CFD Modeling of the Hydrodynamics and Reaction Kinetics of FCC

Drag models of Gidaspow and Syamlal and O'Brien overestimated the drag force for the FCC particles and predicted a greater bed expansion in comparison...
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Ind. Eng. Chem. Res. 2005, 44, 9818-9827

CFD Modeling of the Hydrodynamics and Reaction Kinetics of FCC Fluidized-Bed Reactors Sebastian Zimmermann and Fariborz Taghipour* Department of Chemical & Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, B.C., V6T 1Z3 Canada

The hydrodynamics and reaction kinetics of gas-solid fluidized beds containing fluid catalytic cracking (FCC) particles were simulated using computational fluid dynamics (CFD). Drag models of Gidaspow and Syamlal and O’Brien overestimated the drag force for the FCC particles and predicted a greater bed expansion in comparison to the experimental data. The modified Syamlal-O’Brien drag model based on the minimum fluidization conditions of the FCC particles predicted the expected bubbling fluidization behavior and simulated a bed expansion in agreement with the experimental data. The overall trend of the time-averaged voidage through the bubbling bed was simulated reasonably well at different superficial gas velocities. An additional transport equation with a kinetic term for ozone decomposition was included in the Eulerian-granular multiphase model. The computed conversions of ozone with various catalyst inventories were higher than those measured experimentally. The deviation could in part be the result of the effect of a gas distributor, which was not considered in the CFD simulation. Introduction Fluidized-bed reactors are found in a wide range of applications in various industrial operations, including chemical, petroleum, mineral, and pharmaceutical industries. Understanding the hydrodynamics of fluidizedbed reactors is essential for choosing the correct operating parameters for the appropriate fluidization regime. Computational fluid dynamics (CFD) offers a new approach to understanding the complex phenomena that occur between the gas phase and the particles. The Lagrangian and Eulerian models have been applied to the CFD modeling of multiphase systems. The Lagrangian model solves the Newtonian equations of motion for each individual particle in the gas-solid system along with a collision model to handle the energy dissipation caused by nonideal particle-particle interactions. The large number of equations involved makes this model a very time-consuming computational method for simulating fluidized beds of high particle concentration. The Eulerian model treats all different phases mathematically as continuous and fully interpenetrating. Generalized Navier-Stokes equations are employed for the interacting continua. Constitutive equations are necessary to close the governing relations and to describe the rheology of the solid phase. The kinetic theory of granular flow, introduced by Jenkins and Savage,1 proposes a granular temperature that is proportional to the kinetic energy of the fluctuating component of the particles’ velocity. To model solid particles as a separate fluid phase, physical parameters such as the solids pressure and viscosity can be obtained from granular theory. The highly reduced number of equations solved during each iteration generates a timesaving advantage in comparison to the Lagrangian model, as confirmed by van Wachem et al.2 Modeling of the hydrodynamics of gas-solid multiphase systems * To whom correspondence should be addressed. Tel.: +1604-822-1902. Fax: +1-604-822-5407. E-mail: fariborz@ chml.ubc.ca.

