A RAPID METHOD FOR OBTAINING VAPOR=LIQUID EQUILIBRIUM DATA Distillate Analysis Technique as Applied to a Tevnary System D. W.
BUNCH AND W. J . JAMES
School of Mines and Metallurgy, University of Missouri, Rolla, M a .
R . S. RAMALHO University of Rochester, Rochester, N . Y .
Vapor-liquid equilibrium data were obtained for the system acetone-methanol-water by the d,istillate analysis technique. Distillate samples were analyzed in terms of refractive index and specific gravity using the analytical diagram of Griswold and Buford. Fifty-eight experimental points were obtained with a total of about 24 hours of experimental work, representing a substantial decrease in effort over conventional methods. From previous studies on the corresponding binaries, Wohl constants were calculated and used in checking the thermodynamic consistency of the ternary data. The data are sufficiently similar to those of the literature to indicate that the distillate analysis technique is applicable to ternary systems.
I
(6) a method for rapid determination of isobaric vapor-liquid equilibrium data was described, This method was applied to several binary systems with considerable success. However, since its main feature was the speed with which data could be obtained, it was felt that the method would find its greatest application in obtaining multicomponent vapor-liquid equilibrium data. The ternary system acetone-methanol-water was selected for the present study. The corresponding binaries have been studied (7-6). From these data the binary Wohl constants were calculated (Table I), and used in checking the thermodynamic consistency of the ternary data. N A previous paper
T h e distillate samples were analyzed in terms of refractive index and specific gravity, using the analytical diagram of Griswold and Buford ( 3 ) . Specific gravities of samples were measured using Weld-type pycnometers immersed in a constant temperature bath (+0.2' C.) until they reached the desired temperature. They were then weighed on a n analytical balance with a sensitivity of = t O . O O O l gram. The refractometer used was of the dipping type (Bausch and Lomb) and could be read to 10.0003 unit ( D line). Temperature control was 1 0 . 2 " C. Values of W and x i were then calculated by the material balance equations:
w =w,+z- v wxi = W&i - Z ( V Y i )
(3)
+ zzi
(4)
T h e vapor compositions, yi, were calculated from Equation
2 by using numerical differentiation techniques. The results are presented in Table 11. These data are presented graphically in Figure 1, where they are compared
Table I. Binary Wohl Constants = 0.243 Aai = 0 . 2 4 3
Acetone (1)-methanol ( 2 )
A13 = 0 , 8 9 0 Acetone (1)-water (3) A31
= 0.650
= 0.355 Methanol (2)-water (3) A S ? = 0.255 A23
Ref. ( 7 , 4, 5 )
Water
(7) (6)
Previous workers (3) have obtained direct data on this ternary system by conventional methods. Experimental
The general procedure, equipment used, and possible methods of feed addition for ternary systems have been described (6). In the present study the feed consisted of methanol-water binaries and the original charge was usually a ternary mixture. T h e necessary equations for the ternary system may be developed from the material balance with respect to any desired component, i, which is written in differential form as: d( W X ~=) zidZ - y i d V
(1) Acetone
Solving for yi,
Figure 1 . Vapor-liquid methanol-water system
Methanol
equilibrium data for acetone-
Obtained b y the distillate analysis technique, compared with literature
282
I & E C PROCESS D E S I G N A N D DEVELOPMENT
Table II. Vapor-liquid Equilibrium Data
Acetone Methanol Temp., a C . in Liquid in Liquid 56.5 87,8 1.8 57.1 80.3 2.8 57.6 73.5 3.9 58.1 67.3 4.8 58.6 61.6 5.8 59.1 55.7 6.3 59.5 50.6 7.1 60.0 45.8 8.2 60.5 42.1 9.0 61 . O 36.1 9.6 61.6 31.8 10.3 62.3 27.4 10.9 63.0 23.2 11.5 63.8 19.4 11.9 65.2 l5,7 12.4 66.7 12.0 12.8 68.9 12.9 8.6 66.0 21.1 0.3 66.8 18.7 0.6 67.7 16.3 0.8 68.6 14.1 1.o 69.7 12.0 1.2 71.2 10.2 1.4 73.4 8.6 1.5 76.5 7.1 1.6 78.9 5.7 1.7 81.1 4.3 1.7 85.3 1.7 3.2 89.4 2.2 1.7 91.7 1.6 1.5 36.9 4.6 89.6 57.0 83.6 8.2 57.1 77.9 11.4 57.3 72.5 14.4 57.5 67.3 17.2 57.8 62.3 20.2 58.2 57.3 22.9 58.5 52.7 25.5 58.8 48.3 27.8 59.2 44.1 30.2 59.8 40.1 32,3 60.3 36.2 34.4 60.8 32.6 36.4 61.4 29.0 38.1 62.0 25.7 39.8 63.0 20.4 71.6 64.0 18.6 71 . O 64.9 17.0 70.5 65.6 15.4 69.9 66.4 13.9 69.2 67.2 12.5 68.6 67.8 11.3 68.0 68.2 10.3 67.5 68.7 66.7 9.2 69.0 8.2 66.2 69.4 7.3 65.5 69.9 6.4 64.7 70 2 5.5 64.0 a Calculated from M’ohl’s equation.
