T R IN ID A D L E A S E H O L D S , L T D ., P O I N T E - A - P I E R R E , T R I N I D A D , B . W . I .
R
OSE, W elshans, and Long (5) and Colburn and S team s (2) published m ethods of calculating th e distillation curve of a b in a ry m ixture subjected to b a tc h rectification, where th e effect of column holdup is recognized. In both cases a constant reflux ratio is assumed so th a t th e dis
tillate composition varies continually.
In practice th e im p o rta n t question usually is, how m uch dis
tillate of a given com position can be obtained from a gi\ren charge? To conserve h ea t, common practice is to s ta rt w ith a low reflux ratio an d increase it as th e cutting point is ap
proached; th e com position of th e distillate is th u s m ain
tained approxim ately constant a t th e desired value through
out the distillation. U nder these conditions th e yield of dis
tillate cannot readily be com puted by m ethods which sta rt by assuming a constant reflux ratio.
Two factors reduce th e actual yield of distillate below 100 per cent—incom plete fractionation and column holdup. The relative im portance of these factors varies w ith circum stances and governs th e type of colum n w hich will be m ost efficient for a p articular d u ty . F or example, packed columns usually have a m uch lower holdup th a n plate columns of equal frac
tionating ability; b u t th e num ber of theoretical plates which can be economically provided in a packed column is limitée by the well-known channeling effect, which increases w ith the height of th e column. In certain circum stances, however, the holdup effect m ay be preponderant, so t h a t a packed column w ith relatively few theoretical plates and low hold
up will give far b e tte r yields th a n a plate column w ith m any more theoretical plates and a higher holdup. I t does no t seem possible by existing m ethods to decide upon th e m ost a vantageous arrangem ent w ith o u t long and tedious calcu a- tions, and th e n only in th e case of bin ary m ixtures.
Equations are developed here w hich give th e yield from batch rectification directly and ta k e into account b o th t e factors m entioned above. T h e basic assum ption is th a t t i e reflux ratio is progressively increased th ro u g h o u t th e distilla
tion, so as to m ain tain th e distillate com position constant and reaches infinity a t th e cu ttin g point. T he assum ption o
constant distillate composition perm its th e final distribution of com ponents to be com puted from conditions a t th e cutting p oint alone, using th e com paratively simple equations appli
cable to to ta l reflux. The m ethod can be extended w ith good approxim ation to complex m ixtures.
B IN A R Y M I X T U R E S
Consider first an ideal column having N theoretical plates and no holdup. A b atch of F moles of a binary m ixture, in w hich th e mole fraction of th e more volatile com ponent (A) is aj, is distilled w ith progressively increasing reflux ratio to m aintain th e distillate composition constant a t ap. This m ay be done b y keeping th e overhead vapor a t constant tem pera
tu re b y autom atic control; a constant rate of h e a t in p u t to th e still is also m aintained. If tem perature control is no t sensitive enough, B ogart’s m ethod (I) of calculating how th e reflux ratio should vary m ay be applied. Such conditions will henceforth be referred to as constant distillate composition (C. D. C.) conditions. A t th e end of the distillation th e reflux ratio is infinity.
F or to ta l reflux th e Fenske equation (4) applies, and th e com position of th e b ottom s is, therefore,
Clp
a“ = a'v + 1 ( 1 - ap) + ap
F rom m aterial balances a t th e end of th e distillation, p + w = F
Pap + Waw = Fcif S ubstituting for a» and simplifying,
T he to ta l q u a n tity of distillate of com position av contained in th e original charge is F (a //a p). D ividing b y this q u an tity gives th e yield fraction as shown in E qu atio n 1.
4 0 8 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 V o l. 3 5 , N o . 4
V = XN+ 1 _ i (1)
This equation represents the yield from an ideal column having no holdup. I t is less than unity owing to incomplete fractionation—i. e., because
N
is finite and a certain quantity of A m ust therefore rem ain in the still.Now consider an actual column having a holdup of
Q
moles per theoretical plate with other conditions the same as for the ideal column. At the beginning of the distillation the column is assumed to be em pty. The final bottom s composition, a», is the same as for the ideal column, bu t there is held up in the column
NQ
moles of a mixture, the average composition of which lies between aw and ap. To calculate the yield fraction it is necessary to find the average composition of this mixture, deduct the total moles of A and B held up from those present in the original batch, correct F and a, accordingly, and insert these corrected quantities in Equation 1.
