ENGINEERING AND PROCESS DEVELOPMENT
Reflux and Plate Determinations for Batch Distillation S. R. M. ELLIS Chemical Engineering Department, The University o f Birmingham, Birmingham 15, England
I
?rT ASSESSING the number of plates in a binary distillation it is usual to calculate the minimum reflux ratio and minimum number of plates by using the Underwood (19) and Fenske (11) equations, and to calculate the operating reflux ratio and number of plates by using the graphical McCabe-Thiele (16) construction. When the relative volatility is less than 1.25 and the number of theoretical plates in the column is high, the graphical hIcCabeThiele construction is difficult to apply. I n such cases the number of plates can be accurately determined using the Smoker (17) and Dodge and Huffman ( 7 ) equations. The use of such equations is time consuming and requires a high degree of arithmetical accuracy. As a rapid and reasonably accurate method for the preliminary determination of the number of theoretical plates in a column, Brown and Martin ( a ) and Gilliland ( l a )have proposed empirical correlating equations involving the number of plates, the minimum number of plates, the reflux ratio, and the minimum reflux ratio. These equations apply to continuous distillation. Brown and Martin and Gilliland allow for different feed conditions. The correlating curves, although drawn through a band of points, give reasonably accurate results for continuous distillation. However, when applied to batch distillation these correlations give inaccurate results. Cichelli ( 4 ) and Zuideiweg (21 ) have proposed correlations for batch distillation between minimum requirements, the plate number, and reflux ratio, where the difficulty of separation is defined by the “pole height.,’ I n batch distillation it is desirable, however, to be able to calculate rapidly the reflux ratio a t any stage in the distillation. The need for such calculations is emphasized in the application of Bogart’s ( I ) equation to the separation of high purity components from close boiling mixtures.
The object of this paper is to re-examine Gilliland’s method and to see if it can be extended to batch distillation. If this is possible, the method would also be of value in locating the feed plate in continuous distillation. Procedure Includes Correlating Curves Based on Underwood, Fenske, and Smoker Equations
The procedure was to consider the systems, benzene-toluene, benzene-n-heptane, phenol-o-cresol, and ideal mixtures where the relative volatilities of the binary components or key components in multicomponent distillation are 1.1, 1.05, 1.025, 1.01, and for a number of separations in each system to calculate minimum and operating reflux and plate requirements. For benzene-toluene the equilibrium data of Griswold, Andres, and Klein (IS)were selected, whereas for the system benzene-nheptane equilibrium data of Ellis (10) were used. Underwood’s (19) equation was used to calculate all minimum reflux ratios. Except for benzene-n-heptane, the Fenske (11) equation was used to determine minimum plate requirementa The minimum number of plates for benzene-wheptane was evaluated graphically.
Table I.
Calculation of Reflux and Plate Requirements
xw
(lav.
Dlstillatc 0.9 8 . 9 0 9 Bottoms 0.02 0.05 0.3 10.7 9.4
