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Fully-3D DEM simulation of fluidised bed spray granulation using anexploratory surface energy-based spray zone concept

D.K. Kafui , C. ThorntonSchool of Engineering, The University of Birmingham, Edgbaston B15 2TT, UK

Available online 3 December 2007

Abstract

An exploratory spray-zone modelling concept which uses energy of adhesion at the contact of particles has been incorporated in a fuDiscrete Element Method (DEM)-based granular dynamics fluidised bed model and applied to fluidised bed spray granulation. In this proof-of-concept spray model, simple functional relationships are used to notionally model surface energy pick-up by particles traversing the spraand an increase in energy of adhesion at drying interparticle bonds. The formation and breakage of interparticle bonds is thus govertheoretical contact mechanics. Early-stage granulation simulation results provide qualitatively realistic granule size evolution trends. 2007 Elsevier B.V. All rights reserved.

Keywords: Granulation; Spray zone; Discrete element method; Fluidised bed

1. Introduction

Granulation is an important size enlargement process inwhich fine powdery materials are agglomerated into larger granules by the addition of a liquid binder. Different processingequipment such as fluidised beds, high shear mixers, rotatingdrums and pans are utilised for granulation in such diverseindustries as pharmaceuticals, mineral processing, food tech-nology, detergents, iron and steel, agricultural products,specialty chemicals and biotechnology[1,2]. Although the physical mechanisms underlying granulation in the various process vessels may be similar, the process variables can havesignificantly different effects on the granulation process.

In fluidised bed spray granulation, liquid binder isintroduced into the bed from the top, bottom or side as a finespray of liquid droplets using an atomizer. Particles traversingthe spray zone are coated with liquid binder droplets andsubsequent collisions with other particles may lead to granulenucleation and growth. The granulation process is an extremelycomplex one involving several mechanisms. Iveson et al.[3]have proposed a description of granulation based on three setsof rate processes: (i) wetting and nucleation (ii) consolidation

and growth (iii) attrition and breakage. Controlled wetting an

nucleation is seen as one of the key requirements for obtainin product granules with the required attributes.

Population balance is frequently employed in modellin particulate processes such as comminution, crystallization an polymerization. The complexity of fluidised bed granulatio probably accounts for the paucity of models which incorporadetailed physical mechanisms for the constituent rate processeand resort to population balance modelling in which variouempirical or semi-empirical models of coalescence andbreakageare used to calculate the extent and rate of granulation whilensuring a balance in the particle population. Ramkrishna[4] provides an extensive review of the application of populatio

balance modelling to particulate systems. An increasing numbeof particulate system properties are being employed in multdimensional population balance models in order to describ particulate processes to the level of detail required fooptimisation and control. Vemury et al.[5] used particle volumeand particle charge to describe coagulation in aerosols anIveson [6] used granule size, porosity, binder content andcomposition for a granulation model. Recently, Tan et al.[7]employed granule size and tracer mass for a population balancmodelling of fluidised bed melt granulation. Verkoeijen et al.[8]have arguedthat three intrinsic propertiesof particle systems: thvolume of each solid component, the volume of liquid and th

Available online at www.sciencedirect.com

Powder Technology 184 (2008) 177 188www.elsevier.com/locate/powtec

Corresponding author. E-mail address: [email protected](D.K. Kafui).

0032-5910/$ - see front matter 2007 Elsevier B.V. All rights reserved.doi:10.1016/j.powtec.2007.11.038
mailto:[email protected]://dx.doi.org/10.1016/j.powtec.2007.11.038http://dx.doi.org/10.1016/j.powtec.2007.11.038mailto:[email protected]


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volume of air are the fundamental properties required in a three- property population balance model. As multi-dimensional population balance variants replace the basic one-dimensionalformulation in the attempt to more accurately model the in-herently complex, often multiphase, particulate processes, therelationship between the coefficients in these solutions and theunderlying physics and chemistry driving the processes becomemore tenuous[8]. A fundamental weakness of population bal-ance modelling is that there is no procedure for choosing theform of the kernels and the empirically fitted parameters arelimited to the range of conditions in which they were fitted[6].Most population balance models assume well mixed systemsfor batch processes and spatial uniformity with regard to flow incontinuous processes, conditions which rarely apply. In sum-marising the limitations of applying population balance mod-elling to wet granulation processes, Iveson[6] suggests that, perhaps this is an application area for which the methodology isnot suited and that discrete element method modelling may be

