Professor W.A. Wakeham, Director of IUPAC's Transport Properties Data Centre, for providing us with information about the activities of the IUPAC Subcommittee of Commission 1.2, and to Dr. A. Laesecke, University of Siegen, for making information on the MIDAS Data Bank System available to us.

References 1 2 3 4 5

6

Sengers, J.V. and Klein, M. (Eds) The technological importance of accurate thermophysical property information, NBS Special Publication 5th), NBS. USA (1980) Zudkevitch, D. Imprecise data impacts phmt design and operation Hydrocarbon Processing (1975) 54 97 Zudkevitch, D. and Gray Jr, R.D. Impact of fluid properties on the design of equipment for handling LNG Adv Cryog Eng Plenum Press, New York, USA (t9751 20 1113 Chappelear, P.S., Chen, R.J.J. and Elliot, D.G. Pick K correlations carefully Hydrocarbon Processhlg (1977) 56 215 Miller, E.J. and Geist, J.M. Impact of recent developments in thermodynamics on chemical process design, Paper presented at the Joint Meeting of the Chemical Industry Engineering Society of China and the AIChE, Beijing, China (19821 Williams, C.C. and Albright, M.A. Better data saves energy

Transport properties of fluids: W.M. Haynes et al. Hydrocarbon Processing (1976) 55 115 Elliot, D.G., Chappelear, P.S., Chen, R.J.J. and MeKee, R.L. Thermophysical properties: their effect on cryogenic gas processing, in: Phase Equilibria and Fluid Properties in the Chemical Industry, Am Chem Soc Syrup Ser (Eds Storvick, T.S. and Sandier, S.I.) American Chemical Society, Washington, DC, USA (1977) 60 289 8 Wishart, R.S. Industrial energy in transition: a petrochemical perspective Science (1978) 199 614. 9 Mah, R.S.H. Effects of thermophysical property estimation on process design Chem Eng Comput (1977) I 183 10 Medina, A.G., McDermott, C. and Ashton, N. On the effect of experimental error on the calculation on the number of stages for a given distillation separation Chem Eng Sci (1974) 29 2279 11 Baker, O. The value of enthalpy research to the petroleum industry Proc 39th Annual Convention National Gas Processors Assoc (1960) 12 Najjar, M.S., Bell, K.J. and Maddox, R.N. The influence of improved physical property data on calculated heat transfer coefficients Heat Trans Eng (1981) 2 27 13 Hanley, H.J.M. and Baltatn, M.E. Data and thermal design: the role of fluid property data and their significance in design calculations Mech Eng (1983) 105 68 14 Mickley, M. and Hanley, H.J.M. The influence of physical property data on the design of shell and tube heat exchangers, Paper presented at the ASME Winter Meeting (1982), paper No. 82-WA/HT-60 15 Le Neindre, B. Thermal Conductivity (Ed Marsh, K.N.) IUPAC Subcommittee on Physicochemial Measurements and Standards, in preparation 16 Johnston, H.L. and Grilly, E.R. The thermal conductivity of eight common gases between 80 and 390 K J Chem Phys (1946) 14 233 17 Saxena, V.K. and Saxena, S.C. Measurement of the thermal conductivity of helium using a hot-wire type of thermal diffusion column Br J Appl Phys (1968) 1 1341 18 Needham, D.P. and Ziebland, Ft. The thermal conductivity of liquid and gaseous ammonia, and its anomalous behaviour in the vicinity of the critical point Int J Heat Mass Transfer (1965) 8 1387 19 Guildner, L.A. Thermal conductivity of gases: I. The coaxial cylinder cell J Res Nat Bur Stand (US) (1962) 66A 333 20 Le Neindre, B., Bury, P., Tufeu, R., Johannin, P. and Vodar, B. Recent developments at Bellevue on thermal conductivity measurements of compressed gases, in: Thermal Conductivity, Proc Seventh Conf (Eds Flynn. D.A. and Peavy, Jr, B.A.) NBS, US. Special Publication 302 (1968) 579 21 Michels, A., Botzen, A., Friedman, A.S. and Sengers, J.V. The thermal conductivity of argon between 0 and 75°C at pressures up to 25(X) atmospheres Physica (1956) 22 121 22 Sengers, J.V. Thermal conductivity measurements at elevated gas densities including the critical region Thesis University of Amsterdam. The Netherlands (1962) 23 Pittman, J.F.T. Fluid thermal conductivity determination by the transient line source method Thesis University of London, UK (1968) 24 Haarman, J.W. Thesis Technische Hogeschool Delft, The Netherlands (1969) 25 Mani, N. Precise determination of the thermal conductivity of fluids using absolute transient hot-wire technique Thesis University of Calgary, Canada (1971) 26 de Groot, J.J., Kestin, J. and Sookiazian, H. Instrument to measure the thermal conductivity of gases Physica (1974) 75 45,1 27 Mani, N. and Venart, J.E.S. Thermal conductivity measurements of liquid and gaseous methane Adv Cryog Eng Plenum Press. New York, USA (1973) 18 280 28 Nieto de Castro, C.A., Calado, J.C.G., Wakeham, W.A. and Dix, M. An apparatus to measure the thermal conductivity of liquids J Phys E Sci lnst (1976) 9 1073 29 Nagasaka, Y. and Nagashima, A. Absolute measurement of the thermal conductivity of electrically conducting liquids by the transient hot-wire method J Phys E Sci Inst (1981) 14 1435 3() Wakeham, W.A. Fluid thermal conductivity measurements by the transient hot-wire technique, Paper presented at Symposium on Transport Properties of Fluids and Fluid Mixtures: Their Measurement, Estimation. Correlation and Use, NEL, Glasgow, UK (1979) 31 Roder, H.M. A transient hot-wire thermal conductivity apparatus for fluids J Res Nat Bur Stand (US) (1981) 86 457

