E
Consequently the 2-hexene reacts in the same way as in step 23. T h e formation of olefin-catalyst complex in a rate-controlling step does not necessarily imply carbonium ions. Benzene is a strong nucleophile (as inclicated by the constancy of k?3 values. irrespective of the nature of the catalyst complex).
total fractional conversion of olefin fractional conversion of olefin to 2-phenylhexane $ 2 = fractional conversion of olefin to 3-phenylhexane E* = total fractional conversion of olefin to complex 6 = time derivative of
Nomenclature
literature Cited (1) Bell, R. P.: Higginson, \C. C. E., Proc. Roy. Soc. A197, 141 (1949). (2) Dalziel, K., Acta Chem. Scand. 11, h-0. l o ? 1706 (1957). (3) Knight, E. S.. Anal. Chem. 30, 9 (1958). (4) LineweaLer, H.: Burke: D.. J . ,4m. Chem. Soc. 56, 658 (1934). (5) Schmerling. L.. Znd. Eng. Chcm. 40, 207Z (3948). (6) Setty, H. S. S . , "Kinetics of Homogeneous Liquid Phase Reactions. Alkylation of Benzene w i t h Hexene-l Using AICI,: N 0 2 R Catalvsts." Ph.D. dissertation, University of Houston, Houston, Tex., 19\13. (7) Setty, H . S. N.: Barona! N., Prengle, H. IC.,Jr., IND. ENG. CHEM.FUXDAMESTALS 3, 294 (1964).
A , A * , B , C? CS, D1: D2,S = reactant and product species ai = activity of species i k l , k.: k3: k-,, k p l : kp3 = specific reaction rate constants k23 = (kr k3) nA, = initial number of moles of olefin n, = total number of moles in reactor at any time t V = volume of reaction mixture Xes,, = initial mole fraction of catalyst
+
GREEKSYMBOLS LY = initial benzene-olefin ratio yt = activity coefficient of 1' = initial catalyst-olefin ratio
E1
= =
SUPERSCRIPTS ( l ) , (0) = first approximation, and extrapolated value to xcs = 0
RECEIVED for review August 23, 1963 ACCEPTED August 28: 1964
ION EXCHANGE RESIN CATALYSIS OF SUCROSE INVERSION IN FIXED BEDS ELDON W .
R E E D ' A N D JOSHUA S. DRANOFF?
Department of Chemical Enpneering. Columb~a C;izLerst/), .Vezt l h r k , .V. 1'
The kinetics of continuous sucrose inversion catalyzed by fixed beds of acid form ion exchange resin was studied. A reactor 1 inch in diameter was used and solution flow rate and catalyst particle size were varied to cover a modified Reynolds number range of 0.014 to 4.8. Reaction terr.perature was varied from 50" to 75" C. The reaction was clearly first-order over this range and showed an activation energy of 15,950 cal. per gram mole. The data indicate that the observed rate of reaction is strongly influenced by diffusion within the resin particles and that external (film) mass transfer is not significant for the range of conditions explored.
