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Ind. Eng. Chem. Res. 2001, 40, 5526-5532
A Comparison of Two- and Single-Phase Models for Fluidized-Bed Reactors Navid Mostoufi Department of Chemical Engineering, Faculty of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran
Heping Cui and Jamal Chaouki* Department of Chemical Engineering, E Ä cole Polytechnique de Montre´ al, P.O. Box 6079, Station Centre-Ville, Montre´ al, Que´ bec, Canada H3C 3A7
Simulations of a bubbling/turbulent fluidized-bed reactor have been studied using the catalytic oxidation of n-butane to maleic anhydride (MAN) in the presence of a vanadium phosphorus oxide catalyst. The performance of the reactor was investigated using three different models: (a) a simple two-phase flow model, (b) a dynamic two-phase structure model, and (c) a plug-flow model. The simple two-phase model was found to underpredict the performance of the fluidizedbed reactors because of the oversimplified assumptions involved in this model. By analyzing the mass transfer in the two-phase models, it was shown that the conversion of reactants occurs mainly in the emulsion phase at low gas velocities and in the bubble phase at high gas velocities. The performance of the reactor, in terms of n-butane conversion, yield of MAN, and selectivity of produced MAN, was analyzed at different superficial gas velocities, initial n-butane concentrations, and deactivation rates of the catalyst. 1. Introduction Fluidized-bed reactors have found application in many chemical processes involving gas-solid and solidcatalyzed gas-phase reactions. Examples of industrial applications of such reactors include catalytic cracking of hydrocarbons; coal gasification; ore roasting; and synthesis reactions such as Fischer-Tropsch synthesis, polyethylene production, and maleic anhydride production.1 The problems of predicting the performance and scaleup of fluidized-bed reactors are very important for reasonable research and development of new chemical processes. The uncertainties associated with the scaleup and modeling of fluidized beds represent a significant obstacle to the widespread use of fluidized beds in chemical industries. Several methods of fluidized-bed reactor modeling are available for different regimes of fluidization such as the generalized two-phase model2 and the Kunii-Levenspiel model1 for the bubbling regime, the plug-flow model3 and the modified twophase model4 for the turbulent regime, and the coreannulus model5 for the fast fluidization regime. However, none of these models is satisfactory. Moreover, every fluidization regime is treated differently and each model is applicable for one regime. Despite the different modeling approaches, there is evidence that different regimes of fluidization obey the same flow principles.6,7 Recently, Thompson et al.8 proposed a new generalized bubbling/turbulent model that predicts a smooth transition from bubbling two-phase fluidization to singlephase axially dispersed flow. A large variety of fluidized-bed models are based on the two-phase concept of fluidization. In the simple two* Corresponding author. Tel.: +1(514)340-4711 (ext. 4034). Fax: +1(514)340-4159. E-mail:
[email protected].
phase model, it is assumed that all gas in excess of that required for minimum fluidization passes through the bed as solid-free bubbles. However, the existence of solid particles in the bubbles has been shown both experimentally9,10 and theoretically.11,12 The emulsion also does not stay at the minimum fluidization state but can contain more gas at higher gas velocities.10,13 These phenomena result in a dynamic distribution of solids between the two phases as has been extensively studied by Cui et al.14 over a wide range of superficial gas velocities, covering both the bubbling and turbulent regimes of fluidization. This study compares the predictions of the performance of an industrial-scale fluidized bed by different two- and single-phase fluidized-bed reactor models. The production of maleic anhydride (MAN) by the catalytic oxidation of n-butane in a fluidized bed of vanadium phosphorus oxide (VPO) catalyst is considered as the example reaction in the present work. The bed can operate in either the bubbling or turbulent regime of fluidization. Fresh catalyst from the regenerator enters the bed at the bottom, where the reactants (i.e., air and n-butane) are introduced. Solids and the products exit the reactor at the top, where the deactivated catalyst is separated from gases and sent to the regenerator. 