Physical properties of sea water solutions: viscosity

Dcsatirrrrtion- Etsevier Publishing ampany,

PHYSICAL

(Raxivcd

PROPERTIES

Now&et

Amsterdam - Printed in The Netherlands

OF SEA WATER SOLUTIONS:

VISCOSlTY

25. 1971)

The viscosity of sea water solutions has been measured in the temperature range 20 to 180°C for salinities up to 150 g/kg. In the range 20 to 75°C measurements were made by master viscometer. and above 75°C by a pressurized falling

body viscometer.. An equation is given which fits the new measurements combined with other data to give viscosity values with an estimated accuracy of + 1%.

New measurements of the viscosity of sea water solutions are desrribed, in the temperature range 20 to f8U”C and in the sahnity range 0 to 150 g/kg. These new data are expected to be of significant vahre when desalination plant is required to operate at temperatures above the present limit of about t2WC. At! measurements were made on synthetic sea water soWions which contained no scale forming components; the measurements below 75°C were made in a suspended level master viscomctcr. and those above 75°C in a pressurised falling body viscometer. 2.

PUBLISUEV

OATA

The most important viscosity measurements of sea water are those of Fabuss and Korosi (1). These ‘Here made in the temperatu~ range 25 to 150°C for salinities up to 110 g/kg using a pressurised master viscometer and are estimated to be accurate to ~fi O.2!?& The measurements were made relative to the viscosity of water at 2O’C. Data are reported by Dorsey (2) from early measurements by Krummel (3) using U-tube viseometers in the temperature range 0 to 30°C ior salinities up to 40 e/kg. The measurements were made relative to the viscosity of water at 0°C and are estimated to be accurate to about 3_ 0.5%. Miyake and Koirumi (4) investigated a similar temperature and salinity range, also using U-tubes, with an estimated accuracy of rk: 0.25%. In this case the measurements were relative to water at the same temperature. The measurements of Ponizovskii

320

J. D.

ISDALE,

C. M. SPENCE

AND

1. S. TUDHOPE

also relative to water at the same temperature, and were made on soIutions of salinity up to 170g/kg at IO,20 and 30°C. These investigators (3.4.5) used solutions obtained from natural sea water in contrast to the present NEi.. measurements and those of Fabuss which were made on synthetic solutions. tv u/_

3.

(5)

were

EXPERIMENTAL

PROCEDURE

Wow 75°C measurements were made using a suspended level master viscometer, with measuring :.ecciop 400 mm long and 0.45 mm bore. The viscometet was immersed in a water bath and its temperature nept constant towithin _tO.OtC”. The vatues of kinematic viscosity obtained in this way we= converted to dynamic viscosity usins density values from reference (6). At temperatures above 75 “C viscosity was measured in a fafling body viscometer. In this type of viscometer the liquid to be measured is sealed in a cytindrical tube mounted verticaIIy. A cylindricaf sinker is allowed to fail down the axis of the tube and its terminal velocity is measured. The viscometer tube is iftustrated in Fig. I.

LOAEINC

ASSEMBLY

VlSCONETER

ASSEMBLY

Fig. I. Falling body viscometer and loading anangement. The tube and sinker used for the measurements were machined from titanium t6 take advantage of its exceptional corrosion resistance to sea water, and a PTFE bellows at one end allowed for expansion of the test liquid. The sealed vi-meter tube was enclosed

in a pressure

vessel,

through

which

a pressurized,

temperature

controlled liquid was circulated. The pressure of the circulating liquid was transmitted to the test liquid by the bellows, and this pressure was maintained at one

atmosphere

above the vapour pmsure

of the specimen for all measurements. Desaiination. 10 (1972) 319-328

PHYSICAL PROPERTIES OF SEA WATER SOLUTXMS:

YiSCOSlN

321

Before each series of measurements the viscometer tube was dismantled and soaked in a 0.1 N solution of potassium hydroxide in isopropanol far fifteenminutes. Each part was then rinsed several

times in filtered distilled

water and assembled.

