Towards a complete population balance model for fluidized bed spray granulation:
Simultaneous drying and particle formation

M. Peglow, S. Heinrich, E. Tsotsas

Faculty of Process and Systems Engineering, Otto-von-Guericke-University Magdeburg

Abstract: This paper concerns the simultaneous processes of agglomeration and drying. In order to predict temperatures and moisture content in gas and particle phase, heat and mass transfer mechanism and particle size enlargement has been considered simultaneously. The presented model takes heat and mass transfer phenomena between particle phase, suspension gas and bypass gas into account. The disperse phase is modelled by a three-dimensional population balance (PBE), which can be reduced to a set of three one-dimensional PBE. The latter are coupled with heat and mass transfer balances of the gas phase. Furthermore some simulation and experimental results are presented.

INTRODUCTION

The process of particle size enlargement can change properties of granular materials significantly. By agglomeration fine sized primary particles are transformed into free-flowing and dustless consumer products. The fluidized bed technology offers a possibility to combine the process of agglomeration and drying in a single apparatus. The product to be dried is fluidized by passing hot air through it. A rapid drying rate is known to be the advantage of fluidized beds, since the mixing of solids and gas is very efficient. In the literature, many attempts have been made to describe the process of particle formation in a fluidized bed in terms of population balances. The population balance approach describes the temporal change of particle property distributions (PPD). As a result, one obtains the temporal change of the particle number distribution with respect to selected particle properties. The latter are named as the internal coordinates. Frequently, the particle size or volume have been considered as the only significant internal coordinate of the disperse phase. Thus, a one-dimensional population balance equation (PBE) for growth, agglomeration and breakage of particles has been applied to numerous processes in chemical engineering such as crystallization, granulation and agglomeration. see (Bramley et al., 1996; Ding et al., 2006). The concept of one-dimensional PBE faces several problems and limitations, see (Iveson, 2002). Therefore, the number of significant internal coordinates has to be increased. As soon as the number of internal coordinates is extended, the mathematical and numerical effort increases rapidly. In the framework of Adetayo et al. (1995), and Hounslow et al. (2001), a high shear granulation in rotating drums in terms of population balances is investigated. Hounslow et al. (2001) extended the internal coordinates by the particle tracer mass. The resulting two-dimensional PBE was reduced to a set of two one-dimensional PBE assuming that particles of the same size contain the same amount of tracer mass. Tan et al. (2004) applied this model to fluidized bed melt agglomeration.

For the more general case of liquid spray granulation, one-dimensional population balance models can be found, see e.g. Saleh et al. (2003), but studies on the simultaneous description of agglomeration and drying in a population balance model are missing. The impact of operating conditions on the PPD has been investigated by various authors, see (Adetayo et al., 1995; Watano et al., 1996; Schaafsma, 2000). Watano et al. (1996) observed that the moisture content in solids is one of the most important particle properties to control the agglomeration process. This leads to the conclusion that properties such as particle size and moisture content have to be considered simultaneously in a population balance model. Our study presents a novel model that is capable to eliminate the missing link between the processes of agglomeration and drying.

THEORY AND NUMERICAL METHODS

A two-dimensional particle property distribution is defined as f(t,v,c), where v and c are two distinct properties, usually the granule volume (size) and any extensive property of the
particles such as moisture of particles or enthalpy. In a first step, we want to follow the idea of Hounslow et al. (2001). Beside the granule volume v they considered the tracer mass c as the second internal coordinate, see (Hounslow et al., 2001). The total number of particles N in a domain D is given by

(1)

It should be noted that the granule volume v contains volume of tracer mass and volume of particles, that is c ≤ v. The two-dimensional population balance equation can be obtained by extending the classical one-dimensional PBE to two-dimensional space as in (Hounslow et al., 2001),

(2)

Hounslow et al. (2001) reduced the two-dimensional population balance model to a set of one-dimensional population balances using the marginal distribution approach. The reduced population balance for the particle number distribution n(t,v) can be deduced as

(3)

The temporal change of tracer distribution m(t,v) is given by

(4)

Thus, the above continuous system of equations may be applied for the computation of temporal change of particle number and tracer mass distribution. It is difficult to solve this system analytically, so numerical methods have to be applied for the solution. One way to solve such systems numerically is to discretize the size domain into small sections and to reduce the system into a system of ordinary differential equations.