more appropriate for such heterogeneous systems.Heinrich et al.[9] developed a detailed physically basedmathematical heat and mass transfer formulation in whichspraying, wetting, drop deposition and drying were modelled ina study of the temperature and concentration fields in a liquid-sprayed fluidised bed. The process domain is treated as acontinuum multicomponent mixture and macroscopic balanceequations for heat, mass andmomentumused with state equationsto model evaporation and drying. Full wetting with constant filmthickness is assumed in calculatinga wetting efficiency. A conicalspray nozzle jet region is assumed and concepts of impingement efficiency, adhesionprobability, droppenetration depth and linear liquiddrop path and constant liquiddrop velocityareemployed inmodelling the liquid deposition. The simulations suggested that liquid droplet deposition occurred mainly in the spray nozzleregion and that equilibrium between spraying, deposition,evaporation, heat transfer and dispersion resulted in a constant average temperature in the bed. The spray nozzle region wasfound to be characterised by high wetting efficiency.

Goldschmidt et al.[10]presented the first known applicationof the discrete element method to spray granulation. Liquiddroplets, which are introduced into the bed in a spray zoneaccording to a predetermined rate and velocity, are modelled asdiscrete entities in addition to the discrete spherical particles andencounters between these two species leads to coalescence and

the formation of a wetted particle. Hard-sphere collision lawsgovern the interaction between the solid spheres resulting inrebound or agglomeration, with a larger sphere replacing thecolliding spheres in the latter case. The main weaknesses of thismodel are the inability to handle multiple contacts and bond breakage. Nevertheless, this model produced reasonablegranule size evolution trends and qualitatively illustrated theeffects of process conditions such as fluidisation velocity, sprayrate and spray pattern.

A discrete particle-based codewith realisticcontact mechanicsand particle particle bonding formulations is capable of adequately simulating the consolidation and growth as well asthe attrition and breakage processes. A discrete model for thewetting and nucleation process is therefore the remaining main

challenge in applying the discrete element method to wet granulation. A spray zone in which liquid droplets are introducedinto the bed at predetermined rates and size distributions is anappropriate way to model the region where most of the primarywetting which takes place in the bed occurs. The possibility of modelling the interactions between solid particles and liquiddroplets using the discrete particle model when combined withdroplet drying models can provide a microscopic tool for simulating droplet deposition and nucleation. A significant limitation with this approach is the computational power requiredto model anything approaching a laboratory scale system.

In this paper, a proof-of-concept exploration of the sprayzone modelling ideas discussed above is carried out, not withdiscrete liquid droplets, but using surface energy based on thetheory of Johnson et al.[11] as the binding mechanism. The useof surface energy simplifies the problem by not introducing anadditional phase into the system and may be notionallycompared to binderless granulation [12]. This approach is

taken because the primary objective of this work is to test out the methodology within a fully-3D DEM based LagrangianEulerian fluidised bed model. In this context the spraygranulation simulation of a Geldart group A particle bed is performed. Conceptual notions of wetting (surface of particle becomingactive as a result of picking up surface energy in thespray zone, drying (increase in surface energy or adhesionenergy value with time),wet surface energy (surface energythat can still form bonds and has not reached some terminaldried out value) have been used here but are not to claim or imply any equivalence to liquid binders.

2. Modelling technique

Details of the discrete particle-continuum fluid model have been given by Kafui et al.[13]and only a very brief summary is presented here. The spray model and the basis of theassumptions made are detailed here as is the procedure adoptedfor the granulation simulation.

2.1. Fluidised bed model

For the particulate phase, the translational and rotationalmotions of each particlei of massmi and moment of inertiaI iare calculated using the equations

mid vidt

f ci f fpi mig 1

I id x idt

Ti 2

where f ci is the out-of-balance force of the particle due to the solid particle particle contact force, f fp i is the fluid particle interactionforce,mig is the weight of the particle, Ti is the torque due to thetangential components of the contact forces, and vi and i are thelinear and angular velocities respectively of the particle.