2. Modeling 2.1. Hydrodynamics. The fluidized-bed reactor in this work operates in either the bubbling or turbulent regime of fluidization. Three different hydrodynamic models were considered for predicting the performance of the fluidized bed. These models are described below. In the present work, the radial concentration gradients within the bed are neglected in the mole balance equations. In two-phase models, it is assumed that the bubbles reach their equilibrium size quickly after the
10.1021/ie010121n CCC: $20.00 © 2001 American Chemical Society Published on Web 10/13/2001
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5527 Table 1. State Equations for the Simple Two-Phase Model (STP) mole balance for species A in the emulsion phase
dCAe RAe(1 - mf)Fs(1 - δ) + Kbeδ(CAb - CAe) ) dz Umf(1 - δ)
mole balance for species A in the bubble phase
dCAb Kbe(CAb - CAe) )dz Ub
mean concentration of species A
CA )
bubble fraction
δ)
average bed voidage
) (1 - δ)mf + δ
Table 2. Fluidization and Mass Transfer Correlations minimum fluidization UmfFgds ) x27.22 + 0.0408Ar - 27.2 velocity15 µg bubble diameter16
db [-γM + (γM2 + 4Dbm/Dt)0.5]2 ) Dt 4 Dbm ) 2.59g-0.2[(U0 - Ue)At]0.4 γM ) 2.56 × 10-2
bubble velocity17
(Dt/g)0.5 Umf
Ub ) U0 - Ue + ubr ubr ) 0.711xgdb
bubble-to-emulsion gas interchange coefficient1
1 1 1 ) + Kbe Kbc Kce Kbc ) 4.5
() (
)
Ue DAB1/2g1/4 + 5.85 db db5/4
Kce ) 6.77
(
)
DABeubr db3
1/2
gas enters the bed; hence, all bubbles are considered to have a uniform size throughout the bed. 2.1.1. Simple Two-Phase Model (STP). According to the traditional simple two-phase model, the fluidized bed consists of two phases, i.e., the bubble phase and the emulsion phase. All gas in excess of Umf, the minimum fluidization velocity, flows through the bed as bubbles while the emulsion stays stagnant at the minimum fluidization conditions. Because this model assumes that the bubbles are solid-free, reactions occur only in the emulsion phase. The state equations for this model are given in Table 1, and the fluidization and mass transfer correlations required to solve these equations are listed in Table 2. Note that, for the simple twophase model, the emulsion is at minimum fluidization sate (e t mf), i.e., Ue ) Umf and e ) mf. 2.1.2. Dynamic Two-Phase Structure Model (DTP). The actual flow structure in the fluidized beds is more complicated than that described in the simple two-phase model. In a real fluidized bed, the concentration of particles in the emulsion phase can be less than that at the minimum fluidization, and the bubbles can contain various amounts of particles.14,18 Therefore, this model considers the progress of the reaction in both bubbles and the emulsion phase. The state equations
Umf(1 - δ) Ub δ CAe + C U0 U0 Ab
U0 - Umf Ub - Umf
for this model are given in Table 3, and the fluidization and mass transfer correlations required for solving these equations are listed in Table 2. Note that, because the size and physical properties of the VPO catalyst are very close to those of FCC, the constants used in the Cui et al.14 correlations were chosen accordingly. Cui et al.14 gave the constants of their correlations for the center of a 152-mm column, which can be rationally applied to the column in this study because of negligible wall effects present in an industrial-scale unit. 2.1.3. Plug-Flow Model (PF). At high superficial gas velocities and high catalyst recirculation rates, the fluidized reactor can be modeled by a simple singlephase plug-flow reactor.3,4 In such a model, the solids are assumed to be uniformly distributed in the bed with an average voidage of , and the flow field of the gas passing through the bed is modeled by that of plug flow. A mole balance on species A over the differential reactor volume gives
dCA Fs(1- )RA ) dz U0
(1)
