020703 measurement of stress deformation characteristics for a polypropylene particle of fluidized bed polymerization for dem simulation

Measurement

of

Stress-Deforemation Characteristics

for a Polypropylene Particle

of Fluidized Bed Polymerization

for DEM Simulation

M. Horio, N. Furukawa, H. Kamiya and Y. Kaneko

Department of Chemical Engineering

Tokyo University of Agriculture & Technology

Graduate School BASE

Koganei, Tokyo 184-8588, Japan

The scale-up of fluidized bed polyolefine reactors tends to

accompany agglomeration troubles in the reactor.

The cause of such tendency may be enhanced by liquid

bridging, van der Waals interaction and/or electrostatic

interaction that may suppress heat release from particles.

The authors group ( Kaneko et al. (1999) , (2000) ) has

developed DEM simulation for polyolefine reactors and

demonstrated that even a slight change in the distributor

design can affect solid mixing and cause temperature

maldistribution in the bed.

Background

Background (continued)

In their simulation, however, the cohesive force was not

taken into account.

Surface roughness affects cohesive interaction.

(In our DEM simulation for sintering particles ( Kuwagi et al.

( 2000 ) ) we found that the surface roughness affects very

much the sintering behavior. In the surface force dominant

range, the force-deformation relationship in a very

microscopic sense may affect the cohesive interaction.)

Objectives: Preliminary screening of factors significant in

DEM simulation of PP reactors

1) DEM simulation of thermal behavior of a PP bed with and

without van der Waals force.

2) A microscopic measurement of the force-deformation

relationship chasing surface roughness effects.

DEM, the last 10 years

DEM: Discrete Element Method

Fluid phase: local averaging

Particles: rigorous treatment User friendly compared to Two Fluid Model & Direct

Navier-Stokes Simulation

•A new pressure/tool to reconstruct particle

reaction engineering based on individual

particle behavior

•Potential for more realistic problem definition/

solution

SAFIRE: Simulation of Agglomerating Fluidization for Industrial

Reaction Engineering

Normal and tangential component of F collision

and F wall

Surface/bridge force

Rupture joint h c

Attractive force F c

No tension joint

Normal elasticity k n

Normal dumping h n

Tangential dumping h t

k t Tangential elasticity

Friction slider m SAFIRE is an extended Tsuji-Tanaka model

developed by TUAT Horio group

SAFIRE (Horio et al.,1998~)

(Non-linear spring)

t

t n t x

x F F m = n t F F m >

dt dx

x k F n n n n n h - D =

dt dx

x k F t t t t t h - D = n t F F m

km g = h 2 ( )

( ) 2 2

2

ln ln

p + = g

e e

w/wo Tangential Lubrication

w/wo Normal Lubrication

Soft Sphere Model with Cohesive Interactions

I-H

1998

Ash

Melting

Olefine

Polymerization

PP, PE

Kaneko et al.

1999

Scaling Law

for DEM

Computation

Kajikawa-Horio

2000～

Natural Phenomena

Catalytic Reactions

CHEMICAL REACTIONS

Structure of

Emulsion Phase

Kajikawa-Horio

2001

FUNDAMENTAL LARGE SCALE SIMULATION

OTHER

AGGLOMERATION COMBUSTION

Coal/Waste

Combustion

in FBC

Spray

Granulation/Coating

Agglomerating

Fluidization

FB of

Solid Bridging

Kuwagi-Horio

1999

Tangential

Lubrication

Effect

Kuwagi-Horio

2000

Particles w/

van der Waals

Interaction

Iwadate-Horio

1998

Single Char

Combustion

in FBC

Rong-Horio

1999

Parmanently

Wet FB

Mikami,Kamiya,

Horio

1998

FB w/

Immersed

Tubes

Rong-Horio

1999

FB

w/ Immersed

Tubes :