32

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Cryogenics 1987 Vol 27 July

13 893 ASHRAE Handbook 1981 Fundamentals Amer Soc Heating Refrig Air Cond Eng, USA 119811 84 Friend, D.G. and Rnder, H.M. The thermal conductivity surface for mixtures of methane and ethane Int J Thermophys (1987) 8 13 85 Rnder, H.M. and Friend, O.G. Experimental thermal conductivity values for mixtures of methane and ethane, NBS1R 85-3024, NBS, USA 119851 86 Stephan, K. and Laeseeke, A. The thermal conductivity of fluid air J Phys Chem RefData (1985) 14 227 87 Hemminger, W. The thermal conductivity of gases: incorrect results due to desorbed air Int J Thermophys in press 88 Kadoya, K., Matsunaga, N. and Nagashima, A. Viscosity and thermal conductivity of dry air in the gaseous phase in a wide range of temperature and pressure J Phys Chem Ref Data (1985) 14 947 89 Wakeham, W.A. Dept Chem Eng and Chem Tech, Imperial College of Science and Technol, London, UK, personal communication (1986) 90 Ynunglove, B.A., Ely, J.F., Friend, D.G. and lngham, H. Thermophysics Div NBS, Boulder, Colorado, USA, personal communication 119861 91 Menashe, J., Mustafa, M., Sage, M. and Wakeham, W.A. The thermal conductivity of normal alkanes in the dense fluid state Proc Eighth Syrup Thermophysical Properties, Vol I (Ed Sengers, J.V.) ASME, New York, USA (1982) 254 92 Dymnnd, J.H.Hard-sphere theories of transport properties Chem Sci Reviews (1985) 3 317 93 Nagasaka, Y. and Nagashima, A. Simultaneous measurement of the thermal conductivity and the thermal diffusivity of liquids by the transient hot-wire method Rev Sci lnstrum 119811 52 229 94 Knibbe, P.G. and Raal, J.D. Simultaneous thermal conductivity and thermal diffusivity measurements lnt J Thermophys (1987) 8 181 95 Giddings, J.G., Kao, J.T.F. and Kobayashi., R. Development of a high pressure capillary-tube viscometer and its application to methane, propane and their mixtures in the gaseous and liquid regions J Chem Phys (19661 45 578 96 Flynn, G.P., Hanks, R.V., Lemaire, N.A. and Ross, J. Viscosity of nitrogen, helium, neon and argon from -78.5 to 101YC below 200 atmospheres J Chem Phys 119631 38 154 97 van den Berg, H.R. and Trappeniers, N.J. The density dependence of the viscosity of krypton including the logarithmic term Proc Eighth Syrup Thermophysical Properties, Vol 1 (Ed Sengers, J.V.) ASME, New York, USA (1982) 172 98 Michels, A. and Gibson, R.O. The measurement of the viscosity of gases at high pressures - the viscosity of nitrogen to I(X)0 arm Proc Roy Soc 11931) AI34 288 99 Michels, A., Schipper, A.C. and Rintoul, W.H. The viscosity of hydrogen and deuterium at pressures up to 21100 atmospheres Physica 