MODELING AND SIMULATION IN A RISER CIRCULATING FLUIDIZED BED REACTOR

Berpun, Rungthip*; Limtrakul, Sunun; Vatanatham, Terdthai

Department of Chemical Engineering, Faculty of Engineering, Kasetsart University,

50 Paholyothin Rd., Chatuchak, Bangkok 10900, Thailand. Tel./Fax: +662-942-8444 Ext.1232

E-mail : berpun@yahoo.com

ABSTRACT The behavior of gas-solid mixing in the riser circulating fluidized beds (CFBs) is performed by using Discrete Element Method (DEM). DEM is used to predict the particle motion in the riser reactor. The force acting on the particles consists of the particle contact force and the force exerted by the surrounding fluid. The motion of individual particles is specified by the Newton second’s law of motion. Combining the equations of gas motion and particle motion, the particle velocities, gas velocities, pressure and void fraction can be obtained. Using the simulation model, the effects of gas velocities and solid circulation rates on the gas-particles mixing were investigated. The simulation results showed that particle velocity profiles are almost flat, except in the area near the wall. The particle velocity increase with increasing gas velocity but it dose not significantly change with increasing solid circulation rate. The solid holdup at all heights are uniform in the core region but very high near the wall. It is decreasing with increasing gas velocity and increasing with increasing solid circulation rate. Keywords Simulation, Circulating fluidized bed, Discrete Element Method, Fluidization, Riser 1. INTRODUCTION

Gas/solid fluidization processes in CFBs have been widely applied in industry, including coal combustion and catalytic cracking of petroleum. The gas-solid mixing in a circulating fluidized bed is more uniform than a simple fluidized bed. Behavior of gas-solid in a CFB depends on several parameters and reactor geometry. However, studies on CFB at high fluidization velocity are comparatively scarce. Therefore the hydrodynamics of high fluidization velocity is not well understood. Because of the complexity of gas-solid flow behavior in CFB, it still needs more information to successfully design and scale up of the systems. Apart from experimental

investigation, in recent years, a rapid growth of computer simulation of gas-solid two-phase flow appears [1-6]. Most of these simulations are based on the two-fluid model which assumes the particle as a continuum phase. In this study, more realistic model, Discrete Element Method (DEM) is used to predict the particle motion in the riser reactor. In DEM, the collision force acting on particle is calculated using the analogy of spring, dash-pot, and friction slider [7-11]. Thus the model depends on the parameters of stiffness, dissipation and friction properties of the particles. This collision force is coupled with drag force exerted by surround fluid to total force acting on the particle. Positions of individual particle are tracked by the solution of Newton’s equation of motion. The continuum phase assumption for solids phase is not needed. Navier-Stokes equation is applied for gas motion [12]. It is solved by the Simi-Implicit Method for Pressure-Linked Equation (SIMPLE) to provide the local averaged gas velocities [13].

2. MATHEMATICAL MODELING

The mathematical model consists of equation of particle motion and equation of gas motion.

2.1 Particle Motion The particle movement is evaluated by the Newton’s law of motion. Total force acting on particle includes the effects of gravitational force, particle contact force, and fluid drag force. Individual particle has two types of motion, translational and rotational motions which can be written as:

gmFas

vv

v += (1)

IT

s

vv =α (2)

where the linear acceleration of particle ( is a function o he sum of normal forces acting on the particle

)f t

sav

( )Fv

. The angular acceleration of a particle

( )sαv depends on the torque, Tv

, caused by the

The model estimates the contact forces using the same concepts of spring, dash-pot, and friction slider. Thus the model depends on the parameters of stiffness, dissipation, and friction coefficients which can be obtained from the physical properties of the particles. The estimated values of each parameter were shown in the previous work [14]. The normal and tangential contact forces as shown in Fig.1(b) and (c) are given as:

tangential contact force and moment of inertia of the particles, I .

v= v

r0v

= ωv

ω

fv

=

)

d

The new velocity and position after a time step t∆ are given by

(3) tav sss ∆+ 00vv

vv (4) tvr s ∆+= 0

vv( ) ijijrijnnijncnij nnvkf vvvv

.ηδ −−=v

(7) vv

t∆+ 00 αω (5)

where vv is a linear velocity vector, rv is a position vector, and

v is an angular velocity vector.

