A quantitative assessment of the influence of primary particle size polydispersity on granule inhomogeneity

Chemical Engineering Science 71 (2012) 104–110

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A quantitative assessment of the influence of primary particle size polydispersity on granule inhomogeneity Rohit Ramachandran a,n, Mansoor A. Ansari b,1, Anwesha Chaudhury a, Avi Kapadia a, Anuj V. Prakash a, Frantisek Stepanek b,c a

Rutgers, The State University, Piscataway, NJ, USA Imperial College London, UK c Institute of Chemical Technology, Prague, Czech Republic b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 August 2011 Received in revised form 28 November 2011 Accepted 29 November 2011 Available online 8 December 2011

This study is concerned with quantifying the effect of primary particle size polydispersity on granule inhomogeneity for fluid-bed granulation. Specifically, it looks at how the variability in the PSD affects key granule properties at the granulation end-point. For the first time, the distribution of primary particles among different size fractions of the final granules was investigated computationally, together with experimental validation. Granulation was carried out from primary particles with the same mean size but different widths of the size distribution and the granules were subsequently ‘‘disassembled’’ both physically and computationally to analyze their composition. The particle size distribution did not have any effect on the size distribution of the granules, but strongly influenced their composition and porosity. Interestingly, the incidence of coarse primary particles ( 4 180 mm) was highest within the smallest granule size fractions, and conversely, large granules contained predominantly fine ( o 125 mm) primary particles. These findings have significant implications for the granulation of heterogeneous powder mixtures (e.g. API and excipient). & 2011 Elsevier Ltd. All rights reserved.

Keywords: Granulation Multi-dimensional population balance model Particle size distribution Porosity Granule inhomogeneity Fluid-bed

1. Introduction and objectives Granulation is a particle formation process of converting fine powdery solids into larger free-flowing agglomerates. It finds application in a wide range of industries (e.g. pharmaceuticals, fertilizers and minerals) (Ennis and Litster, 1997). Granulated products often have notable improvements compared to their ungranulated form and some of these include increased or decreased bulk density, improved flow properties and uniformity in the distribution of multiple solid components. Granulation processes have been ubiquitous in the industry for many years with significant research undertaken to gain further insight into the underlying phenomena occurring during the process. In granulation, it is now generally accepted that three rate processes are sufficient to elucidate its behavior. These are namely wetting and nucleation; consolidation and growth; and breakage and attrition (Iveson et al., 2001). The formation of granules is first initiated by the nucleation of fine powder (primary particles). This involves the distribution of liquid binder among the powder,

n

Corresponding author. E-mail address: [email protected] (R. Ramachandran). 1 Current address: Controlled Therapeutics, Glasgow, UK.

0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2011.11.045

followed by the penetration of the droplet into the powder wherein the binder droplet will capture the particles surrounding it thereby converting it into a nucleus (Hapgood et al., 2002). The nuclei particles will continue to grow via aggregation and consolidation, as they collide with other (nuclei) particles and the walls of the granulator. Granule breakage may also result due to collisions. Intragranular inhomogeneity within a product batch is one of the major issues in granulation processes (Schaefer et al., 2004). Inhomogeneous (or undesired) distribution of binder and active ingredients, and/or primary particles in different size fractions of granules may influence the uniformity of the final dosage form and hence the application performance (Iveson et al., 2001; Scott et al., 2000; Knight, 2001; Stepanek, 2004). The distribution of all the above mentioned components among different size classes of granules is profoundly affected by both processing and formulation conditions. For instance, the impeller speed in high shear mixers, droplet size of liquid binder in fluid bed processes, binder viscosity and its solidification/drying rate and the corresponding process temperature all play an important role in uniform (or otherwise) distribution of binder in the final granulated particles (Ansari and Stepanek, 2006a,b). Similarly the method of addition of active ingredient and its relative size are among the many factors that control its radial arrangement in the granule matrix

