FaJPf
1
PHASE EQUILIBRIA MOLECULAR TRANSPORT THERMODYNAMICS
Saturation Composition of Steam-Helium-Liqu
d
Water System
a n d P-V-T Data for a Superheated Steam-He1 urn Mixture JAMES A. LUKER, THOMAS GNIEWEK', AND CHARLES A. JOHNSON' Syracuse University Research Institute, Syracuse University, Syracuse, N. Y. F o r 70 years many investigators h a v e measured P-V-T data of pure g a s e s , and accurate d a t a are available for most of the common g a s e s over rather wide ranges of temperature and pressure. While s u c h d a t a a r e of great scientific value, most engineering problems require specific knowledge of g a s e o u s mixtures rather t h a n pure components. B y comparison with pure components only a very limited amount of mixture P-V-T data h a s been measured, and, for many mixtures t h e engineer must attempt t o predict the P-V-T behavior. Usually mixture P-V-T histories are predicted from one of the mixture laws, by using the P-V-T data of t h e pure components. A few rather important generalizations have b e e n made regarding the applicability of mixture l a w s for several t y p e s of g a s e o u s mixtures. No s u c h generalization h a s b e e n postulated, however, for a mixture at a temperature below the critical temperature of one of t h e components. T h e purpose of t h i s investigation w a s to study steam-helium mixture. s u c h a g a s e o u s mixture-a Two t y p e s of problems a r e encountered with s u c h mixtures. In many i n s t a n c e s conditions of temperature and pressure a r e s u c h that a two-phase region is present. It is often n e c e s s a r y t o attempt t o predict the composition of the vapor phase in equilibrium with t h e liquid phase. Bartlett (1) in early work investigated t h e water-steam-nitrogen and w a t e r steam-hydrogen s y s t e m s , and compared experimentally determined vapor compositions with compositions calculated from the Poynting relation. A s the first p h a s e of t h i s investigation, t h e equilibrium composition of the vapor p h a s e w a s determined for a watersteam-helium system at 3OO0C., and 2000 pounds per square inch absolute. T h e experimental technique used w a s o n e of dynamic equilibrium. Several methods of predicting t h e equilibrium vapor composition w e r e attempted. T h e results of t h e s e calculations a r e compared with t h e experimental corn position. T h e second problem is prediction of t h e P-V-T history. T h e P-V-T d a t a for a steam-helium mixture of t h e determined saturation composition were measured in the superheated region. Several methods of predicting t h e P-V-T history of t h i s mixture wereltried and are d i s c u s s e d herein. 1958
APPARATUS
Saturation Study. A s c h e m a t i c diagram of t h e apparatus used in the saturation study i s shown in Figure 1. T h e high temperature salt bath w a s especially constructed t o contain the saturator and preheating coils. T h e fluid in t h e bath w a s a eutectic mixture of potassium nitrite and sodium nitrite sold commercially by t h e American Cyanamid Co. under the trade name Aeroheat. F i g u r e 2 is a sketch of t h e salt bath and temperaturecontrol circuits. F i v e 500-watt h e a t e r s were controlled manually by a variable transformer to give c o a r s e temperature control. F i n e control w a s effected by a 750-watt U-tube heater controlled by a Brown Electronik potentiometer recorder controller. T h e temperature of t h e bath w a s controlled to within k0.3OC. at 3OOOC. T h e bomb or saturator w a s a standard Aminco T y p e 347 s t a i n l e s s s t e e l pressure v e s s e l with a chrome-vanadium head. It had an inner volume of approximately 1730 cc., w a s 23/,, inches in inside diameter, and w a s 21 inches deep. T h e top of t h e pressure v e s s e l had two g a s o u t l e t s and a thermowell which extended into the center of the v e s s e l . T h e saturator w a s filled t o a depth of 4 inches with s t a i n l e s s s t e e l packing in the form of '&inch rings t o ensure good gas-liquid contact. Helium w a s supplied t o t h e system, a s shown in F i g u r e 1, through a line which led into t h e preheating coil. T h i s line w a s equipped with a p r e s s u r e regulator, rupture disk, a pressure gage, a needle valve, and t h e preheating coils. T h e preheating coils consisted of 4 0 feet of s t a i n l e s s 304 tubing, 5/4 inch in outside diameter and 'Al inch in inside diameter. An orifice immersed in t h e s a l t bath controlled t h e bleed rate of the saturated mixture. T h e vapor from the saturator w a s analyzed by condensing the water in a n ice trap, in a dry i c e trap, and finally by adsorption in a Drierite tube. T h e remaining helium w a s metered by a wet-test meter. ' R e s e n t address, E. I. du Pont de N e m o w s 8s Co., Inc., W i l mington, Del. 