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TitleVISCOSITY OF AQUEOUS SODIUM CHLORIDE SOLUTIONS FROM 0 - 150oC

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AuthorOzbek, H.

Publication Date1977-10-01

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Presented in Part at the American Chemical Society 29th Southeast Regional Meeting, Tampa, PL, November 9 - 11, 1977.

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LBL-5931 c" \

Viscosity Of Aqueous Sodium Chloride Solutions From 0 - 1500 C

H. Ozbek, I.A. Fair, S.L. Phillips

December 1977

..-------- LEGAL NOTICE ----------.

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the Depart­ment of Energy, nor any of their employees, nor any of their con­tractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, appa­ratus, product or process disclosed, or represents that its use would not infringe privately owned rights. i

I,)

Presented Part at the American Chemical Society 29th Southeast Regional Meeting,' Tampa, November 9-11, 1977

LBL - 5931 December 1977

VISCOSITY OF AQUEOUS SODIUM CHLORIDE SOLUTIONS FRrn 0 - 1500 C

by

H. Ozbek, J.A. Fair, S . Phillips

Energy and Environment Division Lawrence Berkeley Laboratory

University of California Berkeley, CA 94720

Sponsored by the U.S. Department of Energy

-1-

Abstract

A critical evaluation of data on the viscosity of aqueous

sodium chloride solutions is presented. The literature was screened

through October 1977, and a databank of evaluated data was estab­

lished. Viscosity values were cGnverted when necessary to units of

°c, centipoise and molal concentration. The data were correlated

with the aid of an empirical equation to facilitate interpolation

and computer calculations. The result of the evaluation includes

a table containing smoothed values for the viscosity of NaCl solutions

to 150°C.

MFa = 106 N/m2 = 10 bar = 145.04 psi

~Pa s = 10-6 kg/s m = 10-Sp = 103 cp

1 Pa s = IN s/m2 = 1 Kg/s M = 10 Poise

-2-

Table of Contents

A. Introduction

B. Analytical Expressions and Correlations

C. Methods for Measuring Viscosity

D. Evaluation Procedure

E. Summary and Conclusions

F. Recommendations

G. Acknowledgment

H. References

Appendix I - Dynamic Viscosity of Water Substance

)

- 3 -

A. Introduction

The need for critically evaluated basic scientific data in geothermal

and other energy research and development is obvious. Only a brief

reflection is needed to realize the great frequency with which scientists

and engineers look up tabulated data in handbooks, reports and computer

print-outs. Before the advent of computer manipulation of data, only

elementary methods could be used for statistical calculations of data

evaluation. Now it is possible for specialized information analysis

centers to use modern computer methods for storage, retrieval and statis-

tical calculations involving large quantitiies of numerical data. The

saving in time and cost to provide the scientific community with critically

evaluated recommended values, correlations and non-duplication of

research effort is substantial.

The National Geothermal Information Resource (GRID) of the Lawrence

Berkeley Laboratory is sponsored by the Department of Energy to compile

and evaluate data on geothermal energy for electrical and non-electrical

uses. Included in this compilation are both site-dependent and site-

independent material related to geothermal exploration, reservoir engineer-

ing, reservoir utilization, physical chemistry, as well as environmental,

legal, and economic aspects of geothermal energy. While the larger work

covers the areas listed, this report is limited to a critical evaluation

Supported by the Department of Energy: Division of Basic Energy Sciences Division of Geothermal Energy; Office of Environmental Information Systems; and Office of Technical Information.

- 4 -

of data on the viscosity of sodium chloride solutions to elevated~

temperatures, pressures, and saturation concentrations.

The development geothermal resources requires scientific and

engineering calculations based on the basic energy properties of aqueous

sodium chloride and other electrolyte solutions. In this context, GRID

has developed a computer file to store, retrieve and index worldwide

publications relevant to the thermodynamic and transport properties of

aqueous sodium chloride and other solutions. Data from this file are

extracted for status of data reviews and critical evaluations. The

objective is establishing a databank of published data on basic energy

properties of aqueous NaCl solutions covering the ranges of geothermal

interest: temperatures to 350°C, pressures to 50 mPa (SOO bars), and

concentrations to saturation (Ref. I). The present work gives the

results of a survey and evaluation of a subset of this databank: that

dealing with the viscosity of sodium chloride solutions.

The literature screened in compiling the viscosity data covers the

time span from 1929 to 1977; data prior to 1929 are contained in the Inter­

national Critical Tables (Ref. 2) for NaCl solutions at atmospheric

pressure over the temperature range O°C to 100°C, and concentrations

from 0 molal to 5 molal. Published viscosity data from 1929 to July 1977

are largely at atmospheric or saturation vapor pressure with the highest

temperature being ISO°C (Ref. 3,4). See Table I. Recently,

.J

- 5 -

Kestin has provided extensive experimental data to pressures of 30 MPa

in Table 1 (Ref. 5-7).

Besides laboratory data on viscosity, this report includes a summary

of selected analytical expressions and correlations which describe the

change in viscosity of NaCl solutions as a function of concentration,

temperature, and pressure. Density data needed, for example, to convert

NaCl molar concentrations to molal units can be obtained from Rowe and

Chou (Ref. 8) or from Potter and Brown (Ref. 9). To provide for calcu­

lating relative viscosity, we have included as an Appendix, data on the

temperature dependence of the viscosity of water and the corresponding

correlation equation from the Eighth International Conference on the

Properties of Steam. See References 10 and 11 for more detailed infor­

mation on the viscosity of water to elevated temperatures and pressures.

While it is our intent that this compilation on the viscosity of

NaCl solutions be comprehensive, it is recognized that there may be

important omissions. The reader is urged to communicate such omissions

to the National Geothermal Information Resource for inclusion in this

databank.

Listings containing information on the basic energy properties of

NaCl and other electrolyte solutions (e.g., KCl, CaCI2) can be obtained

from the computer files

additional and

- 6 -

the National Geothermal Information Resource.

evaluation of data on the viscosity of both

water and NaC! solutions, the is referred to the following refer-

ences:

Dynamic Viscosity of Water Substance (Ref. 10,11)~

Thermophysical Properties of Matter, Vol. II, Viscosity (Ref. 12),

"The Volumetric Properties of Aqueous NaCl Solutions from Oo~ to 500°C

at Pressures up to 2000 Bars Based on a Regression of Available Data

in the Literature" (Ref. 9), and "Viscosity of NaCl Solutions" (Ref. 2,5).

- 7 -

B. Analytical Expressions and Correlations

This section covers a survey analytical expressions and

correlations which have been used to describe changes in viscosity for

aqueous NaCl solutions as a ftmction of temperature, concentration, and

pressure. It not exhaustive, and the interested reader is referred

additional information to references cited,

For NaCl solutions up to few tenths molal concentrations, the

variation in viscosity with concentration is commonly described using

the Jones and Dole equation (Ref, 13):

nr "" 1 ... A ~ ... :aM

nr "" relative viscosity (n/nHzo)

M "" molarity

A,B "" constants

(1)

The constant ~ has a theoretical basis as shown by Fa1kenhagen and

Vernon who derived the following equation based on theoretical consider-

ations (Ref, 14):

nr '" 1 ... A IM- (2)

where

AO "" limiting conductivity of electrolyte

- 8 -

29.16 X 2 12 no (DT)1/2

viscosity of water

D '" dielectric constant of H20

T "" temperature, oK

Suryanrayana and Venkateson (Ref. 15) measured the viscosity of aqueous

NaCl solutions over the temperature range 30°C to 55°C and the concen­

tration range 1 molal to saturation. In developing an expression for

the concentration dependence of NaCl, they found that at each temperature

a plot of log (n/nsatJ is linear; consequently, they suggested the

following exponential relation between viscosity and NaCl concentration:

l1!l1sat. =: A expo (Bm!msat ) (3)

where

A '" llwater!l1sat .

B "" In [l1sat,!nwater]

nsat . :: viscosity of saturated NaCl solution,

nwater "" viscosity of water

m "" molality of NaCI solution

msat. '" molality of saturated NaCI solution

Korosi and Fabuss (Ref. 3) used an extended form the Jones-Dole

Equation to develop an empirical correlation for their measurements of

tj ,

•. $ ;<1 ,_J

- 9 -

the viscosity of NaCl solutions covering temperatures from O°C to 150°C:

nr "" 1 + A M + BM + DMZ (4)

where

nr '" relative viscosity Cn/nHzo)

M "" molarity

A,B,D :::: temperature dependent coefficients

The coefficients A, B, and D were evaluated as discussed in their

publication:

Ii Unfortunately, limiting conductances for NaCl and KCl and limiting ionic conductances are available only in the 5 to 55°C temperature range. Using these available data, with the viscosity and dielectric constant data given by Harned and Owen, the A values were calculated.

This means that the limited slope values used in this evaluation in the 55 to 150 0 temperature range were determined by extrapola­tion 6f the limiting ionic conductances, and using correct data for the viscosity of water and its dielectric constant. For this reason the limiting slope values can be considered only as empirical constants over this temperature range.

