Experimental and theoretical investigation of mass transfer in a circulating fluidized bed

Chemical Engineering Science 102 (2013) 354–364

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Experimental and theoretical investigation of mass transfer in a circulating fluidized bed Baolin Hou, Hailong Tang, Haiying Zhang, Guoqiang Shao, Hongzhong Li n, Qingshan Zhu nn State Key Laboratory of Multi-phase Complex Systems, Institute of Process Engineering, Chinese Academy of Sciences, P.O. Box 353, Beijing 100190, PR China

H I G H L I G H T S


Cluster phase plays a key role in gas-solid transport phenomena in CFB.
Mass transfer in CFB is dominated by mass exchange between meso-scales.
The MSMT model can capture the effect of meso-scale cluster in CFB.

art ic l e i nf o

a b s t r a c t

Article history: Received 20 December 2012 Received in revised form 20 June 2013 Accepted 26 June 2013 Available online 18 July 2013

Catalytic oxidation of carbon monoxide over a Pt catalyst was employed as a model reaction to investigate the effect of meso-scale structure on gas-solid mass transfer in a circulating fluidized bed (CFB). Both experimental and theoretical analyses were performed to determine the conditions under which the reaction process was dominated by mass transfer. The experimental works involved the measurements of the axial distribution of carbon monoxide concentration, whereas the theoretical analyses were on the use of an Multi-Scale Mass Transfer (MSMT) model with considering effects of clusters on gas-solid transport phenomena in the CFB. The results of MSMT model show a good agreement with experimental data, suggesting that the particle clusters play an important role in the gas-solid momentum transfer and mass transfer in CFBs. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Circulating Fluidized Bed Mass Transfer Cluster Phase Multi-Scale Mass Transfer Meso-Scale Dispersed Phase

1. Introduction Circulating fluidized beds (CFB) offer some distinct advantages including excellent solid mixing, high heat and mass transfer rates and uniform distribution of temperature and gas concentration, and have therefore been used widely as gas-solid reactors in petrochemical, metallurgical and energy industries. Over the past few decades, momentum transfer, heat and mass transfer in CFB have been intensively studied. However, scale-up CFBs remains a challenge, which is partially due to lack of understanding the meso-scale effect of clusters on the momentum, mass and heat transfer. The existence of clusters phase in CFBs has been confirmed firstly by Li et al (1991) in as early as 1991. According to their experiments, the particles aggregate (forming the cluster phase) and disperse frequently in a fast fluidized bed, leading to two phases, the cluster phase and the dispersed phase. In the

n

Corresponding author. Tel.: +86 10 6255 6951; fax: +86 10 625 36108. Corresponding author. Tel./fax: +86 10 6253 6108. E-mail addresses: [email protected] (H. Li), [email protected] (Q. Zhu).

nn

0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.06.050

dispersed phase, solid particles move individually, while in the cluster phase aggregation occurs among solid particles, forming clusters enmeshed in the dispersed phase. The clusters show a strand-like shape at center of the bed, while a spherical shape is observed near the wall region. The effect of clusters on momentum transfer between gas and solid phases in CFBs has been investigated by Yang et al. (2003) in as early as 2003, and the results showed a reduction in the momentum transfer coefficient by several orders of magnitude due to the presence of the clusters. Recent years have seen more reports on the deterioration of mass and heat transfer efficiency between gas and solid in CFBs due to clusters; see for example Hou et al., 2010a, 2010b; Chalermsinsuwan et al., 2009a, 2009b; Dong et al., 2008a, 2008b. However, these have been based on theoretical analyses and little experimental evidence is available to validate the models. On the other hand, up to now, the mass transfer coefficient in CFBs are still mainly estimated on the basis of semi-empirical equations from experimental data-fitting in the literature (Breault., 2006). These mass transfer data in CFBs have been obtained by using ozone decomposition, naphthalene adsorption process, solid sublimation or liquid evaporation (Scala., 2007;

B. Hou et al. / Chemical Engineering Science 102 (2013) 354–364

Ouyang et al., 1995). These lead to mass transfer coefficient data published in the literature diverge significantly, reaching several orders of magnitude (Breault., 2006). Such large differences could be partially explained by different experimental conditions of the reported studies. The rates of intrinsic reaction and mass transfer are in the same order for most of above model reactions, it is therefore difficult to distinguish whether the overall reaction rate is dominated by mass transfer based on the macro reaction phenomena Venderbosch et al. (1999). Based on the above, one can see that selection of a “good” or suitable model reaction system is essential for accurate characterization of gas-solid mass transfer in CFBs. Venderbosch et al. (1999) proposed to the use of the catalytic oxidation of carbon monoxide over Pt catalyst as a model reaction for determining mass transfer coefficient in a fluidized bed. The main advantage for this lies in its easiness to judge whether the process is dominated by mass transfer through measuring the dependence of carbon monoxide conversion on the inlet concentration. Other advantages include easy preparation, low reaction temperature and the absence of side reactions. However, little has been reported in the literature on experimental data of mass transfer in CFBs based on this reaction model. In this paper, the model catalytic oxidation reaction of carbon monoxide is employed to investigate the influence of particle clusters on mass transfer in a CFB. The experimental conditions are selected in such a way that the process is dominated by mass transfer. Such conditions are clearly identified through both experiments and theoretical considerations. Gas phase mass exchange between the cluster phase and the dispersed phase is theoretically analyzed. The experimental process is simulated by using the MSMT model (Hou et al., 2010a, 2010b) coupled with external and intraparticle diffusion of reactants and reaction intrinsic kinetics, with the effect of meso-scale clusters on mass transfer and momentum transfer considered. Good agreements have been found between the simulation results and experimental data for pressure drop, solid mass flux and axial distribution of carbon monoxide concentration. Although the focus of this paper is to investigate mass transfer in CFBs, in order to obtain a universal model for catalytic reaction processes, reaction kinetics and intraparticle diffusion of reactants are also considered in the model development.