'Present address, Atomic Power Division, Westinghouse Electric Corp., Pittsburgh, Pa. C H E M I C A L AND E N G I N E E R I N G D A T A S E R I E S
3
THERMOCOUPLE
Figure 1. Saturation apparatus and heating bath Calibration of Instruments. T h e pressure gage w a s a I d i n c h United States Laboratory t e s t gage, range 0 t o 4000 pounds per square inch gage, calibrated periodically on a Crosby dead-weight tester. I t s precision w a s + 2 pounds per square inch over t h e range studied. T h e temperature in t h e saturator w a s measured with a %gage Chromel-Alumel thermocouple, calibrated t o within k0.2OC. by making u s e of t h e pressure temperature relationship of saturated steam. T h e electromotive force output of the couple w a s measured with a Rubicon Type B high precision potentiometer. p.V.T Apparatus. B a s i c a l l y t h e same apparatus w a s used for the P-V-T investigation (Figure 3). T h e exact volume of t h e bomb w a s determined t o b e 1726.1 cc. a t 2OoC. T h e entire v e s s e l , including s e a l i n g g a s k e t s , w a s made of s t a i n l e s s s t e e l . A three-way valve w a s used t o connect t h e pressure v e s s e l t o t h e Bourdon-type pressure gage. T h e tubing from t h e valve t o t h e gage w a s mercuryfilled, A s a result of this, t h e dead s p a c e volume w a s reduced t o 1.4 cc., of which only 1.1 cc. remained out of t h e s a l t bath during t h e experimental runs.
TFWSFORMER TFWSFORMER
BROWN ELECTRONIC CONTROLLER (FINE CONTROIJ
BROYlN POTENTIOMETER (LIMIT CONTROL)
4 S O U J
TI II
-I
II
TEST PROCEDURE
T h e technique used to determine t h e saturation composition of the steam-helium-water system was one of dynamic equilibrium. T h e saturator w a s evacuated and half-filled with distilled, degassed water. T h e n t h e saturator and preheating c o i l s were lowered into t h e s a l t bath, heated, and maintained at 30OoC. for at l e a s t 4 hours. Next, helium g a s w a s slowly bled into t h e bottom of t h e saturator through t h e pressure regulator until t h e total pressure read 2000 pounds per square inch absolute. T h e saturation system w a s maintained at 30OoC. for at l e a a t 12 hours. Before a run w a s begun, a volume of vapor greater than t h e vapor volume of Saturation Study.
4
INDUSTRIAL AND ENGINEERING CHEMISTRY
750 WATT HEATER CONTROLLED
5-500 WATT HEATERS NOT CONTROLLED
Figure 2. Heater circuits
VOL. 3, NO. 1
RUPTURE DISC
GLASS BULB FOR CHARGING WATER 347 STAINLESS STEEL PRESSURE VESSEL F i g u r e 3. P -V-T apparotus
t h e saturator w a s bled off, T h e saturated vapor mixture w a s expanded through t h e bath-immersed orifice while a tot a l pressure of 2000 pounds per square inch a b s o l u t e w a s maintained by adding helium t o t h e system through t h e p r e s s u r e regulator. Bleed r a t e s of approximately 0.1 t o 0.5 c u b i c foot per hour of helium were used t o e s t a b l i s h t h e dynamic equilibrium. After expanding through t h e immersed orifice, t h e superheated vapor p a s s e d through t r a p s and a Drierite t u b e t o remove t h e water. T h e water c o l l e c t e d w a s weighed on a n a n a l y t i c a l balance. T h e dried helium w a s t h e n metered by the wet-test meter. P-V-T Study. Prior t o beginning e a c h run, t h e bomb and tubing were removed from t h e s a l t bath. T h e h e a d w a s removed from t h e bomb and a l l p a r t s were thoroughly c l e a n e d and dried. Distilled, d e g a s s e d w a t e r w a s drawn i n t o a tared g l a s s pellet, weighed, and s e a l e d . T h e volume of t h e g l a s s pellet w a s next determined by water displacement. T h e g l a s s pellet w a s placed i n t h e bomb and t h e v e s s e l h e a d w a s secured. T h e bomb w a s then e v a c u a