March, 1935
INDUSTRIAL AND ESGIKEERING CHEMISTRY
PRESENT DEWELOPMENT~ Xotwithstanding the economy of the present operation, a modification has recently been made, and is the basis of a patent application, which makes an important saving in the size (and consequent cost) of the equipment and of the steam consumption. This improvement is now being incorporated in the operations and has cut the steam cost as given above some 28 per cent t o about 25 pounds steam per pound anhydrous acid from 6 per cent liquor, or 20 pounds steam per pound anhydrous acid from 8 per cent liquor. The capacity of the azeotropic unit has a t the same time been increased some 45 per cent. This large increase in capacity (or decrease in size necessary for a given throughput) coupled with the fact that, many simplifications of equipment have been found possible will make additional units much cheaper to install and operate
255
ACKNOWLEDGMENT Thanks are due the late M. C. Burt, president of the Gray Chemical Company, for permission to use data obtained a t this plant, as well as to T. 0. Wentworth of the Vulcan Copper and Supply Company, engineers and builders of the distillation equipment. LITERATURE CITED (1) Keyes, D.B., IND.ENG.CHEM.,21, 998 (1929). (2) Othmer, D.F.,Chem. & M e t . Eng., 39, 136 (1932). (3) Ibid., 40, 631 (1933). (4) Othmer, D.F.. IND.ENG.CHEX.,20,743 (1928). ( 6 ) Othmer, D.F., Trans. Am. Inst. Chem. Engrs., 30,299 (1933) (6) Othmer, D. F.,U S. Patent 1,930,146(Oct. 10, 1933). (7) Young, Sidney, German Patent 142,502 (June 25, 1903).
RBCEIYED January 18, 1935.
Distillation and Absorption in Packed Columns A Convenient Design and Correlation Method T. H. CHILTONAND A. P. COLBURX,E. I. du Pont de Nemours & Company, Wilmington, Del.
T
HE widespread use of columns packed with various materials for the absorption of soluble gases and for distillation, principally analytical but also on a limited commercial scale, makes desirable the development of a simple
continual evaporation of liquid and condensation of vapor at the interface proceed a t a rate so great that the surface layer of vapor is always in equilibrium with the liquid, and the only resistance to the exchange of material is that of diffusion in method for determining the height to perform the required the vapor phase. Owing to the diffusion of the low-boiling seDaration. Since emerimental data on such columns are component in the vapor, the concentration of this comporeiatively few and cover for the nent in the vapor increases conmost part only narrow ranges t i n u o u s l y as the vapor passes The proposal is made that the dificulty of of the variables, it is particularly upward, rather than in steps as separation in a packed column be expressed, d e s i r a b l e that these s h o u l d in a plate c o l u m n . A treatbe c o r r e l a t e d in ajs general a ment of the transfer of material instead of in terms of the “number of theoretical manner as possible, so that their in a p a c k e d c o l u m n must be plaies,” as the number of “transfer units” dereliability can be estimated and based, therefore, on a considerafined, f o r distillation, as that they can be extended as tion of the differential nature widely as possible for the soluof the changes. tion of various design problems. It can b e c o n s i d e r e d that It is the purpose of this paper to over a differential element of describe a convenient method height, d H , the partial pressure for the d e s i g n of packed coland, f o r absorption, as of the low-boiling c o m p o n e n t umns and, conversely, for the in the vapor is increased by the correlation of experimental data differential a m o u n t , d p , and from such columns. since in distillation t h e t o t a1 moles of vapor passing successive points remains essentially conL4PPLICATION TO DISTILLATION The eficiency of a column would then be expressed stant, the d i f f e r e n t i a l rate of as the “height of a transfer unit” ( H . T. U.) inIn a p a c k e d column u s e d increase of moles of low-boiling stead of the “height equicalent to a theoretical for distillation, an a s c e n d i n g component in the vapor is given stream of vapor passes counterplate” (H. E. T. P.). The d u e s so obtained are by the equation: c u r r e n t t o t h e liquid reflux. directly related to coeflcients f o r the transfer of At all points the concentration material by diffusion, but the calculation of the of the lower boiling component necessary height of column to effect a gicen sepain the vapor a t the ,vapor-liquid ration is made more convenient by the use of the i n t e r f a c e is greater than that This rate must be equal to the in t h e v a p o r s t r e a m . As a transfer unit concept. r a t e of t r a n s f e r by diffusion result, there is a diffusion of the It is shown that f o r many cases of distillation which may be expressed: lower boiling component away the H . E. T. P. and H. T. U.are nearly identical from the l i q u i d s u r f a c e and but that there may be large differences between of the higher boiling component dw = K A p d A = K o A p S d H themfor certain absorption problems. t o it. It is assumed that the (2)
INDUSTRIAL
256
AND
ENGINEERING CHEMISTRY
For this case, where diffusion occurs equally in both directions, mass transfer coefficient, K , is theoretically independent of the partial pressure of the component considered (6).
