Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory
Title VISCOSITY OF AQUEOUS SODIUM CHLORIDE SOLUTIONS FROM 0 - 150oC
Permalink https://escholarship.org/uc/item/3jp6n2bf
Author Ozbek, H.
Publication Date 1977-10-01
eScholarship.org Powered by the California Digital Library University of California Ii' . . ,i. /
Presented in Part at the American Chemical LBL-5931 Society 29th Southeast Regional Meeting, c" \ Tampa, PL, November 9 - 11, 1977.
C1 i".• _ HI.. ' "I g. -f' ('3
Ll{"jaAF?Y '(\ND t:)OCUlv'IENTS SECTION
.For Reference
Not to be taken from this room
Environment Division
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 Depart ment of Energy, nor any of their employees, nor any of their con tractors, 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, appa ratus, product or process disclosed, or represents that its use would not infringe privately owned rights. i I,)
Presented Part at the American Chemical Society LBL - 5931 29th Southeast Regional Meeting,' Tampa, December 1977 November 9-11, 1977
VISCOSITY OF AQUEOUS SODIUM CHLORIDE SOLUTIONS FRrn 0 - 150 0 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 - 6 -
from the computer files the National Geothermal Information Resource. additional and 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 (1) nr "" relative viscosity (n/nHzo) M "" molarity A,B "" constants
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 extrapola tion 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:
2 1 0,5649 x 10- :::: 0,23092 10- A0 "" BO x DO '" 0.25651 x 10 -4 2 -3 Al '" 0.2012 x 10 Bl 0.23206 x 10- Dl '" 0.39857 x 10 6 4 -5 Az '" 0,1200 X 10- BZ "" 0.22124 X 10- D2 '" 0.43024 x 10 9 7 -7 A3 :::: 0,4514 X 10- B3 ::::: 0.82313 X 10- D3 '" 0,15500 x 10
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 2 3
-1 j=O 1.6560 O.7221x10 O. 2460x1 0-:-.1 O.1448xlO -2
-1 -2 2 -4 1 -O.4304xlO 0.1275.10 -O.1294xlO- -0. 2994xlO
-3 -8 2 O.5769xlO -O.5876xlO-4 O.282lx10-4 O.9443xlO
3 -O.3l94xlO -5 O.5550xlO- 6 -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:
~ (P,T,c) = ~O(T,c) [1 + a (T,c) P] (7) where
~ = 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. 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 c '" 0.1256735 l a1 =-0,04296718 C L Z65347 =:: z '" a2 0,3710073 c =-1.105369 3 a3 ;:: 0.4230889 c ::= 0,2044679 4 a4 =-0.3259828 c5 '" 1. 308779 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 IS0 a 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). - 22 - 10. International Association for the Properties of Steam, Release on Dynamic Viscosity of Water Substances, Sept. 1975. See Mech. Eng., July 1976. 11. Hendricks, R.C., McClintok, R.B., Silvestri, G.J., "Revised Inter national 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) . 12. 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. 13. 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). 14. Falkenhagen, H., Vernon, E.L., Physik Z., 33, 140 (1932). IS. Suryanarayana, C. V., Venkatesan, V.K., liThe Viscosity of Concentrated Aqueous Solutions of Sodium Chloride," Trans. Fraraday Soc., 54 (11), 1709-1711 (1958). -- 16. 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. 17. 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). 18. ,2nd ed., John Wiley &Sons, Inc. ~~~~--~~=-~~~------~~. 19. Ezrokhi, L.L., 'Viscosity of Aqueous Solutions of the Individual Salts," J. Appl. Chern. USSR, .e., 917-926 (1952). 20. Postnikov, V.A., IiDensity and Viscosity of Some Saturated Aqueous Solutions," Russ. J. Phys. Chern., 44 (1), 129-130 (1970). 21. 