P, = a constant in the equation of the installed or P, =
Q,
Qc
or
Qcoal r
q qmx qm, Rmn Rmx
r,
= = = = = = = = = =
s= S I tl
= =
t* = t3 = t4
t j ,
=
TS = tu, =
t,,, = t/ = t, =
u= = u1 = u,=
Uh,
u 3
=
u 4
=
v= v,,= w1 = w2 = XI, x / = 7.2
=
= xi = x, = yl = x3
fabricating cost of pumps and motors a constant in the equation of the installed or fabricating cost of an absorber heat load heat load in a condenser heat load in a cooler heat load in a reboiler q-value maximum q value minimum q value reflux ratio of a stripper upper constraint for R random number number of stages steam consumption in a reboiler operating temperature of an absorber feed temperature to a stripper dew point of top product bubbling point of bottom product from a stripper inlet temperature to a cooler inlet temperature of cooling water outlet temperature of cooling water temperature a t the feed plate in a stripper saturated temperature of steam in a reboiler linear velocity in a stripper over-all heat transfer coefficient over-all heat transfer coefficient in a condenser over-all heat transfer coefficient in a reboiler over-all heat transfer coefficient in a heat exchanger over-all heat transfer coefficient in a cooler vapor load in a stripper specific molar volume cooling water consumption in a condenser cooling water consumption in a cooler feed composition to a stripper composition of an absorbent fed to an absorber (bottom composition in a stripper) composition or purity of top product independent variable see section “inequality constraints” feed composition to an absorber
ye = exhaust gas composition from an absorber y( = see section “inequality constraints” 2 = height of an absorber
GREEKLETTERS a,
P = constants in cost data equation Y = reflection factor in Complex method c = void in a packed bed (fraction) ILE = viscosity of gas or vapor kl = viscosity of liquid = viscosity of water Pa = density of gas or vapor pi = density of liquid
fill
Literature Cited
American Institute of Chemical Engineers, Xew York, “Bubble Tray Design Manual,” 1958. Box, M. J., Computer J . 8, No. 1, 42 (1965). Chilton, C. H., Ed., “Cost Engineering in the Process Industries,” McGraw-Hill, New York, 1960 Fenske, M. R., Ind. Eng. Chem. 24, 482 (1932). Gilliland, E. R., Ind. Eng. Chem. 32, 1220 (1940). Lobo, W. E . , et al., Trans. Am. Inst. Chem. Engrs. 45, 693 (1945). Nielder, J. A., Mead, R., Computer J . 7, Xo. 4, 308 (1965). Perry, J. H., Ed., “Chemical Engineers’ Handbook,” 4th ed., pp. 14-29, McGraw-Hill, New York, 1963. Peters, M. S., “Plant Design and Economics for Chemical Engineers,” McGraw-Hill, Xew York, 1958. Sawistowski, H . H., Smith, W., “Mass Transfer Process Calculations,” Interscience, Kew York, 1963. Smoker, E. H., Trans. A m . Inst. Chem. Engrs. 34, 165 (1938). Souders, M., Brown, G. G., Ind. Eng. Chem 26, 98 (1934). Spendley, W., Hext, G. R., Himsworth, F. R., Technometrics 4, Xo. 4, 441 (1962). Umeda, T., M.S. thesis in chemical engineering, University of Minnesota, 1966. Underwood, A. J. V., Chem. Eng. Progr. 44, 603 (1948). RECEIVED for review May 29, 1968 ACCEPTED January 16, 1969
SORPTION OF SULFUR DIOXIDE BY ION EXCHANGE RESINS LAWRENCE
L A Y T O N ’ A N D
G .
R .
Y O U N G Q U I S T
Department of Chemical Engineering, Clarkson College of Technology, Potsdam, AV.Y . 13676 Rate and equilibrium data are presented for sorption of sulfur dioxide on a weak base, macroreticular ion exchange resin. Rates are limited by intraparticle diffusion. Equilibrium loadings a t 25’ C. compare favorably with other adsorbents.