With these limiting slope values, the experimental viscosity data at each temperature were evaluated, and by a least square method the best values of the constants B and D were determined. The experimentally determined and derived A, B and D constants were expressed as functions of temperature by a cubic temperature relationship of the form:

A ::: AO + Alt + A2tZ + A3t3

B "" BO + BIt + BZt2 + B3t3

D = DO + Dlt + D2 tZ + D3t3

- 10 -

The constants of these equations as calculated by Korosi and Fabuss

(Ref, 3) are:

A "" 0 0,5649 x 10-2

BO :::: 0,23092 x 10-1 DO '" 0.25651 x 10

Al '" 0.2012 x 10 -4 Bl 0.23206 x 10- 2 Dl '" 0.39857 x 10 -3

Az '" 0,1200 X 10-6 BZ 0.22124 X 10-4 -5 "" D2 '" 0.43024 x 10

A3 :::: 0,4514 X 10-9 B3 ::::: 0.82313 X 10-7 D3 '" 0,15500 x 10 -7

The empirical equation reproduces their data with an estimated precision

of ~ 0.2%.

a recent study, Goncalves and Kestin (Ref. 6) measured the viscosity

of aqueous NaCl solutions at temperatures of 25°C, 30°C, 40°C, and 50°C

over a range of molalities up to about saturation. The laboratory data

at each temperature were correlated with the aid of polynomials of the

form

n::::: n + n c + n c2 + n c 3 012 3 (5)

where n ,n ,n ,n are temperature dependent coefficients, Each of o 1 2 3

these coefficients is a smooth function temperature, and each one

is correlated with the aid of a third order polynomial. The resulting

correlation equation can be represented by the double sum

n "" (6)

j ./

The correlation reproduces their data within accuracy of the measurements

which is !O.l% The coefficients a .. are listed below: 1.J

Coefficients a. 0 of Equation 6 (Ref. 6) 1J

o 1

j=O 1.6560 O.7221x10 -1

1 -O.4304xlO -1 0.1275.10 -2

2 O.5769xlO -3 -O.5876xlO-4

3 -O.3l94xlO -5 O.5550xlO-6

2 3

O. 2460x1 0 -:-.1 O.1448xlO -2

-O.1294xlO- 2 -0. 2994xlO -4

O.282lx10-4 O.9443xlO -8

-O.2228x10-6 O.3086xlO -8

An additional source of data on the viscosity of aqueous NaCl solutions

at elevated temperatures is contained in the publication Pressure

Buildups and Flow Tests in Walls (Ref. 16), The data is presented as

a family of curves covering the temperatures 4°C to 204°C, and NaCl

- 12 -

concentrations from 0 molal to about 6 molal. However, data from these

plots are not included in our evaluation because the numerical data from

which these plots were drawn are not available for critical evaluation.

Currently the experimental data on thl= pressure dependence of the

viscosity of aqueous NaCl solutions is that provided by Kestin for

temperatures to 150°C, over the concentration range of 0.47 molal to 5.4

molal, and pressures to 30.0 MPa (300 bars). See Ref. 5 and 7. The

authors found that the viscosity increases with pressure by about 1%.

See Table 1. The empirical correlation developed by Kestin and coworkers

reproduces their NaCl data with a standard deviation of !O.5% and

is of the form:

where

~ (P,T,c) = ~O(T,c) [1 + a (T,c) P] (7)

~ = viscosity

P = pressure

T = temperature

c = concentration

a = pressure coefficient

~o = zero-pressure viscosity

The reader is referred to Reference 5 for detailed illformation.

In summary, empirical correlation equations are available which reproduce

the viscosity of NaCl solutions; however statistically developed empirical

I

- 13 -

equations are valid only for interpolation and machine computation in the

concentration and temperature range stated. The theoretical equation

developed by Falkenhagen and Vernon (Ref. 14) can be used to predict

the viscosity of aqueous NaCl solutions, but is limited to dilute solutions,

e.g. <O.1m. MOreover, the coefficient ~ in the Falkenhagen-Vernon equation

requires data on limiting conductivities of both the electrolyte and the

ions, as well as the dielectric constant of water. Addition of a higher

order concentration term to the Falkenhagen-Vernon equation results in

the Jones-Dole equation which applicable to concentrations to about

0.1 molal. Much work has been done to theoretically evaluate the ~

coefficient; see, for example, the literature review by MandaI, Seal

and Basu (Ref. 17), A successful prediction of the ~ coefficient does

not appear important to geothermal applications because the viscosity

of NaCl solutions to saturation concentrations is required.

- 14 -

C. Instrumentation for Measuring Viscosity

This section summarizes laboratory instrumentation for measuring

the viscosity of aqueous NaCl and other electrolyte solutions. The

discussion includes instrumentation used at 25°C, but emphasis is on

those methods which have been applied to elevated temperatures and

pressures. For additional information, a good discussion on viscosity

measurements is given in the Encyclopedia of Chemical Technology (Ref.

18), and in the publications by Kestin (Ref. 7), and Korosi and Fabuss

(Ref. 3).

The four viscometers commonly used to measure the viscosity of NaCl

aqueous solutions are the following: capillary, rotational, falling

sphere, and oscillating disk. For temperatures above about SO°C, the

most widely used is the capillary-type, for example, the Ostwald,

Cannon and Ubbelohde viscometers. These viscometers are based on

Poiseuille's Law which describes laminar flow in pipes.

Goncalves and Kestin used both the Ostwald and Ubbelohde viscometers

in measuring the viscosity of NaCl and KCI solutions over the range 25°C

to SO°C. Calibration was performed with respect to water at 20, 2S, 30,

40, and 60°C, with temperatures controlled to to.loC. The solutions were

prepared by weighing the desired amount of reagent grade NaCl

- 15 -

in double-distilled water, Measurements of NaCl viscosity were at

25, 30, 40 and 50°C, with temperature controlled to to.loC. The

accuracy of the viscosity measurements was taken as to.l% (Ref. 6).

Korosi and Fabuss measured NaCl viscosity over the temperature

range 25°C to 150°C (Ref. 3), using a specially built Cannon glass

capillary viscometer with 470 rum overall length secured into a metal

support frame by means of two screw clamps. The ends of the 3/8 in,

O.D, receiving tube and a 1/4 in. O.D. capillary side tube of the visco-

meter were connected to the manifold and valve system with two Cajon

o ring fittings, The capillary side of the viscometer joined a stain-

less steel holder enclosing a palladium silver membrane, which was

connected to a normally open, air pressure-operated Nupto bellows

valve, The line rejoined the receiving side of the viscometer in a

T fitting. From here connection was made to the source of pressurized

hydrogen, through an air pressure operated, and normally closed, Whitey

valve, and through the panel terminal located on top of the assembly.

The whole assembly was submerged in a thermostat filled with oil for

temperature control.

Ostwald-type viscomcters were also used by Ezrokhi in measuring

NaCl viscosity at 25, 40 and 60°C (Ref, 19), by Postnikov ternper-

atures to 80°C (Ref, 20), by Suryanarayana and Venkatesan for temperatures

to 55°C (Ref. 15), and by Jones and Christian at 25°C (Ref. 21).

- 16 -

Recent viscosity measurements at pressures to 300 bars by Abe,

Grimes, Kestin, Khalifa, Sookiazian and Wakeham were made using a

modified oscillating disk viscometer. The instrument consisted of a

high-pressure bomb of type 347, 18-8 stainless steel, sealed with the

aid of bolts made from Inconel X, and provided with a synthetic sapphire,

Bridgman-type window. The oscillating system was enclosed in the bomb,

and carried a reflecting mirror on a stem. The bomb was mounted on a

titanium-carbide ball bearing, and enclosed in an automatically controlled

heater surrounded by a radiation shield. Oscillation was initiated

by rotation of the bomb on its bearing, and observed by a telescope

which was trained on a precision scale. For brines such as NaCl solutions,

the following parameters were used: natural period of TO ~ 16 sec.,

stainless steel disk with R = 33.9725 mm radius and d = 3.2131 mm

thickness between two fixed plates of widespacing b = 2.9782 mm. Pressure

measurements were made using high-precision Bourdon gauges, each accurate

to 0.2% of its maximum range. Temperatures were measured with calibrated

thermocouples. See Reference 5.

In summary, the Ostwald, Cannon and Ubbelohde-type capillary visco­

meters are the instruments mainly used for measuring the viscosity of

NaCl solutions for temperatures to lSOaC. An oscillating-disk viscometer

was used for measurements at pressures to 30 MPa (300 bars), and tempera­

tures to lSO°C (Ref. 23).

J

- 17 -

D. Evaluation and Correlation

A comprehensive search the published literature for NaCl

viscosity data was made, covering the time span from 1929 to July 1977.