If Q2 represents the total moles of A held up in the column, th e m aterial balance equations become:
P + w = F - NQ term s of product composition. Substituting according to the Fenske equation:
- K i b ,og[
i +flp( c 1)
Hi - op) + Op] (2) This expression was derived by integrating between 1 and N theoretical plates, assuming a continuous change of com
position. Hence it is strictly valid only for packed columns.
F or a plate column it gives a value of 2 somewhat too low.
This can be seen b y p u ttin g
N
= 1, when for a plate column 2 should be num erically equal to ax = aP/ [ a ( l — aP) + aP],The correct value for plate columns is found by integrating between 0.5 and
(N
+ 0.5) theoretical plates:fect of vapor on the average composition of th e m aterial held up. According to Underwood (6), th e Fenske equation m ay be applied to all binary m ixtures in which th e components can be assumed to have a constant average relative volatility throughout the distillation, even though th e y do no t conform to R aoult’s law.
portion of A is required to be separated by b atch rectification under C. D. C. conditions. A an d B are th e key components, and the distillate m ay, w ithout serious error, be assumed to consist of these com ponents only.
Provided the key com ponents obey R a o u lt’s law, the
The im portant difference betw een b inary and complex mix
tures lies in the effect of column holdup. Consider a complex
As"
A
j-st'0
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
mixture an d a corresponding binary m ixture in which the relative proportions of A an d B are th e same. F moles of the complex m ixture contain m uch less of com ponent A th a n F moles of th e b in a ry m ixture owing to th e presence of the heavier com ponents. Y et a t th e end of th e distillation the am ount of A held up in th e column from th e complex m ixture will be nearly as great as th a t from th e bin ary m ixture.
Therefore th e reduction in yield fraction due to holdup will be much greater in th e case of th e complex m ixture.
April, 1943
consist principally of th e key com ponents. The holdup of A in th is region is th u s practically the same as th a t w ith the corresponding binary m ixture. Lower down th e column sub
stan tial concentrations of heavier com ponents appear, which reduce th e holdup of lighter com ponent per theoretical plate below th e value obtaining for th e corresponding binary mix
tu re. B u t since th e holdup per plate in th a t region is al
ready low, th e effect on th e to ta l q u a n tity of d istillate held up is slight.
C o u rte sy , F o s te r W h e e ler C o rp o ra tio n
S te d m a n B a tc h D is tilla tio n U n it a t T r in id a d
The fact th a t nearly as m uch of com ponent A is held up from th e complex m ixture as from a corresponding binar}
mixture is easily understood when it is rem em bered th a t t e lighter com ponent is held up chiefly in th e to p few p a es.
Here, even w ith th e complex m ixture, b o th liquid and vapor
T a b le I
p l a t e M o le F r a c t i o n (fr o m U n d e r w o o d C u rv e s ) N o . H e x a n e H e p t a n e O c ta n e D is tilla te
21
3 4 56
7 T o ta l f o r 7
p la te s
0 .5 4 0 .3 4 5 0 .1 8 0 .0 9 5 0 . 0 4
0.02 0.01
NU__
0.690
0 . 4 6 0 .6 4 0 .7 8 5 0 .8 2 5 0 . 7 9 0 .6 6 5 0 .4 9 0 . 3 0
NU
0 .0 1 5 0 .0 3 5 0 .0 8 0 . 5 0 0 .3 1 5 0 . 5 0 0 . 7 0
M o le F r a c t io n H e x a n e fo r C o r r e
s p o n d in g B in a r y M ix t.
0 . 5 4 0 .3 5 0 0 .1 8 6 0 .1 0 3 0 .0 4 8 0 .0 2 9
0.020 NU__
0 .7 3 6
An illustration is the plate-to-plate com putation of U nder
wood (6) for a m ixture of hexane, heptane, octane, nonane, and decane; th e column holdup of hexane m ay be com pared w ith th a t which would occur w ith th e corresponding binary m ixture of hexane and heptane. _ .
Only th e first seven plates need be considered, since below them th e hexane concentration is negligible. In th is region th e only com ponents present in appreciable q u a n tity are hex
ane, heptane, and octane as shown in T able I. T he to ta l column holdup of hexane for th e five-com ponent m ixture is th u s only 6 per cent lower th a n th a t for th e corresponding bin ary m ixture.
I n view of th e relatively sm all proportion th e q u a n tity ol m aterial held up in th e column norm ally bears to th e to ta l q u a n tity of distillate, a reasonable approxim ation in Hie case of complex m ixtures is to assum e th a t th e value of 2 is th e same as th a t calculated for th e corresponding bin ary mix
tu re. T his is given by E quations 2 or 3 according as the column is of th e packed or plate v ariety. In other words, th e i nocimorl tn r>r>nt,nin A and B only.