R. Ramachandran et al. / Chemical Engineering Science 71 (2012) 104–110

which further go on to affect the properties of the final product (Ansari and Stepanek, 2006a,b; Stepanek et al., 2009). The phenomenon of preferential growth of smaller primary particles and their segregation towards the larger granules has been observed by several workers (Schaefer et al., 2004; Scott et al., 2000; Rahmanian et al., 2006). Their studies were mostly empirical and involved experiments with particle size distribution of different median sizes. Despite this, their work provided useful insights into intragranule heterogeneity and suggested possible methods of controlling it (Faure et al., 1999, 2001). Their work also reveals little about the net effect of variability in particle size distribution with constant median diameter. In other work, experimental studies were undertaken to understand the relationship between granule inhomogeneity phenomena and granule growth processes (van den Dries and Vromans, 2002, 2003; van den Dries et al., 2003; Nieuwmever et al., 2008). Several studies also extensively detailed the effect of primary particle size on granule growth and endpoint determination (Mackaplow et al., 2000; Badawy and Hussain, 2004; Badawy et al., 2004). However primary particle size distribution which is an important source of variability for such distributed systems was not considered. Inhomogeneity in the granules with respect to PSD can lead to uniformity problems in subsequent downstream processing. In this work, we present a systematic approach that combines both experimental analysis and computational methods to qualitatively and quantitatively assess the impact of primary particle size distribution width on granule inhomogeneity. Granule inhomogeneity is defined to be inconsistencies in the key granule properties at the granulation end-point. Quantifying and understanding the impact of this variability in PSD would be crucial to the overall control and operation of the granulation process.

2. Population balance model A three-dimensional population balance model that was utilized in a previous study for modeling the granulation process which considers aggregation and consolidation is employed in this work (Immanuel and Doyle, 2005; Poon et al., 2008, 2009). The resulting three-dimensional population balance equation is then given by     @F @ dg @ ds ðs,l,g,tÞ þ Fðs,l,g,tÞ þ Fðs,l,g,tÞ @t @g dt @s dt   @ dl Fðs,l,g,tÞ ¼ Rnuc ðs,l,g,tÞ þ Ragg ðs,l,g,tÞ þ Rbreak ðs,l,g,tÞ þ @l dt ð1Þ where Fðs,l,g,tÞ represents the population density function such that Fðs,l,g,tÞds dl dg is the number density of granules (although in this work it is converted to mass basis so as to be aligned with experimental data) with solid volume between s and s þ ds, liquid volume between l and l þdl and gas volume between g and g þdg. The partial derivative term with respect to s accounts for the layering of fines onto the granule surfaces; the partial derivative term with respect to l accounts for the drying of the binder and the re-wetting of granules; the partial derivative with respect to g accounts for consolidation which, due to compaction of the granules, results in an increase of pore saturation and decrease in porosity. In this study, layering and drying are neglected and the simplified equation is given by   @F @ dg ðs,l,g,tÞ þ Fðs,l,g,tÞ ¼ Rnuc ðs,l,g,tÞ @t @g dt ð2Þ þ Ragg ðs,l,g,tÞ þ Rbreak ðs,l,g,tÞ The formation and depletion terms associated with the aggregation phenomenon (Ragg ) are defined in Eqs. (3)–(5) (Ramkrishna,

105

2000; Immanuel and Doyle, 2005). In these equations, snuc is the 0 0 solid volume of nuclei (assumed constant), and bðs0 ,ss0 ,l ,ll ,g 0 , 0 gg Þ is the size-dependent aggregation kernel that signifies the rate constant for aggregation of two granules of internal coordinates 0 0 (s0 ,l ,g 0 ) and (ss0 ,ll ,gg 0 ). b is essentially a measure of how successful collisions between two particles resulting in a larger granule are: Ragg ðs,l,g,tÞ ¼ Rformation Rdepletion agg agg

ð3Þ

where 1 2

Rformation ¼ agg

Z

ssnuc

Z

snuc

Z

lmax 0

g max

bðs0 ,ss0 ,l0 ,ll0 ,g 0 ,gg 0 Þ

0

0

0

0

0

Fðs0 ,l ,g 0 ,tÞFðss0 ,ll ,gg 0 ,tÞ ds dl dg ¼ Fðs,l,g,tÞ Rdepletion agg 0

Z

smax

Z

snuc

lmax

Z

0 0

0

Fðs0 ,l ,g 0 ,tÞ ds dl dg

g max

0

ð4Þ

bðs0 ,s,l0 ,l,g 0 ,gÞ

0 0

ð5Þ

2.1. Identification of kernels A primary challenge in the development of population balance models is the identification of appropriate kernels that describe the individual mechanisms. While the development of a multi-dimensional population balance model is motivated by the physics of the problem, it is a tougher task to obtain three-dimensional kernels that account for the dependence of the rates on the particle traits (i.e., size, binder content and porosity). In previous work, we have developed and validated mechanistic (i.e., based on fundamental physics and chemistry) kernels for nucleation, aggregation and even breakage (Poon et al., 2009; Ramachandran et al., 2009). However, in this work, empirical and semi-empirical kernels are considered since the focus is on the qualitative and quantitative validation of the effect of particle size distribution on granule inhomogeneity and not on the validity of the kernel development. The nucleation model/kernel (Wauters, 2000; Wauters et al., 2002) is represented mathematically as shown in Eq. (6) Rnuc ¼ B0 dðVV 0 Þ