It is evident from eq 1 that the method of evaluating the solids concentration is an important factor in predicting the performance of the reactor. Because the plug-flow model is unable to provide the voidage of the fluidized bed, this value should be obtained from other models or correlations. In the present work, the average voidage of the bed used in the plug-flow model is estimated using the dynamic two-phase structure of the bed (see Table 3). The reasons for choosing this method for estimation of the voidage in the plug-flow model are that (a) the dynamic two-phase structure model provides a more realistic description of the solids distribution in the fluidized beds than other models and (b) the effect of difference in the solids concentration will be eliminated from comparisons of the plug-flow model with the dynamic two-phase structure model; hence, only the models themselves will be compared with each other. 2.2. Reaction Kinetics. Intrinsic rate equations and a reaction pathway for the partial oxidation of n-butane to maleic anhydride (MAN) on a vanadium phosphorus oxide (VPO) catalyst have been proposed by Centi et al.19 The complete reaction pathway involves both series and parallel reaction steps
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Table 3. State Equations for the Dynamic Two-Phase Structure Model (DTP) mole balance for species A in the emulsion phase
dCAe RAe(1 - e)Fs(1 - δ) + Kbeδ(CAb - CAe) ) dz Ue(1 - δ)
mole balance for species A in the bubble phase
dCAb RAb(1 - b)Fs - Kbe(CAb - CAe) ) dz Ub
mean concentration of species A
CA )
average emulsion voidage14
e ) mf + 0.000 61 exp
average bubble voidage14
b ) 0.784 - 0.139 exp -
bubble fraction14
δ ) 1 - exp -
emulsion velocity
Ue )
average bed voidage
) (1 - δ)e + δb
Ue(1 - δ) Ub δ CAe + C U0 U0 Ab
(
Table 4. Kinetic Parameters parameter
value
units
k1 k2 k3 KB R β γ δ
6.230 × 10-7 9.040 × 10-7 0.966 × 10-7 2616 0.2298 0.2298 0.6345 1.151
mol1-R LR/(g s) mol1-β Lβ/(g s) molγ-δ L1-δ-γ/(g s) mol/L
n-C4H10 + 3.5O2 f MAN + 4H2O
)
U0 - Umf 0.272
)
U0 - Umf 0.62
U0 - δUb 1-δ
(2)
parameter
value
Dt H ds Fs mf T P U0 CB0 Gs deactivation of catalyst at exit
2 6 75 1500 0.5 340 202.65 0.4, 0.9, 1.5 5, 10, 20 200 0-90
da ) kda dt
(3)
MAN + 3O2 f 4CO2 + H2O r3 ) k3CMAN(COγ/CBδ) (4) The kinetic parameters are summarized in Table 4. 2.3. Catalyst Deactivation. The vanadium present in the VPO catalyst is the main oxygen carrier and during the reaction with the hydrocarbon in the gas phase, certain crystalline phases on the surface of the solid catalyst are transformed via a reduction process, i.e., V+5 f V+4.20 The reduction of the VPO catalyst is an example of parallel deactivation (which is not true catalyst deactivation but should more precisely be regarded as the rate of lattice oxygen insertion into substrate), where the reactants form products and, at the same time, deactivate the catalyst. There is no explicit expression for the deactivation rate of the VPO catalyst in the literature, and extracting such rate from the available data in the literature is beyond the scope of the present work. Therefore, although the reported data might suggest a nonlinear relationship between the catalyst deactivation rate and the fraction of active catalyst,21 we assumed a first-order deactivation rate
units m m µm kg/m3 °C kPa m/s % kg/(m2 s) %
as this assumption has been previously used by other researchers22
n-C4H10 + 6.5O2 f 4CO2 + 5H2O r2 ) k2COβ
)
U0 - Umf 0.262
Table 5. Summary of Specifications and Operating Conditions Used for the Computer Simulation
The reactions and rate equations are19
k1KBCBCOR r1 ) 1 + KBCB
( (
(5)
or
a ) e-kdt
(6)
Therefore, the rate of reaction incorporating catalyst deactivation can be obtained from
r1d ) r1a ) r1e-kdt
(7)
The time for which the catalyst has been in the reactor when it reaches a height z is
t)
Fs(1 - )z z ) Vs Gs
(8)
The rate of reaction incorporating catalyst deactivation can be obtained by combining eqs 7 and 8. 3. Computer Simulation The three models described above were solved for an industrial-scale reactor under different operating conditions. These conditions are listed in Table 5. It was assumed in the simulations that complete oxidation of
