ENGINEERING AND PROCESS DEVELOPMENT
Height of Equivalent Theoretical Plate in Packed Fractionation Columns Empirical Correlation D.
P. MURCH
Givoudon Carp., Delowanno, N. 1.
A
GREAT deal of work has been done on distillation calculations, and i t is now possible to calculate the number of theoretical plates and reflux ratio with considerable accuracy. However, a complete design necessitates prediction of the system efficiency, and design calculations are no better than the accuracy of this step. For bubble-plate columns recent work enables a designer to predict plate efficiency with fair accuracy. For packed columns, however, very little information is available. Colburn and Pigford (7) offer suggestions and Gilliland (la) gives an equation which he states is only an approximation. This paper presents an empirical equation which correlates the major variables encountered in the prediction of packed column efficiency. All data in the literature which were readily available, a s well as unpublished work by the author, were used. The measure of packed column performance used in this paper is the height of packing equivalent to a theoretical plate, HETP. This method has been criticized because it is not sound from a theoretical basis, as it assumes finite steps of concentration change rather than the continuous change which actually occurs in a packed column. Nevertheless, the convenience of this method and the large amount of literature data presented in this form favor its use. The work of Bowman ( 3 )indicates t h a t the actual error involved in using the method is small. The H T U (height of over-all transfer unit) method (6) is more difficult t o use and fewer literature dat8ausing heights of over-all transfer unit are available.
G = mass velocity of vapor, pounds per hour per sq. foot of d
tower cross-sectional area
= tower diameter, inches
h = packed height, feet f f = relative volatility c c = liquid viscosity, centipoises P = liquid density, grams per cc.
1
Average values determined from compositions at top and bottom of column K1 a proportionality constant, obtained directly from experimental data K2 = an exponential constant applied to the mass velocity term, G. This constant is the numerical slope of the line obtained when G is plotted against HETP on logarithmic coordinates. Ka = a n exponential constant applied t o the tower diameter, d. This constant is the numerical slope of line obtained when d is plotted against the HETP on logarithmic coordinates. The following discussion takes up each major variable in turn and shows how the equation was developed. Mass Velocity. The relationship between mass velocity and height of equivalent theoretical plate is complex. many factors appear to contribute to the over-all effect. The general relation is shown by the curve of Figure 1. This paper is based upon experimental work carried out at total reflux or high finite reflux ratios. Therefore. the term “mass velocity’’ includes the effect of both liquid and vapor rates.
Many Factors Affect Performance of Packed Column
A very large number of factors affect t h e performance of a packed column. The following list summarizes the most important ones. Liquid and vapor rates (mass velocity). Shape, size, and material of tower packing. Degree of wetting of packing. Tower diameter. Packed height. Ratio of tower diameter to packing size. Effectiveness of liquid distribution over tower area. Operating pressure. Physical properties of materials being fractionated. Viscosity, density, diffusivity, surface tension, and relative volatility The equation t h a t has been developed accounts for all the major variables except operating pressure.
where the symbols and their units are as follows:
HETP 2616
=
height of packing equivalent to one theoretical plate, inches
VAPOR
Figure 1.
MASS VELOCtTY
-
Effect of Vapor Mass Velocity
With the data available a t the present time, i t is difficult to determine the relative importance of liquid and vapor rates upon packed column efficiency. This paper correlates efficiency against vapor mass velocity but cautions that a t low reflux ratios abnormally high values may occur. A study of the curve of mass velocity us. HETP fihows five dis-
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 12
ENGINEERING AND PROCESS DEVELOPMENT
” VAPOR MASS VELOCITY-POUNDS/HR,/SO, FT.
VAPOR MASS VELOCITY-POUNDS/HR~/SQ. FT.
Vapor Mass Velocity vs. HETP for Ring Packings
Figure 2.
[Figure 3.
Packing
Size, System
Inch
Reference
CClr-benzene Methanol-water Trichloroethylene-toluene Ethyl alcohol-water
1 /2 1 /2
(16) (16)
Symbol
0
a A
Symbo!