Subscript 0 denotes the old value, and subscript s refers to the particle.

sijttijtctij vkf ηδ −−=

(8)

where nijδv

and tijδv

are displacements of particle caused by the normal force and tangential force respectively, rijvv is the velocity vector of particle i

relative to particle j, ijnv is the unit vector directed

from the center of particle i to that of particle j,

and are the normal and tangential stiffness

coefficient of the spring respectively;

nk

tk

nη and tη are the normal and tangential damping coefficient respectively, and vsij

v is the slip velocity which is

The forces acting on h article consist of the particle contact force

t e p( )Cfv

and the force exerted

by the surrounding fluid ( )Dfv

.

DC fFvv

+ (6) In the DEM, the particles are assumed not to be deformed during the contacting but overlap with each other shown in Fig.1(a). The particle contact forces between two particles, which compose of normal ( cnf

v, and tangential ( )ctf

v components

can be predicted by the simple model as shown in Fig.1(b) and (c). It was first proposed by Cundall and Strack in 1979 [8].

( ) nrnnvvv jiprijrijsijvvvvvvvv ×++−= ωω).( (9)

where is the radius of particle, pr iωv and jωv are angular velocities of particle i and j respectively.

spring slide

ash-pot

j

i

i-Particle

nijδ

j-Particle

dash-pot

If the following relation is satisfied

cnijfctij ffv

µ> (10)

particle i slides and the tangential force is given by

spring

i

j

(a)

(b)

(c)

sij

sijcnijfctij v

vff v

vv

µ−= (11)

where fµ is the friction coefficient.

The contact force could be obtained from both contacting of particle to particle and particle to wall. If the adjacent particle j is the wall of bed,

jvv and jωv are zero.

2.2 Fluid Flow The motion of fluid is described by the equation of continuity and the equation of momentum with the local mean variables. The fluid is assumed to be incompressible. The equations are written as follows:

Figure 1. Models of contact forces (a) Displacement of particles in contact

(b) Normal force (c) Tangential force

Equation of Continuity

( ) 0. =∇+∂∂ v

tvεε

(12)

Inlet gas

Feeding

Downer ----Riser

Storage tank ---

Outlet gas

Riser height = 5.5 m

Equation of momentum conservation

( ) ( ) sifpvv

tv

+∇

−=∇+∂

∂ρεεε vv

v. (13)

vwhere ε is the void fraction, v is the velocity vector of fluid, ρ is the fluid density, p is the

pressure of fluid, and sifv

is the fluid drag force exerted to the particles, which is given by:

( )vuf psivvv

−=ρβ

(14)

where puv is the particle velocity vector averaged

in a cell. The coefficient β depends on the void fraction given by [15]:

( ) ( )[ ] ( 8.0Re75.1115012 ≤+−−

= εεε

)εµβpd

(15)

( ) ( )8.0Re143 7.2

2 >−

= − εεεµ

βp

D dC (16)

where is the particle diameter,pd µ is the fluid

viscosity, and C is the drag coefficient on each single particle given by:

D

Figure 2. Pneumatic transportation system

( ) ( )000,1ReRe

Re15.0124 687.0

≤+

=DC (17)

Table1 Simulation Conditions and Particle Properties. ( )000,1Re43.0 >=DC (18)

vv

Properties Value

Riser Size

Bed height, H

5.5 m Bed diameter, D

0.0762 m

Physical Properties of Particle

Particle diameter, pd

1.5 mm

Particle density, sρ

2,620 kg/m3

Solid circulation rate, G s

50-400 kg/m2s

Coefficient of damping, η

0.9

Coefficient of friction, µ 0.3

Coefficient of stiffness, k

800 N/m

Fluid Properties and Condition Gas density, ρ

1.20 kg/m3

Gas viscosity, µ 1.82x10-5 kg/(m.s)