Figure 1.
February 1954
6.5
Extrapolation of Curves Calculated for Benzene-n-Heptane
-
S-Sm 5*
0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96
0.30 0.30 0.30 0.10 0.10 0.10 0.04 0.04 0.04
1.238 1.238 1.238 1.238 1.238 1.238 1.238 1.238 1.238
S
Sm
s+ 1
R
Rm
R Rm R + 1
Benzene-Toluene 10.2 4.24 0.53 8.3 4.24 0.44 5.9 4.24 0.24 5.4 4.24 0.18 0.12 4.9 4.24 8.4 6.28 0.22 7.55 6.28 0.15 6.28 0.07 6.85 0.36 10.33 6 . 2 8 8.1 0.07 9.1 0.13 9.5 8.1 0.21 10.5 8.1
2.27 2.45 3.58 4.58 5.58 13.6 18.0 35.5 10.8 48.0 36.6 27.0
2.25 2.25 2.25 2.25 2.25 10.2 10.2 10.2 10.2 25.5 25.5 25.5
0.01
Benzene- n-Heptane 10.3 9.4 0.08 12.3 9.4 0.22 9.4 0.30 lX8 9.4 0.13 10.9 0.12 12.3 10.7 11.6 0.07 10.7 12.9 0.16 10.7 14.0 0.5 6.5 0.18 8 2 6.5 0.29 9,6 6.5 0.38 11.2 6.5 0.15 6.5 7.8
44.0 21.5 18.6 30.0 64.3 97.0 50.0 3.5 8.0 5.0 4.2 10.0
16.6 16.6 16.6 16 6 43 0 43. I) 43.0 3.1 3.1 3.1 3.1 3 1
0.61 0.22 0.10 0.43 0 32 0.56 0.14 0.09’ 0 54 0.32 0.21 0.63
47.0 23.0 15.0 47.0 96.0 67.0 200.0 150.0 120.0
13.1 13.1 13.1 40. 1 40.1 40.1 100.6 100.6 100.6
23.2 25.4 34.9 36.4 27.8 30.6 33.6 35.8 39.4
Phenol-o-Cresol 18.8 0.18 18.8 0.25 18.8 0.44 25.1 0.30 25.1 0.09 25.1 0.16 29.8 0.11 29.8 0.16 29.8 0.24
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.06
0.29 0.42 0.57 0.23 0.41 0.69 0.05 0.46 0.29 0.05
0.50 0.41
0.11 0.14 0.58
0.40 0.49 0.33 0.16
279
ENGINEERING AND PROCESS DEVELOPMENT Table II. XU
ZIP
Calculation of Reflux and Plate Requirements s - Sm R - Rm Sfl R S S7n Rm R + 1 a = 1.1
0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90 0.90
0.25 0.25 0.25 0,2;2 0.50 0.50 0.50 0.10 0.10 0.10
80.0 37.5 19.0 23.0 30.0 100.0 120.0 200.0
34 5 34 5 34 5 34 5 15 8 13 8 15 8 88 8 88 8 88 8
0.83 0.85 0.85 0.96 0.95 0.95 0.80 0.80 0.80 0.80 0.80
0.80
0.40 0.40 0.40 0.06 0.05 0.05 0.50 0.50 0.50 0.10 0.10 0 10 0.10
83.3 48.3 40 6 500.0 428,O 800.0 28 0 36 8 50.0 175 0 200,o 230.0 315.0
37.3 37.3 37.3 378.9 378.9 378.9 23.6 23.6 23.6 155.3 155.3 155.3 155 3
, O . 80 ,O. 80 0.80 0.80 ,O. 80 0.80
0.50 0.50 0.50 0.30 0.30 0.30
56.0 60.0 95.0 125.0 150.0 182.0
47.6 47.6 47.6 94.9 94.9 94.9
0.80 0.80 0.80 0.80 0.80 0.80
0 50 0.50 0.50 0.60 0 60 0.60
130 6 180 0 230.0 95.5 120 3 170 0
119 6 119.6 119.6 82.8 82.8 82.8
$1.2 00.0
0 16 0 36 0 56 0 078 0.16 0 30 0 46 0 11 0 26 0 49
61.7 48.7 42.6 71.5 48.2 38.4 32.7 73.0 62.8 53.5
34.5 34.5 34.5 34.5 23.0 23.0 23.0 46.1 46.1 46.1
0 0 0 0 0 0 0 0
44 28 18 51 51 39 28 36 26 14
57.3 75.3 107.4 169.8 174.2 136.1 63.9 47.0 38.5 127.2 110.8 100.4 88.6
43.8 43.8 43.8 120.6 120 6 120.6 28.4 28.4 28.4 73.4 73.4 73.4 73 4
0 0 0 0 0 0 0 0 0 0 0 0 0
23 42 58 23 30 11 35 39 27 42 34 27 17
128 0 110.2 75.4 151.7 122.8 112.0
56.3 56.3 56.3 90.6 90.6 90.6
0 5s 0 48 0 25 0 39 0 26 0 19
0 0 0 0 0 0
0 47 0 36
0 0
a = 1.05
Q.80
0.55 0.23 0.078 0 24 0.11 0.53
O,l5
0.35 0.52 0.11 0.22 0.32 0.50
a = 1.022
d =
0.13 0 20 0.49 0.24 0.36 0.48 1.01 0.20 0.33 0.47 0.13 0.31 0.51
278 219 189 226 173 132
6 3 5
3 9 3
140 140 110 99 99 99
0 0 0 0
26 56 40 23
For benzene-toluene and benicne n-heptane, operating reflux and plate requirements n ere determined froin graphical 3IcCabe-Thiele constructions. In all other cases calculations n ere made using the Smoker equation Calculations a l e eunimari/cci in Tnblcs I and 11.