t e d and flushed with helium s e v e r a l times. Next t h e bomb w a s filled with helium t o t h e desired p r e s s u r e and w a s allowed t o s t a n d overnight t o attain thermal equilibrium. On t h e following day t h e press u r e and temperature of t h e bomb were recorded, so that t h e quantity of helium added could b e c a l c u l a t e d by making u s e of P-V-T d a t a for helium (2). After checking for l e a k s , t h e bomb w a s lowered into t h e s a l t b a t h and heated until t h e g l a s s water pellet burst. When a l l water had vaporized, t h e bomb w a s heated w e l l above t h e saturation point and allowed t o s t a n d for s e v e r a l d a y s t o e n s u r e that t h e mixture w a s uniform throughout. T h e v e s s e l w a s t h e n brought t o thermal equilibrium a t s e v e r a l different temperatures and t h e p r e s s u r e and temperat u r e were recorded. A portion of e a c h isochore w a s reproduced, t o e n s u r e that no l e a k s had developed during t h e run. RESULTS
T h e experimental and calculated r e s u l t s a r e presented i n T a b l e s I to VI1 and F i g u r e 4. D I S C U S S I O N OF R E S U L T S
T h e equilibrium d a t a measured a r e presented in T a b l e I. In e s t a b l i s h i n g t h e dynamic equilibrium, t h e helium flow r a t e w a s varied from 0.164 t o 0.56O1cubic foot per hour. A s the composition of t h e vapor w a s shown t o b e independent of t h e helium flow rate i n t h e range studied, it w a s con1958
cluded t h a t dynamic equilibrium w a s attained in a l l experimental determinations. T h e mean equilibrium composition of the vapor p h a s e of a water-steam-helium system w a s determined t o b e 70.54 mole % steam and 29.46 mole % helium a t 300°C. and 2000 pounds per square inch absolute. In T a b l e I1 predicted v a l u e s of t h e equilibrium vapor composition a r e presented. Dalton's law used with t h e P-V-T d a t a for t h e pure components resulted in t h e c l o s e s t approximation. In making t h i s calculation t h e P-V-T d a t a of steam presented by Keenan and K e y e s ( 5 ) were used. T h e p-V-T d a t a on helium were taken f r o m a compilation presented by B e a t t i e and Bridgeman (2); their original s o u r c e w a s the Leiden Laboratory and t h e R e i c h s a n s t a l t . T h e Poynting relationship integrated by u s e of t h e compressibility c h a r t s (3) used with Dalton's law a l s o gave a c l o s e e s t i m a t e of t h e composition. In using Dalton's law for t h i s c a s e t h e P-V-T v a l u e s for steam were estimated from t h e compressibility chart, a s steam d o e s not e x i s t a t 300°C. a t a vapor pressure of 1298 pounds per s q u a r e inch absolute. T h e c h a n g e in t h e vapor pressure of t h e water with total pressure a s predicted by t h e Poynting relations h i p did not significantly affect t h e calculated composition. B a s i c a l l y the major correction made by both of t h e s e methods of prediction w a s for deviation of t h e vapor p h a s e from the ideal g a s law. A s helium is rather soluble in water (7) at t h e s e conditions, it is interesting that t h e equilibrium vapor composition may be reliably predicted by simply correcting for vapor p h a s e deviation from t h e i d e a l g a s law. P-V-T D A T A
T h e P-V-T d a t a for t h e steam-helium mixture a r e presented i n F i g u r e 4 and T a b l e 111. T h e d a t a in F i g u r e 3 a r e presented in the form of isochores. A s rather complete and accurate P-V-T d a t a a r e a v a i l a b l e for both components of t h i s mixture, attempts were made t o predict t h e mixture P-V-T behavior from t h e c o n s t i t u e n t s ' data. T h e m u r c e s for t h e pure components' P-V-T d a t a T a b l e 1.
Run No.
Saturation Vapor Composition of a Steam-Helium-Liquid Water System a t 3 0 0 ° C . and 2000 Pounds per Square Inch Absolute
Helium Flow Rate, Cu.Ft./Hr., 7S°F., 1 Atm.
Saturation Vapor Mixture Composition, Mole Yo
0.560 0.507 0.560 0.249 0.263 0.235 0.250 0.330 0.164
1 2 3 4 5
6 7 8 9
Steam
Helium
70.79 70.43 70.70 70.73 70.67 70.17 70. I2 70.62 70.60
29.21 29.57 29.30 29.27 29.33 29.83 29.88 29.33 29.40
Mean saturation vapor mixture composition 70.54 mole % steam29.46 mole % helium, standard deviation i0.23%.
