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Statistical modelling of the spouted bed coating oricess using position emission particle tracking (PEPT) data.


Production of particulate products often demands a final step m which each particle is covered with a thin layer of coating material in order, for example, to control release (of a pharmaceutical active ingredient), to protect the particle or to enhance its appearance. Equipment for applying such coatings particularly includes rotating pans and variations on fluidized beds (Pandey et al., 2007; Saleh and Guigon, 2007). Most if not all coating devices share the fact that the particles are caused to circulate within them between a zone where the coating liquid is applied and a zone where the resulting layer can dry before (perhaps) returning to the coating application zone. The key objective is usually to apply a coat which is as uniform as possible in thickness, both particle-to-particle and point-to-point on each particle. The objective of the work reported here was to investigate the potential of a spouted bed for coating comparatively large particles, to measure the resulting coating uniformity, and to develop a statistical model for variation in the particle-to-particle coating amount, using particle trajectory data obtained from a unique particle tracking method--positron emission particle tracking (PEPT).

PEPT has been developed at the University of Birmingham as a method for tracking a single particle accurately and noninvasively in various applications in engineering and science (Stein et al., 1997; Seville et al., 2005). A single tracer particle is labelled with a radionuclide which is subject to [[beta].sup.+] decay with the emission of a positron. Each positron rapidly annihilates with an electron, giving rise to a pair of 511 keV y-rays which are emitted almost exactly back-to-back. In this work, the "positron camera" consisted of two position-sensitive detectors, each with an active area of 500 x 400 m[m.sup.2], mounted on either side of the field of view, and used to detect the y-ray pairs. The two y-rays resulting from each annihilation are simultaneously detected in the two detectors and define a line passing close to the source. In principle, two such lines can be used to determine the position of the source; in practice, about 100 are used to determine each location, an algorithm being used to eliminate outliers and spurious emissions.

The spouted bed is a well-known particle mobilization technique which is favoured over conventional fluidization for large particles (approximately > 1 mm). The most common design consists of a cylindrical column on a conical base. Gas is injected vertically through a centrally located inlet at the base of the vessel (Epstein and Grace, 1997). If the fluid injection rate is high enough, the resulting jet forms a cylindrical cavity, the spout, which breaks through the bed surface. In this high-voidage spout, a stream of particles rises rapidly to a height above the surface of the surrounding settled bed and rains down onto the annulus in the shape of a fountain (Benkrid and Caram, 1989; Epstein and Grace, 1997). The spout and the spout-annulus-boundary are generally very stable, with fluid from the spout leaking into the annulus (Sullivan et al., 1987; Epstein and Grace, 1997). Particles in the annulus move downwards and, to some extent, radially inwards until they are eventually entrained into the spout (Sullivan et al., 1987; He et al., 1994; Epstein and Grace, 1997). A systematic cyclic pattern of solids movement is thus established, which lends itself to operations like particle coating, where controlled application of the coat on the particles is essential. The first air-suspension coating concepts were developed in the early 1950s and one of these was a spouted bed (Singiser et al., 1966). In a spouted bed coater, a nozzle is placed centrally below the bed of particles, establishing a distinct coating zone. The coating formation in a spouted bed depends on many variables, including the physical properties of the materials used and the operating parameters of the bed. Of these, among the most important are (i) the particle motion, that is, how often and where particles enter and traverse the coating zone and (ii) the extent of droplet collection by individual particles passing through the coating zone. The intention in such processes is that the particles are coated in the lower portion of the spout, while accelerating away from the entry region, so that they are never in close enough proximity, while surface wet, for undesirable agglomeration to occur. How ever, solids attrition in the spout, caused by particle collisions, can present a significant problem in certain applications.

The spouted bed coating model proposed here is based on the statistical history of individual particles, whose projected area governs the collection of spray droplets in the coating zone. Its practical usefulness has been investigated using an experimental system of polyvinylchloride (PVC) spheres coated with polyethylene glycol (PEG) 1500. The model itself shares some features with classical filtration models (Seville and Clift, 1997). PEPT measurement data were used to determine the particle trajectories, cycle time and the size and voidage of the spout. Probability parameters for spray-to-particle contact in the model were defined by making simplifying assumptions and quantified using experimental data.


The materials for experimental spouted bed coating work were PVC spheres with a diameter of 9.5 mm and a specific gravity of 1.37 and the hot-melt coating material polyethylene glycol (PEG) 1500. PEG 1500 was chosen as it is water-soluble and can thus be easily removed from particles and equipment parts.