The frictional solid particle particle interactions are mod-elled using theoretical contact laws for elastic particles,

178 D.K. Kafui, C. Thornton / Powder Technology 184 (2008) 177 188


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elastoplastic particles, elastic particles with adhesion andelastoplastic particles with adhesion[14 17] from which theout-of-balance contact forcef ci and torque Ti are obtained.

In coupling the discrete particle phase and the continuumfluid phase, the fluid particle interaction forcef fp i acting on a particle is the key term which is calculated using

f fpi v pij p v pij :s f e f d i 3

Herep is the fluid pressure,v pi is the volume of particlei, f isthe viscous stress tensor which is obtained from a generalconstitutive equation given by Bird et al.[18] for a Newtonianfluid, is the local void fraction andf di, the drag force, iscomputedfrom theempirical relationship given by Di Felice[19].

The fluid phase is modelled as a continuum for which thecontinuity and momentum equations respectively are

eqf t

j : eqf u 0 4

eqf u t

j : eqf uu j : p j :s f F fp eqf g 5

In Eqs. (4) and (5), u and f are the fluid velocity and densityrespectively, andF fp, the fluid particle interaction force per unit volume, is computed by summing up the fluid particleinteraction force acting on all the particlesnc in a computationalfluid cell and dividing by the volume of the fluid cell, V c:

F fp Pnci1 f fpiDV c

6

An explicit finite difference scheme is used to incrementallycalculate the motion of the particles while a semi-implicit finitedifference scheme based on a staggered grid is used for discretising the fluid hydrodynamic equations. The details of the numerical schemes have been given in[13,20].

2.2. Spray zone model

The spray is one of the primary mechanisms by which binder is introduced into a wet granulation processing environment andis thus a key factor in wetting and nucleation. Iveson et al.[3]define the nucleation zone as the region where the binder and

the powder particles first come into contact and form the initialnuclei. This is essentially a region around the spray nozzle,referred to here as the spray zone, where there is a high probability of binder-to-particle encounter. Iveson et al.[3]haveargued that the two processes that are important in thenucleation zone are nuclei formation and binder dispersion,the former being a function of wetting thermodynamics andkinetics and the latter controlled by the process variables.

Wetting thermodynamics has been described in terms of thecontact angle between the solid and binder and the spreadingcoefficients of the phases over each other. In the extreme case of very low contact angle between solid and binder or a positive binder-to-solid spreading coefficient [21], full wetting willoccur resulting in a film of binder covering the powder particle.

This is also equivalent to a full coverage arising from thdistribution mechanism proposed by Schfer and Mathiese[22] where fine droplets of binder cover and coalesce on th powder particle surface to form a film.

On the basis of the above and in the context of this study, full and uniform coverage of our notional surface energ binder is a reasonable first assumption to make for the particles which pick up surface energy in the bed.

The following assumptions and notions are adopted informulating a conceptual representation of a surface energspray zone:

a. Thesprayzone is representedas a conical regionwith thespraysource or nozzle at the apex. (Fig. 1). A notional concept of anultra-fine mist of adhesive is assumed to be constantlyinjected into and limited to this region by the nozzle.

b. Particles entering the spray zone are assumed to be uniformwetted as they pick up surface energy at a rate which

depends on the time spent in the zone and the distance of th particle from the source.c. Inside the spray zone, surface energycoating on exposed

surfaces remainswet but once particles exit the spray zone,the surface energy increases in value as thecoating starts todry . A dry out period is associated with any value oexposed surface energy beyond which the surface becomeinactive outside the spray zone.

d. A particle particle bond startsdrying on formation with aconsequent increase in surface energy to an asymptotic uppelimit and such a bond is not penetrated bywet surfaceenergy in the spray zone.

2.2.1. Surface energy pick-up in the spray zoneBased on the preceding assumptions, simple exponentia

functions have been employed to formulate the spray model. A particle located in the spray zone at a distances p from the spray

Fig. 1. Notional representation of spray zone as a conical region.