Vapor Mass Velocity vs. HETP for Saddle Packings Packing Size, Inch 1 1/ 2
System Ethyl alcohol-water Ethyl alcohol-water
0
a
(16)
7.0.
3.0
I 0
J
f 3.0 Lo
I
(1 7) (1 1 )
318
5.0
8f
Refer. ence
I
2.0
P IW
r 1.0 100
&Figure5.
I.”
500
700
1000
200a
Symbo1
VAPOR MASS VELOCITY-POUNDS/HR./SQ. FT.
Figure 4. I
Symbo1
0
A
0
Vapor Mass Velocity vs. HETP for McMahon Packing
System EDC-benzene EDC-benzene EDC-benzene
Packing Size, Inch
lj4 13/8 /2
Reference (10)
(9) (9)
tinct regions designated as A,B,C,D, and E. Regions A and E are fairly easy to explain. A t A the liquid rate is too low to wet the packing completely, and channeling of liquid and vapor occurs. A t E the flooding point of the packing has been reached and efficiency decreases rapidly. It is more difficult t o explain the reasons for regions B, C, and D . Many examples in the literature substantiate this irregular relation between height of equivalent theoretical plate and mass velocity. Kirschbaum (16)shows curves for several sizes of rings; Fisher and Bowen (9) noted this effect for l/*-inch McMahon packing; Bragg ( 4 ) found the same situation with Stedman packing; and Ryan ($1) and Manning’s (18) data for 0.16-inch protruded packing are similar. The explanation is not
December 1953
200 300 500 700 1000 VAPOR MASS VELOCITY-POUNDS/HR./SQ. FT.
0
A 0
A
2000
Vapor Mass Velocity vs. HETP for Protruded Packing System n-Heptane-methyl cyclohexane n-Heptane-methyl cyclohexane n-Heptane-methyl cyclohexane n-Heptane-methyl cyclohexane
Packing Size, Inch
0.16 (1/4)
Reference (18)
0.24 ‘(3/8)
(27)
0.48 (3/4)
(27)
1 .O
(27)
simple; perhaps the irregular relationship is caused by the combined effect of two factors, contact time and liquid-vapor turbulence. At low mass velocities the high contact time produces a minimum H E T P (point B), and a t higher mass velocities another minimum HETP is obtained (point D ) as a result of the better liquid-vapor mixing. This’correlation does not attempt to predict the existence of the minimum points for the following reasons: (1) A column designed on the basis of these minimum HETP’s would have only a narrow operating range where i t would perform according to design; (2) the data in the literature do not substantiate these minima for all types and sizes of packings; (3) it is difficult to express the irregular relationship mathematically.
INDUSTRIAL AND ENGINEERING CHEMISTRY
2617
ENGINEERING AND PROCESS DEVELOPMENT
I
1.01 1.0
Figure
6.
Symbo1
0 0 A
A
I
I
2.0 3.0 5.0 TOWER DIAMETER
Tower
I
20
I
10.0
- INCHES
Diameter vs. Packings
3
HETP for Various
System EDC-benzene n-Heptane-methyl cyclohexane
Packing Stedman Protruded
Nz-02
Saddles McMahon Rings
EDC-benzene Methanol-water
I
200
Reference (4)
Rings Saddles McMahon Protruded
(7)
(9,231 Author (see Table Ill
Stedman Protruded McMahon Solid saddles Rings
Helices are very effective in small columns but have not been used extensively in larger sizes. I n general, the smaller packing sizes produce a lower height of equivalent theoretical plate.