with Eulerian models using different CFD codes has shown the suitability of this approach for modeling fluidized-bed reactors.3-6 An understanding of the dominant forces in a fluidized bed is key to the successful simulation of the hydrodynamics. From an analysis of the momentum balance in a gas-solid system, van Wachem et al.2 concluded that gravity and drag were the dominant forces for the majority of flows, except for very dense flow, for which the frictional stresses became more important. Several drag laws have been developed to express the interactions between the particles and the gas.7-9 Taghipour et al.10 simulated a 2D fluidized bed of glass beads classified as Geldart B particles using the drag laws of Wen and Yu, Syamlal and O’Brien, and Gidaspow. No significant difference in the fluidization was observed with the various drag laws. McKeen and Pugsley11 used the MFIX code with the SyamlalO’Brien drag law and experienced a high overprediction of the hydrodynamics for their system of small fluid catalytic cracking (FCC) particles (Geldart A). McKeen and Pugsley’s11 approach to reduce the drag was an empirical method using a constant scale factor. Syamlal and O’Brien12 introduced a method to modify their drag law based on the minimum fluidization velocity of the particles. This model was reported to be reasonable for finding suitable values for the drag adjustment, when applied to a bubbling fluidized bed.13 In addition to the drag force, the fluidization behavior can be influenced by inelastic interparticle collisions resulting in kinetic energy dissipation. The restitution coefficient represents the elasticity of particle collisions and ranges from fully inelastic (e ) 0) to fully elastic (e ) 1). The restitution coefficients of some particles have been measured experimentally.14 Mostoufi and Chaouki15 measured velocity changes of FCC particles with a radioactive particle tracking (RPT) system in a fluidized bed and estimated a restitution coefficient of 0.63. Gidaspow et al.16 calculated the restitution coefficient from a relation between the Reynolds stress and the

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granular temperature and proposed a value of 0.99 for FCC particles. This large difference in results shows the difficulty in determining the restitution coefficient for small particles such as FCC catalysts. The influence of the restitution coefficient on a multiphase system was studied by Goldschmidt et al.17 The authors reported that the Geldart B particles became closely packed in the densest regions of the bed when the collisions became less ideal (with lower restitution coefficients), resulting in sharper porosity contours and larger bubbles. McKeen and Pugsley11 observed a different response of no significant changes in the bubbling-bed behavior and the bed expansion for FCC Geldart A particles at restitution coefficients from 0.5 to 0.99. Fluidized beds are often used to carry out chemical reactions involving solid particles as catalysts. The overall conversion in a fluidized-bed reactor is a function of bed hydrodynamics and reaction kinetics. The integration of chemical reactions in a CFD model of bed hydrodynamics enables the simulation of overall reactor performance. The decomposition of ozone has been used in CFD simulations for modeling reactor kinetics.13,18 Although this reaction has no commercial application, the simple first-order kinetics and the large amount of published experimental data19,20 make it suitable for CFD model evaluation. Syamlal and O’Brien13 performed simulations of ozone decomposition in a laboratory-scale bubbling fluidized bed (particles with diameters of 117 µm and a density of 2650 kg/m3) using the CFD code MFIX. The experimental data reported by Fryer and Potter19 were used for model evaluation. The mesh-independent results were in good agreement with reported experimental data on total conversion over a range of fluidization velocities. The agreement in the bed expansion was good at low fluidization velocities, but not as good at high fluidization velocities. Despite some studies on the modeling and model evaluation of fluidized-bed hydrodynamics,21 only a few works have been published on the CFD modeling and model validation of combined reactor hydrodynamics and kinetics. Also, only limited work has been reported on the successful CFD modeling of fluidized-bed hydrodynamics containing fine particles (Geldart A). The main objectives of the current study were to model the hydrodynamics and reaction kinetics of a bubbling FCC fluidized-bed reactor and to evaluate the CFD model prediction by comparing the simulation results with the relevant experimental measurements. Two-dimensional (2D) simulations of the fluidized bed were performed, as three-dimensional (3D) simulations of multiphase systems with chemical reactions are unfeasible with current computational power. The Fluent CFD software package (version 6.1) along with subprograms to include the reaction kinetics and to modify drag laws were used for simulation. The effects of model parameters such as drag function and restitution coefficient were evaluated. The experimental work was performed by the Fluidization Research Group of the University of British Columbia using fluid catalytic cracking (FCC) units, in which the particles act as a catalyst for a gas-phase chemical reaction.20,22,23 CFD Model The simulation of the fluidized beds was performed using the Eulerian-granular model of Fluent, consisting of a set of momentum and continuity equations for

each phase, which are linked through pressure and interphase exchange coefficients. The properties for the solid phase are obtained by applying the kinetic theory of granular flows. Governing Equations. The governing equations of the system include the conservation of mass, momentum, and energy. The continuity equation for the qth phase (gas or solid) without mass transfer between the phases is written as