355

Fig. 1. Sketch of experimental equipment for kinetics parameters.

2. Experimental 2.1. Experimental set-up 2.1.1. Catalyst preparation A 0.3 wt % Pt/γ-Al2O3 catalyst with an average diameter of 75 μm was prepared by impregnating γ-Al2O3 with an H2PtCl6 aqueous solution. Before each of the experiments, the required amount of catalyst was calcined firstly in air for 4 h at 400 1C in a high temperature furnace, and then reduced under a constant flow of hydrogen (flow rate 100 ml/min) for 3.5 h at 400 1C in a 10 mm ID quartz tube packed bed. The as-reduced catalyst was then activated in a mixture of oxygen (2.5 V%) and carbon monoxide (1.2 V%) before the experiments for the kinetics and mass transfer studies in a CFB. 2.1.2. Apparatus for kinetics measurement Kinetics of carbon monoxide oxidation was studied in a packed bed with 0.5 m length and 0.006 m ID with a down-flow configuration; see in Fig. 1. Quartz wood was placed on a perforated plate distributor with 4 holes at a height of 0.25 m from the top to hold the catalyst powder. A gas mixture of oxygen, carbon monoxide and argon, controlled by mass flow meter (Seven Star Co.,

Fig. 2. Sketch of experimental equipment for mass transfer in CFB.

China), was heated to the setting temperature before entering the catalyst bed. A thermocouple was inserted into the catalyst bed to measure the temperature, which was protected by a 2 mm ID quartz tube to avoid any influence on conversion of carbon monoxide. The gas composition in the off-gas was analyzed by a process mass spectrometer (ProLIN, Ametek Process Instruments, USA).

2.1.3. Setup for mass transfer measurements The experimental facility for mass transfer measurements is shown in Fig. 2 with the circulating fluidized bed made of stainless steel. The CFB consisted of a riser (50 mm in inner diameter and 4 m in height), two cyclones, a bag-filter at the exit of cyclone for dust collection, and an L-valve (ID 60 mm) for control of solid recirculation. The whole circulating fluidized bed was put in an electric furnace (ID 750 mm, H 6 m). There are seven ports for

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(Voltz et al., 1973): Rðcco ; co2 Þ ¼

r 1 ⋅cco ⋅co2

ð1Þ

ð1 þ r 2 cco Þ2


 Ea r 1 ¼ K 1 exp  RT
r 2 ¼ K 2 exp

ΔH a RT

ð2Þ

 ð3Þ

where, Rðcco ; co2 Þ is the reaction rate of carbon monoxide; K 1 and K 2 are the pre-exponential factors; Ea is the activation energy of reaction; and ΔH a is the activation energy of carbon monoxide adsorption. The effect of mass and heat transfer were checked by the criteria developed by Mears, (1971), and the results are shown in Table 1. Acoording to the results in Table 1, the effect of mass and heat transfer can be ignored. In addition, the mass and heat transfer coefficients in Table 1 can be obtained by the following equations: Fig. 3. Sketch of tee joint for measuring radial distribution of pressure and gas concentration.

pressure and concentration measurements along the riser at an interval of 500 mm. A carrier gas of 5 ml/min was flowed into Port 7 to prevent blockage, and 20 ml/min gas stream was withdrawn by an aspirator from Port 4 for gas composition analyses; see Fig. 3. In order to obtain the radial average concentration of CO, a quartz sampling tube was used, which has 5 holes (ID1mm) at interval of 10 mm along the top section of the tube and the top section of sampling tube was filled with quartz wood also to prevent blockage (Fig. 3). The experimental results were from the average of at least two replicates, and the experimental uncertainties were kept lower than 5%. In each of the experiments, pure γ-Al2O3 particles with the same diameter as the catalyst were used as the inert material to avoid any effect of particle size.

Dco Dco Dco kg ¼ Sh ¼ 2:0 þ 0:69 dp dp dp

hg ¼ Nu

λg λg λg ¼ 2:0 þ 0:69 dp dp dp

U s dp ρf μf

U s dp ρf μf

!1=2

μf ρf Dco

!1=3

!1=2
 C p μf 1=3 λg

ð4Þ

ð5Þ

where, kg and hg are the gas-solid mass transfer coefficient and heat transfer coefficient respectively; Sh and Nu are Sherwood number and Nusselt number respectively; Dco is mass diffusion coefficient of carbon monoxide in gas mixture; U s is the relative slip velocity between gas and solid; λg is the thermal conductivity of gas mixture; ρf is the density of gas mixture; C p is the constant pressure heat capacity; μf is the viscosity of gas mixture. dp is the particle diameters. Table 1 The effect of diffusion and heat on the kinetics parameter.