ð6Þ

where B0 represents the nucleation rate constant, d the DiracDelta function, V the size of the particles which is defined to be V ¼ s þ l þ g and V0 the size of the nuclei which is defined to be V 0 ¼ s0 þl0 þ g 0 , where the subscript 0 indicates the critical lower limit, above which nucleation occurs. The consolidation model is represented by an empirical exponential decay relation and is shown in Eq. (8) (Verkoeijen et al., 2002). The porosity of granules is defined by Eq. (7) and substituting Eq. (7) into Eq. (8) gives a formal expression explicitly in terms of the three independent internal coordinates (see Eq. (9)), which can then be used in Eq. (2). lþg s þ l þg

ð7Þ

de ¼ cðeemin Þ dt

ð8Þ

  dg cðs þ l þ gÞð1emin Þ e s ¼ l min þ g dt s 1emin

ð9Þ

e¼

Here emin is the minimum porosity of the granules (set at emin ¼ 0:2 as per the work of Immanuel and Doyle, 2005) and c is the compaction rate constant. Compaction rate is defined to be the rate of change of volume of air that is escaping from the particle/granule as it compacts/consolidates.

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R. Ramachandran et al. / Chemical Engineering Science 71 (2012) 104–110 0

0

The aggregation kernel (bðs0 ,ss0 ,l ,ll ,g 0 ,gg 0 Þ) used in this study is based on the equi-partition of kinetic energy (EKE model) first described by Hounslow (1998), which assumes that particles collide as a consequence of their random component of velocity and that the random components result in equal distribution of the particles kinetic energy and is described in Eq. (10)

bðs0 ,ss0 ,l0 ,ll0 ,g 0 ,gg 0 Þ ¼ b0 ðDðs0 ,l0 ,g 0 Þ

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 þ þ Dðss ,ll ,gg ÞÞ 0 0 D3 ðs0 ,l ,g 0 Þ D3 ðss0 ,ll ,gg 0 Þ 0

0

0

2

ð10Þ 0

where D is the particle diameter in size classes s0 ,l ,g 0 and 0 ss0 ,ll ,gg 0 and b0 is the aggregation rate constant. Dðs,l,gÞ can be obtained from the relation Dðs,l,gÞ ¼ ½ð6ðs þ l þ gÞÞ=p1=3 .

Table 1 Mass fraction (%) for individual size classes of D-mannitol that was used as primary particles. Size ðlmÞ

Mannitol 125/180 (M3)

Mannitol 106/212 (M4)

Mannitol 75/250 (M5)

o 75 75–106 106–125 125–180 180–212 212–250 4250

0.83 2.70 16.63 63.24 14.17 2.32 0.10

4.60 10.92 21.24 49.70 12.13 1.02 0.37

16.01 15.95 13.64 33.46 14.62 5.04 1.26

3.1. Granulation protocol 2.2. Numerical methods In this study, the particle population is first discretized into subpopulations and the population balance is formulated for each of these semi-lumped sub-populations. This is obtained by the integration of the population balance equation (see Eq. (2)) over the domain of the sub-populations and re-casting the population into finite volumes. In this finite volume scheme, Eq. (2) may be re-written in a discrete form as shown in Eq. (11).   dF 0i,j,k F 0i,j,k dg  F0    i,j,k þ 1 dg  þ ¼ Rnuc ðsi ,lj ,g k Þ þ Ragg ðsi ,lj ,g k Þ  dt Dg k dt gk Dg k þ 1 dt g k þ 1 ð11Þ F 0i,j,k