A conventional spouted bed apparatus with a conical-cylindrical vessel, shown schematically in Figure 1, was used for the coating experiments. The experimental set-up included a high velocity centrifugal blower (Model 492/3, Klaxon-Secomak, Elstree, Herts, UK), an orifice plate meter, a butterfly valve, pipework, and a conical-cylindrical column. The orifice plate meter was calibrated by measuring the flow rate at a number of positions in the pipe using an FC0520 Air Pro velocity meter (Furness Controls Ltd., Bexhill-on-Sea, East Sussex, UK). To operate the spouted bed apparatus as a coating device, a spray nozzle (Model SU2A, Spraying Systems Ltd., Farnham, Surrey, UK) was inserted below the bed of particles. The coating material was heated in a glass beaker, using a hotplate, and transported by a peristaltic pump (Model IOIU/R, Watson Marlow Ltd., Flamouth, Cornwall, UK) to the spray nozzle. The atomizing air, supplied via a compressed air network, was fed into the system under controlled pressure using a pressure manometer. The atomizing air was heated in an air heater, which was filled with oil and equipped with a copper coil helix through which the air could pass. Figure 2 is a schematic of the coating set-up.


Coating Method

Prior to a coating experiment, the particle charge was weighed out and added to the apparatus, heating of the atomizing air was started and the spouting regime established at the required flow rate. After a set period of time, allowing the nozzle set-up and the coating material to be heated, the beaker containing the hotmelt was weighed and the peristaltic pump set to its operating conditions. The coating period was counted from the time the peristaltic pump was started (t = 0). It took a finite time [t.sub.1] for the fluid to travel from the container to the nozzle and the appearance of a "cloud" of coating material in (or above) the spouted bed column was taken as the onset of spray coating, which defined [t.sub.1]. Coating was then continued for a time [DELTA]t. At the end of this time, the pump was reversed, to instantly terminate the coating spray, and the silicone inlet tube transferred immediately to a second beaker. As a result, the mass decrease of the original beaker was directly related to the steady-state liquid transport during the time [t.sub.1] + [DELTA]t and could be used for mass balance calculations. The system was left spouting for a fixed period of time, before switching off the atomizing air and, with some delay, the entire system. This sequence was found necessary in order to cool the spray set-up well below the melting point of the coating material, before allowing the bed to become stationary. The entire bed of particles was then reweighed and a sufficiently large sample of particles was taken for analysis. The other coated particles were washed and dried for further use.



Mass Analysis of PVC Spheres Coated with PEG 1500

Two methods to determine the mass of coatings on PVC spheres were undertaken: (i) bulk particle analysis to determine the mean properties of the system and (ii) analysis of sets of particles individually, that is, single particle analysis, to identify weight distributions.

For the bulk particle analysis, two sets of 200 coated PVC spheres were counted out, weighed and collected in marked glass beakers. These beakers were then filled with hot water and detergent and left standing for a few hours to aid complete dissolution of the coating material. The washed particles were collected in a sieve, returned to the individual beakers and left to dry overnight in a conventional oven, heated to 40[degrees]C. When cooled to ambient temperature, the particle ensembles were reweighed. The average coating mass per particle ([m.sub.c]) was then calculated from the difference between the total mass of the coated and uncoated particles.

For the single particle analysis, 250 coated PVC spheres were weighed individually and stored in numbered trays. Once all the particles had been weighed, they were washed individually in hot water and detergent and placed in a second type of numbered tray. The trays containing the particles were left to dry overnight at 40[degrees]C in a conventional oven. When cooled to ambient temperature, the particles were reweighed individually. The difference between coated and uncoated particle weight was taken as the coating mass (mc) deposited on the individual particle.

Spray Angle Measurements

The spouted bed column was removed from the apparatus to give free visual access to the spray nozzle. To improve visibility of the spray pattern, measurements were performed in a dark room with a light source directed at the spray, and a dark background was placed immediately behind the nozzle. Pictures of the spray pattern were taken with a digital camera after 2, 3, and 4 min, counted from the start of the peristaltic pump. The digital images were then analyzed on a computer for the included angle of the recorded spray pattern.

