SCALING-UP A REACTIVE EXTRUSION OPERATION IPR · PDF fileSCALING-UP A REACTIVE EXTRUSION OPERATION Estanislao Ortíz-Rodríguez and Costas Tzoganakis 6/4/2008 IPR Annual Symposium

SCALING-UP A REACTIVE EXTRUSION OPERATION

Estanislao Ortíz-Rodríguez

andand

Costas Tzoganakis

6/4/2008 IPR Annual Symposium 1

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Scale-up calculations for reactive extrusion operations

Outline

BackgroundProblem DescriptionResultsConclusionsFuture WorkFuture Work


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Background Problem description Future workResults Conclusions

(a)

Figure 1Figure 1. Modular configuration in a CSCO extruder. Modular configuration in a CSCO extruder(b)


gg gg(data (data Leistritz®).®).

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REX d liREX modeling.

- Conservation of mass, momentum and energy equations aswell as the reaction kinetics equations need to be solved.

- One-dimensional (1D) and three-dimensional (3D) models canb d i l hbe used to simulate the system.

- 1D models: geometrical and flow simplifications are used.Th d l i ld l f i tThese models yield average values of processing parametersalong the extruder, from hopper to die.

3D models are less simplified than 1D models- 3D models are less simplified than 1D models.Conventionally, only fully filled sections of the extruder aresimulated in 3D modeling.


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(a) (b)

[After Michaeli et al., 1995] [After Vergnes et al., 1998]

Figure 2. Simplified flow geometries used in 1D modeling. a) Curved channels. b) “C-shaped” chambers.


g ) ) pIP

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S li l i Equations 2Scaling-up relations- Variables are scaled-up by a

power of the diameter ratio ( l i d )

Equations 2. -Conventional scale-up approach for non-reactive systems(scale-up index). systems.

dDD 1 D[2.a]vldt −−∝ 1

l

h

dLL

dHH

dDD

12

12

12

=

=

=1

2

DD

d = [2.b]

[2.c]

vhdM ++∝ 2

hlnhnndSEC −+−+∝ ν

[Christiano, 1994; Rauwendaal, 1986, 1987]

2 ) A id i 2 b) MvdNN

d

dLL

12

12

12

=

= βφφ[1]

whereD=Diameter, H=Max. channel depthL=Screw length, φ=Helix angle,

2.a) Average residence time, 2.b) Mass throughput, 2.c) Specific Energy Consumption (SEC).


N=Screws rotating speed n=Power-law indexIP

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Fi 3 PP d d ti (b i h i )[After Xantos, 1992]


Figure 3. PP degradation (basic mechanisms). IP

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Proposed scale-up approachProposed scale up approach.-To scale-up the REX operation from a reference extruder keeping a constant thermal time, tT.

A i i f h i d ’ d id i l

∫= −t tRTET dtet 0

)(/ '' [3] [Nauman, 1977]

E=Activation energy of the reaction. T and t’ temperature and residence time along a pathline.

-Simulation software (Strutt, 1998). Kinetics and rheokinetics parameters from Tzoganakis et al. (1988) and Wang (1996).

Additionally, comparison between scaling-up under constant y, p g ptT and SEC.

- The yielded Mws and PDIs, for scaling-up under the above procedures are the evaluation parameters


procedures, are the evaluation parameters.IP

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Table 1 Material data used for simulationsTable 1. Material data used for simulations.Parameter Value

Number-average molecular weight 51,800 g/mol

W i h l l i h 279 700 / lWeight-average molecular weight 279,700 g/mol

Melt density 750 kg/m3

Solid density 905 kg/m3

Bulk solid density 560 kg/m3Bulk solid density 560 kg/m

Pellet hydraulic diameter 2 mm

*Power law index 0.35

Consistency index 75480 Pa sn

Temperature factor (β) 0.0243(1/ºC)

Melt thermal conductivity 0.185 W/(m ºC)

Melt specific heat capacity 2.428 kJ/(kg ºC)

* This value is used for all of the calculations to evaluate the scale-up index v

Melting point 170 ºC

Heat of fusion 133.850 kJ/kg


from the equation of constant SEC.IP

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Table 2. Summary of geometrical parameters of the extruders(data Leistritz®).