2.2. Experimental conditions 2.2.1. Kinetics experiments The intrinsic kinetics parameters have to be determined by the kinetics experiments before characterizing the mass transfer in the CFB. In this set of experiments, effect of inert material on the conversion of carbon monoxide was firstly checked by the blank experiments with pure γ-Al2O3 particles in a temperature range of 423–503 K. In the kinetics experiment, gas velocity was set within the range of 1.2–1.5 L/min. A higher velocity would result in a higher pressure drop, which would influence the kinetics parameters measurements, while a velocity lower than 1.2 L/min would not be compatible with the plug flow assumption. Concentrations of carbon monoxide and oxygen were in the range of 0.2– 1.2 mol/m3 and 0.5–3.0 mol/m3, respectively. Because nitrogen in air has the same molecular weight as carbon monoxide, rates of reaction was determined by using the process mass spectrometer to measure the concentration of carbon dioxide to get around of issues associated with the interference of N2 on CO. 50 mg catalyst and pure γ-Al2O3 were mixed with a mass ratio of 1:5. There was additional 50 mg pure γ-Al2O3 below and above the active bed to eliminate back mixing of gas and keep flow stable, respectively, as shown in Fig. 1. Because the oxidization of carbon monoxide over Pt/γ-Al2O3 catalyst has been widely studied over past few decades, the reaction order and mechanism of carbon monoxide and oxygen are not studied in this paper. Here, the following widely accepted L–H kinetic mechanism is used

Citation

Influence to be eliminated

The value in this paper

ðRðcco ;cO2 ;TÞÞR2P o 0:3 cco Dco ðRðcco ;cO2 ;TÞÞRP jnj o 0:15 cco kg

Internal diffusion

2.4  10  2

Mass transfer

0.12

Heat transfer

2.05  10  2

ðRðcco ;cO2 ;TÞÞRP E a ΔH r hg T 2

o 0:15

Fig. 4. Active energy and pre-exponential factor for the catalytic oxidization of carbon monoxide.

B. Hou et al. / Chemical Engineering Science 102 (2013) 354–364

357

the conversion can be obtained as: x ¼ 1 1

kt

1 !1n

ð1nÞ 1n

c0

ð8Þ

When the reaction becomes mainly dominated by gas-solid mass transfer, the reaction order changed to 1, leading to: x ¼ 1ekt

Fig. 5. Active energy and pre-exceptional factor for oxygen adsorption.

2.2.2. Kinetics parameters Under the conditions of free effects of intraparticle diffusion, mass and heat transfer, the kinetics measurements have been carried out at 423–503 K. r 1 and r 2 were obtained by Newton downhill method. Activation energy (Ea ¼71.8 kJ/mol, ΔH a ¼ 4:20 kJ=mol) and preexponent (K1 ¼ 1.43  1011 m3/mol s  1, K2 ¼ 27.3 m3/mol s  1) were evaluated by the least square method, as shown in Fig. 4 and Fig. 5.

ð9Þ

A comparisons of Eqs. (7)–(9), one can see a clear feature of the process mainly dominated by mass transfer that the conversion of carbon monoxide is independent of the initial concentration of carbon monoxide. This makes the conditions of process dominated by mass transfer to be easily determined based on the macro phenomena, as reported by Venderbosch et al. (1999). Based on Venderbosch et al. (1999) method, equations for the reactant diffusion coupled with reaction kinetics and thermal conductivity in a single catalyst particle can be solved. As a result, the relationships between apparent reaction order and temperature can be obtained. This is shown in Fig. 6, where the concentration of oxygen and carbon monoxide are 2.0 mol/m3 and 0.2 mol/m3, respectively, Sherwood and Nusselt number are respectively 0.5 and 1.0. With an increase in the reaction temperature, the reaction can be divided into three regions. In region I, the reaction is dominated mainly by the intrinsic kinetics with the apparent reaction order slightly higher than 1 due to the effect of intraparticle diffusion and reaction heat. In region II, the reaction is influenced by both mass

2.2.3. Mass transfer experiments In order to obtain appropriate conversion of carbon monoxide, the catalyst was diluted by pure γ-Al2O3 with the same diameter in a mass ratio of 2.8:10,000. Oxygen concentration was in the range of 4.7–5.0% (V%). Carbon monoxide concentration was between 0.5% and 2.5%( V%). N2 was used as the balance gas. The gas flow velocity was in the range of 0.9–1.5 m/s. Temperature was in the range of 623–723 K. Because the whole reactor was placed inside the high temperature electrical furnace, in-situ measuring solid mass flux was not possible. Therefore, in this experiment the solid flux was obtained by measuring the time of collecting a calibrated volume of particles under the condition of environmental temperature by using the same gas flow velocities as the actual operations in the L-valve and riser.

3. Theoretical considerations Fig. 6. Apparent reaction order of carbon monoxide and oxygen for various temperatures.

3.1. Conditions of mass transfer dominated regime Oxidation of carbon monoxide is a -1 order reaction in L–H Eq. (1). To be concise, the L–H kinetics equation is replaced with a 1 order reaction power equation for the analyses. In the case of no transport effects, the reaction rate can be expressed as follows: dc ¼ kc1 dt

ð6Þ

Eq. (6) is integrated with an initial condition to give the following expression: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c0 c 2kt ð7Þ ¼ 1 1 2 x¼ c0 c0 where, x is conversion of carbon monoxide. c0 is the initial concentration of carbon monoxide. c is the concentration of carbon monoxide at the time t. When the reaction is affected by mass transfer and intrinsic kinetics, the apparent reaction order can be expressed asnðn≠1Þ. Based on the same method as Eq. (7),

Fig. 7. Distribution of dimensionless concentration for carbon monoxide and oxygen inside and outside of catalyst particle.