Gas velocity, gU

8-11 m/s

Time step, t∆

0.00003 sec.

where µ

ρε pp dvu −=Re (19)

The equation of fluid motion was solved simultaneously with the equation of particle motion. The numerical method, SIMPLE, developed by Patankar [13], was used. 3. PNEUMATIC TRANSPORTATION SYSTEM FOR SIMULATION A typical pneumatic transportation system is shown in Fig.2, which consists of a storage tank, a cylindrical downer column, a feeding valve, and a riser column of 0.0762m diameter. The simulation was carried out in this system with a riser column height of 5.5 m from gas distributor to top region. 4. SIMULATION CONDITIONS The conditions and the physical properties of the particles for the simulation are shown in Table 1.

5. RESULTS AND DISCUSSION 5.1 Particles Movement in the Riser Reactor Fig.3 shows the particle movement in the riser reactor. The reactor can be divided into three regions, the bottom region, the developed region, and the top region. The particles flow pattern in the riser reactor is shown in Fig.3(a). It can be seen that the particles are non-uniform at the bottom region due to the entrance effect. At the developed and top region the particles are more uniform and the particle movement is closed to the plug flow except in the area near the wall. 5.2 Effect of Gas Velocity and Solid Circulation Rate on Radial Profiles of Particle Velocity and Solid Holdup

Fig.4(a) shows the particle velocity along the radial position in the riser reactor. The profiles of particle velocity at the bottom regions are non-uniform. In the developed and top regions, all of particle velocity profiles are almost flat, except in the area near the wall where the particle velocity is lower. It was found that the particle velocity increases with increasing axial position. The particle velocity increases with increasing U but it dose not

significantly change with increasing G . g

s

Fig.4(b) shows the solid holdup along the radial position. In overall, the profiles of solid holdup at all heights are non-uniform. The solid holdup is uniform in the core region but very high near the wall. The core-annulus profiles were found at all heights. The solid distribution is dilute in the core region and dense near the wall. In the developed

region, increasing U slightly decreases solid

holdup. On the other hand, increasing G increases solid holdup.

g

s

5.3 Effect of Gas Velocity and Solid Circulation Rate on Axial Solid Holdup Distribution The axial solid holdup distributions along the column height with variations of U and are

shown in Fig5. At constant , solids holdup in the riser decreases with increasing U due to increasing of particle velocity as shown in Fig.5(a). At a given U , the solid holdup in the riser

increases with increasing G as shown in Fig.5(b) due to higher solid to gas ratio.

g sG

sG

s

g

g

At very high U , the solids holdup in the riser is very low and the solid holdup is relative uniform along the height. On the other hand, at lower U , the particles move upwards with lower velocities. Therefore with relative lower velocity, some particles trend to accumulate and form dense phase leading to less uniform along the height.

g

g

As G is increased, a condition is reached in which

is insufficient to entrain all the solids entering into the riser. Solid accumulates at the bottom of the riser so that a dense phase is formed. It can be shown that at high G , the particle distribution is less uniform in the riser reactor.

s

gU

s

5.500 m

4.125 m

2.750 m

1.375 m

0.0 m 0 1

H=4.81 m

18 m/s III--

H=4.38 m

H=3.01 m 18 m/s II--

H=2.58 m

H=1.11 m

9 m/s I--

H=0.68 m

r/R

t=0.2s t=0.6s t=0.8s t=1.2s Section Vector Plot

(a) (b)

Figure 3. Simulation result in riser reactor at Ug=9.0m/s, Gs=70 kg/m2s. (a) Variation of 3D-flow pattern with time, (b) 2D-flow pattern and solid velocity vector plot at 1.2s, in the bottom region (I), developed region(II), and top region(III).

