Paper was presented at 2nd ECOREP held at Lyon, France. The content is related to DEM simulation for fluidized beds.

1. 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

2. Background
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.

3. In their simulation, however, the cohesive force was not
taken into account.
Background (continued)
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.

4. 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

5. Normal and tangential component of Fcollision
and Fwall
Fn = k nD x n - h dx n
n
dt
Ft = m Fn x t Ft > m Fn
x t
Ft = k tD x - h dx t
 m Fn
t t Ft
dt
h = 2g g = ( ln e ) 2
km
( ln e ) 2 + p 2
SAFIRE (Horio et al.,1998~)
Rupture joint h c
Attractive force Fc Surface/bridge force
(Non-linear spring)
kn Normal dumping h n w/wo Normal Lubrication
Normal elasticity
No tension joint Tangential dumping h t
Tangential elasticity k t
SAFIRE is an extended Tsuji-Tanaka model
developed by TUAT Horio group
Friction slider m
w/wo Tangential Lubrication
Soft Sphere Model with Cohesive Interactions

6. COMBUSTION Spray Agglomerating AGGLOMERATION
Granulation/Coating Fluidization
FB
w/ Immersed Ash
Tubes : Melting
FB of Particles w/
Pressure Effect I-H
Solid Bridging van der Waals
Rong-Horio 1998 Tangential
2000 FB w/ Interaction
Kuwagi-Horio Lubrication
Immersed Iwadate-Horio Effect
1999
Coal/Waste Tubes 1998
Kuwagi-Horio
Combustion Parmanently
Rong-Horio 2000
in FBC Wet FB
1999
Mikami,Kamiya,
Fluidized Bed DEM Horio
Started from 1998
Particle-Particle Dry-Noncohesive Bed
Single Char Heat Transfer
Tsuji et al. 1993
Combustion Rong-Horio Natural Phenomena
in FBC 1999
Rong-Horio
OTHER
1999 Lubrication
Force Effect
SAFIRE Olefine Scaling Law
Achievements Polymerization Noda-Horio for DEM Scaling Law
for DEM
PP, PE Structure of
2002 Computation
Computation
Kaneko et al. Emulsion Phase Kajikawa-Horio
2000～ Kuwagi-Horio
1999 2002～
Kajikawa-Horio
Catalytic Reactions
2001
CHEMICAL REACTIONS FUNDAMENTAL LARGE SCALE SIMULATION

7. Sintering of 10 m m
neck
neck
x
2x
,
steel
neck diameter, 2
neck diameter
particles in
FBR (a) 923K (b) 1123K
SEM images of necks after 3600s contact
Steel shot :d p=200 m m, H 2 , 3600s
30 from
Calculated
25 surface diffusion model
20
Neck diameter 2x
15
10 d p=200 m m
d p=20 m m
5
0
700 800 900 1000 1100 1200 1300
Temperature [K]
Neck diameter determined from SEM images
after heat treatment in H2 atmosphere
Experimental Data of Solid Beidging Particles
(Mikami et al , 1996)

8. 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
1/ 7
4
56gd 3
x neck = DS rg t
kBT
Ds = D0,s exp (-Es /RT)
-2 5
D0,s =5.2x10 m/s, E =2.21x10 J/mol (T>1180K)
3. Neck breakage
Fnc = s neck  Aneck
Ftc = t neck  Aneck Kuwagi-Horio
Kuwagi-Horio 1999

9. Kuwagi-Horio
Steel shot Cross section 6mm
200mm
rg = 10mm
neck
Surface Roughness and Multi-point Contact
Kuwagi-Horio 1999

10. 1273K, u 0 = 0.26 m/s, Dt=0.313s
Kuwagi-Horio
t= 0.438s 0.750s 1.06s 1.38s 1.69s
2.00s 2.31s 2.63s 2.94s 3.25s
Snapshots of Solid Bridging Particles
without Surface Roughness
Kuwagi-Horio 1999

11. dp =200mm, T=1273K, u0 =0.26m/s
Kuwag
i-Horio
(a) Smooth surface (b) 3 micro-contact points (c) 9 micro-contact points
(Case 1) (Case 2) (Case 3)
Agglomerates (or “dead "dead zones") grown on the wallthe1.21 s). (t = 1.21 s).
Fig.7 Agglomerates (or zones”) grown on (t = wall
Kuwagi-Horio 2000

12. Intermediate condition Weakest sintering Strongest sintering
condition condition
(a) Smooth surface
(b) 3 micro-contact (c) 9 micro-contact
points points
Kuwagi-Horio d p =200mm, T=1273K, u 0=0.26m/s
Agglomerates Sampled at t = 1.21s
Kuwagi-Horio 1999

