Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 3.4.2 - Bed Expansion and Particle Mixing and Segregation in Multi-Fluid Model of Bi-disperse Gas Fluidized Beds
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 Material Information
Title: 3.4.2 - Bed Expansion and Particle Mixing and Segregation in Multi-Fluid Model of Bi-disperse Gas Fluidized Beds Computational Techniques for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Olaofe, O.
Bokkers, A.
van Sint Annaland, M.
van der Hoef, M.
Kuipers, H.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: multi-fluid model
fluidized bed
bed expansion
particle mixing
segregation
 Notes
Abstract: Generally, it is necessary to understand the mixing and segregation phenomena in gas-fluidized beds for the optimal design, operation and scale-up of their processes. To gain more insight into these phenomena, bed expansion and particle mixing and segregation rates in bi-disperse, freely-bubbling, fluidized beds have been studied using a newly developed Multi-Fluid Model (van Sint Annaland, 2009), a continuum model in which both gas and solid phases are described as interpenetrating continua with the solid phase rheology described by the kinetic theory of granular flow. In the resulting closure equations in the model, the rheologic properties of the particle mixture are explicitly described in terms of the particle mixture velocity and granular temperature, and the diffusion velocity and granular temperature of the individual particle phases are computed from the mixture properties, a major advantage with respect to the numerical implementation. Simulation results from the new MFM have been compared with Two-Fluid Model (TFM) and the experiments conducted by Goldschmidt et al. (2003).
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Source Institution: University of Florida
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Resource Identifier: 342-Olaofe-ICMF2010.pdf

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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Multi-Fluid Model Simulation of Bed Expansion, Particle Mixing and Segregation in
Bi-disperse Gas Fluidized Beds

Olasaju Olaofe, Albert Bokkers, Martin van Sint Annaland, Martin van der Hoef
and Hans Kuipers

Fundamentals of Chemical Reaction Engineering Department
University of Twente, Enschede, 7500 AE, The Netherlands
o.o.olaofe@utwente.nl, m.vansintannaland @utwente.nl, m.a.vanderhoef@utwente.nl andj.a.m.kuipers @utwente.nl


Keywords: Multi-Fluid Model, fluidized bed, bed expansion, particle mixing, segregation



Abstract

Generally, it is necessary to understand the mixing and segregation phenomena in gas-fluidized beds for the optimal design,
operation and scale-up of their processes. To gain more insight into these phenomena, bed expansion and particle mixing and
segregation rates in bi-disperse, freely-bubbling, fluidized beds have been studied using a newly developed Multi-Fluid Model
(van Sint Annaland, 2009), a continuum model in which both gas and solid phases are described as interpenetrating continue
with the solid phase rheology described by the kinetic theory of granular flow. In the resulting closure equations in the model,
the rheologic properties of the particle mixture are explicitly described in terms of the particle mixture velocity and granular
temperature, and the diffusion velocity and granular temperature of the individual particle phases are computed from the
mixture properties, a major advantage with respect to the numerical implementation. Simulation results from the new MFM
have been compared with Two-Fluid Model (TFM) and the experiments conducted by Goldschmidt et al. (2003).


Nomenclature

c particle velocity (m/s)
C fluctuating component of the particle velocity
(m/s)
DPM discrete particle/element model
e normal coefficient of restitution (-)
g gravitational acceleration (in s-
h height (m)
I unit tensor (-)
J diffusion flux (kg/(m2s))
m mass (kg)
n number of particles per unit volume (m-3)
Ncells number of Eulerian cells (-)
NP number of components (-)
Npart number of particles in bed (-)
P pressure (Pa)
q granular energy flux (kg/(ms))
t time (s)
u continuum velocity (m/s)
u, ensemble average particle velocity (m/s)
Ubg background fluidization velocity (m/s)
xsmal volume fraction of small particles (-)

Greek letters
P inter-phase momentum transfer coefficient
(kg/m3s)
Zp collisional source
e volume fraction of the gas phase (-)
e, volume fraction of the solid phase, species n
only (-)


es volume fraction of the solid phase (-)
e max maximum particle fraction for radial
distribution function (-)
7 dissipation of granular energy due to inelastic
particle-particle collisions (kg mi, 3))
0 granular temperature (kg m2/s2 or m2/s2)
0 collisional flux
p density (kg/m3)
7 stress tensor (Pa)


