Residence time distributions of different size particles in the
spray zone of a Wurster fluid bed studied using DEM-CFD
Liang Li1, 2, Johan Remmelgas2, *, Berend G.M. van Wachem3, Christian von Corswant2, Mats
Johansson2, Staffan Folestad2, Anders Rasmuson1
1Department
of Chemical and Biological Engineering, Chalmers University of Technology, SE-412
96, Gothenburg, Sweden
2Pharmaceutical
3Division
Development, AstraZeneca R&D, Mölndal, Sweden
of Thermofluids, Department of Mechanical Engineering, Imperial College London,
Exhibition Road, London SW7 2AZ, United Kingdom
*Correspondence
should be addressed to Johan Remmelgas at
Tel +46-(0)-31-7065838 / Fax +46-(0)31-7763729
[email protected].
Abstract
Particle cycle and residence time distributions in different regions, particularly in the
spray zone, play an important role in fluid bed coating. In this study, a DEM-CFD
(discrete element method, computational fluid dynamics) model is employed to
determine particle cycle and residence time distributions in a laboratory-scale Wurster
fluid bed coater. The calculations show good agreement with data obtained using the
positron emission particle tracking (PEPT) technique. The DEM-CFD simulations of
different size particles show that large particles spend a longer time in the spray zone
and in the Wurster tube than small particles. In addition, large particles are found on
average to move closer to the spray nozzle than small particles, which implies that the
large particles could shield small particles from the spray droplets. Both of these effects
suggest that large particles receive a greater amount of coating solution per unit area
per cycle than small particles. However, the simulations in combination with the PEPT
experiments show that this is partly compensated for by a longer cycle time for large
particles. Large particles thus receive more coating per unit area per pass through the
spray zone, but also travel through the spray zone less frequently than small particles.
Keywords: fluid bed, coating, spray zone, residence time distribution, discrete element
method
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1. Introduction
The Wurster process [1] has been widely used to coat particles in industry for a number
of different purposes [2]. In the pharmaceutical industry it is used to coat tablets or
pellets with drug substances or functional films that, e.g. control the release of the drug
substance [3-6]. The process typically takes place in a fluid bed, as illustrated in Figure 1,
in which particles are kept near minimum fluidization by a fluidization air flow that is
supplied through a distributor plate at the bottom of the fluid bed. One or more twofluid nozzles located at the bottom of the bed supply an atomization air flow and a liquid
suspension in the form of droplets. The liquid droplets are deposited onto the particles
that pass through the spray zone. The particles are then dried by the air flow as they
move upwards and as they settle back towards the bottom of the fluid bed.
Figure 1
Schematic of the Wurster process and the different regions: 1) the spray zone, 2)
the Wurster tube, 3) the fountain region, 4) the downbed region, and 5) the horizontal transport
region.
The fluid bed can be divided into different regions as shown in Figure 1 [7-9]. The
particle coating cycle, i.e. the sequence of coating and subsequent drying, is also
illustrated in Figure 1. It is here defined as the trajectory in which the particle travels
through the spray zone, the Wurster tube, the fountain region and the downbed region
before it reappears in the spray zone to begin the next coating cycle. The total amount of
coating deposited onto a particle depends on the number of times the particle passes the
spray zone and on the amount of coating solution that the particle receives per pass [1013]. Thus it is clear that the cycle time distribution (CTD) and the residence time
distribution (RTD) in the spray zone of particles are important factors in determining
the quality of the product such as the film thickness and the film thickness variability.
Furthermore, the RTDs in different regions determine the drying rate of the particles in
different regions, which plays a key role in the film formation process.
There have been a number of experimental studies on CTDs and RTDs in previous work.
Mann and Crosby [14] and Shelukar et al. [12] measured the CTDs using radioactive or
magnetic particles in spouted beds and Wurster beds respectively, and San José et al. [15]
investigated the CTDs by monitoring colored particles in spouted bed dryer. While the
CTD certainly affects the amount of coating solution deposited onto the particles, the
RTD in the spray zone and the detailed motion of particles in the spray zone also play an
2
important role. Moreover, it has been proposed that particles of one size receive a
smaller portion of the coating solution due to shielding by particles of a different size.
For example, Cheng and Turton [16] reported that the major cause of coating variation
can be attributed to particles receiving different amounts of coating when passing
through the spray zone. Recently, Li et al. [17] presented an experimental study of
particle cycle and residence time distributions in different regions using the positron
emission particle tracking (PEPT) technique. The results from the PEPT technique
confirmed clear differences in the RTD for different size particles, also for mixtures of
particles. Unfortunately, because of limitations with the PEPT technique the particle
motion in the spray zone could only partially be characterized. Additional studies were
therefore suggested by Li et al. [17] to provide further insight into the detailed particle
motion in the spray zone and its contribution to particle coating process.
In order to shed light on the detailed particle motion in the spray zone, DEM-CFD
(discrete element method, computational fluid dynamics) modeling may be employed.