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 AlkaIi Halogenid-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) .SOQ 0 U (/) I--! .:> I J K L M N o ~ .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; 0 00 0 0 0 19 0 G.Doe 0 CtJ Cb 0 0 CDJ DOom !flU :ii'll I am 0 0 5.000 oomno 4.eec lID ctl 00 0 o GIl 'l.oee 1.000 o o o 0000 CIllO 00 000 D.CCC ~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 000000 ~O~~t [J[[J ",iiIn IIID U [1 0 "" I 00000 00 00 ~ ocno 1.JO.D cu:tt LUllL 0 JI c:r-cm a:::o 0 o 0 OCb 00 0 i 0 'I.'Zo.c 000 0000~ 0 CIIID I I llllln)~ rnmoo 1.1.0.c 000 0 0 a 'I.0c.C o Eb cPrD CD &E 011llThmJ oam aJUJru I ~.= .90.0 ItlIil~ om BO.O od;;; Ii18l1i1ltH ?o.o .. ~.. L~_ ~CDO GO.O 011[; IiUIJ! ®!IIJ I1II1J[]!l OD [Ill 0 O~.riimDo "enm emIl so.O ': :=~t' I': rn o 0 [[JO •• .30.0 '20.0 o '10.0 a a 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. IONAL HER MAL INfORMATION RESOURCE DECEM8F.R 191'7 VISCOSITY OF NACL SOLUT NS UNITS TEMPE U = GR S aLSIUS CONCENTPATICN=MCLALITY PRESSUR9AR VISCOS Y= NfIPOI Tf:: MPOl CONC .. PRESS .. S RT CODE lJ .. ij~20ll0 1 .. 0 1,,7'8 60 JONr::S t\ "C.5:lJJ 1 .. t' 1 .. 181 I'i JONES 31 (I .. 0 UHHl J 1 .. 0 1 .. 18&29ll JONES 37' .. 02thl1Q 1,,0 1 .. 789 JONfS 37 "c .. 0 sao l§C lil1 110 JONES 31 (I .. 100.150 1 .. 0 1,,7'93830 JON 37 13 .. 2"J59t:; 1 .. 0 1.. ;) JONES 37 iJ .. 5, :3 1,,1J 1" Hl JONES 31 o 1 .. 0 500 1 .. 0 1" 614561l JON 37 o 2 .. 0688 1,,( 2.,11 sao JONeS 37 1f ., C tl "l~986j~J 1 "a:; 1,,3 a LEN L ~ 00 .. 4-31'.1,CiQ 1<110 1.. 0 Lf::NGYEl 64 1(1 .. GO .. 9865(;,) 1 .. 0 1 .. 398 tl GYEL 64 If .. Uy i .. 993JOu 1 .. '3 1.. 990!l LENGYEL 64 10., DC 2,,929600 1 .. 0 1",6 3ilil NG l ,,00 3 .. 486S0(J 1 .. 0 1 .. 816 0 LENGYEL 64 1C "ilt 3" 987' 3iJJ 1,,1J 1 .. 93lHHHJ L GYEl 64 1C" 00 5",495200 1 .. 0 2,,383300 L GY€l 1~ .. GIJ 5 .. ~V2 C l .. t) 2,,489 1) L GYEL 64 12 " .. (1 1uCj l .. iJ 1" S8lf) KAMINSKY "SO ",0,:)204:10 1IDe :1" 8960 KAMINSKY 56 12 .. St! "ljl'5JCO 1 .. (; 1,,219380 KAMINSKY 56 12 " ",(31i.)" 11; l .. C 1 .. 219950 KAMINSKY 56 12 .. fil020J20 1 .. (: 1,,221010 KAMINSKY 56 12., 5C .. 079:) l .. fJ 1,,23111U KAMINSKY 56 12",5G ,,4 3\i4C 1 .. (: 3'3 KAMINSKY 56 12 .. 50 .. $[47'30 1 .. 0 I) KAMINSK'1 56 l~ .. tO ",I)J10Cu 1 .. (: 1" 9280 KA MIN S K\' S 6 lS"t'I) .. (I ,2,)O~ l"f 1", 139 '+412 KAMINSKY S6 15"QO 00GS(JOC 1 .. 13 1 .. 139840 KAM SKY 56 "U(j .,C1J.H.,i 1"e 1 .. 14ll40,:) KAMINSKY S6 15 .. uC ",(iZJi.> ' 1,,(' 1" KAM INSK Y S6 15 dl il .. 2'JG860 1,,0 1,,157380 KAMINSKY 56 " ao .. 4" 317 ~ 1",(; 1 .. 174830 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 13tHI 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 ~\ l' 18 .. (;5 '+,,13 e (; (i 1 .. (, @ 25.00 1.D 25$(141 106 25 .. CiJ • 1@0 0 2S00U 'ill l~C 25 .. DO (I :1 '"@ .. DC .. 4 4JJil 1",1i @ @OO .. 49 ao 1 .. 0 @ 25 .. 130 "S:d)\JQO 1",C " @CIJ • 10W 9 25 .. 00 .. 1~' ~ 1,,1} 25 .. 00 '" 25 .. 6(1 1",{: '" '" ~ 25.,00 .. 683900 1 .. 0 ~ 25 .. 00 ,,7:6 J l .. lJ " 25,.(l~f "85382,, 1 .. tf .. 17 .. 00 .. 869301l 1@0 .. B 25 .. 00 .. 98 Ilu 1 .. ( " G "Uti ;) ,,(;0 J 25110C U .. 00 ~ .. 00 U 25 .. 00 Il 1 .. .,CO 1 .. 0 1$ " 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 :',,{) " " 1 .. (1 .. so J 9 .. 3 " 34 .. 8 27 .. 69 5 21 .. 50 1(;6.,5 21 .. 141,,1 1 .. 5 .. 4'5 \.1 176 .. !." 1 .. 51> 209 .. 6 1 .. .. iJ 246 .. 1 1" " i! 2781>2 1 .. 27 .. 50 0 .. 9 1® '" 6,,2 1 .. 21", 5,,4, r " l .. v 1® 11S .. 86 5 .. 614!JOU 1 .. (') 1 .. .. 86 5 .. 614iHH: 33 .. 4 1 .. " 5,,6 Ill) 33 .. 4 1 .. C;'r97!)U 27" 87 5,,61.~OiJlJ 100 l'l1 2tHl .. 