R si þ 1 R lj þ 1 R gk þ 1

¼ si Fðs,l,gÞds dl dg, si is the value of the Here gk lj solid volume at the upper end of the ith bin along the solid volume axis, lj is the value of the liquid volume at the upper end of the jth bin along the liquid volume axis, gk is the value of the gas volume at the upper end of the kth bin along the gas volume axis. Dg k is the size of the kth gas bin with respect to the gas volume axis. The particle population is assumed to be uniform within each of the finite volumes. Thus, by this technique, the integro partial-differential equation as represented by the population balance equation, is reduced to a system of ordinary differential equations in terms of the rates of nucleation (Rnuc ðsi ,lj ,g k Þ), aggregation (Ragg ðsi ,lj ,g k Þ). Off-line semi-analytical solutions are proposed for Ragg ðsi ,lj ,g k Þ and Rbreak ðsi ,lj ,g k Þ (Immanuel and Doyle, 2003, 2005). This results in casting the complex triple integrals in simpler addition and multiplication terms, major portions of which are computed once a priori to the start of the simulation. Rnuc being much less computationally intensive, is updated at every timestep. The ordinary differential equations (ODEs) are then integrated via a first order explicit Euler method. Stability conditions (e.g. CFL condition) were checked similar to previous work in Ramachandran and Barton (2010).

3. Materials and methods Granules were prepared by fluid-bed granulation of D-mannitol ‘‘Pearlittol 200SD’’ (Roquette, France) using 15% aqueous solution of HPC or hydroxy propyl cellulose (Fisher Scientific) as binder. Both mannitol and HPC are common examples of pharmaceutical excipient and aqueous binder respectively. Table 1 shows different size ranges of primary particles used in this study. These distributions are customized into relatively narrow (1252180 mm), medium (1062212 mm) and wide (752250 mm) size ranges, further referred to as M3, M4 and M5 respectively. The mean volume diameter of all the primary particle was kept at 155 7 10 mm.

Granulation was performed in a desktop fluidized-bed granulator of the 4M8 range (Pro-Cept, Belgium). A mass of 200 g of mannitol was fluidized by providing the air flow rate at 0.6 m3/ min at 25 1C. The binder, aqueous hydroxy propyl cellulose (HPC), was sprayed through a top-spray dual fluid nozzle. Regulated pressurized air was used in the nozzle to atomize the viscous liquid stream into fine droplets. The binder addition rate was maintained at 5 ml/min and as the binder was introduced, the fluidizing air flow rate was gradually increased from 0.6 to 1.2 m3/min to maintain the bed height. The dosing was stopped after the addition of 70 ml of aqueous HPC (molecular weight of 100,000 and viscosity of 3.25 Pa s) and the temperature of the bed was then slowly raised at the rate of 2–3 1C/min. The granulation end point was taken when the bed temperature reached 60 1C. For the given equipment and raw materials, this set of conditions ensures minimum wastage and preparation of granules with reasonable strength and size to withstand the subsequent sieving procedure. 3.2. Particle size analysis The particle size measurements were performed in duplicate by automated image analysis of approximately 5000 particles from each well-mixed sample using Ankersmid DSA-10 particle size and shape analyzer. In order to analyze particle size distributions in different fractions of granules; the granules were first gently sieved (sieve type BS-410) into 500–710, 710–1000, 1000– 1400 and 4 1400 mm fractions. Each fraction was then gently crushed between a stainless steel roller and a hard, smooth wooden surface. To encourage only granule breakdown and minimize primary particle breakage, the steel bar (1.3 kg) was rolled over a mono-layer of granules for a specified time and the crushed mass was sieved on a 250 mm mesh. The process was repeated with the over size content until all passed through the sieve. More details can be found in Ansari (2008). 3.3. Porosity analysis Granule porosity evaluation was based on the measurements of envelope and absolute densities, re and ra respectively, of the granules. The porosity (pore volume fraction) was determined from the following equation:

E ¼ 1

re ra

ð12Þ

The envelope density of the granules was measured by using a quasi-fluid composed of small and rigid spheres that have a high degree of flowability; known as Dryflo (Micromeritics, USA). The measured amounts of sample and Dryflo were mixed and filled into a 10 ml graduated cylinder and after specified number of taps

R. Ramachandran et al. / Chemical Engineering Science 71 (2012) 104–110

the volume of the mixture was noted. The procedure was repeated without sample and the difference between the two volumes was used in envelope density calculation. The absolute density of the granules was determined from the following equation:

dM9i ¼ A,B,CðconsolidationÞ ðs,l,gÞ ¼ Gconsolidation nFðs,l,gÞnmFracðs,l,gÞ ð15Þ

dM9i ¼ A,B,CðaggÞ ðs,l,gÞ ¼

rs rb ra ¼ ss rb þ sb rs

Z

ð13Þ

snuc smax snuc

0

where rs and rb are the absolute densities of mannitol and HPC binder and ss and sb are the mass fractions (average values as set by the formulation) of mannitol and HPC in the granule respectively.