In this modeling approach, every particle is modeled (as a discrete element) while the
gas phase is treated as a continuum. When the number of particles is large, as is typical
in particle coating processes, the computational time can become very long. For many
particle coating systems used in the pharmaceutical industry, however, batch sizes of a
few hundred grams are often employed during development. Depending on the particle
size, these systems thus contain between tens of thousands and a few million
particles. Simulations involving tens of thousands of particles are fairly straightforward,
while simulations involving a few million particles are challenging but still feasible (see
e.g. [18]). In the pharmaceutical industry, CFD-DEM modeling thus offers a unique
opportunity to study process systems that are commonly used for small-scale
production.
The discrete element method was proposed for granular assemblies by Cundall and
Strack [19] and was first introduced into research in fluid beds by Tsuji et al. [20]. The
DEM-CFD approach is increasingly applied in modeling of particle/powder processes
[21-29] and has become popular [30] because interparticle interactions are accounted
for in a straightforward manner. For example, Link et al. [22] assessed the capability of
DEM to reproduce several important flow regimes observed in a 3D spout-fluid bed and
van Buijtenen et al. [31, 32] investigated the effect of elevating the spout on the
dynamics of a (multiple) spout-fluidized bed. In the work by Fries et al. [26], an example
of the RTD in the spray zone of a Wurster coater was reported by means of DEM-CFD
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simulations. In addition, Yang et al. [29, 33, 34] presented the hydrodynamics in a 3D
spouted bed and found that the solid residence time is shortest in the spout region.
The aim of the present study is to establish and validate a DEM-CFD model for
simulations of particle motion in a Wurster fluid bed. This is performed as an important
step in developing a simulation tool for the entire particle coating process. By following
particle trajectories, the CTDs and RTDs in different regions of the Wurster fluid bed
process are determined and compared to data from recent PEPT experiments [17]. In
these recent experiments, it was pointed out that it is difficult to detect the tracer
particle in the spray region towards the bottom of the bed because the -rays tend to be
absorbed by the bulky metal parts in this region. Since it was not possible to employ the
PEPT technique to measure the particle residence time in the spray zone, special
attention is in the present study paid to evaluate the predicted particle motion in the
spray zone. The validated DEM-CFD model is thus employed to simulate particle motion
in the spray zone to gain an improved understanding of the coating process. These latter
simulations are used to predict the residence time in the spray zone and to examine
whether particles of one size may preferentially shield particles of a different size from
the spray droplets. Lastly, the results are discussed in the context of coating and the
effect on the overall coating process.
2. Mathematical model
2.1. Equations of particle motion
The motion of an individual particle is described using Newton’s second law
𝑚𝑝,𝑖
𝑑𝒗𝒑,𝒊
𝑉𝑝,𝑖
=𝛽
(𝒖𝒈 − 𝒗𝒑,𝒊 ) + 𝑚𝑝,𝑖 𝒈 − 𝑉𝑝,𝑖 𝛻𝑃 + 𝑭𝒄,𝒊
𝑑𝑡
𝜀𝑠
(1)
where 𝑚𝑝,𝑖 is the mass of the 𝑖 𝑡ℎ particle, 𝒗𝑝,𝑖 is the particle velocity, 𝒖𝑔 is the gas
velocity, 𝒈 is the gravitational acceleration, 𝑉𝑝,𝑖 is the particle volume, 𝛻𝑃 is the gas
pressure gradient, 𝜀𝑠 is the particle volume fraction, 𝑭𝑐,𝑖 is the contact force during
particle-particle and particle-wall collisions and 𝛽 is the interphase momentum transfer
coefficient.
The particle volume fraction is calculated using
𝑛
𝜀𝑠 = ∑
𝑖=1
𝑉𝑝,𝑖
𝑉𝑐
(2)
where 𝑉𝑐 is the volume of the computational cell. The coupling between the discrete and
continuous phase is handled based upon a multigrid technique [35], as described by e.g.
4
Bruchmüller et al. [36]. The particles are tracked on a so-called particle mesh, which is a
Cartesian mesh with the size larger than the particle. All the coupling terms, including
the volume fraction and the drag forces, are determined on the length-scale of this
particle mesh. In case the local fluid cell is smaller than a particle, the coupling between
that fluid cell and a particle occupying that fluid cell will be length-scale weighted and
thus remain physical. The procedure has been described and tested by Mallouppas and
van Wachem [37], and has been further worked out in the recent work of Capecelatro
and Desjardins [38].
The interphase momentum transfer coefficient is based on the Ergun equation [39] in
the dense regime and on the Wen and Yu drag correlation in the dilute regime [40],
𝜇𝑔
𝜀𝑠 2
+ 1.75𝜀𝑠 𝑅𝑒𝑝 ) 2
(150
𝜀𝑔
𝑑𝑝
𝛽=
𝜇𝑔 𝜀𝑠 −2.65
3
𝑅𝑒𝑝 𝐶𝐷 2 𝜀𝑔
𝑑𝑝
{ 4
𝜀𝑠 > 0.2
𝜀𝑠 ≤ 0.2
(3)
where 𝜀𝑔 = 1 − 𝜀𝑠 is the gas volume fraction, 𝜇𝑔 is the dynamic viscosity of air, and 𝑑𝑝 is
the particle diameter. In equation (3), 𝐶𝐷 is the drag coefficient, which is written as
1 + 0.15𝑅𝑒𝑝 0.687
) 𝑅𝑒𝑝 < 1000
𝐶𝐷 = {
𝑅𝑒𝑝
0.44
𝑅𝑒𝑝 ≥ 1000
24 (
(4)
where 𝑅𝑒𝑝 is the particle Reynolds number
𝑅𝑒𝑝 = 𝜀𝑔 𝜌𝑔 |𝒖𝒈 − 𝒗𝒑,𝒊 |
𝑑𝑝
𝜇𝑔
(5)
In equation (5) 𝜌𝑔 is the air density.