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source (Fig. 1) accumulates wet surface energy w (

wetting

)according to

g w g wmaxe s 1 et s 7

Dg w g wmaxe s et s 1 D s et s Dt s 8

where wmax is the limiting surface energy of the spray,s (=s p / sm) is the normalised distance of the particle from the spraysource andt s is the time spent in the spray zone. This simpleformulation approximately reflects the expectation that particleswill pick up less surface energy farther away from the sourcedue to blockage by other particles in the zone and/or a lower concentration of adhesive in the regions farthest from thesource and is considered adequate for the objectives of thisstudy. In any future formulation based on discrete liquid binder droplets, the motion of the droplets through voidages between particles/granules in the zone will be better captured by thediscrete element formulation for the particles and liquiddroplets. Fig. 2 illustrates the accumulation of surface energyfor (i) a particle at different fixed distances from the spraysource; (ii) a particle which enters the spray zone near to andmoves away from the source; (iii) a particle which enters thezone farthest from and moves towards the source.

2.2.2. Drying of surface energy outside the spray zoneExposed wet surface energydries up rapidly outside thespray zone and the model associates with this an increase in theactive wet surface energy w and an active periodt ds duringwhich the surface can form a bond with another particle. Both w and t ds depend on wo , the wet surface energy of the particle when it last left the spray zone and are modelled usingthe expressions

g w g wo 1 e 1t so=t ds 9

t ds g wo

g wmax t d max 10

The surface is considered to havedried and lost all itsactivity whent so , the time since the particle last left a sprayzone, exceedst ds and w is set to zero. Using Eqs. (9) and (10),the surface active w values obtained for wmax = 0.5 Jm

2 andt d max =10 s is shown inFig. 3 for various values of wo .

2.2.3. Drying of particle particle bondsTwo adhering surfaces are said to possess energy of

adhesion per unit area equal in total to the work done inseparating them[23]. The nature of the interacting solids (ionic,metallic or van der Waal's) significantly influences the valuesof the surface energy or adhesion but in general, although themagnitudes of the adhesive traction are large (~0.5 GPa at separation distance of 2 for rubber with =0.04 Jm 2 ), their range of action is very small. The JKR theory[11] extends theHertz theory to include adhesive contact of perfectly elasticsolids. The degree of adhesion is highly influenced by thesurface roughness and also the degree of ductility of the

asperities, factors which are not accounted for in the JKR theory.The strength of the adhesion between elastic bodies depends

on the surface energies of the interacting surfaces. According tothe JKR theory, for two adhering elastic spheres with surfaceenergies 1and 2 , interfacial energy 12 and radiir 1 and r 2, theforce required for separation is 3 r /2 where r =r 1r 2/(r 1 +r 2)and the energy of adhesion = 1 + 2 12 .

In the notional drying concept adopted, increasing energy of adhesion d (=2 d) at a drying particle particle bond isevaluated using

gd

gw

1

d fac

1

1

et b 11

In Eq. (11), an average wet surface energy w of the twosurfaces (=( w1 + w2 )/2) when the bond was first formed isused, t b is the age of the bond andd fac ( 1), the dry-out factor,is used to model a limiting drying-induced increase in adhesive

Fig. 2. Accumulation of surface energy for fixed and moving particles in sprayzone for wmax =0.5 Jm

2.

Fig. 3. Notional drying of wet surface energy outside spray zone for wmax =0.5Jm 2 and t d max =10 s.



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energy at the bond. The drying process modelled by Eq. (11) isrestricted to a bond dry-out periodt db given by

t db g w

g wmaxt d max 12

wheret d max is the maximum dry-out time associated with wmax .If the age of the bond exceedst db , the bond strength or energy of adhesion d is set tod fac w. The value of d fac is chosen to reflect the final dried-bond value attainable by d . The increase in theenergy of adhesion during drying for bonds formed for variousvalues of wet surface energy is shown inFig. 4 for a dry-out factor d fac =2.0.

2.3. Simulation procedures

A Geldart group A powder bed consisting of five particlesizes 45, 47.5, 50, 52.5 and 55m was used in the

simulations. The particle properties used in the study are:Young's modulus E = 700 MPa; density =2500 kg m 3 ;coefficient of friction =0.30; Poisson's ratio =0.33. Thesevalues are based on glass beads except for the elastic moduluswhich is reduced by two orders of magnitude from the actualvalue in order to increase the time step used in the simulations.A yield stress of ~1%E ( y =7 MPa) is employed. A total of 50,000 particles with a mean particle diameter of d p = 50 mand size distribution shown inFig. 5 were used in the powder bed.

