Proceedings of the 6th International Conference on Process Systems Engineering (PSE ASIA)

25 - 27 June 2013, Kuala Lumpur.

Computational Fluid Dynamic and Population

Balance Modeling of Industrial Fluidized Bed

Polymerization Reactor

V. Akbari, T. N. G. Borhani, H. Kazemi, M. K. A Hamid

Process System Engineering Center (PROSPECT), Faculty of Chemical Engineering,

Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor Bahru, Johor, Malaysia

Abstract

This work aims at developing a transient computational fluid dynamic (CFD) coupled

with population balance (CFD-PBM) model for investigating the grid sensitivity, on one

hand and predicting the flow behaviour, on the other hand in the industrial linear low

density polyethylene (LLDPE) gas-solid fluidized bed reactor. The Eulerian-Eulerian

model coupled with the DQMOM (direct quadrature method of moment) is used to

describe flow behaviour and the particle size distribution. The pressure drop and bed

height agree well with those obtained from industrial reactor. The results reveal that the

various grid number effects on the flow behaviour. Smaller grid size lead to increase

pressure drop and decrease the bed height. The model predicts the Well-Mixing along

the fluidized bed reactor.

Keywords: Gas-Solid Fluidized Bed Reactor; Euler-Euler Model; Population Balance.

1. Introduction

Low pressure gas-phase polymerization is widely used for polymerization of olefin in

fluidized bed reactors. Because of the complex flow behaviour that is characteristic of

poly-disperse gas-solid systems (e.g., mixing/segregation, aggregation, breakage and

growth of the particles), designing and scaling-up of these systems is still a challenging

task (Detamore et al., 2001; Yan et al., 2012).

A population balance is a powerful tool to investigate the impact of particle size

distribution (PSD) on the hydrodynamics of the fluidized bed reactors, particularly

when coupled with computational fluid dynamics (CFD) method. Fan and co-workers

(Fan, 2004) suggested CFD-PBM coupled model to simulate polydisperse gas-solid

fluidized bed reactors. Recently, The QMOM and DQMOM were widely used to solve

the PBE, and they were implemented in a Eulerian-Eulerian model to simulate

polydisperse gas-solid FB (Ahmadzadeh et al., 2008; Yan, et al., 2012).

The objective of this work is to test and validate a Eulerian-Eulerian model to solve gas-

solid flow based on the Direct Quadrature Method of Moments (DQMOM) approach.

The effect of grid sensitivity and flow field are simulated.

2. Model Description

2.1 Eulerian-Eulerian CFD model

746 Akbari et al.

The multi-fluid continuum model assumes that different phases behave as

interpenetration continuum and the instantaneous variables are the average over the

region that is large compared to a particle space but much smaller than the flow domain.

Each particulate phase is characterized by the unique diameter, density and other

features. The continuity and momentum equations for gas and solid phases are:

(1)

(2)

(3)

Where is the Phase (solid and gas) stress-strain tensor, is an

interaction between phases and is the pressure that shared by all phases. is the

momentum exchange coefficient between phases, and is the gravity vector.

(4)

and are the shear and bulk viscosity of phase .

The Eulerian-Eulerian two-fluid model requires closure equations to describe the

rheology of the solid phase. Due to collisions between particles in dense gas-solid

systems, the concepts from gas kinetic theory can be employed to describe the motion

of particles. The geometry used in this work, representing an operational British

Petroleum (BP) reactor, is cylindrical with a bulb at the top, about 30m height and 5m

wide as shown in Figure 2. The detailed setting in the software (Ansys Fluent 14) are

listed in Table 1, 2 and 3.

2.2 The population balance model and DQMOM

The PBE is a balance equation for the population of the particles and it can be derived

in the same way, as many other balance or continuity equations in the continuum

mechanics are derived. A general form of PBE can be expressed as:

(5)

The first term on the left hand is the transient term, second term is the convective term

and the third term is growth term. And the terms on the right hand are the source term

describing aggregation and breakage, respectively. is the number density

function with particle diameter (L) as the internal coordinate. For simplicity, the growth,

aggregation and breakage phenomena were not considered.

The advantage of DQMOM is that it is directly applicable to the population balance

equation with more than one internal coordinate. This method has been described

Computational Fluid Dynamic and Population Balance Modeling of Industrial Fluidized Bed

Polymerization Reactor 747

extensively by some researchers (Fan, et al., 2004).This discussion is limited here to a

brief review of the equations.

DQMOM approach also uses number density function and quadrature

approximation, and each node (different solid phase) represents the solid phase

properties. So in the Eulerian-Eulerian multi-fluid model each solid phase has its own

momentum balance.

(6)

Where is the weight of the delta function centered on the character length

Table 2. Boundary condition and model parameters

Description Values

Granular viscosity Gidaspow (Chen et al., 2011)

Granular bulk viscosity Lun et al(Chen, et al., 2011)

Frictional viscosity Schaeffer(Chen, et al., 2011)

Restitution coefficient 0.8

Granular temperature Algebric

Diffusion coefficient Syamlal(Chen, et al., 2011)

Drag law Gidaspow (Chen, et al., 2011)

Inlet boundary condition Velocity inlet

Outlet boundary condition

Wall boundary condition

Pressure outlet

No slip for gas, free slip for

solid phase

Initial bed height (m) 10

Initial solid volume fraction 0.5

Operating pressure (Bar) 24

Time step (s) 0.01

Superficial gas velocity (m/s) 0.5

Table 1. Physical properties of gas and solid phases and operation conditions.