The angular momentum of the particle is calculated by
𝐼𝑝,𝑖
𝑑𝝎𝒑,𝒊
= ∑ 𝑻𝑝,𝑖
𝑑𝑡
(6)
where 𝐼𝑝,𝑖 is the moment of inertia of the particle, 𝝎𝑝,𝑖 is the rotational velocity and 𝑻𝒑,𝒊
is the total torque acting on the particle.
2.2. Soft sphere model
In general, particle-particle and particle-wall collisions can be modeled using the hard
sphere or soft sphere model. In the hard sphere model, the interaction forces are
assumed to be impulsive and all other forces are negligible during collisions [41]. In the
soft sphere model, the deformation of particles in contact is modeled by relating the
5
local linear deformation in the normal and tangential directions to a force in these
directions, using Hertz-Mindlin theory [42]. The hard sphere model is easier to use but
applicable only to binary collisions. The soft sphere model directly implements the
physics of collisions but is computationally costly. In this study, since there are dense
regions where many particles can be in contact for a long time, the soft sphere model is
used.
In the soft sphere model, deformation of particles is replaced with overlap of two
particles and the energy loss during collisions is taken into account through a springdashpot system. This system is characterized using the spring stiffness, 𝑘, the damping
coefficient, 𝜂 , and the friction coefficient, 𝜇. The former two quantities are calculated
using Hertz contact theory [42, 43], as explained below.
The normal and tangential contact forces acting on the particle, 𝑭𝒄𝒏,𝒊𝒋 and 𝑭𝒄𝒕,𝒊𝒋, are
given by
3/2
𝑭𝒄𝒏,𝒊𝒋 = −𝑘𝑛 𝛿𝑛 𝒏𝒊𝒋 − 𝜂𝑛𝑗 (𝒗𝒊𝒋 ∙ 𝒏𝒊𝒋 )𝒏𝑖𝑗
𝑭𝒄𝒕,𝒊𝒋 = {
(7)
−𝑘𝑡 𝜹𝑡 − 𝜂𝑡𝑗 𝒗𝒄𝒕
𝑖𝑓 |𝑭𝒄𝒕,𝒊𝒋 | ≤ 𝜇|𝑭𝒄𝒏,𝒊𝒋 |
−𝜇|𝑭𝒄𝒏,𝒊𝒋 |𝒕𝑖𝑗
𝑖𝑓 |𝑭𝑐𝑡,𝑖𝑗 | > 𝜇|𝑭𝒄𝒏,𝒊𝒋 |
(8)
where 𝛿𝑛 and 𝜹𝒕 are the normal and tangential displacements of the particle, 𝒏𝒊𝒋 and 𝒕𝒊𝒋
are unit vectors normal and tangential to the contact plane, respectively, 𝒗𝒊𝒋 is the
relative velocity between the 𝑖 𝑡ℎ and 𝑗 𝑡ℎ particles, and 𝒗𝒄𝒕 is the slip velocity of the
contact point.
The normal and tangential stiffnesses, 𝑘𝑛 and 𝑘𝑡 , are expressed by
−1
4 1 − 𝜎𝑖2 1 − 𝜎𝑗2
𝑘𝑛 = (
+
)
3
𝐸𝑖
𝐸𝑗
1 − 𝜎𝑖2 1 − 𝜎𝑗2
𝑘𝑡 = 8 (
+
)
𝐻𝑖
𝐻𝑗
−1
𝑟𝑖 + 𝑟𝑗
(
)
𝑟𝑖 𝑟𝑗
𝑟𝑖 + 𝑟𝑗
(
)
𝑟𝑖 𝑟𝑗
−1⁄2
(9)
−1⁄2
1/2
𝛿𝑛
(10)
where 𝐸 is the Young’s modulus of the particle, 𝐻 is the shear modulus, 𝜎 is the
Poisson’s ratio and 𝑟 is the radius. The suffixes 𝑛 and 𝑡 denote the components in the
normal and tangential directions, while the suffixes 𝑖 and 𝑗 denote the 𝑖 𝑡ℎ particle and
the 𝑗 𝑡ℎ particle respectively.
According to Tsuji et al. [20], the damping coefficients 𝜂𝑛 and 𝜂𝑡 represent the viscoelastic dissipation of kinetic energy in the normal and tangential directions, respectively.
These are given as
6
1/4
𝜂𝑛 = 2𝛼 √𝑚𝑝 ∗ 𝑘𝑛 𝛿𝑛
(11)
𝜂𝑡 = 2𝛼 √𝑚𝑝 ∗ 𝑘𝑡
(12)
where 𝛼 denotes a constant related to the coefficient of restitution [44], and 𝑚𝑝 ∗
represents the effective particle mass and is calculated by
𝑚𝑝 ∗ =
𝑚𝑝,𝑖 𝑚𝑝,𝑗
.