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B. Hou et al. / Chemical Engineering Science 102 (2013) 354–364

transfer and intrinsic kinetics. In region III, the whole reaction process is dominated by mass transfer only. As shown in Fig. 6, reaction becomes the first order at above 750 K, which indicates that the reaction is dominated by mass transfer. As mentioned above, the distributions of carbon monoxide concentration, oxygen concentration and temperature in the catalyst particle are obtained by solving the single particle model (Venderbosch et al., 1999). This is done for the reaction at 750 K and the results are shown in Fig. 7. Where, the symbol δ represents the thickness of gas film outside the particle. One can see that the effects of the gradients of oxygen concentration and temperature on the conversion of carbon monoxide can be neglected, when the process is dominated by mass transfer between bulk gas phase and catalyst particle in this study. 3.2. Mass exchange between cluster phase and dispersed phase According to the model of MSMT (Hou and Li, 2010a), multiscale flow structures in the CFB could be divided into three phases: dispersed phase, inter-phase phase and cluster phase. The conservation laws for momentum, mass and energy can be applied in every phase. Thus, momentum, mass and energy transfer between gas and solid in the whole system can be obtained by summation of equations for each individual phase (Hou and Li, 2010a). The effect of clusters on momentum exchange between gas and solid phase in the CFB is considered by simply replacing the diameter of particles with that of clusters. However, the effect of cluster on the gas-solid mass transfer is difficult either by theoretical analyses or experimental determination because the dispersed phase and cluster phase are converted to one another frequently. To simplify this problem, the following assumptions have to be made: (1) Due to the pressure drop balance between the dispersed phase and cluster phase, convection mass exchange between them can be neglected; (2) Contacting time between dispersed phase and cluster phase is assumed to be approximately equal to the dwell time of gas in cluster; (3) Gas concentrations in the dispersed phase and cluster phase are assumed to be uniform; (4) Clusters are treated as a sphere. According to the above assumptions, the mechanism of gas mass exchange between the dispersed phase and the cluster phase is described as shown in Fig. 8. Thus, the unsteady spherical symmetric one-dimension model can be developed as following:
2  ∂c ∂ c 2 ∂c ¼D ð10Þ þ ∂t ∂r 2 r ∂r Boundary and initial conditions: t¼0

c ¼ cd

( t 40

dc 2

c ¼ cc

r¼1

c ¼ cd

r¼

ð11Þ

where, dc is diameter of cluster, cc and cd are gas concentration in the cluster phase and the dispersed phase, respectively. The solution of the above equations can be expressed as: ! ccd dc rdc =2 erf c ¼ ð12Þ cc cd 2r ð4DtÞ1=2 The rate of diffusion through the surface of cluster can be expressed as: ! ∂c  2 1 þ ð13Þ ðcd cc Þ  dc ¼ ∂r r ¼ 2 dc ðπDtÞ1=2 The average rate of diffusion over the time t can be given as: R t1 ∂c  !  0 ∂r r ¼ dc dt ∂c  2 2 2 ¼ þ ¼ ðcd cc Þ R t1 ∂r r ¼ dc =2 dc ðπDt 1 Þ1=2 0 dt

ð14Þ

Porosity of cluster surface is assumed as εc . Rate of diffusion on unit surface area can be expressed as: ! ∂c  2 2 ðcd cc Þ N ¼ K dc ðcd cc Þ ¼ Dεc r ¼ dc =2 ¼ Dεc þ ∂r dc ðπDt 1 Þ1=2 !
1=2 2Dεc D þ 2εc ð15Þ ðcd cc Þ ¼ πt 1 dc The gas mass exchange coefficient between dispersed phase and cluster phase can be obtained by comparing between right and left of Eq. (15):
1=2 ! 2Dεc D K dc ¼ þ 2:0εc ð16Þ πt 1 dc Based on assumption (2), the contacting time in Eq. (16) can be expressed as: t1 ¼

dc uf c εc

u

pc  1ε c

ð17Þ

3.3. Mass transfer model Traditional CFD model assumes gas concentration to be uniform in each calculating grid, which is composed of two parts in the MSMT model (Hou et al., 2010b): gas concentration in the dispersed phase cd and that in the cluster phase cc . According to the MSMT model, the active component is transported by mass transfer between gas and solid in each phases and mass exchange between cluster phase and dispersed phase in each calculating grid. Thus, mass conservation in each phase can be written as follows: In the dispersed phase: ∂ðð1f Þεd ρg X d Þ þ ∇ðð1f Þρf X d U f d ð1f Þεd ρf D∇X d ÞSd Ma ¼ 0:0 ∂t ð18Þ

In the cluster phase: ∂ðf εc ρf X c Þ þ ∇ðf ρf X c U f c f εc ρf D∇X c ÞSc þ M a ¼ 0:0 ∂t

ð19Þ

where X d and X c are mass fractions of the active component in the dispersed phase and cluster phase respectively, and can be calculated by the following equations:

Fig. 8. Sketch for gas mass exchange between dispersed phase and cluster phase.

Xd ¼

cd M ρf

ð20Þ

Xc ¼

cc M ρf

ð21Þ

B. Hou et al. / Chemical Engineering Science 102 (2013) 354–364

where M is the molecular weight of active component. Sd and Sc are the source terms for Eqs. (18) and (19), respectively, which include mass transfer between gas and solid and mass exchange between the cluster phase and dispersed phase. Sd consists of three components: M d mass transfer between gas and solid in dispersed phase, M i mass transfer between gas in dispersed phase and solid on the surface of cluster and M dc gas mass exchange between cluster phase and dispersed phase. These can be expressed as: M d ¼ K d ap ð1εd Þð1f ÞðX sd X d Þ

ð22Þ

M i ¼ K i ac ð1εc Þf ðX si X d Þ

ð23Þ

M dc ¼ K dc ac f εc ðX c X d Þ

ð24Þ

Sd ¼ M d þ M i þ M dc

ð25Þ

Sc consists of two components: mass transfer between gas and solid in cluster phase M c and gas mass exchange between cluster phase and dispersed phase M dc , and can be expressed as:

359

Gas concentration on the surface of particles in the cluster phase:  E   a K 1 exp  RT ⋅csc ⋅cO2 dp η ð1ε Þf 2ð1ε Þf c c   a  2 dc 1 þ K 2 exp ΔH RT csc ð32Þ ¼ K c ½ð1εc Þf ap ð1εc Þf ac ðcc csc Þ Gas concentration on the surface of particles in the inter-phase phase:  E  a ⋅csi ⋅cO2 K 1 exp  RT dp ð33Þ    2 2:0ð1εc Þf d η ¼ K i ð1εc Þf ac ðcd csi Þ a c c 1 þ K 2 exp ΔH si RT where η, the effectiveness factor of reactants intraparticle diffusion in the pore of catalyst, can be obtained by the model of reactants diffusion coupled with reaction kinetics and thermal conductivity heat transfer in a single particle (Venderbosch et al., 1999). In addition, the average concentration of gas active component in the calculating grid can be obtained from the following equation: εf cf ¼ ð1f Þεd cd þ f εc cc

ð34Þ

M c ¼ K c ðap ac Þð1εc Þf ðX sc X c Þ

ð26Þ

3.4. Momentum transfer model

Sc ¼ M c M dc

ð27Þ

In order to describe the multi-scale structure in the CFB, there are eight local structural parameters need to be given (Yang et al. 2003): voidage values in the dispersed phase εd and cluster phase εc , respectively; superficial gas velocities in the dispersed phase U f d and cluster phase U f c , respectively; superficial particle velocities in the dispersed phase U pd and cluster phase U pc , respectively; diameter of cluster dc ; volume fraction of cluster phase f . The superficial slip velocity in each phase is given as followings: Superficial slip velocity between gas and solid in the dispersed phase: ε U sd ¼ U f d U pd d ð35Þ 1εd

where K d , K c and K i are mass transfer coefficients between gas and solid in dispersed phase, cluster phase and inter-phase phase, respectively. They can be calculated by the following expressions: !1=2 !1=3 μf D D U sd dp ρf K d ¼ 2εd þ 0:69 ð28Þ dp dp εd μf ρf D D D þ 0:69 K c ¼ 2εc dp dp

U sc dp ρf εc μf

D D K i ¼ 2εd ð1f Þ þ 0:69 dc dc

!1=2

μf ρf D

U si dc ρf εd ð1f Þμf

!1=3

!1=2

ð29Þ !1=3 μf ρf D

ð30Þ

M a in Eqs. (18) and (19) means mass transfer from particles to gas due to aggregation and dispersion of particles. There are two kinds of case for dispersion of cluster: a single particle leaves the cluster due to collision of particles and drag of gas, and a bigger cluster is broken into several smaller ones. But, meanwhile, the reverse of these two processes for aggregation of particles also happened. Therefore, the effects of positive and negative on mass transfer between gas and solid in CFB are counteracted. Effect of M a can be neglected under the case of steady state process. X sd , X si and X sc are active components concentration on the surface of particles in the dispersed phase, the inter-phase phase

 β¼

2 ð1f Þð1εd Þ C Dd 12 ρf jU sd jU sd 4π dρ 3 π d 6 p

Superficial slip velocity between gas and solid in the cluster phase: εc ð36Þ U sc ¼ U f c U pc 1εc The superficial slip velocity between gas in dispersed phase and solid on the surface of cluster:
 Uf d U pc U si ¼  ð37Þ ε ð1f Þ εd 1εc d The voidage of cluster can be expressed as: εi ¼ εd ð1f Þ

ð38Þ

The momentum exchange coefficient can be expressed as following (Hou and Li, 2010a):



 d 2 2 cÞ þ 12 dpc f ð1ε C Dc 12 ρf jU sc jU sc 4π dp þ π f 3 C Di 12 ρf jU si jU si 4π dc ⋅εf 2 π 3 d 6 p

d 6 c

ð39Þ

ðug us Þ

and the cluster phase, respectively. These parameters can be obtained by solving mass balance equations between reaction and transport as given in the following: Gas concentration on the surface of particles in the dispersed phase:

The drag coefficient between gas and solid in dispersed phase can be calculated as: C Dd ¼ C D0 ε4:7 d

ð40Þ

where C D0 can be obtained by the following expressions:

 E  a K 1 exp  RT ⋅csd ⋅cO2  ΔH  2 ð1εd Þð1f Þη ¼ K d ð1εd Þð1f Þap ðcd csd Þ 1 þ K 2 exp RTa csd ð31Þ

C D0 ¼

8 < 0:44 24 : Re p

ð1 þ 0:15Rep

Rep 4 1000 0:687

Þ

Rep ≤1000

ð41Þ

360

Rep ¼

B. Hou et al. / Chemical Engineering Science 102 (2013) 354–364

ρf dp U sd μf

The drag coefficient between gas in dispersed phase and cluster can be expressed as: 8 < C D0 εi 4:7 εi ≥0:8 ð1εi Þμf C Di ¼ ð45Þ 7 : 200 ε 3 ρ dc U þ 3ε 3 εi o 0:8

ð42Þ

The drag coefficient between gas and solid in the cluster phase can be written as: 8 < C D0 εc 4:7 εc ≥0:8 ð1εc Þμf ð43Þ C Dc ¼ 7 : 200 εc 3 ρ dp U sc þ 3εc 3 εc o 0:8

i

f

si

i

With the assumption that the clusters are of spherical shape, Reynolds number of cluster can be obtained as following equation:

f

Rep ¼ where C D0 can be calculated by Eq. (41), but Reynolds number was defined as:

