THE JOURNAL OF INDUSTRIAL A N D E'MGINEERZNG CHEMISTRY
June, 1922
TEST1 dn dx 111 95 107 51 31 14.3 9.0 7.5 6.3 4.6 3.6 3.7 4.7 7.3
0,829 0,815
0,838 0.828 0.515 0.783 0.753 0.703 0,656 0.634 0.613 0.581 0.548 0.463 0,575 0.300 0.05
0.8
0.75 0.7 0.6 0.5 0.45 0.4 0.3 0.2 0.1 0.05 0.03 0.01 0.003 0.001 0.0001
I
kd"
k-
Y
2:
dx
.... .
.
0.005 0 0005
1
.
.
I
.
333' 27.8 14.3 6.8 4.5 3.9 4.2 5.0 35.3 117 349 3250
.... .... .... ....
0.01Ti
.
481
of the plate efficiency cannot be made by merely testing the slop when the alcohol is so nearly completely removed. In order to obtain data on which the efficiency can be calculated, it would be necessary to draw samples from plates higher up in the column on which there was a liquid containing a measurable amount of alcohol. The value of this paper should then lie in its exposition of a method for the calculation of tests on continuous stills. The wide variations in results thus obtained from the same still operating under not widely varying conditions indicate the desirability of a considerable factor of safety in column design.
NOMEKCLATURE Mole fraction of alcohol in the liquid. Mole fraction of alcohol in the vapor. Number of plates above feed. Number of plates below feed. Average plate efficiency. Composition of vapor leaving column. Composition of waste liquid leaving column. Reflux ratio above feed. Reflux ration below feed. Ratio feed to distillate. Molal heat of vaporization in KaI. Cp Specific heat. Kal. = Kilogrdm calories.
x y
= = n = m = k = yc = xw = R, = Rm = Rj = M, =
-
The Simple Distillation of Hydrocarbon Mixtures' By W. K.Lewis and Clark S. Robinson
FIG. 2
DEP.4RThKcNT OF C H E M I C A I , ENGINEERING,
This plot indicates that the optimum point for introduction of the feed would have been a t that point in the column where x = 0.12, the number of plates required being a minimum a t that point. I-Iowerer, a t that point the ratio of the
dn dx
dm
*
area under the - curve is to that under the - as 13.76
dx
is to 3.08, or 4.47, while the ratio of the actual number of plates in the rect,ifying column to that in the exhausting column was 30 to 16, or 1.88. It is therefore necessary to find by trial that value of x where the ratio of the areas is dn 1.88. This was found to be a t about 0.5 where - = 11.88
dx drn and - = 6.35, the total number of plates thus required, ax
if 100 per cent efficient, being 18.23. The average efficiency therefore was 18.23 X 100 = 40 per cent. 46
MASSACHUSSTTS I N S T I T U T E OF
TECHNOLOGY, CAMRRIDG MASS. ~,
the laboratory the simple distillation of hydrocarbon inixtures is most nearly represented by the Engler distillation, which consists of the distillation of a known volume of mixture from a simple flask and the recording of the relation between the vapor temperature and the percentage by volume of the original mixture distilled over. When plotted the data give a curve of the type illustrated in Fig. 1 (solid line). This Engler distillation is used universally for the purpose of comparison of petroleums and petroleum distillates, coal tar, light oils, and other complicated hydrocarbon mixtures. The other extreme from simple distillation is complete fractional distillation which separates a mixture into its several pure components. giving a distillation curve of the type indicated by the broken line in Fig. 1. T\T
I
I
r I
The plate efficiency for all the tests is:
.................... .......
Test number Plate efficiency, per c e n t . . Reflux ratio.. Composition of distillate. . . . . . . . .
...................
1 40 4.06 0.842
2 24 3.04 0.816
3 56 2 75 0.844
More careful tests on alcohol stills of a similar type by W. A. Peters, Jr.,6indicate that the plate efficiency is approximately 70 per cent. He has calculated Test 1 of this paper on the basis of a 70 per cent efficiency and found that the slop should be approximately 0.000002 mole fraction alcohol, instead of the assumed value of 0.0001. Since both of these values of the concentration are so small that they are practically immeasurable, it is evident that a true determination 6
See first paper in Symposium.
w-
---I
&J
0
Pe r ceo t Disti/ied 0 v e r
I
FIG.1 1 Published a s Contribution No. 15 from the Department of Chemical Engineering, M . I . T.
