R. EDGEWORTH-JOHNSTONE
Trinidad Leaseholds L im ited, P o in te-a -P ierre, Trinidad, B. W. I.
A general method is described for calculating yields from batch rectification o f binary mixtures under constant distillate conditions for any given final reflux ratio. The method allows for the effect o f column holdup. Simplified equations are derived for both binary and complex mixtures
which are applicable to certain cases in which holdup is negligible.
A N EA RLIER paper (2) described a method of calculating the A \ final yield of distillate from batch rectification, allowing for the effect of column holdup, when the reflux ratio is continu
ously increased to infinity in such a manner as to keep the distil
late composition constant. This was termed “ batch rectification under constant distillate” (c.d.) conditions. In the present paper a general method is presented for cases where the finat reflux ratio has a finite value. This enables a curve to be plotted showing the relation between final reflux ratio and yield fraction, the Ry curve, which is important to the plant designer.
Such a curve was, in effect, proposed by Bogart (I), who carried out a number of McCabe and Thiele constructions at different re
flux ratios, keeping the distillate composition constant, and plotted reflux ratio against composition of residue. He did not, however, allow for the effect of column holdup.
BLNARY M IX T U R E S W IT H C O LU M N H O LD UP The previous paper (2) showed that the moles of lighter com
ponent A held up in the column is equal to Q2, where Q = total moles of the mixture held up per theoretical plate, and
2 *» ai ■+• ai -f- a » + a.v
It was further shown that in the special case where the reflux ratio is infinite, 2 can be calculated from aP, N, and a.
Consider a batch rectification under c.d. conditions in which the final reflux ratio is only moderately high, so that the yield of
distillate is substantially lower than when the final ratio is infin
ite. The column is assumed to be empty at the beginning of the operation. If it is not, its contents must be added to the charge, and the quantity and composition of the latter modified accord
ingly.
A McCabe and Thiele construction for the desired final reflux ratio gives the final bottoms composition a „; gives the sum of the final plate-to-plate liquid compositions, a: + at + at -f aN = 2 ; and enables Q2, the total column holdup of A, to be calculated. Taking material balances at the end of the batch rectification:
p + W = F - QN TV; -f- TFa„ = Fat — Qx whence
p = p ai **** q 2 Nau o p — aM Op — a„
Substituting y = Pap/Fa, and Q/F — q gives the required yield:
_ Qp[(o/ ~ a .) - q (2 - N o .)) , .
v a, (a, - a„) W
By carrying out a number of computations of a» for different reflux ratios and repeating the above calculations, the complete Ry curve can be drawn, showing the variation of reflux ratio with yield fraction required to maintain a given distillate composition.
I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 1069
R at* S V
4 0.443 8.177 ( - 0 . 3 6 5 )
7 0.260 7.253 0.319
12 0.157 6.552 0.563
20 0.117 6.190 0.659
This is essentially Bogart’s curve (1) corrected for column holdup, except that residue composition is replaced by yield fraction, which is more easily observed during the course of rectification.
Graphical integration of this curve gives the quantity of reflux which must be vaporized for a given yield of distillate, whence the economic limit of reflux ratio can be decided upon.
Ta b l e I. Da t a f o r Ry Cu r v e i n Re c t i f i c a t i o n o f Ch l o r o- b e n z e n e a n d Br o m o b e n z e n e
V i
(- 0 .1 B 8 ) 0.476 0.723 0.803
As an example, take the separation of chlorobenzene and bro
mobenzene, using the volatility data published by Young (4).
Assume N = 10, a/ = 0.40, ap = 0.98, Q/F = q = 0.01. The latter is a high value, taken to exaggerate the column holdup ef
fect for purposes of illustration. For rectification at atmospheric pressure the average value of a is 1.8896.
By carrying out several McCabe and Thiele constructions for different reflux ratios, the corresponding values of o„ are found.
For each value of a» the plate-to-plate compositions a, + a, + a , + on are read off and added together to give 2. y is then calculated from Equation 1. The Calculations are sum
marized in Table I. For comparison with y, the yield fraction taking account of column holdup, a calculation has also been made of y0, the yield fraction for a corresponding value of a« neg
lecting holdup:
_ aP(af ~ a .)
£V(o, - a»)
Figure 1. IFinal] Reflux Ratio vs. Yield Fraction, without and with Column Holdup, for Chlorobenzene-
bromobenzene
These results are plotted in Figure 1. The negative value of y for R => 4 shows that this reflux ratio is below the required initial value. It can, however, be used for plotting the lower end of the Ry curve and saves calculation of the initial reflux ratio. The Ry, curve corresponds to Bogart’s curve, neglecting column holdup.
V A R IA T IO N IN R E L A T IV E V O L A T IL IT Y
In continuous distillation it is legitimate to assume a constant average relative volatility in the column. In batch rectification the value changes during distillation. Plotting a against a . from Young’s data for chlorobenzene and bromobenzene (4), and taking the arithmetic mean of the value in the still (variable) and that at the top of the column (constant), the following values are obtained:
a te 0 .4 0 0 .3 0 0 . 2 0 0 .1 5
a (average) 1.8949 1.8943 1.8894 1.8867
In the example given above, it was found that the use of these values in place of a constant value of 1.8896 produced a change in the Ry curve that was barely visible. If, however, the change in relative volatility during distillation is large, the correct aver
age value should be used for each value of a».