𝑚𝑝,𝑖 + 𝑚𝑝,𝑗
(13)
More detailed description of the model can be found in literature [19, 20, 30, 41].
2.3. Equations of gas flow
A characteristic time scale of the flow may be calculated based on the atomizer flow rate
and the nozzle diameter. The Reynolds number thus calculated is approximately 104
and single-phase flow of air may therefore be expected to be turbulent. However, since
the Stokes number of the particles is quite large, turbulence is not expected to have a
direct influence on the particle trajectories. In addition, for dense gas-solid flows, such
as the one in this study, the particle stress is expected to be much greater than the stress
due to turbulence [45]. A turbulence model is therefore not used in the DEM-CFD model.
The continuity and momentum equations for gas flow are then written as follows
𝜕
(𝜀 𝜌 ) + 𝛻 ∙ (𝜀𝑔 𝜌𝑔 𝒖𝒈 ) = 0
𝜕𝑡 𝑔 𝑔
(14)
𝑛
𝜕
(𝜀 𝜌 𝒖 ) + 𝛻 ∙ (𝜀𝑔 𝜌𝑔 𝒖𝒈 𝒖𝒈 ) = −𝜀𝑔 𝛻𝑃 − 𝛻 ∙ (𝜀𝑔 𝝉𝒈 ) + 𝜀𝑔 𝜌𝑔 𝒈 − ∑ 𝛽(𝒖𝒈 − 𝒗𝒑,𝒊 )
𝜕𝑡 𝑔 𝑔 𝒈
𝑖=1
(15)
where 𝝉𝒈 is the viscous stress tensor for incompressible flow,
𝑇
𝝉 𝒈 = 𝜇𝑔 (𝛻𝒖𝒈 + (𝛻𝒖𝒈 ) )
(16)
3. Experimental
3.1. The Wurster bed configuration
The model of the fluid bed used in this study is based on the geometry of the Strea-1
fluid bed. The fluid bed is 380 mm high, with top and bottom diameters of 250 mm and
114 mm respectively. Detailed dimensions are given in the experimental paper [17].
The atomization air flow was supplied through a nozzle with a diameter of 5 mm located
3 mm above the bottom of the fluid bed. This nozzle was only a big circular inlet with
no opening for any liquid suspensions. Even in this case, the nozzle air velocity is high,
7
e.g. 50 m/s. This nozzle was used in the experiments in anticipation of future
computational work so as to avoid the numerical difficulties associated with simulating
sonic air flow while at the same time maintaining a high velocity jet.
The fluidization air flow passes through the bowl-shaped distributor, which consists of a
central base and an outer annular region. While the central base of the distributor is
fully open, the spray nozzle at the center implies that the region is also annular. The
outer annulus region of the distributor has a number of orifices with a diameter of 3 mm,
as illustrated in Figure 2. A wire mesh screen was put over the distributor to prevent
particles from falling down below the distributor.
Figure 2
A sketch of the bowl-shaped distributor: 1) nozzle, 2) solid, 3) fully-opened central
base, and 4) outer annulus
3.2. PEPT data
In this work, calculations using the DEM-CFD model are compared to recent PEPT
experimental data [17]; no additional experiments are performed. In the PEPT
measurement system, a radioisotope is incorporated into a tracer particle. As the tracer
particle moves around in the vessel the radioisotope decays in beta-decay and releases
back-to-back γ-rays. These γ-rays are detected via two large position sensitive detectors.
After a sufficient number of γ-rays are collected the location of the tracer particle can be
found through three dimensional triangulation. More details about the technique and
the algorithms used to determine the location have been reported by Parker et al. [4648].
3.3. Material
As a common material in the pharmaceutical industry, microcrystalline cellulose (MCC)
spheres were employed in the PEPT experiments, as well as a model particulate material
in the DEM-CFD simulations. The pellets that typically are used in practice have a
diameter that ranges from 200 µm to 1 mm. However, smaller or larger particles, such
as tablets, are also coated using the Wurster process. In order to limit the number of
particles, the particle size of 1749 and 2665 µm, which is still relevant and applicable to
product development, was selected. In the PEPT experiments, the particle size was
measured using a QICPIC Particle Size Analysis (Sympatec GmbH), and the sphericity
ranged from 0.85 to 0.95 (see [17] for a photograph of samples).
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4. Numerical
4.1. Meshing
To solve the equations of particle motion and gas flow, a fully coupled multi-phase flow
solver, MultiFlow (www.multiflow.org) is employed. The model of the fluid bed is the
same as in the PEPT experiments. Figure 3 shows the global mesh and close-ups of the
surface mesh at the bowl-shaped distributor and nozzle. Approximately 65000
hexahedral cells are required based on a grid independence check via simulations of
single phase gas flow. The computational mesh near the distributor and inside the
Wurster tube is locally refined in order to properly capture the flow characteristics in
this region.
Figure 3
(a) The surface mesh of the fluid bed and (b) the close-up of the bowl-shaped
distributor (from top view)
4.2. Boundary and initial conditions
In the recent PEPT experiments, the flow rates of the atomization and fluidization air
were measured separately using rotameters [17]. These measurements provide the
global flow rates, but they do not give any information about the flow distribution at the
distributor. In order to specify the flow distribution at the distributor, a single-phase
CFD model including the air supply chamber, the distributor, the wire mesh screen, and
the fluid bed was developed in Ansys Fluent. In this single-phase CFD model, the
distributor was modeled with all its orifices, but the wire mesh screen was included as a
region with a specified pressure loss (see e.g. [49]). The results obtained using this
single-phase CFD model (not shown) show that the air flow passing through the central
base of the distributor is in between 53% and 64% of the total fluidization air flow.