107

Z

lmax

0

Z

g max

0

0

0:5nbðs0 ,l ,g 0 ,ss0 ,ll ,gg 0 Þ

0

0

0

Fðs0 ,l ,g 0 Þ  mFracðs0 ,l ,g 0 Þ  Fðss0 ,ll ,gg 0 Þ Z snuc smax Z lmax Z 0 mFracðss0 ,ll ,gg 0 Þ ds dl dg snuc

0

g max 0

bðs,l,g,s0 ,l0 ,g 0 Þ  Fðs0 ,l0 ,g 0 Þ  mFracðs0 ,l0 ,g 0 Þ  Fðs,l,gÞ mFracðs,l,gÞ ds dl dg

3.4. Computational sub-model

mFraci 9i ¼ A,B,C ðs,l,gÞ ¼

M9i ¼ A,B,C ðs,l,gÞ

ð17Þ

Si ¼ A,B,C Mi ðs,l,gÞ

Here, M represents the mass (calculated from the number density) of the granules, mFrac represents the normalized mass fraction of the granules and G is the consolidation rate. The subscripts A, B and C denote the initial bins in which primary particles originated from. The initial conditions for the mass fractions are mFracA ð1; 1,1Þ ¼ 1, mFracB ð2; 1,1Þ ¼ 1 and mFracC ð3; 1,1Þ ¼ 1. All other mFracs are set to zero. 60

M3−exp M4−exp M5−exp

50

Mass Fraction (%)

Conventional PBMs are able to track number (or mass/volume) densities within each finite volume (which represents a certain size range). At the granulation end-point (or at intermediate times), the model can track evolutions and distributions of key granule properties such as size, binder content and porosity of which, size and porosity are simulated in this study. At t ¼0, the initial conditions are such that all primary particles (in terms of mass densities) are placed in different proportions in finite volumes (1,1,1), (2,1,1) and (3,1,1) to simulate the differing variability of the PSDs (see Fig. 1). It can be seen there is perfect overlap between the experimental and simulated PSDs indicating that the PBM is calibrated with the experimental observations and can be used for simulation. As granulation occurs, it is known that any granule is inevitably comprised of primary particles originating from the three finite volumes henceforth known as bins A, B and C. To compare the simulations with experimental observations it is imperative that the proportion of particles from bins A, B and C are tracked throughout the simulation till endpoint, as current PBMs do not incorporate this. Therefore, an algebraic model based on mass fractions of particles in bins A, B and C was developed and incorporated within the overall PBM. The overall model is able to report on a mass fraction basis, of particles present from bins A, B and C for any finite volume at any point of time. The algebraic model was developed in MATLAB along with the PBM (see Eqs. (14)–(17)).

ð16Þ

40

30

20

10

 dMi  ðs,l,gÞ ¼ dM9i ¼ A,B,CðconsolidationÞ ðs,l,gÞ þ dM9i ¼ A,B,CðaggÞ ðs,l,gÞ dt i ¼ A,B,C

0

0

200

400

600

800

1000

1200

1400

1600

1800

Size Range (µm)

ð14Þ 60

M3−sim M4−sim M5−sim

70 M3−exp

50

M4−exp

60

M5−exp M4−sim

Mass Fraction (%)

Cumulative Fraction (%)

M3−sim

50

M5−sim

40

30

20

40

30

20

10

10 0

0

0

50

100

150

200

250

300

350

Size Range (µm) Fig. 1. Initial primary particle size distribution (experimental and simulation).

0

200

400

600

800

1000

1200

1400

1600

Size Range (µm) Fig. 2. Size distribution of granules produced from different starting particle size (legend shows the type of initial primary solids). (a) Experimental (exp). (b) Simulation (sim).