All available copies of the original publications were a~sembled using

the following main sources for literature references: The Department of

Energy Technical Information Center's RECON System which includes the

following databases: Energy Data Base, Water Resources Abstracts, and

Engineering Index (COMPENDEX); Chemical Abstracts; the International

Critical Tables; and relevant journals and reports.

The data selected for correlation from a larger list (Ref. 22) are

the reported experimental values, and do not include either smoothed or

calculated data. Nickels' data at 25°C were consistently low and were

not included here (Ref. 30). See Table 1. All data in this table have

been converted where necessary to the 12C scale of atomic weights, to the

g/cm3 basis for density, to centipoise for viscosity, from molar to molal

concentrations, and from relative to absolute viscosity values, The

needed water viscosity data were taken from the results of the Eighth

International Conference on the Properties of Steam (Ref, 10,11).

The following empirical equation developed from this data was found

convenient for correlation to 30 MPa and 150°C:

- 18 -

n ::= cl + Cz exp(alT) + c3 exp (a2m) + c4 exp [a3 (O.OlT + m)] (11)

+ c5 exp [a4 (O.OlT - m)]

where

~ ;:: viscosity, cp

T ::= temperature, °C

m = concentration, molality

cl '" 0.1256735

Cz '" L Z65347

c3 =-1.105369

c4 ::= 0,2044679

c5 '" 1. 308779

a1 =-0,04296718

a2 =:: 0,3710073

a3 ;:: 0.4230889

a4 =-0.3259828

Equation 11 is valid only to pressures of 30 MPa and temperatures to 150°C,

Figure 1 shows the viscosity data versus concentration for temperatures

of 10, 20, 30, 40, 50, 75, 100, 125 and l50°C, and the corresponding

correlation plotted using Eq. 11. Figure 2 is a plot of viscosity versus

temperature, using Eq, 11, Data maybe interpolated with Eq. 11 to a

standard deviation of 1.5% over the entire temperature, pressure, and

concentration range. See Figure 3, The standard deviation for all

c611centratiolls is SHuwn in Figure 4; and, for 100C to 150°C in Figure 5.

Table 2 contains smoothed values ,calculated Erom Equa.tiori-11,

/

- 19 -

E. Summary and Conclusions

The currently available experimental data on the viscosity of NaCl

solutions is sparse and covers mainly pressures from atmospheric to

30 MFa (300 bars), concentrations to saturation, and temperatures below

7SoC. Above 7SoC the available data is that of Korosi and Fabuss,and

Kestin. An empirical correlation equation was developed which reproduces

the experimental data by l.~% over the temperature range 10 to IS0a C.

The equation is convenient for interpolation, and for machine calcula­

tions. Additional laboratory measurements on the viscosity of NaCl

solutions to 3S0°C are needed for statistical calculation to provide

the basis for recommended values to 3S0oC. Laboratory data are also

needed for pressures to 500 bars.

- 20 -

G. Acknowledgment

Thanks are given to the following for their review and comments:

James W. Mercer, u.s. Geological Survey, Reston, VA; Joseph Kestin,

Department of Engineering, Brown University, Providence, RI;

Y.S. Touloukian, CINDAS, Purdue University, West Lafayette, IN; and

R.L. Nuttall, Physical Chemistry Division, National Bureau of Standards,

Gaithersburg, MD.

u .;

- 21 -

G. References

1. A Recommended Program in Geothermal Chemistry, R.N .. Lyon and G.A. Kolstad, eds., Department of Energy, ~H - 1344, October 1974. Available from National Technical Information Service, Springfield, VA 22161.

2. International Critical Tables, MCGraw-Hill Book Co., Inc., NY 10036, vol. V, p. 15 (1929), E.W. Washburn, ed.

3. Second Report on Thermophysical Properties of Saline Water Systems, Fabuss, B.M., Korosi, A., Monsanto Research Corp., Everett, MA. Office of Saline Water Progress Report No. 249 (1968), Department of Interior. Available from U.S. Government Printing Office, Washington, DC 20402.

4. Korosi, A., Fabuss, B.M., "Viscosities of Binary Aqueous Solutions of NaCl, KCl, Na2S04, and MgS04 at Concentrations and Temperatures of Interest in Desalination Processes", J. Chern. Eng. Data, 13, 548- 552 (1968). -

5. Abe, Y., Grimes, C.F., Kestin, J., Khalifa, H.E., Sookiazian, H., Wakeham, W.A., liThe Effect of Pressure on the Viscosity of Aqueous NaCl Solutions in the Temperature Range 20-1S0°C", submitted for publication.

6. Goncalves, F .A., Kestin, J., "The Viscosity of NaCl and KCl Solutions in the Range 2S-50°C", Ber. Besunges (in press).

7. Kestin, J. Khalifa, H.E., Ro, S., Wakeham, W.A., "Preliminary Data on the Pressure Effect on the Viscosity of Sodium Chloride - Water Solutions in the Range 10-40°C", J. Chern Eng. Data, 22 (2), 207-214 (1977). -

8. Rowe, A.M., Jr., Chou, J.C.S., "Pressure-Volume-Temperature-Concentration Relation of Aqueous NaC1 Solutions", J. Chern. Eng. Data, IS, 61-66 (1970). -

9. Potter, R.W., II, Brown, D.L., "The Volumetric Properties of Aqueous Sodium Chloride Solutions from 0° to SOO°C at Pressures up to 2000 Bars Based on a Regression of the Available Literature Data", U.S. ' Geological Survey Bulletin l42l-C (1977).

10.

11.

12.

13.

14.

IS.

16.

17.

18.

19.

20.

21.

- 22 -

International Association for the Properties of Steam, Release on Dynamic Viscosity of Water Substances, Sept. 1975. See Mech. Eng., July 1976.

Hendricks, R.C., McClintok, R.B., Silvestri, G.J., "Revised Inter­national Representations for the Viscosity of Water" and Steam and New Representations for the Surface Tension of Water", Lewis Research Center, Cleveland, OH 44135. NASA TM X-73483, Technical Memorandum (1976) .

Thermophysical Properties of Matter, Vol. II, Viscosity, Touloukian, Y.S., Saxena, S.C., Hestermans, P., CINDAS, Purdue University, West Lafayette, IN 47906 (1970). Available from IFI/Plenum, New York.

Jones, G., Dole, M., liThe Viscosity of Aqueous Solutions of Strong Electrolytes with Special Reference to Barium Chloride," J. Am. Chern! Soc., 51, 2950-2964 (1929).

Falkenhagen, H., Vernon, E.L., Physik Z., 33, 140 (1932).

Suryanarayana, C. V., Venkatesan, V.K., liThe Viscosity of Concentrated Aqueous Solutions of Sodium Chloride," Trans. Fraraday Soc., 54 (11), 1709-1711 (1958). --

Matthews, C.S., Rossell, D.G., eds., Pressure Buildu~ and Flow Tests in Wells, MOnograph Volume 1, H.L. Doherty Series, ociety of Petroleum Engineers, Dallas, TX 75206, 1967.

MandaI, P .K., Seal, B.K., Basu, A.S. ,ilStructural Aspects of Ionic Viscosity B-Coefficients in Relation to Ion-Solvent Interaction in Aqueous Solution (1), Ii Z. Physik, Chern. N. F., ~, 295-307 (1973).

,2nd ed., John Wiley & Sons, Inc. ~~~~--~~=-~~~------~~.

Ezrokhi, L.L., 'Viscosity of Aqueous Solutions of the Individual Salts," J. Appl. Chern. USSR, .e., 917-926 (1952).

Postnikov, V.A., IiDensity and Viscosity of Some Saturated Aqueous Solutions," Russ. J. Phys. Chern., 44 (1), 129-130 (1970).

Jones, G., Christian, S.M., "The Viscosity of Aqueous Solutions of Electrolytes as a Function of the Concentration. V. Sodium Chloride," J. Am. Chern. Soc., 59, 484-486 (1937).

· ,

- 23 -

22. National Geothermal Information Resource, 'Viscosity Tables of Sodium Chloride Solutions", (Compilation), Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720.

23. Kestin, J., Khalifa, H.E., Appl. Sci. Res. 32, 483 (1976).

24. Lengyel, S., Tamas, J., Giber, J., Ho1derith, J., 'Vizes AlkaIi­Halogenid-Oldatok Viszkozitasanak Vizsgalata," Magyar Kemiai Foly, 70, 66-77 (1964).

25. Kaminsky, M., "Experimentelle Untersuchungen uber die Konzentrations und Temperaturabhangigkeit der Zehigkeit wassriger Losungen starker Elektrolyte. II. Mitteilung: NaCl-, Li2S04-, FeCIZ und CeC13-Losungen," Z. Phys. Chern. (Neue Folge), §..' 173-191l1956).

26. Chacravarti, A.S., Prasad, B., 'Viscosity of Electrolytic Mixtures in Dilute Solution," Trans. Faraday Soc., 36, 557-560 (1940).

