Population Balance Models for Granulation Process Design

Jim LitsterSchool of Chemical Engineering

Department of Industrial and Physical PharmacyDepartment of Industrial and Physical PharmacyPurdue University

AcknowledgmentsAcknowledgments• Collaborators: • Current and formerCollaborators:

– Sotiris Pratsinis

– Brian Ennis

Current and former students– Anthony Adetayo

– Charles Emmanuel

– Frank Doyle

– Lian Liu

– Simon Iveson

– Ian Cameron

– Fu Yang Wang

C l W

– Karen Hapgood

– Hans Wildeboer

B F i i h– Carl Wassgren – Ben Freireich

– Jonathan Poon

– Rohit RamchandranRohit Ramchandran

OutlineOutline

• Introduction to granulation processes

• Modelling coalescence– A little bit of history

– Multidimensional PBM

• Modelling nucleation and layering

Size enlargement by granulationSize enlargement by granulationE=(e1, e2,..., ej)

X=(x1, x2,..., xn) Y=(y1, y2,..., yn)Process vesselP d t

j

Feed Product

%

x

%

y

(x or y) = (size, voidage, strength, surface properties, quality metric)

• liquid binder used to form interparticle bonds• agitation of “wet mass” to promote liquid binder dispersion and granule growth

y

• fluid beds, tumbling drums, mixers

Granulation equipmentGranulation equipment

Fl id B dMi Fluid BedSprayNozzle

Mixer

Impeller

Chopper

Tumblingd

Fluidising airdrum

Powder flow in a mixer granulatorPowder flow in a mixer granulator

P ti l D i P i i lP ti l D i P i i lParticle Design PrinciplesParticle Design Principles

Product EngineeringDeveloping the

Process Engineering‐ Developing the

formulation‐ Process choice, design & scale up

Designer particle withcontrolled properties(size porosity )(size, porosity, ....)

Granulation Rate ProcessesGranulation Rate Processes

1) wetting, nucleation and binder distribution

2) consolidation and growth

3) attrition and breakage

(Ennis & Litster, 1997)

G l ti tGranulation rate processes

Mechanicalno change Mechanicalno change

1.0E+1

τp

MechanicalDispersion

regime

Intermediate

1.0

no changein distribution

τp

MechanicalDispersion

regime

Intermediate

1.0

no changein distribution

1.0E-1

1.0E+0

U2 /2

Y (-

)

InductionNucleationSteady Grow th

Steady Growth

Tardos et al . (1998) Crumb

Iron Ore in Drum

Ballot ini & PEG in M ixer

Iron Ore in M ixer

Na2SO4 in M ixer

Dropcontrolled

narrower nucleisize distribution

0.1

Caking

Dropcontrolled

narrower nucleisize distribution

0.1

Caking

1.0E-3

1.0E-2

Stde

f = Rapid Grow th

NucleationRegion

RapidGrowth

Induction

Chalcopyrite in Drum

Ballot ini & Water in Drum

Iron Ore in Drum

Ballot ini & Glycerol in Drum

Ψa0.01 0.1 1.0 10Ψa0.01 0.1 1.0 10

1.0E-40.600 0.800 1.000 1.200 1.400

Pore Saturation (-)

Controlling groups are known for nucleation and growth.  Regime maps are available.

Current status for designCurrent status for designMeasure Formulation 

iEstimate Process 

Properties:dp, γcosθ, µ, Y, ………

parameters:Uc, Rω,………

Calculate important dimensionless groups:ψa, tp , Stdef , S, ………ψa, p , def , ,

• Formulation design• Process choice• Rational scale up• Trouble shooting

An Engineering Design ApproachAn Engineering Design Approach

Measure FormulationMeasure Formulation Properties:dp, γcosθ, µ, Y, ………

Rate expressions

Population balance model

Granule propertiesEstimate Process  p p•Size distribution•Density•Strength

parameters:Uc, Rω,………

•Dissolution•……….