2618
Ks
(74, 27)
If the height of equivalent theoretical plate is plotted against the mass velocity on logarithmic coordinates, nearly straight lines are obtained for most of the packings when the mass velocity varies from 25 to 80% of the flooding point (see Figures 2 to 5 ) . Packings with a high free space such as protruded packing, Mchlahon packing, and Stedman packing show H E T P directly proportional t o mass velocity. The packings with low free space, such as rings and saddles, show HETP inversely proportional to mass velocity. The smaller packing sizes show a greater effect of mass velocity. The only exception to this rule is 0.16-inch protruded packing, which has a very irregular relationship between H E T P and mass velocity. Type and Size of Packings. KO single work in the literature compares all the major types of packings under identical conditions. Therefore, the performance of different packings can be compared only after the effects of other variables have been accounted for by the use of the empirical relationships discussed in this paper. If only the height of equivalent theoretical plate is considered and such factors as cost, maximum capacity, pressure drop, holdup, and ease of installation are disregarded, the different types of packings would rate as follow in order of decreasing efficiency: 1. 2. 3. 4. 5.
The effect of the material of construction is rather uncertain; probably i t is a minor factor. Kirschbaum (15, p. 319), found glazed rings as effective as unglazed porcelain and the author has found borosilicate glass rings to be as good as porcelain. Forsythe et d.( I O ) found brass McPvIahon packing somewhat better than Monel; however, this may have been caused by differences in fabrication. T h e mesh packings (Stedman, protruded, and McMahon) give higher efficiency than solid types. Different packings affect the height of equivalent theoretical plate in a t least three ways: by the degree of liquid-vapor contact obtained, by the effect of mass velocity, and by the effect of tower diameter. It is for this reason that there are three constants in the equation. It has been impossible to obtain any suitable quantitative correlation of packing effectiveness in terms of packing constants such as free space or surface area per unit of volume. Degree of Wetting of Packing. .4lmost all the workers who have studied packed column efficiency have found that the degree of wetting of the packing has a great effect upon performance. The column should be thoroughly flooded before the distillation is started, to ensure maximum efficiency. Peters (10)stated that protruded packing is not as sensitive to this factor as other packings. Column Diameter. The column diameter is one of the most important factors. The principal disadvantage of packed columns is their failure t o give high efficiency in columns of large diameter because of poor liquid distribution over a large area. This disadvantage appears to be diminished by the newer packings, notably protruded packing and Stedman packing. h comparison of the constant, KS, in the equation shows this clearly:
Stedman
1.24 1.11 1.0 0.30
0.24
~
32
5
3
PACKED HEIGHT
Figure 7.
- FEET
10
0
Packed Height vs. HETP
System. Ethyl alcohol-water Packing. 8-mm. Raschig rings Column diameter. 4.33 inches Reference ( 2 4 )
K , would be zero if tower diameter had no effect upon height of equivalent theoretical plate. There are not sufficient data to evaluate the effect of packing size upon liquid distribution; therefore K3 is the same for each type of packing regardless of size, However, if the packing size is greater than I/* t o of the column diameter, the fractionating ability of the column is reduced tremendously.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 45, No. 12
ENGINEERING AND PROCESS DEVELOPMENT 30
38 34
32
30 28
d 28 'r
3
24
P2
-. n
c 4
'
'
I
'
'
I
'
I
"
'
I
I
I
'
I
20
18 18 14
12
Figure 8.
Effect of
Physical Properties of Materials Distilled
10
H
Figure
a. Relative volatility liquid viscosity, centipoises liquid density, g./cc. Reference ( I 6) p. p.
9.