11953) 19 11111 100 Dawn, R.A. and Smith, E.B. Viscosities of thc inert gases at high temperatures J Chem Phys (19711) 52 693 101 Guevara, F.A., Mclnteer, B.B. and Wageman, W.A. Hightemperature viscosity ratios for hydrogen, helium, argon and nitrogen Phys Fluids (1969) 12 2493 1(12 DiPippo, R., Kestin, J. and Whitelaw, J.H. A hightemperature oscillating-disk viscometer Physica (1966) 32 21~4 103 Kestin, J. and Wang, H.E. Corrections for the oscillating-disk viscometer J Appl Mech ( 19571 24 197 1114 Kestin, J., Leidcnfrost, W. and Liu, C.Y. On relative measurements of the viscosity of gases by the oscillating-disk method Z Ang Math Phys (1959) 10 558 105 Van Itterbeek, A., Zink, H. and Hellemans, J. Viscosity of liquefied gases at pressures abovc one atmosphere Physica 119661 32 489 106 Mason, W.P. Measurement of the viscosity and shear elasticity of liquids by means of a torsionally vibrating crystal Trans ASME 119471 69 359 107 Webeler, R.W.H. Viscosity X density measurement for normal liquid hydrogen and various ortho-para mixtures PhD Thesis University of Cincinnati, Ohio, USA (19611 108 Haynes, W.M. Viscosity of gaseous and liquid argon Physica 119731 67 440 109 Tough, J.T., McCormick, W.D. and Dash, J.G. Vibrating wire viseometer Rev Sci Instrum (1964) 35 1345 110 Broschi, L. and Santini, M. Vibrating wire viscometer Rev Sci 83

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lnstrum (1975) 46 1560 Charles, E., Molenat, J., Abaehi, H., Michel, J. and Malbrunot, P. The use of a vibrating wire viscometer in liquids J Phys E: Sci Instrum (1980) 13 829 Diller, D.E. Measurements of the viscosity of compressed gaseous and liquid methane Physica (1980) 104A 417 B i n , R.S. and Sengers, J.V. Viscosity of nitrogen near the critical point J Heat Transfer (1979) 101 3 Diller, D.E. and Van Poolen, L.J. Tests of models for shear viscosity coefficients High Temp High Press (1985) 17 139 Hildebrand, J.M. Viscosity and Diffusivity J. Wiley, New York, USA (1977) Stephan, K. and Lucas, K. Viscosity of Dense Fluids Plenum Press, New York, USA (1979) Diller, D.E. Measurements of the viscosity of compressed gaseous and liquid nitrogen Physica (1983) 119A 92 Haynes, W.M. Measurements of the viscosity of compressed gaseous and liquid fluorine Physica (1974) 76 1 Diller, D.E. and Ball, M.J. Shear viscosity coefficients of compressed gaseous and liquid carbon dioxide at temperatures between 220 and 320 K and at pressures to 30 MPa lnt J Thermophys (1985) 6 619 Diller, D.E. and Saber, J.M. Measurements of the viscosity of compressed gaseous and liquid ethane Physica (1981) 108A 143 Diller, D.E. Measurements of the viscosity of saturated and