In addition to this single phase CFD model, the particle velocity in the lower part of the
bed is also used as an indication of the flow distribution at the distributor. Since the
resolution of the PEPT measured particle trajectories towards the bottom of the bed is
low, it is necessary to employ measurements higher up. The resolution of the PEPT
measurements is estimated at several positions along the length of the Wurster tube and
a location at the middle of the Wurster tube, 90 mm above the bottom, is selected in
order to compare experimental data with calculated results.
The boundary condition employed in the DEM-CFD simulation reflects a flow
distribution where 55% of the fluidization flow enters normal to the boundary in the
9
central region and 45% enters normal to the boundary in the outer annulus region.
Figure 4, which shows the average vertical particle velocity as a function of the radial
coordinate, illustrates that the particle velocity calculated in the DEM-CFD simulation
agrees with that measured in the PEPT experiment [17].
Figure 4
The average vertical particle velocity along the radial direction for case #1 (VMD
1749 µm, batch size 200 g, fluidization air flow rate 73.3 m 3/h and atomization air flow rate 3.50
m3/h).
As already discussed, the atomizer flow is imposed as a velocity inlet normal to the
boundary at the nozzle. The walls of the fluid bed and the Wurster tube are set to be noslip for the gas flow. The outlet of the domain is considered to be pressure outlet. At the
start-up of the simulations, 200 g (between approximately 15000 and 270000 particles
depending on the particle size) particles are put into the vessel at a certain height above
the distributor and are allowed to settle down without any gas flow. After 2 s, when
particles are at rest near the bottom of the equipment, the gas flow is turned on.
4.3. Cycle and residence time distributions
For simplicity we define the start of a particle coating cycle when a particle enters into
the spray zone from the horizontal transport region or the lower region in the Wurster
tube. The particle coating cycle then ends when the particle reappears in the spray zone
after having subsequently traveled through the Wurster tube, the fountain, downbed,
and horizontal transport regions. When one particle coating cycle ends, the next one
begins. The particle coating cycle time is thus defined to be the time it takes for a
particle to complete one cycle.
In the recent PEPT experiments [17], the bulk of the particulate material that was used
in each process experiment contained only one single tracer particle. This tracer particle
was then followed via PEPT monitoring for 1.5 hours and the cycle and residence time
distributions were calculated from different cycles for the same tracer particle. In the
present DEM-CFD simulations, on the other hand, the calculation of the cycle and
residence times is based on data from many particles within a short period of time. For
the pseudo-steady particle dynamics in this fluid bed, as long as one particle is followed
the information obtained (such as the particle velocity or the cycle time distribution) is
assumed to be representative of the motion of all particles in a short period.
10
This study does not include any liquid spray. However, it is nevertheless of interest to
understand the particle motion near the spray nozzle. A spray zone is therefore defined
as shown in Figure 5, which gives a schematic of the shape of the spray zone, i.e. a solid
cone. This model is mainly conceptual and similar to the one in the work by Fries et al.
[26]. The height of the spray zone, L, is assumed to be 45 mm, which corresponds to the
height where the cone approaches the tube wall. The spray half-angle, θ, is assumed to
be 30 degrees. In order to study the shielding effect of different size particles, an
entrance distance into the spray zone is defined as the distance between the spray
nozzle and the location where the particle enters the spray zone (see Figure 5).
Figure 5
A schematic of the spray zone
4.4. Simulation time
In order to estimate the required simulation time the cumulative cycle time
distributions are plotted for different simulation times, as shown in Figure 6. It can be
seen that the CTD is not sensitive to the simulation time provided that it is at least 25 s,
and this simulation time is therefore chosen for purposes of studying particle cycles and
the CTD. Similar plots were also made for the RTD in the spray zone and in the Wurster
tube (not shown). It was found that 10 s is sufficient in order to obtain a reasonable
compromise between the computational cost and the quality of the data in order to
calculate the RTD in the spray zone and in the Wurster tube.
Figure 6
The cumulative cycle time distributions for different simulation times (with the
first 2 s discarded), for case #1 (VMD 1749 µm, batch size 200 g, fluidization air flow rate 73.3 m3/h
and atomization air flow rate 3.50 m3/h).
4.5. Simulation parameters
The parameters used in the simulations are presented in Table 1 and the operating
conditions for each case are summarized in Table 2. For Run #1 the same conditions as
the base case in the experimental study are used, and the results are used for evaluating
the DEM-CFD model in detail. Runs #2 and 3 with larger batch sizes of 400 g and 600 g
are used to further evaluate the model as well as to verify the interpretations made in
the experiments. The effect of particle size is studied in Runs #4 and 5 by increasing or
decreasing the particle size by approximately 0.8 mm. Lastly, the effect of mixtures with
11
different components is studied in Runs #6-8 by replacing 25%, 50% or 75% (by mass)
of 1749 µm particles with 2665 µm particles. A typical simulation is run in parallel using
32 CPUs and takes 12 hours per second.
Table 1
The numerical parameters used in the simulations [50-52].