E TP
Symbol
Packing Stedman McMahon Protruded Saddler Rings
+0 0
-
0
The graphs in Figure 6 are plots of H E T P vs. column diameter on logarithmic coordinates, and the slopes of the curves are the constants, K,. The type of liquid and vapor distributors used in large columns has a great effect upon the efficiency. The author has seen a case where the failure of the liquid distributor a t the top of a column 30 inches in diameter increased the H E T P threefold. Packed Height. The effect of packed height has not been studied very completely; only one set of data was found by Weimann ( 2 6 ) . The value of the exponent for the term h in the equation is the slope of the curve shown in Figure 7. This value is which checks other data for protruded packing where height was varied along with diameter. Liquid redistributors should be used in tall columns, especially where the diameter is large. The term F, in the equation is considered to be the distance between redistributors if they are used. Operating Pressure. The operating pressure is not considered in t h k paper because of the conflicting information given in the literature. Peters (20),Berg and Popovac ( 2 ) ,and Hawkins and Brent (IS) state t h a t pressure has little effect upon efficiency, The results of Struck and Kinney (94) show some effect, and Myles, Wender, Orchin, and Feldman (19) show a great effect of pressure upon height of equivalent theoreti'cal plate. It is possible that the mechanism of vapor-liquid mass transfer changes considerably as the pressure is reduced and the major
A
e
I.
Size, Inches 1/2
1 0 2 0
Gaddles
1/2
Mch'lahon
Stedman
KI
Ka
'/4
8/g
Protruded
Summary of Packing Constants
5.62
-0 37 -0 24 -0
0
10
-0.46
Remarks Estimated values of
0.76
-0.14
1.11
0.017 '/e '/a
0.20 0.33
i-0.50 +0.25 +0.20
1.00 1.00 1.00
0.39 0.076 0.45 3.06
+0.50 +0.30
0.30
+0.12
0.30
4-0.48
0 24 0.24 0.24
1/d0.16
Y2;{2!
116(6
0.077 0.363 0.218
+0.25
+0.26
+0.32
Kz
1.11
1.0
8/s(0.24] 8/r(0.48) 1.0
December 1953
2 10 8 53 0 57 042
Ka 1 24 1 24 1 24 1 24 1.24
0.30
Raschig rings of protruded metal
(4) (9, 10) ( 7 8,211 (11 )
( 7 6, Author's data)
53 -s n t
w I
H
Figure 10.
ET
P (EXPERINENTALI
Accuracy of HETP Correlation (High Range)
Symbol
A Table
References
n
0
Type of Packing Rings
(EXPERIMENTAL)
Accuracy of HETP Correlation (Low Range)
Packing Saddles Rings
References (7 7)
( 1 1)
factors governing efficiency at 760 mm. may be much different from the major factors at 10 mm. Physical Properties of System. The physical properties of the materials being distilled were found to be the most important factor affecting height of equivalent theoretical plate. The large number of physical properties which conceivably could affect the H E T P makes the evaluation of these factors very difficult. The data of Koffolt, Duncan, and Withrow (16) were valuable for this part of the work because five different systems were studied under identical conditions. A great many combinations of variables were compared; the combination which gave the best correlation was a @ / p . 01.
fi. p.
Relative volatility Liquid viscosity, centipoises Liquid density, grams per cc.
INDUSTRIAL AND ENGINEERING CHEMISTRY
2619
ENGINEERING AND PROCESS DEVELOPMENT Table II. System Methanol-water Trichloroethylenetoluene CCL-benzene Acetone-water Ethyl alcohol-water Ethvl alcohol-watei Ethyl alcohol-water Methanol-water
Type of Packing CaFbon rings
Ceramic saddles Ceramic saddles Ceramic rings
Data Used in Developing . - Correlation
Size of Column Packing, Diam Inch Inch;; >/Z 5
Packed Height, Feet 9.0
HETP Calcd. Actual 33.8 36.0 15.2 15.1
Deviation,
%
+.7
695
10.7
8.5
1-20.5
910 627 146 Q62
18.0 20.0 13.9 16.8 8.2 19.0
32.5 54.0
17.4 23.5 13.2 18.5 8.6 21.8 11.8 29.0 53.3
+3.3 -17.5 +5.0 -10.1 -4.9 -12.8 -12.8 f10.8
...
...
...
...
4.75
565 1013
1.67 2.18
1.73 2.07
-3.6 4-4.1
1
12
9.0
1s;
12
9.67
1
14 18 30 2-8
9
190 915 800 770 600
18 10 4.8
...
19.0
+1.3
...
8 mm.