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 I~ ,,94 ~h132ij{j 28@00 0479500 209 .. 9 ~ 28dHl .. 479SlHi 2 01 '" 2 8 IHi .. 4195ui) 5 .. 4 ~ 28 .. 00 .. 4795i:ill 106 28@83 4 .. 132",C ..i 3G 7 @1 1 .. ~ 30 .. 00 ®£iJ7dltO 1 .. 0 ",7':18 G .. Ot) 1",(: .. C128 '" 891Q ",00 .. L1598'; 10(: II 220 .. 00 .. C2il 1 .. 0 550 eDC "" 1""t "" 2 n 30 .. 00 1 .. 0 !!HHHI 3;} " C! iJ " 1 .. (, ~ 30 "U i! ,,230 1 ,,( @ 10 30 .. 00 .. 49710:) 1@0 @ Il .. 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 3~ ,,(1 (i 1 .. 471:h':\J 1,,0 .. 918(1)0 30"ilC 1 .. 47131,)0 34,,8 ,,919000 3;;; ,,04) 71),,( 1 .. 4113JJ " 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~ .. 00 1,,471300 238 .. 9 .. &iillO 3~",YO 1 .. 471 iJ 273",0 (joe "I'~ . '" 3( .. i,;C 104 I\. -y " 3e7 .. l 31 .. (\(1 vI 139.,6 d"O 3 .. 2 174 .. 8 ;31 .. UO 3 .. Z 8 .. 2 310 DU 3@2 \J 2 .. 10 31 @OO 3 .. 2 215.9 31 .. 013 3 .. 2 311 .. 3 31 .. (iD 3 .. 2 1 02 31 .. 00 3 .. 2 1.e 34 .. 15 5 .. 614001) 1" fJ 1 .. 3't38 5 .. 6 1,) 113 .. 1+ 1 .. 34" 1+2 5"b:'~OJO 36 .. 5 1 .. 34" 1+3 5 .. 614!J!J;; 36 .. 5 1 .. 34" 5 .. :'1J1,j~~ 1t .. 1 34 .. 45 5 .. 6141J0J .. 7 3 .... 45 506141.1::;,4 138 .. 2 {i .. .itS 5<1 .. 000 138,,2 3.. ,,46 5,,61 .. Jl1i: 1 .. r; 3i.t,,46 5" 61i+1Hlt 1f15 .. 1 34" 5<16140Jil 1,,0 34 .. 41 S .. b14~C.; 4 .. 1 34 .. 48 5 .. 6 ",0::; 1(15,,1 34 .. 48 5 .. 6:131>\)00 114 .. 1 34 .. 49 5 .. 6!1+'(jIJ; 2(1 .. 2 1 .. 34,,5t 5 .. 614;,1(;" 1 .. 34 .. 50 5 .. 614000 ,,6 1 .. 34 .. 5 .. 6141Hh, '5 .. 4 4 i -'i!'-' , 3*" 5" , 1 ~ 241,,6 I) 3.... 51 5 .. OOIl 275 .. 4 34 .. 51 5 .. 6i4JOJ 1 .. 3 11 34 .. 53 5,,10 OiJ 311 .. 3 KESTIN 71 35 .. 00 €I IHl1 Oil 0 leO KAt'! SKY 35 .. CO "Ilu 2u!hj 1,,(1 KAMINSKY 56 35 .. l~ • C' 5J 1@C KAMI KY 56 .. CO oOlilOilO 1,,0 A AVA I "QU ,,(il;)U5J l"li M NSKY 56 35 .. ('(; ,,(\2i)~0.J l"t A AV I 35dHI ,,020120 1@0 ~6 35 .. fHi ,,~3I)jHHi 1 .. t: I 3S,,(iG ,,( (1 iJ ;j l .. C .. ACRAVA I ",DO iii " JOIl:) 1 .. C A AVARTI 3S .. tO .. CGQOY,,~ 1 .. 0 .. A All I "He. "cr 1\1(; 0 1." r, .. 72566lJ A A I .00 ,,2:1920 l"lj ",1 KAMIN KY 56 35 .. iJ" .,4 528.1 1,,(' .. 9090 MINSKY 56 35 .. ((\ ,,5 5j lot .. 6377 KAMINSK'I 56 35,,00 l®D::JllGQO 1 .. 0 '" SGOQ RY ARAY 5 35 .. 00 1 .. lJJO" 100 .. 3 0 SURV ARA 5e9 \l J I,);j .~'" 2 .. (;: 1 .. Li '" 53;)C S YANAF 350r~ 4.428 ;1 156 .. 2 1,,.1, il jJ 35 .. 0(1 i.h 8913:; ,1,,0 1,,166000 35,,01) 4,,5;'~HHHj 1,,(1 .1 0)6 586 35 .. 1)0 5 .d) ll{!t;n 1,,0 1@2 o{Hi 586 35 " 4 .. 4289C~ 1,,;; 1@1 (Hl " 4 .. 42 890tJ 35 .. 3 1,,1 (HHl 35\1150 4 .. 89JO 10 .. 0 1,,1 000 35 .. 50 4 .. 890,) 1 .. 3 1 .. 1 COil 35 .. 4 .. 428'3aQ 139,,6 1 III 1!:: enH)!l 35 .. 50 4,,428900 113,,7 000 .. 50 4,,428~OJ 2(l 2 .. 9 ooa .. " .. 4289~G 2 .. 1 01)0 35 .. 5£ 4,; 8 0 217' .. 3 0110 35" 4 .. 8 a 3:07",1 30;)~ 35 .. 50 4 .. 8900 157 .. 2 000 4., 428'3IH} 1 .. ':' coa " t 35 .. 4,,428 .J :1 ",t; 1 .. 1 uJ3 35 .. 51 4 .. 1 0011 l",G 1" 11500!) .. 51 4,,132~OC 1 .. <11 6(1) .. 53 4,,13 13l, 1 .. (;) 35,,56 4,,132000 1 .. (; 35,,56 ",,132~il,1 34,,7 1 .. 35 .. 56 ,+.132JilJ 34",7 1@ T I) 35.58 lh132000 l®O 1 .. 1 7ilG 77 3~,,~9 4 .. 13 C'.! 101 .. 5 1 .. 1217\Hl 35 .. 4 .. 132JOJ 7;1.,(; 1 .. 11710{l .,60 4 .. 132000 70.,( 1@ 1'SOO 35 .. E>C 4 .. 132tiJli 70,,(l 1 .. 831)1.) 35 .. 4 .. 132~H)J if; 3,,8 1 .. C 35 .. 63 i+ .. ! OiHi 1C3,,8 1 .. 1189QO .. 64 4,,1320UO 138 .. 3 1 .. Il Q 35" 4 .. 13 ~¥ ~ 138@3 :1@ 12 as,) JJ 35 .. 4@1 UOO 201: .. 6 1 .. 5600 77 3$ .. 66 4 .. 1320Jl] 2,,3 1 .. 1225Q(l 77 .. 66 4" 13 2tHH! 1 .. 2 (l 35 .. &8 It .. 1320CHI .. 3 1 .. &600 35,,69 4,,132iJll~~ 211:>@(1 1 .. 