Acknowledgment
I t is a pleasure to acknowledge the contribution of Giuseppe Marrucci, and work done by Antonio Patierno, Vincenzo Perrotti, Arturo Saponara, and Renato Toncelli. Literature Cited (1) Andrews, S. P. S., personal communication to Danckwerts, P. V., A.Z.Ch.E. J. 1, 456 (1955). (2) Astarita, G., Ric. Sei.31(11-A), 177 (1961). (3) Astarita, G., Beek, W. J., Chem. Eng. Sci. 17, 665 (1962). (4) Astarita, G., Marrucci, G., IND.ENG.CHEM.FUNDAMENTALS
(6) Davidson, J. F., Trans. Znst. Chem. Engrs. (London) 37, 131 (1959). (7) Marrucci, G., Astarita, G., Rend. Cl. Sei. Fis. Mat. Nut. Accad. Limei, VIII-33,459 (1962). (8 Njising, R. A. T. O., Ph.D. Dissertation, Univ. of Delft, 1956. Patierno, A., Chem. Eng. Thesis, Univ. of Naples, 1962. 10) Perrotti, V., Chem. Eng. Thesis Univ. of Naples, 1962. (11) Perry, R. H., Pigford, R. L., Znd. Eng. Chem. 45, 1247 (1953). 12) Saponara, A., Chem. Eng. Thesis, Univ. of Naples, 1961. 13) Sherwood, T. K., Pigford, R. L., “Absorption and Extraction,” McGraw-Hill, New York, 1951. (14) Toncelli, R., Chem. Eng. Thesis, Univ. of Naples, 1961.
2. 4. (1963). -7 \ - - --,-
(5) Astarita, G., Marrucci, G., Di Blasio, G., Chim. Znd. (Milan) 44, 142 (1962).
RECEIVED for review April 24, 1962 ACCEPTED August 14, 1963
FOAM FRACTIONATION Standard Separator and Rej7uxing Columns C A R L A.
B R U N N E R ’ A N D
R O B E R T L E M L I C H
Defiartmcnt of Chemical Engineering, University of Cincinnati, Cincinnati 21, Ohio
A reliable, recirculating, one-theoretical-plate separator was developed to serve as a standard means for measuring separability in foam fractionation. Tests, using humidified nitrogen with the system Aresket-300 in water, yielded reproducible results. Utilizing the same system, experiments were conducted with en,iching columns where a portion of the collapsed foam was returned to the top of the column to serve as reflux. The degree of enrichment increased with reflux ratio. The experimental results support a theoretical equation for very long enriching columns based on a simple physical mechanism involving rising enriched bubble surfaces carrying liquid entrainment countercurrent to a downcoming liquid stream. OAM fractionation has recently been the subject of increased Fattention. I t has been investigated as a method for removing objectionable surfactants and certain other impurities from waste water (3,4, 7), a means for eliminating radioactive contaminants from dilute effluents ( 2 ,Q), a technique for the selective separation of certain complex organic materials such as proteins (8). and a tool for studying surface phenomena p e r se (5). The fundamental mechanism of separation depends on the adsorption of a surface active solute a t the interface of the solution. Bubbling gas through the solution generates interfacial surface as foam, which rises, carrying off solute. The use of reflux enhances the separation (6). A foam fractionation column can operate as a stripper, a n enricher, or a combined column. The performance in each case depends in large measure on the fundamental ease or difficulty of separating out the one or more surface active constituents involved. Accordingly, the first part of the present study was devoted to the development of a reliable, recirculating, “one theoretical-plate” separator to serve as a standard for obtaining equilibrium relationships in current and future studies of foam fractionation. The second part of the study consisted of a n investigation of enriching (refluxing) columns that operate by foam fractionation.