Meso scale modelling of granulation processesMeso scale modelling of granulation processes

• Pop lation balan e models an tra k tra k• Population balance models can track track product attributes:

(x)dV(x)bVx

t)Gn(x,V(x)nQ(x)nQt

t)Vn(x,exexinin

⋅⋅⋅⋅

−+∂

∂−−=

∂∂

),()()()(),( **

exexinintvnAGVvnQvnQtvVn &&

∂−∂

−−=∂

∂

))()()()()((

)()(

brcoalbrcoalnuc

exexinin

vdvdvbvbvbVv

QQt

&&&&& −−+++∂∂

A little bit of historyA little bit of history 

E i t l (1991) fi t tEnnis et al. (1991) first to focus on effect of granule properties

coalescewillgranulesStStv ⇒< *

4 dU

Early work by Kapur Sastry and

μρ

94 gcg

v

dUSt =

⎟⎞

⎜⎛

⎟⎞

⎜⎛ h1Early work by Kapur, Sastry and 

Fuerstenau focused on coalescence  ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛+=

a

b

r hh

eSt ln11*

A little bit of historyA little bit of historyAdetayo, A.A., J.D. Litster, S.E. Pratsinis and B.J. Ennis, Powder Technol., 82, 37 (1995)

Adetayo and Ennis, 1998( )

k 6lSt * 9μ⎛

⎜ ⎞ ⎟ l

μ⎛ ⎜ ⎞

⎟ ktmax = 6lnμ

8ρgucd0⎝ ⎜

⎠ ⎟ ∝ ln

μρgucd0⎝

⎜ ⎠ ⎟

b

a

*

*o

)vu()uv(wwhere

ww,0ww,k

)v,u(+

=⎩⎨⎧

><

=β

Modelling Coalescencegu0

u1 u2u3

ha

δ2h0

Rr

H2h0

D u1u2 u3

2a

u0u3

h0

h⎛ ⎞0St hhva

<⎛⎝⎜

⎞⎠⎟ln 0

( )Y D h h~//

/⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎡ ⎤ ⎛ ⎞1 2

9 82 5 4 20172

Type I:

Type II:( )Y

ESt

StDh

Sthh

hh

ddef

visvis

a a*. ln

/⎛⎝⎜

⎞⎠⎟

<⎛⎝⎜

⎞⎠⎟ −

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ −

⎛

⎝⎜

⎞

⎠⎟

−9 8

0

0 02

0172 1 1Type II:

Liu et al., AIChE J, 46, 529-539 (2000)

1002 )

10

8mU

0)/(

3D

2

Rebound

β=0

β=β 2

Stv

= (8 Type II

Coalescence

Rebound

β=β 1

11.E-6 1.E-5 1.E-4 1.E-3 1.E-2 1.E-1

St def = (0.5mU 02)/(D 3Y d )

Type I critical condition Type II, critical condition

Type I Coalescence

0 8

1

actio

n

Type I critical condition Type II, critical conditione=1, boundary of β1 and β2

0.2

0.4

0.6

0.8

mul

ativ

e m

ass

fra

00 5 10 15 20

Granule size (mm)

Cum

initial size distribution exp.(100rev.)p ( )

exp.(300 rev.) exp.(400.rev.)exp.(500 rev.) model (100 rev.)

model (300 rev.) model (400 rev.)

model (500 rev.)Liu & Litster, 2002

Multidimensional PB modelsMultidimensional PB models

T k th di t ib ti ( l )• Tracks the distribution n(s,l,g)),,,(),,,(),,,(),,,( gls

gtglsnVG

ltglsnVG

stglsnVG

ttglsVn

∂

∂+

∂∂

+∂

∂+

∂∂

)),,,(),,,(),,,(

),,,(),,,((),,,(),,,(

brcoalbr

coalnucexexinin

tglsdtglsdtglsb

tglsbtglsbVtglsnQtglsnQg

&&&

&&&&

−−+

++−=

• Challenge for efficient numerical solution• Challenge for experimental validation• Challenge for experimental validation

Evolution of Two Dimensional Distribution• Simulation result

‐ binder‐to‐solids ratio of 0.11

Evolution of Two‐Dimensional Distribution

binder to solids ratio of 0.11t = 0 s

t = 900 sparticles

t = 900 s

al particles

Total 

F i l bi di l di ( )

29/10/2008t = 300 s

Tota

s Fractional binder content

Fractional binder contentParticle diameter (μm)

Particle diameter (μm)t = 300 s

Total particles

18Fractional binder contentParticle diameter (μm) Poon et al., Chem Eng Sci, 63, 1315-1329 (2008)

Batch Granulation ResultsRamchandran et al., (2008)

‐ clear evidence of multi‐dimensional heterogeneity

Binder content distribution

Granule size distribution

Porosity distribution

19 29/10/2008

Granule size distribution

binder‐to‐solid ratio = 0.125 drum load = 1.75 kg

• Multidimensional PB approaches:– allow incorporation of more physics in the rate expressions

– Track property distributions of interest to us

• But powder flow and particle interactions still represented in a crude, lumped parameter format