122 123 124 125 126

127 128 129

compressed liquid propane J Chem Eng Data (1982) 27 240 Diller, D.E. and Van Peolen, L.J. Measurements of the viscosities of saturated and compressed liquid normal butane and isobutane lnt J Thermophys (1985) 6 43 Watson, J.T.R., Basu, R.S. and Sengers, J.V. An improved representative equation for the dynamic viscosity of water substance J Phys Chem Ref Data (1980) 9 1255 Diller, D.E. Measurements of the viscosity of compressed gaseous and liquid nitrogen + methane mixtures lnt J Thermophys (1982) 3 237 Diller, D.E. Measurements of the viscosity of compressed gaseous and liquid methane + ethane J Chem Eng Data (1984) 29 215 Diller, D.E., Van Poolen, L.J. and Santos, F.V. Measurements of the viscosities of compressed gaseous and liquid carbon dioxide + ethane mixtures J Chem Eng Data submitted for publication Huang, E.T.S., Swift, G.W. and Kurata, F. Viscosities and densities of methane + propane mixtures at low temperatures and high pressures AIChE J (1967) 13 846 Cullick, A.S. and Mathis, M.L. Densities and viscosities of mixtures of carbon dioxide and n--decane from 310 to 403 K and 7 to 30 MPa J Chem Eng Data (1984) 29 393 Ely, J.F. and Hanley, H.J.M. Prediction of transport properties: 1. Viscosity of fluids and mixtures ! & EC Fundamentals (1981) 20 323

Appendix Table A1 Evaluated thermal conductivity datasets in MIDAS (as of December 31 198541) Substance

Temperature range (K)

Pressure range (MPa)

Physical state a

points

Number of

Helium Helium Neon Neon Argon Argon Krypton Krypton Xenon Xenon Hydrogen Hydrogen Hydrogen Parahydrogen Parahydrogen Parahydrogen Nitrog en Nitrogen Oxygen Oxygen Air Air Ammonia Ammonia Carbon dioxide Carbon dioxide Water Water Water Sulphur hexafluoride Sulphur hexafluoride Methane Methane Ethane Ethane Propane Propane Normal butane Normal butane Isobutane Isobutane Normal pentane Normal pentane

25-750 2-2400 26-44 26-1300 90-1300 87-150 120-1300 119-209 170-1300 164-289 16-33 15-1200 16-32 16-1200 16-32 16-33 80-1400 70-126 70-154 70-1400 70-1000 65-132 220-405 240-700 220-1300 220-1304 275-645 275-1100 275-647 230-400 230-318 100-190 100-700 177-306 190-800 220-475 220-369 272-425 280-675 195-410 195-408 300-475 300-469

0.1-120 0.1 0-2.6 0.1-100 0.1-100 0.1-4.8 0.1-100 0.1-5.5 0.1-100 0.1-5.8 0-1.3 0.1-60 0-1 0.1--60 0-1.1 0-1.2 0.1- 100 0-3,3 0-5 0.1-100 0.1-100 0-3.7 0-11.3 0.1-60 0.1-250 0.5-7.3 0-21.5 0.1-100 0-22 0.1-50 0.3-3.7 0,03-4.6 0.1-110 0-5 0.1-115 0.1-50 0-4.2 0.1-3.7 0.1-50 0.1-50 0-3.6 0.1-230 0-3.3

G G SL-SV L-G L-G SL-SV L-G SL-SV L-G SL-SV SL L-G SV L-G SV SL L-G SL-SV SL-SV L-G L-G SL-SV SL-SV L-G L-G SL-SV SV L-G SL L-G SL-SV SL-SV L-G SL-SV L-G L-G SL-SV SL-SV L-G L-G SL-SV L-G SL

196 48 13 1834 1688 22 1758 27 1758 33 10 591 9 591 9 10 530 23 35 1236 592 29 39 373 608 36 38 1056 39 252 24 37 586 51 571 325 31 40 328 416 28 193 14

Continued overleaf

Cryogenics 1987 Vol 27 July 357

Transport properties of fluids: W.M. Haynes et al. Table A1 Continued Substance

Temperature range (K)

Pressure range (MPa)