126(\00 35.69 4,,132~;id.~ 2t:5,"(~ 1@ 61:10 35 .. 69 4,,132iluu ,,3 1@ 77 ,,711 4 .. 1321)Jl1 27 4hZ 30" 35 .. 4 .. 13 J 1) 274 .. 2 77 35,. 4,,1 Jilt) 4@lt 77 .. 70 4,,132UOiJ 6 .. 5 .. 89 2,,6' ,) t1D J 1@( .. 96 2" IH1O~ 1,,0 @ 36 .. [j6 2 .. Oi.HICl 35,,3 36"Ci8 2 .. 6 . .1:1(..) (1 35",3 36,,11 2 .. 6~ 00 1 .. 71 36" 2 .. 6 ooca 7J .. L,. .. 923 36019 2,,6 '~l\Hl:J 7f~ ,,4 36 .. 24 2 .. 6,,0000 104",4 36,,24 2 .. 6,JJOO 174 .. 1 '" 77 36,,25 2.6i,JI:';)(l 1f: 4 "L,. .. 36,,26 2 " l)UOO 139 .. 2 .. 36 .. 27 2., lOOt] 139,,2 J€h36 2@6.:'0000 ~C5.1 .. 8100 36 .. 36 2 .. 6::JilllOi:; 27 .... 7 .. 66013 36 .. 38 2,,6~CJC 27~ ~O"OO 1IJ1l1719G 1<110 A tJ \,p 1 .... @ 54GQ 588 ~O" DO 1 .. 993CC~ 1 .. 0 .80! 0 4r; .. OC 2 .. t1)J..iOJ 1 .. 0 .. 58B ,; (l {I 2 .. 35546,j 1,,(: " 8319 40 " IlG 2 " aDO;) 1 .. 0 ,,842200 5 4,'" ,,1:'0 2 .. il.! 11 \1 1"O .. 868CIJ Q 4;- .. to 2" 92 963 il 1@i: .. SB6 tl 40 4C @50 047954iO 1,.1) @679000 KESTIN 11B 4~; @SO 1. .. 4 30;) 1 .. <: €I it!;j J KE IN , .. 5G 1 .. 471 ;j 34 .. 8 .. 153G1)~ KESTIN 11B 41: @50 1 .. 4713Gu 70 .. C @1530 il 0 KESTIN 178 L!.I: .. 5(; 1 .. 471JOIJ 4 .. 4 .. 30JO KE IN 4t e 50 1@ 3{! U 138@6 @ no STIH 40 $ 5iJ 10) JOu 173 .. 4 III 755000 KESTIN .. 5(J 1 .. 4713eu (@2 .. 000 IN "\ 4: $ 50 1 .. 471 ;....1 241 .. 6 .. 1'570IlG IN 1 .. 4 lOy 4(1 " 276@5 " 0110 KE IN 4C .. SO 1@4113(') 31~ .. 6 1Il760000 STIN 4!: ,,50 1 .. 47130;) 157@2 @ U(H KESTIN 71'B 40 '1>50 1@47130i) 1 .. 0 .. 1)(;00 KESTIN 4P "sa 1,,4713J\; 1 .. i.i-, .. 80tH} KE, IN 4·'; @57 5 .. 6i"'{Hhl 1 @8 :1<.211+ !J KESTIN 77 ... IJ ,,68 5 .. 61400':; 1 .. t" 1 .. 8610 KE.STIN 4:w ,,68 5,,614+uOIi 104", 1" 7C 0 rJ KES N 4C ,,68 5 .. 61400 0 308 .. 5 1 .. 2 Q KESTIN .. 08 5 .. 4(;OJ 308 .. 5 1 .. 00 KESTIN 4' .. 69 5 .. bl,+lI,'uw i .. 4 .. 1.. 1 .. n S N 4( .. 10 5,,614+000 36 0 3 1 .. l)4JO KESTIN 4" .. 7U 5 .. oOC 138 .. 2 1@ 9 v KE IN 4''. " S .. 614;:;~V 241",6 10; 8 U KESTIN ... J .. 1(1 5 .. 614uCiO 241,,6 1 .. 9J~O KEST!N 71 4;) .. 71 5,,614~OIJ i"t 1 .. 1i:l6C100 KESTIN 4,; .. 71 5 .. 614,j~ 1t: .. i 1 .. Z;':15G,J KESTIN 40 .. 71 5 .. 614000 36,,3 1 .. 2020QO KESTIN 4'J .. 71 5 .. 614(!j II 70 .. 1 1 .. 2 U I<£ST11\ 17 40 <}) 11 S",614di)(] 138 .. 2 1 .. 2lrl69f3f; KESTIN 17 4+0 <}) 5,,014JJJ 206 .. 5 1 .. GO IN 4,,; .. 11 5 .. 6j"4 O.J ... 276 .. 8 1 .. Z () KESTIN 41' @11 S .. *,140U~ 276,,8 1", 3(dlO K!:.STIN 4(l " 5,,61 ... 000 1'73 .. 4 1111212500 KESTIN 17 4t" 12 5 .. 6~4uOJ 2(: *' .. 5 1 .. 5201) KESTIN 4t ,,73 5 .. 6!4:lJY 173 .. 4 1 .. 14:)(; K£STIN 77 41" tu') 2,,551 I) 1.,C OJO KESTIN 41 .. au 2., l~~h, 36 .. 2 ilG KESTIN 178 41..,00 2@5S1"'0G 7i .. t iJOe KE IN 'tl .. O(l 2 .. 351 ... 0iJ 105,,8 @8 000 KE IN 778 41@C() 2"S51-.CD 142,,7 .,84UOQ;J KESTIN 8 41 .. (C 2,,5S1LjOi~ 2 .. 7 .. 8431;30 51IN B 41,,(;0 2,,5:;1400 209.,2 ,,848000 KES"IN 718 41 .. 00 2.,551 ;,. 24') ,,6 .. 845iHIJ KESTI~ 7 41 .. t)1.I 2,,5S1'tC,0 267,,1 ,,844C11 IN 778 41 .. CO 2. l1.+JD 30803 .. O!)O IN 778 41 .. CC 2 .. 55140':1 157 .. 5 .. 84+0 (j ~ 0 KESTIN 17B 41 "t( 2@5S14'.1J 1"r: 0;8J4GOi) STIN 778 42" 5 (; "O~lIHIQ 1,,0 .,623643 KAMINSKY 56 .. SCI .. {' ,; 1J 1 "I; .. :3 780 KAMINSKY 56 42., 5t "t 5 iJ 3·) 1 .. ,~ III KAMINSKV 56 ,,50 .. 0100aJ 1@0 .. 4 ~ MINSKY 56 42.,50 .. 02:1 lJ i®t .. 5289 KAMINSKY 56 42" 5;j 02 2.i+8,; 1 .. f .. 637821 KAMINSKY 56 42 .. 50 .. ~:6460 1,,0 @6S1300 KAMINSKY 56 42 " 51) ,,59J-t~ 1"r .. ByTe KAMINSKY 56 "...... 5" 't ' J,] 1 .. (j 1 .. u920)1'l KESTIN B "'1+ .. 5G 5 ,,4~ uv 35 .. 0 1,,::191.+000 STtN ...... 5 .. ~' 5 .. 