Pressure Effect

Rong-Horio

2000

Particle-Particle

Heat Transfer

Rong-Horio

1999

Fluidized Bed DEM

Started from

Dry-Noncohesive Bed

Tsuji et al. 1993

Scaling Law

for DEM

Computation

Kuwagi-Horio

2002～

Lubrication

Force Effect

Noda-Horio

2002

SAFIRE

Achievements

700 800 900 1000 1100 1200 1300 0

5

10

15

20

25

30

Nec

k d

iam

ete

r 2

x

Calculated from surface diffusion model

Steel shot :d p =200 m m, H 2 , 3600s

d p =200 m m d p =20 m m

Temperature [K]

ne

ck d

iam

ete

r, 2

x

neck

(b) 1123K (a) 923K

ne

ck d

iam

ete

r ,

2x

neck

10 m m

SEM images of necks after 3600s contact

Neck diameter determined from SEM images

after heat treatment in H2 atmosphere

Experimental Data of Solid Beidging Particles

(Mikami et al , 1996)

Sintering of

steel

particles in

FBR

Model for Solid Bridging Particles

1. Spring constant: Hooke type (k=800N/m)

Duration of collision: Hertz type

2. Neck growth: Kuczynski’s surface diffusion model

D = D exp (-E /RT)

D =5.2x10 m/s, E = 2.21x10 J/mol (T>1180K)

3. Neck breakage

s = neck neck nc A F

t = neck neck tc A F

7 1

3 4 gd 56

/

= t r D T k

x g S

B

neck

0,s

0,s

s s -2 5

Kuwagi-Horio 1999

Kuwagi-Horio

6 m m

r g = 10 m m

Steel shot

200 m m

neck

Cross section

Surface Roughness and Multi-point Contact Kuwagi-Horio 1999

Kuwagi-Horio

Kuwagi-Horio

t= 0.438s 0.750s 1.06s 1.38s 1.69s

2.00s 2.31s 2.63s 2.94s 3.25s

1273K, u = 0.26 m/s, Dt=0.313s

Snapshots of Solid Bridging Particles

without Surface Roughness

0

Kuwagi-Horio 1999

d =200mm, T=1273K, u =0.26m/s

(a) Smooth surface (b) 3 micro-contact points (c) 9 micro-contact points

Fig.7 Agglomerates (or "dead zones") grown on the wall (t = 1.21 s).

p 0

(Case 1) (Case 2) (Case 3)

Agglomerates (or “dead zones”) grown on the wall (t = 1.21 s).

Kuwagi-Horio 2000

Kuwag

i-Horio

Intermediate condition

Agglomerates Sampled at t = 1.21s

(a) Smooth surface (b) 3 micro-contact

points

(c) 9 micro-contact

points

dp=200mm, T=1273K, u =0.26m/s

Weakest sinteringcondition

Strongest sinteringcondition

0

Kuwagi-Horio 1999

Kuwagi-Horio

AGGLOMERATION

■ Agglomerating Fluidization

by Liquid Bridging

through surface diffusion through viscous sintering by solidified liquid bridge

by van der Waals Interaction

by Solid Bridging

Coulomb Interaction

■ Size Enlargement

by Spray Granulation (Spraying, Bridging, Drying)

by Binderless Granulation (PSG)

■ Clinker Formation in Combustors / Incinerators

in Polyolefine Reactors

in Fluidized Bed of Particles (Sintering of Fe, Si, etc.)

in Fluidized Bed CVD (Fines deposition and Sintering)

(Ash melting)

(Plastic melting)

Industrial Issues & DEM

CHEMICAL REACTORS

Heat and Mass Transfer gas-particle particle-particle

Heterogeneous Reactions

Homogeneous Reactions

Polymerization

Catalytic Cracking

Partial Combustion

(with a big gas volume increase)

COMBUSTION / INCINERATION

Boiler Tube Immersion Effect

Particle-to-Particle Heat Transfer

Char Combustion

Volatile Combustion (Gas Phase mixing / Reaction)

Combustor Simulation

(high velocity jet)

Industrial Issues & DEM

t=6.0 sec t=9.1 sec t=8.2 sec

Hot spot

Particle circulation (artificially generated by feeding gas nonuniformly from distributor nozzles)