Initial bed preparation was carried out by randomlygenerating the particles in a space of 2 mm2 mm base areaand 5 mm height followed by pluvial deposition. This procedureyielded a bed, shown inFig. 6(a), with an initial height 1.46 mm(~29d p) and a void fraction =0.408.

Fluidising gas (atmospheric air at 313 K) at a uniform flow of 57.1 mm/s (~20umf ), introduced into the bed from the base, wasthen used to fluidise the bed prior to the introduction of thesprays. For the bed employed in this study, the minimumfluidisation velocity is estimated at ~2.9 mm/s using the cor-

relation of Baeyens and Geldart [28]and the fluidising gas flowused is of the order of 12.4umb according to Abrahamsen andGeldart [29]. Although much higher gas velocities in the high bubbling to turbulent regimes would normally be used and thgas flow rate increased with granule growth to maintain goofluidisation ([10], [30]), in our set-up with no re-circulation for particles leaving the bed, the judgement was made to stay the lower end of the bubbling regime for this study. Periodivertical boundaries were employed for both the fluid and paticle systems. Bottom and top horizontal wall boundaries werused for the particle system while prescribed normal gas influat the base and a prescribed atmospheric outflow pressure at thtop were employed for the fluid system.

After fluidising the bed for 24 ms, four identical spray zonewere located symmetrically in the bed with the base of eacconical zone a height of 5d p above the top of the initialdeposited bed. The particle configuration and the spray locations at this stage are shown inFig. 6(b) and (c) respectively.Each spray zone is defined by specifying the coordinates of thsource, the height hc and anglec of the spray cone, the maxi-mum wet surface energy wmax , the dry-out factor d fac and themaximum dry-out timet d max . The values employed for these parameters in the current simulation are:hc = 20d p, c =28.07o , wmax =1.0 Jm

2 , d fac =2.0, t d max =10 s. The spray zone di-

mensions and locations were selected such that the circulasection of each spray at its fullest extent covered half the linedimension of the quarter of the bed cross-section. Considerations of the estimated total simulation time achievable (~0.5 led to the choice of values for wmax, d fac and t d max after anexamination of the surface active w values obtained inFig. 2.

3. Granulation simulation

3.1. Granulation and bonds

Granulation was simulated with the four spray zonedescribed in the preceding section for 525 ms. InFig. 7, thetrends in the number of granules with three or more primarFig. 4. Evolution of adhesive energy during bond drying for various initial wet surface energy values.

Fig. 5. Particle size distributions by mass fraction and number fraction.



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particlesn g 3+ , the numbers of bonds and active sprayed particlesduring the simulation are shown. On introduction of the sprayzones, the number of bonds increases rapidly to ~7000 in thefirst 100 ms, then increases more slowly in the next 250 ms to~12,000 followed by a period of a fairly constant averagenumber of bonds. The fluctuations which are a feature of thetrend are indicative of bond formation and breakage. Thenumber of active sprayed particles exhibits a similar trend but shows a slight drop in the latter stages of the simulation which isdue more to the limited definition of active sprayed particleswhere bonded particles without free active surface energy arenot counted. Nevertheless, the fluctuations are illustrative of particles picking up surface energy and then drying with or

without the formation of bonds. Granulation, as measured bythe number of granules with three or more primary particlesn g 3+ ,shows a rapid increase to ~75 granules immediately after theintroduction of the sprays followed by a slow fluctuatingdecrease to ~45 granules and then a gradual increase to ~450granules when it then fluctuates for about 10 ms. A further slowincrease in the numberofgranules toa peak of~750, leading toadecrease to ~550 and an even slower fluctuating increase to~650 in the last stage of the period simulated completes thetrend. Overall, the number of granules increases with time at adecreasing rate within the time scale investigated. Theconsistency in the trends shown by the number of bonds andnumber of granules is expected since bonds give rise to granules.

Fig. 6. Initial deposited bed (a) fluidised bed prior to introduction of spray (b) location of spray zones (c).

Fig. 7. Evolution of the numbers of granulesn g 3+

, bonds and active sprayed particles during granulation. Fig.8. Evolution of thenumber of granulescomparedto the maximumand meanadhesive bond energies.