ρf dc U si μf

ð46Þ

4. Numerical solutions

ρf dp U sc Rep ¼ μf

ð44Þ

Gambit 2.2 was employed for computational grid, and commercial CFD software Fluent 6.2.16 was used as solver. The schematic diagram of simulating 2d riser is given in Fig. 9, which shows the initial height to be 0.5 m. Eulerian–Eulerian model (called as Two Fluid Model) was developed to simulate flow in circulating fluidized bed, in which particles and gas were both treated as fluid phase in fluidized bed. And the granular kinetic theory was used to calculate viscous forces and solid phase pressure. The eight structure parameters in the calculating grid can be solved by EMMS model (Wang and Li, 2007) based on the averaged voidage and the velocities of gas and solid from CFD. Thus, the momentum transfer and mass transfer coefficients can be calculated in each calculating grid. The governing equations notation in Eulerian are given in Table 2 and solved by a finite volume method. The first-order upwind differencing scheme over the used finite volume was employed to discretize the differential equations. The popular SIMPLE algorithm by Patankar (1980) was used to solve the pressure from gas phase momentum equations. Each simulation lasted 30 s at least. The inlets at the bed bottom and on the two sides of bed were set as the velocity inlet boundary condition for both gas and solid phases respectively, as shown in Fig. 9. The boundary condition at top was fixed as atmospheric pressure. Solids left from top due to drag force and then returned to the

Fig. 9. Schematic diagram of the simulating 2D riser.

Table 2 Governing equations for two-fluid model and its constitutive relations. Continuity equation ðk ¼ g; sÞ

∂ðεk ρk Þ ∂t

þ ∇ðεk ρk uk Þ ¼ 0

Momentum equation ðk ¼ g; s; l ¼ s; gÞ ∂ðεk ρk uk Þ þ ∇ðεk ρk uk uk Þ ¼ ∂t εk ∇pg þ εk ρk g þ ∇τk þ βðul uk Þ

qffiffiffi Solid phase bulk viscosity λs ¼ 43 ε2s ρs dp g 0 ð1 þ eÞ Θπ   1 1=3 ε Radial distribution functions g 0 ¼ 1 εsmg

h

Gas phase stress τg ¼ 2μg Sg

Granular temperature equation

3 ∂ðεs ρs ΘÞ ∂t 2

i þ ∇ðεs ρs us ΘÞ ¼ τs : ∇us ∇q

γ þ βC g C 3βΘ

Solid phase stress τs ¼ ps þ λs ∇μs δ þ 2μs Ss

Collisional energy dissipation γ ¼ 3ð1e2 Þε2s ρs g0 Θ Flux of fluctuating energy q ¼ k∇Θ

Deformation rate Sk ¼ 12 ½∇uk þ ð∇uk ÞT  13 ∇uk δ Solid phase pressure ps ¼ εs ρs Θ½1 þ 2ð1 þ eÞεs g 0 

Conductivity if the fluctuating energy k ¼ pffiffiffiffiffiffiffi 75 k d ρ Θπ k ¼ 384 p s c

2k ½1þ65ð1þeÞεs g 0  ð1þeÞg 0 k

k ¼ 2ε2s ρs dp g0 ð1 þ eÞ

Solid phase shear viscosity μs ¼ 43 ε2s ρs dp g0 ð1 þ eÞ  2 2μs:dilute 4 1 þ ð1 þ eÞεs g0 þ 5 ð1 þ eÞg0 pffiffiffiffiffiffiffi 5 ρ dp πΘ μs:dilute ¼ 96 s

h qffiffiffiffiffiffiffi i 4 Θ π ∇us dp

qffiffiffi Θ π

rffiffiffiffi Θ π

Momentum exchange coefficient: The Eq. (39)

2

þk

c

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Table 3 Parameters of the simulation. Particle diameter Particle density εm Riser height Grid size Δx Grid size Δy Superficial gas velocity at inlet boundary Inlet vodiage of solid inlet Initial bed height H 0 Initial bed voidage ε0 Coefficient of restitution Wall boundary Time step

60 μm 1326 Kg/m3 0.63 4m 0.25 mm 2 mm 1.3 m/s 0.5 0.5 0.5 0.9 No slip 5.0e–5 s

computational domain from the bottom inlet with the same mass flux, as shown in Fig. 9. Other boundary conditions were specified as the wall, which were all set as no-slip wall boundary conditions for both gas and solid phases. The parameters of the simulations were listed in Table 3. And the effect of mesh grid has been checked and could be ignored for all calculations. The convergences criteria of the sum of normalized absolute residuals, which are defined as the sum of the absolute residuals values per grid point over all grid points normalized by the value of that same summation at the beginning of the each time step iterative solution procedure for energy equation is set to 1.0  10  6, for the rest of equation are set to be 1.0  10  3. The maximum iterations per time step are 30.

Fig. 10. Effect of inert particle and reactor on the CO conversion.

5. Results and discussion Firstly, the blank tests with pure γ-Al2O3 powder were performed to evaluate the effect of inert materials and reactor wall on the conversion of carbon monoxide. The experimental results show that the conversion of carbon monoxide is approximately 2.5% at 400 1C (Fig. 10). However, when the temperature is further increased and reached to 4501C, the conversion of carbon monoxide exceeds 6%. Therefore, temperature below 400 1C should be selected in all other experiments. Here, the conversion of carbon monoxide is defined as: x¼

cinlet coutlet  100% cinlet

Fig. 11. Carbon monoxide conversion versus inlet concentration under 350 1C.