Subscripts
g
n p
P r
s S


;as
)article specie
)article
olid


Introduction

Gas-fluidized beds are essential units in the operations of
many process plants. In many industrial poly-disperse
gas-solid fluidized bed applications, particle mixing and
segregation play important roles. For example, in gas-phase
olefin polymerization processes, minimal contamination of
larger product particles, collected at the bed bottom, by
smaller particles is desired. In these beds, the particle
distribution changes from an initially mixed state to one in
which the heavier particles migrate to the bottom of the bed
and the smaller particles to the top. The dynamics of the
bubbles in these beds play an important role. Bubbles cause
segregation when heavier particles fall preferentially
through disturbed regions behind the bubbles. Conversely,









mixing, which is desirable for better heat and mass transfer
characteristics, is enhanced by the rising bubbles.

A reliable model of the hydrodynamics of poly-disperse
fluidized beds is essential to the design, development and
optimization of many of these processes. Such models
should give more insight into the mechanisms and rate at
which particle segregation occurs. They should, in addition,
be able to describe quantitatively the sensitive transition
between particle mixing and segregation. Several attempts
have been made to predict the dynamics of a bi-disperse gas
fluidized bed using models for two-phase flow (for example:
Goldschmidt et al., 2001; Huilin et al., 2003a,b), however, a
quantitative description of mixing and segregation rates in
such beds have not yet been reported.

The Multi Fluid Model (MFM), a continuum approach, is the
most promising model for industrial-scale simulations, due
to the computational limitations of the (in principle) more
reliable and detailed Discrete Element Model (DEM). In the
MFM, which is basically an extension of the Two Fluid
Model (TFM) consisting of only one particulate phase, both
the gas and particulate phases are treated as interpenetrating
continue, with the rheology of the particulate phases
described by closures derived from the Kinetic Theory of
Granular Flow (KTGF).

In this work, results from simulations with the newly
developed MFM are compared with the more established
TFM (van der Hoef et al., 2006). Also, results from the
MFM of a 2D bi-disperse bed are compared with digital
image analysis experiments by Goldschmidt et al. (2003).


New Multi-Fluid Model (MFM)

In van Sint Annaland et al. (2009), a new set of closure
equations for the rheologic properties of dense gas-particle
flows was presented. Closure equations for a
multi-component mixture of slightly inelastic spheres were
derived to third-order accuracy using a Chapman-Enskog
solution procedure of successive approximations. In the
derivation, the particle velocity distribution of all species
was assumed to be nearly Maxwellian around the particle
mixture velocity with the particle mixture granular
temperature. In the theory, differences in the mean velocities
and granular temperatures of the particle species result from
higher-order perturbation functions. A special effort was
made to ensure thermodynamic consistency between radial
distribution function and the chemical potential of a
hard-sphere particle specie appearing in the diffusion driving
force when applying the revised Enskog theory.

In the resulting closure equations, the rheologic properties of
the particle mixture are explicitly described in terms of the
particle mixture velocity and granular temperature, and the
diffusion velocity and granular temperature of the individual
particle phases are computed from the mixture properties.
This is a major advantage in the numerical implementation
of the model.

Table 1 gives the main micro balance equations of the MFM.
Full details on the model equations are reported in van Sint


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Annaland et al. (2009).

Table 1: Conservation equations for MFM.
Species continuity equation:
+a(E V)+ 7.[J7 +E, = 0 (TI-1)
at


where = ,p,(C7)
Mixture continuity equation:
) + V ( )= 0
at
Mixture momentum equation:
a( + V. (+EpUa )= -E VP
at
NP
VP n +1gig iT)+ Pp
n11


(T1-2)


(T1-3)


where p +


NPn( M NP +
n=-1 p=1


Mixture granular temperature equation:
3 [( +V (n)V. )=-( = j:V
+2 o m ] I k Ji),


NP /3
-V., C 3 -- y,
I '"


(T1-4)


S NP ( 1 -- NP / 1 N
where NP= N + C0 -M N)i
n1m2 \ -- 2
andn

P NP NP /
n-p-1 2 ll



Comparison of MFM with TFM

Since the MFM is basically an extension of the TFM, the
closure equations should become identical to those of the
TFM in the case the physical properties of all particle classes
are the same. Trial simulations were carried out, with the
MFM, to simulate a 2D mono-disperse bed in the bi-disperse
mode, that is, the bed was set to consist of two particulate
phases of exactly the same size and density. Results from
these simulations were compared with simulations of similar
systems using the traditional TFM.