Physical statea

Number of points

Isopentane Normal hexane 1-Octene Cyclohexane Methylcyclohexane Ethylcyclohexane Benzene Benzene Toluene Ethyl benzene Methanol Ethanol 1-Propanol 2-Propanol N-Propylacetate N-Butylacetate R12 (dichlorodifluoromethane) R13B1 (bromotrifluoromethane) R22 (chlorodifluoromethane) R22 (chlorodifluorometha ne) R113 (trichlorotrifluoroethane)

250-700 300-640 300-490 290-520 290-530 290-530 290-550 290-550 295-550 300-560 290-550 270-540 320-550 430-530 290-500 290-500 250-575 290-435 250-365 250-363 240-480

0.1 0.1-230 0.1-50 0.1-50 1-50 1-50 0-4.2 0.1-40 0.1-40 0.1-40 0.1-80 0.1-100 0.1-50 0.1-80 0.1-45 0.1-50 0.1-60 0.1-60 1-60 0.2-4.4 0.1-60

L-G, SL-SV L-G L L L L SL-SV L L L L-G L-G L-G L-G L L L-G L-G L SL L

48 378 208 306 294 294 54 320 300 210 210 330 150 132 228 240 364 638 234 23 306

aAbbreviations: L -- liquid, G = gas, V = vapour, S = saturated

Table A2 Fluids selected for numerical data analysis at CINDAS4° Acetone Acetylene Air Ammonia Argon Benzene Boron trifluoride Bromine Isobutane Normal butane Carbon dioxide Carbon monoxide Carbon tetrachloride Carbon tetrafluoride Chlorine Chloroform Normal decane Deuterium Ethane Ethyl alcohol (ethanol) Ethyl ether Ethylene Ethylene glycol Fluorine Glycerol

4He Normal heptane Normal hexane Hydrogen Parahydrogen Hydrogen chloride Hydrogen iodide Hydrogen sulphide Iodine Krypton Methane Methyl alcohol Methyl chloride Neon Nitric oxide Nitrogen Nitrogen peroxide Nitrous oxide Normal nonane Normal octane Oxygen Normal pentane Propane Propylene Radon

R11 (trichlorofluoromethane) R12 (dichlorodifluoromethane) R13 (chlorotrifluoromethane) R13B1 (bromotrifluoromethane) R21 (dichlorofluoromethane) R22 (chlorodifluoromethane) R23 (trifluoromethane) R113 (trichlorotrifluoroethane) R114 (dichlorotetrafluoroethane) R115 (chloropentafluoroethane) R142b (chlorodifluoroethane) R152a (difluoroethane) R216 (1,3-dichlorol, 1,2,2,3,3,-hexafluoropropane) RC318 (octafluorocyclobutane) R500 (R12, R152a azeotrope) R502 (R22, R115 azeotrope) R503 (R13, R23 azeotrope) R504 (R32, R115 azeotrope) Sulphur dioxide Toluene Tritium Water Xenon

Table A3 List of substances for which CINDAS compiled and assessed transport property data for the gas industry42 Ammonia Isobutane Normal butane Carbon disulphide Carbon dioxide Carbon monoxide Carbon oxysulphide Cyclopentane Ethane

358

C r y o g e n i c s 1987 V o l 27 J u l y

Helium Hydrogen Hydrogen cyanide Hydrogen sulphide Methane Nitric oxide Nitrogen Nitrogen peroxide

Nitrous oxide Isopentane Normal pentane Neopentane Propane Sulphur dioxide Sulphur trioxide Water

Transport properties of fluids: W.M. Haynes et al. Table A4 Evaluated viscosity datasets in MIDAS (as of December 31 198541) Temperature range

Pressure range

Substance

(K)

(MPa)

Physical state a

Number of points

Helium

80-1300 26-1300 26-44 90-1300 90-150 120-209 120-1300 170-1300 170-289 15-1000 15-100 70-1400 65-126 55-154 60-1500 90-300 220-510 85-1000 200-600 220-405 310-900 275-1100 275-647 100-520 95-190 300-750 189-367 175-750 300-850 31 0-850 320-900 280-750 380-1000 300-620 320-670 290-540 300-470 280-520 300-520 300-520 180-520 180-282 180-364 180-520 280-375 300-490 300-490 290-520 290-530 290-530 290-550 290-550 295-550 300-560 290-550 270-540 320-550 430-530 290-500 290-500 250-575 290-435 250-365 250-363 240-480