ð47Þ

where cinlet and coutlet are the concentration of carbon monoxide at the inlet and outlet, respectively. Figs. 11 and 12 show the influences of temperature, initial concentration of carbon monoxide and gas velocity on the conversion of carbon monoxide. At 350 1C, the conversion of carbon monoxide decreases with the increase of initial carbon monoxide concentration and gas velocity, as shown in Fig. 11, which indicates that the process is not dominated by mass transfer. However, at higher temperature, i.e. 400 1C, the conversion of carbon monoxide is independent of the initial concentration of carbon monoxide up to 0.75%, as shown in Fig. 12, which demonstrates that the condition of process dominated by mass transfer can be attained when the concentration of carbon monoxide is lower than 0.75% and the gas velocity is not greater than 1.5 m/s. In this set of experiments, the operational superficial velocity of gas is 1.3 m/s, and the temperature of reaction is set to be 400 1C. The calculated and measured bed pressures are compared in Fig. 13, and there is good agreement except for the bottom of reactor. This exception can be attributed to high solid concentration at the bottom of reactor, which leads to high energy dissipation of turbulence and wall friction. In Fig. 14, comparison for the solid mass flux between the calculated results of transient behavior and the steady state

Fig. 12. Carbon monoxide conversion versus inlet concentration at the temperature 400 1C

experimental data is shown. The average solid flux of simulating results over the range of flow time from 10 s to 40 s is 8.95 kg/(m2 s), which is slightly higher than the experimental data 7.5 kg/(m2 s). These indicate that the momentum exchange coefficient in Eq. (39) could relatively accurately predict momentum transfer between gas and solid in CFB.

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Fig. 13. Comparison for bed pressure between calculating results and experimental data.

Fig. 14. Comparison for mass flux of particles between simulation results and experimental data.

Fig. 15 shows the experimental data for axial dimensionless concentration distribution of carbon monoxide at various inlet concentrations. In Fig. 15, the dimensionless concentration is calculated by normalizing the experimental data with inlet concentration of carbon monoxide. As shown in this figure, when the inlet concentration of carbon monoxide is lower than 1.12%, its effect on conversion of carbon monoxide can be ignored, which indicates the catalytic reaction between gas and solid is mainly dominated by mass transfer. From Fig. 15, it can be observed that the conversion of carbon monoxide occurs mainly at the bottom of reactor no matter whether the reaction is dominated by mass transfer or not, this is mainly due to S-style axially distribution of catalyst particles in CFB. In addition, the comparison for the experimental data with the MSMT model′s results is shown in Fig. 15, which demonstrates that the process of mass transfer between gas and solid in CFB can be well predicted by the MSMT model. In Fig. 16, a comparison of the outlet concentration of carbon monoxide for the transient simulation results is given considering the cluster effect and the experimental data are given. The simulated average outlet concentration of carbon monoxide at the flow time 10–40 s is 0.17, which is slightly lower than the steady state experimental data (0.22). Concentrations of carbon monoxide in dispersed phase and cluster phase and instantaneous and average solid particles concentration are

Fig. 15. Comparison between the simulation results and experimental data for the axial concentration distribution of carbon monoxide.

Fig. 16. Comparison between calculation and experimentation for the outlet carbon monoxide concentration.

shown respectively in Fig. 17 a, b, c and d. Fig. 17 shows that the concentration of carbon monoxide in the dispersed phase is significantly higher than that in the cluster phase. On the other hand, the concentration of carbon monoxide in the cluster phase is quite low except for the bottom of reactor as shown in Fig. 17b. This might be caused by the fact that most of catalyst particles are included in the cluster phase, while carbon monoxide is mainly in dispersed phase. Therefore, mass exchange between the dispersed phase and the cluster phase becomes the controlling step in this process. Fig. 17c gives the snapshot of solid phase concentration, which indicates that the cluster structure can be simulated by using the drag coefficient Eq. (39) based on the local structure parameters. Fig. 17d shows that the non-uniform structure can be captured by momentum transfer coefficient of Eq. (39), for example, the radial core-annular structure in which the concentration of solid phase is low in the core while high on the walls, as well as for axial S-type structure, that is, solid concentration is low on top and high at bottom.

6. Conclusions In this paper, we use a catalytic oxidization reaction of carbon monoxide over Pt catalyst as a model reaction to study mass transfer in a CFB. At the limit of mass transfer, which can be

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Fig. 17. Snapshot and contours of carbon monoxide concentration and solid phase concentration ((a) snapshot of carbon monoxide concentration in the dispersed phase, (b) snapshot of carbon monoxide in the cluster phase, (c) snapshot of the solid phase concentration, and (d) contours of average simulating solid phase concentration from 20 s to 30 s).

identified by checking the dependence of inlet concentration of carbon monoxide on conversion, the axial distribution of carbon monoxide concentration was measured in the circulating fluidized bed. Experimental data of pressure drop, solids mass flux, axial distribution of carbon monoxide concentration and that in the offgas are employed to compare well with the results of model simulations using the Multi-Scale Mass Transfer (MSMT) model. This indicates that momentum and mass transfer between gas and solid phases in the CFB could be relatively accurately predicted by the MSMT model. The results also demonstrate that the cluster phase in the CFB plays a key role in transport phenomena between gas and solid phases. Although MSMT model shows a relatively good accuracy, mass transfer in the CFB still gives an over estimated as no consideration is made on mass exchange of gas between the cluster phase and the dispersed phase due to the cluster dispersing and aggregating. This is one of the main subjects in our future research.