THEsorption of gases and vapors by ion exchange resins has been given little attention. Cole and Shulman (1960) showed that the equilibrium uptake of sulfur dioxide by several types of dry ion exchange resins compared favorably with that of commercial adsorbents such as silica gel, activated charcoal, and molecular sieves. Although no definitive rate measurements were made, qualitatively the rates of approach to equilibrium were so low as to
‘Present address, E. I. du Pont de Kernours and Co., Inc., Parlin, N. J.
make industrial applications doubtful. The resins used were of the microreticular type, generally characterized by low surface areas (less than 1 sq. meter per gram) and low porosity (less than lei). Pores in the resin consist of spaces between polymer chains, are of molecular size, and may be very small or nonexistent unless the polymer matrix is swollen by the presence of a solvent such as water. The sorption process for a microreticular resin is somewhat akin to absorption and the low sorption rates observed by Cole and Shulman may perhaps be attributed to the slow diffusion of sulfur dioxide through the unswollen polymer matrix of the dry resins. VOL. 8 NO. 3 JULY 1969
317
More recently, macroreticular resins having relatively high surface areas and porosities (compared to microreticular resins) have been introduced. Methods of preparation and the physical properties of several such resins are discussed in detail by Kun and Kunin (1967) and Millar et al. (1963, 1964). The much larger pores of the macroreticular resins, approximately 300 to 1200 A. in diameter, provide greater accessibility to the interior of the resin particles than for the microreticular resins. Hence, higher sorption rates are to be expected. Moreover, significant adsorption may occur on the relatively large surface area due to the pore walls, adding to the sorption capacity of the resin. Pollio and Kunin (1968) have recently described the sorption of hydrogen sulfide by dry macroreticular quaternary ammonium ion exchange resins using a fixed-bed system. They report essentially quantitative removal of hydrogen sulfide, but make no attempt to analyze the rate characteristics of the system. A similar fixed-bed study in Czechoslovakia (Krecjar, 1965) showed that sulfur dioxide could be sorbed by both weakly basic and strongly basic anion exchange resins, with the amount sorbed dependent upon the moisture content of the resin. Hydrogen sulfide also could be sorbed by two of the strongly basic resins tested. I n the present work, sorption of sulfur dioxide by Amberlyst A-21, a weak base macroreticular ion exchange resin manufactured by the Rohm and Haas Co., was studied. Rate and equilibrium data were obtained gravimetrically for resin samples exposed to pure sulfur dioxide in order to examine the rate characteristics of the system.
PORE DIAMETER (MICRONS)
042-050rnm(-35*401
(0297rnm (-501
5
I
2
3
5
PRESSURE ( P S I A ) ~
Figure 1 . Mercury porosimeter results showing variation of pore diameter with particle size
Experimental
A-21 is a tertiary amine resin derived from the reaction of a secondary amine with a chloromethylated styrenedivinylbenzene copolymer. Physical properties of the resin have been reported by Kun and Kunin (1967). As received from the manufacturer, the resin was in the form of small spherical beads ranging in size from approximately 0.2 to 3 mm. in diameter. Since the resins were received wet, they were initially dried a t 80°C. in an atmospheric oven for approximately 12 hours, then screened into various size fractions. Pore size distributions for each size fraction as determined by mercury porosimetry are shown in Figure 1. The pore size decreases with decreasing particle size. For the smallest particles, the middle 80% of the measured pore volume consists of pores between 400 and 800 A. in diameter; for the largest particles, between 700 and 1000 A.; and for intermediate sizes, between 500 and 1000 A. The B E T surface area for -16- +20mesh particles as determined by N 1 adsorption was 28 sq. meters per gram. Sorption rate measurements were made with a recording electrobalance system (Figure 2) used to detect the change in weight which occurred as sorption took place on a resin sample exposed to pure sulfur dioxide in pressure steps. The electrobalance was the Cahn RG automatic recording electrobalance, a continuous weighing device with an ultimate sensitivity of lo-' gram. Pressures were measured using either a tilting McLeod gage or a mercury manometer. The volume of the system was sufficiently large so that the pressure remained constant during sorption. Temperature was maintained constant using a controlled water bath placed around the sample hangdown tube and measured with a thermocouple. 318
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
I
Figure 2. Sorption apparatus A. Sulfur dioxide tank 6. Nitrogen tank
C. Molecular sieve bulbs D. Cahn RG electrobalance E. Electrobolonce control
J. Powerstot
K . Manometer 1. Mcteod gage M. Bennert gage N. Constant temperature unit 0. Heating unit for regeneration P. Bronwill constont temperature circulator
F. Recorder G. Gas storage vessels H. Thermocouple reference junction Q. Vocuum pump S. Constant temperature bath 1. Temperoture recorder
To remove residual water or other sorbed materials, the resin sample was pretreated in situ prior to sorption measurements by evacuation to approximately 1 micron of Hg and heating at 90°C. Temperatures much above 100" C. result in degradation of the resin. These conditions obtained constant minimum weight in about one hour. With the system still under vacuum, the temperature was reduced to 25. C. and allowed to equilibrate. Research grade sulfur dioxide, passed initially through a drying tube containing Type 4A molecular sieves, was then admitted to the system, raising the pressure to a predetermined value, and the uptake to equilibrium was observed. When no additional uptake was noted, usually after one week, the pressure was increased and the uptake to equilibrium again observed. Desorption measurements were made in similar fashion, incrementally reducing rather than increasing the pressure.