410 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 V o l . 3 5 , N o . 4
com ponents in order of decreasing volatility mole fraction of com ponent A in charge, distil
E f f e c t o f T e m p e r a t u r e
o n
L i q u i d - L i q u i d E q u i l i b r i u m
B E N Z E N E —A C E T O N E —W A T E R S Y S T E M A N «
D O C Ö S A N E - 1 . 6 - D I P I I E N Y L H E X A N E —F U R F U R A L S Y S T E M
S ta n fo rd W. B rig g s 1 Edw ard W. C om in gs
U N I V E R S I T Y O F I L L I N O I S , U R B A N A , I L L .
R
E C E N T articles u , 5) have pointed out th e expanding application of solvent extraction to industrial separations and have stressed th e value of liquid-liquid phase equilibrium studies. A wide variety of ternary system s has been investigated, but the m ajority of th e work has been con
fined to a single tem perature. No relatively complete study of th e effect of tem perature on equilibrium for a system th a t is likely to be used in extraction has been published in the readily available literature. T em pera
ture has a m arked effect on liquid-liquid phase equilibrium . T his effect on tw o sepa
rate systems was determ ined, and its conse
quences are discussed.
Phase equilibrium d a ta for th e system s benzene-acetone-water an d docosane-1,6- diphenylhexane-furfural over a range of tem peratures are reported. T he former sys
tem appears to be representative of m any involved in recovering solvents from aqueous solutions by extraction. T h e la tte r is re
lated to th e complex system s encountered in the solvent refining of lubricating oil.
Special experim ental m ethods which are particularly useful in dealing w ith volatile materials were developed.
1 P r e s e n t a d d r e s s , M e r c k & C o m p a n y , I n c ., R a h w ay, N . J .
E x p e r im e n ta l E x tr a c to r C o lu m n U sed a t t h e L a b o r a to r y o f
M e r c k & C o m p a n y , I n c .
4 1 2 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 V o l. 3 5 , N o . 4
B E N Z E N E -A C E T O N E -W A T E R
Reagent-grade acetone, distilled water, and reagent-grade benzene were used w ithout further purification or prepara
tion. Refractive indices of these materials showed no deviations from values given in the literature.
F ig u re 1. E x p e r im e n ta l G lass T u b es
A .
D .
T u b e f o r c l o u d - p o i n t a n d m o s t o f t i e - l i n e d a t a .
T u b e A * f ille d . T u b e f o r d e t e r m i n i n g
t i e l i n e s i n s y s t e m d o c o s a n e - d i p h e n y l - h e x a n e - f u r f u r a l a t 80°
a n d 115° C .
T u b e D f ille d a n d i n p o s i t i o n t o r e m o v e s a m p l e o f t o p la y e r .
Two different procedures were used, one for determining the tem perature a t which a solution of known composition was saturated, the other to obtain the compositions of two liquid phases in equilibrium. The determination of the tem perature of saturation was obtained by the sealed tube technique {!) . This method consisted in observing the
tem-perature a t which a cloud formed in a single-phase liquid of known composition. The determ ination of th e compositions of pairs of liquid phases in equilibrium , or the tie lines, was obtained by sampling these phases after equilibrium had been reached a t constant tem perature. T he samples were ana
lyzed by determ ining the refractive indices w ith a Zeiss Abbe refractom eter.
Glass tubes, about 5-10 cc. in volume (Figure 1A and B), were used for determ ining the satu ratio n tem perature.
Acetone, water, and benzene were m easured into a tube from carefully calibrated pipets and th e tube was sealed. Because of the small effect of tem perature on solubility in this system, compositions had to be selected w ith care in order to obtain a cloud point. The tube was ag itated in a stirred liquid bath while the tem perature was gradually lowered from a point above th a t necessary for m iscibility to th e point a t which a cloud formed due to th e separation of a second liquid phase.
The latter point was recorded as th e cloud point tem perature (Table I).
Binodal curves representing th e boundary between the single-phase and th e tw o-phase regions were constructed at 15°, 30°, and 45° C. by graphical interpolation of the cloud point data. P a rt of the d ata was divided into groups, each w ith a constant ratio of benzene to acetone. T he d ata in each single group resulted in a straig h t line when plotted as log of per cent w ater against th e reciprocal of th e absolute tem pera
ture of the cloud point. Similarly, another p a rt of the d ata was divided into groups in each of w hich th e ratio of acetone to w ater was constant and th e corresponding curves of log of per cent benzene vs. th e reciprocal of th e absolute cloud point tem perature were p lotted. T he two sets of curves are shown in Figure 2. Com positions a t 15°, 30°, and 45° C. from these curves, as well as cloud points which did not fall in these groups and th e d a ta of o ther investigators (2), were used to determ ine th e binodal curves shown in Figure 4 and Table I II .