suspecting that the relative volatility would influence their correlations, found no e\Tidence for this effect,. Figure 2 shows s - As?, that when the intercept value, __- , is plotted against R,,, a S-tl series of curves are obtained, each of which is related to the relat'ive volatility of the system. For relative volatilities less than 1.25, the slope of the linear plots of Figure 3 can be corrclated by plotting against the relative vo1atilit)-. Calculation of Reflux Ratio and Number of Plates. From Tables I and 11, the resulting curves of the type illustrated in Figure 1 have been grouped together into a family of curvcs, as shown in Figure 4. I n the application of Figure 4, t'he first' step is to decide nhich correlating curve is to be used for the calculation. From R,,, or
Figure 4 gives the appropriate correlating curve and, if R,, and S , are known, either R or S can be calculated. The application of the above method can be illustrated by the three following esamples. SEPARATIOS O F CHLOROBESZEKE AXD H R O l f O B . Young (20) gives the relative volatility of chloro- and bromobenzrne as 1.889. Consider a batch distillation in a 10-theoretical-plate column, where it is desired to calculate the necessary reflux ratio to give an overhead product containing 98.0% chlorobenzene arid a bottoms product containing 11.'7yo of chlorobenxenc. The Underwood equation gives a R,, v:ilue of 9.4 and the Ii'enske equation gives a S , value of 9.3. If the I?,, value of (3.1 is taken, from Figure 2 by- interpolating betmen the curvefi, the intercept for 01 = 1.88!1 is 0.4'7. Prom the raluc of the ST1 correlating curve in Figure 4 correspontliiig t,o intercept value R - Ren s -t-s,,,18. 0.14. For 0.4; and for R + 1 = 0.52, the value of ___S,,= 9.3 this gives a reflux ratio of 20.5, Edge\~orth-Johnslonc ( 8 ) ,using a XcCai,e-Thiclc coristruct,ion, calculated a reflux ratio of 20.0. A comparison is made in Table I11 of the reflux ratios calculated by li:tlgcir-orth-Johnstone (8).using a i\IcC~"ahc-Thiele
1.0
Correlations Provide Rapid and Accurate Calculation of Reflux and Plate Requirements
s-- s, -
R -- R , at zero value of SS.1' R i l can be evaluated froin &her Figure 2 or 3. This intercept on
S , the extrapolated intercept,
I
The results for the benzene-n-heptane system (Table I ) have been expressed graphically in Figure 1. For benzcue-n-heptane separate curves are obtained for varyiii.s tlrgrtw of separation. Similar graphs (riot shown) for the other tahles result in curves having a sixiilar trend. R - Xnz For values of ___- less than 0.05 the cu
s - s,, value of+unity I I2 - R,,, approaches zero. 13y esas S+1 R + l s - s, are obtained trapolation of the curves, intercept values of an
Si-1
I
0
Figure 2 .
I
I
20
40
- R,
-
I
I
80
60
Correlation with Minimum Reflux Ratio
which can be correlated by plotting against t h e ratio of the volatile conmonent in the overheads and bottoms, or against the minimum reflux ratio, R,,,, or the minimum number of plates, S,n. The use of these extrapolated curves does limit the correlation to those values of R greatei than 1.05 E,. Such correlations are shon-n in I'iyuies 2 and 3. When the relatire volatility is greater than 1.25 the correlation of s -' Sm the s inteicept n-ith R,, is probably the 7-1
most convenient. If the relative volatility is less than 1.25, the linear correlation mith S, is the most valuable. Gilliland ( I d ) and Zuiderneg ( Z l ) , although
280
- sm' Figure 3.
Correlation with Minimum Number of Theoretical Plates
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 46,No. 2
ENGINEERING AND PROCESS DEVELOPMENT 07.5
1
\\\
I ” ’
I
I
i
I
I
I
1
025
0
Figure 4.
I
#
1
1
1
0.5
1
1
075
sm
s Correlation of ____ Intercept with Reflux S+ 1 and Plate Requirements
method, those calculated by Gilliland’s correlation, and by the method proposed in this paper. Gilliland’s correlation does not apply to batch distillation. This is not a criticism of the method, since it was developed for continuous distillation.
These examples show that this graphical method for calculating the reflux ratio or the number of plates approaches the accuracy of the Smoker and Dodge and Huffman equations. Although the correlating curves are based on the Underwood, Fenske, and Smoker equations, the method might not have been expected to give such accurate results in view of the ease with which it may be applied. The method can be equally well applied to the separation of key components in an ideal multicomponent mixture if the correct minimum reflux ratio is used. Continuous Distillation and Feed Plate Location. To determine the total number of plates in the distillation column for a given reflux ratio, it is necessary to use the correlating curves of Gilliland ( l a ) or Brown and Martin ( 8 ) . If the total number of plates is known, numerous methods have been proposed for locating the feed plate-Le., hlcCabe-Thiele construction, plate-to-plate analysis, the Smoker equation, and the empirical correlation of Kirkbride (14). It was considered feasible that Figure 4 should be applicable to the location of the number of trays above the feed plate. The feed composition entering the column a t ita boiling point is considered to be the equivalent of a composition in a reboiler in a batch distillation. This is probably best illustrated by the following examples. SEPARATION OF BENZSNE AND TOLUEXE. Consider a continuous still fractionating a mixture of 40.0y0 benzene and 60.0y0 toluene a t a reflux ratio of 3 to 1, so that each product is 99.0% pure. The Smoker and RlcCabe-Thiele methods give 7.9 plates above the feed plate. The total number of theoretical plates is 15.7. The relative volatility a t the feed point is 2.45 and the average value between the feed and overhead compositions is 2.40, R , = 1.65, and S , = 5.6.