∂ (R F ) + ∇‚(RqFqb v q) ) 0 ∂t q q

(1)

vq are the density and velocity, respecwhere Fq and b tively, of phase q. The conservation of momentum for the gas phase, g, is described by

∂ (R F b v ) + ∇‚(RgFgb v g‚v bg) ) ∂t g g g -R∇p + ∇‚τcg + RgFgb g + Kgs(v bg - b v s) (2) The conservation of momentum for the solid phase, s, can be expressed as

∂ (R F b v ) + ∇‚(RsFsb v s‚v bs) ) ∂t s s s -Rs∇p - ∇ps + ∇‚τcs + RsFsb g + Kgs(v bg - b v s) (3) The conservation of the kinetic energy of the moving particles is described as follows by the granular temperature, Θs, which is derived from the kinetic theory of granular flow

3 ∂ (F R Θ ) + ∇‚(FsRsb v sΘs) ) 2 ∂t s s s (-psCI + τcs):∇‚v bs + ∇‚(kΘs∇Θs) - γΘs + φgs (4)

[

]

Constitutive relations required to close the governing equations are as follows: The momentum exchange between the solid and gas phases is expressed by the drag force, which is represented by an interphase exchange coefficient. Several drag models exist for the gas-solid interphase exchange coefficient Kgs, including the drag laws of SyamlalO’Brien and Gidaspow. The drag law of SyamlalO’Brien3 is based on the measurements of the terminal velocities of particles in fluidized or settling beds. The interphase exchange coefficient is expressed as

Kgs )

( )

Res 3 RsRgFg CD |v b -b v g| 2 4v d vr,s s r,s

s

(5)

where CD, the drag coefficient, is given by

(

CD ) 0.63 +

4.8

xRes/vr,s

)

2

(6)

and vr,s, a terminal velocity correlation, is expressed as

vr,s ) 0.5[A - 0.06Res +

x(0.06Res)2 + 0.12Res(2B - A) + A2]

(7)

with A ) Rg4.14 and B ) PRg1.28 for Rg e 0.85 and B ) RgQ for Rg > 0.85. The values of P and Q can be modified to match the minimum fluidization conditions of the particles; the default values for P and Q are 0.8 and 2.65, respectively.

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The solids Reynolds number, Res, is calculated as

µs,kin )

Fgds|v bs - b v g| Res ) µg

(8)

Gidaspow6

The drag law of is a combination of the Wen and Yu model7 for dilute flow and the Ergun equation24 for dense flow. For Rg > 0.8, Kgs is calculated with the equations from the Wen and Yu model as

bs - b v g| -2.65 3 RsRgFg|v Rg Kgs ) CD 4 ds

(9)

where CD, the drag coefficient, is expressed as

CD )

24 [1 + 0.15(RgRes)0.687] RgRes

Rs2µg

RsFg|v bs - b v g| + 1.75 Kgs ) 150 2 ds Rgds

(11)

Other constitutive equations are as follows: The phase stress tensor of the qth phase (gas or solid), which accounts for interactions within the corresponding phase, is given by

2 τcq ) Rqµq(∇‚vq + ∇‚vqT) + Rq λq - µq ∇‚vqCI 3

(

)

(12)

The solids pressure, which describes the change in the total momentum transport of the motion of particles and their interactions, is used for the pressure gradient term, ∇ps, and is expressed as

ps ) RsFsΘs + 2Fs(1 + ess)Rs2g0,ssΘs

[ ( )]

g0,ss ) 1 -

1/3 -1

(14)

Rs,max

0,ssRs(1

+ ess)

µs,fr )

]

2

ps sin φ

(18)

(19)

2xI2D

The solids bulk viscosity, which accounts for the resistance of the solid phase to compression and expansion, is expressed by26

( )