Ind. Eng. Chem. Res., Vol. 40, No. 23, 2001 5529 Table 6. Overall Reaction Rates A
RA
n-C4H10 MAN CO2 O2 H2O
-r1d - r2 r1d - r3 4r2 + 4r3 -3.5r1d - 6.5r2 - 3r3 4r1d + 5r2 + r3
both n-butane and MAN produces only CO2 and H2O, i.e., the production of CO by the partial oxidation of these reactants is neglected. The overall reaction rates for all of the species involved in the kinetics are listed in Table 6. 4. Results and Discussion In this section, the results of the simulations are compared with each other in terms of the conversion of n-butane, i.e., X ) (CB0 - CB)/CB0; the yield of MAN produced, i.e., Y ) CMAN/CB0; and the selectivity of MAN, i.e., S ) CMAN/(CB0 - CB). 4.1. Effect of Superficial Gas Velocity. Profiles of the n-butane conversion, MAN yield, and MAN selectivity along the reactor are presented in Figure 1a-c, respectively, for two different superficial gas velocities. It is worth mentioning that for the VPO catalyst, the transition to turbulent fluidization is estimated on the basis of absolute pressure fluctuations to occur at 0.5 m/s.23 The effect of increasing the superficial gas velocity is a dilution of the bed and a decrease of the residence time of the reactants in the reactor. As a result, a decrease in the conversion of n-butane is observed at higher gas velocities for all hydrodynamic models (Figure 1a). The same trend can be observed in the yield of MAN produced (Figure 1b). However, the selectivity of MAN produced is higher at higher superficial gas velocities (Figure 1c). The latter effect can be explained by the kinetics of MAN oxidation. According to eq 4, the rate of oxidation of MAN decreases at higher n-butane concentrations. Because the conversion of n-butane is lower at higher gas velocities, the rate of oxidation of MAN is, therefore, lower, and the selectivity of MAN grows higher with increasing superficial gas velocity. The simple two-phase model predicts lower n-butane conversion than the dynamic two-phase structure model at all gas velocities. The reason for this difference is that, according to the simple two-phase model, no reaction takes place in the bubbles because of the absence of catalyst in this phase so that the conversion of n-butane happens solely in the emulsion. This is an oversimplification of the real flow pattern in fluidized beds. In a real fluidized bed, the particles can enter the bubbles, and the emulsion can contain more gas than the minimum fluidization condition, as addressed in the dynamic two-phase structure model. Therefore, the simple two-phase model represents the worst solid mixing case in fluidized beds, and the conversion calculated using this model is lower than the actual conversion. The plug-flow model predicts lower n-butane conversions than both the simple two-phase and the dynamic two-phase structure models at low velocity, whereas it predicts higher conversion at high velocity. This difference is directly related to the superficial gas velocity. In the two-phase models, the reaction occurs only (STP) or mostly (DTP) in the emulsion, whereas, in the plugflow model, the reaction takes place everywhere in the
Figure 1. Prediction of performance of the fluidized-bed reactor by different hydrodynamic models at different superficial gas velocities: (a) n-butane conversion, (b) MAN yield, (c) MAN selectivity.
bed uniformly. Because the emulsion phase is more concentrated in catalyst than the average solids concentration in the bed, the rate of reaction is higher in the emulsion of the two-phase models than in the plugflow model. This explanation justifies the higher conversion observed for the two-phase models at lower gas velocities where the emulsion fraction and the fraction of gas passing through this phase are higher. However, there is another important factor in the two-phase models, namely, the mass transfer from bubble to emulsion, that can affect the concentration profiles in fluidized beds. The number of transfer units for mass
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Figure 2. Evolution of number of mass transfer units with superficial gas velocity in the fluidized bed based on two-phase flow models.