4.3
EDC-benzene
1/c
6.0
EDC-benzene
McMahon
Z/I
4
5.6 (two sections)
675 1840
3.44 4.21
3.66 4.09
-6.4 +2.8
EDC-benzene
AlcMahon
";a
4
5.5 (two sections)
570 1780
3 70
2.78
2.89 3.44
-3.9 4-7.0
EDC-benzene
hIobIahon
I/t
7.8
650
6.0
6.6
-10.0
n-Heptane-Me cyclohexane
Protruded
0 24
9.7
8TO 870
2.93
6.0
4.01
2.14 3.95
f4.0 +l.5
n-Heptane-Me cyclohexane
Protruded
0 24
12
2.8
508 1050
2.04 2.98
2.10 3.10
-2.9 -4.0
n-Heptane-hIe cyclohexane
Protruded
0.48
12
3.0
508 1380
3.48 4.69
3.35 4.66
t3.7 +0.9
n-Heptane-XIe cyclohexane
Protruded
3.0
725 1580
8.94
7.75 9.00
f3.4 -0.7
n-Heptane-hle cyclohexane
Protruded
0 16
5.75
6.1
180 786
2.56 1.76
2.00 1.49
-1.5 +l5.3
EDC-benzene
Stedman
S o . 128
2.08
3.0
184 1810
0.65 1.95
0.72 2.00
-10.8 -2.5
EDC-benzene
Stedman
S o . 107
3 08
3.0
142 1500
1.00 1.85
0.92 1.73
+12.5 $6.5
EDC-benzene
Stedman
S o . 115
0.08
3.0
132 1266
0.95 1.91
1.00 1.89
-1.0
1;r
6
3.5-13.3
(three sections)
2
12
1 0
12
The factor 01 seems t o be the most important single physical property affecting the HETP. A fairly good correlation is obtained between CY and HETP. The theoretical reason for this relationship is not clear, but i t might be noted t h a t CY is proportional t o the quantity of material transferred between phases per HETP. The addition of the ratio p / p is in agreement with the prediction of SherKood and Holloway (39) t h a t liquid phase transfer coefficients should be proportional t o the Schmidt number, D ~ P . As there are very few literature data on liquid diffusivities, they were omitted from the factor. The curve of Figure 8 shows the good correlation of the factor o p / p with HETP.
5.02
Pnrpare of B u n
-6.5
Ceramic saddles Porcelain rings AIcMahon
N2-01
Etbvl alcohol-water
-5.2
Effect of physical properties
umn diameter us. HE*? for 1-inch lings Column diameter as. HET P for '/Anoh saddles H E T P 11s. packed height
Mass velocity us. K E T P for i/r-inch McMahon packing Mass velocity us. H E T P for '/pinch MoMahon packing Mass velocity os. H E T P for s/s-inch Mchlahon packin Used wifh data from Fisher and Bowen for effect of column diameter upon H E T P Column diameter us. HET P for 0.24-inch nrotruded packing hIms velocity US. H E T P for 0.24-inch protruded packing Mass velocity US. H E T P for 0.48inch protruded packing Mass velocity us. H E T P for 1.0-inch protruded packing Mas8 velocity os. H E T P for 0.16-inch protruded packing Mass velocity us. H E T P for 2-inch Stedman column Maas velocity us. H E T P for 3-inch Stedinan column Mass velocity DS. H E T P for 6-inch Stedman column
Summary of Constants. Table I summarizes the constants K1,
Kz,and Ka as a function of packing size and type. K1 varies widely in an irregular manner with no apparent relationship to the packing performance, largely because the exponential constants, Kz and Ka,exert a great influence upon the value of the proportionality constant, K I . Accuracy of Equation. Figures 9 and 10 show the accuracy of the correlation. The HETP predicted by the equation is within & l o % for about 95% of the data studied. Therefore i t is recommended that in design work a safety factor of 20% be applied to the HETP calculated from the equation. Data Used in Developing Correlation Are Summarized
Complete Equation I s Obtained by Combining Individual Factors
The complete equation is obtained by combining all the individual factors, determining the constants Kz and K I from curves 2 through 6, and solving for K I by using the experimental values.