Results and Discussion
As a separate check on the reaction of the sulfur dioxide a t the exchange sites of the resin, a simple weighing expcriment was conducted. Using the 1-mm. diameter size, I O C particles each of fresh resin and saturated resin were dried to constant weight a t 90°C. Since the fresh resin had. never been exposed to sulfur dioxide and the Saturated resin had been exposed for over one year, the difference in weight of the two samples was attributed to the sulfcr dioxide-exchange site reaction. This weight difference corresponded to 5.05 meq. per gram, in good agreement wit?c the sorption-desorption experiment and with the statcd exchange capacity of the resin. I n addition, infrared spectra were obtained for dried samples of the fresh and the saturated resin. The spcctrs (Figure 4) differ principally in the frequency range 9 G O to 1000 cm. ’, which is the absorbance band for the sulfite ion. SO, -, indicating that this species accounts for t h , residual SO?. In view of the fact that the resin was obtained wet and that it may not be possible to remuve completely water hydrated a t the exchange sites by evacuation and heating, the sulfur dioxide possibly reJcts according to
Two series of sorption-desorption experiments were conducted. one with resin never exposed to sulfur dioxide and a second with resin exposed t o a sulfur dioxide atmosphere for more than one year. (Hereafter, the former is referred to as “fresh“ resin and the latter as “saturated” resin.) The experiments were carried out a t 25°C. and covered a pressure range of about 0.35 to 540 mm. of Hg. Figure 3 shows the equilibrium data obtained for two fresh resin samples of different particle size. The equilibrium loadings of sulfur dioxide are high, corresponding to more than SO‘, of the dry weight of the resin at the highest pressures used and more than 10‘r of the dry weight even a t pressures less than 1 mm. of Hg. The loadings are dependent on particle size, the larger particles giving the higher values. This is not unexpected, since the measured pore size distributions showed different pore sizes for the different particle sizes, probably giving rise to diff‘erent surface areas and porosities. The data also indicate that the sorption process is not completely reversible. As the pressure in the system is decreased, not all of the sulfur dioxide is desorbed, even after evacuation to 1 micron of Hg and heating a t 90°C. for 12 hours. The residual sulfur dioxide for the 1-mm. diameter particles was 5.5 meq. per gram, which corresponds approximately to the exchange capacity of the resin stated by the manufacturer as 4.8 to 5.0 meq. per gram. This indicates that some of the sorbed sulfur dioxide has reacted irreversibly a t the exchange sites of the resin. For the 0.2S-mm. particles the residual sulfur dioxide was 3.6 meq. per gram; the difference was probably due to the different physical properties of the smaller size resin. Cole and Shulman (1960) also noted that sulfur dioxide could not be completely desorbed from the resins they tested, but found no apparent relationship between the residual sulfur dioxide and the exchange capacity of the resins.