T a b l e II. Experimentally Determined and C a l c u l a t e d Saturated Vapor Composition a t 3OO0C. and 2000 Pounds per Square Inch Absolute
Method Experimental Dalton's law with perfect g a s law Dalton's law with con* stituents' P-V-T data Poynting relationship, perfect g a s laws Poynting relationship, compressibility charts for vapor, Dalton's law
Mole 7 ' Water
Mole % Helium
Vapor Pressure of Steam, Lb./Sq.Inch Abs.
70.54
29.46
....
62.3
37.7
1246
70.6
29.4
1246
64.3
35.7
1286
71.2
28.8
1298
C H E M I C A L AND E N G I N E E R I N G D A T A S E R I E S
5
Table
0.07845 Pressure, (lb./sq. inch abs.) 784 829 878 93 1 979 885 832 835 817 784 752 717 695 681 676 544 542 692 724 753 698 72 1 72 1 734
111. P-V-T D a t a for 70.54 Mole % Steam-29.46 Mole % H e l i u m Mixture, Molal Density, Lb. Mole/Cu. F o o t
0.09835
0.1186
0.1446
0.1624
T a b l e IV.
Prediction of Steam-Helium P.V.T
0.2184 Temp., OC. 317.7 338.4 337.7 337.9 353.7 353.8 367.0 377.4 376.6 375.8 359.8 343.3 341.6 342.1 326.5 326.4 310.8 310.8 312.9 312.9 294.7 294.9 300.4 300.1 2 99.4 301.4 311.6 311.6
D a t a i n Superheated Region by Dalton's L a w and Constituents' P-V-T D a t a
Temperature,
OF.
580°
630'
700 '
8000
9000
Pressure, Lb./Sq. Inch Abs.
Pressure, Lb./Sq. Inch Abs.
Pressure, Lb./Sq. Inch Abs.
Pressure, Lb./Sq. Inch Abs.
Pressure, Lb./Sq. Inch Abs.
Molal Density, Lb. Mole/ Cu. Ft. Exptl. Calcd. 0.07845 813 815 0.09835 991 1002 0.1186 1203 1184 0.1446 1414 1407 0.1624 1579 1551 0.1889 1757 1755 0.2184 1950 1966 aExtrapolated data.
70
error f0.25 +1.06 -1.58 -0.50 -1.77 -0.11 -0.82
Exptl. 830 1017 1235 1455 1625 1820 2039
Calcd. 834 1026 1216 1446 1598 1813 2034
%
error +0.54 +0.93 -1.54 -0.62 -1.66 -0.38 -0.24
70
Exptl. 915 1142 1388 1644 1846 20868 2376
were t h e same as were used for t h e saturation vapor composition predictions. As no a c c u r a t e helium P-V-T d a t a were available above 400 O C . , t h e Beattie-Bridgeman equation of s t a t e w a s used t o extrapolate t h e helium P-V-T d a t a t o 500°C. Methods of prediction tried included (1) Dalton's law of additive pressures; (2) Amagat's law of additive volumes; and (3) the generalized compressibility chart with mixture pseudocritical constants. As shown i n T a b l e IV, Dalton's law of additive pressure u s e d with components' P-V-T d a t a predicted t h e P-V-T behavior of the mixture t o within t1.24% over t h e entire superheated range investigated. Some difficulty w a s encountered in applying Amagat's law of additive volumes, s i n c e steam e x i s t s onlv a s a liauid a t the total mixture pressure over part of t h e temperature range studied. T h e P-V-T behavior of t h e mixture w a s , however, predicted by t h i s method a t conditions of temperature and pressure where steam e x i s t s a s a vapor (Table V). T h e predicted P-V-T v a l u e s deviated from the experimental d a t a by a n average of -3.21%. T h e prediction by t h e u s e of t h e generalized compressibility chart with pseudocritical c o n s t a n t s is presented in T a b l e VI. T h e calculated mixture P-V-T behavior deviated t 1.44% on t h e average from t h e experimental P-V-T d a t a in
6
0.1889