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Fig. 8compares the evolution of the number of granules withthe maximum ( max ) and mean ( mean ) adhesive bond energy inthe granules. The maximum adhesive bond energy exhibits anear-linear increase punctuated with step drops which indicate breakage of maximum-strength bonds resulting in a slightlynonlinear overall increase as the granulation progresses. Duringthis early stage of granulation, the maximum adhesive bondenergy max increases according to the bond drying Eq. (11). Asteady, initially nonlinear increase followed by a mildlyfluctuating linear increase characterises the evolution of theaverage granule bond strength which reaches a value of ~0.076 Jm 2 compared to 0.62 Jm 2 for max at the end of the simulation period. Significantly more simulation time isrequired to reach average adhesive bond energies of the order of 1.0 Jm 2 which is the value potentially attainable for themaximum wet surface energy value used for the spray zones.

3.2. Granule size evolution

Two definitions of granule size have been explored in thiswork: the number of primary particles in a granulesnp (whichhas been found to give the same trends as the mass of thegranule) and the circumscribing radius of the granulesrad . Thesesizes were monitored throughout the simulation and the meanand maximum sizes are shown together with the number of granules inFig. 9(a). The means of these size definitions,snpmeanand sradmean , both exhibit pronounced growth in the first 20 ms at the start of granulation, followed by about 90 ms of granule breakage and coalescence which is evident in the largefluctuations in the mean size. Subsequently, steady mean sizesof the order of snpmean ~20 and sradmean ~0.09 mm are attainedduring the rest of the simulation with only small fluctuations.This may be likened to the steady growth behaviour whichIveson and Lister [24] associate with systems with relativelycoarse, narrowly sized particle distributions and low viscosity binders leading to weak deformable granules. The maximumgranule sizessnpmax and sradmax also show fast early growth trends but subsequently, extreme variability marked by sharp falls andrises in the maximum granule size becomes the dominant characteristic of the growth profiles. This trend is indicative of the growth and breakage of rather large granules, some of theorder of 4500+ primary particles (~1.5 mm). No intrinsic direct relationship between the growth in the number of granulesn g 3+

and the maximum granule size trends is expected and none isevident in the semi-log plots shown inFig. 9(a). However, acloser inspection of the linear-scale plots of the evolution of n g 3+and snpmax in Fig. 9(b), where linear approximations have beensuperimposed to show the trends in different periods, suggeststhat the general trends in the evolution of the size of the largest granule is mirrored in the evolution of the quantity of granules.An overall increasing trend insnpmax between 0.1 s and 0.2 s leadsto an increasing n g 3+ trend which levels off as thesnpmaxfluctuations become bigger towards the end of this period.Following that, a predominant breakage period with no overallchange insnpmax ensues, resulting in an increasingn g 3+ trend from~0.23 s to 0.30 s. A steeper overall increasingsnpmax trend between ~0.30 s and 0.37 s on the other hand, triggers a fall

in n g 3+ (suggestive of coalescing granules) while a steep fallintrend followed by a fairly steady trend insnpmax produces a moregradual rise in the number of granules. The trend in thesradmaxevolution did not display the same consistent level of correlatiowith then g 3+ trend but this may well be due to an inadequacy othe circumscribing radius as a measure of granule size.

The location of granulesn g 3+ in the bed at three instances,0.118 s, 0.354 s and 0.525 s during granulation are shown iFig. 10in colours according to sizesnp . Visually, granule sizesin the range snp [201 1000] which are formed by 0.12 ssubsequently appear to be coalescing and breaking up to formlarger granules in the rangesnp [1001 2000] and some smaller granules. An increase in the number of granules in the size rang snp [11 50] for example, is clearly evident inFig. 10 from0.118 s to 0.525 s. Granules are seen to be located in all regionof the bed indicating no strong bias attributable to the sprazone locations and a uniform dispersion of coated particles ithe bed. The largest granules, however, have not moved

significantly away from the vicinity of the spray zones in thduration of the simulation of this study, a feature attributable the relatively low fluidising gas velocity employed in thsimulation.

Fig. 9. (a) Maximum and mean granule size ( snp , srad ) evolution during

granulation, (b) Comparison of approximate trends in the evolution of n g 3+

and snpmax during granulation.