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According to the sieve cuts made in the experimental analysis, the code was structured to report data within the same intervals for which size distributions, porosity and the mass fractions can be obtained. All simulations were performed in MATLAB, using a (8,8,8) finite volume grid on a 16 GB RAM, 2.94 GHz desktop. Subsequent sections present both the experimental and simulation results obtained from the integrated PBM and algebraic model. The model was also calibrated (using psd experimental data of M3, M4 and M5—see Fig. 2a) by systematic variations of the kernel constants to ensure a good visual match between experimental and simulated data. From model calibrations, the 2 aggregation constant (b0 ) reported was 9e3 mol m6 s1 , the nucleation constant (B0) reported was 2e1 s1 and the consolidation constant (c) reported was 5e2 s1 . It should be noted that in study, breakage of primary particles or granules are not assumed and hence not tracked, although the PBM and algebraic model can be extended to account for particle/granule breakage.

4. Experimental and simulation results 4.1. Primary particle size polydispersity

100021400 mm and 4 1400 mm size ranges. The presence of fine, medium and coarse particles in each sieve cut were characterized and their mass fraction versus size range was plotted in Figs. 3–5. Fig. 3a represents the batch prepared with M3 particles. It shows that the amount of fine particles was slightly higher in the larger (4 1400 mm) granules while the quantity of each primary particle size class was comparable in all other granule fractions. Similar trends can be observed in Figs. 4 and 5 which are illustrating the granules produced with M4 and M5 particles respectively. That is the proportion of smaller particles in the granules was increased gradually with the product size class. The presence of medium and coarse did not significantly vary in any size fractions except 4 1400 mm in Fig. 5 that shows the least amount of coarse particles. It may be argued that these size profiles are biased towards fines because of the method employed to crush the granules. Although precautions had been taken to avoid grinding any primary particles, in absolute terms it may be unavoidable. However even in the presence of some error, the trends explained in Figs. 3–5 provide good qualitative analysis and the basis to carry out a computational study to confirm or otherwise. The corresponding simulations (see Figs. 3b–5b) report trends similar to those observed experimentally. This confirms to a more

This study (Fig. 1) incorporated realistic variability in the primary PSD. In industry, it is typical to have a uni-modal PSD with constant mean diameter but due to batch-to-batch or supplier-to-supplier variability, the width of the size distribution (variance of the distribution) can fluctuate. These different PSDs (M3, M4 and M5) were used as the initial distributions both for the experiments and simulations.

<125µm 125−180µm >180µm

45

Mass Fraction (%)

Fig. 2a shows the experimental granule size distributions (GSDs) of three batches of granules produced by M3, M4 and M5. It can be seen in the figure, that the amount of ungranulated fines was insignificant and therefore indicated that despite varying the initial PSD, the chosen identical processing conditions were suitable for adequate granulation to occur from which detailed data characterization could be performed. It may also be noted that the distributions of all granule batches are more or less similar except in the mid size cut of 60021000 mm, where proportion of the granules gradually declined as the width of the initial PSD increased. These profiles provide indication of the effect of variability in the initial PSD on end-point granule size distribution. Moreover, the simulations of the GSD (see Fig. 2b) demonstrated good agreement with experimental observations indicating that the simulation has the potential to be used as a surrogate process for further analysis to be discussed in the next sections. It is also interesting to note that M5 which comprised of the highest amount of fines as well as the coarse particles, resulted in granules with a distribution slightly skewed towards the upper size range. This implies that wider distribution of primary particles promotes the formation of larger granular product; however it also appears these granule sieve cuts were not significantly responsive to moderate variation in the width of feed distribution as both M3 and M4 produced comparable proportion of higher end granule fractions.

50

40

35

30

25

20 600

800

1000

1200

1400

1600

1800

Size Range (µm) 50

45

40

Mass Fraction (%)

4.2. Granule size distribution

55

<125µm 125−180µm >180µm

35

30

25

20

4.3. Distribution of primary particles within different granule fractions In order to simplify the distribution profiles, the primary particles were classified into o 125 mm, 1252180 mm and 4 180 mm as fine, medium and coarse particles respectively. The granules were gently crushed after sieving into 5002710 mm, 71021000 mm,

15 600

800

1000

1200

1400

1600

1800

Size Range (µm) Fig. 3. Distribution of fine ( o 125 mm), medium (1252180 mm) and coarse (4 180 mm) particles within different granule sieve cuts. The batch was produced with M3 (see Table 1) particles. (a) Experimental. (b) Simulation.

