Znd. Eng. Chem. Process
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Analysis of Spouted-Bed Coating and Granulation. 1 Batch Operation Uzl Mann Department of Chemical Engineering, Texas Tech Universw, Lubbock, Texas 79409
A mathematical model to analyze the performance of batch spouted-bed coating and granulation units is described. The model is based on describing the hlstory of a single particle In the unit. The amount of coating deposited on the particles during the operation is expressed in terms of the cycle time distribution of the particles and the distribution of the coating amount deposited on a particle in one cycle. Both c a n be experlmentally determined in short experimental runs. It is shown that in most practical applications, when the average number of cycles is larger than 50, the distribution of the coating deposited on the particles can be approximated by a normal distribution. Applications of the model in estimating a priori the coating uniformity, selecting an operating strategy to obtain specifled coating uniformity, and selecting system design variables are discussed.
Introduction Coating and encapsulation of solid particles are being used in a wide variety of products, mainly to protect the particles from the environment or to control the release rate of a compound (see brief review by Goodwin and Somerville, 1974). At present, particulate coating is used commercially mainly in the pharmaceutical industry, in small-volume specialized products in the food industry (see,for example, Jackel and Belshaw, 1971), and in health related applications (see, for example, Sparks et al., 1969). In the past 15 years agricultural applications of particulate coating and encapsulation have been investigated, mainly in coating seeds for delayed germination (Schreiber and LaCroix, 1967; Porter, 1978) and controlling the release rate of fertilizers (Hignett, 1971) and pesticides (Cardarelli, 1975; Coane et al., 1977). However, the commercial implementation of these applications depends on the development of an economical large-scale process to coat particles. One of the most promising routes to do so is spouted-bed coating. The objective of this two-paper series is to describe a modeling technique for analyzing the performance of spouted-bed coating processes. Part 1 considers the performance of batch processes and part 2 considers the performance of continuous processes. Batch spouted-bed coating has been commercially used to coat pharmaceutical tablets for over 20 years (Wurster, 1957,1959; Singiser et al., 1961, 1966; Heiser et al., 1960). Spouted-bed granulation has also been used in various applications (Mathur and Epstein, 1974). Both operations are based on circulating the particles in the bed and continuously spraying them with a coating solution. In the coating process, a relatively small amount of material is added to the particles which does not affect their size and properties. In the granulation process, a substantial amount is added and the particles grow during the operation. This paper considers processes in which the particle properties do not change during the operation. A batch spouted-bed coating unit with a draft tube is shown schematically in Figure 1. This system will be used as an illustration in this paper. A batch of the particles to be coated is charged into the unit and is retained there during the entire operation. In this system, two air streams are continuously introduced into the unit and induce the particle circulation. One stream is injected into the center of the bed, inside the central tube, and the other into the annulus. The flow rate of the center stream is high and the air pneumatically conveys particles upward through 0196-4305183f 1122-0288$01.50/0
the central tube (or spout) into the disengagement chamber. There, due to the large cross-section area, the air velocity is small and the particles fall into the annulus. The particles descend in the annulus and when they reach the bottom of the annulus, they move toward the center and are carried upward through the central tube. The annular air stream fluidizes the annular bed, thus enhancing the downward particle flow. The particle circulation rate and flow patterns are controlled by adjusting the two air streams. An atomizer installed at the center of the distribution plate continuously sprays a solution of the coating material into the system. Every time a particle passes through the spray a certain amount of the solution wets its surface. As the particle moves upward in the central tube the solvent evaporates and its vapors are carried out of the system with the spouting air while the coating material remains on the particle surface. The solvent evaporation continues during the particle descent in the annulus. The temperature of each air stream can be adjusted to ensure complete solvent evaporation in each cycle. The operation continues until the desired amount of coating has been deposited on the particles. A more detailed description of the system operation is provided elsewhere (Mann, 1972). Despite its long commercial use, the design and operation of spouted-bed coating is still an art. Very little information has been reported in the literature on methods to estimate, a priori, the coating uniformity or to select operating strategy and design parameters in order to improve the process performance. This is perhaps because of the difficulty in measuring experimentally the key operating parameters. The amount of coating deposited on a particle depends on the number of times this particle passes through the spray zone and on the amount of coating deposited on it in each passage. The latter can be determined experimentally by collecting numerous particles after one passage through the spray and measuring the amount of coating deposited on each one of them. However, direct experimental determination of the number of cycles and its distribution among the particles is virtually impractical. It involves counting the number of passages a single tagged particle completes during a given operating time and then repeating it over numerous operations. This, of course, should be done for every unit design and configuration, every operating condition, and every operating time. The modeling technique derived and described below enables one to estimate the coating uni0 1983 American Chemical Soclety
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983 289
t. The mean amount of coating deposited on a particle in operating time t is p,(t)
= E [ C ( t ) ]= J m c d 8 ( c , t ) = Jmch(c,t) dc (3) 0
where h(c,t) = dH(c,t)/dc is the density distribution function of C ( t ) . The variance of C ( t ) is
PARTITION
To obtain a useful expression for H(c,t) the distribution functions of W and N ( t ) should be available. The distribution function of the amount of coating deposited on a particle in a single passage, F(w), is defined by F(w) = Iw) (w I 0) (4) Assuming F(w) is a continuous function, the mean of the distribution is
p1w
AIR DISTRIBUTION PLATE ATOMIZER
I /I I
ATOMIZING AIR
-w
+LIOUID FEED
where f(w) = dF(w)/dw is the density distribution function of W. The variance of the distribution is uw2= Var[WI = Jm(w
- pJ2 d$(w) =
t PROCESS AIR
Figure 1. Schematic description of a batch spouted-bed coating unit.