Extruder model

Barrel diameter

(mm)

Channel depth (mm)

d h v

*LSM 30 34 34 00 3 99*LSM-30.34 34.00 3.99 --- --- ---

ZSE-50 50.00 7.21 1.47 1.52 2.02

ZSE-67 67.00 8.05 1.98 1.03 0.11

*Indicates the reference extruder.

ZSE-96 96.00 12.10 2.84 1.06 0.25

It can be noticed from the values of h and v that the ZSE-67 and ZSE-96 extruders are close geometrically scaled-up versions of the reference device.


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Start

Evaluate tT for the reference extruder ,tTf, and

MRt is the mass throughput obtained assuming constant

fMRt for the large extruder, Mi.

E l f hobtained assuming constant residence time.

The screw speed, N, is kept

Evaluate tT for the larger extruder, tTi.

constant during the calculations. tTf = tTi Mi=Mi±ΔMi

Yes

No

Fi 4 I l t d l d f t t

Stop

Yes


Figure 4. Implemented scale-up procedure for constant tT.IP

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[After Strutt, 1998]

Fi 5 E t d fi ti f th LSM 30 34Figure 5. Extruder screw configuration for the LSM-30.34extruder.The peroxide injection port, IP, is located at a dimensionless axial distanceThe peroxide injection port, IP, is located at a dimensionless axial distanceequal to 0.45.

For the larger extruders, the length of the screw elements and kneading blocks is scaled up proportionally to d1


blocks is scaled-up proportionally to d1.IP

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Table 3. Initially simulated processing conditions.

Extruder model

Mass Throughput

(kg/hr)

Screw speed (rpm)

Peroxide concentration

(wt %) LSM 30 34 5 0 100 150 200 0 01 0 02 0 10LSM-30.34 5.0 100, 150, 200 0.01, 0.02, 0.10

ZSE-50 19.65 100, 150, 200 0.01, 0.02, 0.10

ZSE-67 39.52 100, 150, 200 0.01, 0.02, 0.10

ZSE-96 122.02 100, 150, 200 0.01, 0.02, 0.10

The mass throughput for the larger extruders corresponds to the scaled-up value of this parameter from the equation of constant residence time.


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0 02 % 100 LSM 30.34 ref[I] = 0.02 wt% , N=100 rpm

1.00

LSM_30.34_ref

ZSE_96_Rt

ZSE_96_tT

0.60

0.80

sion

less

)

0 20

0.40

DO

F (d

imen

0.00

0.20

0.00 0.20 0.40 0.60 0.80 1.00

D

Figure 6. Degree-of-filling at the center of the screw

Dimensionless axial distance


Figure 6. Degree of filling at the center of the screw channel (DOF).

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0 02 % 100 LSM 30 34 ref[I] = 0.02 wt% , N=100 rpm

5.5

LSM_30.34_ref

ZSE_96_RtZSE_96_tT

5.2

sionl

ess)

4.6

4.9

PDI (

dim

en

4.30.60 0.80 1.00

Dimensionless axial distance

Figure 7. PDI variation along the axial distance of the


Figure 7. PDI variation along the axial distance of the extruder.

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tav(N=100)[I] = 0.02 wt%

120e

(s)

220

e ( º

C).

tav(N=100)tav(N=150)tav(N=200)

80

100

denc

e tim

212

216

eper

atur

e

Tav(N=100)Tav(N=150)Tav(N 200)

40

60

rage

res

i

204

208

rage

tem

e Tav(N=200)

20

0.00 1.00 2.00 3.00 4.00 5.00

Ave 200

Ave

r

30.3

4

E-50

E-67

E-96

Figure 8. Temperature of reaction and residence time

LSM

-

ZSE

ZSE

ZSE


g pvariations for the constant thermal time scale-up approach.