Gs = 70 kg/m2s Ug = 9 m/s Gs = 70 kg/m2s Ug = 9 m/s

4

6

8

10

12

0.00 0.25 0.50 0.75 1.00

4

6

8

10

12

8.5 9.010.0

Ug [m/s]

4

6

8

10

12

84152188

Gs [kg/m2s]

0.00 0.25 0.50 0.75 1.00 0.00

0.02

0.04

0.06

0.08

0.00 0.25 0.50 0.75 1.00

0.00

0.02

0.04

0.06

0.080.00

0.02

0.04

0.06

0.08

8.5 9.010.0

Ug [m/s]

0.00 0.25 0.50 0.75 1.00

84152188

Gs [m/s]

H = 4.6 m H = 2.8 m H = 0.9 m

Axi

al P

artic

le V

eloc

ity [m

/s]

Solid

Hol

dup

[-]

Radial Position, r/R [-] Radial Position, r/R [-]

(a) (b) Figure 4. Simulation result. Top row is in top region at H=4.6m, middle row is in developed region at H=2.8m, and bottom row is in bottom region at H=0.9m, (a) Radial profile of particle velocity at various U g

and , (b) Radial profile of solid holdup at various U and GsG g s

0 . 0

1 . 0

2 . 0

3 . 0

4 . 0

5 . 0

6 . 0

0 0 . 0 1 0 . 0 2 0.0 3

7.0 m/s 8.5 m/s 9.0 m/s1 0.0 m/s

G s = 7 0 k g/m2s

U g [m/s]

7.0

8.5

9.01 0.0

0 0.0 2 0.0 4 0 . 0 6

8 2 1 5 02 0 5

U g =9 m / s

G s [k g / m 2 s ]

Hei

ght [

m]

Average Solid holdup [-] Average Solid holdup [-]

(a) (b)Figure 5. (a) Solid holdup along the riser axis at various height for different U , (b) Solid holdup along the

riser axis at various height for different .

g

sG 5.4 Effect of Gas Velocity and Solid Circulation Rate on Axial Profile of Pressure In the riser, the observed incremental pressure gradient along the riser height is exponential. The axial pressure gradient profiles along the riser height of CFB for different U and G are shown in Fig.6. The pressure gradient shown is the difference between pressure at various height and exit pressure. It can be seen that at the bottom, pressure gradient is high and slowly decreases to zero at the reference point (exit point).

g s

Fig.6(a) shows the pressure gradient profile for given . It can be seen that the pressure gradient increases with decreasing U . For given

shown in Fig.6(b), the pressure gradient increases with increasing of .

sG

g

gU

sG 6. CONCLUSIONS The discrete simulation of gas-solid flow is a good tool to investigate gas-solid flow behavior in the riser reactor. In simulation, the gas velocity and solid circulation rate are varied. The results indicate that the radial profiles of solid holdup and particle velocity in a riser reactor are nonuniform in the area near the wall and more uniform at the core region. The particle velocity increase with increasing gas velocity but it dose not significantly change with increasing solid circulation rate. Solid holdup decreases with increasing gas velocity and increasing with increases solid circulation rate.

Gs = 70 kg/m2s Ug = 9 m/s

0 . 0

1 . 0

2 . 0

3 . 0

4 . 0

5 . 0

6 . 0

0 1 0 0 0 2 0 0 0 3 0 0 0

เอ็กซโพเนนี

( 8.5)เอ็กซโพเนนี

( 9.0)เอ็กซโพเนนี

(10

.0)

U g [ m / s ] 8 . 5 9 . 0 1 . 0 0

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 1000 2000 3000

เอ็กซโพเนนเชียล ( 8.5)เอ็กซโพเนนเชียล ( 9.0)เอ็กซโพเนนเชียล (10.0)

Gs [kg/m2s]

84152188

Hei

ght [

m]

Pressure, P-Pexit [Pa] Pressure, P-Pexit [Pa]

(a) (b) Figure 6. (a) Pressure profile along the riser axis at various height for different U , (b) Pressure profile along

the riser axis at various height for different G .

g

s

7. ACKNOWLEDGEMENTS Financial supports from Thailand Research Fund (TRF) under Research Career Development Project, Kasetsart University Research and Development Institute (KURDI), CHE-ADB Graduate Research and Education Development Program in Chemical Engineering at Kasetsart University, and Kasetsart University Graduate School are acknowledged. We are pleased to acknowledge Prof. Dr. Yutaka Tsuji and Assist. Prof. Dr. Toshihiro Kawaguchi for their collaboration. 8. NOTATIONS ar particle acceleration vector rg gravity acceleration vector vF sum of force acting on the particle rT torque I moment of inertia of the particle r