formity and to select the design variables and operating conditions on the basis of a small number of experimental runs. Analysis Consider a batch spouted-bed coating unit shown schematically in Figure 1. It is assumed that the system is at steady state (particle circulation rate and flow patterns are constant), and that the particle properties do not change during the operation. For convenience, it is also assumed that all the coating material introduced into the system is deposited on the particles and that no attrition is taking place. The latter two assumptions are made in order to describe the concepts used on a simplified system, but they can be removed without loss of generality. The amount of coating deposited on a particle in operating time t , C(t),depends on the number of times this particle passes through the coating spray zone during the operation and on the coating amount deposited on it in each passage. Let Wi denote the amount of coating deposited on a particle in the ith passage. The total amount of coating deposited on the particle is C(t)= + ... + Wiqt) (1)
w, w,+
where N ( t )is the number of passages this particle completes in operating time t. Since the amount deposited on the particle may vary from passage to passage, and the number of passages the particle completes in time t can also vary, both Wand N ( t ) are random variables. Thus, C ( t )is also a random variable and ita distribution function, H(c,t),is defined as the probability that a coating amount of no more than c is deposited on a particle during operating time t , i.e. (c 2 0;t 1 0) (2) H(c,t) = p1C(t) Ic ) When all the particles in the bed have similar properties (size, shape, surface roughness, etc.), H(c,t) can be interpreted as the fraction of particles on which no more than c grams of coating were deposited during operating time
Similarly, the distribution of N ( t ) ,the number of cycles distribution (NCD),G(n,t),is defined by (n = 1, 2, ...) G(n,t)= q N ( t ) In) (7) and ita probability function is g(n,t) = P ( N ( t )= n) = G(n,t)- G ( n - 1,t) (8) The mean and the variance of N ( t ) are m
pn(t)
= E[N(t)I = C ng(n,t)
(9)
n=l
m
u,2(t) = Var[N(t)I = C (n - d 2 g ( n , t ) n=l
(10)
respectively. When the particle properties do not change during the operations, W iand N ( t ) are two independent random variables. Then, the probability that a coating mass of no more than c is deposited on a particle which passes through the spray exactly n times is
q C ( t ) Ic I N ( t ) = n) = [F'*"I(c) (11) where the term on the left side is the conditional probability that C ( t ) Ic given that N ( t ) = n,and [Fn](c) is the nth order convolution of F(w), (see, for example, Feller, 1971). Since a given amount of coating can be deposited on a particle while it completes different number of cycles, H(c,t) is given by m
H(c,t) = CPfC(t)< c I N ( t ) = n) x PfN(t)= n] = n=l
C g ( n , t ) [ F " I ( c )(12)
n=l
In principle, whenever g(n,t)and F(w) are known, H ( c , t ) can be calculated directly from (12). As mentioned above, F(w) can be easily determined experimentally, but direct determination of the N C D is virtually impractical. However, Mann et al. (1974) have shown that the N C D at any operating time can be calculated directly from the cycle of time distribution (CTD). The latter is experimentally
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determined by tagging one particle and measuring the durations of numerous cycles. This can be completed in a single short run. An experimental technique for measuring the CTD in spouted beds is described elsewhere (Mann and Crosby, 1975). Furthermore, as shown below, for most practical cases it is not necessary to determine F(w) and the CTD explicitly but rather it is sufficient to estimate only their means and variances. This requires of course a much smaller number of experiments. It has been shown (see, for example, Cox, 1967)that for long operating times H(c,t) approaches asymptotically a normal distribution with mean
-5.0
1
0 3-
c
.
u
s
:
v
4 0.2-
and variance
where pT and uT2 are the mean and variance respectively of the cycle time. Thus
0.1
-
-3
-2
I
I
O
2
Cct1 -/.t//.