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[I] = 0 02 wt% tav(Ni=100)[I] = 0.02 wt%

100

120m

e (s

)

225

230

re (

ºC)

tav(N 00)tav(Ni=150)tav(Ni=200)T (Ni 100)

60

80

100

side

nce

tim

215

220

225

mep

erat

ur Tav(Ni=100)Tav(Ni=150)Tav(Ni=200)

20

40

60

vera

ge r

es

200

205

210

vera

ge te

m

20

0.00 1.00 2.00 3.00 4.00 5.00

Av 200 Av

-30.

34

SE-6

7

SE-9

6

SE-5

0

Figure 9. Temperature of reaction and residence time

LSM ZS ZSZS


g pvariations for the constant SEC scale-up approach.

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[I] = 0 02 wt% SEC[I] = 0.02 wt%

2 2

2.6ss

)tT(N=100)

tT(N=150)

tT(N=200)

1.8

2.2

dim

ensio

nles

( )

1.0

1.4

M/M

Rt (

d

0.60.00 1.00 2.00 3.00 4.00 5.00

E-67

E-96

E-50

-30.

34

Figure 10. Scaled-up mass throughput variations for

ZSE

ZSE

ZSE

LSM

-


g p g pboth tT and SEC.

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0 02 % tT(N 100)[I] = 0.02 wt%

2.320

tT(N=100)tT(N=150)tT(N=200)SEC(Ni=100)

2.280

+05

(g/m

ol) ( )

SEC(Ni=150)SEC(Ni=200)

2.240

Mw

E+

2.2000.000 1.000 2.000 3.000 4.000 5.000E-

67

E-96

E-50

30.3

4

Figure 11 Mw and PDI variations for both t and SEC

ZSE

ZSZSE

LSM

-3


Figure 11. Mw and PDI variations for both tT and SEC.IP

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Under the constant thermal time scale-up approach:

- Good agreement between the PDIs and Mws of the referencegand scale-up extruders are obtained.

- When the residence time decreases, the temperature of reactionW e t e es de ce t e dec eases, t e te pe atu e o eact oincreases.

- No significant variations of PDI and Mw as a function of theNo significant variations of PDI and Mw as a function of thescrew speed are observed.

Overall, the constant thermal time scale-up procedure is abetter way to scale-up the REX system than the constant SECapproach


approach.IP

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3D simulations:

- To perform simulations for specific conditions selected from1D simulations in order to get additional insight of the REXs u at o s o de to get add t o a s g t o t eoperation.

To perform a mixing and residence time distribution (RTD)- To perform a mixing and residence time distribution (RTD)analysis.

- To calculate the average thermal time distribution, Mw, andPDI and compare these results to those of the 1D analysis.


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(a) (b)

Figure 12. Sample 3D results. (a) Velocity field for a cut y-plane


(b) Shear rate contour plot for a cut z-plane.IP

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Figure 13. Sample 3D results. Particle tracking analysis.


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Acknowledgements

The financial support from the Mexican National Council forScience and Technology (CONACYT) is gratefullygy ( ) g yappreciated.


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THANK YOU FOR YOURTHANK YOU FOR YOUR ATTENTION

QUESTIONS/ANSWERSTIMETIME


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Figure A.1. General description of an extrusion operation.IP

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(a) (b)[After Booy, 1978] [After Yang and Manas-Zloczower, 1992]

Figure A.2. a) Additional geometrical considerations for a twin

tαπ

screw extruder system. b) Kneading block geometry

( )DC αcos= [A 2]


22t

i nαπα −= ( )iSL DC αcos=[A.1] [A.2]

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0 02 % 100 LSM 30 34 f


[I] = 0.02 wt% , N=100 rpm

220C

)

LSM_30.34_ref

ZSE_96_Rt

ZSE_96_tT

210

erat

ure

( ºC

190

200

rage

tem

ep

1800.00 0.20 0.40 0.60 0.80 1.00

Ave

Dimensionless axial position

Figure A.3. Temperature variation along the axial


Figure A.3. Temperature variation along the axial distance of the extruder.