Hounslow et al. (1988) developed a discretized method for population balance equation as given in equation (3). A discretization scheme of reduced PBE (4) is suggested by Hounslow et al. (2001). In both approaches the particle volume domain is divided into small sections and the density is assumed to be constant within each section. The final set of equations preserves particle numbers and mass. However, for certain application the discretization given in Hounslow et al. (2001) is inconsistent with intensive properties of solid phase. Therefore, Peglow et al. (2006) suggested a modified discretization of Hounslow et al. (2001). The modified method which preserves the mass and the number of the system as before and predicts the intensive properties such as temperature of solids or concentrations within a granule as well. The final set of discretized equations for a grid of type

(5)

is given by

(6)

for the evolution of number distribution and

(7)

for evolution of tracer distribution. The correction factors are given by

(8)

An extended formulation of equation (7) for an adjustable geometric grid of type

(9)

is presented in Peglow et al. (2006). Now in the next section we want to derive a population balance model for simultaneous drying and aggregation. For this purpose we are going to apply the reduced set of population balances as given in equations (3) and (4). Furthermore a selected simulation result will be presented.

MODELLING OF GAS AND SOLID PHASE

To describe the simultaneous agglomeration and drying process, we use a heterogeneous fluidized bed model which incorporates the active bypass. This model is based on the assumption, that a certain fraction of fluidization gas passes the solid phase as a bypass. Burgschweiger (2000) applied this model for drying of porous materials using adsorption isotherms. To model the heat and mass transfer processes, the following assumptions are made

The bypass fraction is free of solids and it is in plug flow.
All solids are in the suspension phase. The suspension is in plug flow. No back mixing occurs.
The particles are ideal mixed.
Vapor and heat transfer take place between suspension and bypass phase.
Vapor and heat transfer take place between surface of particles and gas in suspension phase. Water sprayed in is deposited on particles.
The wall may exchange heat with environment, particles, suspension gas and bypass gas.

In Figure 1 the balance scheme is shown. All heat, mass and enthalpy fluxes between solid and gas phase considered in the model are depicted in Figure 1.

Figure 1: Balance scheme of the fluid bed model

Modeling of solid phase

The agglomeration process for batch vessels is described by means of the one-dimensional PBE

(10)

The parameter influencing the shape of PPD is the agglomeration rate β defined by

(11)

Since the model describes heat and mass transfer processes, we need the corresponding kinetic expressions. According to Groenewold and Tsotsas (1997) the mass transfer between the solids and the suspension gas is determined by

(12)

where Yeq denotes the equilibrium moisture content. This property depends on the sorption equilibrium of the solids and can be expressed in terms of the sorption isotherm. The heat transfer between the granules and the gas phase is given by

(13)

The kinetic expressions in equations (12) and (13) contain two more properties of solid phase, the temperature of particles Jp and the moisture content X. It is clear that these properties have to be considered in the model as the combined description of agglomeration and drying is the objective of this study. Since the population balance for agglomeration is not capable to predict intensive properties of solid phase (temperature and moisture content) directly, we need to express those properties in terms of the corresponding extensive properties. In our case the temperature and moisture content will be represented by the enthalpy and the mass of liquid respectively. According to previous section, see equation (4), balances for the enthalpy of particles

(14)

and the mass of liquid

(15)

can be formulated. To incorporate the solid and gas phase in one model, additional terms have to be included in equations (14) and (15), which take the heat, mass and enthalpy flux between these two phases into account (see Figure 1). Thus the coupling of the solid and gas phase is established.