The main parameters used in the simulations are
summarized in the Table 2. The boundary conditions for
both models were essentially the same in all simulations. A
no slip wall condition was applied for the gas phase and a
free slip wall for the particle phase on the left and right
boundary walls, while no slip for gas and particle phases was
applied to the front and rear walls. Wang et al. (2010)
reported that the wall conditions have negligible effect on
bed dynamics. At the bed bottom, the pressure and velocity
of the gas are fixed, and at the top the pressure was specified
as atmospheric. In the MFM, the initial solid fractions were
set for a static bed height corresponding to the height used in
the experiment. Simulations using the MFM and TFM do
not require initial mixing of the particles by fluidizing at
high velocity since in the continuum description of the
particulate phase, a fully mixed state can be specified as
initial condition. In order to mimic the gas inlet flow
conditions in the experiments, a random fluctuation of 5%






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


was applied to the inlet gas velocity.

The bed-average granular temperatures and particle height
predicted by the simulations are shown in Figures 1-3.

Table 2: Configuration of pseudo-bidisperse and bidisperse
beds in continuum-based models.

MFM and TFM
Cells in x-direction 45 (system width: 0.15 m)
Cells in y-direction -
Cells in z-direction 120 (system height: 0.40 m)


Background velocity (m/s)
Coefficient of restitution
Maximum solid fraction
Drag model

Time step (s)
Gas


1.05, 1.20
0.97, 1.00
0.60
Ergun (1952), Wen
and Yu (1966)
1.0 x 105
air


0018

0016

- 0014

E 0012
a.
E oOl
E 001
F_
- 0008

r 0006
0C 0004

0002


TFM granular temperature
- MFM granular temperature
-TFM bed height
MFM bed height


* |.' .-A,,-v A '"A


0 5 Time (s0


015




01 E
2
00
"I
005 g
mos


15 20


Figure 1: Bed-average granular temperature and particle
height (e=0.97, eax =0.60, Ubg=1.20 m/s).


MFM
Diameter Density Volume
(mm) (kg/m3) fraction
Phase 1 1.5 2526 25%
Phase 2 1.5 2526 75%

TFM
Diameter Density Volume
(mm) (kg/m3) fraction
Phase 1 1.5 2526 100%



Granular Temperature

In the Kinetic Theory of Granular Flow employed by van
Sint Annaland et al. (2009), the bed can be characterized by
the fluctuating energy associated with the random particle
motion, the granular temperature, which is defined here as


O=n1-
where C is the random fluctuating velocity, which is the
actual particle velocity minus the local mean velocity.

A close inspection of Figure 1 shows that the granular
temperature profiles in both models are similar. Both the
intensity and frequency of the fluctuations are comparable
with a striking similarity for the first two seconds of the
simulation. Note that the profile for the two particulate
phases in the MFM simulations were the same, hence only
one phase is indicated here. In Figure 2, where the restitution
coefficient is set to 1.0, the fluctuation in the granular
temperature of the TFM is slightly more pronounced though
both models exhibit a somewhat smooth profile, resulting
from homogeneous fluidization (Goldschmidt et al., 2002),
at virtually the same level after 4 s. When the background
velocity is changed to 1.05 m/s (Figure 3) both models give
similar results.


0.016

0.014

^ 0.012

0.01
Q.


2 0.008

0.006

, 0.004

0.002


0 5 10
Time (s)


015




01 E

0)

005
005 0


15 20
15 20


Figure 2: Bed-average granular temperature and particle
height (e=1.00, eax=0.60, Ubg=1.20 m/s).


0.012


0.01

"E 0.008
C.
E
5 0.006

c 0.004

0.002

0


015




01 E


05
"o
005 (S


0 5 10 15 20
Time (s)

Figure 3: Bed-average granular temperature and particle
height (e=0.97, eax =0.60, Ubg=1.05 m/s).