27. Gaeta, F.S., "Low Shear, High Sensitivity Electromagnetic Viscometer," Rev. Sci. Instrum., 37(7), 844-849 (1966).

28. Drucker, C., 'Viscometric Studies of Chemical Equilibria," Ark. Kemi, Mineral Geol., 22A (21), 1-17 (1946).

29. Janz, G.J., Oliver, B.G., Lakshiminarayanan, G.R., Mayer, G.E., "Electrical Conductance, Diffusion, Viscosity, and Density of Sodium Nitrate, Sodium Perchlorate, and Sodium Thiocyanate in Concentrated Aqueous Solutions," J. Phys. Chern., 74 (6), 1285-1289 (1970). -

30. Nickels, L., Allmand, A.J., "The Electrical Conductivities and Viscosities at 25°C of Solutions of Potassium, Sodium, and Lithium Chlorides, in Water and in One-Tenth MOlar Hydrochloric Acid," J. Phys. Chern., 41, 861-872 (1937).

31. Ostroff, A.G., Snowden, Jr., B.S., Woessner, D.E., 'Viscosities of Protonated and Deuterated Water Solutions of Alkali Metal Chlorides," J. Phys. Chern., 73 (8), 2784-2785 (1969).

-24-

Figure 1. Viscosity of NaC1 solutions versus concentration using Eq 11.

Curve °c

A 0 B 10 C 20 D 30 E 40 F SO G 60 H 70 I 80 J 90 K 100 L 110 M 120 N 130 a 140 P ISO

UISCDSITY OF RQUEOUS NRCL SOLUTIONS

2.50C

2"OCC

'l. oc C

Q..

U

)-

t--I--! (f)

0 .SOQ

U (/)

I--! .:>

o ~ I J K L M N

.soo 'l. SOO 2.0eo 2.500 :J.DO:) :J.SOO 'LOCO ~.~oo 5,000

NRCL CONCENTRRTION,MOLRLITY

-26-

Figure 2. Viscosity of NaCl solutions versus temperature using Eq 11.

Curve Molalitl

A 0.5 B 1 C 2 D 3 E 4 F 5

u -27-

~ISCOSITY or qQUEOUS NRCL SOLUTIONS

/

"k. 1 tJ(l

CL U

.>-r-H

lIJ , t;,. e;.~ .. 0 LJ U'J H

=>

, b Cl" _,,_~_ ... <---_ . - .. _<____"'""-_---L~-"__ _ _<___-__4.,--c.__-.......... -___'_ _ ____< __ _<___-_<_-___<_----'

() .t:'. J." .. (" 'lO .. (' ,}O • C "''' " ,e; () • C' .. P . 0 :' V • 0 t: 0 • C ,', (I (' '!!H', (' 'L 1. I' ,(" '1'2",,, 'l:' C' • r ''&'''', (' ',&'; p • !'

-28-

Figure 3. Comparison calculated NaCl viscosity using Eq 11 with measured values. Deviation for all values is 1.5%.

-29-

2ea~)

(l.

U

)-

~ 1.'>% H (/)

0 U (f)

H => l.ilce

0 W -a ...J :J

c ',1)(; U ...J a u ,

/ :i..SO(; '1.500

MERSURED UISCDSITY,CP.

-30-

Figure 4. Deviation of Eq. 11 from data f~r NaCl concentration range D.DIm to saturation.

% Deviation = (measured) - (calculated) x 100 (measured)

I l

-:u-

?oer;

G.Doe

CDJ DOom

5.000

4.eec

'l.oee

1.000

o o o 0000 CIllO 00 000

D.CCC

0 0

0 CtJ

0 0

oomno

lID ctl 00 0 GIl

00 0

190 0

Cb 0 0

!flU :ii'll I am

o

~6.000 A4.DCO A'l.OOO AO.OOO -B.OOC -6.000 -4.000 -2.00C O.COO 2.000 ~.OOO G.oce £.000

-32-

Figure S. Deviation of Eq. 11 from data for temperature range 10°C to 150°C.

% Deviation = ~measured) - (calculated) x 100 (measured)

1.5C.0 o

1.JO.D

'I.'Zo.c

1.1.0.c

'I.0c.C

.90.0

BO.O

?o.o

GO.O

so.O

.30.0

'20.0

'10.0

;/ ."

000000 ~O~~t [J[[J ",iiIn IIID U [1 0 "" I

00000 00 00 ~ ocno J cu:tt LUllL 0 I c:r-cm a:::o 0

o 0 OCb 00 0 i 0

000 0000~ 0 CIIID I

I llllln)~ rnmoo

000 0 0 a

o Eb cPrD CD &E 011llThmJ oam

aJUJru I ~.= I tlIil~ om

o d;;; Ii18l1i1ltH

.. ~ .. L~_ ~CDO

011[; IiUIJ! ®!IIJ I1II1J[]!l OD

[Ill 0 O~.riimDo "enm emIl

': :=~t' I': rn o 0

[[JO ••

a a

o

o 0

C.o ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~6.00~ ~4.CCO ~2.00C ~o.cco -B.OOC -6.000 -4.000 -2.000 0.000 2.000 4.000 6.000 ~.OOO

-34-

Table 1. Experimental data on the viscosity of NaCl solutions used in this evaluation and for developing the correlation Eq 11. References to the literature are given as Short Code, which contains the last name of the first named author of each publication and the last two digits of the year of publication.

VISCOSITY OF NACL SOLUT NS

UNITS

TEMPE U = GR S aLSIUS CONCENTPATICN=MCLALITY PRESSUR9AR VISCOS Y= NfIPOI

Tf:: MPOl

lJ t\ (I

" c (I

13 iJ o o

1f ., C tl ~ 00

1(1 .. GO If .. Uy 10., DC

,,00 1C "ilt 1C" 00 1~ .. GIJ 12 "

"SO 12 .. St! 12 " 12 .. 12., 5C 12",5G 12 .. 50 l~ .. tO lS"t'I) 15"QO

"U(j 15 .. uC 15 dl il

" ao

CONC ..

.. ij~20ll0 "C.5:lJJ .. 0 UHHl J .. 02thl1Q .. 0 sao .. 100.150 .. 2"J59t:; .. 5, :3

1 .. 0 500 2 .. 0688 "l~986j~J .. 4-31'.1,CiQ .. 9865(;,)

i .. 993JOu 2,,929600 3 .. 486S0(J 3" 987' 3iJJ 5",495200 5 .. ~V2 C

.. (1 1uCj ",0,:)204:10 "ljl'5JCO ",(31i.)" 11;

fil020J20 .. 079:) ,,4 3\i4C .. $[47'30 ",I)J10Cu .. (I ,2,)O~

00GS(JOC .,C1J.H.,i ",(iZJi.> ' .. 2'JG860 .. 4" 317 ~

PRESS ..

1 .. 0 1 .. t' 1 .. 0 1,,0 l§C 1 .. 0 1 .. 0 1,,1J 1 .. 0 1,,( 1 "a:; 1<110 1 .. 0 1 .. '3 1 .. 0 1 .. 0 1,,1J 1 .. 0 l .. t) l .. iJ 1IDe 1 .. (; l .. C 1 .. (: l .. fJ 1 .. (: 1 .. 0 1 .. (: l"f 1 .. 13 1"e 1,,(' 1,,0 1",(;

1,,7'8 60 1 .. 181 I'i 1 .. 18&29ll 1 .. 789 lil1 110 1,,7'93830 1.. ;) 1" Hl 1" 614561l 2.,11 sao 1,,3 a 1.. 0 1 .. 398 tl 1.. 990!l 1",6 3ilil 1 .. 816 0 1 .. 93lHHHJ 2,,383300 2,,489 1) 1" S8lf) :1" 8960 1,,219380 1 .. 219950 1,,221010 1,,23111U

3'3 I)

1" 9280 1", 139 '+412 1 .. 139840 1 .. 14ll40,:) 1" 1,,157380 1 .. 174830

IONAL HER MAL INfORMATION RESOURCE

DECEM8F.R 191'7

S RT CODE

JONr::S JONES 31 JONES 37' JONfS 37 JONES 31 JON 37 JONES 37 JONES 31 JON 37 JONeS 37 LEN L Lf::NGYEl 64

GYEL 64 LENGYEL 64

NG l LENGYEL 64 L GYEl 64 L GY€l L GYEL 64 KAMINSKY KAMINSKY 56 KAMINSKY 56 KAMINSKY 56 KAMINSKY 56 KAMINSKY 56 KAMINSKY 56 KAMINSK'1 56 KA MIN S K \' S 6 KAMINSKY S6 KAM SKY 56 KAMINSKY S6 KAM INSK Y S6 KAMINSKY 56 KAMINSKY 56