The Gas Phase

According to Figure 1, the following mass and heat balances for suspension and bypass gas phases can be derived. The moisture and enthalpy in suspension gas phase are given by

(16)

(17)

Analog to that, that balances for the bypass gas phase can be deduced

(18)

(19)

The parameter n is the ratio of gas flowing through the bypass to total gas flow rate. This parameter depends on Geldart classification of particles and bed height. A briefer discussion of this model is given in Peglow (2005).

SIMULATION RESULTS

In this section a simulation example of an agglomeration process is provided. Such a process is usually characterized by three stages. Firstly the primary particles are dried and heated. In a second stage the particles are wetted by spraying in a liquid binder. At this stage the formation of agglomerates occurs. Finally the wet agglomerates will be dried up to a moisture content defined by product specifications. In our simulation it will be assumed, that the particle size distribution will change only during spraying and remains constant in the first and last stage. The main process parameters are summarized in Table 1. The model has been implemented in the MATLAB suite. For the numerical integration we used the integration routine ode15s. The ode15s is an implicit procedure based on numerical differentiation equipped with an automatic step size control. It is suited for stiff systems. Figures 2, 3 and 4 reflect the transient behavior of properties of solid phase for all three stages. Additionally Figure 5 depicts the progression of mean and outlet moisture of gas phase. As mentioned above the first stage provides drying and heating of particles. During this process the outlet humidity of the gas phase decreases to the value of gas inlet moisture. At the end of this stage the moisture content of solids is equal to equilibrium moisture content determined by sorption isotherm of the granules. In the second stage, the agglomeration stage, a certain amount of liquid is sprayed onto the solids. Thus the moisture content of solids increases rapidly. The temperature of granules decreases due to evaporation. Figure 4 shows that small particles are drier than larger particles. This effect is caused by the size dependency of heat and mass transfer coefficients. Since a size independent kernel has been assumed for this agglomeration stage, a change of particle size distribution can be observed. Any type of agglomeration kernel can be chosen, but for simplicity size-independent kernel has been assumed. The actual value of β0 can be calculated by defining the degree of aggregation Iagg. Here we set this value to Iagg = 0.8. Finally, the particles are dried in the last stage. Since no liquid is sprayed onto the granules, the moisture content decreases and the particle temperature increases again. No change on particle size occurs, since the agglomeration rate is set to zero. Summarizing we can conclude, that the model is capable to predict the transient behavior of solid phase and gas phase properties as well. In the next section we want to turn to the experimental validation of this model.

Figure 2: Evolution of Particle Size Distribution

Figure 3: Progression of particle enthalpy temperature

Figure 4: Progression of amount of particle moisture content

Figure 5: Progression of outlet and mean gas moisture content

EXPERIMENTAL VALIDATION

The objective of the experiments was to investigate the simultaneous agglomeration and drying. For the experiments we used microcrystalline cellulose, also known as MCC. It is widely used in pharmaceutical industry as a carrier material for active agents. Pharmacoat 606 was used as a binder. Experiments have been conducted in a commercial fluidized bed (Type GPCF 1.1) of Glatt company. The main component of this plant is the conical fluidization chamber with a diameter of 138 mm at the bottom and 304 mm at the top. The height of the chamber is 565 mm. The process can be observed through two glass slits. A blower sucks the fluidization gas into an electro heater of 3.96 kW. The electro heater controls the inlet temperature of the fluidization gas. The actual value is measured by a thermo couple which is fixed below the air distribution plate. An electrical adjustable flap placed in front of the blower controls the air flow rate. Outlet air is cleaned by the two tube filters which are at the top of the apparatus. The filters are cleaned asynchronously in fixed time intervals. For sampling during the agglomeration process a small discharge pipe is provided. A glass valve is connected in a gas-tight junction with the pipe. By spring mechanism the removal is opened and the valve is filled with granules from the bed. The binder solution is sprayed onto the fluidized bed by the two-component nozzle (Type 970/0-S04) of Schlick company. The throughput and the spray pattern is controlled by the air pressure and an air flap. During the experiments the nozzle was used in a top spray configuration. A gradual adjustable flexible-tube pump controlled the flow rate of binder to the nozzle. A balance was used to measure the actual throughput.