I
I
I
I
CH
CH)
. H L O+ SO? = R-A-H
R-k
CH,
+ H‘ t S O , ’
CH 3
to give the sulfite ion. Similar behavior was noted by Krecjar (19651, who observed that sulfur dioxide was on a weakly basic polyamide resin, as sorbed as SO,,’ HSO I on two strongly basic styrene-divinylbenzene resins, and as mixtures of SO.;’ and H S 0 3 - on four other resins. These resins, of Czechoslovakian manufacture, were all moist. Since the rate and equilibrium data obtained for the fresh resin were complicated by reaction, a second series of experiments was run with saturated resin. The equilibrium data obtained (Figure 5) show some irreversibility upon desorption. Since for saturated resin reaction a t the exchange sites should be complete, the irreversibility is attributed to some swelling of the resin on sorption and subsequent shrinkage on desorption, which traps some of the sulfur dioxide in the interior of the ~
I
h S O R P T l O N 0 2 5 m m DIA DESORPTION
0 SORPTION I m m DIP, DESORPTION
WITHOUT
EXPOSURE T O SO2
-J-
-Jj
IO ’
-
---I -+
1001
I I
I
I
I
2 3 4 LOADING ( G S02/G DRY RESIN)
I 5
Figure 3. Equilibrium loadings for fresh resin
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I I.l-ii
I
Figure 4. Infrared spectra for fresh and saturated resin VOL. 8 NO. 3 JULY 1969
319
RUN P, ?, 3-la O 6 2 m m Hg 3-20 062 5 0 3-3a 5 0 315 >40 315 I 5 4 3-50 154 531
6
Figure 6. Sorption rate curves for saturated resin I O I
0
I
I I I 2 3 4 LOADING(G S O d G SAT RESIN)
I
1
1
1
l
polymer matrix of the resin. This phenomenon is common to many cases of sorption by polymers (Helfferich, 1962). For both fresh and saturated resin, the sorption and desorption rates were characterized by a rapid initial uptake or loss during the first half hour or less, followed by a very slow approach to equilibrium over a period of one week or more. Figures 6 and 7 show the early portions of the rate curves for sorption and desorption, respectively. Harvie and Nancollas (1968) noted similar behavior for sodium-hydrogen exchange on zirconium phosphate. They interpreted the exchange rate as limited by separate cases of particle diffusion of the exchanging ions, initially a fast step, followed by a slow step, and involving different hydrogen atoms. I t has long been recognized that adsorption by porous solids frequently is limited by diffusion of the adsorbate through the pores of the solid. Similarly, for sorption by nonporous solids, the rate is limited by diffusion of the sorbate through the solid matrix. Diffusion through the solid matrix is usually substantially slower than pore diffusion. T o account for the shape of the rate curves observed here, the rapid initial uptake or loss was attributed to reversible adsorption of sulfur dioxide on the walls of the large pores of the resin and the subsequent slower uptake or loss to absorption by the polymer matrix. This explanation seems plausible because of the relatively high surface area of the resin that is available for adsorption, the large pores through which the sulfur dioxide may penetrate the resin particle, and the fact that the sulfur dioxide is absorbed by the polymer matrix as indicated by reaction a t the ion exchange sites. Rate data for the initial uptake or loss were analyzed by assuming the rate of adsorption to be negligible during this period. During the slow approach to equilibrium, the adsorption occurring in the large pores was assumed to be a t equilibrium. Equilibrium values for adsorption were assigned by noting the weight change to the time when the rate of weight change became negligible to the initial portion of the rate curves. Equilibrium values for absorption were obtained from the I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
1
1
1
RUN?,, 3-la 5 j l 3-2c I89
5
Figure 5. Equilibrium loadings for saturated resin
320
1
9
3-Si 3-46
1
1
1
l
1
1
I
I
I
I
?,,
I89 mm Hg 66
23 70
66 23
.7
0
I
I
I
I
I
I
I
I
I
I
I
differencebetween the total weight change and the change for adsorption. The equilibrium data for adsorption obtained in this fashion represent from 50 to 60‘; of the total weight change and show complete reversibility (Figure 8). Figure 9 shows the fit of these data to the familiar BET adsorption isotherm (Brunauer, 1945). From the slope and intercept, values for the monolayer coverage, C[)-, and the constant, C, were found to be 0.138 gram of SO? per gram of saturated resin and 145, respectively. The surface area was estimated from the monolayer coverage and found to be 274 sq. meters per gram, a value greater by a factor of 10 than that obtained by nitrogen adsorption of fresh resin. The difference may be attributed to the difference in adsorbates, the difference in resin properties caused by saturation with sulfur dioxide, or both. The constant C is given approximately by C = exp [ ( Q L Q a ) / R T ]and was used to estimate the heat of adsorption. A value of 8.60 cal. per mole was obtained, which is reasonable when compared with the heat of liquefaction equal t o 5.96 cal. per mole. Heats of sorption lying between 7.49 and 16 cal. per mole were observed by Cole and Shulman (1960) for the several resins they used. Equilibrium values for absorption are shown in Figure 10. Some irreversibility is shown, probably due to trapping of some sulfur dioxide in the polymer matrix. Heating the resin to 90’C. caused desorption of the SO?which could not be removed by mere evacuation. This may
103,
I
I
I
I ’-
e
‘t
01
I
I
I
I
I
I
I
ADSORPTION DESORPTION
:
I (G 05 20
25
01
LOADING ( G S02/G SAT R S I N )
05
LOADING
SO$G I5 SAT RESIN)
Figure 8. Adsorption equilibrium loadings for saturated resin
Figure 10. Absorption equilibrium loadings for saturated resin
indicate that the absorption is completely reversible a t 25°C. as well, but that the rate is too low to be detected. The rate of sulfur dioxide uptake or loss for each period was interpreted as diffusion-limited, for adsorption by diffusion through the large pores of the resin particle and for absorption by the much slower diffusion through the polymer matrix. For the diffusion-limited adsorption, a material balance written about a spherical shell of the particle gives
some have been tested by experiment, with reasonable success (Henry et al., 1967; Wakao et al., 1965). Assuming pointwise equilibrium between the gas and the adsorbed layer and isothermal conditions, Equation 1 becomes
a CLJ -dt
-
L!