T H E JOURNAL OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
482
Vol. 14, No. 6
It is possible to predict the Engler distillation curve (first type) if the composition of the mixture be known. It is theoretically but not practically possible to make the reverse prediction, that is, the composition of the mixture, if the Engler distillation curve be known. The simplest case,
of the ratio may be taken as an approximate constant within this range. Combining this approximation with Raoult'a Law, the integrated Rayleigh equation is as follows:
that of a mixt'ure of two components, will be taken for the purpose of illustration. The well-known Rayleigh equation for simple distill at'ion is as follows:
where a is the ratio of the vapor pressures of the less volatile and the more volatile components. In this equation, however, w is expressed as moles. The use of this equation is shown in the following example: One hundred moles of a mixture conrainine fi5 of .. ner cent h v weieht .."~.~ benzene and 36 per cent of toluene are distilled. This compo&tion corresponds t o a mole fraction of 0.686. T h e ratio of t h e vapor pressure of toluene t o t h a t of benzene a t 98' C., half-way between their boiling points, ~~
is
where
w
= x = y =
weight of liquid being distilled, composition of liquid being distilled, and vapor in equilibrium with liquid.
The integration of this equation can be much simplified if Raoult's Law be assumed. Fortunately mixtures of hydrocarbons most frequently met with, such as homologs of the benzene series, or homologs of the methane series, come very close to following this Law. It is probable that any hydrocarbon mixture, the boiling points of the components of which do not differ too greatly, follows it closely enough for practical purposes. I n a binary mixture of two members of the same liomologous hydrocarbon series, such as benzene and toluene, whose boiling points are not far apart, the ratio of the vapor pressures a t one boiling temperature does not differ greatly from that a t the other boiling temperature, and an average value
so
= 0.436.
When the distillalion has progressed t o such a point
t h a t z, the mole fraction of t h e benzene in the liquid, ha3 dropped from the original value $1 = 0.686 t o x2 = 0.6
loo = o,406--1(0.406 In 0 . 6 + In O0 . 6 -m1 when a'z = 60.6. T h e weight of benzene present in the residue wz will be 6 0 . 6 X 0 . 6 X 78 = 2830 and that of the toluene will be 60.6 X 0 . 4 X 92 = 2130
1
)
. . . . ........ .
Total weight of residue.. . . , , 4960 T h e total weight of liquid a t t h e s t a r t was 100 X 0.686 X 78 = 5350 100 X 0.314 X 92 = 2890 8240
T h e per cent by weight distilled over will be 8240 8240 -4960 X 100 = 3 9 . 8
The temperature a t which a inixtiire containing 60 per cent mole per cent benzene will boil a t one atmosphere can be read from the boiling-point, curve shown in Fig. 2, as 89.5" C.,
r I/
t
I
0
W e i g h t P e r c e n t O v e r (W) Fro. 5
--
1
June, 1922
T H E JOURNAL OF INDUSTRIAL A N D ENGINEERING CHEMISTRY
giving a point on the Engler curve, if the Engler curve be plotted as weight per cent over. These calculations can then be repeated for several values of 22 as given in Table I. These values, plotted as a curve, are shown by the solid line in Fig. 3. TABLR I Y2
1V2
0.686 0.5 0.5
0.4 0.3
14.75
0.2 0.1
Per cent Over by Weight
Temperature
39.8 61.9
75.7
87 3 89 5 92 4 95.6
84.3 90.3 95 0
102.4 106.2
...
100 60.6 36.9 23.2 8.95 4.57
c.
98 9
483
It is the conviction of the writers that the practice in all Engler distillations should be so modified as to eliminate partial condensation of the vapors. This can be accomplished by providing a chimney around the top of the still so it will be jacketed with flue gases hotter than the vapors. Superheating the vapors cannot change their composition short of cracking, but partial condensation does. The thermometer must he kept wet with liquid by some sort of “percolator.” These simple precautions will make the Engler curve reproducible by anyone and independent of rate of distillation.
t
3
T
FIG. 6
The dotted line on Fig. 3 is the Engler curye given by F. E. Dodge.2 This curve was given for volume per cent distilled over, but in the case of benzene-toluene mixtures weight and volume per cents are nearly identical. When compared with the theoretical curve, it shows unmistakable evidence of fractional Condensation. Coleman and Yeoman3 give a graph for determining the composition of benzene and toluene mixtures. According to them, when a 65 prr cent mixture is distilled, the temperature will have reached 90’ C . when 48 per cent has bcen distilled over. This point is indicated on Fig. 3 by an arrow. The variation between the value given by Dodge of 37 per cent and that by Coleman and Yeoman of 48 per cent, and the calculated value of 42.5 per cent, indicates the difficulties which can be expected from partial condensation in the Engler distillation, and emphasizes the care that must be taken to avoid it. 2
3
Rogers’ “Industrial Chemistry,” 2nd editlon, 490. J SOC.Chem. Ind., 38 (1919), 612.