s - s,
Comparison of Methods of Calculating Reflux Ratio R
From Figure 2 the intercept is taken as 0.52 and from Si-1 R - R, -+8, = 0.25. S , the number of Figure 4, with -___ as0.34, -
Distillate
Bottoms
a
MoCabe-Thielea
Ellis
Gilliland
0 98 0 98 0 98
0.26 0 175 0 117
1 889 1 889 1 889
7 0
7.0
8.1 19 0
plates above the feed, is 7.8, which is in close agreement with the above result. SEPARATION OF 0-, m- and p-MONONITROTOLUENE. In the srparation of this ternary mixture, Coulson and Warner (6) have shown by plate-to-plate analysis that a reflux ratio of 5 to 1 requires 21 theoretical plates for the specified overhead and bottoms compositions. The number of plates above the feed is 11.0. For the key components, 0- and p-nitrotoluene, the relative volatility is 1.7, R, = 2.23, and S , between the feed plate and over-
Table 111.
a
12 0
12 0
20 0
20 5
31.0
Edgeworth-Johnstone ( 8 ) .
For the separation of oxyS C P ~ R ~ T OF I O OXYGEV N ISOTOPES. gen isotopes, Dodge and Huffman ( 7 ) give a relative volatility of 01 = 1.006. For a distillate composition of 2.54%, a bottoms product of 0.20%, and a reflus ratio of 3920, Dodge and Huffmaq (1)and Smoker ( I ? ) calculated the number of theoretical trays as 521. If R, is taken as 1960 and S, is taken as 430, then from Figure 3, by interpolation and extrapolation, the intercept value of ___ - Sm is 0.58. Csing the appropriate curve of Figure 4,for S + l R m _ _R_ - sm has a value of 0.19. The number of - 0.5> ___
R +1
’s + 1
+
s
; ‘ ;%
head compositions is 7.9. From Figure 2 the
-___
intercept is
0.58, which locates the appropriate curve on Figure 4. From R - R, S - S, Figure 4 for = 0.46, ~= 0.22, such that S = 10.5. R + l Multicomponent Systems. I n continuous multicomponent distillation the presence of other components influences the separation of the key components and the evaluation of their minimum reflux ratio. Figures 3 and 4 can be rapidly applied to the location of the feed plate with a reasonable degree of accuracy if the following procedure is adopted: ~
+
plates obtained by this procedure is 529, which is in close agreement with the above calculated result. SEPI R ~ T I O N OF ~L-HEPTAKE AND ~IETHYLCYCLOHEXANE. In 1. R, is determined using the equation of Underwood (18) the separation of n-heptane and methylcpclohexane (with a relbetween the overhead composition and the composition of the liquid fraction of the feed. The Colburn (6) equation can be ative volatility of 1.07) to give an overhead and bottoms product similarly used for evaluating R,. of 06.0 and 3.33%, respectively, and using a reflux ratio of 1000, 2. For a liquid feed, S, is determined between the ratio of key Dodge and Huffinan ( 7 ) calculated that 105 theoretical plates components in the overhead composition and the ratio in the feed were required. Since R,, = 415 and S, = 97.0, for S, = 97.0 and by using the Fenske (11) equation. I n the case of flash vaporieaS -+S, is 0.35. tion of the feed, S, is determined between the ratio of key coma: = 1.07 from Figure 3 the intercept value of ponents in the overhead composition and the ratio in the liquid fraction of the feed. R - Rm This locates the cun’e on Figure 4, and from = 0.59 the 3. For a liquid feed, S = n 1 and S,, n, 1 are equal R f l to the theoretical and minimum number of theoretical trays above the feed plate. I n the application of Figures 3 and 4 to feed plate is 0.09. This gives the number of plates as value of S + l location the assumption is made that the ratio of key components 105.6, which again is in good agreement with the calculation of in the feed entering the feed tray is the same as that in the liquid leaving the tray above the feed plate. Dodge and Huffman.