Table 2
The operating conditions for each DEM-CFD simulation.
5. Results and discussion
In this study the performance of the DEM-CFD model is evaluated by comparing the
calculated results with the results from previous PEPT experiments for the base case
and for different batch sizes. In addition, simulations for different particle sizes and
mixtures of different particle sizes are performed with emphasis on evaluating the effect
on the RTDs in the spray zone and in the Wurster tube.
5.1. Validation of the DEM-CFD model
5.1.1. The general particle movement for the base case
Figure 7 shows the particle velocity field determined in the DEM-CFD simulation and in
the PEPT experiment respectively. It is seen that the characteristic motion of the
particles in the Wurster fluid bed is predicted quite well using the DEM-CFD model. The
particles accelerate in the Wurster tube to reach a maximum velocity of approximately
3.0 m/s (this maximum value is difficult to observe in the figure due to an overlap of the
particle trajectories), and then fall down through the downbed region.
Figure 7
The particle velocity field at a vertical cross-section through the center of the bed
(a) simulated using DEM-CFD and (b) measured using PEPT (VMD 1749 µm, batch size 200 g,
fluidization air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).
By following particle trajectories, the cycle time and the residence times in different
regions can be obtained. In Figure 8, the CTD of particles in the DEM-CFD simulation is
compared with the CTD determined in the PEPT experiment. Since the actual simulation
time is 25 s (with the first two seconds discarded), only particle cycles shorter than 25 s
are used for this comparison, both in the simulation and in the experiment. Since only
12
cycles that are shorter than 25 s are used for the comparison, the experimental values of
the cycle time and the RSD in the cycle time may be slightly different from those
presented in the previous experimental study [17] in which all cycles were included.
Figure 8 shows good agreement in terms of both the shape of the distribution and the
actual values. In the DEM-CFD simulation, the CTD has a larger percentage of short cycle
times compared to the CTD in the PEPT experiments. This difference may be attributed
to a greater weight factor of short cycles in the DEM-CFD simulation since the DEM-CFD
model follows many particles for a short time whereas the PEPT experiment follows a
single tracer particle for a long time.
Figure 9 shows the mean residence times of particles in different regions and the mean
fractions of the cycle time spent in different regions. The DEM-CFD simulation predicts
that particles spend the longest time in the horizontal transport region, and that the
residence time is considerably shorter in the Wurster tube and in the fountain and
downbed regions. This result corresponds closely to the corresponding values measured
in the PEPT experiment, especially in terms of the mean fractions of the cycle time spent
in different regions. That is, particles spend 19% of cycle time in the Wurster tube, 5%, 4%
and 73% of cycle time in the fountain, downbed and horizontal transport regions in both
the DEM-CFD simulation and in the PEPT experiment.
Figure 8
The cycle time distribution (for cycles shorter than 25 s) calculated in the DEMCFD simulation and measured in the PEPT experiment (VMD 1749 µm, batch size 200 g, fluidization
air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).
Figure 9
(a) The mean residence times in different regions and (b) the mean fractions of the
cycle time spent in different regions for case #1 (VMD 1749 µm, batch size 200 g, fluidization air
flow rate 73.3 m3/h and atomization air flow rate 3.50 m 3/h).
5.1.2. Effect of batch size
In addition to the general particle movement for a batch size of 200 g, simulations of
different batch sizes of 400 g and 600 g are also performed. It is clearly shown in Figure
10, which shows the time-averaged solids fraction at a vertical cross-section through the
center of the bed for different batch sizes, that a higher fountain is obtained with an
increase in the batch size. As reported earlier [17], this increase in the fountain height is
due to a higher gas flow rate and, hence, a faster acceleration of particles in the Wurster
tube. In the PEPT experiments, this effect was attributed to an increased resistance in
the downbed region, which increased the air flow rate through the Wurster tube. Here it
13
is possible to verify this interpretation by noting that the dense region in the downbed
region increases when the batch size increases. As a result, the air flow rate passing
through the Wurster tube increases from 34.9 m3/h to 40.1 m3/h, and to 51.7 m3/h
when the batch size increases from 200 g to 400 g, and to 600 g respectively.
It is also of interest to examine the effect of the batch size on the cycle time. In addition,
the relative standard deviation (RSD) in the cycle time is calculated, since a variability in
the cycle time can affect the quality of the product. Figure 11 shows the effect of batch
size on the cycle time as well as on the RSD in the cycle time. There is good agreement
between the measured and calculated mean cycle time. The measured and calculated
values of the RSD do not agree so well, which could be due to the fact that spherical
particles are assumed and the VMD of particles is employed in the simulations rather
than the actual particle size distribution. But there is good agreement in the trend of a
decreased RSD when increasing the batch size, except for the very slight increase in the
RSD determined experimentally (from 63 to 66%) when the batch size increases from
200 to 400 g. This slight increase in the experimental RSD is different from the values of
the RSD calculated based on all cycles, i.e. 77 and 76% for 200 and 400 g respectively
[17]. Since only particle cycles shorter than 25 s are used for the comparison in Figure
11, the RSD in the cycle time is smaller than the RSD presented in the earlier study.