01 11@2 1" J 990 \1;l Kt: IN ~4 .. 5C 5 .. 4 ., He ,,3 1 .. ~ 99 1) '1 ") KESTIN "'~ .. 50 5 ""..":$1.+ 0 (l 142@4+ 1111(5000 KESTIN 77B 44" SO 5 .. 4 :l~ 1.76 .. 5 1 .. 1IJ 1C 0; STIN B l;4,,~;: 5 .. 4 S.i+C ;j 208 .. ,1 1,,111~i)!1 KESTIN , , L.i.h SO S,,4.5LtliJ 24,3,,9 44@ 5 .. '*" 218",6 .. 5~ 5,,4 0 313 .. (' 441il 5",4;; J 113,,9 ~4 .. 50 5 .. 4" ~ 1,,( .. QU 1,,1J ')/&(;:) 1 .. ( ,,00 1 @ 5,1 () C 45" OU 2,dJ IhhU 1 .. ( ,,(10 2@S~()OOO 1,,6 45 .. (iC J",CLJ,iiC:) 1 .. (1 lOtH) 3 .. 5'hd:D 1,,\:' ,,00 4" (hhhH)0 1,,0 ,,00 4" 8 (l 1.,(' <1J(u 4@ 8 ;,' 34 .. 8 4S" 00 4,,~28'10:l 12",0 .. CLJ 4" 8 .j 10!:L.1 4S .. ~l ,*,,4289,lC 141.,(" 45 .. 00 "+,, 890!) 17~,,2 ,,00 4 .. 428 lJ 8.,9 45 .. CL Iv" 8 g~ ~i 242 .. ( ,,(HI 4" 8 oJ 274,,2 4S .. GO ,+" aSH)!} 2.,3 45"iIf: 4,,428 '" 159 6 .. 00 4®428900 1 .. 0 .. (;u ,+" 8Shbll 1 .. {; 45 .. r'L 4"sa~c~; 1 .. f 5 4! ,,00 5 .. 0,lJJU;J 1,,;:' sse 5° Ii! !A~, 1" 50 .. 0C .O~3 10 1®O ,,172 J 1"C "t(; ,,558 ~3~: 1. ~r' ,,{;O 1" 0(01) 1,,0 ~ .. iJa 1 .. 139 7<2 1 f 1@5 J~IGn 1 .. !; Sf" OC 2,dhil co l"y !'l< .. ("l,i 2::5 OJ 1. ~; '"C'; .. c, 588 ,,{lO 300~J((;iHHl 1",0 5 3" C:iJ~1 5 BS "CI.! 3@81' 9"! 1 .. t! 5G" DG 4 ,.€J" (! ac a 1.0 5813 .. oc 4 .. 1",[ 58B 5\, "C(: 5" (; \) ,dh} 1 .. ( 58B ,,00 IS" 2 0 1.,0 .. (;0 1"i) "Cit) 1 C @oo 35,,7 54 .. () IJ 7'1l 1 H:46 54@ Ot 1£+1 .. 0 S4 .. Ql; " (; 11'4,,8 5'h r;:, ,,41550 ~ 2(: 7'" 9 S4 " CD ,,47 J Sit .. ( ~ ,,4;"550:; 27 ,,1 54" (c. ,,4755,\1:, 312.,4 " () I:i ,,4,15SiJO 158,,9 "ill! 1,,471 iJ L.:l @ L !. 1,,4113J~ 34 .. 8 ,,00 1,,4713tJO 1C,,(j .. {It 1" 1~.J 104.,4 1"4713,,,,' 139,,3 1,,4 13Jil 174,,1 -48- Sit .. /j C 1 .. 1 3t: Y 1",1 ..6Z::SC,)(j 54 .. 0 Ci 1047130) 24302 0 501)1} 540130 1 .. 4713iHl 21601 0 10110 ;' 54 .. OC 10411 " 311 .. 3 ,,6C:1!lIHl 54,d.iC 10 3C J 158,,4 III 3eOn 54 .. Ou 1111471 () 1,,0 1Il600(J~£1 S5,,(10 1 .. " !: !) IHLl l .. C JO 588 .. lJij 1 .. 5,' II 0 J (l 1 .. 0 .. 5891 (J I) SSB .. CO 2.,(LIlOOO 1. .,el ., Z 0 SS8 55 .. 0t 2"S J (l J ~J 1 ,,( .. 9 4l SS8 55,,00 :3 " tHJlHl 0 i) 1 .. 0 OGO 5 .,01) 3.,2 ij 1.,0 " 30tH; "OC 3 .. 26120J 1.,(; .. oa ,,0(1 3,,2612CO 4,,5 " 3000 55 .. (lLi 3.,Z6721)[J 1~.,1 .. Selle 55 .. 0C :3 .. 2 672;L~ 32.,9 ., JOO!) "to 3,,261200 69,,6 0126000 718 55" 00 3 .. 2 2i;1( 4 .. 1 .. 8(lJ a .. ij (i 3 .. 2E7 "\.! 139,,3 9(1')0 .. 00 3,,2 200 173 .. 4 .. 1000 .,Ct 3 .. 2672;)., 2(' 7" 9 .. 3GOtl 55 ~dJ(, 3 .. 2612~i.! 1 .. 4- 01I13200C 55 .. tJ C 3 .. 267~1J~ 216 .. 8 011136000 .. ot 3 .. 2 Z(JC u,,6 ,,73900(1 55 .. ul 3.,26720(; 159,,6 .,i'3/)OiJ,') ,,00 3 .. 2 (J 1 .. 0 .. 725 t: !l 0 5S .. UO 3 .. 5~OJ~w 1"1,, .. 73~8tHI 589 "fit 4 .. t: i) 'HI .j 1,,{j " Z 0 589 55 .. tHi 4,,5'JiJJJ 1,,( " 81 ijU 589 "'O~ 5 " (J ") ,; '):j 1 .. 0 .. 869 0 5 S6 .. 11C 4,,428 £) 1.,0 ill 8COO 56 .. (,0 4 .. 42S u 36.,3 .. 8171HHl .. r.c It '" 42 89lHi 711,,1 >;; 8210 (H) STH' Sb"OO &'h4289Cl(l Hi 6,,5 00 KESTIN 5f)"CCi 4 .. 8geJ 141" () 00 STIN ,,(I (, 'h 42890" 114,,8 " STIN sOu 4,,428~OO 2C 1.,9 .. KE IN 5f)"GC 4 .. 42 8 u 241,,6 .. 828000 STIN S6,,{:it 4 .. 42890 I) 11) 276,,8 " KESTIN 56 I> tHl 4 .. 428900 0 .. 6 ",!B4000 KE IN .. nc 4 .. 42 8 sw\. 158 .. 6 >;; 3250(10 IN ~6 .. (';(, 4,,4Z890Q l"iJ .. 814(0) N 60., (HI ,,099900 1,,0 I) I 66 6[ .,,, 0 " .. 7:690J 1 .. (' " 0 I 68 61. @co :1 ®L 94"dl,~ l .. C 00 KHI 6G" 00 1,,413800 1 .. il IiJ 00 OSI 68 6 " 0 (l 2 .. 5S14C} 2,,1 "GiSQQa IN B 6(.; 0 u~ 2,,5514j{(J 31,,2 .. 619GOO KESTIN 60 ,,(10 2",551 G 7C.,7 .. 10110 KESTIN .. co 2 .. 5S!-.J; 1(4 .. 4 .. ceilO KESTIN 6..: "t~ 2" 1 iJ 141,,1 JO IN Ell> " CO 2,,551 11 174 .. 