-36-15 .. tu .. 5 49 1 .. (1 l.d8371J V 56 17 .. 99 4e13200J leO 11ll6319lHJ 18 .. 00 .. Oil 1 .. 0 1 .. ll 001l 18 .. 0t; '" UJ 36",2 1@O 60 18 .. 00 ., Oil .. 7 1 .. 086000 18 .. 0G thl 4 .. 8 1<00 00 18 .. 01; 139 .. 9 1 .. 08 00 18 .. !lC 157 .. 9 1@08401HI 18,dlC ao $ .. 1 1.dl83~HHl 18 .. 00 .. or; 206 .. 1 1@08 \)IJ 18 .. 00 @ 011 239 .. 9 1 .. 08'+090 18 .. 00 .. Cit) 26'+<04 1<.!>1l 13tH I 18 .. 00 O(J 302" 7 1'lOQ8 18 .. DQ OJ 1@C 1 .. 0 18 .. !:!) 'J J \l l .. { 1 .. 18 .. (-1 ,+ .. 132J()0 1 ,,( 1 .. 18,,01 '+ .. 2iJOC l@C 1 .. 18 .. 02 &t,,132(HH) 1 .. 4$ 1 .. 71 18 .. 05 '+ .. 132JOiJ 34 .. $ 1 .. 1800$ '+,,132000 2CS .. (l 1 .. 1~"O5 4 .. 1 ;:;ihJ S,,{1 1 .. 71 18 .. (;5 '+,,13 ~\ l' 243<)!: 1 .. <J'" 18,,06 4,,132lllJO 34 .. 5 1 .. 71 18<)06 4013 (F, 137.,9 1 .. 18,,(16 4<)13 i,J'1 137<)9 1 .. 18$06 'h132ilOO 112 .. 8 10 18/006 4/0132GOJ 112 .. 8 1$ 77 18 .. (J6 4,,1 ;J IHJ @C 1 .. 18 .. 06 4<)13200~ .. 1 111 71 lS®1J6 4 .. 132IJv~ ,,7 1 .. 77 18.,('6 4,,132;;;0(' 31:) 7 .. 8 1 .. 18,,06 4 .. 13200lJ 301 .. 8 1 .. 18 .. 07 4 .. 132lJ1,JU 69,,3 1 .. 18,.07 4,,1 :C;j 69 .. 3 18 .. 08 4 .. 1323QO 104@2 17 18 .. 08 4,,132vO\) 4,,2 17 18@1&t 2.,6 (,),.;01) l"t H!,.26 2 .. 6JOuu~ 173.,4 1'1 18 .. 2 6 l)JOJ 274,,(;: 1 .. 17 18.,46 2 .. 6 )Ct'!(; 2 .. r 1 .. 18tH) 18 .. 48 2, .. " \J.:.iO I.i 309,,9 1 .. 339800 71 18 .. 49 Z<)6!JGu~i.l 9.,9 1 .. 3 sail 77 11L, 2 .. 6 ()III)';; 172@7 1@ 2 \l 18 .. 2 .. OUO~ 6 .. 5 1<);)34300 HL.51 2 .. 6'QuUtJ 2®3 1® 4 I) 17 18 .. 52 2@6',!]!1(!,J 172 .. 7 10 1 f.l 18 .. 52 2 .. 6' (lJ;,) 2.,3 1", 6 0 17 18,,53 2 .. 6 GilOIJ 138<)9 1 .. 9300 77 18,,53 2@6,JOt.~ 138,,9 1€j331iHI() 77 18 .. 54 2,,6l~JOatl :10 31l~ 111:330 0 18,,54 2 ~ 6 "ltLhl j 2COt.,5 1 332 a 71 18<) 2,,6 !), \hJ 11; 3,,4 1 .. 326 0 18 .. 56 2,,6;;()jtlO 68<il9 1 .. 4 a 18.,56 2.,6 JIJIJ .. 68 .. 9 1 .. 70ilu 113,,67 2,,6 )J(U 34 .. 8 1 .. :3 I)

18969 2 .. 6SJOOe 34,,8 1 .. 2 tl 77 18 .. 72 2 .. 6;j~~v l .. Q 1 ... 0 0 18 .. 73 2 .. 6 J \,1~. \J leE 1 .. il610 19,,00 10 471.3lJ~ 35 .. '5 1 .. 164000 17B 19 .. CiC .i .. 471;3ti~ 66 .. 5 1,,1 0')0 19<illJlJ 1., 13~ J 4 .. 4 1 .. 16800C 718

"IHl 1 .. 4713JJ 138 .. 9 1,,1 (jlle

-37-

19 .. tlO 1 .. 47.L 30,J 174" 8 1", 19 .. 00 1 .. JOIl 201®9 1",1 19®CC 1 .. 130l:l 241<\\4 1",1 19 .. aW 1 .. 41131:0 212<\\3 l®i 19@CC 1 .. 13011 309<\\6 1<\\1 71B 19 .. f/I(; 1<\\471 -, 156<\\8 1 <Ill 1 I.i

19 .. f.lO 1 .. 13t,; , l.d': 1 .. 1 19 .. 00 1 .. 4 30l 1<\\0 1 .. 1 19<\\00 1 .. 4713JIJ 35 .. 5 1 19<\\l:tC 2,,551 ) 1,,(\ 19 \,,(10 2.,SS140l:l 36",5 19" (:Q 2 .. 5 ,J 14",1 1", 19"CO 2 .. 14(,~ 1,,2 19 .. 00 2@5;i140Q 143,,4 19,,(;0 2" :1 ~ 115,,4 1", 19,,(0 2" 1 J 2t! e" 5 1<\\ 19"IJO 2 .. 14Ju 233 .. 4 1", B 19 .. 00 2 .. 551400 2 <\\6 B 19.dH:l 2 .. 5S1,+n~ 3f 2 .. (:} B 19 .. $0 3 .. 2 0 1,,(; B 19 .. 5C 3,,2672ii~ 35 .. 5 718 19,,50 :3 .. '2 672:J~ "" 71B .. I

19 .. 50 3 .. 2 'ZOU 104<\\8 B 19 .. 51; 3 .. 261 J 139<\\1 1<\\ !j

191il5i,; 3 .. 267';;0" 113 .. 4 B 19 .. 50 3 .. 2612uG 2C 3", 6 B 19 .. 5(; 3 .. 2 2n~ 243",(i 1<\\ B 19/0 3,,2672~h! 278",(; 19<\\50 3,,267 0 312,,5 19 .. 50 3",2 20;; 154 .. 8 19 .. 51; 3 .. 2 2 rl('! 1 .. (

"iH) "O"386i.lJ l@O 2'; "C!,) " 4971i);J 1",0 21: '" il i: .. 986500 l"lj 2'J .. GV 1,,99 (l~ 1 .. {) 1 ..

",1](1 2" 9296tn; 1,,( 1@ 2« '" ct 3,,413 00 1"J 2C .. ~ (; J .. 9873Qj 1 .. t 64

"CC 5" 2(111 1 .. C .. 00 5,,8~2300 1 .. 0

2\l .. Cle 6,,14\lOJJ 1,,(' 7~ 22", 8(; 2 .. 6 JC\lj 1 .. 1" 1 .. 2.3 .. 00 2 .. 6~ yO 173<!>4 1 .. 23 .. tJ2 4,,13 JQ 1 .. (1 1 .. 23" (,,9 4 .. 1,32J,)J l .. t 23 .. 11 4 .. 1 GOl l .. L ~ ,., .. 23 .. 18 4,,132J(lQ 35,,4 1 .. 23 .. 2C '+ .. 132uJ'J 35 .. 4 1 .. 4 23 .. 24 2 " 1l0GO 245 .. 8 1",206 0 23 .. 24 2 .. 6 "i !) 0 J jJ 280" 2 1", 75\)0 23 .. 24 2@6 :J;p(;J 314 .. 7' 1,,2(7 G 23026 2 .. 6JOaaJ 209 .. 9 1 .. 2C44!lO 23 .. 26 2 .. G~Jj0 4 .. 7 1,,2115J~ 23@26 !it<\\13ZiJ,;1; 7(1 .. 9 23 .. 21 2 .. 600(1110 139,,6 17 23,,27 2,,6,tJJ~~ 174,,1 23027 4 .. 132dviJ 7P ,,9 Ij

23",28 2.,6J{JOOO lt3~7 0 23,,28 2.,6:irJ~J::; 245 .. 8 17 23 .. 28 2,,6 :J td;; C 28t; .. 2 1~ 17 2,~ .. 29 2 .. 60tlCOG 17'4~1 77 23 .. 29 2,,6~~'CHH: 209,,9

-38-23 $ 30 2>ll6,.JdOJ) 69$3 2311130 2 .. 6LliHHlll 139 .. 6 71 23" 2"G.iHlulJ 34 .. 8 23111 2 .. 6 .HHIOU lG 310 7 23" 2 .. 00 69 .. 3 110 23<il34 2 .. 00110 .. 8 1", Q 23",35 2,,6 JtiOO 1 @f, 1", 0 23@35 4@132000 104@1 1@ I) 23., 35 4 .. 13 JjJ 4",1 G 231136 2 .. 6 JthHi 1 " <iliJ 11 23,,41 4 .. 13Z!HHl 138",9 1", 0

