Ind. Eng. Chem. Res. 1992,31,369-373
(2) A power law model for the specific rate of breakage was found to describe the milling process. The power law constant was estimated to be equal to 1.457 when the constant of the breakage function was 1.564. The particles of size 1.0-1.5 pm appeared to have the more pronounced increase, and for the fine particles production a simple model was proposed. (3) Dispersions with high solids loading can be prepared if pH is controlled in the range 3.5-3.8. The dispersions are stable when the approximately 10.0% solids particles have diameters less than 1pm. (4) Impregnation of ceramic monolithic structures with different particle size distributions affects the alumina coatings pore structure in the intermediate pore radius region.
Acknowledgment C.P. acknowledges the Hellenic Cement Research Center for the X-ray diffraction and granulometric analyses of the samples. Thanks are also due to The Aluminium of Greece for the supply of hydrated alumina and Mr. D. Tsamatsoulis who helped in the kinetics models evaluation. Nomenclature a = constant, eq 2, dimensionless al = constant, eq 2, h-I b = constant in the breakage function, eq 3, dimensionless bij = material fraction of size i obtained by primary breakage of material size j , dimensionless Bij = breakage function, eq 3 c = constant of power law, eq 5 i , J’ = denote material size k = specific rate constant, eq 5, h-’ L = characteristic particle diameter, pm
369
n = uniformity or distribution factor, dimensionless
N = number of sizes
Pi,t = weight percent of material coarser than size i at time t
Si, Si= specific rate of breakage, h-’ t = grinding time, h X i , X, = weight of material size i or j , respectively u = spindle velocity, rpm Registry No. A1203, 1344-28-1; HC1, 7647-01-0.
Literature Cited Austin, L.; Kimpel, R.; Luckie, T. Process Engineering of Size Reduction: Ball Milling; Society of Mining Engineers: New York, 1984, pp 61-74. Beck, J.; Arnold, K. Parameter Estimation in Engineering and Science; Wiley: New York, 1977; pp 167-184. Dwyer, T.; Pesansky, D. U.S. Patent 3,873,350,1975. Hoyer, A.; Johnson, L. U S . Patent 4,039,482, 1977. Keith, C.; Kenah, P.; Bair, D. US.Patent 3,331,787, 1967. Keith, C.; Kenah, P.; Bair, D. U.S. Patent 3,565,830, 1971. Lapidus, L. Digital Computation for Chemical Engineers; McGraw-Hill: New York, 1962; p 98. Reid, K. A Solution to the Batch Grinding Equation. Chem. Eng. Sci. 1965,20,963-963. Shimrock, T.; Taylor, R. D.; Collins, J. Eur. Patent 0157651, 1985. Sowards, M. D.; Stilea, B. A. U S . Patent 3,518,206,1970. Stiles, B. A. Catalyst Manufacture, Laboratory and Commercial Preparations, Chemical Industries; Marcel Dekker, Inc: New York, 1983; Vol. 14, pp 86-99. Tangsathitkulchai,C.; Austin, L. G. Rhelogy of Concatrated Slurries of Particles of Natural Size Distribution Produced by Grinding. Powder Technol. 1988,56, 293-299. Tangsathitkulchai,C.; Austin, L. G. Slurry Density Effects on Ball Milling in a Laboratory Ball Mill. Powder Technol. 1989, 59, 285-293.
Received for review December 17,1990 Revised manuscript receiued July 17, 1991 Accepted August 13, 1991
Analysis of Zeolite Crystallizations Using the “Crystallization Curve” C. J. J. den Ouden* KoninklijkelShell-Laboratorium,Amsterdam (Shell Research B. V.),Postbus 3003, 1003 A A Amsterdam, The Netherlands
R. W . Thompson Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, Massachusetts 01609
Zeolite crystallization experiments are quite commonly analyzed by means of a “crystallization curve“. These curves, collected for batch zeolite crystallizer operations, represent the evolution of zeolite mass in the crystallizer in the course of an experiment. The data are frequently presented as the zeolite mass, the zeolite yield, or the percentage of zeolite in the solid phase as a function of the crystallization time. One type of analysis of zeolite crystallizations involves the measurement of the induction time and the slope of the crystallization curve to quantify the nucleation and crystallization rates, respectively. It is shown here that these analyses of the crystallization curve, though commonly performed, are likely to give misleading or innacurate results, principally due to the insensitivity of measurements of the mass of zeolite by conventional methods. Although the analysis allows a reasonable comparison of similar systems, it cannot be used to reveal details regarding the crystallization kinetics or to compute activation energies from such an analysis.