13. AGGLOMERATION
Industrial Issues & DEM
■ Agglomerating Fluidization
by Liquid Bridging
by van der Waals Interaction
by Solid Bridging through surface diffusion
through viscous sintering
by solidified liquid bridge
Coulomb Interaction
■ Size Enlargement
by Spray Granulation (Spraying, Bridging, Drying)
by Binderless Granulation (PSG)
■ Clinker Formation
in Combustors / Incinerators (Ash melting)
in Polyolefine Reactors (Plastic melting)
in Fluidized Bed of Particles (Sintering of Fe, Si, etc.)
in Fluidized Bed CVD (Fines deposition and Sintering)

14. CHEMICAL REACTORS
Industrial Issues & DEM
Heat and Mass Transfer gas-particle
particle-particle
Heterogeneous Reactions
Homogeneous Reactions
Polymerization
Catalytic Cracking (with a big gas volume increase)
Partial Combustion (high velocity jet)
COMBUSTION / INCINERATION
Boiler Tube Immersion Effect
Particle-to-Particle Heat Transfer
Char Combustion
Volatile Combustion (Gas Phase mixing / Reaction)
Combustor Simulation

15. Particle circulation Kaneko et al. 1999
(artificially generated by feeding gas nonuniformly from distributor nozzles)
t=9.1 sec t=6.0 sec t=8.2 sec
393
(120℃)
343
293
T [K] (20℃) 2.5umf 2.5umf
2umf 2umf
3umf 3umf 3umf
9.3umf
Ethylene polymerization 15.7umf
Number of particles=14000
Gas inlet temp.=293 K Hot spot
u0=3 umf
Tokyo University of Agriculture & Technology Idemitsu Petrochemical Co.,Ltd.

16. Uniform gas feeding Nonuniform gas feeding
particle temp. particle velocity particle temp. particle velocity
vector vector
t=9.1 sec t=8.2 sec
: Upward motion 2umf 2umf
3umf 3umf 3umf
: Downward motion 15.7umf
Stationary
circulation
Stationary solid revolution helps
the formation of hot spots.
Tokyo University of Agriculture & Technology Idemitsu Petrochemical Co.,Ltd.

17. Kaneko et al. (1999)
Energy balance uy fluid cell
Gas phase :
ε( ) ∂εu T )
∂ Tg ( i g 1 particle
+ = Q
∂t ∂i
x ρcp,g g
g
Particle : vy ε Tg ux
dTp Qg
Vpcp,pρp
dt
H (
= Rp (- Δ r ) - hp Tp - Tg S ) vx
Tpn
6(1- ε)
Qg =
dp
(
hp Tp - Tg ) heat transfer hpn external gas film
E coefficient
Rp = k exp ( ) w cPr (different for each particle)
RTp
1 1
Nu = 2.0 + 0.6 Pr Rep 3 2 (Ranz-Marshall equation)
Nu = hpdp / kg Pr = cp,gμ / kg
g Rep = u - v ρdp / μ
g g
Tokyo University of Agriculture & Technology Idemitsu Petrochemical Co.,Ltd.

18. Heat Transfer / Heat Transfer Characteristics of Individual Particles
r+d l AB r+d
Rong-Horio 1999
A B
r
particle gas film
when l AB > 2r + d : no particle-particle heat conduction
contact point heat transfer
A B
5.8%
0.4 nm
radiation
20.1%
51.3%
28.5 45.5%
%
A B
convection
28.5%
particle-thinned film-particle heat transfer
when l AB < 2r + d : particle-particle heat conduction

19. DEM simulation

20. van der Waals force: by
Dahneke model
Had p  x
FvdW = 2 
1+ 
24d  d 
δ
dp Ha: Hamaker constant [J]
2 dp: particle diameter [m]
X : overlap amount [m]
δ: distance of particles 0.4 nm
x

21. Iwadate- dp =1.0mm, rp =30kg/m3
Horio
(a) Ha=0.39×10 J
(b) Ha=4.01×10 J
Snapshots of Geldart C particles ( Iwadate & Horio, 1998 )

22. 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

23. 0 7 15 ΔT [K]
Snapshots of temperature distribution in PP bed
(without van der Waals force)

24. Ha = 5×10-20 J
Ha = 5×10-19 J
0 7 15 ΔT [K]
Snapshots of temperature distribution in PP bed
(with van der Waals force)

25. Relative Particle Temperature [⊿K]
15
12
9
6 (c)
(b)
the maximum temperature
3 (a)
change of a particle in bed
0
0 10 20
Time [s]
30 40 with time
Distance from the distributor [m]
Distance from the distributor [m]
Distance from the distributor [m]
0.004 0.004 0.004
3.9 3.9 3.0 3.7 3.5 7.8 7.7 5.3
3.6
4.2 3.8 5.9
0.003 0.003 0.003
4.6 4.0 3.9 3.6 7.9 7.8 7.8
3.6 3.8
4.4
0.002 0.002 0.002 7.7
4.6 4.4 4.0 4.7 3.8 3.8 7.9 7.9 7.9
0.001 4.7 0.001
0.001
4.9 4.8 4.5 5.0 3.2 4.2 3.6 7.9 7.9 7.9 7.8
0 0 0
0 0.001 0.002 0.003 0.004 0 0.001 0.002 0.003 0.004 0 0.001 0.002 0.003 0.004
Distance from the left wall [m] Distance from the left wall [m] Distance from the left wall [m]
(a) without van der Waals force (b) Ha = 5×10-20 J (c) Ha = 5×10-19 J
with van der Waals force
Relative particle temperature rise in the bed at its left corner
( number indicates temperature rise above 343 K; t=8.4s )