TFM granular temperature
--MFM granular temperature
TFM bed height
MFM bed height
-----------------






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Bed Expansion Dynamics

In fluidized beds, the bed expansion dynamics is
characterized by the average height of all particles in the
bed:


Npart

part
hP bed art


Ncells
Cs,khk
k
Ncells
y es,k


Clearly, the profiles in Figure 1 are very similar in intensity
and frequency of fluctuations. Thus, the performance of
MFM in comparison with the TFM is satisfactory. Figures
1-3 show that the predictions of bed expansion in the MFM
remain very similar to the TFM in level, frequency and
intensity of fluctuations even when changes are made to the
normal restitution coefficient and background velocity.


Bi-disperse Simulation

The next step is to simulate a true bi-disperse system with
the MFM, and compare with laboratory experiments. A
bi-disperse bed consisting of 1.5 mm and 2.5 mm particles
was simulated with the MFM and the results were compared
with the digital image analysis experiments reported by
Goldschmidt et al. (2003). Details of the bed, which were set
to mimic the experiments conducted by Goldschmidt et al.
(2003), are given in Table 3. Snapshots of the bed in the
MFM and the experiments are shown in Figure 4.

In accordance with the experiments, a layer of flotsam was
formed on top of the mixed bed and a layer of jetsam at the
bottom of the fluidized bed. The model thus correctly
predicts particle segregation, resulting from 'sedimentation'
of the heavier particles from the mixture. Note that the MFM
with closures by Manger (1996) did not predict the
formation of a layer of small particles on top of the bed.

Table 3: Bed configuration for bi-disperse bed in
Multi-Fluid Model.

Cells in x-direction 45 (system width: 0.15 m)
Cells in y-direction
Cells in z-direction 120 (system height: 0.40 m)
Background velocity (m/s) 1.20
Coefficient of restitution 0.97
Maximum solid fraction 0.60
Drag model Ergun, Wen and Yu
Time step (s) 1.0 x 105
Initial bed height (m) 0.15
Gas air


Diameter Density
(mm) (kg/m3)


Volume
fraction


3 s
Figure 4: Top:


0.9

0.8
0.7

0.6

0.4


0.3

02
0.1


ls
10 s 15 s 30 s


experiments by Goldschmidt at al. (2003);


middle: void fractions; bottom: mass fraction of small
particles. Left: void fraction scale; right: mass fraction
scale.

Segregation rates: comparison of MFM results with DEM
and experiments

For a model to be valid, not only must it predict adequately
the bubbling characteristics and porosity distribution in a
multi-component system but also the degree and trend of
mixing and segregation. A key parameter for evaluating the
mixing and segregation phenomena in a fluidized
bi-disperse bed is the rate of segregation. Here, the relative
segregation, s, for a binary mixture is defined as:


S-1
S= -

where:

S, h = sa/ and S .
(i1 )


2 -x
S smaX


and (h) is the average height of particles of type i, and
s,,m is the volume fraction of the small particles.

It is demonstrated in Figure 5 that the new MFM predicts the
evolution of the relative segregation in time much better than
the MFM using closures derived by Manger (1996).
Goldschmidt et al. (2001) and Huilin et al. (2003a,b) also
reported that MFMs using closures of Manger (1996)
substantially over-predicted the particle segregation rates in
freely bubbling bi-disperse fluidized beds. By contrast, the
new MFM seems to even underestimate the rate of
segregation compared with the experiments: after 15 s of
simulation, the relative segregation remains almost constant.
This is most probably a consequence of the neglect of the
frictional stresses associated with long-term
multiple-particle contacts in the current implementation of
the MFM. Without these frictional stresses, the mobility of
the emulsion phase is largely over-predicted. This leads to a
continuous back-mixing of the segregated flotsam and


Phase 1 1.5 2526 25%
Phase 2 2.5 2526 75%









jetsam due to the macro-scale circulation pattern induced by
the bubbles in the fluidized bed. Moreover, this assumption
was supported by DEM simulations (Figure 6) in which the
effect of particle-particle, and particle-wall friction was
explored.


70.6

0.5

0.4

- 0.3

0.2

0.1 -

0.0
0 5 10 15
Time [s]
Figure 5: Relative segregation comp
MFM and with the MFM using cl
Manger (1996) for case with 25%, 1.5
75%, 2.5 mm glass beads.