FIG.7
Moreover, t>he results will then hare sound theoretical significance. The method for the prediction of the Engler curve for mixtures of more than two components will now be indicated. A s before, it depends upon the assumption of Raoult’s Law. In order to make the method general, assume 100 g. of a mixture with a very large number of components, all belonging to the same homologoiis hydrocarbon serirs, as the paraffin series, whose boiling points as function of their molecular weight may be indicated a t least approximately by a curve of the type shown in Fig. 4,the actual values lying between the dotted lines, the solid line being an average value. If this mixture be distilled through a fractionating column of sufficient size so that it is separated into its pure components, the resulting fractionation curve would resemble the dotted line in Fig. 5 . For a large number of components, this dotted line could be very closely represented by a smooth curve as shown by the solid line. By combining the curves in Figs. 4 and 5 , the curve shown in Fig. 6, plotting 1/M against w is obtained. The area under this curve up to any value of w represents
P
P
Y Fro. 9
484
T H E JOURA’AL OF I N D U S T R I A L A X D ENGINEERING CHEMISTRY M E =
p I
wa
which is the number of gram moles distilled over, based on the original 100-g. sample, the total area being the total number of moles in the original 100 g.
Vol. 14,No. 6
At the start of a simple distillation a t constant temperature, that component, represented by dy, will start to distil over, as will any other component, d’y, whose vapor pressure at this temperature will be P’. When a differential amount d(dy) of the first has gone over, an amount d(d’y) will also have volatilized. The ratio of these amounts will equal the ratio of their partial pressures, or
which when integrated, P and P’ being constants, gives
Iff represents that fraction (molal) of d y that has not come over then P’ lnf = P Inf’ (5)
Y FIG. 10
Indicate the ratio of the number of moles over at any point in the distillation, divided by the total number of moles, by the letter y. Comparing several values of y by means of Figs. 6 and 4, a curve giving the relation between y and t can be constructed as indicated in Fig. 7. Now construct a curve a t some constant temperature of the vapor pressures of the pure components in the mixture a t that temperature as a function of the boiling temperatures, t, of these same components a t one atmosphere pressure, the result being shown in Fig. 8, where P represents the vapor pressures of the pure components. Figs. 8 and 7 can be combined as shown in Fig. 9, which is an isothermal diagram. Select some pure component, such as that indicated by dy in Fig. 9, which in the pure state cxerts the vapor pressure a t this constant temperature of P. When in the mixture, however, its partial pressure (by Raoult’s Law) will be Pdy. The total pressure exerted by the mixture at the constant temperature chosen will be equal to the sum of all the partial pressures of the components or will be f Pdy, which is the area under the whole curve in Fig. 9.
Fill. 11
This equation is fhe generalized form of Equation 2. Since in this equation P and P’ appear as a ratio, the expression is valid over any temperature range in which the ratio remains substantially constant. Suppose that d’y or f’ represents, for instance, the most volatile component in the mixture, it is now possible to calculate the fraction of all the other components which have not gone over when f ’ has any specific value, for instance, f ’ = 0.10, by substituting the proper values for P and P’ and solv-
1
I
%lo/$ FIG. 12 (for f’ = 0.10 isothermal)
jng Equation 5 for f. These several values o f f (when f’ = 0.10) can then be plotted as a curve against y, as shown in Fig. 10. The area under this curve is the total number of moles of all the components which have not gone over when f ’ = 0.10, and the area up to any value of y represents from Fig. 9 the moles remaining in the shell up to the corresponding value of P. Construct from Fig. 10, when f’ = 0.10, a series of areas for the several values of y, and plot as moles up to that value of y (Fig. 11). Then, combining Figs. 11 and 9, plot moles left in the still up to pressure P divided by total moles left in the still (i. e., mole fraction up to the point P) against the corresponding value of P as shown in Fig. 12. The area under this plot will be the total pressure a t thie point, in the distillation from which can then be calculated the boiling temperature. By repeating this process for other values of f‘ (for instance, 0.20) a series of points on the Engler curve can be determined.