Solutions to be loaded into the viscometerwere first deaewted by vigorousagitation under vacuum in the loading attachment vessel shown in Fig. 1. This procedure has previously been shown to produce no significant change in salinity (6). The assembled tube was then evacuated to dryness and the deaerated solution was allowed to run through the OSpm filter into it. The transfer was compteted by &owing a little air into the loading vessel. This method of loading removed sufficient air front solution to prevent formation of bubbles at high temperature. Temperature was measured by thermocouples attached to the outside of the vixometer tube, and was manually controlled by adjusting the electrical heaters. The thermocouples were calibrated over the full temperature range against a standard platinum resistance thermometer, The design of the sinker was chosen so that the forces acting on it produced a self-centering action, and, provided the tube was accurately vertical, the sinker aiways travelted down the tube axis (7). The terminal velocity of the sinker was measured by timing its fall over a fixed length, Embedded in the sinker was a smalt ferrite core which activated the timing device by changing the inductance of a pair of coils at eath end of the viscumeter tube. The four coits fat ;;;:*! s bridge which was unbalanced by the passage of the sinker through each coit in turn. When the ferrite core was midway between the first pair of coifs the out of balance signal was instantaneousfy zero and at this point a trigger actuated an electronic timer. The second pair of coil stopped the timer in a simiiar manner. Because of its shape the sinker could only be used for measurement in one direction, and it was returned to its starting position by inverting the comptete pressure vessel and tube. 4.

lF;?ERPRE’r.~TlON Oft MEASUREMENT3

For a plain cylindrical body falling axially down a closed vertical tube with terminal velocity V, at constant temperature fo and with laminar flow prevailing, the equations governing the motion can be solved to give

V -;: _ m@P- (Pf./fGl 2xqL*

where m g Pi, A

= = = =

I-() fn

r1

mass of sinker gravitational constant liquid density sinker density

For a particular

‘t

instrument

_

(4 - 4,” +“: - 6

I

= viscosity of liquid lS 11:sinker length 12 = tube radius = sinker radius. *1 with tube and sinker of the same material

operating at some temperature t, Eq. 1 can be reduced to DesnIinatim, 10 (f972) 319-328

322

J. D. ISDALE.

C. M. SPENCE

AND

1. S. TUDHOPE

where T = time for Sinker to fall fixed length it = a constant which is independent of temperature 3t = linear coefficient of expansion of material Pr = liquid density at tempemture t pa = sinker density at temperature l

To keepentry und *:xit effects fow it is nt?rrrssary to have a low sinker velocity, and this is achieved by maintaining a small artnutar cfcarancc between sinker and !ube_ When this condition exists I very small error in the measurement of either radius produces a large error in the calculation of the viscumeter constant A. The constant is therefore more accurately determined by calibration with Iiquids

of known viscosity. To confirm that this theory applied to the visco-neter c series of timings were taken

with distilled

water

as the test liquid.

The \iscometer

ctirtstant

was then

calculated using API values for water viscosity (8) and NEL Steam Tables for (9). Viscosities above I WC were taken from an equation given by Fab~~ss fan). The vafue (9 x IO-” de%“‘) supplied by the manufacturer for the linear co&icient of expansion of titanium was used in the equation and a&o to apply a temperature correction to the sinker density which had been measured at 2lVC. density

At least five fatf times were rcccrded

at each temperature

and the average taken.

The maximum difference in fall times at any temperature was always lessthanU_2%, The results of this test are shown in Table 1. The maximum difference in the derived. values of A was O&O/,,which confirms that the viscometer was operating according to theory.

27.23

50.69 52.05 76.32 96.43 117.12 139.01 158.30 179.37

268.18

267.00 266.79 267.26 268.40 268.27 268.10 267.48 267.40

PHYSICAL PROPERTlES OF SEA WATER SOLUTIONS: ViSCUSITY

323

For the measu~m~nt of each sea-water solution, fal1 times were first taken at three temperatures below 80°C. Calibration constants were then calcuiared using viscosities previously measured in the master viscometer and densities from reference (6). These were averaged and used to calculate viscosities from fall times taken at temperatures above 80°C. This calibrating procedure was used because it was found on early test runs that the vaiue of A derived varied slightly (& 2.5 “/,) with the axial orientation of the sinker relative to the tube. The effect was attributed to slight ovality of a short section of both the sinker and the tube. The procedure used was found to be the best method of avoiding errors from this source. 5.