4 ".. 3000 STIN €If: '" CO 2,,551 'I"': 206 .. U 400(J KESTIN 6' " '" (.C 2 .. 5S1':'J.j 239 .. 6 " KESTIN 6t:l" 00 2 .. l .... 6, o f.' 0 5,,~ Slot C .~: 33@3 GJ fj 5"Lt'S4+CJ 72,,6 (1)0 €In" 00 " 61.>" 00 54";;,.f;,,, 105 .. 1 .. 10aQ 6'\ "or. 5,,4 :h) 131,,2 .. 8621300 60" co 5"itl: IHI 1 "S Ii> ZOllO .. 00 5 .. 4·.; (lJ 21::J1i>8 .. fiijiJ 6~ .. 4) Ci 54:;)'tD.j 2311115 .. (lon ,,(JO 5 .. 4w OJ 2141i>1 .. 9llJO 6~ ., I)(j 5 .. 4~34+Jw 313,,9 Ii) !)\)O I,j 6i .. (' 5,,4. 0(1 156,,( (il LOO E:Q"DO 5,,4'; IHI l"C Ii) 51100 6C III co 6,,150')C'; l"d~ >!> 6000 6. ,,0 tl 6 .. 3:dJO~ 1,,0 " Qtli) 0 69,,011 ~v 1,,,(l >!> 43 (Hd3 !l 118 69,,(\12 " so l: 36,,2 ",4 :11 69 .. 00 "it :JuG 11,,0 .. 43Z(JIJO 69"ro "~7SS,,,2 it: Lt" 8 " 1+33000 69,,0(' ,,~75S~h 139 .. 8 .. 4.35rro 69 .. 0(; ,,41ssca 115,,1 1/)4 000 69 .. 0(; " 201,,9 .. 434,,)00 69 "t(· HI) 241"t, ,,439!JOO 69"iHl 3,,2 .. 438000 .~' 69"OG ., 1; I) 3119,,1 .. 44HlJll 6g"UL ,,47'55!:)!; 152 .. 7 " 43&(;()(1 69 .. (!O .. I) 'J 1,,0 .. 4290HI 77B 7t .. i:ti 1,. 13~,j 16 .. 2 ,,47fH)~G 11B .,1,'1,; 1 .. Lt713tlL 36,,2 OJ ., .. OC 1 .. 471 \J 7/),,0 OIlO .. (,G 1 .. 13JiJ 1e 3" 8 DuO ;- lice 1 .. 13~1 J 131,.4 OJD 10 ,,0 C 1 .. 1 114,,8 Oi)O 1;: ,,01.: 1" :1. ;; 1,,7 .." 4810110 ( ,~ " " '~. :1." 4113:):1 242 .. (; 04 [' lO .. O#J 1 .. 4713JJiJ 21'5 .. 9 114 000 1l; .. OC 1 .. 47'13;),,; 31f! .. 6 .. 4 .) I) N 1 o (. f\\,. 1" 4 713:; 'I 15£: .. 5 ,,4 KES HJ 7!J "CJ 0 1 " 30.; 1106 ,,4 000 ST!N " (1(,; 3 .. 2 2lJU 1,,9 .. 841HJil S I~ " C(1 3 .. 267znc 7 .. 9 ,,5 OJ KE. ST!N .. 00 3,,2ETZOiJ 9,,0 ,,5 000 TIN 7 "DC .3 2 zen 21 .. 1 ,,5 000 STIN 1ie "Oli 3,,2 " 2109 05 {gCHJ SlIN 70,. no 3 .. 2672&0 35 .. 1 .. $ 86dHJ 0 STIt-; "co 3 .. 261' ;J .. 4 "S88GOt Kt:STIN 1, "t;ji.l 3 .. 267 n 11;4,,3 KE It-J 10 "GO 3,,261~()C 13<;},,6 I(E IN 3,,2 1t" tt i.i 113 .. 4 '" STIN 7:' "il (; 3 .. 2 2en 8,,2 KES IN .. 00 3,,261200 242,,3 STIN 7:J " IJ (i 3,,2 20", 216,,8 STIN 3,,267 ~"t 3H,,,8 "co '" " . i)c:O'J srlN "GO 3,,2 20~ 158,,2 ,,5 IJiJO KE IN {} CO 3,,2 2C ,) 12 .. 4 ",586(;1)0 KESTIN B 1fj " (d" fh 43J "(;,, 1,,[ " 8 fJ -ill: STNII(CV 10 ,,1)1:1 4" 428900 7,,9 .. 6fSlOIHl K[STlt-< 7 71" Ct, 4.,Lt28 2(;)0 il 34 .. 8 " KESTIN "C( 4,,4289:'~1 10,,( .. 3{;,~H! S IN 11" (; C 4 .. 42890J 104"E; I+OJO STIt\ 7'78 11,,(W 4,,428 13<;}.,6 " 6(1;)0 .. " KlSTlt-J 8 11"LO 4. 8 '3t~ , 175,,1 " !l C J i' Ki:':STI~l B 71,,00 4,,42B'30~ 207,,9 ,,6110()O KE:STIN 8 710utl 243,,~ .. "42830,,, '" 1000 K£STIN B -50- 7101H 4 .. 42 89t ,; 2711$1$ $ 0·10 Rf S1! N B 71,,00 4 .. 428'3QI) 311 .. 1 .. liGu Ki:.STIN 11'9 71",C( 4" 42 89\1:1 157",S SO 1 .. 4713UO H14 .. 6 .. 9000 KESTIN 78 .. 1 .. JJij 139,,& .. 429(,0(\ KESTIN 78 .. SI;; 104:'13(h 173 .. 4 e 10iJiJ STIN 78 .. 50 1 .. 130) 207 .. 9 .. 43JOJIJ KESTIN 78 .. 50 1,,,4713f1C 242 .. 2 .. .. 33 C, \) 0 IN 78 .. S0 1 .. 471301, 275~6 .. 433(\0(; STIN 78@SO 1",4713(lJ 311",3 .. ~3(1)(HI KESTIN 78",50 1 .. 47130,', 156 .. 2 <11 11100 STIN 76 .. 50 1 .. 4113J;.; l .. C ",426\100 KE IN 15 .. 5G 1 .. 4713IJJ l<11Q '" 428~ l 0 KESTlt\ 8,' "ill) 2" S51~i1 ') 1,," " CGil KE IN 8~j "uO '" l~ijJ 36 .. 2 .. OlO KESTI~ 8,} .. 00 ""2,,5!3 .:J 71<113 .. tOG KE IN Be" ct.:. 2 .. ;i51Ltill' HS,,5 ",479i,!i)r: KE. IN 8G "co 2." 5S1-+ihl 141 .. 0 .. 4 ClO KESTIN 8'~ ,,00 2" 5314(ilJ 113 .. 4 ",481~OC KESTIN 8,' '" OiU 2 .. SS14(L 2(' f" 5 64 (Oil KESTIN B 8:J ,,00 2 .. 5~1 .. 00 239,,6 ",483COO Kt:: IN B S:! .. IJ!l 2" 5?14~:.i 274 .. 7 ,.tfJ 4. 89l1~ 28(;,,9 @ JllilO KESTIN 7 '97,. 