Introduction Molecular sieve zeolites are crystalline aluminosilicates with regular pore structures suitable for use in several industrial processes. They are commonly formed by hydrothermal synthesis in caustic media in the presence of a precursor amorphous gel phase. Thus, during a typical zeolite crystallization, at least three phases are present:
amorphous gel, caustic solution, and crystalline product. Under normal circumstances, the aluminosilicates crystallize from the solution phase and are replenished there by dissolution of the gel phase. As a result of this process, if a sample of the ‘solid phase” is collected at some intermittent stage in the process, ita analysis by powder X-ray diffraction techniques
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370 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992
will reveal a partially crystalline solid, the remainder being
amorphous. In the course of the synthesis, the data so collected form an S-shaped (or sigmoid) curve beginning at 0% zeolite and ending at 100% zeolite upon complete conversion, at least under ideal circumstances. Such curves have been reported for over 30 years in the literature on zeolite synthesis, and they provide some indication of the progress of the synthesis reactions. Examples of such crystallization curves, as they are called, and thorough analyses of these, can be found in the literature (for example, Aiello et al., 1980; Culfaz and Sand, 1973; Dai et al., 1986, 1989; Hayhurst and Sand, 1977; Hu and Lee, 1990; Huang et al., 1986; Schwieger et al., 1989). The analysis of these crystallization curves was first reported as a way of rationalizing the relative rates of nucleation and crystallization in a zeolite synthesis and as a means of comparing these rates for similar systems at different temperatures (Culfaz and Sand, 1973). The essence of the analysis,as s u m m a r i d previously (Thompson and Dyer, 19851, is to assume that the induction time, i.e. the time prior to the observation of X-ray crystallinity, is related to the nucleation rate. As the relation is reciprocal in nature, shorter induction times result from higher nucleation rates, and vice versa. In a similar fashion, the slope of the crystallization curve has been taken as a measure of the speed of the synthesis process, after nucleation, and has, consequently, been labeled the “crystallization rate”. It has previously been suggested that factors other than the crystallization of zeolites may affect the induction time (Warzywoda et al., 1989). Thus, it has been shown recently that any precrystallization reaction (hydrolysis, condensation, etc.) may significantly affect the induction time observed in systems of this type (den Ouden and Thompson, 1991). The intent of the present work is to show that quite simple experimental details may have a significant influence on the observed induction time in zeolite crystallization and that, therefore, analyses of the sort reported previously are likely to give misleading resulta. In addition, it will be shown that the crystallization rate actually depends on the events occuring during the nucleation phase of the process as well as on the linear crystal growth rate.
