By L oren H . S h irk an d R a lp h E. M o n to n n a
Sc h o o l o r Ch e m i s t r y, Un i v e r s i t y o r Mi n n e s o t a, Mi n n e a p o l i s, Mi n n.
D
u r i n g the past five years the rapidly increasing literature in the field of chemical engineer
ing has contained numerous a r tic le s d e a lin g with the theory of fractionation and various equations have been d e v e lo p e d by different in
vestigators for the calculation of the theoretical number of plates or length of column required for a given separa
tion. Most of these equa
tions have been based upon a very limited amount of ex
perimental data, and there is little evidence to show the
engineer seeking to use them for the practical design of stills how well they actually represent the conditions of plant prac
tice. Furthermore, the m ultiplicity of methods leaves the designer in doubt as to which one would give the best ap
proximation of plant conditions and at the same time be the
1 Presented before th e D ivision of I n d u s tria l a n d E n g in eerin g C h em istry a t th e 72nd M ee tin g of th e A m erican C hem ical Society, P h ilad elp h ia, Pa., S eptem ber 5 to 1 1, 1920.
1 A b stracted from a th esis s u b m itte d b y L oren H . S h irk to th e fa c u lty of the G rad u ate School of th e U n iv e rsity of M in n eso ta in Ju n e , 1926, in Partial fulfilm ent of th e re q u ire m e n ts fo r th e degree of m a ster of science in chemical engineering.
e a s ie s t and most rapid to apply to the desired problem.
It seemed desirable, there
fore, to secure experimental data on a scale approaching plant conditions and to apply th e m o s t promising equa
tions to these data for the purpose of finding out which o n e s m o s t nearly approxi
mated the results and how close an agreement was to be expected for the particular system chosen.
T h e s y s t e m water-ethyl alcohol was chosen for study, for several reasons. It is a common commercial mixture and data might be of practical use; results would be more comparable with those of other investigators, m ost of whom have worked with this system; reliable liquid-vapor equi
librium data3 are available for the range covered by this investigation; and finally, simple, accurate, and reliable analytical methods are known. A suitable still was designed and the column constants for different ethyl alcohol-water mixtures were determined with varying and carefully con
trolled rates, of distillation and reflux ratios. Using these constants, the theoretical number of plates required for the
‘ T h i s J o u r n a l , 1 2 , 4 9 6 ( 1 9 2 0 ) ; 1 3 , 1 6 8 ( 1 9 2 1 ) .
T h e variou s proposed r e ctifica tio n e q u a tio n s have b een su b je c te d to c r itic a l a n a ly sis.
T h e m e th o d o f M cC abe a n d T h ie le h a s b een fo u n d to b e th e m o s t p ra ctica l an d a c cu ra te for u se in c o lu m n d esig n .
A n a p p a ra tu s h a s b een d esig n ed to sec u r e th e d ata n e cessa ry for a co m p a riso n o f th e m e th o d s o f c a lc u la tio n o f th e n u m b e r o f p la te s req u ired for a given sep a ra tio n .
D a ta sh o w in g th e over-a ll efficien cy o f a b u b b ler-cap p la te c o lu m n w ith a lc o h o l-w a te r m ix tu r e s u n d er v ariou s c o n d itio n s have b een o b ta in ed .
A m e th o d o f d e te r m in in g th e p ercen ta g e o f a lcoh ol in ex trem ely d ilu te w a ste liq u ors h a s b een d evised .
T h e c r itic is m o f m a th e m a tic a l m e th o d s w h ic h a s s u m e c o n tin u o u s in s te a d o f ste p w ise c o n d itio n s h a s b een sh o w n to be ju stified .
908 I N D U S T R I A L A N D E N G INEE RIN G C H E M IS T R Y Vol. 19, No. 8 separation of the various mixtures was calculated by each of
the chosen methods. A comparison of the methods is thus secured on the same set of data both as regards ease of cal
culation and accuracy of prediction.