HE inversion of sucrose in acid solutions has been well Tstudied in the past. I n fact. the measurement of the rate of this reaction in 1859 by \Vilhelmy ( 7 7 ) was the first kinetic study reported in the chemical literature. T h e heterogeneous catalysis of this reaction by suitable acid catalysts has also been investigated, especially since the advent of statle synthetic ion exchange resins. T h e latter are particularly convenient for such reactions because of the ease of separating catalyst from reaction products without chemical purification steps. With but one recent exception, however, previous stu' ies of ion exchange-catalyzed sucrose inversion in aqueous solutions have been carried out using batch-stirred reactors. T h e most complete work of this type was reported by Bodamer and Kunin ( 7 ) , who found that the reaction remained apparently first-order, as in the homogeneous catalyzed case. that the rate was strongly influenced by pore ciffusion. and that the reaction had a n activation energy of from 18:300 to 25:000 cal. per
1
2
304
Present address, Mobil Oil Co., Paulsboro, N.J . Present address. North\\eestern University, Evanston. I11 I&EC FUNDAMENTALS
gram mole, depending on the resins used as catalyst. Bodamer and Kunin also measured the activation energy for the honiogeneous reaction and found it to range between 28.000 and 30>000cal. per gram mole. Later studies of the reaction have been reported by Hsieh and Su (5). Govindon and Bofna ( 2 ) , and Taufel and Grunert (70). T h e latter showed that the effects of separate homogeneous and heterogeneous catalysii could be linearly combined to describe the behavior of a reactor in which both acted simultaneously. They also reported activation energies in the same general range reported earlier by Bodamer and Kunin. The only paper dealing Lvith fixed bed catalpis of this reaction was published recently by Saito et ai. (9). They reported the kinetics of several liquid phase reactions catalyzed by ion exchange resins (Dowex i o ) . I n particular. their data for sucrose inversion sho\v deviation from first-order kinetics with increasing ?pace velocities. This suggests an effect of external diffuiion or mass transfer on the observed reaction rates which Lvould make scale-up from stirred reactor data difficult. .4s a result of these data it was decided to carrv out further
inveytigations of this reaction in fixed beds. I t was anticipated that this might shed additional light on the importance of the mass transfer effects on fixed bed reactor performance. T h e results of the present study. in contrast to the \vork of Saito. indicate no effect of external mass transfer over a \vide range of Reynolds numbers. However, strong influence of intrapart i d e diffusion \vas found. Experimental
A glass reactor assembly \vas designed and constructed for this research. T h e reactor consisted of a vertical glass tube, 1 .O-inch i d . , surrounded by a glass water jacket, 1.5-inch i.d. Resin catalyst was supported \vithin the reactor tube by 100mesh stainless steel screens located a t the top and bottom of the bed. Each screen was fixed in position by small Teflon rings \vhich could be placed anyLvhere in the tube in order to accommodate a desired resin bed volume. T h e reactor sections upstream a n d doxvnstream of the catalyst bed were packed with glass beads '6 inch in diameter. These ensured uniform velocity profiles in the reactant fluid and provided a heating zonc where the entering reactant could be brought to operating temperature. 'l'emperature in this system was controlled by circulating water from a constant temperature bath through the reactor jacket a t a high rate of flo\\-. I n this \Yay reactor temperature could be maintained consrant Lvithin 0.2' C . Entering feed liquid \vas heated not onl>- within the reactor but also by floiving through a copper coil immersed in the bath upstream of the reactor. l'he liquid reactant stream \vas supplied to the top of the reactor from a constant-head feed bottle located approsimately 6 feet above the reactor outlet. .All feed lines except the preheating coil tvere made of glass and Tygon tubing. T b v o small rotameters in the feed line \cere used to indicate flow rates: although accurate determination of flow rate \vas by timed collection of liquid samples from the reactor outlet. Flow \vas controlled bv several small needle valves located upstream of the rotameters and a t the reactant outlet. Excellent control was obtained and steady flow rates were easily maintained. 'The reactor effluent \%'ascollected i n a flask immersed in an ice bath. T h e hot stream \.vas thus chilled quickly to avoid excessive loss of lvater b\ evaporation. I n addition to the reactor, another larger fixed bed column was set u p and used to purify feed liquid before reaction. This column was 2 inches in diameter and 5 feet long and was packed Ivith a mixture of anion resin (Amberlite IRA-402) in the h>-drox>-lform and Lveakly acid cation resin (Amberlite IRC-50) in the hydrogen form. ,411 feed liquidswere de-ionized bypassage through this mixed bed before being placed in the feed bottle. T h e purpose of this pretreatment \vas to remove all dissolved salt ions from the feed. in order to prevent subsequent deactivation of the acid catalyst due to exchange of such ion with the hydrogen ions of the catalyst. l ' h e success of this operation is indicated by the fact that no deactivation of the actual catalyst bed \vas experienced \vhen the pretreated feeds \-zedfor sucrose by polarimetr>-,rising a commercial saccharimeter. Measurements ivere made \vith a \vater-jacketed polarimeter tube 2 d m . long and at a temperature of 2.5' +r 0.1' C . T h e measured optical rotations of sucrose and invert sugar solutions Tvere compared tvith standard values ( 3 ) and found to be in close agrermrnt. .As a rcsult, the usual linear relation bet\veen rotation and extent of reaction \vas assumed to apply in the present case.