bottoms concentration constant and thus permit attainment or steady-state operation in about a n hour. The entire column held about 500 ml. of liquid, and was operated a t 25’ C. A schematic diagram is shown in Figure 1. Further details have been placed on file ( 7 ) . The system employed \vas the surfactant Aresket-300 (monobutyl diphenyl sodium monosulfonate) in distilled water. Initial charge concentrations ranged from 5 X lop4 to 3 X M . Prepurified nitrogen, carefully humidified in a separate column, \vas used as the gas. A
. \ \
H I G H CONCN. FOAM BREAKER
LOFoiiNCN.7 BREAKER
\!J
I
RETURN RE 3
I
PUMP
Development of Standard Separator
The standard separator consisted essentially of a :vertical glass column 1.6 cm. in diameter over most of its SO-cm. length, flared a t the bottom to receive a special bubbler, and connected a t the top to a foam breaker. For low surfactant concentrations. the foam breaker consisted of a n inverted Erlenmeyer flask with a bent rotating stirring rod. For higher concentrations a perforated can spinning inside a n inverted plastic bottle was used. Collapsed foam was returned to the bottom via a Sigmamotor finger pump so as to keep the
’
Present address, Taft Sanitary Engineering Center, U. S. Public Health Service, Cincinnati, Ohio.
TOP VIEW OF BUBBLER BUBBLER
Not To Scole
HUMIDIFIED SAMPLER
Figure 1.
Standard separator
VOL. 2 NO. 4 NOVEMBER 1 9 6 3
297
I
CONCENTRATION IN
Figure 2.
I
LIQUID
I
I
-
d
I
REFLUX
I mg,moies/iiier )
t
Results with standard separator
SAMPL
~
RETURN
BUBBLER
I
HUMIDIFIED
N,
'f SAMPLER
Not To S c a l e
Figure 4.
Enriching column
40
30 0.0 I
01
10
1
CONCENTRATION
Figure 3.
(mg.
moles/
Iller)
Surface tension
For each run the rate of foaming was recorded. Concentrations of liquid pool and collapsed foam were measured with a Beckman DU spectrophotometer. The rate of gas flow was measured with calibrated rotameters, and bubble sizes were determined optically with a Brinell microscope. From these data the excess solute per unit surface area was calculated by material balance in the form of Equation 1 :
rw
=
( C D - Cw)Q/GS
(1)
Results, shown in Figure 2, proved to be consistent and reproducible. Each of the four points plotted in this figure is actually a n average of a set of four to 10 individual runs. Despite considerable variation in Q/G within each set, the standard deviation in Fw for runs within any set did not exceed 3%. Q/G ranged from about 0.12 to 0.20 at the lawest charge concentration of 5 X 10-4M, from about 0.07 to 0.14 a t the next higher concentration, and from about 0.07 to 0.09 a t the two highest concentrations. Within reasonable limits, foam wetness and column dimensions were not significant, so long a- thr concentration in the liquid pool was sufficient to generate a foam stable enough to prevent appreciable bubble brcakage in the column pr3per. Several types of bubbler were investigated, including a spinneret and various fritted-glass tubes. However, the bubbler that gave by far the most uniform and reproducible bubbles was a rubber stopper holding 13 capillary tubes of 0.08-mm. diameter (Figure 1). A number of runs were also conducted without recirculation, using modified apparatus. Columns of several different heights and diameters and various gas rates and liquid concentrations were used. For each run the bubbler was placed in a 2-liter flask of liquid at the bottom of the column. The purpose of this relatively large liquid supply was to furnish a substantially constant liquid concentration during a run. This technique proved reasonably effective, but not as satisfactory as recirculation. 298
I&EC F U N D A M E N T A L S
Figure
5. Solute material balance around refluxing column
Direct comparison with the idealized Gibbs adsorption equation (Equation 2) is of questionable significance here.
Applicability of the idealizations, including the extent of surfactant ionization in the surface, is uncertain in the present case. Nevertheless, the comparison was made, with the slope d y / d In C determined from surface tension measurements (Figure 3) obtained with a ring tensiometer. The results agreed within 10% over the range of interest Enriching Columns with Reflux
The experimental approach M ith reflux was basically similar to that described above, except that a portion of the collapsed foam was re-introduced via a pump through a small glass tube near the top of the column to serve as the reflux (Figure 4) Further details have been placed on file ( 7 )
Table 1. Column Length, Cm. 75
75 100
100
151 151 197 194 See discussion immediately following Equation 100
a
Gas Rate, Ml./Min. 114 114 115 114 131 131 132 131 131 130 163 164 160 163
Bottoms Concentration, Mg. MoleslLiter 2.21 2.15 2.10 2.11 1.48 1.90 1.90 1.83 1.79 1.83 1.68 1.35 1.52 1.52 1.46 ~
1.02 0.96 0.62 0.63 4 in text.