The basic equations upon which the theory of fractional distillation of binary mixtures is built have been derived by three different lines of reasoning, all leading to practically the same result. Sorel,4 who did the pioneer work in this
F i g u r e 1— A p p a r a t u s f o r C o m p a r i s o n o f M e t h o d s o f C a l c u l a t i o n o f N u m b e r o f P l a t e s R e q u i r e d f o r a G iv e n S e p a r a t i o n
field, derived his equations from material balances. A sec
ond method which was essentially the same in theory and gave similar results, was that of Gay,5 which was based en
tirely on heat balances. The latest procedure, which has a somewhat different foundation but gives the same type of
■equations, is Murphree’s method6 based on the gas absorp
tion equations of Lewis and Whitman.7
These fundamental equations have been applied to the
■calculation and design of fractionating columns in four dif
ferent ways. These methods are (1) the algebraic stepwise procedure, which was used by Sorel,4 Gay, 5 and Murphree, 6 (2) the graphical stepwise method, used by Rodebush,8 Mc
Cabe and Thiele,9 Murphree, 10 Ponchon,11 and Savarit,12 (3) the use of graphical integration as employed by Lewis13 and Leslie;14 and (4) Peters’ method, 15 which consisted in
< C o m p t.rcn d ., 108, 1 1 2 8 , 1 2 0 4 , 1 3 1 7 ( 1 8 8 9 ) ; 118, 1 2 1 3 ( 1 8 9 4 ) ; see also
“ L a R ectificatio n <lc t ’A Icool," P aris, 1 8 9 3 .
* C him ie b> industrie, 3, 1 5 7 ; 4 , 1 7 8 , 7 3 5 ( 1 9 2 0 ) ; 6, 5 6 7 ( 1 9 2 1 ) ; 1 0 , 8 1 1 , 1 0 2 6 ( 1 9 2 3 ) .
* T h i s J o u r n a l , 1 7 , 7 4 7 ( 1 9 2 5 ) .
* Ib id ., 16, 1 2 1 5 ( 1 9 2 4 ) .
• Ib id ., 1 4 , 1 0 3 6 ( 1 9 2 2 ) .
• I b i d ., 17, 6 0 5 ( 1 9 2 5 ) .
>» Ib id ., 1 7 , 9 6 0 ( 1 9 2 5 ) .
t> Tech. moderne, 13, 2 0 , 5 5 ( 1 9 2 1 ) .
11 C him ie &* industrie, 9, Special N o ., M ay , 1 9 2 3 , p. 7 3 7 .
» T h i s J o u r n a l , 1 4 , 4 9 2 ( 1 9 2 2 ) .
11 “ M o to r F u e ls,” p. 70, C hem ical C atalo g C o., In c ., N ew Y o rk , 1923.
Js T h i s Jo u r n a l, 1 5 , 4 0 2 ( 1 9 2 3 ) .
combining the liquid-vapor equilibrium equation with the basic equations of distillation and mathematically integrating the combined equation so obtained. None of the methods representing the first class was applied to the data because, although mathematically exact, they are obviously too long and involved to warrant their use in engineering practice.
The graphical methods of the second class appeared rapid and easy to apply and three of these were applied to the data—
viz., those of Rodebush, McCabe and Thiele, and Murphree.
Both representatives of the third class, the methods of Lewis and of Leslie, were used because of the variation in their method of integration, and finally Peters’ method was tried as representing the fourth procedure.
The work of Van N u ys16 consisted of a lengthy mathe
matical presentation of the principles of rectification, which serves excellently as a study of the factors involved but is unnecessarily complicated for practical use. The best ex
perimental work has been that of Peters,17 who used Lewis’
method13 of calculation, and that of Calingaert and Huggins18 on packed columns using Peters’ modification15 of Lewis’
formula. Peters does not give sufficient data to make his experimental work available for calculation by other methods, while that of Calingaert and Huggins applies only to packed columns. Clark S. Robinson19 attempted a test of the effi
ciency of a plate column, but his results are less valuable except as a method of conducting tests, because he did not determine the percentage of alcohol in the waste liquor.