T h e sucroLe used in this work was ordinary granulated sugar, but sufficiently pure that the optical rotation of sucrose solutions agreed well \vith standard values for pure sucrose ( 3 ) . T h e feed solutions used for all experiments contained 15 weight Ycsucrose (17.7 grams per 100 ml. of tvater). 'I'he resin catalyst used was Amberlite IR-120> 8 to lOyc divinylbenzene, in the hydrogen form. T h e measured exchange capacity of the resin \vas found to be 5.20 meq. per gram of dry resin, by standard batch techniques. T h e packing density of the resin in water was also measured and found to be 0.35 g r a m of dry resin per milliliter of packed \vet resin bed. T h e acid form resin \vas separated into three size fractions by wet-screening with U . S. standard sieves. T h e screening operation \vas repeated several times under a stream of distilled water to ensure good classification. T h e three size ranges used for these experiments were 16-20, 20-30, a n d 30-40 mesh. T h e resin particles were packed into the reactor tube by allowing them to settle through a column of \vater with much shaking and tapping to ensure reproducible packing. I n making actual runs \vith this equipment, sufficient time was allowed to achieve steady-state isothermal operation before effluent samples were taken. T h e experimental samples were generally analyzed Lvithin one day, although tests indicated that the samples Fvere stable for longer periods in the absence of catalyst particles. Further details of the experimental equipment and procedures are presented elsewhere (8). Results and Discussion
A series of experiments was made with varying feed f l o ~rates, . reaction temperatures, and catalyst particle sizes. .4fter it was demonstrated that no reaction took place in the equipment in the absence of catalyst particles, several runs liere made to determine the basic rate equation for sucrose inversion. T h e reaction is irreversible, as follo\vs: H+
C:2HnOii
+ HsO --+ C6H1206 +
(+)-Sucrose
D-(f)-Glucose
D-(
CGHinO,
(1)
-)-Fructose
Previous studies have indicated that the reaction is pseudofirst-order. If it remains in the plug flow packed bed reactor: Equation 2 rvill relate sucrose conversion and space time (6). In (1 - X,)
(2)
= -kT
where X , = fractional conversion of sucrose k = apparent first-order rate constant. (time)-' 7 = space time. V,'q, time
A plot of In (1 - X,) 1's. 7 \vi11 be linear, lrith a slope equal to - k if first-order kinetics apply. T h e data for several runs a t 70' C. with 20- to 30-mesh particles are shown in Figure 1. T h e data fall on a straight line, thu; confirming first-order kinetics for the fixed bed reactions. Some deviation from the line is apparent for conversions greater than about 90Yc, but the deviations (on the order of l 7 c conversion) are within the probable experimental error. T h e logarithmic scale of the figure also tends to magnify the deviation of the experimental points in the high conversion region. As shoivn in Figure 1: the points were obtained in brds of three different volumes. but all fit a single line well. indicating no effect of reactant flow rate on the specific rate constant. Similar results \vere obtained using catalyst particles in the 16-20- and 30-40-mesh size rangrs. although the specific rate constant \vas different in each case. T h e results of these runs are summarized in Table I . As resin particle size increases: the effective rate constant falls. I n fact. an inverse relationship exists. as shown on Figure 2. This is good evidence of either strong pore diffusion influence on the reaction rate or rate control by slo\v reaction a t the exterior surface of the catalyst particles ( 7 ) . VOL.