1
(1/K + p i t ) r’ dr
a c,i
[r2Dn,(l/K)
T I (2)
If the isotherm is linear, or a t least piecewise linear, and
D, is constant, Equation 2 may be integrated directly which assumes that the flux of gas is directed on the average toward the center of the particle and may be described by Fick’s first law. The “diffusion” coefficient, D,, takes into account all modes of pore transport, including molecular diffusion, Knudsen diffusion, bulk, and transition flow. Surface migration is assumed negligible. Various models for predicting D, have been proposed and
to give the concentration distribution of adsorbate in the particle a t any time. For the conditions of the present experiments, the necessary initial and boundary conditions are:
CD(r,0 ) = C , , uniform initial concentration corresponding to adsorption equilibrium with the surrounding gas a t pressure Po C D ( a ,t ) = CIl,, constant surface concentration corresponding to adsorption equilibrium with the surrounding gas a t pressure P I dCD/ar (0, t ) = 0, zero gradient a t the center of the particle The result is
2a 1+-z rr
nLk‘Deff t
(-1)” ~
n
exPC-
aL
] sin
nkr
__
a
(3)
where P/F, x 102
(4)
Figure 9. Fit of adsorption equilibrium data to BET equation VOL. 8 NO. 3 JULY 1 9 6 9
321
The weight of a particle at any time is given by
Integrating Equation 5 using 3, the fractional weight change is
wt-wo = 1 w1-wo
6
-
1 exp (-n27r2T)= M , / M , (6) n
-;i 7r n - 1
where
T = De, t / a 2
(7) Since the experimental data are in the form of M t / M , as a function of time, it is apparent that a plot of evaluated using Equation 6 for a given M t / M , us. the corresponding value of the experimentally observed time should give a straight line through the origin with slope De,/a2. Figure 11 is typical of the data, all of which gave good straight-line fits. I n some cases, however, the straight lines do not pass through the origin. This is not unexpected, because of difficulty in accurately assigning time zero when additional gas is admitted to the apparatus, and the possibility of an initial effect of the heat of adsorption. Similar behavior has been noted for adsorption of nitrogen on silica gel (Testin and Stuart, 1966). Values of De, obtained from the slopes of the T us. t plots were essentially constant and in the range lo-’ to sq. cm. per second. Values of Dg were calculated from Equation 4 assuming the isotherm to be piecewise linear and thus the isotherm slope
Figure 12 shows the apparent dependence of D, on pressure. For comparison, values of D, were predicted using the model of Wakao, Otani, and Smith (1965). Fairly
;v
5 4
3
2 I
0
1
I
I
28-
2
4
6
20-
I
C B ( Z0, ) = CBo,uniform initial concentration corresponding t o absorption equilibrium with the surrounding gas a t Po CB(2, t ) = C B , , constant surface concentration corresponding to absorption equilibrium with the surrounding gas a t P I
aCB/&(O, t ) = 0, zero gradient a t the center of the gel Assuming the gel diffusion coefficient, DB, to be constant, the expression for the fractional weight gain is equivalent to Equation 6, with the dimensionless time T = DBt/ 2’. As shown in Figure 13, the fit of the absorption rate data to the model was good. Values of DB were evaluated from ”I us. t plots, using a characteristic radius for the polymer gel 2 = 3.16 x cm. estimated by a method proposed by Frisch (1962). The resulting diffusion coefficients were of the order of sq. cm.