Θs 4 λs ) RsFsdsg0,ss(1 + ess) 3 π

1/2

(20)

The diffusion coefficient for granular energy, kΘs, is expressed by two different models. The SyamlalO’Brien model expresses kΘs as

kΘs )

15dsFsRsxΘsπ 4(41 - 33η)

[1 + 125η (4η - 3)R g 2

s 0,ss

+

16 (41 - 33η)ηRsg0,ss (21) 15π

]

with

1 η ) (1 + ess) 2 and the Gidaspow model express kΘs as

kΘs )

150FsdsxΘsπ

384(1 + ess)g0,ss

[1 + 56R g

s 0,ss(1

2

]

+ ess) +

2FsdsRs2g0,ss(1 + ess)

(13)

The radial distribution function, g0,ss, which represents the probability of particle collisions when the granular phase becomes dense is given by

Rs

96Rs(1 + ess)g0,ss

[1 + 54g

Friction stress, which plays a significant role when the solid-phase volume fraction gets close to the packing limit, is expressed by25

(10)

and the solids Reynolds number is calculated with eq 8. For Rg e 0.8, Kgs is calculated with the Ergun equation as

10FsdsxΘsπ

x

Θs (22) π

The collision dissipation of energy, γΘm, representing the rate of energy dissipation within the solid phase due to inelastic particle collisions is calculated from

γQm )

12(1 - ess2)g0,ss FsRs2Θs3/2 dsxπ

(23)

The solids shear viscosity, µs, which contains a collision term, a kinetic term, and a friction term, is

The transfer of kinetic energy, φgs, due to random fluctuations in particle velocity is expressed as

µs ) µs,col + µs,kin + µs,fr

φgs ) -3KgsΘs

(15)

The collision term is expressed by

( )

Θs 4 µs,col ) RsFsdsg0,ss(1 + ess) 5 π

1/2

(16)

The kinetic term is expressed in the Syamlal-O’Brien model as

µs,kin )

RsdsFsxΘsπ

2 1 + (1 + e )(3e [ 5 6(3 - e ) ss

ss

ss

- 1)Rsg0,ss

]

(17) or by the Gidaspow model as

(24)

Modification of Drag Laws. The drag force between the gas phase and the particles is one of the dominant forces in a fluidized bed. Drag laws, which are applied to model the momentum exchange between the phases, are often developed empirically. Such general drag correlations typically cannot predict the drag force precisely for a number of reasons, such as the inability to include accurate information about particle size and shape distributions. Syamlal and O’Brien12 introduced a method to modify their original drag law for correct simulation of the minimum fluidization conditions. The modification of the Syamlal-O’Brien drag law is based on the minimum fluidization conditions, commonly available experimental information for the specific

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Figure 1. Solids volume fraction with the Gidaspow drag law (H0 ) 0.51 m, vg ) 0.3 m/s, e ) 0.9). The scale indicates the value for the solids volume fraction ranging from 0 (no particles) to 0.55 (initial packing limit).

material. The parameter P in eq 7 is related to the minimum fluidization velocity through the velocityvoidage correlation and the terminal Reynolds number, Ret. P is varied until vg, expressed by the following equation, equals the minimum fluidization velocity determined experimentally

Rgηg vg ) Ret d p Fg

(25)

voidage correlation

Q ) 1.28 + log(P)/log(0.85)

Reaction Kinetics. The reaction kinetics for ozone decomposition was included in the CFD model to evaluate the predictions of the fluidized-bed reactor kinetics. Ozone decomposition follows a first-order reaction kinetics19,20 kr

where Ret, the Reynolds number under terminal settling conditions for the multiparticle system, is given by

Ret ) vr,sRets

(26)

(30)

O3 9 8 1.5O2 catalyst

∆hr ) 143 kJ/kmol

(31)

Because the first-order rate of decomposition depends on the presence of catalyst, the solids volume fraction is included in the kinetic rate