Acetone in Vapor 92.8 91.4 86.9 85.9 86.1 85.5 86.2 85.5 84.1 83.0 81.8 80.8 77.4 76.5 72.5 69.8 58.5 80.3 79.8 79.8 77.0 75.0 73.4 67.1 61.8 56.7 51.7 42.0 32.2 21.3 93.5 89.6 87.3 85.7 83.5 81.4 80.6 77.2 75.1 73.0 70.5 68.2 65.7 63.5 59.9 37.1 34.7 32.6 30.2 28.9 26.2 25 .O 23.4 21.8 20.5 19.6 18.2 15.8
yo,Activity Coeficient for Acetone Obsd. Calcd.a (Eq. 5) ( Wohl) 1.02 1.08 1.05 1.09 1.09 1.13 1.22 1.14 1.32 1.20 1.28 1.40 1.52 1.36 1.45 1.65 1.76 1.53 1.70 1.98 2.17 1.84 2.44 2.01 2.70 2.20 2.41 3.12 2.64 3.47 2.92 3.92 3.24 4.53 3.06 2.83 3,33 3.02 3.61 3,32 3.91 3.61 4.21 4.06 4.52 4.37 4.84 4.50 5.13 4.50 5.47 4.79 5.81 5.07 6.12 5.25 6.42 5.24 6.67 4.82 1.01 1.02 1.03 1.04 1.05 1.09 1.17 1.14 1.21 1.19 1.24 1.24 1.28 1.32 1.31 1.36 1.35 1.43 1.38 1.50 1.41 1.56 1.64 1.44 1.73 1.37 1.84 1.41 1.92 1.44 1.45 1.38 1.44 1.39 1.43 1.39 1.43 1.40 1.48 1.41 1.45 1.41 1.51 1.42 1.53 1.42 1.72 1.43 1.65 1.43 1.75 1.44 1.82 1.44 1.83 1.45
Methanol in Vapor 1 .o 2.2 0.5 1 .o 0.5 0.8 1. o 0.8 1.8 2.1 1.8 2.5 4.7 5.1 6.0 8.2 17.4 0.5 0.5 0.8 0.8 1.2 1.5 3.4 3.4 5.2 4.9 6.6 8.2 8.2 2.8 5.8 7.6 8.0 9.7 11.1 12.5 14.0 14.6 17.1 18.6 20.0 22.2 24.0 26.9 60.6 62.0 62.6 64.8 64.7 66.0 66.7 67.6 68.5 69.5 70.1 71.2 71.8
with the data from the literature. T h e largely vertical lines are constant per cent acetone in vapor and the largely horizontal lines are per cent water. T h e boiling point diagram is shown in Figure 2 . Activity coefficients were calculated from the Wohl equation (7), using a ternary constant of 1.0 and the binary constants from Table I. T h e constant was chosen by a n iterative method to yield the best representation of the experimental data. T h e observed values of the activity coefficients were obtained from Y1 =
TYyi
-
PIOXl
and are compared with the calculated values in Table 11.
(5)
ym, Activity Coeficient f o r Methanol Obsd. Calcd .a( E q . 5) (Wohl) 1.88 1.27 1.08 1.08 0.17 0.97 0.27 0.89 0.85 0.11 0.81 0.16 0.80 0.17 0.80 0.12 0.81 0.24 0.26 0.84 0.87 0.20 0.92 0.25 0.98 0.44 1.04 0.44 1.12 0.48 1.22 0.60 1.34 1.13 1.03 1.59 1.10 0.76 1.18 0.87 1.26 0.67 1.35 0.83 1.44 0.81 1.52 1.62 1.61 1.34 1.70 1 .77 1.52 1 .80 1.89 1.77 1.93 1.97 2.04 1.87 1.41 0.84 1.30 0.96 1.21 0.91 1.15 0.75 1.10 0.75 1.06 0.73 1.03 0.71 0.70 1.02 0.67 1 .oo 0.71 1 .oo 0.70 0.99 0.65 0.99 0.71 1 .oo 0,72 1 .oo 0.75 1.01 0.91 1.03 0.90 1.03 0.90 1.03 0.90 1 .03 0.88 1.02 0.87 1.03 0.87 1.03 0.87 1.03 0.88 1.03 0.89 1.03 0.90 1.03 0.90 1.04 0.91 1.04
y W , Activity Coeficient for Water_ Obsd. Calcd.a ( E q . 5) ( Wohl) 3.50 3.48 2.22 3.00 3.29 2.64 2.36 2.62 2.24 2.13 1.92 1.93 1.59 1.78 1.52 1.57 1.44 1.43 1.34 1.37 1.30 1.34 1.23 1.24 1.19 1.22 1.15 1.15 1.11 1.21 1.10 1.08 1 .oo 1.11 1.09 0.95 0.91 1.07 0.85 1.06 0.91 1.04 0.91 1.03 1.02 0.88 1.02 0,92 1.01 0.94 0.92 1.01 1 .oo 0.95 1 .oo 0.93 1 .oo 0.92 1 .oo 0.98 3.76 3.51 3.28 3.08 2.76 2.75 2.72 2.50 2.30 2.46 2.41 2.14 2.01 1.92 1.90 2.20 1.80 2.33 1.73 2.03 1.67 2.04 1.61 2.02 1.56 1.91 1.52 1.82 1.48 1 .78 1.47 1.28 1.48 1.38 1.48 1.60 1.48 1.34 1.48 1.43 1.48 1.52 1.47 1.44 1.46 1.42 1.45 1.38 1.44 1.32 1.43 1.26 1.42 1.19 1.41 1.31
Conclusions
T h e data obtained for this ternary system are sufficiently similar to those of the literature (3)to indicate that the method is applicable to ternary systems. The thermodynamic consistency check is satisfactory, in view of the fact that those points giving the poorest agreement are consistently in the low concentration range for the component in question. Experimental activity coefficients are very sensitive to small errors in concentration a t these values. The order of accuracy is not as good as for binary systems, but this stems largely from errors in the analytical method. As each successive point calculated is dependent on previous points, this may introduce considerable error if a run is conducted over a wide range of composiVOL. 2