Positron Emission Particle Tracking (DEPT) Procedure

Water was irradiated for typically half an hour in a cyclotron, which produced the radionuclide 'IF. Resin beads of approximately 600 [micro]m diameter were placed in the radioactive water, until a desirable level of activity, resulting from ion exchange, was reached. An irradiated bead was then placed in a previously prepared PVC sphere, where a 1 mm diameter channel had been drilled to the centre. Once the resin bead had been inserted, the channel was sealed with silicone rubber. The tracer particle was ready for use once the silicone rubber had fully dried. For each experiment, the apparatus was filled with 2.5 kg of PVC spheres, one of which being the tracer particle. Once the desired operating conditions were established, the system was monitored for 1 h using PEPT.


The model presented here is based on probabilistic definitions of spray-to-particle contact in the coating zone of a spouted bed. Figure 3 shows a diagram of the spouted bed coater, identifying the geometrical features used in the model. The spray nozzle, located at height [y.sub.o], introduces a fully developed conical spray pattern into the apparatus. A coating zone of height [DELTA]ho can then be defined between the positions [y.sub.1], that is, the height of first contact between spray and particles, and [y.sub.2], that is, the height above which no coating occurs. The velocity vectors shown in Figure 3 describe the particle motion in the apparatus, showing that particles from the annular region can enter the spout over the entire bed height. The extent of spray-to-particle contact for one passage of the coating zone by an individual particle can thus vary considerably. The model postulates that the projected area of the particles governs the collection of spray droplets in the defined coating zone. Assumptions for the defined coating zone are (i) that both the axial spray and particle velocities are constant and (ii) that the axial velocity of the spray is higher than that of the particles. The system can then be regarded as a quasi-stationary ensemble of particles with relative spray motion. To enable the calculation of an axial spray mass profile in the coating zone, it is assumed for the coating zone that the particles are distributed uniformly and that the spout voidage (asp) is constant.


Projected Area of a Particle Ensemble

Assuming that the particles are distributed uniformly in the coating zone and that [[epsilon].sub.sp] is constant, the number of particles can be related directly to any spout volume. The total projected area of a particle ensemble, []([V.sub.i]), in any spout volume [V.sub.i] can thus be defined as follows:

[]([V.sub.i]) = []n([V.sub.i])= [][V.sub.i] (1-[[epsilon].sup.sp])/V

=[pi]/4[d.sup.2][V.sub.i](1-[[epsilon].sup.sp])/([pi]/6)[d.sup.3]= 3[V.sub.i](1-[[epsilon].sup.sp])/2d (1)

where n ([V.sub.i]) is the number of particles present in a volume [V.sub.i], [] is the projected area of a spherical particle ([M.sup.2]), V is the volume of a spherical particle ([m.sup.3]), [[epsilon].sub.sp] is the spout voidage, and d is the particle diameter (m).


Axial Spray Mass Distribution

When coating material is sprayed into a bed of particles, the spray mass generally decreases with axial distance from the spray nozzle, since droplets are collected by the contacted particles. The model derivation below therefore follows the approach used in filtration in granular beds (Seville and Clift, 1997), which is somewhat analogous. Using the spout volume element shown in Figure 4, the following mass balance on the spray mass [m.sub.spray] at steady state can be defined:

[m.sub.spray] - ([m.sub.spray] + d[m.sub.spray]) = d[m.sub.s] (dV) (2)

where dmspray is the spray mass differential (kg), dV is the volume element (m3), and dms(dV~ is the particle mass increase (due to spray deposition) in the volume element (kg). The increase in particle mass, dins (d V), in the volume element can be calculated as shown below, where Apr (dV) is substituted with Equation (1):


where [A.sub.dV] is the cross-section of the defined volume element ([m.sup.2]).

Substitution of Equation (3) in Equation (2) gives the following differential equation:

[dm.sub.spray]/dy= - 3(1- [[epsilon].sub.sp])/2d[m.sub.spray] (4)

The differential Equation (4) can be integrated and solved as shown below:


where [m.sub.spray,o] is the initial (standardized) spray mass before particles are contacted (kg) and [y.sub.1] is the height above which the spray mass starts to decline due to particle contact (m).


Geometry of the Coating Zone

As discussed previously, a coating zone can be defined between the axial levels [y.sub.1] and [y.sub.2], shown in Figure 3. With the definition of an overall coating efficiency n, which is the percentage of the introduced coating material that ends up on the particles, [y.sub.2] and thus the height of the coating zone [DELTA][h.sub.o] can be calculated as shown below:

[m.sub.spray] ([Y.sub.2]) = 11 - n) [m.sub.spray,0] (6)

(5) in (6):


where [y.sub.2] is the height above which no coating occurs (m) and a; is the collection efficiency.