I
I
I
I
I
12
14
16
18
I
ADSORPTION mDESORPTlON
MODEL lWAKAO,eio1.,1965)
I
(8)
again taking the geometry to be spherical, and subject to the conditions
2, -I
I . 20-
-
I d 01
Figure 1 1 . Fit of adsorption rate data to diffusion model 322
-1
I
E (MIN)
.24-
aCB 1 a 2 aCB - - - - - [DBZ az az at
RUN 3-10 TEMP 2 5 O C Po=0,P; = O 6 2 mrn Hg
j$ I
good agreement is obtained a t low pressures, but while the model predicts a modest increase in D, with increasing pressure over the range tested, the experimental data show a decrease of about two orders of magnitude. N o satisfactory explanation for this behavior is available at present. One possibility suggested by the fact that the pressure dependence of Dg is identical for both adsorption and desorption is that accumulation of sulfur dioxide in small pores which may connect larger ones restricts the movement of the diffusing molecules, giving rise to a decrease in D, as the accumulation increases with increasing pressure. The uptake by absorption was assumed to be limited by diffusion of the sulfur dioxide through the polymer matrix. Assuming adsorption equilibrium, the rate was characterized by a diffusion equation for a homogeneous medium
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
I
I
10
100
I
1000
P (mm.Hq)
Figure 12. Apparent dependence of D, on average pressure
J
,
IO
,
,
l
l
l
(
[
l
l
.
-
9-
a
IO'
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8-
7-
-
6-
-
loz
-
k-'
2
3
4 5 6 T ~ M EMNMO-~
7
8
9
1
0
5
-E om
-
-
8-
-
1612
e
W
-
I
-
-
Ne
2420 -
I
SORPTION, FRESH RESIN, Irnm DESORPTION, FRESH RESIN, Irnm SORPTION, FRESH RESIN,025mm -SATURATED RESIN DATA
*
-
100
IO
Conclusions
per second and with some scatter, independent of pressure or loading, as indicated by Figure 14. The data obtained for the fresh resin were complicated by the apparent reaction of sulfur dioxide a t the exchange sites of the resin. Qualitatively, however, the rate characteristics were similar to those observed for the saturated resin, indicating that diffusion limitations were again present. Figure 15 compares the diffusion coefficients for the short time uptake for the fresh resins (due to adsorption and reaction) with those for the saturated resin. Reasonably good agreement was obtained for the 1-mm. particles, but the data for the 0.25-mm. particles differ markedly, probably because of the differences in the pore structure for the different size particles. Since the rate data for the long-time uptake by the fresh resins were scanty, i t was not possible to evaluate diffusion coefficients for this period.
I
I
The equilibrium loadings obtained are compared with the data reported by Cole and Shulman (1960) in Table I. Of the materials cited, the fresh A-21 resin shows by far the greatest equilibrium uptake of sulfur dioxide. Since a large fraction of the sulfur dioxide sorbed on the fresh resin apparently reacts and cannot be desorbed by heating or evacuation, the data obtained for the saturated resin are applicable for repeated use. I t seems probable, however, that the usable sorption capacity of the resin is that attributed to adsorption on the saturated resin, since only here are high sorption rates obtained. This capacity remains large when compared to that of silica gel and activated charcoal and the complete reversibility exhibited for adsorption indicates that regeneration may be accomplished easily. The relatively large heat of adsorption indicates that the equilibrium capacity for sulfur dioxide decreases rapidly with increasing temperature. This would be advantageous for regeneration, but restricts the usefulness of the resin for sorption to relatively low temperatures.
I
0 ABSORPTION DESORPTION
Table I. Sorption Capacities for Sulfur Dioxide
8 I
I
I
8
a
Sorbent Molecular sieves (Type 5A)" Activated charcoal" Silica gel" IRA-400 resin" A-21 resin, fresh (total) A-21 resin, saturated (total) A-21 resin, saturated (adsorbed only)
I
I
I
I IO
-
I
1000
P (mm.HgJ
Figure 13. Fit of absorption rate data to diffusion model
I
I
I
I I
lo4
100
Equilibrium Loading at 50 Mm. Hg, G. 100 G. 27 16 9.2 28 35.0 22.4 13.2
I 1000
P(mm.Hg1
Cole and Shulman (1960)
Figure 14. Dependence of DB on pressure VOL. 8 N O . 3 J U L Y 1 9 6 9
323
Acknowledgment
Literature Cited
The financial support .of the National Science Foundation through an NSF Traineeship for L. Layton is gratefully acknowledged.