RO3 ) -krRsCO3

(32)

vr,s, the terminal velocity correlation, is given by The following transport equation for ozone was included in the model

A + 0.06BRets vr,s ) 1 + 0.06Rets

(27)

and Rets, the Reynolds number under terminal settling conditions for a single particle, is given by

Rets )

(x

)

4.82 + 2.52x4Ar/3 - 4.8 1.26

2

(28)

Ar is the Archimedes number, which is given by

(Fs-Fg)ds3Fgg Ar ) ηg

(29)

The parameter Q in eq 7 has to be modified according to eq 30 to ensure the continuity of the velocity-

∂RgFgXO3 ∂t

m v gXO3 ) RO ) -krRsFgXO3 + ∇‚RgFgb 3

(33)

The source term on the right-hand side represents the mass reaction rate of ozone decomposition. Simulation Setup. The two-dimensional (2D) computational domain was discretized by 55 000-65 000 rectangular cells, with cell boundary layers close to the walls where the velocity gradients increased and a finer resolution was necessary. The maximum cell dimension of 0.002 m was used for discretizing the fluid bed. Cells of this dimension were found to be adequate for achieving mesh-independent results in a similar study performed by Syamlal and O’Brien.13 Because instability and convergence were problems for multiphase simulations, a very small time step (0.0005-0.001 s) with around 20-40 iterations per time step was chosen, until

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Figure 2. Solids volume fraction with the Syamlal-O’Brien drag law (H0 ) 0.51 m, vg ) 0.3 m/s, e ) 0.9).

Figure 3. Solids volume fraction with the modified Syamlal-O’Brien drag law (H0 ) 0.51 m, vg ) 0.3 m/s, vmf ) 0.0027 m/s, e ) 0.9).

convergence was reached. A convergence criterion of 10-4 for each scaled residual component was specified for the relative error between two successive iterations. The governing equations using a laminar viscous model for gas turbulent flow were solved using the finitevolume approach. The Phase-Coupled SIMPLE (PCSIMPLE) algorithm,27 which is an extension of the SIMPLE algorithm to multiphase flows, was applied for the pressure-velocity coupling. Second-order upwind discretization schemes for the convection terms were used. Experimental Setup. The experimental data from two fluidized-bed reactors with comparable dimensions containing FCC particles with similar properties were used to evaluate the CFD predictions of hydrodynamics and reaction kinetics. For hydrodynamic evaluation, the experimental data in a bed of 0.286-m diameter and 4.5-m height obtained by Ellis et al.22,23 were used. For kinetic evaluation, the ozone decomposition study of a

fluidized bed of 0.102-m diameter and 2.6-m height performed by Sun20 was used. Only a few hydrodynamic measurements were available for this reactor, which did not allow for a CFD evaluation of bed hydrodynamics in detail. Table 1 summarizes the columns and particle properties of these beds (used for the CFD modeling setup). Results and Discussion Fluidization Hydrodynamics. Correct simulation of the hydrodynamics is essential for the successful modeling of fluidized-bed reactor performance. Therefore, model parameters such as the drag law (describing the momentum exchange between the phases) or the restitution coefficient (accounting for the dissipation of energy through particle-particle and particle-wall collisions) have to be investigated for their influence on the fluidization.

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Figure 4. Solids volume fraction after 10 s with different restitution coefficients (modified Syamlal-O’Brien drag law, H0 ) 0.51 m, vg ) 0.3 m/s, vmf ) 0.0027 m/s).