Tie lines were determ ined b y preparing two series of syn
thetic mixtures of known com position in th e two-phase re
gion. One series was rich in benzene; th e other, rich in water. Each m ixture was sealed into a tu b e as in measuring cloud points, and the m ixture was brought to equilibrium by shaking in a constant-tem perature b a th . T he tip of the tube was then broken open, a sample of th e upper phase was transferred to th e refractom eter b y m eans of a long-nosed
F ig u r e 2. C orrelation o f Cloud P o in t Data f o r System Bensene-Acetone-W ater
L e f t , c o n s t a n t r a t i o o f b e n r e n e t o a c e t o n e ; r i g h t , c o n s t a n t r a t i o „ f w a t e r t o a c e t o n e .
A p r i l , 1 9 4 3 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 413 th e former was interm ediate between the refractive indices of th e benzene phases of th e la tte r. These three m ixtures are
4 1 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 V o l. 3 5 , N o . 4
ACETONE
F igure 3. C o n s tr u c tio n o f T ie L in e s in B e n ze n e - A c e to n e -W a te r S y s te m
tween Wi and determined by linear interpolation on the basis of th e refractive indices of the benzene phases. The intersection of this tie line with the benzene-rich branch of the binodal curve gave a good approxim ation of the com
position of the benzene phase which separated from mixture B. The composition of the benzene phases from the other benzene-rich mixtures was similarly determined. This gave the relation between refractive index and composition along the benzene-rich branch of the binodal curve. A like pro
cedure was followed for each of the water-rich mixtures, resulting in the relation between composition and refractive index along the water-rich branch of the binodal curve.
These preliminary calculations allowed the composition of the benzene-rich layer to be plotted against th a t of the water- rich layer in equilibrium with it; the conjugate curve a t one tem perature was thus obtained. This curve was smoothed and used as a basis for repeating the entire
calculation which led to the tie lines given in Table IV. The conjugate curves are shown in Figure 4 and the corresponding equilibrium curves in Figure 5.
D O C O S A N E -D IP H E N Y L H E X A N E -F U R F U R A L
Docosane was synthesized by the Kolbe electrolytic oxidation of lauric acid. Its re
fractive index a t 45° C. was 1.4358, and its kinem atic viscosities a t 45° and 85° C. were 6.03 and 2.84 centistokes, respectively. 1,6- Diphenylhexane was m ade b y a Friedel-Crafts condensation of adipyl chloride with benzene, followed by pressure hydrogenation with copper chromite catalyst. Its refractive index a t 20° C.
was 1.5381, and its kinem atic viscosities a t 45° and 85° C. were 8.36 and 2.34 centistokes, respectively. F urfural was obtained from E a st
m an K odak Com pany. I t was vacuum-distilled w ithin one or two days before use. Its refrac
tive index was 1.5259 a t 20° C.
Cloud points were determ ined in essen
tially the same m anner as in the previous system . The tubes were smaller and the m aterials were weighed into them . To limit the decomposition of furfural, the tem pera
ture was m aintained in th e vicinity of the cloud
point for only a short time. Cloud point d ata are given in Table V.
The construction of the binodal curves m ay be understood by reference to Figures 6 and 7. T he cloud points of doco- sane-furfural m ixtures are plotted in Figure 6. For each mixture containing diphenylhexane, the cloud point a t the same per cent furfural was tak en from th is curve. The pairs of points were plotted as log of per cent docosane, on a furfural-free basis, against th e reciprocal of th e absolute cloud point tem perature. A and A ' (Figure 7) are such a pair. A is an experim ental point, an d A ' is th e point from Figure 6 which has th e same per cent furfural as A. A straight line through A and A ' represents fairly accurately the solubility tem peratures of m ixtures having this same per cent furfural. A nother experim ental point, B, having a
T a b le IV . T ie L in e s in B e n z e n e - A c e t o n e - W a te r S y s te m
B en z en e P h a s e C o m p n ., W t. %
W a te r P h a s e C o m p n ., W t . %
R a tio , A ce
to n e in B e n z e n e /A c e
B en A ce B e n A ce to n e in
zene to n e W a te r zen e to n e W a te r W a te r
T e m p e r a t u r e , 15° C .