.. 42 4 .. 13 OtJ 138 .. 9 1 .. 0

.. 48 4,,1 :$ 0 Ii 113"t+ 1. Il ,,48 4 .. 132ilOC 173 .. 4 1" 200

23 .. 51J " OJ 1"lj " IH~OC

23 " " 5 l,; 31+ .. 6 " noo 23 .. 50 @~75S00 "'0,,3 • 90\10 778

" 5(1 " 0,1 103 .. 4 @ 9tH)!,l .. !,li,; 139 .. 8 @ (;00 ,,50 00 174@2 .. 7(Jao

23 .. Ldl 4,,6 .. 6ClD 23 " CJ 241' ,,:3 .. (iU'G 23@50 CHi 274 .. 4 III 000

.. 50 '" au 7,,5 '" (1 /J 0 ,,5C .. ~5n\3 157,,2 & O~ 77B

23 .. 5(1 ,. 47 OJ 1",0 '" coa B .. 1+,,1321l0J 2{j 1,,:1. 1" 71

23,,53 4 .. 13 D iJ 2f1,,1 1", 23 .. 59 4,,1 ace 138 .. 8 1" 23,,59 4",13Z!JO~ 2,,3 1 .. 23 .. 59 4,,13 1,),,; 2 .. 3 1 .. 23 .. 62 4 .. 132000 1 .. (1 1", 17 23,,63 1+,,132J:lQ 275,,4 1", 23 .. 63 4,,132.if'C: 5 .. 4 1", 23 .. 61 4,,132JOO 31)9,,8 1 .. 23 .. 68 4,,132 til:: 309" 8 1& 23" ,,3 U ~i~ 0 :1 ,,(,

'" 23 .. 03JlJOOO l"ij '" 23 .. Be ,,3: (H1Ou 1 .. (; " 2t+" (HI 2" 5 . J;~ ilL :1 '" fj :1,,,

21+ ,.I111 2,,5,JIHltlJ l",u 1 .. 2t+,,(jCl 2,,5CJJU~ ;1,,0 1" 25 .. 00 '" 0" HlO:; 1 .. 0 " 50, 25"OU .,t 2,J(hl 1 .. !:;

012(, @ ~~l 2,; 1(: 1 .. L '" 56 .. 00 .. Q;:SOOJ 1 .. 0 "Ot ,,(;.,;502:1 1 .. C

25" CO .. 0 181+'j 1 "r, "Oil " iHlOD 1 .. 0 '" .. !It .. (,10\J3,j 1 .. 1J .. .. (Jr~ ,,('12 1 Ii ®, ® 9 elH:J ,,0159!HI 1,,0 ",892130 "uc .. G2ililt::J 1,,(

" 6 .. LIJ .. 020:;7.) 1 .. ( .. 59':

25 .. 00 ,,02J271l 1,,(; .. 892i+10 ,,00 .,£i5J~OC 1,,( .. 2"~ ,,(;{J >1>0 110 1 f~ @\c, t1>8 2 .. DC ,,£188803 1,,(; 0l898~10

25 .. (;0 @O'3350( l .. C " 87\)0 LENGYI;'L 2S" 14 r "t 99 ~t 1 .. ~' ,,69900'" K I b8 2S,,(JC "lJ IHHH) 1 .. (1 3!J1l JANZ 10

.,oe ,,1..UJ;;iw l"C 59 JONES 37

- , d U ; '3 i ~39-

e (; (i 1 .. (, @ 25.00 1.D 25$(141 106 <!>

25 .. CiJ • 1@0 0 2S00U 'ill l~C '" 25 .. DO (I :1 @

.. DC .. 4 4JJil 1",1i @ @OO .. 49 ao 1 .. 0 @

25 .. 130 "S:d)\JQO 1",C " @CIJ • 10W 9

25 .. 00 .. 1~' ~

25 .. 00 '" 1,,1} '" 25 .. 6(1 '" 1",{: ~

25.,00 .. 683900 1 .. 0 ~

25 .. 00 ,,7:6 J l .. lJ " 25,.(l~f "85382,, 1 .. tf .. 17

.. 00 .. 869301l 1@0 .. B 25 .. 00 .. 98 Ilu 1 .. ( " G

<l>Oii :i.d:J iI J n ,; l"d @ 25 .. (,0 1"O~OO!lO 1@0 @ 25 .. 0 IJ 1 .. C2J01)", 1 .. ( .. 25@CI{! 1 .. ('

,,1l1J 1<1> 1 .. 0 II

,,(it) 1 .. 1$iJ "iHi 1 .. fJ 1 ~~; 1 .. J2!liJihl

25 iii 00 1 .. 0 35 .. 0 1,,0190;)0 " at 1 .. 4 713!J (1 b9 .. 8 l .. iJl Oli

25 .. (; {\ 1" 4<1>4 1@021'1<30 25 ,"'HI 1 .. 138 .. 9 1110190ao

.. Oll 1 .. 173 .. 4 1",.'J2 00 "O~ 1 .. 2( 7 <I> 9 1 .. a 2H)(Hl ,,{)O 1 .. 241,,6 1~O23!l3!) .. au 1 .. .:} 276 .. 8 1 .. J23£10fJ " [Hi 311 .. 6 1~tl Dno ",on 156d~ L.l' 1000 "O~ 1,,4 ;J 1,,0 1,,02iJL:iOG .. H: 1 .. 5€H 1 .. t, 1,,:)18 "uo 1 .. "393.ilJD 1®O 1",iH'3 (I

'" 1313 2"Ci+3IJi,Ju 1",'J 1"il88ll00 ,,00 2,,(\89 wi :1 ~ 1,,08 {]

,,00 2 .. 1110000 1 .. C 1,,;) !!lOO " oe 2 .. 393:; 1,,1J 1,,134 0 "CiO 2 .. 551 L ." 1 0''' "" 1~13

25"QO 2 .. 140!J 36,,5 ,,00 2" 1 ~O;)

25,,(;0 2 .. :1 " ;,

25" 00 2" 1400 ()CHI

'" Ilt 2,,, 1 \j Oi)(1 25,,00 2 " :1 J 8 .. 15 1 .. 1 Clan

"co 2 .. 1 £) 242,,3 11l149(1)0 .. oc 2 .. 140;:; 276 .. 8 ou

25"t~ 2 ,,551-.iJi:; 310,,6 OG .. oc 2 .. 1:;aO;)Q :1 !l 1 .. ilJ \) 52 .. co 2 .. 9296(1) 1..G 1 .. 86\1Y 13 C' fl 3 .. L9392J 1,,0 11l 003U

25 .. 0 (! ],,2;JIlGJO 1",0 1tJJ 8!HHI " 1:10 3®2:,)i.;UC 1 "t( 1 .. 23!l~i)~

25 .. cr 3s2E:72uO 1 "l' 1,,24Hl(JO 2«; .. OC 3@2672UO 36,,2 1", (lilO 215,,(,0 3 .. 261.2(;\; 10 .. 1 1 .. 0(11)

25 .. IJL 3iJ)Z67Zt~ :' 1I':51l1 4 Il i) C 4 ..

25 .. 00 3,,267200 139116 1 .. 241000

-40-

"Uti ;) ,,(;0 J

25110C U .. 00 ~ .. 00 U

25 .. 00 Il 1 .. .,CO 1 .. 0 1$ " O(l illt 1 .. 1I0G 3 .. 1 .. 0 1 ..

25.,0(; 3 .. .31H.' 1.,(; 1 .. " 00 4 .. 3000JO 1 .. 0 1"

25 .. &0 4 .. 3 ute 1 .. 0 1 .. 25"tC 4 .. 4 ~JiHl ~ l .. C 1 ..

,,00 5 .. 2432 1 .. ( 1 .. .. Il (; 5 .. 38JJJnJ 1,,0 1 .. ,dHJ 5,,4g52(J;J 1,,( 1 .. " IJ

.. Ou S" 6(;, iHlJu 1 .. 1) 1$

.. GO 5,,6,;4yOJ 1 .. (; 1" .. co S • .!L23CJ 1,,(, ,,00 5 .. 8226 1 .. 00 6 .. 1 UGti l"L 1 ..

1"1,, 1 .. 35 .. 5 1"

" \j 1" @5U 4 .. 42890;:;

25,,$0 4 .. a90:1 25 .. 5& 4 .. 428~O'; 1 ..

.. 4 .. 89th" 1 .. 4,,42890,) 1" 4 .. S90J 1 .. 4" 8 '" 1 .. 5 1 .. 4 .. 890J 156,,2

" :',,{)

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27 .. 69 5 21 .. 50 1(;6.,5 21 .. 141,,1 1 ..