Vol. 27, No. 3
tained from correlations of mass transfer factors. Procedures for integrating Equation 6 are also given in detail later. As a matter of interest, the relationship between H. T. U. and K is seen from Equations 4 and 5 to be:
H.T . U.
=
H n
=
G KaIIM,,,
(7)
This concept of the height of a transfer unit is, therefore, similar in some respects to that proposed several years ago by Peters (9),the "height equivalent to a theoretical plate." Continued use of this latter concept since it was formulated has demonstrated its value, even though it has been recognized that there are no real "plates" or integral steps in a packed distillation column. Under certain special conditions, as will be shown later, these concepts become identical. APPLICATION TO ABSORPTION >t ' ovO,l
I
, &9
~
0.3
The process of absorption of soluble gases is very similar to that of rectification, in that a gas stream passes countercurrent to the absorbing liquor, and in the absence of an appreciable liquid-film resistance, the resistance to transfer is entirely one of diffusion from the main gas stream to the gasliquid interface. For this case, however, the total number of moles passing successive points in the column changes, and the rate of absorption must be written:
~
0.4
0.5
0.6
0.7
0.8
0.9
FIGURE1. MCCABEAND THIELEDIAGRAM FOR RECTIFICATION OF ETHANOL-WATER (EQUILIBRIUM DATAFROM CAREY) Composition of feed, 10 mole per cent ethanol; composition of waste, 0.1 mole per rent ethanol: composition of product, 80 mole per cent ethanol, reflux ratio, 2.5 moles liquid run-bac,k per mole of iroduct: L / V above feed 0.715.
-
Equations 1 and 2 can be combined and rearranged to give the relation :
dw = d(pG/M,)S/E (8) As previously shown (2), this equation becomes, upon differentiation of the product, (pG/M,) : dw
which becomes on integration: (4)
Thus the required height of column for any problem could be determined by a solution of Equation 4, provided that the value of K can be predicted. There is another way of looking a t the problem, however, which has proved to be more convenient. The quantity,
L:
can be considered a measure of the difficulty of a
desired separation, just as the required number of theoretical plates is a measure of the difficulty of a separation to be carried out in a plate column. Because of the similarity of the two concepts, as is later discussed in detail, the authors have called the solution of the above integration "the number of transfer units." Thus the number of transfer units, n, is: n = J,p2
3
(5)
This equation can be expressed in terms of mole fraction in the vapor, y, as well as partial pressures:
By this means, without any consideration being given to the calculation of the total number of moles being transferred, any problem can be directly expressed as a required number of transfer units. Then if experimental data are available as values of height per transfer unit (H. T. U.), the determination of column height involves merely the multiplication of n by H. T. U. It is shown later that the values of H. T. U. can' be conveniently correlated with vapor velocity or ob-
dpGS
= -
pa
-vm
(9)
Furthermore, for this case diffusion occurs chiefly in o n e direction, and by the Stefan diffusion e q u a t i o n (6) t h e r a t e is greater t h a n for two-dir e c t i o n a l diffusion by t h e factor rI/pu, where pu is the logarithmic m e a n of (n - p ) and (II--p*). Thus the value of K in E q u a t i o n 2 is no longer independent of concentration but varies inversely with p g f , and it is the product, Kpd, which is independFIGURE 2. GRAPHICAL DETER- e n t of concentraMINATION OF NUMBER OF TRANSFER tion. Accordingly, OF ETHAUNITSFOR RECTIFICATION from Equations 9 NOL-WATER(DATAFROM FIGURE 1) and 2 the following Y Y* AV I/ AY e q u a t i o n is ob0,009 125 0.001 0.008 tained: 40 0.035 0.01 0.025
0.11 9.1 0.16 0.05 0.17 5.9 0.10 0.27 0.18 5.56 0.20 0.38 0.44 0.14 7.14 0.30 6.67 0.55 0.4 0.15 0.607 0.107 9.13 0.6 0.662 16.0 0.062 0.6 22.2 0.66 0.696 0.046 31.0 0.732 0.032 0.7 0.7725 0 0225 44.5 0.75 59.0 0.017 0.8 0.817 Area under the curve above feed, 9.3 transfer units; area under the curve below feed, 2.76 tranafer units.