Theoretical Development The zeolite crystallization process is an example of a system which can be analyzed by the population balance methods developed over the past several decades (Randolph and Larson, 1988). For the purpose of illustration, the zeolite system of interest here will be one in which zeolite crystals are formed from a clear solution of dissolved aluminosilicates. Such a system, which produces silicalite, has been reported recently (Keijsper and Post, 1989),but many other examples were published in the past. The absence of the gel phase simplifies the mathematics somewhat but will not alter the points to be made here, because the amorphous gel is only a reservoir of reagents which dissolves to replenish the solution. If the zeolite crystal size distribution in a batch crystallizer is represented by the function n(L,t), then the population balance expression for the system is a an -+G-=O at aL In eq 1 it is assumed that the crystal growth rate is independent of crystal size and that crystal growth dispersion is unimportant. Rather than work with the partial differential equation, it is much easier and, in this particular case, far more
informative to work with the moment transformation of the partial differential equation, as this generates a family of ordinary differential equations. Thus, if eq 1 is multiplied by Li and integrated over all possible particle sizes, the following set of moment equations arises for integer values of i ranging from 0 to 3: dm,/dt = B
(2)
dm,/dt = Gmo
(3)
dm,/dt = 2Gm,
(4)
dm,/dt = 3Gm2 (5) It is important to keep in mind that the momenta of the particle size distribution, the mi)s, are related to the properties of the crystal product. Thus, the four momenta listed are proportional to the cumulative number of crystals, the length of the crystals, the area of the crystals, and the mass (or volume) of the crystals, respectively. The nucleation function, B, used in this work is the classical homogeneous nucleation function given by B = j3 exp(-A/(ln2 s)) (6) where s is the apparent supersaturation ratio for the zeolite system of interest. The interfacial energy parameter, A, may also contain a factor to account for heterogeneously facilitated nucleation from solution in the event that colloidal material is present to catalyze nucleation. This modification leaves the form of eq 6 unaltered, however. The linear crystal growth rate, G, will be expressed as being proportional to a linear driving force in concentration: G = k,(C - Ceq) (7) where the term C , corresponds to the final concentration in solution for the zeolite system of interest. (Most zeolites of commerical interest are metastable phases and will degenerate to other more stable phases with sufficient time, in the absence of stabilizing agents. Therefore, the terms equilibrium and supersaturation are used rather loosely here.) The interfacial energy parameter, A, defined in the Nomenclature section, depends inversely on temperature to the third power. Therefore, it can be anticipated that the nucleation rate will be rather sensitive to changes in the system temperature. To complete this theoretical formulation, it will be assumed that the batch vessel is heated to the synthesis temperature at some rate given by the following simple expression:
where Tbstands for the temperature of the bath, oven, or surroundings. The overall heat-transfer coefficient, U, characterizes the physical and thermal properties of the heating system, the autoclave, and the zeolite synthesis medium. Anything which might be done to facilitate heat transfer to the reacting fluid will be manifeated in a larger value of U, which will in turn increase the rate at which the temperature increases. The model for the synthesis is formulated by eq 2-8. Given the initial conditions that T(0) = To, C(0) = C,, and mi(0) = 0, the solution to the system of equations should describe the evolution of the momenta of the crystal population with time after the vessel has been heated to the synthesis temperature at some rate. As the solute concentration decreases, the nucleation and growth processes should stop, since the system will reach its “equilibrium” state. The temperature dependence of the
Ind. Eng.Chem. Res., Vol. 31, No. 1, 1992 371 Table I. Values of Constants Used in Simulations A 5.00 X 108 To 298 K-C, 0.0030 mol/cm3 Tb 369 K C, 0.0020 mol/cm3 j3 6.00 X 1034/(cm3min) k, 9.00 pm cm3/(min mol) ~
1 .oo L3
Table 11. Effect of Heating Rate on Induction Time U1min-I tlplmin tr/min (l/t1)/min-' 0.50 10 60 0.0167 0.10 50 100 0.010 0.02 250 220 0.00466 Time required to reach reaction temperature, Tb.
0.80
1.50
100
0.60
0.40 0.20 0.00
0
200
400
600
TIME (minuter)
Figure 1. Effect of heating rate on the evolution of zeolite crystal mass. The three curves correspond to different heat-transfer coefficients: (-) U = 0.50 min-'; (--) U = 0.10 m i d ; U = 0.02 mi&. (-e-)
crystal growth rate does not have to be included in this scheme, because growth of the newly formed nucleic only occurs at the synthesis temperature once it has been reached, i.e. after the crystal nuclei have been formed. Of course, this omission would have to be reconsidered for systems experiencing long heat-up times.