Apart from the simulated RSD values, good agreement between the DEM-CFD
simulations and the PEPT experiments is obtained for the cycle times, residence times
and the trend of RSD. In the next sections it is therefore of interest to focus on the
simulation results for different particle sizes and mixtures of different particle sizes.
Figure 10
The solids fraction at a vertical cross-section through the center of the bed for
different batch sizes: a) 200 g, b) 400 g and c) 600 g (VMD 1749 µm, fluidization air flow rate 73.3
m3/h and atomization air flow rate 3.50 m3/h).
Figure 11
The mean cycle time and RSD for different batch sizes (VMD 1749 µm, fluidization
air flow rate 73.3 m3/h and atomization air flow rate 3.50 m3/h).
5.2. Simulating with the DEM-CFD model
5.2.1. Effect of particle size
Figure 12 shows that there is a significant effect of the particle size on the residence
times in the spray zone and in the Wurster tube. When the particle size increases from
1000 µm to 2665 µm, there is an almost seven-fold increase in the residence times in the
14
spray zone, from 0.032 s to 0.214 s. For the same increase in the particle size, the
increase in the residence time in the Wurster tube increases by a factor of almost 4, from
0.36 s to 1.38 s. These results indicate that large particles reside longer in the spray zone
than small particles. If all particles of the same size in the spray zone receive the same
amount of coating per unit time, large particles will then obviously receive more coating
per unit area per pass than small particles. Fortunately, as large particles stay longer in
the Wurster tube, they will also have a greater chance of drying as they move upwards
through the Wurster tube.
Figure 13 shows the RTDs in the spray zone for different size particles. Figure 13 shows
that small particles have a narrow RTD in the spray zone while the RTD becomes much
wider for large particles. This difference can be attributed to different terminal
velocities for different size particles. For the same fluidization air flow rate, large
particles are more likely to recirculate in the Wurster tube [17] and return to the spray
zone than small particles. This effect can result in a wider distribution in the coating
thickness.
Figure 12
The simulated residence times in the spray zone and in the Wurster tube for
different size particles.
Figure 13
particles.
The simulated residence time distributions in the spray zone for different size
5.2.2. Effect of mixtures of different size particles
Figure 14 shows the mean residence times in the spray zone and in the Wurster tube for
small and large particles in mixtures with different fractions of small and large particles.
These 200 g mixtures of 1749 µm and 2665 µm particles contain 25%, 50% and 75%
2665 µm particles. It is seen that large particles stay longer both in the spray zone and in
the Wurster tube. A longer residence in the spray zone can lead to more coating being
deposited on the particle surface.
Moreover, as shown in Figure 15, the large particles enter the spray zone closer to the
spray nozzle than the small particles. This latter effect occurs because a greater gas
velocity is required to accelerate the large particles. The large particles therefore have to
move closer to the nozzle, where the gas velocity is higher, to be able to move upwards
through the Wurster tube. The smaller entrance distance into the spray zone for the
15
large particles can result in the large particles shielding the small particles from the
spray droplets. This effect [53], in addition to the effect of a longer residence time in the
spray zone, suggests that the large particles receive more coating solution per cycle than
the small particles. This was experimentally observed by Wesdyk et al. [54] for beads
with a size distribution in the no. 14-20 mesh range.
5.2.3. Effect on coating thickness
Based upon the simulation results above, the effect of the residence time in the spray
zone, the entrance distance into the spray zone, the cycle time and the particle diameter
on the coating thickness may be explored in terms of a simple model. In order to develop
such a model, it is noted that the total amount of coating per unit time deposited on the
surface of a particle, 𝑚𝑓𝑖𝑙𝑚 , can be expected to be proportional to the spray rate, 𝑚̇, the
time spent in the spray zone, 𝑡𝑠𝑝𝑟𝑎𝑦 , and the number of coating cycles, 𝑁𝑐𝑦𝑐𝑙𝑒 . In addition,
the probability that a spray droplet is deposited onto a particle can be expected to be
proportional to the cross-sectional area of the particle and to the droplet flux, which
decreases quadratically with the distance from the spray nozzle for a solid-cone spray
zone. This simple model may thus be written
𝑑𝑚𝑓𝑖𝑙𝑚
𝑡𝑠𝑝𝑟𝑎𝑦
𝜋𝑑𝑝 2 ⁄4
= 𝐾(𝑟𝑒𝑛𝑡𝑟𝑎𝑛𝑐𝑒 )𝑚̇ (
)(
)
𝑑𝑡
𝑡𝑐𝑦𝑐𝑙𝑒 𝑟𝑒𝑛𝑡𝑟𝑎𝑛𝑐𝑒 2
(17)
where 𝑡𝑐𝑦𝑐𝑙𝑒 ~1/𝑁𝑐𝑦𝑐𝑙𝑒 is the cycle time, which is available in Li et al. [17], and 𝐾
represents other factors that may affect the amount of coating solution that the particle
receives such as the shielding effect. Since the shielding effect is predominantly entrance
distance dependent, 𝐾 should be a function of the entrance distance, i.e. 𝐾~1/𝑟𝑒𝑛𝑡𝑟𝑎𝑛𝑐𝑒 .