Ethylene polymerization Number of particles=14000

u0=3 umf

Gas inlet temp.=293 K

3umf 3umf 3umf 2.5umf 2.5umf

9.3umf 15.7umf

2umf 2umf

Idemitsu Petrochemical Co.,Ltd. Tokyo University of Agriculture & Technology

T [K] 293

343

393

(20℃)

(120℃)

Kaneko et al. 1999

particle temp. particle velocity vector

t=9.1 sec t=8.2 sec

particle temp. particle velocity vector

Uniform gas feeding Nonuniform gas feeding

3umf 3umf 3umf

15.7umf

2umf 2umf : Upward motion

: Downward motion Stationary circulation

Stationary solid revolution helps

the formation of hot spots.



gQxu

yu

gTε

pnh

pnT

heat transfer coefficient (different for each particle)

external gas film

particle

fluid cell

yv

xv

Energy balance

gpp k/dh=Nu ggg,p k/c=Pr μgpgp /dvu=Re μρ-

( ) ( )g

g,pgi

gigQ

c

1=

x

Tu+

t

T

ρ∂

ε∂

∂

ε∂

( ) ( )gpp

p

g TThd

16=Q -

ε-

rcp

p Pw)RT

E(expk=R

Gas phase :

( ) ( )STThHR=dt

dTcV gpprp

p

pp,pp --Δ-ρ

Particle :

2

1

p3

1

RePr6.0+0.2=Nu (Ranz-Marshall equation)

Kaneko et al. (1999)

when l AB > 2r + d : no particle-particle heat conduction

Heat Transfer / Heat Transfer Characteristics of Individual Particles

Rong-Horio 1999 l AB r + d r + d

A B

particle gas film r

A B

0.4 nm

A B

radiation

convection

particle-thinned film-particle heat transfer

5.8%

45.5%

28.5%

51.3%

20.1%

28.5

%

contact point heat transfer

when l AB < 2r + d : particle-particle heat conduction

DEM simulation

van der Waals force: by

Dahneke model

+=

dd

xdHF

pa

vdW 124 2

δ

x

2

dp

δ

x

2

dp Ha: Hamaker constant [J]

dp: particle diameter [m]

X : overlap amount [m]

δ: distance of particles 0.4 nm

dp =1.0mm, rp =30kg/m3

(b) Ha=4.01×10 J

(a) Ha=0.39×10 J

Snapshots of Geldart C particles ( Iwadate & Horio, 1998 )

Iwadate-

Horio

Computation conditions

Particles

Number of particles nt 14000

Particle diameter dp 1.0×10-3

m

Restitution coefficient e 0.9

Friction coefficient μ 0.3

Spring constant k 800 N/m

Bed

Bed size 0.153×0.383 m

Types of distributor perforated plate

Gas velocity 0.156 m/s (=3Umf)

Initial temperature 343 K

Pressure 3.0 MPa

Numerical parameters

Number of fluid cells 41×105

Time step 1.30×10-5

s

Snapshots of temperature distribution in PP bed

(without van der Waals force)

0 7 150 7 150 7 15 ΔT [K]

Snapshots of temperature distribution in PP bed

(with van der Waals force)

Ha = 5×10-19 J

Ha = 5×10-20 J

0 7 150 7 150 7 15 ΔT [K]

Relative particle temperature rise in the bed at its left corner

( number indicates temperature rise above 343 K; t=8.4s )

0

0.001

0.002

0.003

0.004

0 0.001 0.002 0.003 0.004

Distance from the distributor [m]

Distance from the left wall [m]

7.9

7.9

7.9

7.8 7.7

7.8

5.3

5.9

7.7

7.8

7.9

7.87.9

7.9

7.9

0

0.001

0.002

0.003

0.004

0 0.001 0.002 0.003 0.004



3.5

3.8

3.64.2

3.8

3.6

3.63.8

3.8

3.25.0

4.7

3.7

3.6

0

0.001

0.002

0.003

0.004

0 0.001 0.002 0.003 0.004



4.0

4.5

3.9

3.03.9

4.0

4.4

4.8

4.7

4.4

4.2

3.9

4.6

4.6

4.9

(c) Ha = 5×10-19 J (b) Ha = 5×10-20 J

with van der Waals force without van der Waals force (a)