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application of fractal geometry to the analysis of the evolvinggranules may give some clues about the mechanisms involvedin a complex granulation process. An index, the fractaldimensiond f with a lower limit of 1 and an upper limit equalto the Euclidean dimension, can be useful in this regard since atenuous granule structure is indicated by a lowd f while thehigher the value of d f, the more space-filling the structure.

For a granule withN p primary particles in a circumscribingsphere of radiusRg, a fractal dimension may be obtained from[27]

N p /R g r p

d f

13

where r p is the mean primary particle radius and is thefraction of the circumscribing sphere volume occupied by solids(except for a straight chain of particles where~1). Acomputer-generated random spherical granule made up of five primary particle sizes, the mean primary particle size being

20 m was found to have a calculated circumscribing sphervolume occupancy = 0.596. Applying Eq. (13) yields a fractaldimension of 2.94 for this spherical granule which is close to thEuclidean dimension limit of 3.0 and confirms a more volumefilling and rotund structure.

Eq. (13) was applied to granules with three or more particleduring the granulation process.Fig. 13 shows the logarithmic plots of Eq. (13) at timest =0.118 s and 0.525 s with linear fits

from which values of and d f have been extracted. The linesfor d f =2.0, 3.0 using the mean value extracted from thelinear fit to the simulation data and the line for d f =1.0 using

= 1 have been superimposed along with a line for the randomspherical granule referred to earlier. At the times examinedFig. 13 suggests granule structures range from near-plana(d f ~2) to near rotund (d f ~3) especially when the number of primary particles is less than ~20. For the larger granulcontaining more primary particles, the figures suggest concentration of the granule structures mid-way between planaand rotund, an effect which appears to shift towards the rotunwith a consequent increase ind f as time increases. Thecircumscribing spherical volume occupancy and fractaldimension d f obtained from Eq. (13) are shown inFig. 14.

Fig. 11. Evolution of cumulative granule size ( snp ) by mass fraction duringgranulation (includes doublets).

Fig. 12. Evolution of cumulative granule size ( snp ) by frequency duringgranulation (includes doublets).

Fig. 13. Plot of the fractal Eq. (13) for granules (n g 3+ ) at t =0.118 s (a),t =0.525 s(b).



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Both d f and exhibit an increasing trend during the granulation

process.A visualisation of the granules enables us to examine thegranules and make deductions on the structures and shapes.Such an examination has revealed that although the granuleswith more primary particles tended to be slightly longer in onedimension and irregular, in general the structure was morespace-filling. For granules with primary particlesN p ~11 200,a large majority of the granules were observed to be rotundwhile a mixture of stringy to rotund shapes were found for N pranging from 3 to 10. An illustration of the granule shapesobtained is shown in the elevation and plan views of Fig. 15for N p ranges 11 20, 51 200, 201 1000 and 1000 2000 at t =0.525 s. Evidently, the mainly rotund shapes observed from

the visualisation are not adequately reflected in the results of thefractal analysis. The circumscribing radius employed in theanalysis is, by definition, the maximum linear dimension of thespace occupied by each granule. Any bias towards onedimension and, for the granules with smallN p, protrusions of two or three particles sticking out from the bulk granule tend toappreciably increase the circumscribing radius and hencesignificantly reduce the circumscribing sphere volume occupancy of the granule. It thus appears that the circumscribingsphere radius may not be an appropriate size measure to use for an analysis of the granules obtained in these simulations.

4. Conclusions

A surface energy-driven spray zone concept has been presented and applied to a fully-3D DEM-based fluidised bedgranulation simulation of a Geldart group A particle bed. Theconcept uses simple functional relationships to model the pick-

up of surface energy (

wetting

) by particles in the spray zoneand the granulation simulation employing four symmetricallylocated spray zones was found to quickly result in uniformdispersion of spray-coated particles in the bed. Sensible trendsin net granule formation have been obtained which can berelated to trends in bond formation, bond strength andmaximum granule mass. Granule formation and breakage areadequately captured as are the evolution of granule mass andlinear size showing mass/size enlargement and reduction. Thefast growth rate of the largest granules may be due to the surfaceenergy values used for the spray zones and the relatively lowfluidising gas velocities used in the simulations. Fractal analysisof the early stage granules confirms that the products are not

Fig. 14. Variation of fractal dimensiond f and circumscribing sphere volumeoccupancy of granules during granulation.