0.7

0.6

S0.5

| 0.4
0)
S0.3

0.2

0.1

0.0


0 5 10 15
Time [s]


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

motion of particles, is a key quantity with respect to mixing,
segregation and attrition phenomena of particulate systems.
It is therefore important to be able to measure and examine
this quantity. Hitherto, there has been no report of
experimental results on granular temperatures of bi-disperse
beds in the open literature. For the bi-disperse simulation
in this work, the predicted granular temperatures, defined
here by Equation (4), are shown in Figure 7.


where is the mass of the particle.
where mI is the mass of the particle.


o o Clearly the average fluctuation in the kinetic energy of the
o T + small particles is consistently larger than those of the large
S -, particles, a consequence of the appreciable difference in the
'- .. drag on both particles. The level of fluctuation in the motion
of the small particles appears to increase slightly over time
relative to the level of fluctuation in the motion of the large
particles. This can be explained by the increase in average
mobility of the small particles as they segregate. In the MFM,
20 25 30 the bottom part of the fluidized bed will not de-fluidize since
the frictional stresses in the current implementation of the
uted with base case MFM is neglected. Also, the fluctuation in the granular
osures obtained by temperature of the small particles is more intense.
mm glass beads and
)nx 10-8


20 25 30


Figure 6: Evolution of the relative segregation in time for
the base case DEM simulation, the DEM simulation
without friction between the particles and the experiments
performed by Goldschmidt et al. (2003).


It clearly demonstrates that hardly any segregation is
predicted by the DEM without friction. Also, the use of drag
correlations, which do not take into account the effect of
bidispersity, may be of influence in the MFM and DEM
simulations. In this respect, it would be useful to include the
correction for bidispersity recently derived by van der Hoef
et al. (2005), which will be subject of future research.

Granular temperature in bi-disperse bed

In the bi-disperse bed, the granular temperature, the
fluctuating kinetic energy associated with the random


E


r 1.2
S 1.4


r 1.0

T_ 0.8

E 0.6

0.4

0.2


5 10 15 20 25 30
Time [s]
Figure 7: Bed averaged granular temperature as a function
of time computed with the new MFM.


Conclusions

A novel multi-fluid model, based on the kinetic theory of
granular flow for multi-component mixtures, is compared
with a more established two-fluid model. Both models
gave fairly the same trend and values of average particle
height. It was demonstrated that both models also give
similar granular temperatures when the maximum packing
fraction in the bed is 0.60. However, the precise role of e-n"
needs to be further elucidated.

Particle segregation rates in a bi-disperse freely bubbling
fluidized bed, computed with the new multi-fluid model, are
compared with well-defined digital image analysis
experiments conducted by Goldschmidt et al. (2003). The


- small particles (d = 1.5 mm)
large particles (dp = 2.5 mm)




/ 4




H- r i ii i
UI '









experiments were carried out in a pseudo-2D fluidized bed
of 15 cm wide, filled with different mixtures of 1.5 and 2.5
mm particles whose collision parameters were accurately
known. The particle segregation rates observed with the new
MFM, compared to other MFMs in use, are in much better
agreement with the experiments. Moreover, the formation of
a flotsam and jetsam layer was predicted correctly. However,
there is an overestimation of the mobility of the emulsion
phase because the frictional stresses associated with
long-term multiple-particle contacts are neglected. The
calculated average granular temperatures of the particulate
phases gave trends consistent with the dynamics of the
particles in the experiments.

Adequate implementation of frictional stresses in the
framework of the kinetic theory of granular flow is
necessary to improve the continuum models for
poly-disperse systems. Also, non-intrusive laboratory
experiments are required to provide granular temperature
data, a key parameter in the dynamics of poly-disperse
systems, for validating the MFM.


Acknowledgements

The authors would like to thank The Netherlands
Organisation for Scientific Research (NWO) and the Dutch
Polymer Institute (DPI) for the financial support of this
work.


References

Ergun, S. Fluid flow through packed columns. Chemical
Engineering Progress, Vol. 48, 89 (1952)

Goldschmidt, M.J.V, Kuipers, J.A.M. & van Swaaij, W.PM.
Segregation in dense gas-fluidized beds: validation of a
multi-fluid continuum model with non- intrusive digital
image analysis measurements. In: Kwauk, M., Li, J., Yang,
W.C. (Eds.), Fluidization X, People's Republic of China,
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Goldschmidt, M.J.V, Beetstra, R. & Kuipers, J.A.M.
Hydrodynamic modelling of dense gas-fluidized beds:
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hard-sphere discrete particle simulations. Chemical
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Goldschmidt, M.J.V, Link, J.M., Mellema, S. & Kuipers,
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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