Spray-to-Particle Contact Probability

The probability [P.sub.1] (y) for an individual particle in the spout to come into contact with a developed spray pattern of included angle a can be defined on the basis of the geometries shown in Figure 5:

[P.sub.1](y)=[[pi].crit [(y).sup.2]/[pi][r.sup.2.sub.max]=[(x(y) +0.5d/[r.sub.max)].sup.2]=[(2x(y)+d/[D.sub.s]-d).sup.2] (8)


x(y) = tan ([alpha]/2) (y - [y.sub.o])

where [r.sub.crit](Y) is the radius of the statistical contact area ([m.sup.2]), [r.sub.max] is the maximum radial position of a particle in the spout (m), x (y) is the radius of the spray pattern at height y (m), [D.sub.s] is the spout diameter (m), a is the included angle of the spray pattern, and yo is the location of the spray nozzle (m).

Spray Mass Collection

The statistical event of spray-to-particle contact is described by [R.sub.1] [less than or equal to] [P.sub.1] (y), where [R.sub.1] is a random variable between 0 and 1. The mathematical description for the extent of contact, defined in the following paragraphs, is best illustrated on the basis of the volume element shown in Figure 4. Equation (9) shows for the volume element dV the mass d[] (dV) collected on a single contacted particle i as a function of the total spray mass, d[m.sub.s] (dV), collected in the element:

d[m.sub.c,i] (dV) = [F.sub.c] d[m.sub.s] (dV) = [F.sub.c] [[m.sub.spray] (y + dy)] (9)

where d[m.sub.s](dV) is the total spray mass collected by the particles present in the volume element (kg) and [F.sub.c] is the statistical collection factor.

[F.sub.c], which has an upper limit of [F.sub.c] = 1, since no more spray mass can be deposited on a single particle than is statistically collected in the volume element, is defined in Equation (10):

[F.sub.c] = [F.sub.A] (Y) R.sub.2] for 0 [less than or equal to] ([F.sub.A] (Y) R.sub.2]) < 1 (10) 1 for 1 ([F.sub.A] [less than or equal to] ([F.sub.A] (Y) R.sub.2])



where [F.sub.A] (y) is the size factor and Rz is the random variable. The size factor [F.sub.A] (y) was introduced to account for the cases where the projected area of a single particle can exceed the crosssection of the spray; this is important, since this increases the probability of a particle collecting large fractions of the total spray mass statistically collected in the element.


The flowcharts in Figures Ga and b show the algorithm of the statistical model, which simulates n individual particles i within the time interval 0 to [t.sub.max]. Coating of a particle can take place when it enters the defined coating zone in the lower portion of the bed. The particle cycle time, defined with reference to the coating zone, governs the contact frequency of individual particles with the coating zone. For the simulation of the particle history, the length of an individual cycle ([DELTA][t.sub.cyc]) was chosen statistically from the cumulative cycle time distribution F([DELTA][t.sub.cyc]). The axial height y for particle entry into the spout was chosen statistically from its cumulative distribution P(y) within the axial boundaries [y.sub.1] and [Y.sub.2] of the coating zone. The axial particle motion through the coating zone is simulated in height intervals [DELTA]y. Contact of a particle i with the spray in the coating zone is governed statistically by the probability [P.sub.1] (y) and a random value [R.sub.1], which are both determined for each height interval [DELTA]y. The algorithm registers spray-to-particle contact for [R.sub.1] [less than or equal to] [P.sub.1] (y). The increase in spray mass (m,, J, collected by a given particle i, is then calculated using the statistical collection factor [F.sub.c]. The statistical nature of this event is accounted for by the random value [R.sub.2] used to calculate [F.sub.c]. The model does not deliver the absolute values of coating mass, but can predict deviations from a mean. For n particles in the simulated time interval, the mean of all m,,i values is related to the mean coating mass ([m.sub.c]) in the bed of particles and mc can be calculated from the gradient (k) of the coating growth curves. This makes it possible to convert values of [m.sub.c,i] into actual values of coating mass.