Brunauer, S., “Adsorption of Gases and Vapors,” Princeton University Press, Princeton, N. J., 1945. Cole, R., Shulman, H., Ind. Eng. Chem. 52, 859 (1960). Frisch, N. W., Chem. Eng. Sei. 17, 735 (1962). Harvie, S. J., Nancollas, G. H.. J . Inorg. Nucl. Chem. 30, 273 (1968). Helfferich, F., “Ion Exchange,” McGraw-Hill, New York, 1962. Henry, J. P., Jr., Cunningham, R. S., Geankoplis, C. J., Chem. Eng. Sci. 22, 11 (1967). Krecjar, E., Chem. Prumsyl 15(2), 77 (1965); CA 62,11183g (1965). Kun, K., Kunin, R., J . Polymer Sei. C, No. 16, 1457 (1967). Millar, J. R., Smith, D. G., Marr, W. E., Kressman, T. R. E., J . Chem. Soc. 1963, 218, 2779; 1964, 2740. Pollio, F., Kunin, R., IND. ENG. CHEM. PROD.RES. DEVELOP. 7, 62 (1968). Testin, R . F., Stuart, E. B., “Diffusion Coefficients Measured from Gas-Solid Adsorption Rate Experiments,” 59th Annual A.1.Ch.E. Meeting, Detroit, 1966. Wakao, N., Otani, S., Smith, J. M., A.1.Ch.E. J . 11, 435 (1965).
-
Nomenclature
a = radius of resin particle C CB CD CDm
= constant in BET equation = amount absorbed = amount adsorbed = amount adsorbed corresponding to monolayer
coverage
c,
= gas concentration Dg = gel phase diffusion coefficient De, = effective diffusion coefficient = ( D , / K )( 1 / K
Dg K MtIM, P P, QD QL
r
R t T T
+PI4
= gas phase diffusion coefficient
= slope of adsorption isotherm = fractional weight gain or loss = pressure = saturation pressure = heat of adsorption = heat of liquefaction = distance from center of resin particle = gas constant = time = absolute temperature = dimensionless time = De, t/i‘ or D B t / Z 2 = weight of resin particle = weight of resin particle + sorbate = characteristic gel distance characteristic gel radius = porosity = density
RECEIVED for review June 19, 1968 ACCEPTED March 24, 1969
w, WD z
z= t
P
Work supported by the Division of Air Pollution, Bureau of State Services, U. S. Public Health Service
TRANSIENT RESPONSE OF A PACKEDCOLUMN TO CHANGES
IN LIQUID AND GAS FLOW RATE C H A l M
GILATH’,
LEONARD
M.
NAPHTALI’,
A N D WILLIAM
RESNICK
Department of Chemical Engineering, Israel Institute of Technology, Haifa, Israel The holdup of a film of liquid flowing down a plate was theoretically found to be a first-order system regarding the flow rate through the film. Based on this conclusion, the dynamic holdup of a packed column can be considered as a system of small first-order elements in series, the response of which can be lumped into a time delay and a time constant. The pressure drop and holdup characteristics were determined for a column packed with Dixon rings and operated with countercurrent flow of air and water. The transient response of the liquid outflow rate to changes in liquid and gas flow rate was investigated. For small step function disturbances the responses to positive and negative step changes were symmetrical; for larger disturbances they were asymmetrical. Time delays and time constants were correlated in terms of theoretical mean response time.
PACKED towers
are among the most common devices used in the chemical industry for continuous contacting. Although the literature is rich in information on mass transfer and flow characteristics, pressure drop, and liquid holdup for various packings, information on the dynamics ‘Present address, Soreq Nuclear Research Center, Yavne, Israel. ‘Present address, 575 West End Ave., New York, N. Y. 324
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
and control of packed columns is scanty and deals with concentration dynamics, startup, and axial dispersion problems rather than flow or pressure drop dynamics. The need for information on pressure drop dynamics is apparent, since pressure drop is used as an indication of flow conditions in a Packed column and can also be used for control purposes.