SOLUTIONS USED

The solutions

chosen for these measurements have been fully described elsewhere (f1)). For measurements at temperatures greater than 100°C it is essential that the sea water solutions contain no calcium sulphate, which would precipitate out and make measu~ment impossible. Calcium sulphate was therefore omitted and the other saits present in natural sea water were included in appropriate proportions. The unit of ~n~ntratjo~ used in this paper is safinity, which is defined as the total weight of satts in grammes, per kitogramme of sofution. The results can therefore be used for natural sea waters of known salinity, since the inclusion of a smaIi proportion of calcium sufphate in the total weight of salts would have no signififzant efiLcL Al1 measurements were made on so!utions having salinities of 32.3, 63.2,

107.2 or f 48.4 g/kg. 6. SOURCES OF ERROR

The accuracy of measurements made in the master viscometer is estimated at + 0.2%. For the falling body viscometer the total error in viscosity resulting from uncertainties in all the parameters in equation 2 plus salinity was calculated and found to be f 1%. Repertt rn~su~ernen~ with fresh solutions fell &thin this band.

The experimental measurements

were smoothed

by fitting to the equation,

[A(1 + a,S -t- n,S7) + B(X + ExS + b2S2) (t - WI (3)

3. D.

324 TABLE

ISDALE,

C. M. SPENCE

AND 1. S. TUDHOPE

II

COhfPARISD?l

OF MfZASURED

AND

SMODTWED

VE4XXWtE.s

148.38 148.3% 148.38 la.38 148.38 148.38 148.38 148.38 107.15 I57.JS JO7.J3 157.35 107.15 JO7.15 107.15 107.15 JOXJS 107.15 JO?*lS 107.15 JO7.15 107.15 63.16 63.16 63.16 63.16 63.16

63.16 63.16 63.16 63.16 63.16 63.16 32.33 32.33 32.33 32.33 32.33 32.33 32.33 3233 32.33 3233 32.33

20.00 5o.tm 75.00 $7.44 121.66 137.84 158.66 178.91 20.00 50.00 103.64 81.87 f00.82 J 20.36 138.14 133.42 J77.88

84.95 82.71 124.28 170.10 J41.51 20.00 35.00 82.22 loo.44 J X8.68

140.58 160.38 f 79.w 12225 140.06 160.97 z: 75.00 83.78 Jab.33 J 19.85 J 39.82 f 59st3 377.83 loQ.98 340.20

f.4405 u.8034 0.~6% 0.4344 0.3459 0.3037 0.2616 0.23@4 J 9700 0.7.153 0.3639 0.4576 83734 0.3077 0.2662 0.2279 fmJO3 0.4406 0.4527 0.2970 0.2128 0.26JtJ J.J39S 0.4447 0.4063 0.3313 0.2773 cf.2305 0.19as 0.1785 0.272a 0.2337 OiXHJ6 1.0663 0.59iM 0.41 JO 0.3624 0.3018 imw 0.2115 0.1824 O.JdJS 0.3054 0.2353

1.4380 0*%0x, 0.5632 0.436s 0.347 J 0.3039 0.2608 A2283 1.2?S7 O.fJS6 0.3647 O&if8 03732 0.3 JO5 0.2684 0.23m iuO1Q 0.4455 0.4572 0.2985 0.2126 0.2614 J-J376 0.4442 &%a65 0.3323 0.2786

0.2314 0.1986 0.1755 0.2696 02323 0.1985 J.u623 0.5877 0.4BQ2 0.3673 O.MS? 0.2530 0.21335 0.1839 0.1624 0.3036 0.2JzQ

0.17 om 0.32 -O-4? --0.35 -U-O6 R3J 0.9J -0.45 - 0.05 -o*n -O.QJ -J-O2 -0.93 -0.84 -J-J2 --0.82 -J.JO -J?oo --OS2 &JO -0.15 0.17 O_JJ - 0.05 -02Q --0.46 -0.38 0.08 1.69 0.81 0.59 1.04 0.38 0.45 0.43 -J.34 -1.2a -1.l6 -0.97 -0.W -0.54 -0.58 i-11

PHYSlCAL

PROPERTlES

OF SEA WATER

SOLUTIONS:

325

VISCOSlTY

where qz,, = viscosity of solution at 2O”U, mNs me1 = 1.002 + c,S -6 c&s = viscosity of solution at t”C, mNs ITI-’ li S = salinity in g/kg.

and A, at, ff2, B, bt, bzr cl, c2 are constants. This form of equation was chosen because it was found to give a more accurate fit than other types when tested with the API water data (8). Fabuss also found that this form of equation gave the best fit to his measurements of water viscosity (10). A comparison of the experimental and smoothed results is given in

Table If, and the smoothing equation constants are given in Table III. TABLE

8.