00 4. d ~u lJ 159,,4 ",,495000 KE.STII\ 778 ,.Ilt 4. a9aJ lJ,,8 ",,488COC KESTIN B 98 " 1.4713,jJ .. C 1)C; KE IN 8 98,.5(1 1.4713u\J 34,,'; ,,341J~OO KCST!N 17B 98 .. 5", l~L 67,,9 ,,341~OO STIN 13 98 .. 5l .J .i.c 3" 8 ® 3()(,)iJ STIN 77B 98", 50 1. C 14C" :3 @ 000 STIN 778 9/3,,50 1,,4713~F 11S@S ,,31+4{i ~ J IN 7 98" 5t 1.47'13"i 2( 6 .. 8 .. t ,1 iJ S IN 98" SO 1.4"131.:0) 242.9 .. tnt STIN 9~,,50 1,,471~JJ 276,,8 J4,~OJC srI" 71~ 98 eSC 1,,<4'l'13uj 31f®9 {) iJ n KE IN 8 98@~!J 1.l;,7';UeJ 185®1 tlJC K STU; B -52- 9B .. 511 .1 .. .1 3~ J 12 .. 2 " ·tHHI 98 .. 5D 3 .. 2672IH) 7 .. 7' .. ~21 00 Q :\ 98 ,,5u 3 .. 2 " 9 .. 3 .. 00 98 .,5~ 3 .. 267 \;> 22 .. 1.1 0') 98 <1>50 3 .. 267200 3S@1 "it220!)Q" 98 .. 3,,2&120i,; 70 .. 1 " llG 98" SCi 3 .. 261201J 1'=~ 101,,00 2 .. 6 .. 5 ;) 000 1(,1;)IHJ 5,,4. 13 .. 8 " ~OOi) 1~1 .. tl 5,,4 :3 35*5 liL+ .. GIJ 4 .. a90e 30"@ 8 @ 114"QU 4 .. 428 J 157 .. 9 ,,4191H't; 114@CC 4 .. 8 d 11".~. $ t' @4j.3CQJ 1 @OO 1 .. 4 300 8 .. 3 .. 2 GJO 1. "IJO 1 .. 471 35 .. 8 .. 211HH) \1 1. "CO 68 .. 8 .. 2 tll1 :1. " Oil 1 .. 1C4"L+ @2 000 B 1. .. GO 1 .. 4 U 138 .. 2 ,,281000 77B 1. 2~ 0 (i (, 1. .. 4713f;~: 114,,4 .. 28ZHlJ 778 1 ,,00 1 .. 411300 207,," 10283000 ? 1 .. (jO 241.,6 1" 1 J " 400(: 11B 12L .. 41 C 1" 130 ') 274101 @Z8S.:.u'1 5T N 120 @ CC 1 @ 47 1 ,3 () i) 1,,6 @286 CO KESTIN a 1 "e!) 1 .. 13J" 15310(; ",2~2c,aJ A :2; IOC!J 11O~+"13ilO 8,,3 @Z71JDO KEST N 121" Q.;J 2 .. 5S14';\J 306,,5 " .HHHI KE IN ...'" " t\~ 2 .. 5514DG 1f ,,7 .. 313tJIHl KLSTIN 2,,5;1 121 .. 00 0 6 .. S " QOO KE IN 12110('111 2 .. 5S1L+tJ;'; 36,,2 3150Q'"1 121,,(:(: 2 .. l~iJJ 68 .. 9 I0315l0C 121 .. CeJ Z .. 5Sl40fl 103 .. 8 10 :3 0;)0 178 lZ~"OO 2 .. 5!; 1 kil'1 ':, 139,,6 ,,3170l)£1 8 121" He 2" 51 ~(~'J 112 .. 1 77B 121 @ 00 2 .. 5514iHI 2C 5,,4 " 121"O~ 2 .. 14.(;;(1 238 .. 2 @ Q 8 121 .. t)" 2 .. 55.1.41 272 .. 1 a 1 .. 00 .. 1:JJ900 1,,0 68 1 "IJC (@1~i+~OJ 1.,r' .. I 68 1 @eo 1,0 890" 1,,1.' 68 1 1000 3.56860il 1 10 (; @ 68 18,,{I('; ,,~:'550J 1,,,C 779 126" Ul • 5 SJ~; 9,,3 ,,2 1 126,,13:) ,,415fJlAlJ 35@1 .. 2 7' 126" 01: .. 4 7 f', I) 87 2 ,,23 126.ClJ .. 4755,)(;"'''' 135,,5 102 11",0:\ 126,dHl .. 5500 HIS"l @2380;)O 126,,00 55(,.t: 1JI]0 " 2521O~ " 126,,(;C .. 4""'SS4",J 3~ 9,.6 ,,2420')0 126 .. 00 00 165,,1 IOZ'!8cao 126,,00 " 15 .. 5 " 4!;O(1 129,,1;0 ... 11.,4 I0361(on 129,,00 4.42890;) 33,,8 " :~ DUO 1 "l,}", 4,,428900 1 i1 "f' ,,3 ry H1 129"IH' .It" 42 8 g;) w 1£5,,1 ,,3 fJ:~ 129,,00 4.42d90J 140,,8 0366caa B 129,,00 4"4289.,,.; 174 .. 1 .. 369CJ~ STIt-. 71B 129 .. Cl~ 4" 42 age " 2[ 7' 10 2 ., .56'3;;'0 fl K(STIN 9 129,,0(; 4" 8130;) 1,,6 @37'OOOO N B 12ge1H· ,+" 89\)0 215,,9 .. :H,~ OJ S'rIN 17B 129,,(r 4 .. 42 390 ,j 3(,:3" 1 ,,3 (i ,) :J KE IN a -54- 129 @ CO 4@42890iJ 161~4 @368(;(JO 129 .. (C 4 .. 42890 J 16 .. ? .. 364\l!);J 131.d;(i 5 .. 4 54Ji; 15 .. 5 1!l3 ~: U 0 131 .. Dt 5 .. 4;:5400 34<1>8 ~3q60QO 131 .. (I!) 5,,4'540'J 69,,3 1!l3 \l!J1,) 131 @L C 5 .. 4 S<+C'J 1(15 .. 8 ",3 ao 719 1 .. 00 5@4(5~Qij 13<:1<.9 .. 3990IJil 131 .. 0(, 5,,4:54Ju 114 .. 4 .. 399iJOJ .1 .. (I (j 5 .. 4 l+uG 1 .. 9 -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" CC 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 ,,27 J)COG KESTIN 2') ,I 154" (311 3 .. 2 ' " 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 -56- Table 2. Smoothed values of the viscosity of NaCl solutions calculated from Eq 11. Viscosity, cp Iii NaCl .. '5 1.0 C0J 3 .. 0 400 ".0 '--o -. ---...., C 0 1 .. 853 1 .. 914 2 .. J&)P, 2 .. 234 2 .. 448 2 .. 701 10 .. 0 l .. 373 1. 428 1 • 55 () 1 .. HZ l,,8C',I9 2 .. 11 g ?O .. O L,0'+9 L098 1 .. ?t2 1 .. :549 1.512 1. 