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NO. 4
NOVEMBER
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305
Effect of Resin Particle Size on Observed Rate Constant at 70" C. Particle Sire _ _ ~ Aa. diameter, &Meshszte mm. k , Win.-' 1.01 16-20 0.134 0 715 20-30 0.168 0.505 0.226 30-40
Table 1.
-
0.02
1
2 0 / 3 0 Mesh R e s i n (7O"C.l
cc. B e d 0 - 6 0 CC. B e d 0 8 0 cc. B e d 0- 4 0
-
IO 15 20 25 30 S p a 9 8 T i m e (min.) Relation of space time to sucrose conversion
5
0 Figure 1.
T h e influence of external mass transfer rvas tested further in a series of runs made a t very slow flow rates, Lvhere film diffusion would be expected to become significant. Small catalyst beds were required for these runs in order to avoid complete conversion of the entering feed stream. Data for runs made with a 5-cc. bed of 30- to 40-mesh particles are shoivn in Figure 3: along \vith data for a 40-cc. bed of the same catalyst. As the figure shows, the 40-cc. bed data fit the first-order plot \vel1 over-all, irhile the 5-cc. bed data apparently deviate someivhat a t space times above 4 minutes. The indicated deviation a t these higher space times (sloiver flow rates) may indicate the beginnings of an external mass transfer effect. but, if so. the effect is so small as to be essentially negligible. These experiments covered a range of particle Reynolds number (D,up;'p) from 0.014 to 4.8. This conclusion is not in agreement ~ v i t hthe data of Saito ~t ai. ( 9 ) : which sholv a p o r e pronounced deviation from first-order behavior and a t lower space times. Bodamer and Kunin reported the strong influence of pore diffusion on the rate of this reaction in stirred vessels. To check this point further in the present study, the effect of temperature on the observed rate constants was measured. A series of runs \vas carried out with 16- to 20-mesh particles a t SOo, 60", and 70" C. T h e data a t each temperature fit the first-order equation lvell. 'The corresponding rate constaits were plotted as In k us. 1 / 7 (absolute temperature) as shoivn in Figure 4. The data clearly conform to the usual Arrhenius model and the measured activation energy bras found to be 15,950 cal. per gram mole. T h e significance of this value can be seen in the light of the assumption of strong pore diffusional effects. Cnder such conditions it has been shown (-1) that the observed activation energy is the average of the activation energies for the diffusion of the reacting species within the catalyst particle and for the catalytic reaction in the absence of diffusional limitations. Bbsd
4:d 0.45 Figure 2.
1 (2.65
0.85 Dp (rnm.1
Effect of resin particle size on observed rate
constant 306
1.05
I&EC FUNDAMENTALS
= ' 1 2 (Ediif
f Ereact)
(3)
I n the present case one may assume Erenot to be characteristic of the homogeneous catalyzed sucrose inversion reaction, since the catalytic acid ions are present within the particles in a relatively free state. not too unlike that in which they might exist in a concentrated homogeneous solution. Thus, EFeact should be about 29.000 cal. per gram mole. E d i r i is normally about 3000 cal. per gram mole for most substances. O n this basis one might expect the observed activation energy to be approximately 16,000 cal. per gram mole. Since this is essentially the value found. it is felt that this constitutes a strong verification of the original hypothesis--i.e., that the rate is strongly influenced by internal particle diffusion of reactant. External mass transfer effects are not significant over the range of conditions studied here and the observed reaction rate is controlled by the actual catalytic reaction within the particles under the strong influence of particle diffusion of reactant. I t is now of interest to compare the actual data
1.0 Table II.
Comparison of Fixed Bed and Stirred Reactor Data
Investigation
0.5
Resin Diameter, Mm.
Resin Density”
Bodamer and Kunin ( 7 ) 0.45 0.0516 This study 0.50 0.875 a Grams dry resin p e r cc. reactor uolume.
0.2 X” 1
-
4
0.1
0.05 30/40 Mesh R e s i n
0.02
0 Figure 3.
2
4
6 8 1 0 1 2 1 4 Space T i m e (min.)
Relation of space time to sucrose conversion
Temp.,
C.