transfer between bubbles and emulsion in the two-phase models can be calculated from
NTU )
kbeSbH KbeH ) UbVb Ub
(9)
The variation of the NTU with the superficial gas velocity is plotted in Figure 2. This figure shows that the NTU decreases with increasing superficial gas velocity. This decrease is due to the increase of the bubble velocity, Ub, and the decrease of the overall mass transfer coefficient, Kbe, that occur with increasing superficial gas velocity. As a result, the overall mass transfer between bubble and emulsion is lower at higher gas velocities. Because the fraction of gas passing through the bubbles at higher gas velocities increases and the overall mass transfer is reduced at the same time, it can be concluded that, under such conditions, the conversion of the reactants is closer to the conversion in the bubbles, which are less concentrated in catalyst than the average solids concentration in the bed. Therefore, the plug-flow model predicts the conversion of n-butane to be higher than the two-phase models do at high enough gas velocities. Such a limitation on mass transfer does not appear at lower gas velocities because of the higher NTU. To put all of these conclusions into simple words, one should note that, in a real fluidized-bed reactor, the progress of the reaction occurs mainly in the dense phase (emulsion) at lower gas velocities, whereas the locus of reaction gradually shifts to the lean phase (bubbles) as the gas velocity increases. Therefore, a fluidized-bed reactor can be regarded as an interpolation between the two limiting casessa lower limit based on the simple two-phase model (bubbling bed with solidfree bubbles) and an upper limit based on fast fluidized reactors (single-phase plug flow). Other researchers have also proposed such a smooth transition between fluidization regimes and interpolation between the two extreme limits for predicting the hydrodynamic status of fluidized beds.7,14,24 Such an approach has recently been adopted by Thompson et al.8 for modeling fluidizedbed reactors. However, this work shows that the same trend in transition between fluidization regimes can be obtained by an easier method, i.e., by combining the dynamic distribution of solids between lean and dense phases with the two-phase flow model. There is a need
Figure 3. Prediction of performance of the fluidized-bed reactor by different hydrodynamic models at different initial n-butane concentrations: (a) n-butane conversion, (b) MAN yield, (c) MAN selectivity.
for more investigation on the performance of these models in terms of comparing these models with each other and evaluating them with experimental data. 4.2. Effect of Feed Concentration. The simulations were performed for feed concentrations of 5, 10, and 20 mol % of n-butane in air. Figure 3a-c illustrates the profiles of n-butane conversion, MAN yield, and MAN selectivity, respectively, along the reactor. Figure 3a indicates that conversion increases with decreasing n-butane feed concentration. The yield of MAN also decreases with increasing n-butane concentration in the feed (Figure 3b), whereas the selectivity of MAN increases with increasing n-butane concentration in the feed (Figure 3c). Figure 3c illustrates that, at high feed
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the MAN selectivity (Figure 4c) because the deactivation directly affects the rate of MAN production (eq 7). It can be seen from Figure 4a-c that, in the lower part of the reactor, the conversion and yield are less affected. However, these profiles begin to separate at higher reactor levels. At the reactor inlet, the fresh catalyst has just entered from the regenerator, and the reaction takes place with its maximum rate in this region. At higher levels, deactivation of catalyst becomes significant, which results in reduced conversion, yield, and selectivity. 5. Conclusions Hydrodynamics, kinetics, and catalyst deactivation models have been combined to form a computer simulation of the catalytic oxidation of n-butane to maleic anhydride. It has been shown that the simple two-phase model underpredicts the performance of the fluidizedbed reactors because of the oversimplified assumptions involved in this model. The plug-flow model predicts lower conversions at lower gas velocities and higher conversions at higher gas velocities compared to the twophase models. An analysis of the mass transfer in the two-phase models revealed that the conversion of reactants occurs mainly in the emulsion phase at low gas velocities and in the bubble phase at high gas velocities. These results confirm that the fluidized bed under any operating conditions is an interpolation between the two limiting cases, i.e., low-velocity bubbling bed and singlephase fast fluidization. The relatively simple model of incorporating the dynamic distribution of solids between the two phases in the fluidized bed and the two-phase flow model is capable of predicting the performance of fluidized-bed reactors over a wide range of superficial gas velocities covering different regimes of fluidization. The calculated results indicate decreased conversion and yield with increased superficial gas velocity because of the dilution of the bed and shorter residence time of the reactants in the reactor, whereas the selectivity of MAN is increased under the same conditions because of the increased n-butane concentration in the reactor. The results also show decreased conversion with increased n-butane feed concentration. However, at lower n-butane concentrations, the MAN selectivity decreases. Deactivation of the catalyst results in reduced conversions and especially lower MAN selectivities along the reactor. Figure 4. Prediction of performance of the fluidized-bed reactor by different hydrodynamic models at different rates of catalyst deactivation: (a) n-butane conversion, (b) MAN yield, (c) MAN selectivity.