(5: where 4(z) represents the standard normal distribution function. Hence for large t , H(c,t) may be approximated by a normal distribution with parameters p,(t) and u,2(t) given by (13)and (14). This limiting distribution is independent of the nature (shape)of either the CTD or F(w) but depends only on their means and variances. However, the range o f t for which the normal approximation can be used does depend on the nature of the CTD and F(w). To determine the range of operating times for which the normal approximation (eq 15)can be used we examine the properties of H(c,t). We consider first the case when a constant amount of coating is deposited on a particle in each passage. For this case, pw = W,, and uw2= 0 and it follows that H(c,t)has the same form of the NCD but with parameters p , ( t ) = W$/I.CT and U: = W ~ U T ' ~ /Mann ~T~. et al. (1974)have shown that the NCD can be approximated by a normal distribution whenever the operating time is longer than 20pp For the case where the amount of coating deposited on a particle in each passage is not constant, one would expect that the convergence to normal distribution is slower. As discussed before (Mann et al., 1974),it is conjectured here that the slowest convergence occurs when both the CTD and F(w)are not symmetric distributions. Thus, to obtain a conservative estimate of the operating time for which H(c,t) can be approximated by a normal distribution, we calculate H(c,t) for the case where both the CTD and F(w)are exponential distributions. For this case, g(n,t) = (n!)-l(t/pT)ne"/'T (see Mann et al., 1974)and the density function of [FC"](c)is a gamma distribution, i.e.
f*%) = D / ( n - 1 ) ! 1 ( 1 / ~ ~ ) ( texp(-t/ccw) /~~)~-~ Hence, from (12)the density function of H(c,t) is
Figure 2 compares the density function of the coating distribution calculated by (16)with the standard normal distribution. It is evident that whenever t 1 50pT the normal approximation can be used. This condition is
A;/t,'/*
Figure 2. Comparisonof actual and approximated coating distribution (both F ( W ) and CTD are exponential distributions).
satisfied in most commercial applications.
Discussion The number of parameters affecting the performance of a spouted-bed coating unit is large. To simplify the diecussion we divide these parameters into three categories. (a) Parameters of the particles, coating material, and coating solution (size and shape of particles, coating properties, solvent viscosity, boiling point and heat of vaporization, solution concentration and viscosity, etc.). These parameters have very little direct effect on the coating uniformity per se. Usually they are selected on the basis of the required end-use properties of the product. From a processing viewpoint they impose constraints on the operating conditions (air temperature and descend time to dry a particle in each cycle, proper air flow rates to avoid attrition, etc.). These parameters are not considered here. (b) Unit design parameters (geometric configuration and dimensions of the units, atomizer type and size, charge of particles per batch, etc.). These parameters cannot be adjusted during a run but can be somewhat altered within the operating constraints from run to run. (c) Operating parameters (air flow rate, coating solution flow rate, operating time, etc.). These parameters can be easily adjusted during a run. To illustrate the applications of the foregoing analysis we consider here three cases: (a) estimation of coating uniformity when the operating conditions and operating time are known,(b) selection of operating strategy in order to meet specified coating iniformity, and (c) determination of optimum unit design parameters. In the discussion below two important assumptions are made. First, it is assumed that the operating time is sufficiently long such that the normal approximation (eq 15) can be used. This assumption applied to all commercial spouted-bed batch coating units. Second, it is assumed that the mass of coating deposited on a particle and its distribution among the particles can be used as measures of the coating uni-
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 2, 1983
formity. This is done because in most commercial applications the coating is measured in terms of the amount deposited on the particle. When the number of times a particle passes through the spray is large, the coating is spread over the entire particle surface uniformly. For casea where the surface coverage is important, a relationship between the coating mass and the surface coverage should be provided. (a) Estimating Coating Uniformity for Known Operating Conditions. In this case, the CTD parameters, pT and uT2, and the parameters of the coating amount deposited per passage, pw and uW2,are known as well as the operating time t. The average amount of coating on a particle, E, is calculated from (13); = p&) = p,t/pT. The coating uniformity can be specified and expressed in several different ways. For pharmaceutical tablets the requirement is usually that the coating be within a specified range, say d, gram, of the mean. Thus, the coating uniformity is expressed in terms of probability or fraction of particles, a (say 99%), which deviates from the mean p, by no more than a specified amount, d,, i.e. P ( ( p c ( t )-
291