Cf contact force r

Df fluid drag force k stiffness of particle vr particle position displacement

vv velocity of particle m mass of particle rn unit vector ru particle velocity rv gas velocity

pr radius of particle

pd diameter of particle p pressure of fluid t time

sG solid circulation rate

gv inlet gas velocity Greek letters rα angular acceleration vector vδ displacement of particles in contact η damping coefficient µ coefficient of viscous dissipation ρ density of gas rω rotational velocity ε void fraction

Subscritpts i consideration particle j adjacent particle n normal direction t tangential direction 9. REFERENCES [1] Deming, M., Jack R.E., Andrey, V.K., and Ravi K.S., Three-dimensional numerical simulation of a circulating fluidized bed reactor for multi-pollutant control, Chemical Engineering Science, 59(20), pp 4279-4289, (2004). [2] Kim, G.H., Tron, S., and Bjorn, H.H., A three-dimensional simulation of gas/particle flow and ozone decomposition in the riser of a circulating fluidized bed, Chemical Engineering Science, In Press, Corrected Proof, Available online 15 September, (2004). [3] Hashem, S., Rahmat, S.G., and Navid, M., .Modeling the acceleration zone in the riser of circulating fluidized beds,Powder Technology, 142(2-3), pp 129-135, (2004). [4] Ning, Y., Wei, W., Wei, G., and Jinghai L., CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient, Chemical Engineering Journal, 96(1-3), pp 71-80, (2003). [5] Luben, C.G., and Fernando, E.M., Numerical study on the influence of various physical parameters over the gas–solid two-phase flow in the 2D riser of a circulating fluidized bed, Powder Technology, 132(2-3), pp 216-225, (2003). [6] Ulrike, L. and Joachim, W., Flow phenomena in the exit zone of a circulating fluidized bed, Chemical Engineering and Processing, 41(9), pp 771-783, (2002).

[7] Tsuji, Y., Kawaguchi, T., and Tanaka, T., Discrete Particle Simulation of Two-Dimensional Fluidized Bed, Powder Technology, 77, pp 79-87, (1993). [8] Cundall, P.A. and Strack, O.D.L., A Discrete Numerical Model for Granular Assemblies, Geotechnique, 29, pp 47-65, (1979). [9] Auggurawirote, K., Modeling and Simulation of Particle Segregation in a Fluidized Bed (M.Eng. Thesis, Kasetsart University, 2000). [10] Chaleamwattanatai, A., Modeling and Simulation of Particle Mixing in a Fluidized Bed (M.Eng. Thesis, Kasetsart University, 2000). [11] Chaisermtawan, P., Modeling and Simulation of Plug Flow of Particle in a Pipe (M.Eng. Thesis, Kasetsart University, 2001). [12] Anderson, T.B. and Jackson, R., A Fluid Mechanical Description of Fluidized Beds, Industrial and Engineering Chemistry Fundamentals, 6, pp 527, (1967). [13] Patankar, S.V., Numerical heat transfer and fluid flow (Hemispher, New York, 1980). [14] Tsuji, Y., Tanaka, T., and Ishida, T., Lagrangian Numerical Simulation of Plug Flow of Cohesionless Particles in a Horizontal Pipe, Powder Technology, 71, pp 239-250, (1992). [15] Ergun, S., Fluid flow through packed columns, Chemical Engineering Progress, 48, pp 89-94, (1952). [16] Aijie, Y., Pärssinen, J. H., and Jing-Xu, Z., Flow properties in the bottom and exit regions of a high-flux circulating fluidized bed riser, Powder Technology, 131(2-3), pp 256-263, (2003). [17] Juray, D.W., Guy, B.M., and Geraldine, J.H., The effects of abrupt T-outlets in a riser: 3D simulation using the kinetic theory of granular flow, Chemical Engineering Science, 58(3-6), pp 877-885, (2003).