Results and Discussion The set of equations previously denoted was solved using a standard computer library Runge-Kutta integration software package. No complications arose during the solution, and computation times were of the order of fractions of a second for each simulation. The transient proflea of the system temperature, solution concentration, and all four moments of the sue distribution were computed. From these results other statistical parameters (average size, standard deviation, crystal yield, etc.) were derived. The values of the constants used in these simulations are given in Table I and were based on previous results (den Ouden and Thompson, 1991) describing clear solution silicalite crystallization. Nucleation. Figure 1 shows the yield of zeolite as a function of time for three different heating rates. The zeolite yield in this case is the third moment of the crystal size distribution, m3,divided by the final equilibrium value. The typical sigmoid shape of the transient profiles is clearly apparent. The features of this sigmoid curve are an accelerating rate of increase at early times due to the autocatalytic nature of the process, followed by a slowing down of the process as the reagent supply becomes depleted. Note that the induction time, that is the period preceding the onset of observable crystal mass formation, changes appreciably with the heating rate. A summary of these values and the time to reach the synthesis temperature is given in Table II. It is immediately apparent from these results that the reciprocal of the induction time for these three profiles leads to quite different predictions of the "nucleation rate", and all of them are incorrect, as will shown presently (for example in the following paragraphs). The nucleation histories predicted from these three simulations are quite similar and are simply offset in time due to the different thermal transients in the three cases. (With long heat-up times the nucleation profile is spread out slightly.) In every case the induction time comprises a heat-up time and a time during which nucleation and
/-
372 Ind. Eng. Chem. Res., Vol. 31, No. 1, 1992 1 .oo 0.80 0.60
0.40 0.20 0.00 0
200
400
600
TIME (minutes)
Figure 3. Effect of the preexponential nucleation rate constant, 8, on the evolution of zeolite crystal m w . The three curves me for (- -) the value of 8 shown in Table I, (-) twice the value of fl shown in Table I, and one-sixth the value of 8 shown in Table I. (-e-)
assumed constant over some time interval, while experimental observations would suggest that this is not exactly the case. Thus, the reciprocal of the induction time provides no more than an indication of the nucleation rate in zeolite crystallizations, and it is a good indication only if the heating time has been eliminated from the induction time. Crystal Growth. The third moment of the crystal size distribution, m3,is proportional to the total mass of the crystal population. Therefore, eq 5 suggests that the slope of the crystallization curve is proportional to the linear crystal growth rate, G, and the cumulative crystal population surface area, m2,at any time. This relationship suggests two observations. First, the frequently mentioned autocatalytic nature of zeolite crystallization is nothing more than a reflection of the fact that the rate of increase of crystal mass is proportional to the crystal surface area, which itself increases with time. Second, the slope of the crystallization curve at 50% conversion used to determine the crystallization rate is in fact a function of these two quantities. That is, the crystallization rate, determined in this way, actually depends not only on the condition in the fluid prevailing at that time but also on the total number of crystals generated during the nucleation phase of the process. This point is illustrated in Figure 3, in which the evolution of zeolite mass is shown for various values of 8, the preexponential constant in eq 6. Larger values of 8 result in more crystals being nucleated in the early phase of the synthesis. It can be seen in Figure 3 that while the induction times are reasonably close to one another, the slopes of the crystalljzation curves are somewhat different. During the early phase of the process the solute concentrations are virtually the same in the three simulations, suggesting that the principal difference in the three cases is the value of m2,the cumulative surface area. Therefore, in this example, the variation in crystallization rates acutally reflects what occurred earlier, and not a difference in crystal growth rates, i.e. the G's. This observation suggests that correlating the differences in crystallization rates with changes in the reagent compositions in the batch certainly will not be very meaningful and may even be entirely incorrect if the nucleation rate and the growth rate depend differently on some reagent concentrations. By this approach, one is not separating the reagent dependence of nucleation from that of crystal growth, and the term crystallization rate, therefore, has a rather ambiguous meaning.
Conclusions It has been shown that events occurring in a batch zeolite synthesis vessel prior to the onset of the actual
crystallization process may have a significant effect on the crystallization curve. Indeed, the rate at which the batch vessel is heated to its reaction temperature will certainly influence the results in that it effects the induction time. The reciprocal of the induction time was shown to be an indicator of the speed of nucleation in the zeolite crystallization system, only if the heat-up time is eliminated, and is not equal to the nucleation rate. The actual nucleation history in a zeolite synthesis is undoubtedly not constant over the entire induction time, as would be required if eq 10 is to be correct. From these results, it should be apparent that the different results reported by different research groups may be attributed to differences in autoclave design, fluid volumes, or any other factors which affect the heat-transfer rate in the experimental systems. It was shown that zeolite crystals actually form and begin to grow prior to the onset of observable zeolite mass formation. This observation undoubtedly stems from the detection limit of most analytical techniques which measure zeolite cryatal mass or percent crystallinity in the solid phase. From thisresult one must conclude that it is almost impossible to learn anything about the nucleation mechanism in zeolite crystallization from the analysis of the mass crystallization curve. The nucleation event is most likely finished before zeolite is observed by these techniques. Finally, the slope of the crystallization curve was shown to be proportional to the cumulative surface area and the linear crystal growth rate at any time. Therefore, the crystallization rate computed from such a slope actually depends on events which occurred during the nucleation phase of the process as well as the instantaneous linear growth rate. As in the case of the correlation of the induction time with the nucleation rate, the slope of the crystallization curve gives an indication of the speed of the crystallization process for similar systems but does not provide any quantitative information. The qualitative value of these analyses was recognized some time ago (Sand, 1984), but the evidence shown here demonstrates these points on the basis of fundamental principles.