70

60

60

50

50

<125µm 125−180µm >180µm

40

30

Mass Fraction (%)

Mass Fraction (%)

R. Ramachandran et al. / Chemical Engineering Science 71 (2012) 104–110

20

10 600

109

<125µm 125−180µm >180µm

40

30

20

10

800

1000

1200

1400

1600

0 600

1800

800

1000

Size Range (µm)

1200

1400

1600

1800

Size Range (µm)

70

60 55

60

<125µm 125−180µm >180µm

50

40

30

<125µm 125−180µm >180µm

45

Mass Fraction (%)

Mass Fraction (%)

50

40 35 30 25 20

20

15 10 600

800

1000

1200

1400

1600

1800

Size Range (µm) Fig. 4. Distribution of fine (o 125 mm), medium (1252180 mm) and coarse ( 4180 mm) particles within different granule sieve cuts. The batch was produced with M4 (see Table 1) particles. (a) Experimental. (b) Simulation.

quantitative extent, that increasing the width of the PSD results in a larger proportion of fines in the largest size range. 4.4. Effect on granule porosity The variation in primary particle distribution also seems to have an influence on the intragranular porosity as depicted by the experimental profiles in Fig. 6a. Considering margins for experimental error, the plots show a declining trend of the porosity with the increasing granule size. Granules produced with narrow size distribution of primary particles show comparatively less significant drop in the porosity; however the porosity change becomes considerable as the size distribution width of the primary solids increased. Since the growing nuclei composed of larger particles are more likely to break under the process dynamics of the fluid bed, this may result in the preferential growth of smaller particles and thus the higher content of fines in the larger granules. The presence of smaller particles in the larger granule fractions could result in the denser, less porous product. This is confirmed by the simulation profiles as well (see Fig. 6b). Therefore primary particle size distribution could be considered as one of the influential parameters to control heterogeneity in the intra-granule

10 600

800

1000

1200

1400

1600

1800

Size Range (µm) Fig. 5. Distribution of fine ( o 125 mm), medium (1252180 mm) and coarse (4 180 mm) particles within different granule sieve cuts. The batch was produced with M5 (see Table 1) particles. (a) Experimental. (b) Simulation.

microstructure. For all experimental data (granule size and porosity) reported, three repeated measurements were performed and error bars indicated that the measurements were reproducible within reasonable accuracy.

5. Conclusions In this study, the effect of primary particle size distribution (with constant median diameter) on granule inhomogeneity (namely the effect on GSD and granule porosity was studied. Both an experimental and computational effort was undertaken. Experiments were performed on a laboratory scale fluid bed granulator and simulations were performed via a 3-D population balance model. Experimental results revealed that the variability in PSD had a quantifiable effect both on GSD and granule porosity. This was further predicted by the simulations after a sub-model was combined with the PBM to track the evolutions/distributions of each finite volume (indirectly tracking each primary particle size fraction) from which a mass fraction of each of these size fractions (three fractions are used in this study) within the granule can be obtained. The primary particle size distribution did not have any effect on the size distribution of

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R. Ramachandran et al. / Chemical Engineering Science 71 (2012) 104–110

0.45

M3−exp M4−exp M5−exp

0.44 0.43

Porosity (−)

0.42 0.41 0.4 0.39 0.38 0.37 0.36 600

800

1000

1200

1400

1600

1800

Size Range (µm) 0.46

M3−sim M4−sim M5−sim

0.44

Porosity (−)

0.42

0.4

0.38

0.36

0.34 600

800

1000

1200

1400

1600

1800

Size Range (µm) Fig. 6. Distribution of porosity within different granule sieve cuts. The batches were produced with M3, M4 and M5 particles as indicated in the legend. (a) Experimental (exp). (b) Simulation (sim).

the granules, but strongly influenced their composition and porosity. In previous work (Ramachandran et al., 2008), the strong effect of several important formulation properties on granule mechanisms (and in turn granule properties) was studied with the study alluding to the effect of PSD as a process disturbance on these properties. The current study lends itself to the overall control framework proposed in that study (Ramachandran et al., 2008), by quantifying the effect of PSD and the proposed model-based approach can be used for overall control and optimization of the granulation process.

Acknowledgements R. Ramachandran would like to acknowledge the National Science Foundation Engineering Research Center on Structured Organic Particulate Systems Grant NSF-ECC 0540855 for funding. M. Ansari and F. Stepanek would like to acknowledge the EPSRC Grant EP/C511301/1, UK for funding. References Ansari, M.A., 2008. The Effect of Formulation and Processing Variables on Granule Microstructure. Ph.D. Thesis. Imperial College London.

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