9 5 .2 4 . 7 0 .1 0 .1 5 . 0 9 4 .9 0 .9 4
8 9 .0 1 0 .8 0 . 2 0 .1 1 0 .0 8 9 .9 1 .0 8
7 3 .4 2 6 .1 0 . 5 0 . 3 2 0 .0 7 9 .7 1 .3 0
5 5 .2 4 3 .0 1 .8 0 .7 3 0 .0 6 9 .3 1 .4 3
3 9 .1 5 6 .5 4 . 4 1 .4 4 0 . 0 5 8 .6 1 .41
2 7 .6 6 3 .9 8 . 5 3 . 2 5 0 .0 4 6 . 8 1 .28
T e m p e r a t u r e ,COO o d
9 4 .0 5 . 8 0 . 2 0 .1 5 . 0 9 4 .9 1 .16
8 6 .7 1 3 .1 0 . 2 0 . 2 1 0 .0 8 9 .8 1 .31
6 8 .7 3 0 .4 0 . 9 0 . 4 2 0 .0 7 9 .6 1 .5 2
4 9 .8 4 7 .2 3 . 0 0 . 9 3 0 .0 6 9 .1 1 .57
3 4 .5 5 8 .9 6.6 1 .8 4 0 . 0 5 8 .2 1 .4 7
2 3 .9 6 4 .1 1 2 .0 4 .1 5 0 .0 4 5 . 9 1 .28
T e m p e r a t u r e , 4 5 ° C .
9 2 .9 6 .9 0 . 2 0 . 2 5 . 0 9 4 .8 1. 38
8 4 .0 1 5 .6 0 . 4 0 . 2 1 0 .0 8 9 .8 1. 56
6 3 .6 3 4 .6 1 .8 0 . 5 2 0 .0 7 9 .5 1..73
4 4 .0 5 1 .2 4 . 8 1 .1 3 0 .0 6 8 .9 1. 71
2 9 .7 6 0 .6 9 . 7 2 . 3 4 0 .0 5 7 .7 1. 65
100
F i g u r e 4 . B i n o d a l C u r v e s f o r A c e t o n e - W a t e r - B e n z e n e S y s t e m
A p r il, 1 9 4 3 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 4 1 5 to equilibrium and had been allowed to settle out, a sample of th e top
T he construction necessary in obtaining th e tie lines a t the higher tem peratures is indicated in Figure 8. <S represents differently. F or benzene-acetone-water it alters th e slope
smaller per ce n t docosane on a furfural-free way. T he binodal curves are shown in Figure 9.
Compositions from th e binodal curves are they varied only slightly w ith com position.
At higher tem peratures tie lines were ob
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
Apr i l , 1 9 4 3 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 4 1 7
quired for given separations show interesting effects of tem perature variation on extraction. In general, fewer stages are required for a high-tem perature extraction of acetone from w ater w ith benzene th a n for a low -tem perature extraction. Conversely, fewer stages are required for a low-tem
perature extraction of acetone from benzene w ith w ater. T he extraction of diphenylhexane from docosane w ith furfural requires fewest stages a t th e lowest tem perature for a given sepa
ration. O perating a t a n interm edi
ate tem perature, or w ith a tem per
atu re gradient through th e several stages and returning reflux formed by cooling th e extract to th e lowest tem perature investigated, yields an extract no more pure th a n th a t ob
(2) International Critical Tables, Vol.
I l l , p. 389, New York, McGraw-
D e s i g n C a l c u l a t i o n s
distillation calculations. F urther, it does not readily lend itself to calculations involving the application of such variables of operation as entrainm ent and more th a n one feed or drawoff.The purpose of this paper is to present a method of cal
culation which has the simplicity inherent in the McCabe- Thiele method bu t which is applicable to problems involving the above variables. This method will be presented with Qd = enthalpy removed from system per mole of distil
late, D, at upper end of column — enthalpy a succession of these will fix th e line.
The h eat and m aterial balances for th e lower operating where F„ = moles of vapor traveling up rectifying section in
unit time
L„ +1 = moles of liquid traveling down rectifying section
in unit time
D = moles of distillate removed in unit time
y „ = mole fraction of more volatile component in vapor leaving nth plate
xn + 1 = mole fraction of more volatile component in liquid leaving plate above the nth plate Xd = mole fraction of more volatile component in
distillate
Similarly, heat balance equations m ay be w ritten:
VnHn — Ln + 1 An + 1 + DQd (4 ) liquid leaving plate above with plate
x „ = mole fraction of more volatile component in
moved by waste minus enthalpy added in still
moved by waste minus enthalpy added in still