Coating Study Coating experiments were carried out as described in Coating Method Section, using a spouted bed unit with column and inlet diameters of 194 and 45 mm, respectively, filled with 2.5 kg of PVC spheres. The atomizing air pressure was 3 barg, the spouting airflow rate was 5200 1 [min.sup.1] and the peristaltic pump was set to 59 percent of its maximum speed. The spray rate, which is equal to the pump flow rate [G.sub.pump], was calculated as follows:

[G.sub.pump] = [DELTA][m.sub.beaker]/t = [DELTA][m.sub.beaker]/[t.sub.1] + [DELTA]T (11)

where [DELTA][m.sub.beaker] is the mass decrease of the coating container during time t (kg), [t.sub.1] is the time delay for the onset of spraying (s), and [DELTA]t is the coating time (s).

Using Equation (11), a spray rate of 4.3 g [min.SUP.-1] was calculated. Figure 7 shows the mean coating mass as a function of time, where each data point represents an independent experiment. It can be seen that the mean growth rate k per particle was approximately 1 mg [min.SUP.-1]. The mass data were generated by the bulk particle analysis of 400 particles, described in the Mass Analysis of PVC Spheres Coated with PEG 1500 section. The collection efficiency, that is, the percentage of introduced coating material that is ultimately deposited on the particles, was calculated by dividing the increase in bed mass ([DELTA][m.sub.bed]) by the total mass of coating material ([DELTA]m([DELTA]t)) sprayed into the bed:

n = [DELTA][m.sub.bed]/[DELTA]m[DELTA]t = [DELTA][m.sub.bed]/[DELTA]t [G.sub.pump] (12)

For the experiments described in Figure 7, a coating efficiency of n = 0.89 was calculated.

Model Parameters Derived from DEPT Measurement Data

A PEPT experiment was carried out as described in the Positron Emission Particle Tracking (PEPT) Procedure section, using the experimental conditions described in the Coating Study section. The main difference from the experiments described in the Coating Study section was that no coating material was supplied to the bed of particles. The PEPT measurement data were used to define the spout size [D.sub.s], the spout voidage [[epsilon].sub.sp], the coating zone geometry (i.e., [y.sub.1], [y.sub.2], [DELTA][h.sub.o]), the cycle time distribution F([DELTA][t.sub.cyc]) and the spout entry height distribution P(y). The following sections explain how these parameters were derived.


Spout size

Figure 8 shows averaged velocity and occupancy profiles, obtained for bin sizes of 5 mm x 5 mm, in polar coordinates. The directions of the velocity vectors in Figure 8 were used to define the spout-annulus boundary [r.sub.bound] and the spout diameter [D.sub.s] as a function of axial height. Elements with positive axial velocities were considered to be part of the spout and the local spout diameter, [D.sub.s] (y), in the bin with upper boundary y, was calculated using Equation (13):

[D.sub.s] (Y) = 2 ([r.sub.bound] (Y) - 2.5 mm + 0.5d) = 2[r.sub.bound] (y) + d - 5 mm (13)

where rbound is the spout-annulus boundary in the bin with upper boundary y (m).

Equation (13) assumes that the spout ends at the centre of the 5 mm bin identified as the boundary. The addition of the particle diameter d accounts for the spout containing particles, whose centres are at the bin centre. From the values for [D.sub.s] (y), the mean spout diameter [D.sub.s] in the height range [Y.sub.min] to [Y.sub.max] can be calculated as shown below:

[D.sub.s] = 1/([y.sub.min] - [y.sub.max]) [[y.sub.max].summation over (y=70mm)][D.sub.s] (Y) Ay (14)

where ymin is the lower boundary for the calculation of [D.sub.s] (m), [y.sub.max] is the upper boundary for the calculation of [D.sub.s] (m), and Ay is the axial bin size (m).

Values for rbound and [D.sub.s], between 70 and 120 mm axial height, are shown in Table 1.

Spout voidage

The fraction of the total time which the tracer spends in each volume element is termed "occupancy". The following proportionality between the occupancy Occ(V) in a given volume V and the volumetric flux of particles [Q.sub.s] can thus be inferred:

V(1- [epsilon])/Occ(V) [varies] [Q.sub.s] (15)

where e is the voidage.

For the same axial region, the downward flow of particles in the annulus has to equal the upward flow of particles in the spout. With this condition, the following relationship can be defined, assuming that spout and annulus voidages are constant:

[V.sub.sp] (1- [[epsilon].sub.sp])/Occ ([V.sub.sp]) = [](1- [[epsilon]])/ Occ([]) (16)

where [V.sub.sp] is the defined spout volume ([m.sup.3]), [] is the defined annulus volume ([m.sup.3]), [[epsilon].sub.sp] is the spout voidage, and [[epsilon]], is the annulus voidage.