The rate of increase in the coating thickness can then be written
𝑑𝑙𝑓𝑖𝑙𝑚
𝑑𝑚𝑓𝑖𝑙𝑚
1
=
𝑑𝑡
𝜌𝑓𝑖𝑙𝑚 𝜋𝑑𝑝 2 𝑑𝑡
(18)
where 𝜌𝑓𝑖𝑙𝑚 is the density of the coating film.
Using equations (17) and (18), the relative rate of increase of the coating thickness
between the large and small particles for different mixtures can be explored in a postprocessing step, as illustrated in Figure 16. Figure 16 shows that the large particles only
have a slightly larger increase in the coating thickness than the small particles when the
fraction of large particles in the mixture is 25%. In this mixture the mean cycle times for
the small particles and the large particles are 4.95 s and 7.94 s respectively [17], which
indicates that the small particles pass through the spray zone 1.64 times more
16
frequently than the large particles. On the other hand, the large particles stay 1.48 times
longer in the spray zone and move 1.06 times closer to the spray nozzle than the small
particles. As a result, the increase in the residence time in the spray zone of the large
particles is almost compensated for by the decrease in the number of passes through the
spray zone. The end result in this particular case is that the large particles grow only
slightly faster than the small particles. As the fraction of large particles in the mixtures
increases from 25%, however, the difference in the cycle time between small and large
particles decreases while the difference in the residence time in the spray zone
increases. For these latter mixtures, the large particles therefore have a greater rate of
increase in the coating thickness than the small particles.
Figure 14
The simulated residence times of small and large particles in (a) the spray zone
and in (b) the Wurster tube for different mixtures of small and large particles.
Figure 15
The simulated entrance distance into the spray zone of small and large particles
for different mixtures of small and large particles.
Figure 16
The simulated relative rate of increase of the coating thickness between the large
and small particles for different mixtures of small and large particles.
6. Conclusions
In this study, coupled DEM-CFD simulations have been performed to study particle
motion in a Wurster fluid bed. The particle trajectories were used to identify particle
cycles and to determine the CTDs and RTDs of particles in different regions.
The DEM-CFD model was validated by comparing the particle velocity field as well as
cycle and residence time distributions with results from recent PEPT experiments. The
general characteristic particle motion was successfully captured and the residence times
of particles in different regions were found to correspond closely to the experimental
results. A shorter cycle time with a larger batch size was also predicted by the DEM-CFD
simulations, in agreement with the PEPT monitored experiments.
The effect of particle size and mixtures of different size particles were studied in the
DEM-CFD simulations. The results show that large particles spend a longer time in both
the spray zone and the Wurster tube, suggesting that large particles get greater amount
of coating solution per cycle compared to small particles. This difference is however,
17
partly compensated for by the fact that large particles pass through the spray zone less
frequently than small particles due to their longer cycle times.
The DEM-CFD simulations also show that the large particles on average enter the spray
zone closer to the spray nozzle than the small particles. This indicates that the large
particles can shield the small particles from the spray droplets, and that the large
particles therefore receive a greater amount of coating solution per pass than what
would be anticipated based on their larger size, and the longer time spent in the spray
zone.
A simple conceptual model was developed to predict the effect of the residence time in
the spray zone, the cycle time, and the entrance distance on the relative rate of increase
of the film thickness between large and small particles. This model showed that as the
fraction of the large particles in the mixture increases, they have a greater rate of
increase in the coating thickness than the small particles. Due to its simplicity, however,
this model should be further developed in the future.
Acknowledgements
This work is undertaken within the EU seventh framework program, the PowTech Marie
Curie Initial Training Network (Project no. EU FP7-PEOPLE-2010-ITN-264722). The
experiments were financially supported by AstraZeneca R&D.
Dr. Andy Ingram at University of Birmingham is gratefully acknowledged for the
cooperation in the experimental work. The authors would also thank the high
performance computing (HPC) team at AstraZeneca R&D for their support throughout
the simulations.
Notation
18
𝐶𝐷
drag coefficient
𝑑𝑝
particle diameter, m
𝐸
Young’s modulus, Pa
𝑭𝒄
contact force, N
𝒈
gravity vector, m/s2
𝐻
shear modulus, Pa
𝑚𝑝
mass of the particle, kg
𝒏
normal unit vector
𝒕
tangential unit vector
𝑰𝒑
moment of inertia, kg∙m2
𝑃
pressure, N/m2
𝑅𝑒𝑝
particle Reynolds number
𝑡
time, s
𝒖
velocity vector of gas phase, m/s
𝒗𝒑
velocity vector of the particle, m/s
𝑉𝑝
volume of the particle, m3
𝝎𝒑
rotational velocity of the particle, rad/s
Greek symbols
𝜀𝑔
gas volume fraction
𝜀𝑠
particle volume fraction
𝛽
interphase momentum transfer coefficient, kg/(m3∙s)
𝜇𝑔
dynamic viscosity, Pa∙s
𝜇
friction coefficient of particles
𝜌
density, kg/m3
𝜂
damping coefficient
𝜎
Poisson ratio
19
𝝉
viscous stress tensor, N/m2
Subscripts
𝑔
the gas phase
𝑝
the particle
𝑖, 𝑗
the 𝑖 𝑡ℎ or 𝑗 𝑡ℎ particle
𝒏
the normal direction
𝒕
the tangential direction
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