0

3

6

9

12

15

0 10 20 30 40Re

lati

ve P

arti

cle

Temp

erat

ure

[⊿K]

Time [s]

(b)

(a)

(c) the maximum temperature

change of a particle in bed

with time

Experimental

determination of

repulsion force

Polymerization in a Micro Reactor

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 10 20 30 40 50 60

Diameter[mm]

Time [min]

The micro reactor PP growth with time

Optical microscope images

5 min 10 min 15 min 20 min 30 min 60 min 1 min 0 min 2 min

Catalyst TiCl3

Pressure 0.98 MPa

Temperature 343 K

Reactor stage φ14 mm

Force-displacement meter

1

1

2

34

7

5

8

6

10

9

1

1

2

34

7

5

8

6

10

9

1: material testing machine’s

stage

2: electric balance

3: table

4: polypropylene particle

5: aluminum rod

6: capacitance change

7: micro meter

8: nano-stage

9: x-y stage

10: cross-head of material

testing machine

0

0.002

0.004

0.006

0.008

0.01

0 5 10 15 20 25 30 35 40

Repulsion Force [N]

Time [s]

without van der Waals Force

Extent of maximum repulsion force in collisions;

k=800N/m

0

0.002

0.004

0.006

0.008

0.01

0 5 10 15 20 25 30 35 40

Repulsion Force [N]

Time [s]

0

0.002

0.004

0.006

0.008

0.01

0 5 10 15 20 25 30 35 40

Repulsion Force [N]

Time [s]

Ha = 5×10-20 J Ha = 5×10-19 J

0

0.02

0.04

0.06

0.08

0.1

0 5 10 15 20 25 30 35 40

Repulsion Force [N]

Time [s]

k=80000N/m DEM results

F k0.5 (Hooke model)

k=80000N/m F~0.01N

800 0.0025

100 0.001 ?

in SOFT SPHERE MODEL for particle collision

Hook’s linear spring and a dashpot

Herz’ spring and a dashpot

/dtdxxkF nnnnn h-D=

])/[(ln)(ln ,)(2 2225.0 p+gg=h eekmp

5.035.0 ]6/)[()/( nppnpc kdkmt rp=p=

5.0max ]/)6/[(/ nppp kdvdx rp=D

dtdxxF nnnn h-D= 2/3

5/122max )/(44.2/94.2 vmvxt pc =D=

5/2225/22max ]/)1([993.0/)8/5(/ Evdvmdx pppp -r==D

Force, deformation and collision time

=Edp1/2/3(1-2)

Repeated force-displacement characteristics of

a polypropylene particle

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 642μm

1st10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 642μm

1st

2nd

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 642μm

1st

2nd

3rd3rd

FE-SEM images: whole grain and its surface

k ~100 N/m

dp=642mm

Repeated force-displacement characteristics

of a polypropylene particle

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 597μm

1st10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 597μm

1st

2nd

2nd

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 597μm

1st

2nd2nd

3rd

3rd


k ~100 N/m Fdp0.5x1.5 (Hertzean spring)

x

dp=597mm

Repeated force-displacement

characteristics of a polypropylene particle (maximum load from first cycle)

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 487μm

1st

1st

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 487μm

1st

2nd

1st

2nd

10-6

10-5

10-4

10-3

10-8 10-7 10-6 10-5

Force [N]

Displacement [m]

dp = 487μm

1st

2nd

3rd

3rd

1st

2nd


Fdp0.5x1.5 (Hertzean spring)

x

dp=487mm

FE-SEM image of the top particle after

three times pressing

Conclusion

DEM simulation and direct experimental

determination of repulsion force with

particle deformation were conducted.

Potential temperature increase with

cohesion interaction predicted by DEM

Potential particle surface morphology

change by collision from observation

Hertz model stands OK but in some

cases F x3 was observed