Figure 5. Solids volume fraction after 20 s with different gas velocities (modified Syamlal-O’Brien drag law, H0 ) 0.51 m, vmf ) 0.0027 m/s, e ) 0.9). Table 1. Specifications of the Fluidized Beds property

Ellis23

Sun20

superficial gas velocity (m/s) Sauter mean diameter (µm) particle density (kg/m3) bulk density (kg/m3) static bed height (m) minimum fluidization velocity (m/s) reaction coefficient kr (1/s) voidage

0.3, 0.4, 0.5 57.4 1560 860 0.51 0.0027 0.45

0.3 60 1586 823 0.164, 0.409, 0.743 0.0028 2.12, 2.17, 2.32 0.45

The corresponding drag equations are typically empirical and might not be applicable in their original form to the conditions of FCC particles investigated in this study. To study the suitability of drag laws for modeling FCC particles, the drag models of Gidaspow and Syamlal-O’Brien were investigated. The Gidaspow drag law was proposed for modeling dense fluidized beds, whereas the Syamlal-O’Brien drag law has a wide range of applications.28 The simulation results of the solids volume fraction using the Gidaspow drag law are shown in Figure 1. The development of the fluidization during the first 8 s of the simulation is illustrated. With a

superficial gas velocity of 0.3 m/s, bubbling fluidization is expected with a bed expansion of about 20%, based on the experimental observations.22 The simulation results show about 100% bed expansion after 3 s, indicating an overprediction of the drag force. There is no formation of bubbles, and the conditions after 8 s are more characteristic of a fast fluidization. Figure 2 shows the results obtained under the same operating conditions using the Syamlal-O’Brien drag law without calibration to the experimental minimum fluidization velocity. The flow pattern is similar to that obtained with the Gidaspow drag law with the same overestimation of the fluidization. This strong similarity in the results indicates that neither of these models can be applied, in its original form, to a fluidized bed containing FCC particles of ∼60-µm diameter. The discrepancy between the modeling and the experimental results might be due to the cohesive interparticle forces due to the van der Waals attraction, which are responsible for agglomeration of particles and lead to a reduced drag force for FCC particles. The lack of consideration of the effects of cohesive forces and

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Figure 6. Time-averaged voidage results at different superficial gas velocities.

agglomeration can result in a higher drag and higher bed expansion. Similar overestimations were observed by other researchers.11,29 One possibility to decrease the drag is a general scaling factor; however, this empirical approach requires an extensive case study for every application. The method employed to modify the Syamlal-O’Brien drag law introduced in the modeling section is a reasonable and generalized way to find suitable values for the drag adjustment. The knowledge of the minimum fluidization velocity is essential for modifying the drag law. The minimum fluidization velocities for similar FCC particles in a bed with comparable dimensions have been measured as 0.0026 and 0.0028 m/s.30 The mean value of 0.0027 m/s was taken to modify the drag law of Syamlal-O’Brien, which resulted in values of 0.920 and 1.795, respectively, for P and Q in eq 7. The flow pattern up to a runtime of 15 s is shown in Figure 3. The flow pattern corresponds to a highly bubbling fluidized bed with bubble coalescences and

splitting, that is anticipated at a superficial gas velocity of 0.3 m/s (100 times higher than the minimum fluidization velocity). The bed expansion of 25% corresponds well to the experimental results of 20% expansion. Simulating the reactor using the modified SyamlalO’Brien drag law with Umf ) 0.3 m/s (1.390 and -0.745 for P and Q, respectively) predicted a bed expansion of about 5%, which underlines the importance of drag force in modeling fluidized beds. A case study was conducted to investigate the influence of the restitution coefficient on the fluidization of the present FCC particles. As shown in Figure 4, the variation of the restitution coefficient from 0.6 to 0.975 has no significant influence on the fluidization. The bubble diameters are approximately equal, and the bed expansion stays constant at various restitution coefficients. This finding is in conflict with some other reported modeling results at much larger particle sizes17 or higher flow velocities,31 where the restitution coef-