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.. 5 .. 614;J();] 70.,3 1" 13~Hl

.. 92 5 .. 614JtI'J .. 3 1 .. (10 ,,93 4,,1.321lIHi 33 .. 6 1 .. CElllll

27,,93 4 .. 132)41 1; 33 6 .1" lOt (, ,') U 77 ,,94 ~h132ij{j<J 1"r. 1 .. 9 I~

J

.. 4,,1 000 1 .. 0 1 .. 8 HIll 2f" .... 132:.HlJ 69,,8 1 .. ::J811,) 28,,(;(; '+ ,,132,1 t; i.' 6~" 8 1 .. 302 " ".}

Z8d)£) .. 479500 1 .. 0 .. 868000 28,,(;iJ Gl

" 35 .. 8 .. 1000 28,,(;(

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28dHl .. 479SlHi 2 01 '" 2 8 <i> IHi .. 4195ui) 5 .. 4 ~

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28 .. 0(1 ",47950;) 1",2 280C() @479SC;; 1 .. (' 28 .. 05 4h13200ij 104@O 28 .. 05 4 .. 13 OJ 4 .. 1.1 1 .. 28 .. u5 5 .. &14aUO 11:4 .. 9 1 .. 28 .. (;7 5 .. 401) ;J 1i:4®9 1 .. 28 .. 12 4,,1 OIlO 139 .. 6 1 .. 28,,13 5 .. 614JOI,I 139,,6 28 .. 14 'h13 11 ~; 139 .. 1)

28 .. 15 5 .. b141l(1) 139 .. 6 28 .. 16 5" 113 .. 4 23e21 $ .. O.i 173,,4 28" 5,,6.l,4000 113 .. 4 28 .. 26 5,,614JO;'; 4,,4 1 .. 28 .. 5 .. 611+J311 ,,+ .. 4 1 .. 28" 30 5 ,,6l,+lHHl 238&5 1& 28 .. 5" 4.) ();J 238 .. 5 1 .. 28&33 5 &614,i (),J 273&4 1& 28,,34 5,,614:;)00 3 .. ,. 1& 28 .. 35 5,,614JO[j 8 .. 5 1,,5 28 .. 36 5,. 614.) ,1 ~ 8 .. $ 77 28 .. 44 2 .. 6t!CJJOQ 1 .. 0 28,,45 4 .. 1320(1:;; 175 .. 7 28(048 '+,,1320L\lj 17507 28@52 20 6J £HHh) 1 .. (; 77 28 .. 53 2 .. tiJ);jQ~ 1 .. i: 11 28 .. 53 4 .. 132~d;'j 205 .. 1 28 .. 5'+ 2 .. 6uaOGC 112(01 26 .. '+,,13 rt "J L !,J 2(1!) .. 1 28@ 2 .. 6 Y~O:.i 35 .. 5 1 .. 0 28 .. 55 2 .. 6t:iilOuO 35 .. 5 28 .. 56 5 .. 614ItO:; 1 .. 0 28 .. 57 2 .. 6 tl rH1.1 69.,9 28 .. 51 2 .. 6CIlO(lC 69@9 26 .. 59 2 .. 61. illHhl 4 .. 4 77 28 .. 59 '+ .. 13 2 ,H);"l 2 .. 9 28 .. 6(; 2 .. 6ilaOOU Hl4 .. 4 11 28 .. 61 2 .. th OCH.i') 139 .. 2 28 .. 2(06:i,hlU,j 139 .. 2 28 .. 6'+ 2 .. 6;J;]OO!J 17'+(01 28,,65 2 .. 6~·O.ui)iJ ,,1 77 28,,66 2 .. 6 J CIO) 207 .. ! 28 .. 66 2" 6", J Qj) 0 ,,6 28,,67 2 .. 6:iHl~\1 7 .. 8 17 28 .. 67 2,,6 ~lJ()ij 21601 28@67 2,,6rJiliJO 310 .. 6 28 .. 68 2 .. 6,: ;l,);;,~ 241 .. f. 1(0 28 .. 68 4,,132Cl>,l 24iJ ,,9 77 28.69 2 .. aaou 276 ,d. 28,,7r! 2" 1ijUG 310 .. 6 28 .. 12 4,,132';:J; 1 .. (1 2a.,15 ,.,,1.52000 101@2 28 .. 7:" 4,,132~C);) 213 .. 0 1" 28@71 4 .. 13241)(' 5 .. 4 1 .. 29lJ 28 .. ~ .. 132YJ(j 3 .. 0 1 .. 29'+ 28 .. 82 4 .. 132JU:J 307 .. 1 1" gal!

-42-

28@83 4 .. 132",C .. i 3G 7 @1 1 .. ~ 30 .. 00 ®£iJ7dltO 1 .. 0 ",7':18 G

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"" 550

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.. Oil .. 5eS7.1.ttJ 1 .. 13 " .. ()i,; " 853821) :1. "Ii {;

3(; .. (,;u @98 O~ l .. fl " ll) "CO 1.(FJJ,HI 1,,0 .. 882800 589

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" 9000 .. ((; 1 .. 4 713(: i,l 1t 4,,4 @ IHHHl ",CO 1 .. 471300 138,,9 @ 9000

3( .. 0 il 1,,471 IJ 173 .. 4 ,,92300C 3'1 .. Cd;; 1 .. 4713.;1,:; 2(; 5 .. 1 ",923(\O~

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I\. -y " 3e7 .. l <Il

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-55-

148 .. 00 5@4;5~uJ 113,,9 " 20(10 KESTIN 718 148<;liC 5,,4. (lC 21L! '!l l+ 0ll3S .. 0l\j KE IN 148,,00 $ .. ~~OC 243",4 ",3 Gilll KESTIN 718 148,,00 5,,4~54Ql,. 211,,3 @ 356(1)(1 KESTIN 118 148etti 5"l+.S4~O 312" 7 III 35SCdHl KESTIN 148 .. 00 5 .. 4;,5 .. 00 161,,1 .. 2000 STIN 719 148" (' t 5,,4!540J 1",1 ill 3l+6((1!) KE 150 ",IHl ,,1 .. 2I,HHI bO ",18581HI K I 68 15t ,,(10 " 1Z17Jrl 1,,0 .. 20iJIl KOROSI 68 lSI' ,,(iQ 1" .. 1.t38v(J 1 .. 0 .. 22131) 0 KOROS! 6e 15u ,,00 3" 6\J 24a D 1,iI,} .. 285200 KOROS! 68 lS!. .. I:lC 2 .. 14(4.1 7 .. 9 .. 21.t90QO KESTIN :1 {let 20 14ut 35 .. 8 .. 25lHica STI~ 118 1 ,,00 2", 1400 59",b @251030 KES N 118 1510(!{J 2 .. 14'- :: lett.,l " 2511H1O KESTIN 778 1 Sl .. (; U 2"SSl"L;.; 138 .. 2 11 253UHi KtSTIN 118 1510 GO 2,,5S1 .. !)!) 174,,8 " call KESTIN 778 151@00 2 .. lttCiJ 2(; 6" 1 " (laO KESTIN 118 151 .. QO 2 .. 551ttc:J 239,,'3 (j~O KESTIN 151 .. 00 2 .. 551 .. 00 27:1" 3 ., 6000 KESTIN 1 .,lie 2" i .. ni;; 3£:5 .. 8 ., 000 KE STIN 151.,(ti 2" 551~~'~ 19 .. 3 .,249!:\(10 KE.STIN 152" 00 1,,~713;J3 3.,4 .. 2180']0 KESTI~ 152"Hi 1., 411 ~l)':' 35 .. 8 .,2191.iJO KESTIN 152 ,,(Iii 1. " 1 3l'1 ;: 1(;., 1 .. 219tHh1 KESTI~ 1 .,oc 1,,411303 lu8 .. 1 .. 2Z!JOIlO KE IN ;'52 .. 00 1 .. 4713\J~ 14{t .. 6 .. 100e KE IN 152" C C 1 .. 41130~ 112(03 " 20~'l KiSTIN 176 152 d)e 1,,411300 21103 ,,2231) 00 KE IN 8 152 .. CO 1" 1 JOG 2tt:3 .. 2 " 3000 KESTIN 7 152eLf! 1047130',' 21601 @ 50;10 KESTIN 118 1 S2 \lIHl 1,,4113UJ 1",6 0225000 KESTIN 119 152 .. 00 1 .. 4713tH! 159 .. 4 OJ 2000 KESTIN 9 152 \I CO 1,,4?'13GO 2C 102 @ 9000 KESTIN 8 15~" 00 30267200 8 01 .. 265000 I(ESTIN 178 1540Cr' 3 .. 2 ;:0 ~.) If) .. 3 .. Z65CHHl KESTIN 7' 154" ut 3 .. 2572;);1 24 .. 8 ®Z65UOO KESTIN 118 154" CC ,3 .. 26721.d 3~"S @Z66\lOO KESTIN 719 154@00 3 .. 2612{;;; 7001 .. 2611l01l KESTIN 119 1 Stt" t~{j ,3 .. 26120.] H,6 .. 2 {ll268C·~!j KESTIN 118 l~~,,(;O 302612CO 13906 ,,270Q~Q STIN 118 151.t"QO 3 .. 2672u,1 173 .. 8 ,,2 7 J)COG KESTIN 154" (311 3 .. 2 2') ,I

' " 208 .. 2 II 271 Cl ':'11) KE IN 8 154 €I 00 3 .. 2E.720iJ 242@3 .. Z12CQQ KESTIN 718 151+,,(}O 3,,2672(;3 21£: .. 5 @212000 KESTIN 8 154 \I 30 .3 \I 2 672.) J 312 .. 1 021 O~ K£STIN 718 1 ~4" 00 3 .. 2672\1"\ 161 .. 1 e2690!lO KESTIN 8

Iii NaCl '-- -. o ---....,

C 0

10 .. 0 ?O .. O 30 .. 0 40 .. 0 50 .. 0 60,,0 70..,0 FI 0" 0 90,,0

100 .. 0 110 .. 0 l20 .. 0 130 .. 0 140 .. 0 1')0,,0

-56-

Table 2. Smoothed values of the viscosity of NaCl solutions calculated from Eq 11.