(10)
The integrated form is :
March, 1935
INDUSTRIAL AND ENGINEERING CHEMISTRY
For this case the number of transfer units is then defined:
The relation between the H. T. U. and the controllingvariables for absorption are considered later. The relationship with K is, from Equations 12 and 11:
For absorption, the general solution of Equation 12 is similar to the general solution of Equation 6. Values of p are calculated a t various values of z by means of a material balance, and then values of p* are obtained a t the same values of z from equilibrium relations, or values of A p are read from an operating diagram similar to the McCabe and Thiele diagram for distillation (8). At each point p , and pol must be calculated, and then a plot is made of p ~ / ( A p ) p vs. , p , and the area under the curve is equal to the number of transfer units. An example illustrating this procedure is shown by Figures 3 and 4.
DETERMIXATION OF NUMBER OF TRAKSFEIL UNITS In continuous rectification a relationship can be derived between the vapor composition, y, and the liquid composition, z, leaving any cross section above the liquor feed level as follows:
om
o
FIGURE3. TION OF
ax
a5 x
of0
0.25
0.m
DI.4GR.4M FOR ABSORPBENZENE IN STR.4W O I L
8.
The reflux ratio, L / V , can be taken as constant. although the values above and below the feed point are different, on the assumptions that the components of the mixture have approximately equal latent heats and negligible heat of mixing, and that the temperature change through the column and heat lossps from the column can be neglected. These equations, with the curve representing the equilibrium composition of vapor from the liquid, permit the solution of Equation 6 for the general case. This solution was developed by Thormann (11). It involves choosing a number of values of z between zv and z p , calculating values of y corresponding to each from Equation 14 or 15, and then a t the same values of x obtaining values of y* from the equilibrium curve. A plot is then made of l/Ay vs. y; and a graphical integration of the area under the curve between the limits of yI [the composition of vapor entering the column (i. e., in equilibrium with z,)] and y2 [the composition of vapor leaving (i. e., the product composition) 1 gives the total number of transfer units. The values of Ay can also be directly obtained from a McCabe and Thiele diagram (7) as illustrated by Figure 1. The resulting graphical integration is shown by Figure 2. The customary procedure in testing packed columns is to operate a t total reflux. This facilitates steady-state operation and eliminates uncertainties in knowing the reflux ratio exactly. Under this condition, L/V = 1, and by Equations 14 and 15, y = 2. If the equilibrium relation between y* and z can be expressed mathematically, a general solution of Equation 6 can be made for this case. Such a relation, in terms of a,the relative volatility of the components, is:
+ (a - l)x
ato
Concentration of benzene in inlet gas, 15 per cent by volume; concentration of benzene in outlet gas, 1.5 per cent by volume; total reasure 1 atmosphere: temperature, 43’ Aa&e benzene solution follows Raoult’s law. Vapor pressure of benzene a t 43O C. = 200 mm. = 0.263 atmosphere. Benzene content of oil entering srrubber = 1.0 mole per cent: benzene content of oil leaving scrubber (about 50 per cent of satu. ration) = 30 mole per cent.
and below the feed by the equation
y* = 1
257
For cases There the mixture is dilute, so that pa/ does not differ much from p,, and There the range of absorption is such that the equilibrium relationship follows Henry’s law (i. e., p* is proportional t o x, or else the values of p* are negligible), Equation 12 becomes:
where Aplm is the logarithmic mean of the terminal values of Ap, and (pufr,’pv)m is the average of the terminal values of this ratio. For cases where p* is entirely negligible, Equation 12 can be simplified to Equation 19.
o
(16)
aoz
MI5
O.M
om
a08
0.10
0.12 014
P
a15
FIGURE4.