According to Mathur (1971), the annular voidage of a spouted bed is generally equal to that in a loosely packed bed. Using Equation (1G), the spout voidage can thus be calculated as shown below:

[[epsilon].sup.] = 1 - (1 - [[epsilon].sub.0])[]/ [V.sub.sp Occ([V.sub.sp])/Occ([ (17) OCC (Vs)

where [[epsilon].sub.o] is the packed bed voidage. From physical and bulk density data generated for the PVC spheres, a value of [[epsilon].sub.o] = 0.415 was calculated. Figure 9 shows the mean spout voidage [[epsilon].sub.sp], calculated in the axial height range [y.sub.min], to y using Equation (1G), as a function of the upper boundary y. A value of 70 mm was chosen for [y.sub.min]., since this represents the approximate lower boundary in the occupancy plot in Figure 8. [V.sub.sp] and [] were calculated on the basis of the spout-annulus and apparatus boundaries, which also identified the relevant occupancy bins for Occ([]) and Occ([V.sub.sp]). It can be seen that [[epsilon].sub.sp] does not vary significantly in the studied range.



Geometry of the coating zone

As explained in the Model Theory section, the coating zone was defined between the levels [y.sub.1] and [y.sub.2]. Figure 10 shows the number of passes of axial levels y as a function of y. Since only a small number of passes reached below a level of 65 mm, the lower boundary [y.sub.1] of the coating zone was defined at this level. For the range of [[epsilon].sub.sp] presented in Figure 9, the height of the coating zone [DELTA][h.sub.o] can be calculated using Equation (7) introduced in Model Theory Section. Table 2 shows [DELTA][h.sub.o] and the corresponding values of [y.sub.2] as a function of [[epsilon].sup.sp], using the collection efficiency value of [eta] = 0.89 quoted in the Coating Study section. Figure 11 shows the PEPTbased spout voidage calculation, using Equation (1G), alongside that from the model theory. The curves intersect at [[epsilon].sub.sp] = 0.625 and [y.sub.2] = 103.4 mm, thus defining, for the model, the spout voidage and the upper boundary of the coating zone. The values for [y.sub.2] were used to identify the reference levels (yPEPT), required to define distributions of (i) particle cycle time and (ii) entry height to the coating zone. Here, values for yPEPT were defined as multiples of 2.5 mm nearest to the value of [y.sub.2], resulting in a value of [y.sub.PEPT] = 102.5 mm. Figure 11. Spout voidage calculations based on the DEPT measurement data and the model theory, respectively, as a function of the upper boundary y.


Particle cycle time distribution

One full cycle was defined as the time elapsed between two consecutive passes of an annular reference level yPEPT in downward motion. Here, the choice of [y.sub.PEPT] [congruent to][y.sub.2] means that particles are for each cycle within the axial boundaries of the coating zone. The cycle time distributions for the chosen reference levels are presented in Figure 12. Cycle times were between 0.8 and 15.5 s and had a mean value of 2.3 s.

Spout entry height

The spout entry height within the axial boundaries of the coating zone is an important parameter, since it directly affects the amount of spray mass that can be collected by an individual particle passing through the coating zone. Here, the spout entry height was defined on the basis of the annular level passes, shown in Figure 10. It was postulated that particles which pass a level [y.sub.a] but not [y.sub.b] < [y.sub.a], must have changed to upward flow direction by entrainment into the spout. This approach was chosen because PEPT generally locates axial coordinates more accurately than radial ones. Below the upper boundary of the coating zone, defined by yPEPT, the probability of spout entry above the height y was thus calculated as follows:

P (y) = 1 - passes(y)/passes [y.sub.PEPT] (18)

Figure 13 shows P(y), which was used in the statistical model, as a function of y.



Spray angle measurements

The spray angle for PEG 1500 was measured as described in the Spray Angle Measurements section, using the same pump settings as in the coating experiments. Three digital images were taken for each condition and anal[y.sub.2]ed for spray angle. The included spray angle was 19.8 ([+ or -]0.8)[degrees].