699 30 .. 0 .. 82"1 .. 871 .972 L,092 L23~ 1039L 40 .. 0 .. 673 .. 71Z 0800 0~05 1.024 L 158 50 .. 0 .. 564 .sqp .A75 .. 76';1 .. 866 .. 978 60,,0 ,,484 " 513 o ~ FlO .. 6jl .. 7 /t3 .835 70..,0 ,,4::' 3 .. 449 0507 0'512 .. 644 .719 FI 0" 0 " 371 .. 3Q9 .. 44() .. 504 .564 .626 90,,0 .. 340 .. '359 .. It 01 0448 .. 498 .. 549 100 .. 0 0310 .. 326 .. 362 .401 .. 4 /t3 • 1.1:11 110 .. 0 .. 285 .. 2Qq .. 329 0363 .39q .439 l20 .. 0 .. 264 .. 276 .. 302 .. 331 .. 363 .402 130 .. 0 0246 .. 256 .. 279 .. 305 ,,136 @ 176 140 .. 0 .. 231 .. 240 0261 0285 .. 316 .361 1')0,,0 " 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 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) 5 4 b. , T* Ji (p ) f] 11 = 110 exp r~ I L (T-- l pi'-l ~" i=O j=O 1] J' where 1.I 0 :::: -J --- (T1'* 1/2 [3L (2 ) l1Pa s k=O The constants appearing in the preceding equations have the numerical values given below and in Table a for ::: GlI7.27 K T* (3) 3 pR ::: 317,763 kg/m } a 0,018 1583 a - a ::: 0,017 7624 l (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, ! -59- Table a Numerical Values of the Coefficients b. j --- .1 i= 0 1 2 3 4 5 ----~------j::::O 0,501 938 0.162 888 -0.130 356 0,907 919 -0.551 119 0,146 543 1 0.235 622 0.789 393 0.673 665 1.207 552 0.OS7 0665 -0,084 3370 :2 -0. ?Ill 637 -0.743 539 -0.959 456 -0.687 343 -0.LI97 089 0.195 286 3 0.145 831 0.263 129 0.347 247 0.213 486 0.100 754 -0.032 932 I~ -0.027 0448 -0.025 3093 -0.026 7758 -0.082 2904 0,060 2253 -0.020 25% 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 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 6 Viscosity in ~Pa s (= 10- 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), -61- APPLNDrx D J}/namic Visc:osit'1 of Water' and ;;team PIT 0.0 25.0 50.0 75.0 100.0 150.0 200.0 250.0 0.1 1792 890.7 54 7.1 378.3 12.28 14.19 16.18 18.22 0.5 1791 890.6 S47.1 378 .. 4 282.3 1 ill .9 If,.07 18.15 1.0 1790 890.5 547.'2 378.6 282.4 J02.0 15.93 18.07 2.5 1786 890.2 547.5 378.9 282.8 182.4 133. 5.0 1780 889.7 J') 7. J 379.6 283.5 183.1 134.5 106.1 7.5 1775 889.3 ')48.3 380.2 284.2 183.7 1.35.1. 106.8 10.0 1769 888.8 548.7 380.8 284.8 184. 11 135.7 107.5 12.5 1764 888.4 54'3.1 381.5 285. ~ 185.0 136. :I 108. / 15.0 1759 888.0 549.6 382.1 286.2 185.7 137.0 10 B. 9 17.5 1754 887.7 ')SO.O 382.7 286.9 1 fl6. 3 137.6 109.S 20.0 17119 887.4 550.4 183.:1 287.5 IB6.9 138.2 110.2 22.5 1741+ 887.1 5:.0.9 :Wli, 0 288.2 J.87.6 138.8 110.8 25.0 1740 886.8 551.4 38 l1.6 2fJ8.') t88.2 13'J.4 111.1) 27.5 1735 886.6 :;51.8 385.3 2tJ'L S 188.8 140.0 112.0 30.0 1731 886.:1 552.3 :J8'j.4 290.2 189.5 140.S 112.li 35.0 1722 . 886.0 553.3 38'1.'2 291.6 )'lO.7 1.'H.7 U3.8 ItO.O 1711+ 885.7 55 l l.3 388.5 292. '.1 191. 9 142.8 115.0 4S.0 1707 885.6 555.3 ,13') . 8 2"4. :;> 1')3. : 144.:.1 116.1 50.0 1700 885.5 :,56.4 391.1 295.6 194. 11 145.1 117.2 55.0 1693 885.5 S57.5 392.4 296.9 195.6 146.2 118.3 60.0 1687 885.7 558.6 393.7 298.2 196.8 147.3 11:1 .4 65.0 1681 885. '1 ~59.7 395.0 299.6 190.1 1',8.4 120.5 70.0 1676 886.2 5(iO.9 396 .Ii 300.9 199.3 149.5 121.5 75.0 1671 886.6 562.1 397.7 302.2 200.5 1.50.6 122.5 80.0 1667 887.1 563.3 399.1 303.6 201.7 151..6 123.5 85.0 1662 887.7 1,00.4 30 11.9 202.9 152.7 124.5 90.0 1659 888. 1) :65.8 401.8 306.3 20 11.1 153.7 125.5 95.0 1655 889.1 567.l 403.2 307.6 205.2 154.8 126.5 100.0 1652 889.9 568.4 1104.6 309.0 206.4 155.8 127 .4 This report was done with support from the United States Energy Re search 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 " (; ) " " to 1lOJ;~ 'f';-~~ f'1 ~ t, f? f' ~ ~. f 0 tl ''':"