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- Reaction kinetics for the peroxide-initiated degradation of PP


Reaction kinetics for the peroxide initiated degradation of PP (Tzoganakis et al. 1988). Initiation, chain scission, transfer, thermal degradation, termination by disproportionation are the steps considered by the model.steps considered by the model.

010 32

QQIkf

dQ

IkdtdI

D

−

−=

( )2102

01

23 22 QQQ

QQQQ −= [A.4]

( ) ( )01

01

01

23/3/

22

2

QQQdQQQ

QIkf

dtdQ

QQIkf

dt

Dp

Dp

+−

−=

−= 01QQ

( )

( )_

010

_

/

/

QQmM

QQmM n =

[A.5]

[A.3]

- I is the peroxide concentration; fp and kd, are the peroxide decomposition

( ) ( )01

0132 23/3/2

QQQQQ

Ikfdt

dQDp −

−+−=

( )

( )230

_120

/

/

QQmM

QQmM

z

w

=

= [A.5]

efficiency and rate constant of decomposition, respectively. t is the time; and Qi is the ith moment of the molecular weight distribution. Mn, Mw and Mz are the number-, weight- and z- average molecular weights, respectively; and m0 is the monomer molecular weight


respectively; and m0 is the monomer molecular weight.IP

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- Equations A 6-A 9 needs to


- Mw is a time dependent function; it depends on the evolution of the reaction (eq

- Equations A.6-A.9 needs to be declared in POLYFLOW® as “user d fi d f i ”evolution of the reaction (eq

15).defined functions”.

- The ith moment of the molecular weight distribution( )

__[A 6] molecular weight distribution

are calculated from relations proposed by Tzoganakis et al. (1988)

( )120 /QQmMW =

⎪⎪

⎨

⎧ <−

0

..

10

. , γγγ n

K

[A.6]

(1988).- The power-law consistency

index, K, and the power-law ⎪⎪

⎩

⎪⎨

>=

− 0

..

1.

0

, γγγ

γη

nK [A.7]

, , pindex, n, are expressed as polynomial functions (Strutt, 1998)

),(__

TMKK W=

),(__

TMnn W= [A.9]

[A.8]


1998).IP

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(b)(a) (b)

Figure A.4. (a) Screws and (b) flow-field meshed t ti l bd i


computational subdomains.IP

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3D simulations.


- Simulation of the flow in conveying screw elements of a CSCO extruder.

- POLYFLOW®, a FEM software, is used; it applies the “mesh superposition technique” (Avalosse and Rubin, 2000). This technique is especially useful in describing the time q p y gdependency of the flow, which is due to the rotation of the screws.A ti P d t d t t ( t d t t f fi d- Assumptions: Pseudo-steady state (steady state for a fixed position of the screws). Newtonian and isothermal flow.

- Boundary conditions: Screw rotating speed=10 rpm. Gravity y g p p yand inertia forces neglected. Non-slip conditions on solid boundaries.M d l G li d N t i fl id Vi it 5 0E04 P


- Model: Generalized Newtonian fluid. Viscosity=5.0E04 Pa·sIP

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T bl A 1 P id h lf li i T bl A 2 P id h lf


Table A.1 Peroxide half-lives in melt (sample results).Ni=150 rpm. [I]=0.02 wt%

Table A.2 Peroxide half-live time as a function of the temperature of reaction.Ni 150 rpm. [I] 0.02 wt% p

Extruder model

ConstanttT

ConstantSEC

Temperature(oC)

[I]1/2

(s)

LSM-30.34 3.25 ---

ZSE-50 3.33 2.23

180 74.00190 36.30200 18 35ZSE-67 3.80 3.68

ZSE-96 4.33 3.92

200 18.35

210 9.54220 5 10

For the higher values of the average temperature of reaction, the lower values of this parameter are observed

220 5.10


p(in agreement with results of Fig. 8).

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Documents

SCALING-UP A REACTIVE EXTRUSION OPERATION IPR · PDF fileSCALING-UP A REACTIVE EXTRUSION OPERATION Estanislao Ortíz-Rodríguez and Costas Tzoganakis 6/4/2008 IPR Annual Symposium