Model Predictions

The statistical model was used to predict coating mass distributions for the experiments described in the Coating Study section, using the parameters determined in the Coating Study and Model Parameters Derived from PEPT Measurement Data sections as follows:

1. Spray angle: a = 19.8[degrees].

2. Spout diameter in the coating zone: [D.sub.s] = 66.1 mm.

3. Spout voidage in the coating zone: [[epsilon].sub.sp] = 0.625.

4. Coating growth factor per particle: k = I mg [min.sup.-1].

5. Collection efficiency: n = 0.89.

The predicted distribution values X were converted to values of coating mass by multiplying each value with the fitting parameter A, calculated as follows:

A = k[DELTA]t/[micro](X) (19)

where k is the coating growth rate factor (kg [s.sup.-1]), At is the coating time (s), and [micro] (X) is the mean of the predicted values X.

Figure 14 shows the predicted coating mass distributions for coating times between 10 and 35 min.



Validation of Model Coating Distributions

Coating mass distributions for the experiments described in the Coating Study section were obtained by the single particle analysis method described in the Mass Analysis of PVC Spheres Coated with PEG 1500 section. Figure 15 shows the predicted and experimental coating mass distributions for coating times between 10 and 35 min. The distributions of the model data were found to agree well with those for the experimental data, with differences between the two being most significant for [DELTA]t = 10 min. These results suggest that the statistical principles developed in this paper can offer a simple means of predicting coating mass distributions. However, the model relies on a number of simplifying assumptions and was only tested for specific experimental conditions and relatively coarse solids. Further experimental work is needed in order to establish a more general validity of the modelling concept.


A statistical model was developed to predict the evolution of coating mass distributions in a spouted bed coater. It was based on a number of basic assumptions, to reduce the complexity of the system, and tested for the coating of coarse PVC spheres. The parameters required in the model were obtained experimentally from spray angle measurements and particle motion studies using PEPT. The latter made it possible to define particle cycle time distributions, probabilities for the entry height of particles to the spout, spout size, spout voidage, and the geometry of the coating zone. The predicted coating mass distributions compared well with the experimental distributions. This suggests that such a statistical approach can offer a simple means of predicting coating mass distributions in spouted bed coaters. However, the model relies on a number of simplifying assumptions and has only been tested for specific experimental conditions and relatively coarse solids.


The authors wish to thank the BBSRC for a studentship to support C. Seiler. We are also grateful for the support from the Erasmus scheme for funds to support C. Nozet as a visiting student from ENSIC (Nancy, France), to whom special thanks are due for her great dedication in generating the experimental coating mass data. We thank Professor D. J. Parker and Dr. R. N. Forster of the Positron Imaging Centre (PIC) of the University of Birmingham for the use of the PEPT facility and their frequent help and advice.

A fitting parameter to convert predicted values
 X to coating mass (kg)
[] projected area of a single particle ([m.sub.2])
[]([V.sub.i]) total projected area of an ensemble of
 particles in a volume [V.sub.i] ([m.sup.2])
[A.sub.dv] cross-section of any spout volume element dV
d diameter of a particle (m)
d[m.sub.c.i] (d V) differential spray mass collected on the
 particle i in the volume element dV (kg)
d[m.sub.s](dV) total spray mass collected by the particles
 present in the volume element dV (kg)
d[m.sub.spray] spray mass differential (kg)
dV volume element (m3)
dy axial height differential (m)
[D.sub.c] diameter of the cylindrical part of a spouted
 bed column (m)
[D.sub.i] diameter of the inlet of a spouted bed
 apparatus (m)
[D.sub.s] spout diameter (m)
[D.sub.s] (y) local spout diameter in the bin with upper
 boundary y (m)
F(i) cumulative distribution value for any variable
[F.sub.A] (y) size factor
[F.sub.c] statistical collection factor
[G.sub.pump] mass flow rate of the peristaltic pump
 (kg [s.sup.-1])
k coating growth rate factor (kg s-1)
[m.sub.c] mass of the coating on a particle (kg)
[m.sub.spray] spray mass (kg)
[m.sub.spray,o] initial (standardized) spray mass before
 particles are contacted (kg)
n number of particles
n ([V.sub.i]) number of particles present in any volume
OCC(V) occupancy value (from PEPT) in a defined
 volume V
passes(y) number of passes of any level y in downward
 particle motion
P(y) probability of spout entry above level y
[P.sub.1] (y) spray-to-particle contact probability
[Q.sub.s] volumetric flow rate of solids (i.e.,
 particles) (m3 s-1)
[r.sub.bound] radial position of the spout-annulus boundary
[r.sub.crit] (y) radius of the statistical contact area at
 height y (m)
[r.sub.max] maximum radial position of a particle in the
 spout (m)
[R.sub.1], [R.sub.2] random variables (with values between 0 and 1)
[S.sub.pump] setting of the peristaltic pump
t time (s)
[t.sub.1] time delay for the onset of spraying (s)
V volume (m3)
[] defined annulus volume (m3)
[V.sub.sp] defined spout volume (m3)
x (y) radius of a conical spray pattern at height y
X distribution parameters from the statistical
y axial height/position (m)
[Y.sub.o] axial position of the spray nozzle outlet (m)
[y.sub.1] height in the coating distribution model, above
 which the spray mass starts to decline due to
 particle contact
[y.sub.2] height in the coating distribution model, above
 which no coating occurs (m)
[Y.sub.PEPT] reference level for the analysis of PEPT data