A p p aratu s
The apparatus (Figure 1) was especially designed with the view to securing the necessary data easily. It consisted of an iron pot still, A , heated by a paraffin bath over a gas plate, I, and carrying a nine-plate cast-aluminum col
umn, D. The reflux condenser, E, was provided with a take
off to the product condenser, G and II, while the refluxed liquor returned to the top plate of the column through the trap, R, where it was measured by an orifice meter. The column and vapor pipes were lagged with one-inch magnesia covering and the latter was wound with a chromel-wire heat
ing element as an additional precaution against condensation.
F i g u r e 2— D e t a i l s o f P l a t e s
The feed tank, F, was equipped with a float gage and level indicator, / , for determining the rate of feed flow, and de
livered into a constant-head tank, C, where it was preheated to the boiling point by means of a steam coil. The heated feed passed through the regulator valve, V, into a trap lead
ing into the third plate from the bottom of the column. A sight glass in the constant-level tank enabled the operator to keep the feed under constant head. The waste liquor was removed through the siphon, B, and flowed through a cooler condenser, IF. A recbrd of still temperature was kept by
I* Chem. M et. E ng., 2 8 , 2 0 7 , 2 5 5 , 3 1 1 , 3 5 9 , 4 0 S ( 1 9 2 3 ) . 17 T h i s J o u r n a l , 14, 4 7 6 ( 1 9 2 2 ) .
'» Ib id ., 16, 5 8 5 ( 1 9 2 4 ) .
■< Ib id ., 14, 4 8 0 ( 1 9 2 2 ) .
August, 1927 I N D U S T R I A L A N D E N G IN E E R IN G C H E M IS T R Y 909 the recording thermometer, T, and readings were periodically
taken of the temperatures in the constant head tank, the top plate of the column, the top of the vapor line, a n d th e waste liquor siphon to record operat
ing conditions during the run.
Details of the plates are shown in Figure 2.
They were of the bub- b l e - c a p t y p e w i t h slotted bell caps, one c a p on e a c h p l a t e . Vapor pipes were one inch in diameter. An average depth of 15/s inches of l i q u i d w a s kept on each plate by t h e o v e r f l o w t u b e s , which were inch in diameter. T h e ca p s averaged thirty-seven slots, V i6 inch wide and l/ i inch long. There were D /s i n c h e s of liquid over the top of the slots. The plates were 9 by 5 inches by 4*/= inches high outside and were 7/ i 6 inch thick.
O p eration o f S till
The still was run for about 3 hours before any readings were taken to insure the establishment of uniform condi
tions. D ata were then collected over a period of 2 hours.
All runs used in the calculations were made in duplicate.
The feed was regulated by setting the valve V and the waste liquor by the siphon valve, B, so that input and output (prod
uct plus waste liquor) were approximately equal. The regu
lation of the flow of ■waste liquor by means of a siphon was difficult, so that there was some accumulation in the still.
Also, the float gage and level indicator, J, did not prove a very satisfactory way of measuring rate of feed input. A material balance between the measured and calculated quan
tities of feed, waste, and product showed, however, that the actual output of the still was within less than one per cent of the liquor fed. Better methods of measuring feed and waste liquor flow will be devised for further work with this appa
ratus. The rate of distillation was controlled by the rate of heating with the gas burner, 7. The reflux condenser was entirely separate from the product condensers to allow of more accurate control. The rate of reflux was kept con
stant by controlling the flow of cooling water with the valve S so that the differential reading across the flowmeter gage, R, remained constant. The flowmeter was calibrated after each run to determine the flow at that reading of the gage.
The chromel heating unit was regulated by means of the lamp-bank resistance, K , to keep the temperature of the vapor pipe slightly above that of the top plate. The feed was kept constant by setting the valve V so that the desired rate of feed was obtained and maintaining a constant level in the sight glass of the tank C by regulating the flow through the valve V from the feed storage, F. At the end of the run the
■distillate and waste liquors were analyzed.
A n a ly tic a l M eth o d s
The alcohol used in the runs was c. p. 95 per cent ethyl alcohol. All percentages down to 0.5 per cent were deter
mined directly by means of the Zeiss immersion refractometer.