S IM P L IF IE D E Q U A T IO N S F O R B IN A R Y M IX T U R E S For columns having a relatively large number of plates (i.e., in relation to the minimum plates for the particular separation) in which holdup is negligible, simplified equations can be ob
tained requiring no McCabe and Thiele construction. These are derived from Underwood’s minimum reflux equation (S) :
R ^ j
a — 1 \ a „ l — o » /
In batch rectification under c.d. conditions the instantaneous reflux ratio R varies with P, the total moles of distillate received;
i.e., R = dO/dP. a«, is also a function of P. From material balances
Fo, - Pn„
Putting P/F = p and substituting for a»,
R 1 ~ V r
n _s_
a — l\_Of —
a (1 — Op) pnp (1 - Of) - p (1 or substituting the yield fraction y = p (Op/ar),
- « s ) ] (2)
p = ~ F<y r I___________________ q (1 — Op) 1 . . . a - 1 L a/(1 ~ y ) a „( 1 - Of) — y a / (l - a , ) J These equations define the manner in which reflux ratio should vary with p and y, respectively, to maintain a constant distillate composition of ap in an infinite column. They can be applied with fair accuracy to finite columns in which the value of aN+l is greater than about 5000 and holdup is negligible.
The total vaporization required to secure p, moles of distillate per mole of charge, or a yield fraction of y,, can be calculated by integrating Equation 4. Putting R = dO/dP - do/dp,
0 . f Vrl p i J p \ ^ j L ___________ g i L - i ?»)____ "I J O a - \ y a , - p n v (1 - o,) - p (l - o„) J
a/
= a" ~ °f a — 1
» — o + p .
Op - 0/
a — 1
In° / ~ PrOp Op
(1 - O/) - Pr (1 - Op) - p,
In • Of
<V - P^p ir In I -Q / + ■ (1 ~ Of) ~ Pr (1 ~ Op)
1 - a.
(4)
I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y Vol. 36, No. 11
These equations give the total moles to be vaporized per mole of charge in order to produce pr moles of distillate per mole of charge, or a yield fraction of y,, under c.d. conditions. They are applicable to finite columns under the same conditions as Equa
tions 2 and 3—namely, when a w+1 is more than 5000 and holdup is negligible.
S IM P L IF IE D E Q U ATIO N S FO R C O M P L E X M IX T U R E S Similar equations can be derived for complex mixtures. Con
sider a mixture consisting of components A, B, C, etc., from which a distillate is to be prepared containing a relatively high propor
tion of A , the lightest component present. A and B are the key components, and the distillate may, without serious error, be assumed to consist of these components only. Provided the com
ponents obey Raoult’s law, the minimum reflux equation applies to the key components as if they constituted a binary mixture—
that is,
From material balances,
Fa, - P a p Fb, - Pbp
° - - F _ p - ” F - P
Putting bP - 1 — ap and P/F = p, substituting for a» and 6», and integrating as for binary mixtures,
- 1
The above equations are applicable to complex mixtures only when the more volatile of the key components is the lightest ma
terial present. They cannot, for example, be applied to petroleum distillation where the distillate has a relatively wide boiling range.
As an example of the use of these simplified methods, consider the rectification of a commercial mixture containing the following mole percentages of components: benzene, 47.4; toluene, 43.5;
xylenes, 9.1. It is desired to extract 99% of the total benzene in the charge by batch rectification, and the distillate is required to contain 98.0 mole % of benzene. The column to be used has fifteen theoretical plates. Holdup is negligible. A constant boil- up rate will be maintained in the still, and the overhead temper
ature will be held constant, automatically or otherwise, by con
tinuously increasing the reflux ratio as distillation proceeds.
In order to calculate the heat input per gallon of product, and hence the duration and cost of the operation, it is desired to know the total moles which must be vaporized in the still per mole of
temperatures are 2.428 and 2.295, respectively. Hence the aver
age relative volatility in the still over the whole operation is 2362, and the mean between this and the relative volatility at the top of the column is 2.453. This is the value taken for a.
T o check whether the simplified equations are applicable, distillate to secure the desired degree of fractionation of the prod
uct and exhaustion of the charge.
CON CLU SION
The methods presented in this and the previous paper (£) rest upon the observation that under constant distillate conditions the equations for batch rectification are very much simplified. Since these are also the conditions for minimum heat input per pound of distillate (for a given final reflux ratio), they represent the most economical procedure as well. For binary mixtures and for complex mixtures, the distillate from which is required to contain a high proportion of the lightest component, a sensitive overhead temperature controller combined with a constant boil-up rate should automatically give the proper Ry curve.
A C K N O W L E D G M E N T
The author wishes to acknowledge valuable criticism from Arthur Rose and to thank the Chairman and Board of Trinidad Leaseholds Limited for permission to publish this paper.
N O M E N C LA TU R E
The nomenclature used is based upon that of Underwood (5), which has certain advantages over the usual x-y system, es
pecially when applied to complex mixtures, a stands for ,the mole fraction of the most volatile component in the liquid, A for the mole fraction in the vapor. Similarly, b and B refer to the next most volatile component, and so on— for example, a,, b», Cn+i instead of z»/, n P, y „ n + 1. Double subscripts are avoided and the symbols are easier to read. In the present paper the vapor composition symbols are not required, and capital letters are used to refer to components.
A, B, C, =■ components in order of decreasing volatility Q = moles of material held up in column per theoretical
plate
R = instantaneous reflux ratio = dO/dP
y = yield fraction— i.e., moles of distillate obtained divided by moles present in the charge.
y0 = theoretical yield fraction corresponding to y, neglecting holdup
y. = value of y corresponding to p,
a *» average relative volatility of components A and B— i.e., arithmetic mean of values in still and top of column throughout distillation 2 *= sum of plate-to-plate liquid compositions, a, + a, +