Results with Enriching Columns
0 0 1.66 2.55
Enrichment Ratio, CD/CW 2.02 1.87 2.47 3.19 10.05 2.10 2.29 2.92 3.07 5.63 1.82 2.15 3.08 4.03
Miscellaneous Runs 0.99 2.08 2.77 3.75
3.80 3.76 2.46 3.39
Rejux Ratio 0 0 1.24 2.38 03
0 0 0.92 1.89 m
The same system-Aresket-300 and water-was used. As before, operation was at 25’ C. The foam column was 4.6 cm. in diameter and either 75 or 100 cm. in height above the liquid pool a t the bottom. Various combinations of gas rate and surfactant concentration were investigated. The experimental procedure was rather tedious, many hours of constant attention being required to achieve steady-state operation for a single run. Samples were withdrawn a t several locations for each run and analyzed for surfactant spectrophotometrically. There \%asvirtually no bubble breakage in the column itself. Nevertheless, considerable enrichment in the overhead foam was obtained. This enrichment, defined as C,/Cw, increased as the reflux ratio increased, confirming preliminary expectations. Increasing the gas rate decreased the residence time, making for less complete drainage and a lo\\er enrichment ratio (Table I). The detailed behavior within a refluxing foam column is extremely complex. Therefore, in a n effort to develop appropriate theory, an over-all solute balance is struck over the column. This is shown schematically in Figure 5 . The two separate streams shown a t the bottom of the column evolve directly from a simple physical model which pictures rising bubble surfaces carrying liquid “entrainment,” Q ’, moving countercurrent to a more or less distinct downcoming liquid stream, (Q ’-D). Solving the balance for the enrichment ratio gives Equation 3
However, concentration C, is not known. T o bypass this difficulty a very long column is considered. With sufficient length, C, will approach C, because of the increased opportunity for contact between the countercurrent streams within the column. (The situation is somewhat analogous to a packed distillation column in which the concentration of the donmcoming liquid stream entering the reboiler approaches the concentration in the reboiler when the height of the column, and hence the number of theoretical trays, becomes infinite.) Equating C, with C , in Equation 3 yields Equation 4 for very long columns. Naturally, the enrichment approaches a maximum as the column length increases.
Total Ouerhead Rate, MI. Collapsed Foam/Min. 1.89 2.11 2.42 2.12
... 1.97 1.64 2.10 2.39
...
CD/CW (CD/CW)max.’
70
100 100 88 78 OQ 00 00 96 85 Oa
2.76 2.23 2.68 2.51
00 00
1.44 1.95 5.70 4.31
... ... ...
95 92
(4)
Equation 4 must not be applied to mutually incompatible conditions. For example, with R = 03 (total reflux) C, must also be infinite, since C , must be finitely above zero so that foam can be generated. An infinite C, is clearly absurd. Indeed, even a finite C, can be absurdly high. Analogous difficulties arise in distillation when conditions of nonzero bottoms concentration, infinite number of trays, and too high a reflux ratio are all imposed simultaneously. Application of Equation 4 to the present experimental data is shown in Table I. For convenience, rather than using Figure 2 and bubble size measurement to find S and rw, their product was determined by running the enriching column a t zero reflux. Sr, \?;as then calculated from Equation 1 (which is really a special case of Equation 3 with no reflux). The average value for each pair of runs a t zero reflux was used for ST, in Equation 4. The last column in Table I shows the degree of approach to maximum enrichment. The smaller the reflux ratio, and consequently the smaller the concentration difference over the column, the better is the approach to maximum enrichment. At modest reflux ratios the approach is fairly close and, as predicted, improves further as the column is lengthened. All in all, it would seem that the simple physical model proposed here has merit. Furthermore, at modest reflux ratios the columns are reasonable approximations of very long columns for M hich performance can be estimated by Equation 4.
Nomenclature C = concentration, mg. moles/ml.
D
= overhead product rate, ml. collapsed foamlmin.