26. Experimental
determination of
repulsion force

27. Catalyst TiCl3 0.35
Pressure 0.98 MPa 0.3
Diameter[mm]
Temperature 343 K 0.25
Reactor stage φ14 mm 0.2
0.15
0.1
0.05
0
0 10 20 30 40 50 60
Time [min]
PP growth with time
The micro reactor
0 min 1 min 2 min 5 min 10 min 15 min 20 min 30 min 60 min
Optical microscope images
Polymerization in a Micro Reactor

28. 1: material testing machine’s
10 stage
2: electric balance
9 3: table
7
8 4: polypropylene particle
5: aluminum rod
6 5 6: capacitance change
1
4 3 7: micro meter
2 8: nano-stage
9: x-y stage
1 10: cross-head of material
testing machine
Force-displacement meter

29. Repulsion Force [N] 0.01 0.01 0.01
Repulsion Force [N]
Repulsion Force [N]
0.008 0.008 0.008
0.006 0.006 0.006
0.004 0.004 0.004
0.002 0.002 0.002
0 0 0
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40
Time [s] Time [s]
Time [s]
without van der Waals Force Ha = 5×10-20 J Ha = 5×10-19 J
Extent of maximum repulsion force in collisions;
k=800N/m F  k0.5 (Hooke model)
0.1
k=80000N/m F~0.01N
Repulsion Force [N]
0.08
0.06 800 0.0025
0.04 100 0.001 ?
0.02
0
0 5 10 15 20 25 30 35 40
k=80000N/m DEM results
Time [s]

30. Force, deformation and collision time
in SOFT SPHERE MODEL for particle collision
Hook’s linear spring and a dashpot
Fn = kn Dxn - hn dx n /dt
Dx max / d p = v[(p / 6)r p d p / kn ]0.5
t c = p(m p / kn ) 0.5 = [(pd p ) 3 r p / 6kn ]0.5
h = 2g(km p ) 0.5 , g  (ln e ) 2 /[(lne ) 2 + p2 ]
Herz’ spring and a dashpot
Fn = Dxn / 2 - hn dxn dt
3
=Edp1/2/3(1-2)
Dx max / d p = (5m pv 2 / 8) 2 / 5 / d p = 0.993 r pv 2 (1 -  2 ) / E ]2 / 5
[
tc = 2.94Dx max / v = 2.44(m p /  2v )1/ 5
2

31. k ~100 N/m
10-3 10-3 10-3
dp = 642μm dp = 642μm dp = 642μm
10-4 10-4 10-4 3rd
Force [N]
Force [N]
Force [N]
3rd
2nd
10-5 10-5 10-5
2nd
1st 1st
1st -6
10 -6 10 10-6
-8 -7 -6 -5 10 -8 10 -7 10-6 10-5 10 -8 10 -7 10-6 10-5
10 10 10 10
Displacement [m] Displacement [m] Displacement [m]
dp=642mm
FE-SEM images: whole grain and its surface
Repeated force-displacement characteristics of
a polypropylene particle

32. k ~100 N/m Fdp0.5x1.5 (Hertzean spring)
10 -3
10-3 10-3
dp = 597μm dp = 597μm dp = 597μm 3rd
10-4 10-4 10-4
Force [N]
Force [N]
Force [N]
2nd
3rd
10-5 10-5 10-5
2nd 2nd
2nd
1st 1st 1st
10-6 10-6 10-6
10 -8 10-7
10 -6
10 -5
10 -8 10-7
10 -6
10 -5
10 -8 10 -7 10-6 10-5
Displacement [m] Displacement [m] Displacement [m]
x
dp=597mm
FE-SEM images: whole grain and its surface
Repeated force-displacement characteristics
of a polypropylene particle

33. Fdp0.5x1.5 (Hertzean spring)
10 -3 10-3 10-3
dp = 487μm dp = 487μm dp = 487μm
10 -4 10-4 10-4 3rd
Force [N]
Force [N]
Force [N]
3rd
2nd
10 -5 1st 10-5 10-5 2nd
1st 1st
2nd 2nd
1st 1st 1st
10 -6 10-6 10-6
10-8 10 -7
10 -6
10 -5 10 -8 10-7 -6
10 10 -5
10-8 10-7 10-6 10 -5
Displacement [m] Displacement [m] Displacement [m]
x
dp=487mm
FE-SEM images: whole grain and its surface
Repeated force-displacement
characteristics of a polypropylene particle
(maximum load from first cycle)

34. FE-SEM image of the top particle after
three times pressing

35. 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