Table I. Design and Operating Parameters parameter no. 1 2 3
4 5 6 I
parameter unit diameter annulus width partition gap atomizer type air flow rate coating solution flow rate operation time
levels t o be tested 3 2 2
3 3 3 5
To find the necessary operating time we use the uniformity requirement, which for specified d, and a is d J u , 5 Za 2. Substituting (18)into this relation and rearranging, the operating time is
and from (19)
4) < W )> ( d t )+ d,)J1 a
(17) For long operating times, the coating uniformity can be estimated by (15)using normal distribution tables. If d, is specified, a can be calculated as follows: first, the standard normal variable, Za12is calculated by
and then the value of a is found in the table. For example, for d, = 0.0251 g and a, = 0.0128 g, Za12= 1.96 and from the standard normal distribution table a/2 = 0.475 and therefore a = 0.950. When a is specified, the acceptable coating deviation is calculated as follows: first, the value of the standard normal variable is found in the table. Then, the coating deviation is calculated by
For example, for a = 0.99 and a, = 0.01 g, from the table Z0.4, = 2.575 and d, = 0.02575 g. (b) Selection of Operating Strategy. In this case we consider the operation of a given system operated at the manufacturer's specified operating conditions (pT and QT are known). The desired amount of coating on a particle, E, the acceptable deviation, d,, and the uniformity specification, a,are given. We want to determine the atomizer operating conditions (the value of p,) and for how long to operate the unit in order to obtain the specified coating uniformity. For the purpose of the analysis, we assume that the relative standard deviation of the amount of coating deposited on a particle in a single passage, uw/pw, is known, say u,/p, = K . This is usually the case since the ratio depends on the system geometry and operating conditions and not on the spray flow rate. From (13),the relationship between the operating time, t , and the mean amount deposited on a particle in one passage, p,, is t = EpT/pw; thus p, = p , p T / t . Substituting this into (14),the coating standard deviation is expressed by
(c) Determination of Unit Design Parameters. In this case the objective is to design an efficient spouted-bed coating system (to select h,uW2, pT, uT2, and t ) which yields coating with specified uniformity ( E , d,, and a)at specified production rate. In principle, a unit can be designed when the relationships between pT, uT2,p,, and uw2and the unit geometry (diameter and length, annulus width, gap between partition and distribution plate, etc.), atomizer type, and operating conditions (air flow rates, solution flow rate) are known. However, in practice such relationships are not available. Then, the unit design is based on experimental measurements of unit performance as a function of the various design and operating parameters. We describe below how the analysis can be used to reduce substantially the number of experiments needed for the design. Consider the design of a coating system which involves the selection of the parameters listed in Table I. Direct measurement of the coating uniformity at all parameter combinations requires 1620 experiments without duplication. Using the results derived above, we immediately recognize that the operating time is not an experimental parameter and that only the effect of the design variables on p ~ UT^, , p,, and uW2should be considered. The CTD (and hence pT and uT2)depends only on design parameters 1,2,3,and 5,can be completely determined at all parameter combinations in 36 experiments. Similarly,F(w)(and hence p, and uw2)depends on design parameters 3, 4,5, and 6 and can be completely determined at all parameter combinations in 54 experiments. Thus, by using the results, the total number of experiments needed to give a complete description of the process at all parameter combinations is 90,about 5% of the experiments needed to obtain the same information by direct measurements. Concluding Remarks The foregoing analysis and discussion demonstrate how the performance of a batch spouted-bed coating unit can be analyzed by a simple modeling technique. The performance is expressed in terms of the cycle time distribution of the particles and the distribution of the coating amount deposited on a particle in a single cycle-both can be readily determined experimentally in short runs. However, one important point should be borne in mind in using the results derived above. The key assumption
Ind. Eng. Chem. Process Des. Dev. 1983, 22, 292-298
292
in the analysis above is that the coating amount deposited on a particle in one cycle is independent of the number of cycles that particle has been completed. Under this assumption, (11)applies and the derived results follow. This assumption is valid in virtually all coating applications since in practice the particle properties do not change during the operation. However, in spouted-bed granulation the particles' size changes during the operation and consequently W depend on N ( t ) . Furthermore, in granulation, the cycle time distribution itself may change during the operation. In this case the relationship between W and t as well as the variation of the CTD with time should be known. This situation will be discussed in a separate article.