Below 0.5 per cent accurate analysis was impossible and a method had to be devised to analyze the extremely dilute waste liquors with accuracy. The apparatus (Figure 3) con
sisted of a 5-liter flask, B, heated by an oil bath, A , and carry
ing a 30-inch (76-cm.) modified Iiempel column, l l/ t inches (3.2 cm.) in diameter, filled with pieces of glass tubing 1/ i inch (6 mm.) long. The column delivered through two 24- inch (61-cm.) Liebig condensers into a graduated flask.
Four liters of the liquid to be analyzed were placed in the flask and 500 cc. distilled off. The heat was regulated so that this distillation required 90 minutes. The alcohol in the distillate was determined by the refractometer and refer
ence to the calibration curve (Figure 4) showed what per
centage of that present in the original waste liquor this amount represented. The calibration curve was secured by accu
rately weighing out varying concentrations between the lim
its of 0.6 and 0.02 per cent alcohol. Three or four determi
nations were made at each concentration and the percentage recovery was averaged. The results were plotted (Figure 4) and gave a smooth curve showing the percentage recovery to be expected by distilling over a 500-cc. portion. The method was checked by analyzing unknown solutions and gave a variation of less than one per cent. Below the limit of 0.02 per cent the concentration of alcohol in the distilled sample was too low for accurate determination with the refractometer, but the waste liquor in these experiments was always above that figure. The use of this method eliminated a criticism of the work of other investigators where this value was only roughly estimated or not deter
mined at all.
D isc u ssio n of R e su lts The observed data are recorded in Table I and the results of the c a l c u l a t i o n s in Table II. The col
umn efficiency (Table II) is the total num
ber of t h e o r e t i c a l plates calculated by McCabe and Thiele’s m e t h o d divided by the actual number of plates used and ex
pressed as per cent.
This represents the over-all efficiency of the column and, al
though accurate as a criterion of the differ
ent methods of calcu
l a t i o n , i t unfortu
nately throws no light on the possible varia
tion in plate efficiency throughout t h e c o l umn. Since no de
t e r m i n a t i o n of the actual feed-plate con
centration was made in most of the experi
ments, the calculated n u m b e r of p l a t e s
represents the sum of the numbers theoretically required above and below a point in the column where the concen
tration of liquid was equal to that of the feed. The calcu
lated rates of feed and waste are given because the observed
F ig u r e 3— A p p a r a t u s f o r A c c u r a t e A n a ly sis o f E x t r e m e l y D i l u t e W a s te L iq u o rs
-C 8
^ 0. 5
$
!
O
£
$
Percent of Total Alcohol Recovered 'in D istilla te
910 I N D U S T R I A L A N D E N G IN E E R IN G C H E M I S T R Y Vol. 19, No. 8 rates, owing to accumulation in the still, are not directly
applicable and the calculated rates have been found to check the actual feed and waste within less than one per cent.
The results of calculating over-all column efficiencies by five different methods are summarized in Table III. Those experiments were chosen for calculation which were con
ducted under widely varying conditions of reflux and rate of distillation and on which m ost reliable data were available.
Table III reveals at once that the graphical methods give results which more nearly approximate the actual condi
tions than do the mathematical methods.
T a b le I— O bserved D a ta
Of all the methods thus far advanced, the graphical method of McCabe and Thiele has been found to be the best adapted to practical use. It is equally accurate as the other graph
ical methods except at very high rates of distillation and low reflux (runs X II and X III)—i. e., where the number of plates is small—and it is much the simplest and most rapid. The only data necessary are the liquid-vapor equilibrium curve, the composition of the product, feed and waste liquor, and the reflux ratio. The method requires only one simple substitu
tion and straight-line geometrical construction. It posses
ses the additional advantage of permitting correction in com
putation in cases where the feed is not at the boiling point when it enters the column or in cases where two feeds are used.
Rodebush’s graphical method most closely approximated the actual conditions. With a small number of plates (small reflux or fast rate of distillation) it gives slightly better re
sults than does McCabe and Thiele’s method, but this ad
vantage is more than offset by its more complicated pro
cedure. The variation m ay be easily understood when it is remembered that graphical computation by Rodebush's
overlapping m ay result in one plate more in the column total, which means a noticeable percentage difference if the num
ber of plates is small. Rodebush’s method requires the same data as that of McCabe and Thiele, but more mathematical transformations m ust be made and the geometrical con
struction is more difficult so that it is more time-consuming.