GRAPHICAL DETERMINATION OF h TOF TRANSFER ~ UNITS ~ ~ FOR ABSORPTION OF BENZENE (DATA FROM FIGURE 3)
Where a can be assumed constant over the distillation range, Equation 6 can be integrated to give:
~ P ui
This equation holds, however, only for total reflux and for cases where a is constant; this is substantially true for mixtures which do not deviate appreciably from Raoult’s lav and which have boiling points close together, and for some other mixtures.
z 0.30 0.25 0.20 0.15 0.10 0.05 0.01
P
0.150 0.1227 0.097 0.0732 0.0514 0.0313 0.0150
P* 0,0789 0.0658 0.0526 0,0394 0.0263 0.0132 0.0283
- -
AP 0.0711 0.0569 0.0444 0.0398 0.0251 0.0181 0.01237
14.1 17.9 22.5 30.4 39.8 55.2 80.8
PO 0.85 0.877 0.903 0.927 0.949 0,989 0.985
PO( 0.92 0.94 0.952 0.963 0.974 0.964 0.992
PAP 15.2 18.6 23.7 30.7 41.0 66.1 81.3
Area under curve 4.48 transfer units; by the approximate method (Equation 18) n 4.18 transfer unita.
~
INDUSTRIAL AND ENGINEERING CHEMISTRY
258
n = 2.3
(E)m (E)
since, by definition, the equivalent diameter D, = 4 S H / A . For solid packings the following Reynolds number has been successfully applied for friction correlations (1):
log
CORRELATION OF VALUESOF H. T. U.
With the problem expressed in terms of a required number of transfer units, to determine the necessary height of column, the height per transfer unit (H. T. U.) must be predicted from existing experimental data. Fortunately, a previously recommended procedure for correlation of data can be directly utilized for this purpose. It was proposed some time ago (3) that forced convection data on heat transfer be calculated as heat transfer factors and these factors be correlated by plotting against the Reynolds number in a manner analogous to that used for friction factors. The heat transfer factor, j, can be expressed in terms either of the temperature conditions or of the heat transfer coefficient, h, as follows:
Extensive correlations were made of j vs. Re for data for flow inside tubes, across tubes and tube banks, and parallel to plane surfaces. At the same time it was suggested, and later confirmed (2) that mass transfer data be expressed as mass transfer factors, j, according to the analogous relation (for rectification) :
where D, = average diameter of packing particle. This is the definition used by Fallah (4) in a recent paper. It is not known which basis will prove the more satisfactory for correlating data; but whichever definition of Reynolds number is applied, it must naturally be the same for design as used for correlation.
H. T. U.
OF AN
UXPACKED TUBE
For the case of rectification or absorption in an unpacked tube, where the liquid completely wets the wall, the mass transfer factor relation with Reynolds number previously obtained (2, 3) can be applied. This relation, for the turbulent region, is approximated by the equation, j = 0.023
DG (--)
-0.2
where D = inside diameter of tube. Since for an empty tube a = 4/D: H. T. U. = 10.9 D
H. E. T. P. The suggestion made by Peters (9) was that a given separaCOMPARISON OF H. T. U.
These mass transfer factors were also to be correlated by plotting against the Reynolds number. The H. T. U. can, therefore, be expressed in terms of these j factors, as follows : H.T.U.=-
G KaII.Mm
1 =-(’) ja
Vol. 27, No. 3
a /a
pkd
It is thus apparent that experimental values of H. T. U. can be readily expressed as mass transfer factors and plotted against the Reynolds number and also that, from mass transfer correlations, values of H. T. U. are easily obtained. Likewise, for absorption,
Since the relationship between H. T. U. and j is, by Equations 22 and 23, identical for both rectification and absorption, it will be of great interest t o compare, when they become available, data for each of the processes using the same packing. For absorption of only slightly soluble gases there exists a resistance to mass transfer in the liquid, and the above equations cannot be directly applied. If it is known that a large proportion of the resistance is due to the gas film, the H. T. U. calculated by Equation 23 should be multiplied by the ratio of the gas-film mass transfer coefficient to the over-all value; ( K / K L ) ]where , K and KL are the this ratio is equal to [l gas and liquid film coefficients, respectively. Correlations of mass transfer factors with Reynolds numbers have been made (9) only for the cases of flow inside tubes, across tubes, and parallel to plane surfaces, for which cases they were found to be in line with heat transfer factors. For the cases studied, the surface was 100 per cent effective, whereas in packed columns the useful area appears to vary with the liquor rate, and this variable may have as much importance as the vapor velocity, or even more. For packed columns the Reynolds number may be calculated as follows:
+
(24)
AND
tion be treated as though it were carried out in a plate column and be expressed as a required number of theoretical plates. The height of the packed column was then divided by this number to give the height equivalent to a theoretical plate (H. E. T. P.). The theoretical plate concept implies that the change in composition of the vapor passing through the plate is equal to the difference between the composition of the enI
FIGURE 5. RELATION OF H. T. U. AND H. E. T. P. One transfer unit gives an enrichment correZ/O = aversponding to Ub’ - go, where Ub’ YO. One theoretig b and Y*O age of U * b ea1 plate gives an enrichment corresponding
-
to
up
-
-
- yo.