Nomenclature C ( t )= coating deposited on a particle in operating time t , g c = coating mass, g = specified amount of coating on a particle, g d, = coating deviation, g E [ ] = expected value operator F(w) = distribution function of W ,dimensionless f(w)= density function of F(w),g-' G(n,t) = distribution function of N ( t ) ,NCD (Eq 7), dimentionless g(n,t) = probability function of N ( t ) ,dimensionless H(c,t) = distribution function of C ( t ) ,dimensionless h(c,t) = density function of H(c,t), 8-l K = u w / p L wdimensionless , N (t ) = number of cycles a particle completes in operating time t , dimensionless n = integer pl = probability operator t = time, s Var[ ] ] = variance operator W i= amount of coating deposited on a particle in the ith passage, g w = coating mass, g
= standard normal variable, dimensionless Greek Symbols a = fraction J?( ) = gamma function p , ( t ) = mean of H(c,t), g p,(t) = mean of G(n,t),dimensionless pT = mean cycle time, min puw= mean of F(w),g u J t ) = standard deviation of H(c,t),g u, = standard deviation of G(n,t), dimensionless UT = standard deviation of the cycle time, s u, = standard deviation of F(w),g Literature Cited
Z,
Cardarelll, N. CHEMTECH 1075, 5(8), 482. Cox, D. R. "Renewal Theory"; Methuen and Co., Ltd.: London, 1967; p 91-101. Doane, W. M.; Shasha, B. S.;Russell. C. R. "Encapsulation of Pestickies within Starch Matrix In Controlled Released Pestlckles", Sher, N. B.,Ed., ACS Symposlm Series No. 53, American Chemical Society; Washington, DC, 1977; p 74. Feller, W. "An Introductlon to Probability Theory and Its Applications", 2nd ed.; Wiley: New York, 1971; Vol. 11. pp 143-148. Goodwln, J. T.; Somervllle, Q. R. CHEMTECH 1874, 4(10). 623. Heiser, A. L.; Lowenthal, W.; Slngiser, R. D. U.S. Patent 3 112220, 1960. Hlgnett, T. P. Fed. News Doc 1071, 16, 42. Jackel, S. S.; Belshaw, F. Food Process. May 1071. Mann, U. Ph.D. Thesis, Unhrerslty of Wisconsin, Madison, WI, 1972. Mann, U.; Crosby, E. J.; Rublnovltch. M. Chem. fng. Sci. 1074, 29, 761. Mann, U.; Crosby, E. J. Can. J. Chem. Eng. 1075, 53, 579. Mathur, K. B.; Epstein, N. "Spouted Beds"; Academic Press: New York, 1974; pp 191-213. Porter, F. E. CHEMTECH 1078, 8(5),284. Schreiber, K.; LaCroix, L. J. Can. J. Rant Sci. 1067, 47, 455. Singlser. R. E.; Lowenthal, W. J. m r m . Sci. 1061, 50(2), 168. Singlser, R. E.; Helser, A. L.; Prllllg, E. B. Chem. fng. h o g . 1866, 62(6), 107. Sparks, R. E.; Salamine, R. M.; Meler, P. M. Trans. Am. SOC.Artif. Intern. Organs 1888, 15, 353. Wurster, D. E. U S . Patent 2799241, 1957. Wurster, D. E. J. Am. Pharm. Assoc. 1858, 48(8).
Received for review October 9, 1981 Revised manuscript received May 17, 1982 Accepted August 19, 1982
Catalytic Hydroprocessing of SRC-I I Heavy Distillate Fractions. 1 Preparation of the Fractions by Liquid Chromatography Leonidas Petrakis,' Raffaele G. Ruberto, and Donald C. Young Gulf Science and Technology Company, Pittsburgh, Pennsylvanla 15230
Bruce C. Gates" Center for Catalytic Science and Technology, Department of Chemical Engineering, University of Delaware, Newark, Delaware 1971 1
Liquid chromatography, with columns containing cation-exchange resin and clay-supported Fe2Ci6,was used on a preparative scale to separate 10 10- batches of a coacclertved liqukl (SRCII heavy distkte) Into nine fractions, each consisting of chemically similar compounds. The fractions are strong, weak, and very weak bases: strong, weak, and very weak acids; neutral oils; neutral resins; and asphattenes. Each fraction has been characterized spectroscopically, and representative structures have been identified. The yleld data indicate good reproducibility in the separations, and the fractions of Bach type have been combined, giving sufficient quantities to allow high-pressure microreactor experiments characterizing the catalytic hydroprocessing of each fraction individually.
Introduction The need for converting coal into economical and environmentally acceptable liquid fuels has led to the development of several technologies now approaching com0196-4305/83/1122-0292$01.50/0
mercial feasibility, including the SRC-11, H-Coal, and EDS processes. The liquids produced in these processes require catalytic upgrading, and the primary requirement is hydroprocessing, which involves reactions such as hydro@ 1983 American Chemical Society