NO. 4 O C T O B E R 1 9 6 3
283
Water
It is felt that additional work on ternary and quaternary systems is warranted. Furthermore, the equipment can be modified for determination of vapor-liquid equilibrium data a t high pressures. Nomenclature pi0
= vapor pressure of component z
V W, W
= initial weight of liquid in flask
x,,( xi
= initial value of x i = weight percentage of component
= total weight of vapor distilled = weight of liquid in flask
i in liquid weight percentage of component i in vapor total weight of feed added weight percentage of component i in feed cumulative weight of component i in successive distillate cuts = activity coefficient of component i = total pressure
= yt Z = = zi 2(Vyi) =
yi 7r
Figure 2. Normal boiling points ( ” C.) methanol-water system
literature Cited
for
acetone-
(1) Bergstrom, H., “Chemical Engineer’s Handbook,” J. H. Perry, ed., p. 528, McGraw-Hill, New York, 1950. (2) Cornell, L. \V., Montanna, K. E., Ind. Eng. Chem. 25, 1331 (1933). (3) Griswold, J., Buford, C. B., I 6 ~ d . ,41, 2347 (1949). (4) Harper, B. G., Moore, J. C., Ibid., 49, 411 (1957). (5) Lang, H., Z. Phys. Chem. 196, 278 (1950). (6) Ramalho, R. S., Tiller, F. M., James, \%‘. J., Bunch. D. \V., Ind. Eng. Chem. 53, 895 (1961). (7) \Vohl, K.. Trans. A m . Inst. Chem. Engrs. 42, 215 (1946).
tions. Because of the rapidity of the method, this is easily avoided by conducting several distillations in different compositional regions. The 58 experimental points were obtained with a total of about 24 hours of experimental work. This represents a substantial decrease in effort over conventional methods for obtaining vapor-liquid equilibrium data for a ternary system.
RECEIVED for re\iew December 17, 1962 ACCEPTEDMay 2, 1963
MODIFICATION OF THE MCCABE-THIELE METHOD FOR SYSTEMS OF UNEQUAL HEATS OF VAPORIZATION G
.
T
.
F ISH E R
,
Department of Chemical Engineering, Vanderbilt University, Nashville, Tenn.
A hyperbolic equation i s developed for use as an operating line on an x - y distillation plot. number of theoretical plates to b e “stepped off” using either mole or weight fraction diagrams.
It allows the The method gives results identical with Ponchon-Savarit for systems with straight enthalpy-composition phase lines; i t gives a larger number of plates than McCabe-Thiele for systems where the more volatile component has a significantly lower heat of vaporization. Minimum reflux ratios can be analytically calculated. Use of the method with log-log or other nonlinear plots requires no more work than the usual McCabe-Thiele calculations.
THE use of the hfcCabe-Thiele ( 6 ) method to calculate the number of theoretical plates in a distillation column separating a two-component mixture is a well established procedure. The method permits easy calculation of stages, and is sufficiently accurate in many instances. I t requires the assumption of equal heats of vaporization of the components from the mixture, and hence must be used in general with mole fraction units in order to validate this assumption. 284
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
There are many systems encountered in distillation practice where the molar heats of vaporization of the components are not equal. Some examples of such systems are given in Table I ; the normal boiling point heats of vaporization are used. Calculation of the number of theoretical plates in a column rectifying any of these systems requires the use of the more complex Ponchon-Savarit (5) method, or of “latent heat units,” as proposed by Peters (7). Peters’ method considerably