HETP = KIGg%!Kfhl'aX E UP
Where the terms are as shown above. Limitations of Equation. Several limitations had to be placed upon the equation: Atmospheric pressure operation only. Mass velocity between 25 and 80% of flooding. Ratio of column diameter to packing diameter greater than 8 t o 1. Total reflux or high finite reflux ratios.
2620
Vapor Rate Lb./Hour/' Sq. Foot 646 676
A brief summary of the data used in developing the correlation is presented in Table 11. The complete data, comprising some 148 different experiments, are on file with the American Documentation Institute. The purpose of each series of experiments is given in the remarks column. Some of the data, presented as heights of over-all transfer unit, were converted to heights of eauivalent theoretical ulate using the McCabe-Thiele method ( 1 7 ) . As the data of Cannon et al. ( 5 )do not give the liquid and vapor concentration, it was necessary to use assumed values of physical properties. The error is not large, however, as cy and other properties do not vary much with changes in concentration. Likewise, no concentration data were available for the results of Keimann, which were used only to predict the effect of packed height. Kirschbaum (16) presents many data on packed columns, but his results do not agree with other work such as t h a t of Furnas and I
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
Vol. 45, No. 12
ENGINEERING AND PROCESS DEVELOPMENT
w
Taylor (11) and Koffolt, Duncan, and Withrow (16). His method of calculating theoretical plates may account for this variation. Some of the data of Furnas (11)for ring packings were not used because they did not agree with other results or cannot be reconciled with the work of other investigators-for example, height of equivalent theoretical plate is lower with a/&nch rings as the packed height is increased, and is lower with 1-inch than with 3/8-in~hrings. For systems such as ethyl alcohol-water or methanol-water, where a varies widely with composition, the average a was obtained by a graphical integration method similar to t h a t used by Koffolt, Duncan, and Withrow (16) to evaluate m, the slope of the equilibrium curve. The author’s data on methanol-water, used to evaluate the effect of column diameter, were obtained a t 40 to 1 reflux ratio rather than total reflux. Koffolt and Withrow ( 1 6 ) and Furnas ( 1 1 ) present a large amount of data obtained a t low reflux ratios, but th’e results show very high values at low vapor-liquid ratios. The reason for this is unknown. Colburn and Pigford (7) suggest t h a t liquid and vapor compositions are so close together that poor distribution at the ends of the column results in low efficiency. Another explanation might be t h a t with low reflux ratios the operating line is very close to the equilibrium curve. The assumption of a straight operating line may not be valid, and if the operating line actually curves toward the equilibrium curve the true number of theoretical plates would be much greater than if a straight operating line is assumed, and hence the values for height of equivalent theoretical plate would be lower. literature Cited
(1) Aston, J. G . , Lobo. W. E.. and Williams. B.. IND. ENG.CHEM., 39, 718 (1947).
Berg, L., and Popovac, D. O., Chem. Eng. Progr., 4 5 , 6 8 3 (1949). Bowman, J. R., IND. ENG.CHEM.,39, 745 (1947). Bragg, L. B., Ibid., 33, 279 (1941). Cannon, M. R., Manning, R. E., and Heinlein, A. C., C h m . Eng. PTOgT., 47, 344 (1951).
Colburn, A. P., and Chilton, T. H., IND. ENG.CHEM.,27, 255 (1935).
Colburn, A. P., and Pigford, R. L., “Chemical Engineers’ Handbook.” 3rd ed.. New York. McGraw-Hill Book Co.. 1950. Deed, D. W., Schutz, P. W., and Drew, T. B., IND. ENG. CHEM., 39, 766 (1947).
Fisher, A. W., and Bowen, R. J., Chem. Eng. Progr., 45, 359 (1949).