Press we, Pres sure, Pressure, Pressure, Pressure, Pres sure, remp., (lb./sq. Temp., (lb./sq. Temp., (lb./sq. Temp., (lb./sq. Temp., (lb./sq. Temp., (lb./sq. C. inch abs.) OC. inch abs.) OC. inch abs.) 'C. inch abs.) OC. inch abs.) OC. inch abs.) 290.0 595 222.4 1559 436.5 1872 441.8 2030 421.2 1195 259.7 1820 317.0 592 122.1 1524 421.2 1794 417.3 413.0 1323 1998 297.1 2188 347.6 714 238.3 1338 353.0 1735 398.8 410.0 1987 2017 355.2 2188 382.2 713 238.2 1292 337.1 1686 385.3 1883 380.4 1876 325.8 2188 412.2 892 262.8 1240 316.9 1554 344.8 1834 368.0 1724 300.2 22 78 353.7 939 282.5 1196 301.3 1496 326.6 1726 341.0 1631 285.9 2278 316.3 9 79 310.6 1130 279.1 1450 3 14.8 1634 318.6 1589 283.9 2353 318.0 1030 32 1.8 1082 265.0 1362 294.0 291.6 1537 1479 275.7 2408 306.6 1080 343.6 1084 265.7 1295 275.6 1500 285.8 1270 260.0 2406 1143 286.3 372.2 1046 2.59.8 1191 265.4 1405 277.9 1129 2404 246.8 973 264.4 1180 389.8 970 253.8 1105 259.4 1340 272.8 231.0 2311 89 1 250.4 1202 398.4 246.0 1285 2217 268.7 241.8 1107 777 354.3 233.2 2209 235.8 1036 669 322.5 219.5 2210 955 226.4 286.7 2116 210.5 765 236.1 2116 210.0 732 238.1 2014 72 2 233.8 236.8 2014 730 252.0 234.8 2032 266.6 894 261.8 2032 784 237.8 243.5 1810 249.4 730 237.9 1806 249.4 1871 256.5 1875 1875 1895 1995 1997
INDUSTRIAL AND ENGINEERING CHEMISTRY
Calcd. 930 1150 1368 1638 1816 2076 2348
error +1.64 +0.66 -1.44 -0.36 -1.62 -0.48 -1.18
Exptl. 996a 1260' 1534 1823' 204ge 2304'
Calcd. 1018 1264 1510 1816 2022 2317
%
error +2.26 +0.32 -1.56 -0.38 -1.32 -0.56
Exptl. 1075" 1374e 1674e 1996' 2245' 2503'
Calcd. 1107 1376 1643 1988 2216 2553
70
error +2.98 fO.15 -1.85 -0.41 -1.24 -2.00
T a b l e V. Prediction o f Steam-Helium P-V-T D a t a in Superheated Region by Amogat's L a w and Constituents' P-V-T D a t a
Temp., OF.
580 600 700 800 900
Molal Density, Lb./Mole/Cu. Ft. 0.1889 0.09835 0.1889 0.09835 0.1889 0.09835 0.1889 0.09835 0.1889 0.09835
Pres sure, Lb./Sq. Inch Abs. Exptl.
Calcd.
70
Error
....
....
....
991
946
-1.54
....
....
....
1016 2086 1141 2304 1259 2503 1373
975 1946
-4.04 -6.71 -2.63 -3.78 -1.51 -1.28 -1.17
1111
2217 1240 2471 1357
t h e superheated region. Kay's method (4) w a s u s e d to determine t h e pseudocritical constants. T h e Newton correction (6) w a s applied for helium in calculating t h e pseudocritical c o n s t a n t s by Kay's method. T h e compressibility chart presented by Brown (3) w a s used for t h e calculations. In addition t o t h e above cited calculations in t h e superheated region, t h e saturation conditions, pressure and temperature, were predicted using Dalton's law and constitue n t s ' P-V-T data. T h e r e s u l t s of t h e s e calculations are VOL. 3, NO. 1
Table
VI. P r e d i c t i o n of Steam-Helium P - V - T D a t a i n Superheated Region by G e n e r a l i z e d Compressibility Charts Used w i t h P s e u d o c r i t i c a l Constants
1.279 (600OF.) Molal Density, Lb. Mole/ Cu. Ft.
P r e s sure, (lb./sq. inch abs.)
Reduced pressure
Exptl.
0.07845 0.09835 0.1186 0.1446 0.1624 0.1889
830 1016 1236 1455 1625 1820
0.3607 0.4415 0.5372 0.6323 0.7062 0.7910
0.9305 0.9085 0,9162 0.8851 0.8798 0.8472
1.399 (700°F.)
Compressibility Factor Charts
% Deviation
Compressibility Factor
Pressure, (lb./sq. inch a b s . )
Reduced pressure
70 Deviation
Exptl.