Greek Symbols

[alpha] included angle of a conical spray pattern
[DELTA][h.sub.o] height of the coating zone (m)
[[DELTA]m([DELTA]t) total mass of coating material sprayed during
 time [DELTA]t (kg)
[DELTA][m.sub.beaker] mass reduction of the coating container during
 time t (kg)
[DELTA][m.sub.bed] bed mass increase due to the coating process
[DELTA]t coating time (s)
[DELTA][t.cyc] cycle time (s)
[[epsilon].sub.o] packed bed voidage
[[epsilon]] voidage in the annulus of a spouted bed
[[epsilon].sub.sp] voidage in the spout of a spouted bed
[eta] collection efficiency
[micro] (i) mean value for any parameter i

Manuscript received January 15, 2008; revised manuscript received February 20, 2008; accepted for publication February 21, 2008.


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Mathur, K. B., "Spouted Beds," Chapter 17 in "Fluidization," J. F. Davidson and D. Harrison, Eds., Academic Press, New York (1971), pp. 711-749.

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Saleh, K. and P. Guigon, "Coating and Encapsulation Processes in Powder Technology," Chapter 7 in "Granulation," A. D. Salman, M. J. Hounslow and J. P. K. Seville, Eds., Elsevier, Amsterdam (2007), pp. 323-375.

Seville, J. P. K. and R. Clift, "Granular Bed Filters," Chapter 9 in "Gas Cleaning in Demanding Applications," J. P. K. Seville, Ed., Blackie Academic & Professional, Glasgow, UK (1997).

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C. Seiler, P. J. Fryer and J. P. K. Seville *

Department of Chemical Engineering, Centre for Formulation Engineering, University of Birmingham, Birmingham B75 2TT, U.K.

C. Seiler's present adrress is merck Sharp & Dohnme, Hoddesdon, Hertfordshire EN 11 9BU, U.K.

J.P.K. Seville's present address is School of Engineering , University of Warwick, Coventry cv4 7 AL, U.K.

* Author to whom correspondence may be addressed. E-mail Can. J. Chem. Eng.86:571-581,2008 [c] 2008 Canadian Society for Chemical Engineering
Table 1. Spout-annulus spout diameter ([D.sub.s]) as a function of axial
height (y) for the PEPT experiment (data from Figure 8)

y (mm) y (mm)

Lower Upper [r.sub.bound] Lower Upper [D.sub.s]
 (mm) (mm)

70 75 30 70 75 64.7
75 80 30 70 80 64.7
80 85 30 70 85 64.7
85 90 30 70 90 64.7
90 95 30 70 95 64.7
95 100 30 70 100 64.7
100 105 35 70 105 66.1
105 110 35 70 110 67.2
110 115 35 70 115 68.0
115 120 35 70 120 68.7

Table 2. Values calculated for the axial height [DELTA][h.sub.0]
(using Equation (7)) and the equivalent upper boundary [y.sub.2]
of the coating zone as a function of spout voidage sp

sp [DELTA][h.sub.0] (mm) [y.sub.2] (mm)

0.565 33.1 98.1
0.570 33.5 98.5
0.575 33.9 98.9
0.580 34.3 99.3
0.585 34.7 99.7
0.590 35.1 100.1
0.595 35.5 100.5
0.600 36.0 101.0
0.605 36.4 101.4
0.610 36.9 101.9
0.615 37.4 102.4
0.620 37.9 102.9
0.625 38.4 103.4
0.630 38.9 103.9
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Author:Seiler, C.; Fryer, P.J.; Seville, J.P.K.
Publication:Canadian Journal of Chemical Engineering
Date:Jun 1, 2008
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