tering vapor and the corresponding equilibrium vapor, or yp - yo = y*o - yo (Figure 5). On the other hand, a If transfer unit is so defined that yb’ - y. = (y* - y),,. the mean value, (y* - y)m, is equal to y*. - yo, the two concepts are identical. This obtains when the equilibrium curve is parallel to the y vs. x or “operating” line, a condition rarely occurring for appreciable ranges of y. A demonstration of this relationship for the process of absorption (in terms of mole ratio units) has been given by Sherwood and Gilliland (IO). If values of Av increase as the vapor passes through
INDUSTRIAL AND ENGINEERIKG
March, 1935
the column, fewer transfer units than theoretical plates are required; if values of Ay decrease, the reverse is true. Because of the ease of “stepping off” theoretical plates on a McCabe and Thiele diagram compared with the trouble required to make an additional plot of l / A y vs. y and to determine the area in order to find the number of transfer units, the following procedure is suggested for distillation problems where extreme accuracy is not necessary. On the McCabe and Thiele diagram, transfer units can be “stepped off,” if care is taken to make the magnitude of enrichment afforded by each unit, yb‘ - Ya, equal to the average of the values, y*. yo and g*b - y b . That is, to choose a point b (Figure 5) on the operating line so located that
- ya)
:= 0.5
[(2/*a
- Ua) + (y*b
- ?/a)]
While this involves a little cut-and-try work, the time required is not a t all great. If the equilibrium curve and the operating line were both straight (though not parallel) over the change yb - ya, and the logarithmic mean value of y*a - ya and y*b - yb were used, the method would be exact. For most problems the inaccuracy involved by the curvature of either or both of these lines and by the use of arithmetic instead of logarithmic mean is of little consequence. TABLEI. COMPARISON OF NUMBER OF TRANRFER UNITS WITH NUMBER OF THEORETICAL PLATESFOR MIXTUREP WlTH CONSTAXT CY UNDER TOTAL REFLUX TRANBFERTHEORETICAL UNITS PLATES 46.5 47.5 50.0 47.5 1 1 0.99 96.5 95.0 1.1 0.99 3.0 3.3 3.0 0.50 3.9 3.3 3.0 0.99 6.9 6.6 3.0 0.01 0 09 a yl = mole fraction low-boiling component in vapor entering column b ys = mole fraction low-boiling component in vapor leaving column. 6 LI = relative volatility u? -- b
(2c
0.50
1.1
V ”.I S
0.01 0.50 0.01 0.01 0.50
In case the equilibrium curve and operating line diverge over part of the distillation range and converge over another part, the total number of transfer units may be practically equal to the total number of theoretical plates. Such a condition exists for total reflux with ideal mixtures with low relative volatilities, if the distillation range is about equally great on each side of 0.5 mole fraction. This is shown in Table I by examples in which the number of transfer units is calculated by Equation 17, and the number of theoretical plates ii: calculated by the following stepwise equation derived by Friiske ( 5 ) : No. theoretical plates
=
log a
(28)
Since many column tests, where results have been expressed as H. E. T. P., were carried out under the special conditions stated above, the values of H. T. U. are practically equal to those of H. E. T. P. In many cases, however, the number of transfer units differs more noticeably from the number of theoretical plates and the application of the latter concept might lead t o an unsatisfactory design. For the example shown by Figure 1, both the number of transfer units and the number of theoretical plates have been determined and are as follows: Below feed Above feed
TRANBFER UNITS 2.76 9.3
THEORETICAL PLATXB 4.25 8.1
If, under comparable conditions, the H. T. U. and H. E. T. P. for the packing to be employed were found to be, for example, one foot, it is apparent that a design based on the H. E. T. P. concept would have the feed a t too high a point. If only the enriching operation were required, the column based on H. E. T. P. would be considerably too short.