800-1100µm 850 20 1.2

3. Simulation condition and CFD modeling strategy

In order to investigate the potentials and limitations of the CFD modeling, the CFD-

PBM with the Eulerian-Eulerian approach was used to study the PSD in this work. The

DQMOM was used to take into account the PSD, whereas the KTGF was employed to

close momentum balance equation for the solid phase. The phase coupled SIMPLE

algorithm was used to couple pressure and velocity. In addition, Workbench Ansys 14

was used to generate the 2D geometry and grids .The comparison was made with the

same initial PSD and thus the initial conditions have been calculated by using the same

set of moments (see Table 2 and 3).

748 Akbari et al.

Table 3. The ith moments of number density function

Moment value

m0 9.50E+08

m1 7.50E-04

m2 1.14E-06

m3 1.74E-09

m4 2.68E-12

m5 4.14E-15

m6 6.41E-18

4. Results and Discussion

Grid sensitivity was carried out initially to match the industrial operation condition, and

the result indicated that a total amount of 52007 nodes were adequate to predict the

hydrodynamic in the FBR (see Figure1 and Table 4) .Figure 1a shows that all the

fluidization bed height at three different nodes reached to a quasi-steady condition at

70s. By increasing the grid numbers, bed height decrease whereas the pressure drop

increases as reported by(Chalermsinsuwan, 2011).From the Figure 1 and Table 4, the

mesh used for reference case seems to give precise enough results for a reasonable

computing time.

Table 4. Grid Analysis

Nodes

Pressure

Drop

Bed

height

%pressure drop

error

%bed height

error

Case1 21464 0.59943 21.55 1.95 7.2

Case2 52007 0.59616 20.15 0.36 0.75

Case3 102343 0.6168 19.5 4.89 2.5

As it was done in the reference case (Case 2), the comparison with industrial data can

perform for pressure drop and bed height which is quite close to the CFD values. On the

other hand, the nodes affect the global behavior of the flow. Figure 2 gives the solid

volume fraction distribution at different times . According to Figure 2, one knows that

the fluidization bed heights increases with the fluidization phenomena. During the start-

up of fluidization, the large particle vorticity in the bottom corners acts as a source of

voidage.

In polydisperse systems small particles tend to fill the coarse interparticle voids that this

feature lead to more homogeneous mixing and reduce the void fraction along the bed

(Figure 2). With the exception of two regions, one located above the gas distributor due

to influence of gas inlet and the other at the top of the bed that fine and coarse particle is

normally found (see Figure 4). Solid volume fraction through the bed height is

constantly close the average value (Formisani, 2001). At an intermediate height in the

bed, the upward solid flow from the bottom section encountered the downward flow

from the top section of the bed in the wall region. Both solid flows merged and the

particle velocity changed towards the bed centre (h=15m). This indicates that in the

intermediate height in the bed (10-15 m), the bubbles moved towards the bed centre and

the upward velocity of solids in the centre increased (Figure 3).

Computational Fluid Dynamic and Population Balance Modeling of Industrial Fluidized Bed

Polymerization Reactor 749

a)

b)

Figure 1. Grid sensitivity analysis (a) pressure drop vs.t, (b) bed height vs. time.

5s 20s 40s 60s 100s

Figure 2. The counters of solid volume fraction at different times

10

12

14

16

18

20

22

0 20 40 60 80 100

Bed

Hei

ght

(m)

Time (s)

Nodes= 52007 Nodes=21464 Nodes=102343 Normal bed height

0.3

0.5

0.7

0.9

0 20 40 60 80 100

pre

ssu

re d

rop

(b

ar)

Time (s)

Nodes= 52007 Nodes= 21464 Nodes= 102343

min pressure drop max pressure drop

750 Akbari et al.

Figure3. Vector of particle velocity Figure 4. Radial particle velocity

at different heights, at t=100 s at different heights, t=100 s

5. Conclusion

A two-dimensional CFD-PBM model incorporating the kinetic theory of granular flow

was developed to validate the hydrodynamic of gas-solid flow in the LLDPE industrial

fluidized bed reactor. A comprehensive CFD-PBM model evaluation by comparing

industrial operation condition was investigated for various grid sensitivity. It was found

that fine mesh lead to increase the pressure drop and reduce the bed height. The

predicted pressure drop and bed height were good agreement with the industrial data.

The model also predicts the flow behaviour and particle velocity along the fluidized bed

reactor. In polydisperse mixing of particle is more homogeneous.

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Yan, W.-C., Luo, Z.-H., Lu, Y.-H. and Chen, X.-D. (2012). A CFD-PBM-PMLM integrated

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0

1

2

3

4

5

0.00E+00 2.50E+00 5.00E+00

velo

city

(m

/s)

Bed Diameter (m) y=1m y=20m