In general, however, graphical methods are preferable to mathematical methods, both for accuracy and for ease of use.
The two previous methods are developed from the equa
ful for calculations when two or three volatile components are distilled, but is needlessly complicated for use with binary mixtures. The fact that mathematical development upon an entirely different basis leads to the same results, however, increases the confidence in the correctness of the assumptions upon which the theory of fractionation is founded.
Lewis’ mathematical method of calculation assumes an infinitesimal rate of enrichment in the column instead of a stepwise process such as is assumed in the above graphical methods. That Lewis recognized this assumption as an approximation is shown by his use of the words “substan
tially identical”20 in deriving his differential equation. For this reason the method gives low values of K (runs VI and V II) when a small number of plates are used—i. e., high rate of distillation or low reflux. This substantiates the crit
icism of McCabe and Thiele9 that "the larger the number of plates, the more accurate is this (Lewis) method, but for columns of but a few plates the error introduced by assuming continuous for stepwise conditions is appreciable.” Lewis’
method has been used extensively and his equations serve as a basis for several other methods of calculation. It is very much simpler than Sorel’s method, but requires con
siderable time to apply so that it is not recommended over the graphical methods discussed above.
The equations derived by E. H. Leslie, using a stepwise balance of heat and material and adopting weight instead of mol fraction basis, are rather more lengthy than Lewis’ method but give results more nearly like the graphical methods.
This is probably due to the stepwise method of plotting the enrichment curve for graphical integration. Leslie’s method of plotting, however, required more time to apply to a given the lower end as in the method of McCabe and Thiele. This
set of conditions than any of the other methods, and the re
sults expressed as fractions of a plate are not more useful than the whole number of plates given by the graphical meth
ods, since practical use requires the addition of one more
*> T h i s J o u r n a l , 1 4 , 494 (1922).
August, 1927 I N D U S T R I A L A N D E N G IN EE RIN G C H E M IS T R Y 911 whole plate. The nomenclature employed is extremely
simple and this method m ight be used to check the graphical results when extreme accuracy is desired. In ordinary prac
tice, however, the tim e required for its use is not justified by its final accuracy.
T a b ic I I I — O v e r-A ll C o l u m n E ffic ie n c ie s b y F iv e M e th o d s Co l u m n Ef f i c i e n c y Wi t h Va p o r Re M c C a b e
d r a w a lof u p f l u x a n d R o d e - M u r
-Run Pr o d u c t Co l u m n Ra t io T h ie le Lew is L e s lie b u s h p h r e e
G rains pe r h o u r % % % % %
VI 1 2 3 7 4 9 7 0 3 . 0 2 4 0 1 0 . 7 6 3 0 . 6 1 4 0 4 0
IX 8 0 9 . 5 3 0 0 5 2 . 7 1 6 0 2 7 . 8 6 5 4 . 4 3 6 0 6 0
XI 1 0 9 5 5 2 8 0 3 . 8 2 7 0 2 2 . 2 0 6 5 . 3 7 7 0 7 0
X I I 1 5 0 4 . 5 4 7 1 0 2 . 1 3 3 0 8 . 3 2 2 1 . 1 4 4 0 3 0
XIII 1 1 0 7 3 3 0 0 1 . 9 8 5 0 3 1 . 4 0 4 4 . 1 0 6 0 5 0
X IV 0 9 4 3 8 9 0 4 . 0 0 9 0 7 5 . 5 0 9 0 . 0 0 9 0 9 0
The equations derived by Peters16 from the Clausius-Cla- peyron equation contain a number of errors which yield ex
pressions incapable of solution when the required values are substituted. His derivations have been carefully followed and corrections made where errors were found. The cor
rected equations give values which check those obtained by the use of Leslie’s method very closely for the number of plates in the rectifying column. For the exhausting column, however, even when the necessary corrections are made, the equations give an absurd result or in some cases an expression incapable of solution. This probably means that the funda
mental assumptions upon which they are based are wrong.
However, no attempt was made to check the derivation of
However, no attempt was made to check the derivation of