concentrations, the selectivities predicted by the three models under investigation in the present work are almost the same. These results indicate that, although higher conversions are attained at lower feed concentrations of n-butane, such operating conditions are not advantageous, as the selectivity of MAN decreases under these conditions. 4.3. Effect of Catalyst Deactivation. The preceding results were obtained assuming no catalyst deactivation throughout the reactor. Values of the decay constant kd in eq 5 were chosen such that the catalyst was deactivated by 90% upon exiting to the regenerator. As shown in Figure 4a, increased catalyst deactivation reduces conversion along the reactor. This effect is greater for the MAN yield (Figure 4b) and even more obvious for
Nomenclature At ) reactor cross-sectional area, m2 Ar ) Archimedes number, ds3Fg(Fs - Fg)g/µ2 a ) fraction of active catalyst CA ) concentration of species A, mol/L d ) diameter, m DAB ) gas diffusion coefficient, m2/s Dbm ) maximum bubble diameter, m Dt ) reactor diameter, m g ) acceleration due to gravity, m/s2 Gs ) catalyst circulation rate, kg/(m2 s) H ) height of reactor, m k1 ) rate constant for maleic anhydride formation, mol1-R LR/(g s) k2 ) rate constant for CO2 formation, mol1-β Lβ/(g s) k3 ) rate constant for maleic anhydride decomposition, molγ-δ L1-δ-γ/(g s) kbe ) bubble-to-emulsion mass transfer coefficient, m/s kd ) deactivation rate constant, s-1
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KB ) equilibrium constant in Centi et al.19 kinetics, mol/L Kbc ) bubble-to-cloud gas interchange coefficient, s-1 Kbe ) bubble-to-emulsion gas interchange coefficient, s-1 Kce ) cloud-to-emulsion gas interchange coefficient, s-1 NTU ) number of mass transfer units P ) pressure, Pa r1 ) rate of maleic anhydride formation, mol/(g s) r2 ) rate of CO2 formation, mol/(g s) r3 ) rate of maleic anhydride decomposition, mol/(g s) RA ) overall reaction rate of species A, mol/(g s) S ) selectivity of MAN, number of moles of MAN formed per mole of n-butane converted Sb ) bubble surface area, m2 t ) time, s T ) temperature, K ubr ) bubble rise velocity, m/s U0 ) superficial gas velocity, m/s Ub ) bubble velocity, m/s Ue ) emulsion velocity, m/s Umf ) minimum fluidization velocity, m/s Vb ) bubble volume, m3 Vs ) superficial solids velocity, m/s X ) conversion of n-butane, number of moles of n-butane converted per mole of n-butane fed Y ) yield of MAN, number of moles of MAN formed per mole of n-butane fed z ) distance above the distributor, m Greek Notation R, β, γ, δ ) exponents in Centi et al.19 rate expressions γM ) parameter in Horio and Nonaka16 correlation δ ) bubble fraction in fluidized bed ) voidage µg ) viscosity, Pa s F ) density, kg/m3 Subscripts 0 ) inlet B ) butane b ) bubble d ) incorporating catalyst deactivation e ) emulsion g ) gas MAN ) maleic anhydride mf ) minimum fluidization O ) oxygen s ) solid