259
Another example may be given, as applied to absorption. Suppose a concentration of 5 per cent (by volume) water vapor in air is to be reduced to (a) 0.05 per cent or (b) 0.005 per cent by absorption in sulfuric acid so concentrated that the equilibrium partial pressure of water vapor is negligible. The number of transfer units can be calculated by Equation 19. A comparison with the required number of theoretical plates is as follows: 0,057 HzO in exit air 0.005k H 9 0 in exit air
-
(US’
CHEMISTRY
T R A N S F E R THEORETICAL UNITS PLATEB 4.6 0.99 6.9 0.999
ADVASTAGES OF USE OF H. T. U.
OVER
Kn
It has been general practice in the past to compute for a given absorption problem the m-eight of solute to be absorbed and the mean driving force, and then from experimental values of R a to calculate the required tower volume. This procedure could, of course, be extended to distillation to eliminate the errors which might be incurred by use of the H. E. T. P. concept. On the other hand, the authors have found the use of transfer units and H. T. U.’s to be not only completely reliable but also particularly coiivenient for both distillation and absorption. The H. T. U. is independent of the concentration of inert gas and, for cases limited by the gas film resistance, varies in the turbulent flow range only slightly with mass velocity of the gas, and often even less with throughput rate when the liquor-gas ratio is kept constant, since the decrease with liquor rate offsets the increase with gas velocity. The H. T. U. has only one dimension, length; and, since it is expected in many cases to vary but slightly with velocity, approximate values can be easily kept in mind. On the other hand, the mass transfer coefficient, Ka, varies markedly with velocity, average molecular weight, and concentration of inert gas (in absorption). It is expressed in terms of four different quantities, and since eaoh investigator may make a different choice for one or more of these from different systems of units, the conversion of units is often laborious. The range of values may be a million fold from one common set of units to another, so that it is difficult to keep typical values in mind or to make comparisons. Finally, as contrasted with the separate use of absorption coefficients, Ka,for absorption, and H. E. T. P. for distillation, it is a simplification to use the same procedure for distillation] absorption, and other mass transfer processes in packed columns, and to have existing data from all the processes correlated on the same basis. At is apparent, for example, that the same methods can be applied to countercurrent liquid-liquid extraction processes when these are carried o u t in packed columns. r\TohfENCLATURE
Any set of self consistent units may be used; those of the foot-pound-hour-” C. system are given for illustration; total and partial pressures are, however, expressed in atmospheres: A D
D, D,
=
interface area, sq. ft.
= diam., ft. = equivalent diam., ft.
= diam. of packing particle, ft. G = mass velocity of gas or vapor, lb,/(hr.) (sq. ft.) H = height of column, or packed section, ft. H. E. T. P. = height equivalent to a theoretical plate, ft. H. T. U. = height of one transfer unit, ft. K = absorption coefficient (gas film), Ib. moles/(hr.) (sq. ft.) (atm.) Ka = absorption coefficient (gas film), lb. moles/(hr.) (cu. ft. packed volume) (atm.) K L = absorption coefficient (liquid film), lb. moles/(hr.) (sq. ft.) (atm.) L = liquor rate, Ib. moles/hr.
INDUSTRIAL AND ENGINEERING
260 Mm Re
s
V a C
d h
av. mol. weight of vapor stream Reynolds number cross-sectional area (over which G is measured), sq. ft. vapor rate, lb. moles/hr. surface area of packing per unit of packed volume, a ft./cu. ft. sp. %eat at constant pressure, P. c. u./(lb.) (” C.) differential operator filyocge\fficient of heat transfer, P. c. u./(hr.) (sq. ft.) b.1
j k kd
n
P P* AP APm APm
Pa Po,
t Atm
W X
Y
heat transfer or mass transfer factor (Equations 20 and 21) thermal conductivity, P. c. u./(hr.) (sq. ft.) (” C./ft.) diffusion coefficient, sq. ft./hr. number of transfer units (Equations 5 and 12) partial pressure of diffusing component, atm. equilibrium partial pressure of diffusing component out of liquid, atm. P
- P*
true mean value of ( p - p * ) over height of column loearithmic mean of terminal values of (2) - m*) y k a l pressure of inert component (atm.1 ri - p ogaritimic mean of (n - p ) and (n- p * ) , atm. temp., C. true mean temp. difference, ’ C. rate of transfer of diffusing component, lb. moles/hr. mole fraction of diffusing component in liquid mole fraction of diffusing COmpOnent in gas = p/n
y*
Ay
n
p”
= =
CHEMISTRY
Vol. 27, No. 3
equilibrium mole fraction of diffusing component out of liquid = p * / n y
- y*
total pressure, atm. = relative volatility = Y* (1 - 2) (1 - Y*) 2 = viscosity, lb./(hr.) (ft.), taken at “film” conditions = density, lb./cu. ft. =
LITERATURE C I T E D
(1) Chilton, T. H., and Colburn, A. P., IND.ESG.CHEW,23, 913-19 (1931); Trans.Am. Inst. Chem. Engrs.,26,178-96 (1931). (2) Chilton, T. H., and Colburn. A. P., IND.ENG.CHEM.. 26, 1183-7 (1934). (3) Colburn, A. P., Trans. Am. Inst. Chem. Engrs., 29, 174209 (1933). (4) Fallah, R., J.SOC.Chem. I d , 53,262-6T (1934). ( 5 ) Fenske. M. R.. IND.ENG.CHEM.. 24.482-5 (1932). (6) Lewis, W. K., and Chang, K. C., Trans. Am‘. Inst. Chem. Engrs., 21, 127-38 (1928). (7) McCabe, W. L., and Thiele, E. W., IND. ESQ. CHEM.,17, 605-12 .--(1Y26).