Acknowledgment This work was carried out while Professor Thompson was on sabbatical leave of absence at the Shell Research Laboratories in Amsterdam, The Netherlands. The support of Shell Research B.V. and the faculty and administration of the Worcester Polytechnics Institute is gratefully acknowledged.
Nomenclature A = interfacial energy parameter: 16~&'~/3(kT')~ B = nucleation rate C, Co = soiute concentration, initial value C,, = equilibrium solute concentration G = linear crystal growth rate k = Boltzmann constant k, = zeolite crystal linear growth rate constant L = characteristic particle size mi = ith moment of the crystal size distribution NT = total number of crystals generated per unit volume n = number density function describing crystal size distribution s = apparent supersaturation ratio: C/CFq T, To= synthesis fluid temperature, initial value Tb= bath, or surroundings, temperature t = time tI = induction time prior to observable crystal maw formation U = heat-transfer coefficient
Ind. Eng. Chem. Res. 1992,31,373-379
B = preexponential nucleation rate constant
r = solid molecular volume
u
= solid f fluid interfacial energy
Literature Cited Aiello, R.; Colella, C.; Casey, D. G.; Sand, L. B. Experimental Zeolite Crystallization in Rhyolitic Ash-Sodium Salt Systems. In Proceedings of the 5th International Conference on Zeolites; Rees, L. V. C., Ed.; Heyden: London, 1980; p 49. Culfaz, A.; Sand, L. B. Mechanism of Nucleation and Crystallization of Zeolites from Gels. In Molecular Sieves; Meier, W. M.; Uytterhoeven, J. B., Eds.; Advances in Chemistry Series 121; American Chemical Society: Washington, DC, 1973; p 140. Dai, F.-Y.; Suzuki, M.; Takahashi, H.; Saito, Y. Mechanism of Zeolite Crystallization without using Template Reagents of Organic Bases. In New Developments in Zeolite Science and Technology; Murakami, Y., Iijima, A., Ward, J. W., Ma.;Ehvier: Amsterdam, 1986; p 223. Dai, F.-Y.; Suzuki, M.; Takahashi, H.; Saito, Y. Crystallization of Pentasil Zeolite in the Absence of Organic Template. In Zeolite Synthesis; Occelli, M. L., Robson, H. E., Eds.; ACS Symposium Series 398; American Chemical Society: Washington, DC, 1989, p 244. den Ouden, C. J. J.; Thompson, R. W. Analysis of the Formation of Monodisperse Populations by Homogeneous Nucleation. J. Colloid Interface Sci. 1991, 143, 77. Hayhurst, D. T.; Sand, L. B. Crystallization Kinetics and Properties of Na, K Phillipsites. In Molecular Sieves-ZI; Katzer, J. R., Ed.;
373
ACS Symposium Series 40; American Chemical Society: Washington, DC, 1977, p 219. Hu, H. C.; Lee, T. Y. Synthesis Kinetics of Zeolite A. Ind. Eng. Chem. Res. 1990,29,749. Huang, C. L.; Yu, W. C.; Lee, T. Y. Kinetics of Nucleation and Crystallization of Silicalite. Chem. Eng. Sci. 1986,41,625. Keijsper, J. J.; Post, M. F. M. Precursors in Zeolite Synthesis. In Zeolite Synthesis; Occelli, M. L., Robson, H. E., Eds.; ACS SymDoeium Series 398 American Chemical Societv: Washington. DC. 1989; p 28. Randolph, A. D.; Larson, M. A. Theory of Particulate Processes, 2nd ed.; Academic Press: New York, 1988. Sand,. L. B. Personal communication, WPI; Oct 1984. Schwieger, W.; Bergk, K.-H.; Freude, D.; Hunger, M.; Pfeifer, H. Synthesis of Pentasil Zeolites with and without Organic Templates. In Zeolite Synthesis; Occelli, M. L., Robson, H. E., Eds.; ACS Symposium Series 398; American Chemical Society: Washington, DC, 1989; p 274. Thompson, R. W.; Dyer, A. Mathematical Analyses of Zeolite Crystallization. Zeolites 1985, 5, 202. Warzywoda, J.; Edelman, R. D.; Thompson, R. W. Thoughta on the Induction Time in Zeolite crystallization. Zeolites 1989,9,187. Zhdanov, S. P.; Samulevich, N. N. Nucleation and Crystal Growth of Zeolites in Crystallizing Aluminosilicate Gels. In Proceedings of the 5th International Conference on Zeolites; Rees, L. V. C., Ed.; Heyden: London, 1980; p 75.
