I
ARTHUR ROSE and ROBERT F. SWEENY Applied Science Laboratories, Inc., State College, Pa.
Ternary Batch Distillation Calculations for Rectification of Naphthalene Tar Acid Oil Here is the first practical method available to the design engineer faced with a problem involving batch fractional distillation of more than two components
To
DECIDE whether or not an existing batch column should be converted to continuous operation, its maximum annual output of naphthalene was estimated. For batchwise distillation, the calculations had to be done for multicomponent rectification, because naphthalene tar acid oil contains a number of components. With the results of such calculations, only straightforward arithmetic is needed to calculate yield, purity, and production. Batch rectification calculations for binary mixtures both with and without holdup have been reported, but little information is available for three components or more. A method (7) has been published for relatively few plates and a high reflux ratio-Le., where the column is operating far from pinch conditions. The method described in this report is applicable also to the more practical case of columns operating near pinch conditions. The calculations, comparatively simple and nearly identical with conventional binary batch calculations using the Rayleigh method, apply where holdup is negligible and sharp separation is achieved.
nary. These results are then combined, consistent with the charge composition, to predict a similar curve for the ternary case. The method is approximate, but gives results accurate enough for practical use. Its success depends on one condition-at some time during the distillation the intermediate component must appear in the overhead with relatively little contamination by the other components. I n the example given, the distillate attains a purity of more than 99% and very good results are obtained. Lower maximum purities would yield answers not so good but still acceptable for most practical requirements. The example used herein is a severe test of the
method, because the reflux ratio is only one half the number of plates; a more economic design might employ a reflux ratio closer to the number of plates. The best test for determining if the method is applicable to a particular problem is to do the two binary Rayleigh calculations ; if they mesh together smoothly and a t a concentration greater than 95% of the intermediate component, the method will prove to be useful.
Example The problem in the case of the naphthalene recovery calculations was to determine the curve of weight per cent
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The Method
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A multicomponent mixture is considered to contain a number of binary mixtures. Thus, for a mixture of three components, L, N, and H, where L is the most volatile and H is the least volatile component, two curves for distillate composition us. per cent distilled are calculated in the usual manner (4, 4), one for the L, N binary and one for the N, H bi-
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1
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ao
r 40
4 $
- 20
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WEIGHT Yo DISTILLED
Figure 1.
At atmospheric pressure a constant-boiling material distills at 21 6 ' C. VOL. 50, NO, 11
NOVEMBER 1958
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Figure 2. Relative volatilities are estimated with the help of the boiling point curve at 100 mm. of mercury
naphthalene in the overhead us. weight per cent distilled of a caustic-washed tar acid oil, with a constant reflux ratio of 8 to 1 (reflux to distillate) and a pressure of I atm. in a batch column containing 15 theoretical plates. This is the essential information required for estimates of yield and purity with a given column. Before any calculations could be done, it was necessary to determine the amounts and relative volatilities of the main components of the oil. T o do this, two precise fractional distillations were made, one at atmospheric pressure, and one a t 100 mm. of mercury pressure. The results of the atmospheric distillation are shown in Figure 1 as per cent naphthalene in the overhead and overhead temperature us. weight per cent distilled. The curve for the 100 mm. of mercury distillations has a similar appearance. The per cent naphthalene values were obtained by analysis of the fractions by determination of the melting points. At atmospheric pressure there is, apparently, a constant-boiling material which distills at 216' C. This material, even though it is only about 96% naphthalene, can be treated as one component for the purpose of distillation calculations. This component is designated as component N.
There is a definite plateau in the boiling point curve at 239' C. This component, and everything that boils higher, is called component H. There is a concentration of material more volatile than N, as indicated by the inflection from 172' to 182' C. on the curve. This fraction is considered to have a boiling point of 180' C. and all material more volatile than N is included in a component, L, which boils a t 180' C. Next, the amount of each of the three components: L, N, and H: in the charge must be determined. The area under the per cent naphthalene curvc in Figure 1 is the per cent of the charge which is pure naphthalene. The area was found to represent 59.3% pure naphthalene, which corresponds to 61.8% of N, the 96% constant boiling naphthalene-rich material. T o the right of the curve is H and L is to the left. The amount of these components is 16.0% L and 22.2%
H. The other information needed is relative volatilities. These are estimated with the help of the boiling point curve (Figure 2) obtained at 100 mm. of mercury. The large plateau, which obviously represents component N, has a boiling point of 144' C. There is an inflection from 110 to 118' C., which cor-
Table I. These Data Are Used for Calculation No. of theoretical plates Reflux ratio Charge composition
%L %N %H cvLN
" a a
15 8 :1
16.0 61.W 22.2 2.2 1.6
Component N is 96% naphthalene.
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INDUSTRIAL AND ENGINEERING CHEMISTRY
Table II.