Viscosity, cp

.. '5 1.0 C0J 3 .. 0 400 ".0

1 .. 853 1 .. 914 2 .. J&)P, 2 .. 234 2 .. 448 2 .. 701 l .. 373 1. 428 1 • 55 () 1 .. HZ l,,8C',I9 2 .. 11 g L,0'+9 L098 1 .. ?t2 1 .. :549 1.512 1. 699

.. 82"1 .. 871 .972 L,092 L23~ 1039L

.. 673 .. 71Z 0800 0~05 1.024 L 158

.. 564 .sqp .A75 .. 76';1 .. 866 .. 978 ,,484 " 513 o ~ FlO .. 6jl .. 7 /t3 .835 ,,4::' 3 .. 449 0507 0'512 .. 644 .719 " 371 .. 3Q9 .. 44() .. 504 .564 .626 .. 340 .. '359 .. It 01 0448 .. 498 .. 549 0310 .. 326 .. 362 .401 .. 4 /t3 • 1.1:11

.. 285 .. 2Qq .. 329 0363 .39q .439

.. 264 .. 276 .. 302 .. 331 .. 363 .402 0246 .. 256 .. 279 .. 305 ,,136 @ 176 .. 231 .. 240 0261 0285 .. 316 .361 " 2 11) .221 .246 .270 0304 • '357

-57-

APPENDIX

Dynamic viscosity of water substance from the Eighth International Conference on the Properties of Steam. Giens, France, September 1974, See Reference 11. Only a portion of the tables is reproduced here.

-58-

Part 2. Recommended Interpolating Equation

The values appearing in Table 1. may be reproduced within the stated tolerances by the USe of the formtua given below, wherein

where

II denotes the dynamic viscodty p denotes density 1,) T denotes absolute temperature on the 1968

Practical Temperature Scale T* and p* denote numerical constants .,hich arc

close to, hut do not represent the corresponding critical constants

a and b .. are numerical constonts. l< 1)

11 = 110 exp r~ ~"

5

I i=O

4

L j=O

b. , 1]

1.I 0 :::: (T -J 1/2 [3 --- 1'* L l1Pa s k=O

(T* J i (p ) f] T-- l pi'-l J'

(2 )

The constants appearing in the preceding equations have the numerical values given below and in Table a for

T* ::: GlI7.27 K } pR 317,763 kg/m 3 :::

(3)

a - 0,018 1583 a a

l ::: 0,017 7624 (4)

a ::: 0.010 5287 2

a - -0.003 6744 3

"'-*"-5 ~--- .. ----For preference and to reproduce the value:; given in Appendix D, the density should be computed with t.he aid of the 1%8 IFe Formulation for Scientific and General Use, If another density formulation is used, a relative departure of /l.p/p induce'; Jt Illost a r'cJ.at ive departure :f Lll1/tJ :: 2.5 6,p!p in viscosity,

i=

j::::O

1

:2

3

I~

!

-59-

Table a Numerical Values of the Coefficients b. j --- .1

0 1 2 3 4 ----~----------

0,501 938 0.162 888 -0.130 356 0,907 919 -0.551 119 0,146

0.235 622 0.789 393 0.673 665 1.207 552 0.OS7 0665 -0,084

-0. ?Ill 637 -0.743 539 -0.959 456 -0.687 343 -0.LI97 089 0.195

0.145 831 0.263 129 0.347 247 0.213 486 0.100 754 -0.032

-0.027 0448 -0.025 3093 -0.026 7758 -0.082 2904 0,060 2253 -0.020

The correlating equation presented in thi~ Appendix is v,,]jd in the range

in temperature, and

/ 3 o < p < 1050 kg m

in density. which corresponds to an approximate pressure range

o <: P <: 100 MPa

its domain of validity can be extended to

p = 1000 MPa in the range 0 <: T < 10Doe

p - 350 MPa in the range lOnoC < T < 560°C

5

543

3370

286

932

25%

The equation adopted in this Appendix is not the only possible interpolation formula, An alternative form 'vias giver~ in the paper, "Correlation of Viscosity for Water and Steam", by A. Nagashima, M. Ikeda anrl I. Tanishita, Proe. Eighth ICPS, Giens, France, 1974.

-60-

~endix D

Viscosity of Compressed Water and Superh~ated Steam

Viscosity in ~Pa s (= 10-6 kg/m s)

Pressure P in MPa

Temperature T in °c,

(Smoothed values obtained with the aid of eqs, 0) and (2) of Appendix C

together with the constants listed therein, and density values based on the

1968 IFC Formulation for Scientific and General lise),

PIT

0.1

0.5

1.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

20.0

22.5

25.0

27.5

30.0

35.0

ItO.O

4S.0

50.0

55.0

60.0

65.0

70.0

75.0

80.0

85.0

90.0

95.0

100.0

0.0

1792

1791

1790

1786

1780

1775

1769

1764

1759

1754

17119

1741+

1740

1735

1731

1722 .

1711+

1707

1700

1693

1687

1681

1676

1671

1667

1662

1659

1655

1652

25.0

890.7

890.6

890.5

890.2

889.7

889.3

888.8

888.4

888.0

887.7

887.4

887.1

886.8

886.6

886.:1

886.0

885.7

885.6

885.5

885.5

885.7

885. '1

886.2

886.6

887.1

887.7

888. 1)

889.1

889.9

-61-

APPLNDrx D

J}/namic Visc:osit'1 of Water' and ;;team

50.0

54 7.1

S47.1

547.'2

547.5

J') 7. J

')48.3

548.7

54'3.1

549.6

')SO.O

550.4

5:.0.9

551.4

:;51.8

552.3

553.3

55 l l.3

555.3

:,56.4

S57.5

558.6

~59.7

5(iO.9

562.1

563.3

:65.8

567.l

568.4

75.0

378.3

378 .. 4

378.6

378.9

379.6

380.2

380.8

381.5

382.1

382.7

183.:1

:Wli, 0

38 l1.6

385.3

:J8'j.4

38'1.'2

388.5

,13') . 8

391.1

392.4

393.7

395.0

396 .Ii

397.7

399.1

1,00.4

401.8

403.2

1104.6

100.0

12.28

282.3

282.4

282.8

283.5

284.2

284.8

285. ~

286.2

286.9

287.5

288.2

2fJ8.')

2tJ'L S

290.2

291.6

292. '.1

2"4. :;>

295.6

296.9

298.2

299.6

300.9

302.2

303.6

30 11.9

306.3

307.6

309.0

150.0

14.19

1 ill .9

J02.0

182.4

183.1

183.7

184. 11

185.0

185.7

1 fl6. 3

IB6.9

J.87.6

t88.2

188.8

189.5

)'lO.7

191. 9

1')3. :

194. 11

195.6

196.8

190.1

199.3

200.5

201.7

202.9

2011.1

205.2

206.4

200.0

16.18

If,.07

15.93

133.

134.5

1.35.1.

135.7

136. :I

137.0

137.6

138.2

138.8

13'J.4

140.0

140.S

1.'H.7

142.8

144.:.1

145.1

146.2

147.3

1',8.4

149.5

1.50.6

151..6

152.7

153.7

154.8

155.8

250.0

18.22

18.15

18.07

106.1

106.8

107.5

108. /

10 B. 9

109.S

110.2

110.8

111.1)

112.0

112.li

U3.8

115.0

116.1

117.2

118.3

11:1 .4

120.5

121.5

122.5

123.5

124.5

125.5

126.5

127 .4

. , "

This report was done with support from the United States Energy Re­search and Development Administration. Any conclusions or opinions expressed in this report represent solely those of the author(s) and not necessarily those of The Regents' of the University of California, the Lawrence Berkeley Laboratory or the United States Energy Research and Development Administration.

) . ·1 " f? to 1lOJ;~ 'f';-~~

f' ~ ''':"

f'1 0 tl ~ t, ~. f

(; ) "