Obserued Rate Constant, M i n . -l
75 75
0.0117 0.314
leads to confusion. Saito et al. in their Figure 5 show data obtained with 16- to 20-mesh particles of Dowex 50-X8 resin a t 50’ C. Csing the measured slope from this figure one may calculate that the rate constant is 1.60 X cc./(gram sec.). Ho\vever. in Table I 1 of the same article the authors report that cc./’(gram sec.). T h e the rate constant was 1.743 X reason for this discrepancy is not apparent. When data of the present study are put on the same basis (by dividing the rate constant by the packing density of the catalyst bed and changing time units to seconds) the value becomes 1.51 X cc./ (gram sec.). This is in reasonable agreement with the tabular value reported by Saito e t al., but not with their actual graphical data. .4t this point one is led to place his confidence in the tabular data presented by these workers rather than in their figure and to claim that the present data are substantiated by those of Saito e t al. O n the basis of present data, it would seem that reasonable scale-up from stirred batch reactors to fixed bed continuous reactors is possible because of the absence of external mass transfer effects. Due caution should be exercised, however. with respect to changes in particle size or resin type, since these will affect the diffusion within the catalyst and may change the rate constants significantly. Such factors, however, should be easily handled by the usual considerations of catalyst effectiveness factor in the literature (4?7 ) . Nomenclature
D,
=
E
= activation energy, cal. gram mole
k q
=
u
= average fluid velocity, cm. k e c . = reactor volume, cc.
=
V
Figure 4. constants
I I
O
~
(
O
K
absolute temperature, OK.
A’,
=
p p
= fluid viscosity, grams] (cm. sec.) = resin packing density, grams dry resin per cc. of packed
7
=
~
Effect of temperature on observed rate
specific rate constant? min.?
= volumetric feed rate, cc. ‘min.
T
I/T x
average catalyst particle diameter, cm.
fractional conversion of sucrose bed space time, V ’ q , min.
literature Cited
measured in this study with those previously reported by others. Since film diffusion is unimportant, it should be possible to check the fixed bed d a t a directly with the stirred reactor data of Bodamer and Kunin, who used the same resin catalyst. T h e coni.itions and reported rate constants for one such comparison are shown in Table 11. If the value reportei: by Bodamer and Kunin is corrected to account for the Lifferences in particle size and resin density within the reactor. it becomes 0.178 min.-’: m-hich is about 437, lo\ver than the value measured in this tvork. This is felt to be a reasonably close estimate for a n extrapolation of this type. A comparison with the published data of Saito t t ~ l is. also of interest. since they carried out experiments in much the same \vay as the present study. However. such a comparison
(1) Bodamer, G., Kunin, R.? Ind. Eng. Chem. 43, 1082 (1951). (2) Govindon, K. P.. Bofna, S. L., J . Sci. Znd. Res. (India) 15B, 6 6 6 (19561. (3) “Handdook of Chemistry and Physics,” p. 2782, Chemical Rubber Publishing Co., 1956. (4) THelfferich, F., “Ion Exchange,” Chap. 11, McGraw-Hill. h e w York. 1962. (5) Hsieh, P. T.. Su, T., J . Chznese Chem. SOC. 3, 41 (1956). (6) Lexenspiel, O., “Chemical Reaction Engineering,” Chap. 5 , LVilrb. Neu York. 1902 (7) Zbtd., Chap. 14. (8) Reed, E. LV., M.S. thesis, Columbia University, New York. 1., 9 _I. 61
(9) Saito, H.; Shimamoto. F.. Mishima. Y . , Sataka, 0.: Kogyo Kagaku Zasshi 64, 1733 (1961). (10) Taufel. K., Grunert. I(.S., Arch. Pharm. 294, 439 (1961). (11) LVilhelmy, L., Ann. Physd. Chem. (Poggendorj) 81, 413, 499
(1859). RECEIVED for review November 12, 1963 ACCEPTED June 29, 1964 VOL. 3
NO. 4
NOVEMBER
1964
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