Ill

COMPARISON

WiTH

PUBLiSHED

DATA

The agreement between the NEL measurements and earlier published data is within the expected accuracy and is illustrated in Figs. 2 and 3 for 20 and 150°C respectively. Where necessary the data have been corrected using the API water viscosities. The comparison shown in Fig. 3 is also typical of that found at lower temperatures and shows that the results of Fabuss tend to follow a linear correlation with salinity more closely that the NEL measurements, The inconsistency of up to 3 %

in the results of Ponizovskii, Fig. 2, may have been due to the difficulty of ob taining high salinity solutions from natural waters, curvature similar to that of the NEL measurements.

9.

CORRELATiON

nevertheless

they have a

OF DATA

The ex~~menta~ data of Fabuss and Miyaki and values given by Dorsey were combined with the NEL smoothed vahtes and fitted to Eq. 3. The measurements of Fabuss and of Miyaki were iuterp~~~t~ to the nearest unit of ten in Desal~can,.

10 (1972)

319-328

326

J, D.

X

NEL

A

MlYAKf (4)

cl

DoRSfT

0

fQNIZOYSKI1 (5)

1SDALE.

EWERIHENTAL

C. M. SPMFE

ANO

1. S. TUDHOPE

0

(2)

0

P

I

t 100

JO SALINITY - q/k,

Fig. 2. Dynamic

viscosity at 20%

wrxus dinity.

salinity and all values at temperatures of 20°C OXrks~2 were used from each. The values given by Dorsey were taken in steps of 10 g/kg for temperatures of 20°C and above. Smoothed NEL vaiues were taken at 20. SO, 75, IOO, 125, 150 ,and 180*C for the. four salinities measured interpolated to the nearest IO g/kg_ API water viscosities were used at S deg intervals from 20°C for a zero salinity solution. ‘IBe correlation fits the data in the ~rn~~~~~ range 20 to 18WC for salinities up to 150 g/kg with a maximum deviation of 1 *A. It also gives values for water which agree with the API values above 2WC to within -t_025 % and can be used to extrapolate sea water viscosities to 0°C without loss of accuracy, that is to within If: l.O$& The viscosities obtained from this correlation ate therefore recommended for

327

TCWptfWkPZ 'C 20.0 I.019 30.0 0‘812 40.0 0.666 50.0 0.558 60.0 0.476 70.0 0.4f3 80.0 0.363 90.0 0.322 fOO.0 0.289 110.0 0.261 I2O.O 0.238 130.0 O-218 140.0 0.201 150.0 0.186 li6O.o 0.173 170.0 0.161 180.0 0.151

1.059 0.846

1 .om

0.855 0.694 0.702 0.583 0.590 0.498 0*5&l 0,433 0.438 0.381 0.385 0.339 0.343 0.308 a3w 0,275 0.279 0.251 0.254 0.230 0.233 0.2112 0.215 0,196 0.199 0.183 0.185 0.170 0.173 0.160 0.162

1.105

0.884 0.727 O*SlI 0.523 0.455 0.400 0.356 0.320 0.290 0.264 0.243 0,224 0.207 0.193 0,180 0.169

1.158 0.928

0.764 0,643 0.551 0.479 0.422 0.376 0.338 0.306 0.280 0,257 0.237 0.220 0.205 0.191 0.179

1.218

0.976

0.804 0.677 0.58f i3SOS 0.446 0.397 0.357 0.324 02% 0.272 0.251 0.233 0.217 0.203 0.190

1.284 1.029 0.848 0.714 0.613 0.534 0.471 0.420 0.378 0.343 0.313 0.28R 0.266 0.247 0,230 0.215 0.202

1.357 1.087 0.896 0.754 0.647 0.564 0.497 0.444 0.399 0.363 0.33x 0.30s 0.282 0.262 0.244 0.229 0.215

I,437 1.150 0.947 0.797 0.684 0.595 0.525 0.469 0.422 0.383 OXG 0.323 0.298 0.277 0.259 0.243 0.228 -

Dpsalifinrion, f0 (1972)319-328

328

J. D. ISDALE, C. M. SPENCE AND J. S. TUDHOPE

general use and are given in Table IV, They are also shown as the continuous Iines on Figs. 2 and 3. Equation constants for the cozrefation are givea in Table III. ACKNOWtEDGEhiEIUTS

This paper is published by permission of the Ditzctor of the National Engineering Laboratory, Department of Trade and Industry. ft is Crown topyt5qht and is reproduced by permission of the Controller of HM Stationery Offtee, The authxs would also tike to acknowfedge the assistance of Mr. R. Morris acd Mr. I. Listerwho made useful contributions to the experimental work REFERENCES