Main process parameters are summarized in Table 2. At the beginning of each experiment, the apparatus was shut down to fill the fluidization chamber with hold-up material. The bed material was dried and heated up for 4 minutes. After the pre-drying process the binder was sprayed onto the bed material. The spraying time was chosen in such a way that a fixed fraction of 10 % binder of hold-up was achieved. The samples were collected during spraying at constant time intervals of 2 minutes. In addition to particle moisture content, measured with Halogen Moisture Content Analyzer, the particle size distribution of these samples was analyzed. The CamSizer system of company Retsch Technologies, based on digital picture processing, was used for particle size and particle shape characterization. Finally the material was dried for 4 minutes after the end of spaying.

Figure 6: Time progression of gas outlet temperature

Figure 7: Time progression of gas moisture at the inlet and outlet

Figure 8: Time progression of mean particle moisture content

The experimental result and comparison with simulation are exemplified in Figure 6 to Figure 9. The progress of gas outlet temperature in Figure 6 shows three characteristic stages. First of all the outlet temperature increases up to t = 240 s. This increase characterizes the pre-drying period (1st stage). During this period the hold-up is been dried and heated-up. This drying process can also be identified by time progression of the outlet gas humidity content in Figure 8. Shortly after starting the experiment, the outlet gas humidity increases rapidly. After this, the humidity decreases up to the value of gas inlet humidity. This point indicates the end of drying. The particle moisture content remains constant. The spraying of binder starts at t = 240 s. Here a rapid decrease of gas outlet temperature can be observed. Simultaneously the gas outlet humidity increases and remains constant after a short time. At this point the total liquid hold-up of the bed material remains nearly constant. The amount of sprayed and dried liquid is the same. The constant value of particle moisture content, shown in Figure 8, confirms this observation. The gas outlet temperature decreases during the entire spraying time. This progression is caused by the slow decrease of wall temperature, which is in heat transfer with particles, gas and environment. The spraying ends at t = 1560 s. The last stage indicates the drying of agglomerates. Again, a decrease of gas outlet humidity and an increase of gas outlet temperature can be observed. To predict the evolution of particle size distribution a size dependent kernel

(20)

has been applied. The fitting parameters a, b and b0 have been determined from the measurement results using an inverse technique. A brief introduction to this approach is given in Peglow et al. (2006). In our case we obtained a = 0.71053, b = 0.06211 and β0 = 5.174.10-4. A comparison of experiment and simulation PSD is presented in Figure 9.

Figure 9: Evolution of particle size distribution (RE – relative error)

CONCLUSION

This paper presents a new modeling approach for simultaneous agglomeration and drying in fluidized bed. Using a heterogeneous fluidized bed model with active bypass, all relevant heat and mass balances have been derived. The solid phase has been described in terms of population balances. Here three one-dimensional PBE, for particle size, for enthalpy and for liquid mass distribution have been applied. Since an analytical solution of the model is not possible, a numerical simulation has been provided. Therefore a new discrete formulation of PBE which is capable to predict extensive and intensive properties of the solid phase has been utilized. For the validation of presented model, agglomeration and drying experiments with MCC have been carried out. Preliminary investigations have been conducted to characterize the drying and adsorption behavior of MCC at different temperatures. The experimental results of this investigations have been used for a validation of the model. For batch-wise agglomeration of MCC it has been demonstrated, that the evolution of PSD and mean moisture content of solid phase are reproduced by the model. The agglomeration kinetic has been determined directly from measured evolution of PSD. Properties of gas phase such as gas outlet humidity gas outlet temperature can be predicted without any fitting.