Forsythe, W. L., Stack, T. G., Wolf, J. E., and Conn, A . L., IND. ENG.CHEM.,39, 714 (1947). Furnas, C. C., and Taylor, M. L., Trans. A m . Inst. Chem. Engrs., 36, 135 (1940).
Gilliland, E .R., “Elements of Fractional Distillation,” 4th ed., New York, McGraw-Hill Book Co., 1950. Hawkins, J. E., and Brent, J. A,, IND.ENG.CHEM.,43, 2611 (1951).
Heinlein, A. C., M. S. thesis, Pennsylvania State College, 1949. Kirschbaum, E., “Distillation and Rectification,” pp. 313, 315, 316, New York, Chemical Publishing Co., 1948. Koffolt, J. H., Withrow, J. R., and Duncan, D. N., Trans. A m . Inst. Chan. Engrs., 38, 259 (1942).
McCabe, W. L., and Thiele, E. W., IND.ENG.CHEM.,17, 605 (1925).
Manning, R. E., M.S. thesis, Pennsylvania State College, 1949. Myles, M., Wender, I., Orchin, M., and Feldman, J., IND. ENQ. CHEM.,4 3 , 1 4 5 2 (1951). Peters, M. S., Ph.D. thesis, Pennsylvania State College, 1951. Ryan, J. F., M.S. thesis, Pennsylvania State College, 1950. Sherwood, T. K., and Holloway, F. A. L., Trans. Am. Inst. Chem. Engrs., 36, 39 (1940).
Sprague, E., and Fletcher, J., Dow Corning Corp., private communication. Struck, R. T., and Kinney, C. R., IND. ENG.CHEM.,4 2 , 7 7 (1950). Weimann, M., Chem. Fabrik, 6 , No. 40, 411 (1933). RECEIVED for review June 14, 1952. ACCEFTED bugust 26, 1953. Prasented at the Meeting-in-Miniature, New Jersey Section, AMERICAN CHEMICAL SOCIETY, Newark, N. J., January 1961.
Application of Computing Machines to Exchange Column Calculations ASCHER OPLER f i e Dow Chemicol Co., Pittrburg, Calif.
T
HIS report represents the results of an intensive exploration of the possibilities of applying digital computing machines to the mathematical treatment of ion exchange column performance. Using a simple, slow speed, punched card operated computer, several different types of calculation were programmed and typical ion exchange problems were solved. This report should be interpreted as indicative of the potentialities of applying computing machines to this problem rather than as an exhaustive study. Rosen and Winsche (18)and Rose, Lombardo, and Williams (19, 17) previously have applied computing machines t o similar problems. Rosen and Winsche used an analog computer in investigating the performance of a coIumn whose feed concentration is a sinusoidal function of time. Rose, Lombardo, and Williams described a finite difference method for calculating the performance of adsorption columns. Recent books have reviewed mathematical treatment of adsorption and ion exchange ( 4 , IO, 16). Although the equations, examples, and discussions will be restricted to ion exchange, in all cases the techniques may be modi-
December 1953
fied for use in adsorption column calculations. Chromatography, selective adsorption, and similar phenomena may be treated by each of the methods described. Computing machines can play a large role in extending the number of practical problems that can be treated mathematically. They may be applied to various theoretical and empirical equations for the purpose of obtaining large quantities of numerical solutions; applications to the equilibrium plate and the kinetic treatment are illustrated. These machines are useful in connection with a finite difference technique t h a t requires the machine to operate as an analog of the column. The probabilistic Monte Carlo method may also be handled by automatic computing machines and may ultimately lead to the most complete treatment of parameters. With one minor exception, all calculations reported here were performed on the 602-A calculating punch of the International Business Machines Co. Other supplementary machines were used in originating and manipulating the more than 50,000 punched cards involved in this study. The 602-A was programmed using both the standard wire-programming method, the
INDUSTRIAL AND ENGINEERING CHEMISTRY.
2621