0.1--80 0.1-100 0-2.6 0.1-100 0.1-4.8 0.1-5.5 0.1-100 0.1-100 0.1-5.8 0.1-100 0.1-35 0.1-100 0-3.4 0-5 0.1-1 50 0.1-20 0.1-80 0.1-100 0.1-50 0-11.3 0.1-100 0.1-100 0-22 0.1-70 0-4.6 0.1-70 0.01-4 0.1-35 0.1-70 0.1-50 0.1-50 0.1-60 0.1-50 0.1-50 0.1-50 0.1-50 0.1-50 0.1-35 0.1-50 0.1-50 0.1-60 0.1-50 0-4.6 0.1-60 0.1-45 0.1-50 0.1-50 0.1-50 1-50 1-50 0-4.2 0.1-40 0.1-40 0.1-40 0.1-80 0.1-100 0.1-50 0.1-80 0.1-45 0.1-50 0.1-60 0.1-60 1-60 0.2-4.4 0.1-60

L-G L-G SL-SV L-G SL-SV SL-SV L-G L-G SL-SV L-G L-G L-G SL-SV SL-SV L-G L-G G G L-G SL-SV G L-G SL-SV L-G SL-SV L-G SL-SV L-G L-G L-G L-G L-G L-G L-G L-G L L L L L L-G SL-SV SL-SV L-G L L L L L L SL-SV L L L L-G L-G L-G L-G L L L-G L-G L SL L

81 1836 20 1743 15 21 1758 1760 27 286 767 944 27 41 1270 476 238 523 381 39 600 1056 77 850 41 900 27 648 620 685 486 572 459 408 432 280 306 266 221 221 378 23 39 378 176 208 208 306 294 294 54 320 300 210 210 330 150 228 228 240 384 638 234 23 306

Neon Neon Argon Argon Krypton Krypton Xenon Xenon Hydrogen Parahydrogen Nitrogen Nitrogen Oxygen Oxygen Fluorine Carbon monoxide Air Ammonia Ammonia Carbon dioxide Water Water Methane Methane Ethane Propane Propane Normal butane Isobutane Normal pentane Isopenta ne Normal hexane Normal heptane Normal octane Isoocta ne Normal nonane Normal decane Normal undecane Normal dodecane Ethene Ethene Propene Propene 1-Hexene 1-Heptene 1-Octene Cyclohexane Methylcyclohexane Ethylcyclohexane Benzene Benzene Toluene Ethyl benzene Methanol Ethanol 1-Propanol 2-Propanol Normal propylacetate Normal butylacetate R12 (dichlorodifluoromethane) R13B1 (bromotrifluoromethane) R22 (chlorodifluoromethane) R22 (chlorodifluoromethane) R113 (trichlorotrifluoroethane)

aAbbreviations: L = liquid, G = gas, V = vapour, S = saturated

Cryogenics 1987 Vol 27 July 359

Transport properties of fluids: W.M. Haynes

et al.

Table A5 List of fluids for which viscosity data have been critically evaluated by Stephan and Lucas116 Air Ammonia Argon Benzene Isobutane Normal butane Butylacetate Carbon dioxide Carbon monoxide Cyclohexane Normal decane Normal dodecane Ethane Ethanol Ethylbenzene Ethylcyclohexane Ethylene

360

C r y o g e n i c s 1987 Vol 27 J u l y

Fluorine Helium Normal heptane Normal heptene Normal hexane Normal hexene Hydrogen Parahydrogen Krypton Methane Methanol Methylcyclohexane Neon Nitrogen Normal nonane Iso-octane Normal octane

Normal octene Oxygen Isopentane Normal pentane Propane Isopropanol Normal propanol Propylacetate Propylene R12 (dichlorodifluoromethane) R13B1 (bromotrifluoromethane) R22 (chlorodifluoromethane) R113 (trichlorotrifluoroethane) Toluene Normal undecane Xenon