L, N Binary
responds to component L. The boiling point of L was taken to be 114' C. The small plateau at about 166' C. represents H. Thus, there are boiling points for each of the three components at two pressures. From these values, and with the assumption of constant heat of vaporization with change in temperature, and of Raoult's law, the relative volatilities were conservatively estimated to be aLN= 2.2 and " a = 1.6 on a weight fraction basis a t atmospheric pressure. The distillation curve in the existing 15-plate tower can now be predicted by the new calculation method. Table I gives a summary of the necessary data. Procedure. The L, N binary consists of all the L and N in the charge. Thus, on a 100-pound total charge basis, L = 16.0 and N = 61.8 pounds. Therefore, on the basis of a binary containing only L and Tu', 16 0 L = 2 100 = 20.6% 77.8 61 8 N =A 100 = 79.4% 77.8
A McCabe-Thiele diagram is plotted for (Y = 2.2 and reflux ratio of 8 to 1. The values for x g for a column of 15 theoretical plates are found for various values of xv. The Rayleigh equation is then used to calculate x D us. per cent L N distilled. The results are plotted in Figure 3 (upper) as x D us. per cent of L N distilled. Points are taken from this graph and x g is converted to weight fraction actual naphthalene, and the per cent of L N distilled is converted to per cent of total charge distilled. As an example :
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At 20% of L N distilled, x g = 0.433. Weight fraction N (pseudo-naphthalene) = 1 - x n = 1 - 0.477 = 0.567 . _. . .. Weight fraction pure naphthalene = Y
0.567 X 0.96 = 0.544
Total charge distilled = 20 IO. distillate 100 Ib. L N
+
Other such calculations are given in Table 11.
Results Are Converted to Ternary Basis
L + N
Total Charge
Wt. Fraction
Distilled, Wt. %
Distilled, wt. %
Naphthalene.
0 10 14 18 20 30 36 40 43
0 7.78 10.9 14.0 15.6 23.3 28.0 31.1 33.5
ZD
1 - ZD
0.999 0.996 0.805 0.530 0.433 0.123 0.0468 0.0237 0.0133
0.001 0.004 0.195 0.470 0.567 0.877 0.9532 0.9763 0.9867
(1
- ZO)(O.SG) 0.00096 0.0038 0.187 0.451 0.544 .O .842 0.914 0.936 0.947
TERNARY BATCH DISTILLATION The N, H binary is taken to consist of all the H component and enough N to give an x D of close to 1.0. In this example enough N was taken to make 50% of the total charge. Thus, for 100 pounds of total charge :
+H
Pounds N
= 50
Pounds H = 22.2 PoundsN = 50 22.2 = 27.8
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Therefore, in the N, H binary
%N
27 8 = --.L X 100 = 55.6%
50
2 % H =' 22 X 50
100 = 44.4%
By use of the McCabe-Thiele and Rayleigh methods as before, the results are obtained and plotted in Figure 3 (lower) as x D (weight fraction N in distillate) vs. weight per cent of the last half of the charge. Points are taken from this graph and x D is converted to the weight fraction of actual naphthalene, and the per cent of the last half of charge is converted to per cent of total charge distilled. As an example : At 50% of the last half of charge distilled, X D is equal to 0.740. Wt. fraction naphthalene = ~ ~ ( 0 . 9 6=) 0.740 X 0.96 = 0.710 % total charge distilled = 50 f [wt. % of last half of charge distilled]l/2 = 50 f [50 X '/2] = 75%
same assumption. There are two prerequisites for making the usual application of the Rayleigh equation. First, the material balance (which is Rayleigh's equation) must be valid. Second, X D must be known as a function of X W ,
sults are shown with, the calculated curve in Figure 4.
Theory One assumption is necessary to calculate the N, H part of the curve-that is, a t some point, pure intermediate (N) component must appear overhead. If it does, it can be stated that (1) all the heavy. component in the charge remains in the pot, and (2) all the light component has been removed. Thus, there is actually a binary in the still a t this point and the usual binary Rayleigh calculation procedure as given by Smoker and Rose (3)and Weissberger ( 4 )applies. The first part of the distillation cannot be calculated so rigorously, even with the 1.0
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expressed for this case as
The L + N second prerequisite is not met rigorously. However, it can be shown that the Rayleigh equation applies to the L, N binary. The amount of distillate removed is equal to the decrkase in pot contents (assuming no holdup).
dD = - d(W) If no heavy component (H) comes out with distillate, -d( W ) = -d(L f N). For component L: I
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d
x
Other such calculations are given in Table 111. The data of Table I1 and Table I11 are plotted in Figure 4.