Charts
0.9445 0.9323
0.960 0.940 0.930 0.920 0.920 0.910
C1.7 4- 0.8 -1.1 f0.6
0.960 0.960 0.969 0.960 0.960 0.910
+2.3
Reduced Temperature
0.930 0.930 0.920 0,910 0,900 0.890
922 1141 1388 1644 1844 2088
0 f2.4 f0.4 f2.8
f2.3 +5.1
0.4007 0.4959 0.6032 0.7145 0.8014 0.9074
0.9402
0.9138 0.9123 0.8881
+O.Y
f2.5
Reduced Temperature
1.520 (800OF.) .___
0.0 7845 0.09835 0.1186 0.1446 0.1624 0.1889
997 1260 1535 1824 2049 2303
0.4333 0.5476 0.6671 0.7927 0.8905 1.009
0,9400 0.9476 0.9570 0.9332 0.9330 0.9016
0.060 0.960 0.950 0.950 0,940 0.910
+2.1 +1.3 +0.7 + 1.8 f0.8
+0.9
1074 1374 1675 1995 2245 2503
1,641 (900’F.)
0.4668 0.5971 0.7279 0,8670 0.9757 1.0878
0.9384 0.9576 0.9677 0.9459 0.9473 0.9080
+0.2
-0.8 f 1.5 + 1.4 +0.2
T a b l e VII. P r e d i c t i o n of P-V-T D a t a of Steam-Helium lsochorer ot Saturation P o i n t Using Dalton’s L a w and P-V-T of P u r e Con stituents
Saturation Temp., O F .
Molal Density, Lb. Mole/Cu. Ft. Exptl.
0.1186 0.1446 0.1624 0.1889
500 524 540 552
Calcd.
502 522 536 552
Saturation Pressure, Lb./Sq. Inch Abs.
Error (Temp. B a s i s ) Exptl.
74
+0.21 -0.20 -0.40 0.000
1064 1284 1485 1658
Calcd.
Yo Error
1075 1301 1453 1675
f1.03 +1.32 -2.15 f1.02
shown in T a b l e VII. T h i s method predicted t h e saturation pressure to within +1.6% on t h e average. As t h i s investigation d e a l t with only one s y s t e m , no generalizations could b e formulated. It h a s been shown, however, that t h i s mixture containing one component below i t s critical temperature adequately follows a mixture law. It may therefore be concluded that t h e saturation vapor composition of a water-steam-helium system may b e predicted from Dalton’s law and components’ p - V - T data. T h e P-V-T behavior of a steam-helium mixture may be estimated by either Dalton’s law and components’ P-V-T d a t a , or by use of the generalized compressibility chart with pseudocritical c o n s t a n t s . T h e applicability of t h e s e methods in predicting t h e s e properties for other mixtures of t h i s type should b e tried a s more data beccrme available. ACKNOWLEDGMENT
T h e authors wish t o e x p r e s s their grateful acknowledgment to the Oak Ridge National Laboratory, and t h e Union Carbide Nuclear Co., under whose a u s p i c e s t h i s work w a s performed ,
TEMPERATURE- “C. Figure 4
Steam-helium isochores
70.54 mole 70 steam 29.46 mole 70helium Isochore
1 2 3 4 5 6 7 1958
Molal Density, 1.b. Mole/Cu. Ft.
0.07845 0.09835 0.1186 0.1446 0.1624 0.1889 0.2184
LITERATURE CITED
I . A m . Chem. SOC., 49, 65-78 (1927). 1 2 ) Beattie. T. A . . Brideeman. . 0. C.. Proc. Am. Acad. Arts S c i . (1) Rartlett, E. P . ,
63, 229” (1928).
(3) Brown, G . G., others, “Unit Operations,” Wiley, N e w York,
1950. (4) Dodge, B. F., “Chemical Engineering Thermodynamics,” McGraw-Hill, New York, 1944. (5) Keenan, J. H., K e y e s , F. G . , “Thermodynamic Properties of Steam,” Wiley, New York, 1936. (6) Newton, R. H., Ind. E n g . Chem. 27, 302 (1935). (7) Stephan, E. F., Hatfield, N. S., P e o p l e s , R. S., Pray, H. A. H . ,
BMI-1067 1956). R e c e i v e d for review August 15, 1956. Accepted July 23, 1957. CHEMICAL AND ENGINEERING DATA SERIES
7