-
February 1954
+
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
+ +
281
ENGINEERING AND PROCESS DEVELOPMENT
__ ~~~~~~l~ ~ ~N ~ t. No. of Stages 1 8.8
~Above l Feed Plate R RTn S,& 9.0
Stages abol e Feed Plate
plate andlysi-
2.0
5.G
6.0
Ihwres 3 and 4 6.2 6.1
2
17.0
3.0
1.35
6.5
6.0
3
16.0
1.6
0.93
3.3
6.0
6.2
4
11.0 26.0 29.8
2.0 10.0 32.3
0.9 B.1 .>.S
2.3 9.5 22.0
3.0 13.0 24.2n
3.1 13.6 23.2
5
6
Iteieience Brown and Soudera ( 3 ) ,column 2 . T ~ W 7, p. 1 . ~ ~ 8 Brown and Rouders ( 3 ) , coliinin 5 , Table 7 , p. 1568 ICdinister (G), exaniple 27 !flash vaporization of feed) Robinson and Gilliland ( 1 5 ) ,p. 261 Robinson and Billiland ( 2 6 ' ) , p. 237 Brown and Martin (11.n. 696. CaSP
a
By absorption factor method.
4. \Vith flash vaporization of the feed the number of theoretical trays and nlinimum number of theoretical trays above the feed plate are taken to be n and ntrL. The ratio of key components in the liquid fraction of the feed is assumed t o be the composition of the liqcid leaving the feed plate. 5. If the optimum ratio of key components o n the feed plate is calculated, then, as in step 4,n and nmare the number of theoretical and minimum number of theoretical trays above the feed plate, The results given in T:rl,lP T V indicate the accur,ic.y of the method.
The calculatioii for e.wmple 3 in Table I V is given a s follows: Minimum number of trays abovc the feed plate:
9Zm
+2
=
5.3
111this instance, with flash vaporization ot the feed snd p:titiaI condensation, the minimum number of t l a n above the ircd plittr is 3.3. In the application of Figures 3 and 1,S,, = 3.3 From Figwe 3 for S, 3.3 and CY = 2.35,
For R = 1.5 and R ,
propriate curve is iocltteci in terms of the minimum reflux 01'mininirim number of plates and the relative volatility oi the system. Tho correlatioii can aim he applied to the locatiori -if the feed plarc ill continuouu dist'illatioit . The method is of particular value in the separation ot clofie h o i l i n g c ornpo 1 i ~ ' iti8 I since it C D I ~be rapidly ripplied with an uecuracy of the orciuv of the Hnioker equation
Calculations for Continuous Multicomponent Systems
Table IV.
=
0.95, then, from Figure 4.
Id
Nomenclature = distillate and still composition = rt:liitive volatili1,y
:ELI, ZIT 01
12
n,,,
= =
number of t,heoret,icwl phtel; in column minimum number of theoretical plates in colurriri
s
= n + 1
R R,,,
= = =
SV,
+
n,,, I reflux ratio = O / l > minimum reflux ratio
Literature Cited (1) I3ogar.r, M . J . P., Tmns. ,in,. rt7sl. (,'hem, Engrs., 33, 139 (193;]~ ( 2 ) Brown. C. G., a n d X n r t i n , TI. Z., Ibi'd., 35, 579 (1939). ( 3 ) 13r.ou-n, C. G., a n d Houders, 31.. "Science of Petroleum," 1.01~ 2, p. 1544, London, Oxford U n i ~ e m i t yPress, 1938.
London. 1949, (7) Dodge, B. F.,nnd Iluft'nixn, ,J. It., Is[).I~NI:.CHRM.,29, 14:% (1937). (8) Edgeirorth-Johiistonc, R., Ibid., 3 6 , 1068 (1944). (9) Edmistor, W.C., P e i d e t ~ nEng?., ~ 19, 74 (June 1948). (10) &Xis, Y. I?. AI., T~uras.I n a l . (,'hem. Rngr.c, ( L o n d o n ) , 30, ,jri
1. R., IND. I h c . C(H€:?,I., 24, 482 (19;32)~ E. Ti.,Ibid.. 32, 1220 (1940). J., Andres, D., and Klein, V , A, Trans, .1m. I N S [ . Chena. Erzgrs., 37, 228 (1943). (11) Kirkhiide, C . G., Petiok:um, Refi7?w,23, (15) MrCahe, W.I,..and Thiele, E . W., I, (1925).
Thus the number of plates above the feed tray is 6.2. It would appear that the main advantage for this method of feed plate lowtion is the rapidity with which it can be applied in the preliminary iissessment of ti problem. Summary
Gillilaud's empirical reflux a i d plate correlation has been extended to batch distillation by using a family of curves. The ap-
END
282
(16) Robinson, C. S., a n d Gilliland, E. I