Table 111. N, H Binary Results Are Converted to Ternary Basis Wt. Fraction Wt. % Naphthaof Last Half of Wt. % lene in Distillate, Charge Charge Distilled Distilled ZD ~~(0.96) 0 20 30 40 44 50 52 60 68 76
50 60 65
70 72 75 76 80 84 88
0.998 0.994 0.988 0.970 0.938 0.740 0.635 0.303 0.104 0.024
0.958 0.954 0.949 0.931 0.900 0.710 0.609 0.291 0.100 0.023
WEIGHT
DISTILLED
0.8 -
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0.6 d
X
0.4
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0.2 Experimental Confirmation of Calculations
Two laboratory distillations were carried out a t the conditions of the example given above. These distillations were done in a laboratory column of 1-inch diameter with a 20-inch packed section of 0.16 X 0.16 inch protruded stainless steel packing. Data for this packing ( 2 )show HETP of 1.26 to 1.4 inches over most of the operating range. Thus, the column was estimated to have 15 plates. The re-
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Points from these graphs are used to find per cent of total charge
N binary, upper N, H binary, lower 1,
With this information the distillation curve in the existing 15-plate tower can be predicted by the new calculation method
VOL. 50, NO. 11
NOVEMBER 1958
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Nomenclature
D
weight of distillate least volatile component; can refer to weight L = most volatile component; can refer to weight N = component of intermediate volatility; can refer to weight W = weight remaining in still pot .yD = weight fraction of more volatile component in distillate xv = weight fraction of more volatile component in still pot aLN = volatility of L relative to N aNR = volatility of N relative to H
H
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Figure 4. agree
XDdD
Experimental and calculated results from ternary (L, N, H) distillation
[(L + N ) ( LkN)] L - ( L + N)d ( L ~ N )(L SL N) d(L -d
=
And -d(L
+ N) = dD,
+
N)
SO
the presence of H does not have a large effect on the relation. For example, the top composition a t 27.8% distilled (see Figure 4) is 5% L and 95% N. The per cent H in the bottoms at this point is
%
=
% H in charge % of charge remaining x
c 2 X 100 72.2 From the above, comes
This is the equation used (L 4- N was taken as the remaining liquid on an H-free basis, and
L was taken as L + N
~
xw on an H-free basis). The relationship between
-L
XD
and
is not independent of H. Therein I, N lies the only important approximation in the method. However, in most cases
=
100 =
Wt. 70 5.0 94.9 0.1
Wt. yo 5.0 95.0
L 0.36 N Bottoms composition 70.26
0.43 99.57
N On H-free basis
0.43 99.57
L N Top composition H
H 29.38 L Bottoms composition 0.51
1 690
99.49
...
. ..
Table I V shows the results of a ternary plate-to-plate calculation and a binary calculation for the above top composition. The difference is not significant. I t is interesting to consider the possibility of correcting for the presence of H by a simple trial and error procedure. Thus, the method as outlined here would be used for the first approximation. Based on the approximation, the relationship between xD and x w could be determined on a ternary basis and a corrected curve calculated. This procedure could be repeated if necesssary, but this would seldom be the case. Conclusions
An easy-to-use method for ternary batch distillation calculations without holdup has been described and an example problem is solved. The method is approximate, but the results are accurate enough for practical use. The method requires one necessary and limiting condition-that the distillation must yield, a t some time during its course, a distillate consisting almost entirely of the component of intermediate volatility. Validity of the method is supported by comparison with the results of two actual laboratory rectifications, and by a discussion of the theory involved.
INDUSTRIAL AND ENGINEERING CHEMISTRY
literature Cited (1) Robinson, C. S., Gilliland, E. R., “Elements of Fractional Distillation,” 4th ed., p. 383, McGraw-Hill, New
York, 1950. (2) Scientific Development Co., State College, Pa., Bull. 12. (3) Smoker, E. H., Rose, Arthur, Trans. Am. Znst. Chem. Engrs. 36,285 (1940). (4) Weissberger, A,, ed., “Technique of Organic Chemistry Distillation,” vol. IV, pp. 104-6, Interscience, Yew York, 1951. RECEIVED for review February 28, 1958 ACCEPTEDJuly 24, 1958 Work supported by the Pittsburgh Coke and Chemical Co. and findings published with its cooperation.
30.8%
+
Table IV. Difference between Ternary and Binary Calculations for 5% L in Overhead Is Not Significant Ternary, Binary,
= =
Correspondence A N e w Type of Nomogram. Aqueous Ammonium Sulfate Solutions SIR: Since publication of my article [IND. ENG. CHEM. 50, 971 (195S)l Francis W.Winn has called my attention to a nomogram of the same type which was described in his article published in the February 1957 issue of Petroleum R&ner. Attention was also called to the series on how to construct nomograms, which appeared in the Petroleum Rtjinei in October and Sovember 1955 and February and March 1956. I regret that these were unknown to me when my article was published. Dr. Winn has suggested that interpolation of my nomogram would be simpler if the intermediate graduations of the composition, density, and viscosity scales had been graduated in tenths or fifths rather than fourths. The vapor pressure scale, being in fourths and fifths, also seems confusing. A. M. P. TANS CENTRAL LABORATORY STAATSMIJNEN I N IJMBURG GELEEN, THENETHERLANDS