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(5) Grace, J. R.; Lim, K. S. Reactor Modeling for High-Velocity Fluidized Beds. In Circulating Fluidized Beds; Grace, J. R., Avidan, A. A., Knowlton, T. M., Eds.; Chapman and Hall: London, 1997; Chapter 15, p 504. (6) Sun, G.; Grace, J. R. Effect of Particle Size Distribution in Different Fluidization Regimes. AIChE J. 1992, 38, 716. (7) Mostoufi, N.; Chaouki, J. On the Axial Movement of Solids in Gas-Solid Fluidized Beds. Trans. Inst. Chem. Eng. A 2000, 78, 911. (8) Thompson, L. M.; Bi, H.; Grace, J. R. A Generalized Bubbling/Turbulent Fluidized-Bed Reactor Model. Chem. Eng. Sci. 1999, 54, 5175. (9) Aoyagi M.; Kunii, D. Importance of Dispersed Solids in Bubbles for Exothermic Reactions in Fluidized Beds. Chem. Eng. Commun. 1974, 1, 191. (10) Chaouki, J.; Gonzalez, A.; Guy, C.; Klvana, D. Two-Phase Model for a Catalytic Turbulent Fluidized-Bed Reactor: Application to Ethylene Synthesis. Chem. Eng. Sci. 1999, 54, 2039. (11) Batchelor G. K.; Nitsche, J. M. Expulsion of Particles from a Buoyant Blob in a Fluidized Bed. J. Fluid Mech. 1994, 278, 63. (12) Gilbertson M. A.; Yates, J. G. The Motion of Particles Near a Bubble in a Gas-Fluidized Bed. J. Fluid Mech. 1996, 323, 377. (13) Abrahamson A. R.; Geldart, D. Behaviour of Gas-Fluidized Beds of Fine Powders: Part II, Voidage of the Dense Phase in Bubbling Beds. Powder Technol. 1980, 26, 47. (14) Cui, H. P.; Mostoufi, N.; Chaouki, J. Characterization of Dynamic Gas-Solid Distribution in Fluidized Bed. Chem. Eng. J. 2000, 79, 135. (15) Grace, J. R. Fluidization. In Handbook of Multiphase Systems; Hetsroni, G., Ed.; Hemisphere: Washington, D.C., 1982; Chapter 8, p 8-1. (16) Horio, M.; Nonaka, A. A. Generalized Bubble Diameter Correlation for Gas-Solid Fluidized Beds. AIChE J. 1987, 33, 1865. (17) Davidson, J. F.; Harrison, D. Fluidized Particles; Cambridge University Press: New York, 1963. (18) Li, J. H.; Wen, L. X.; Qian, G. H.; Cui, H. P.; Kwauk, M.; Schouten, J. C.; van den Bleek, C. M. Structure Heterogeneity, Regime Multiplicity and Nonlinear Behavior in Particle-Fluid Systems. Chem. Eng. Sci. 1996, 51, 2693. (19) Centi, G.; Fornasari, G.; Trifiro, F. n-Butane Oxidation to Maleic Anhydride on Vanadium Phosphorous Oxides: Kinetic Analysis with a Tubular Flow Stacked-Pellet Reactor. Ind. Eng. Chem. Prod. Res. Dev. 1985, 24, 32. (20) Contractor, R. M. Butane to Maleic Anhydride in a Recirculating Solids Reactor. In Circulating Fluidized Bed Technology II; Basu, P., Large, J. F., Eds.; Pergamon Press: Toronto, Ontario, Canada, 1988; Chapter 8. (21) Centi, G.; Trifiro, F. Surface Kinetics of Absorbed Intermediates: Selective Oxidation of C4-C5 Alkanes. Chem. Eng. Sci. 1990, 45, 2589. (22) Pugsly, T. S.; Patience, G. S.; Berruti, F.; Chaouki, J. Modeling the Catalytic Oxidation of n-Butane to Maleic Anhydride in a Circulating Fluidized Bed. Ind. Eng. Chem. Res. 1992, 31, 2652. (23) Bi, H. T.; Grace, J. R. Effects of Measurement Method on Velocities Used to Demarcate the Onset of Turbulent Fluidization. Chem. Eng. J. 1995, 57, 261. (24) Bai, D.; Issangya, A. S.; Grace, J. R. Characteristics of GasFluidized Beds in Different Flow Regimes. Ind. Eng. Chem. Res. 1999, 38, 803.
Received for review February 9, 2001 Revised manuscript received August 17, 2001 Accepted August 17, 2001 IE010121N