NOTATION

a	empirical parameter	-
A	surface area	m2
b	empirical parameter	-
c	particle property	m3
d	diameter	m
I	total number of intervals	-
K	correction factor	-
f	2-D population density function	1/m6
H	enthalpy	J
h	enthalpy density function	J/m3
M	mass	kg
m	mass density function	kg/m3
m	tracer mass density function	kg/m3
n	number density function	1/m3
N	number of particles	-
Q	heat	J
q	parameter for grid adaptation	-
t	time	s
u	volume	m3
v	volume	m3
X	moisture content in solid phase	kgw,l/kgs
Y	moisture content in gas phase	kgw,l/kgg
Greek Symbols
α	heat transfer coefficient	W/(m2s)
β	agglomeration rate	1/s
β	mass transfer coefficient	m/s
γ	integration constant	-
ε	integration constant	-
	normalized drying curve	-
ν	bypass fraction	-
ξ	bed height	m
ρ	density	kg/m3
ϑ	temperature	°C
Subscripts
b	bypass phase
e	environment
eq	equilibrium
g	gas phase
i	interval, Index
j	interval, Index
l	liquid
n	nozzle
p	particle
s	suspension phase
w	water

REFERENCES

Adetayo, A. A., J. D. Litster, et al. (1995). Population balance modelling of drum granulation of materials with wide size distribution, Powder Technol., 82, 37-50.
Bramley, A. S., M. J. Hounslow, et al. (1996). Aggregation during precipitation from solution: A method for extracting rates from experimental data, J. Colloid Interface Sci., 183, 155-165.
Burgschweiger, J. (2000). Modellierung des statischen und dynamischen Verhaltens von kontinuierlich betriebenen Wirbelschichttrocknern, Dissertation, Universität Magdeburg.
Ding, A., C. A. Biggs, et al. (2006). Population balance model selection for activated sludge flocculation modelling, Chem. Eng. Sci., 61, 63-74.
Groenewold, H. and E. Tsotsas (1997). A new model for fluid bed drying, Drying Technol., 15, 1687-1698.
Hounslow, M. J., J. M. K. Pearson, et al. (2001). Tracer studies of high shear granulation: II. Population balance modeling, AIChE J., 47, 1984-1999.
Hounslow, M. J., R. L. Ryall, et al. (1988). A discretized population balance for nucleation, growth and aggregation, AIChE J., 38, 1821-1832.
Iveson, S. M. (2002). Limitations of one-dimensional population balance model of wet granulation processes, Powder Technol., 124, 219-229.
Peglow, M. (2005). Beitrag zur Modellbildung eigenschaftsverteilter Feststoffsysteme am Beispiel der Wirbelschicht-Sprühagglomeration, Dissertation, Universität Magdeburg.
Peglow, M., J. Kumar, et al. (2006). A new technique to determine rate constants for growth and agglomeration with size and time dependent nuclei formation, Chem. Eng. Sci., 61, 282-292.
Peglow, M., J. Kumar, et al. (2006). Improved discretized tracer mass distribution of Hounslow et al., AIChE J., 52, 1326-1332.
Saleh, M., M. Steinmetz, et al. (2003). Experimental study and modeling of fluidized bed coating and agglomeration, Powder Technol., 130, 116-123.
Schaafsma, S. (2000). Down-scaling of a fluidised bed agglomeration process, Dissertation, University of Groningen.
Tan, H. S., A. D. Salman, et al. (2004). Kinetics of fluidised bed melt granulation, Part III: Tracer studies, Chem. Eng. Sci., 144, 65-83.
Watano, S., T. Fukushima, et al. (1996). Heat transfer and rate of granule growth in fluidized bed granulation, Chem. Pharm. Bull., 44, 572-576.

		Prof. Dr. Stefan Heinrich did study process technology at the University of Magdeburg from 1991-96, where he did also obtain his Ph.D. in 2000, a junior professorship in 2002 and where he still works as a scientific group leader. In 2004 he was rewarded with the VDI ring of honour. Contact: stefan.heinrich@vst.uni.magdeburg.de