Received for review December 17, 1990 Revised manuscript received May 15, 1991 Accepted August 13,1991
Kinetics of Sorbent Regeneration in the Copper Oxide Process for Flue Gas Cleanup+,$ Peter Harriott*i*and Joanna M. Markussen Pittsburgh Energy Technology Center, US.Department of Energy, P.O. Box 10940, Pittsburgh, Pennsylvania 15236
In a regenerable process for flue gas cleanup, CuO supported on A1203reacts with SO2 and O2to form CuS04. The sorbent can be regenerated with CH4,but the reaction is slow and strongly inhibited by the SO2 produced. The kinetics of regeneration were studied using a thermal balance reactor, and the influence of the kinetics on design and operation of a reactor is discussed.
Introduction In the Fluidized-Bed Copper Oxide Process for simultaneous removal of sulfur dioxide (SO,) and nitrogen oxides (NO,), flue gas with added ammonia (NH,) is passed through a fluidized bed of sorbent particles at about 400 "C. The sorbent is l/ls-in.-diameter spheres of copperimpregnated alumina. The copper oxide (CuO) is converted to copper sulfate (CuSO,) by reaction with SO2and 02.
CUO + so2 + 7 2 0 2
-
cuso4
(1)
The reduction of nitric oxide (NO) by NH, is catalyzed mainly by CuSO,, but CuO can also act as a catalyst. 4 N 0 + 4NH3+ O2 4Nz + 6Hz0 (2)
-
'Presentad at the AIChE Annual Meeting, Chicago, IL, Nov 11-16, 1990, paper 49c. 5 Reference in this paper to any specific commercial product, process, or service is to facilitate understanding and does not necessarily imply ita endorsement or favoring by the United States Department of Energy. Oak Ridge Associated Univerisities Faculty Research Participant. On leave from Cornel1 University, Ithaca, NY.
The partially sulfated sorbent is heated to 450-500 "C in a separate fluidized bed and is then regenerated with natural gas in a counterflow moving bed. The reaction produces 5 mol of gas per mole of methane (CH,) consumed. CUSO~ + 72CH4 CU + SO2 + 7zC02 + H2O (3) +
The regenerated sorbent is cooled and returned to the adsorber, where the copper is rapidly oxidized by oxygen in the flue gas. c u + y.20, CUO (4)
-
The kinetics of SO2removal have been studied using fEed beds and different size fluidized beds, but there is little information on the kinetics of regeneration. Early fixedbed tests by McCrea et al. (1970) showed slow regeneration with CHI at 400 "C, but nearly complete sulfur removal was obtained in 30 min at 450 "C and in less than 10 min at 500 "C. The sorbent retained about 1%S even after 1-h exposure to CHI at 500 "C. The sulfur, however, was probably bound to the alumina support and did not affect the capacity of the CuO for subsequent SOz removal. Recent tests by Yeh et al. (1987) in a microbalance reactor showed 80% reduction of CuSO, with CHI in 10 min at
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