(8) Murray, I. L., Ibid.. 22, 165-7 (1930). (9) Peters, W. A., Jr., Ibad., 14,476-9 (1922). (10) Sherwood, T . K., and Gilliland, E. R., Ibid., 26, 1093-6 (1934). (I1) K.* l4>61-4 RECEIVED November 9, 1934. Contribution 149 from the Experiments1 Station of E. I. du Pont de Nemours BE Company.
New Design Calculation for Multicomponent Rectification E. R. GILLILAND,Massachusetts Institute of Technology, Cambridge, Mass.
T
method of calculation is to be HE separation of mateA new design method f o r the distillation of able to go from the composition rials is a problem often multicomponent mixtures is proposed. The of the liquid leaving any plate to requiring the attention calculations are based o n the use of “relative that of the liquid leaving the of the chemist and engineer. If volatility” and “relative operability” of the subsequent plate. I t is often the materials consist of a mixconvenient and advantageous components in the mixture. The procedure is t u r e of l i q u i d s , rectification t o d i v i d e t h i s step into two f u r n i s h e s o n e of t h e m o s t rapid and simple, and f o r the condition of infinite portions. The first portion concommon and convenient means r e f u x the calculation reduces to Underwood’s sists in going from the liquid on of performing this separation. modification of Fenske’s “relative volatility” the plate to the vapor over it, Thus, the design of rectifying system. For the case where separation between and the latter portion involves equipment is one of the fundagoing from this vapor to the mental problems with which the adjacent components is not relatively complete, liquid from the plate above. chemical engineer is repeatedly the determination of suitable design conditions by The composition of the vapor confronted. previous design methods has been tedious. The above the liquid is determined It would be fortunate indeed proposed procedure offers a valuable method for f r o m e q u i l i b r i u m data and if a method of calculation for facilitating such calculations. The method is plate efficiencies. The e q u i these designs would r a p i d l y librium data may be obtained useful in determining the proper design condigive results of high accuracy, from published results or, for but such methods are usually tions, such as dependent terminal concentrations h y d r o c a r b o n s , may be estil a b o r i o u s and time-consuming. and number of equilibrium plates. The apmated by the fugacity plots of As a great many of the probplicability of the method is demonstrated by Lewis and co-workers (6,8): lems to be solved are proposed illustrative problems. designs, i t is desirable- to have Y’fr = Z f P (1) a method of calculation that ?- L?‘ For detailed use of these methods the reader is referred to will give a satisfactory solution with a minimum of effort. Commercial rectifying columns consist essentially of two the original articles. The latter portion of the step, that of main types, the plate tower and the packed tower. The former going from the vapor to the liquid on the next plate, is acpredominates in industrial rectification, and the majority of complished by a material balance. The assumption of constant molal overflow leads to considerable simplification; in proposed design methods are for this type of column. Both algebraic and graphical methods of design have been general, it is well within the accuracy of the method of design used to simulate the successive contact of liquid with vapor and will be used in all following derivations. The relation becharacteristic of the plate column. The graphical method is tween liquid and vapor becomes: essentially an attempt to reduce the tediousness of the alge- Above feed plate O”X, P X P = vs-1 y n - 1 braic calculations. The fundamental requirement of a @A) ~
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