Fig. 15. Visualisation of granule shapes/structures for the indicatedN p ranges at t =0.525 s.



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[8] D. Verkoeijen, G.A. Pouw, G.M.H. Meesters, B. Scarlett, Population balances for particulate processes a volume approach, ChemicalEngineering Science 57 (12) (2002) 2287 2303.

[9] S. Heinrich, J. Blumschein, M. Henneberg, M. Ihlow, M. Peglow, L. Morl,Study of dynamic multi-dimensional temperature and concentrationdistributions in liquid-sprayed fluidised beds, Chemical EngineeringScience 58 (2003) 5135 5160.

[10] M.J.V. Goldschmidt, G.G.C. Weijers, R. Boerefijn, J.A.M. Kuipers,Discrete element modelling of fluidised bed spray granulation, Powder Technology 138 (2003) 39 45.

[11] K.L. Johnson, K. Kendall, A.D. Roberts, Surface energy and the contact of elastic solids, Proceedings of the Royal Society of London. A 324 (1971)301 313.

[12] K. Nishii, Y. Itoh, N. Kawakami, Pressure swing granulation, a novel binderless granulation by cyclic fluidisation and gas flow compaction,Powder Technology 743 (1993) 1 6.

[13] K.D. Kafui, C. Thornton, M.J. Adams, Discrete particle-continuum fluidmodelling of gas solid fluidised beds, Chemical Engineering Science 57(2002) 2395 2410.

[14] C. Thornton, C.W. Randall, Applications of theoretical contact mechanicsto solid particle system simulation, in: M. Satake, J.T. Jenkins (Eds.),Micromechanics of Granular Materials, Elsevier, 1988, pp. 133 142.

[15] C. Thornton, K.K. Yin, Impact of elastic spheres with and without adhesion, Powder Technology 65 (1 3) (1991) 113 123.[16] C. Thornton, Interparticle sliding in the presence of adhesion, Journal of

Physics. D, Applied Physics 24 (1991) 1942 1946.[17] C. Thornton, Z. Ning, A theoretical model for the stick/bounce behaviour

of adhesive, elastic-plastic spheres, Powder Technology 99 (1998)154 162.

[18] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York, USA, 1960.

[19] R. Di Felice, The voidage function for fluid particle interaction systems,International Journal on Multiphase Flow 20 (1994) 153 159.

[20] J.A.M. Kuipers, K.J. van Duin, F.P.H. van Beckum, W.P.M. van Swaaij,Computer simulation of the hydrodynamics of a two-dimensional gas-fluidised bed, Computers and Chemical Engineering 17 (8) (1993)839 858.

[21] R.C. Rowe, Binder-substrate interactions in granulation: a theoretical

approachbased on surface free energyand polarity, International Journalof Pharmacy 52 (1989) 149 154.[22] T. Schfer, C. Mathiesen, Melt pelletization in a high shear mixer: IX.

Effects of binder particle size, International Journal of Pharmacy 139(1996) 139 148.

[23] K.L. Johnson, Adhesion at the contact of solids, in: W.T. Koiter (Ed.),Theoretical and Applied Mechanics, North-Holland, 1976, pp. 133 143.

[24] S.M. Iveson, J.D. Litster, Growth regime map for liquid-bound granules,AIChE Journal 44 (1998) 1510 1518.

[25] D.L. Turcotte, Fractals and fragmentation, Journal of GeophysicalResearch 91 (B2) (1986) 1921 1926.

[26] J.L. LaRosa, J.D. Cawley, Fractal dimension of alumina aggregates grownin two dimensions, Journal of American Ceramic Society 75 (7) (1992)1981 1984.

[27] B.B. Mandelbrot, The fractal geometry of nature, Freeman, San Francisco,

USA, 1983.[28] J. Baeyens, D. Geldrat, Proc. Int. Symp. Fluidization and its Applications,Toulouse, France, 1973, p. 263.

[29] A.R. Abrahamsen, D. Geldart, Behaviour of gas-fluidised beds of fine powders: Part I. Homogeneous expansion, Powder Technology 26 (1980)35 46.

[30] C. Turchiuli, et al., Fluidised bed agglomeration: agglomerates shape andend-use properties, Powder Technology 157 (2005) 168 175.


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