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ficient has an impact on the fluidization. Collisions of larger particles or collisions at higher superficial gas velocities result in greater dissipation of kinetic energy due to particle collisions, which can impact the fluidization as a function of the restitution coefficient. It can be concluded that granular stress, which is influenced by the restitution coefficient, has a minor effect on the fluidization of small FCC particles in bubbling fluidizedbed reactors, as confirmed by van Wachem et al.2 The more dominant forces in a bubbling fluidized bed with FCC particles within the examined range are gravity and drag. All remaining simulations were performed with a restitution coefficient of 0.9. Figure 5 shows the solids volume fraction after 20 s at three different gas velocities from 0.3 to 0.5 m/s. At higher velocity, bubbles get larger, and consequently, the bed expansion increases significantly. At the superficial gas velocity of 0.5 m/s, the bed surface is highly fluctuating. These fluctuations are the first indication for a transition to turbulent fluidization, which is in agreement with the experimental observations.23 The voidage profiles of the simulation and the experimental data are compared in Figure 6. They represent the heights of 0.273 and 0.4 m above the distributor at three different superficial gas velocities from 0.3 to 0.5m/s. The general trend of the voidage is simulated correctly, with a higher voidage in the core of the fluidized bed due to the upward flowing bubbles and the characteristic downward flow of the solids close to the wall. The voidage close to the wall is underpredicted in all cases. This might be the result of treating wallparticle collisions as fully elastic with no dissipation of kinetic energy. The occurrence of the electrostatic forces between the wall and the particles, which are not considered in the model, might also be a reason for the discrepancy. Modeling a 3D reactor with a 2D model, as in the present study, could also contribute to the deviation between the modeling and experimental results. The overall flow pattern and the interaction between the particles and a cylindrical wall in a 3D column cannot be simulated correctly by a 2D model. The computed voidage profiles also fluctuate more than those of the experiments, likely because of the smaller time range used to calculate the averaged simulation results. The CFD results are time-averaged from 10 to 20 s (when the bed is operating at statistically steadystate conditions), whereas the experimental data are time-averaged over 100 s of bed operation. Under perfect experimental and modeling conditions where data are collected in long enough time intervals, the plots in Figure 6 should be symmetric about the center line. The deviation of the experimental data from symmetry is probably some indication of a systematic experimental error. The deviation of the numerical data is an indication that the time interval used to average the voidage was not long enough. Kinetics of Ozone Decomposition. To evaluate the CFD predictions of the bed reaction conversion, the simulation results of the FCC fluidized bed for ozone decomposition with three different inventories of catalyst (1.1, 2.75, and 5 kg) were compared to the experimental measurements. The rate coefficient values were determined in the fluid bed using different catalyst inventories. Similar values obtained for the rate coefficient (2.12-2.32 s-1) at various catalyst inventories show the reproducibility of the results. The SyamlalO’Brien drag model was modified based on a minimum

Figure 7. Total conversion of ozone for three different catalyst inventories.

Figure 8. Time-averaged ozone conversion against the bed height of the reactor with respect to the ozone inlet concentration.

fluidization velocity of 0.0028 m/s, which was determined experimentally for the bed. In all catalyst inventory cases, the CFD simulations predicted a higher decomposition of ozone than the experimental data (Figure 7). Modeling simplifications of not considering the gas distribution and the catalyst return system potentially contributed to this deviation. A distributor in a fluidized-bed reactor consists of small orifices that lead to higher velocities and the development of small jet flows, where potentially reactive gas partially bypasses the lower layers of the bed catalyst. The distributor was not considered in the CFD model, because of the challenges of implementing the mesh structure. The lack of considering the distributor in the CFD model and the uniform gas inlet led to a higher conversion in the lower part of the simulation model. Figure 8 shows the CFD-simulated ozone conversion against the bed height for the 5-kg catalyst inventory. The conversion stops at about 0.9 m of the bed height because ozone enters to the free board of the bed, where there is no catalyst. Most of the decomposition occurs right after the distributor. Higher decomposition at the lower heights of the bed is in agreement with Syamlal and O’Brien13 simulation results. The effect of a distributor on reactor conversion has been observed experimentally. Sun20 reported a considerable increase in reactor conversion for ozone decomposition when a more uniform flow (using a distributor with more holes) entered the bed of FCC catalysts. In addition, during the experiments, between 5% and 20% of the total catalyst was in the solids return system.20 This absence of the