The impact of mixing and powder flowThe impact of mixing and powder flow

2.8 cm

7.0 cm

23.8 cm

2.8 cm

6.7 cm

7.0 cm8.4 cm 8.4 cm

0.6 cm

3.3 cm

3.3 cm

23.8 cm

PEPT results (600 rpm)

15

ncy

Impeller speed = 6.6 ms-1

Average speed = 0.84 ms-1

5

10% o

ccup

an

Average speed 0.84 msMaximum speed = 2.95 ms-1

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

Impeller speed [mm/s]Anh Tran, PhD (2008)

Regions for granulation rate processes

15

ncy

5

10% o

ccup

an

0 200 400 600 800 1000 1200 1400 1600 1800 20000

5

Impeller speed [mm/s]

PEPT derived powder flow data

• Data required for models– Occupancy 

– Velocity field 

– Fluxes 

– Stresses 

C lli i f i– Collision frequencies 

– Predictive  

Multiscale modellingMultiscale modelling

Parameter sensitivityParameter sensitivity0.5

0.6

tion

0 2

0.3

0.4

Reg

ion

Solid

Fra

ct

0.0

0.1

0.2

0.E+00 2.E+08 4.E+08 6.E+08 8.E+08 1.E+09 1.E+09

Shea

ring

Dimensionless Contact Stiffness, k* = k/(ρd3γ2)

80

90

100

s)-1

k* = 1e7k* = 7.5e7k* = 1e8

30

40

50

60

70

obab

lity

Den

sity

(m/s k* = 1e9

0

10

20

0.00 0.01 0.02 0.03 0.04

Normal Collision Velocity (m/s)

Pro

Ben Freireich (2008)

Shear Rate, &

Solid Fraction

Collision Velocity DistributionDrum Simulation

Baseline Conditions0.3 300

Collision Velocity DensityShear Simulationν = 0.55 γ = 15.0

0.3 300

s Ta

ngen

tial

ity =

vs/( ω

R)

0 15

0.2

0.25

150

200

250

s Ta

ngen

tial

ity =

vs/( ω

R)

0 15

0.2

0.25

150

200

250

Dim

ensi

onle

ssm

pact

Vel

oci

0.05

0.1

0.15

50

100

150D

imen

sion

less

mpa

ct V

eloc

i

0.05

0.1

0.15

50

100

150

Dimensionless NormalImpact Velocity = vn/(ωR)

D I

0 0.1 0.2 0.3

0 0

Dimensionless NormalImpact Velocity = vn/(ωR)

D I

0 0.1 0.2 0.3

0 0

Dimensionless Spray FluxDimensionless Spray Fluxp yp y

• Area of drops compared to area sprayed, at a flowrate V and a powder flux A and drop size dd

Ψad

VAd

=3

2

&

&

• Low spray flux means a narrow nuclei distribution as most drops are well separated.

• Fraction of nuclei formed by 2 or more drops     

)4exp(1f ψ )4exp(1 amultif ψ−−=

Modelling NucleationModelling Nucleation

P l d t ll d• Purely drop controlled:

)()( vsSnvb snuc ε=&

• Extension to allow for non‐uniform (real) sprays and some drop overlap using Monte Carlo simulationsimulation

Wildeboer, 2002

Modelling consolidation and layeringModelling consolidation and layering

• Consolidating granules pick up• Consolidating granules pick up fines (layering) as liquid is squeezed to the surface

• When fines are used up

Wet spot

Liquid film

Wet spotWet spot

Liquid filmLiquid film

• When fines are used up, coalescence may start a b ca b c

−εε

)(

)( min

defcon

con

Stfk

vkvG

=

−=εεε

• Predict induction time in batch systems

Wildeboer, 2002

2 D distribution for layering2‐D distribution for layering

Mort et al., 2008

And now for something completely different From thisdifferent:  From this…….

Bre kNucleation tion

BreakageAttrition

Wetting

ation

Densificatio

GrowthWe D Grow

to this!……. to this!

Design and control of physically regimeseparated continuous granulators

Stage 1: Wetting and Nucleation

Drop controlledNucleation

Shear controlledNucleation

Controlparameters

Controlparameters

Controlparameters

Stage 2: Densification and growth

Densification andLayering

Densification andCoalescence

Wildeboer et al., Powder Tech, 171, 96=205 (2007)

Regime separated granulators – Hans Wild bWildeboer

• New nucleation device to give• New nucleation device to give nearly monosized nuclei granules

Acoustic controlled– Acoustic controlled showerhead over a thin bed of powder on a conveyor belt

– Effectiveness depends on pdrop‐drop and drop powder interactions at the powder surface

l– Extremely narrow size distributions possible

SummarySummary