G = gas rate, ml./min. Q = total overhead rate, ml. collapsed foam/min. Q ’ = rate of entrainment of liquid from the bottom pool, ml ./min,
R = reflux ratio R’ = gas constant, erg/mg. mole S
T y
I-
= = = =
O
K.
bubble surface, sq. cm./ml. absolute temperature, O K. surface tension, dynes/cm. solute surface excess (adsorbed solute), mg. moles/sq. cm. V O L . 2 NO. 4 N O V E M B E R 1 9 6 3
299
SUBSCRIPTS
D
= overhead (collapsed foam)
L = liquid draining into liquid pool at bottom of column W = liquid pool a t bottom of column
literature Cited (1) Brunner. C. A.. “Foam Fractionation.” Ph.D. dissertation. \
t
6) Lemlich, R., Lavi, E., Science 134, No. 3473, 191 (1961). 7 ) McGauhey, P. H., Klein, S. A., Palmer, P. B., “Study of Operating Variables as They Affect ABS Removal by Sewage Treatment Plants,” Sanitary Eng. Res. Lab. Rept., Univ. Calif., October 1959. (8) Schnepf, R. W., Gaden, E. L., Jr., J . Biochem. Microbiol. Tech. Eng. 1, 1 (1959). (9) Schnepf, R. W., Gaden, E. L., Jr., Mirocznik, E. Y., Schonfeld, E., Chem. Eng. Progr. 55, No. 5, 42 (1959).
,
Universit; of Cincinnati. June 1963. (2) Chem. Eng. 68, No. 7 , 100 (1961). (3) Zbid., 69, No. 9, 62 (1962). (4) Husman, W., Textil-Rundschau 17, 88 (1962). (5) Lauwers, A., Joos, P., Ruyssen, R:, Vortraege Originalfassung Intern. Kongr. Grenzflaechenaktive Stoffe, 3rd, Cologne, Vol. 3, p. 195, 1960.
RECEIVED for review March 15, 1963 ACCEPTEDJune 7, 1963 Division of Water and Waste Chemistry, 143rd Meeting, IACS, Cincinnati, Ohio, January 1963. Work supported directly by U. S. Public Health Service Research Grant WP-161 and indirectly by a National Science Foundation Cooperative Fellowship.
A DIFFERENTIAL STAGE CASCADE DESIGN
FOR SEPARATION OF T W O COMPONENTS
IN A DILUTE SOLVENT G ERA LD T
.
FISH ER
’
AND J 0
HN W
.
P R A D 0 S, The University of Tennessee, Knoxville, Tenn.
The equations of a differential stage cascade are formulated for the separation of two components in a dilute solvent. The solution is presented as a definite integral of unknown general solution; a program is presented for the solution of the cascade differential equation on an analog computer. A specific solution is presented for a thermal diffusion cascade separating CuSOl from Cos04 in HzO. HE SEPARATION of mixtures in mass transfer cascades is Tquite common. The distillation tower is a n example of a cascade of equilibrium stages; it operates usually with all stages of equal size and constant flow rate from stage to stage. A single tower operates with no internal reflux on each stageLe., all of the products from one stage go initially to another stage. A series of distillation towers can be operated as a cascade with unequal size stages and unequal flow rates from stage to stage (7); the purification of heavy water has been performed by such a system ( 2 ) . The advantage of such a system is that it minimizes the total size of the equipment required to perform the separation; this is obtained a t the expense of increased heat loads for a distillation cascade (2,3). In this article, the equations of a cascade for separation of two components which are in a dilute solution with a third component, a solvent, will be considered. The equations were developed for the thermal diffusion separation by horizontal columns (Jury-Von Halle type) of two salts in water solution (4), but the equations will apply to any system which can be characterized by a constant mass transfer coefficient and a linear equilibrium relation.
Equations for a Single Stages of the Cascade I t is assumed that the rate of mass transfer for each component is J = ~ L ( x *- X ) (1) and that the equilibrium relation is y = Kx* If a single unit of the cascade is operated as shown in Figure 1, a material balance on a differential section for constant L is L dx J = - - (3) aS dz 1
300
Present address, Vanderbilt University, Nashville, Tenn. l&EC FUNDAMENTALS
The material balance over the top section of the unit is Vy = LX
+D
x ~
(4)
By combining the first four equations, one obtains
where
Equation 5 may be integrated from x ( 0 ) = x , to x ( Z ) = xD, to obtain, for constant L, V , K , and h,,
(6) where R = L / D and Z is the total length of the column. If one defines the overhead fraction 0 by
e = -D
v
1 R+1
(7)
the equation becomes
For component a, this quantity is defined as w : thus w = - aXL oXD
(9)
If the ratio of the component concentrations, A , is defined as