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catalyst mass, which was not considered in the CFD simulations, could also contribute to the higher simulated conversions. Conclusions The CFD modeling of fluidized-bed hydrodynamics shows that the drag models of Gidaspow and SyamlalO’Brien are not applicable in their original forms for simulating FCC particles classified as Geldart A particles within the examined range. The models overpredict the bed expansion and the momentum exchange between the gas and the solid phase. The modification of the Syamlal-O’Brien drag law based on the minimum fluidization conditions, as a generalized method to decrease the drag, provides modeling predictions that are in reasonable agreement with the experimental data over the range in which the model was evaluated. The dissipation of the kinetic energy of the moving particles due to collisions has a low influence on the overall fluidization of FCC fluidized beds over the range of particle size and bed operating conditions of the present study, where drag and gravity are the more dominant forces. With a mean diameter of around 60 µm, the viscous granular stress of a collision between the particles might play a minor role within a bubbling fluidized bed, where the fluidization is mainly caused by the momentum exchange between the gas and the solid phase. The implementation of an additional transport equation with a kinetic term seems to be an appropriate method for including the kinetics of a chemical reaction in a CFD model. The simulated ozone conversions with various catalyst inventories were higher than those measured experimentally for several reasons. The effects of the gas distributor and the return system on the reaction, which were not considered in modeling, could cause the deviation. In addition, the correct prediction of the reactor kinetics is highly dependent on the modeling of the hydrodynamics, which needs further improvement. Acknowledgment The authors thank Dr. John Grace and Dr. Naoko Ellis for their invaluable comments. Financial support from the German Academic Exchange Service is acknowledged. Nomenclature Ar ) Archimedes number Ci ) species concentration, kmol/kg CD ) drag coefficient Cfr,i ) coefficient of friction di ) diameter, m ei ) restitution coefficient Fi ) force, N g ) acceleration due to gravity, m/s2 g0,i ) radial distribution coefficient H ) expanded bed height, m H0 ) static bed height, m CI ) stress tensor I2D ) second invariant of the deviatoric stress tensor kr ) reaction rate constant, 1/s kΘs ) diffusion coefficient for granular energy, kg/(s‚m) Ki ) interphase exchange coefficient mi ) mass, kg Mi ) molecular weight, kmol/kg

M, N ) consecutive number n ) mole, kmol p ) pressure, Pa r ) radial coordinate, m R ) radius, m Ri ) molar reaction rate, kmol/(m3‚s) 3 Rm i ) mass reaction rate, kg/(m ‚s) Re ) Reynolds number t ) time, s T ) temperature, °C vi ) velocity, m/s Vi ) volume, m3 Xi ) fraction, dimensionless or ppm z ) height coordinate measured from distributor, m Greek Letters Ri ) volume fraction i ) voidage γΘm ) collision dissipation of energy, kg/(s3‚m) Γi ) diffusion coefficient, kg/m ηi ) dynamic viscosity, kg/(s‚m) Θi ) granular temperature, m2/s2 λi ) bulk viscosity, kg/(s‚m) µi ) shear viscosity, kg/(s‚m) νi ) kinematic viscosity, m2/s ∆F ) density difference between gas and solid phase, kg/ m3 Fi ) density, kg/m3 τci ) stress tensor, Pa φ ) angle of internal friction, deg φls ) transfer rate of kinetic energy, kg/(s3‚m) ψ ) particle sphericity Subscripts b ) bulk f ) overall (e.g.. f,i represents the overall voidage in section i of a fluidized bed) g ) gas i ) general index mf ) minimum fluidization p ) particles s ) solids t ) terminal (e.g. vt is the terminal velocity) T ) stress tensor

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Received for review April 25, 2005 Revised manuscript received August 25, 2005 Accepted September 28, 2005 IE050490+