Nomenclature ap ac c c0 cc cco cd C D0 C Dc C Dd C Di cf c O2

surface area of catalyst of unit volume (m2/m3) surface area of cluster of unit volume (m2/m3) mole concentration of gas (mol/m3) initial concentration of carbon monoxide (mol/m3) gas concentration in the particles cluster (mol/m3) mole concentration of carbon monoxide (mol/m3) gas concentration in the dispersed phase (mol/m3) drag coefficient for single particle in gas flow (N/m3) drag coefficient in cluster phase (N/m3) drag coefficient in dispersed phase (N/m3) drag coefficient between cluster and gas in dispersed phase (N/m3) average concentration of gas phase in calculating grid (mol/m3) mole concentration of carbon monoxide (mole/m3)

Cp csd csc csi dc dp Dco D Ea f hg k kg K1, K2 Kd K dc Kc Ki M Ma Mc Md M dc

heat capacity of gas (J/(kg K)) mole concentration of active component on the surface of catalyst in dispersed phase (mol/m3) mole concentration of active component on the surface of catalyst in cluster phase (mol/m3) mole concentration of active component on the surface of catalyst on the surface of cluster (mol/m3) diameter of particles cluster (m) diameter of catalyst (m) mass diffusion coefficient of carbon monoxide (m2/s) mass diffusion coefficient of gas (m2/s) activation energy of reaction (J/mol) volume fraction of cluster phase heat transfer coefficient between gas and solid (W/(m2 K)) reaction rate constant (1/s) mass transfer coefficient between gas and solid (m/s) pre-exponential factor (m3/mol s-1) mass transfer coefficient between gas and solid in dispersed phase (m/s) mass exchange of gas between particles cluster and dispersed phase (m/s) mass transfer coefficient between gas and solid in cluster phase (m/s) mass transfer coefficient between solid on the surface of cluster and gas in dispersed phase (m/s) molecular weight of active component in gas phase (kg/mol) mass transferred from particles to gas due to aggregation and dispersion of particles (kg/(m3 s)) mass transfer between gas and solid in cluster phase (kg/(m3 s)) mass transfer between gas and solid in dispersed phase (kg/(m3 s)) gas mass exchange between cluster phase and dispersed phase (kg/(m3 s))

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Mi

mass transfer between gas in dispersed phase and solid on the surface of cluster (kg/(m3 s)) n reaction order N mass exchange between particles cluster and dispersed phase on unit surface of cluster (mol/(m2 s)) Nu Nusselt number r radial position of particles cluster (m) R ideal gas constant (J/(mol K)) RP radius of catalyst particle (m) Rep Reynolds number for particles Rðcco ; cO2 Þreaction rate of carbon monoxide oxidation (mol/(m3.s)) Sh Sherwood number Sd source term for Eq.(18) Sc source term for Eq.(19) t reaction time (s) t1 contacting time between particles cluster and dispersed phase(s) T reaction temperature (K) uf c gas velocity in the cluster phase (m/s) upc particle velocity in the cluster phase (m/s) Uf c superficial gas velocity in cluster phase (m/s) Uf d superficial gas velocity in dispersed phase (m/s) U pc superficial particle velocity in cluster phase (m/s) U pd superficial particle velocity in dispersed phase (m/s) Us gas velocity (m/s) U sd superficial slip velocity between gas and solid in the dispersed phase (m/s) U sc superficial slip velocity between gas and solid in the cluster phase (m/s) U si superficial slip velocity between gas in the dispersed phase and solid on the surface of cluster (m/s) x conversion of carbon monoxide Xc mass fraction of the active component in cluster phase Xd mass fraction of the active component in dispersed phase X sc mass fraction of active component on the surface of catalyst in cluster phase X sd mass fraction of active component on the surface of catalyst in dispersed phase X si mass fraction of active component on the surface of catalyst on the surface of cluster. Greek letters ε εc εd εi β ΔH a ρf μf λg

voidage viodage of particles cluster phase voidage of dispersed phase voidage of cluster momentum transfer coefficient (N/m3) activation energy of carbon monoxide adsorption (J/mol) density of gas (kg/m3) viscosity of gas (Pa s) thermal conductivity coefficient of gas (W/(m K)).

Subscripts c d fd

cluster phase dispersed phase gas phase in the dispersed phase

fc g i pd pc s sd sc si

gas phase in the cluster phase gas phase inter-phase phase solid phase in the dispersed phase solid phase in the cluster phase solid phase on the surface of particles in the dispersed phase on the surface of particles in the cluster phase on the surface of particles on the surface of cluster.

Acknowledgments The authors are grateful to the support of the National Science and Technology Support Program of MOST, China (Grant no. 2012BAB14B03), the National Natural Science Foundation of China (21206159) and the State Key Development Program for Basic Research of China (973 Program) under Grant no. 2009CB219904. References Breault, R.W., 2006. A review of gas solid dispersion and mass transfer coefficient correlations in circulating fluidized beds. Powder Technology 163 (1–2), 9–17. Chalermsinsuwan, B., Piumsomboon, P., Gidaspow, D., 2009a. Kinetic theory based computation of PSRI riser: Part I-Estimate of mass transfer coefficient. Chemical Engineering Science 64, 1195–1211. Chalermsinsuwan, B., Piumsomboon, P., Gidaspow, D., 2009b. Kinetic theory based computation of PSRI riser: Part II-Computation of mass transfer coefficient with chemical reaction. Chemical Engineering Science 64, 1212–1222. Dong, W.G., Wang, W., Li, J., 2008a. A multiscale mass transfer model for gas-solid riser flows: Part 1-sub-grid model and simple tests. Chemical Engineering Science 63, 2798–2810. Dong, W.G., Wang, W., Li, J., 2008b. A multiscale mass transfer model for gas-solid riser flows: Part 1-sub-grid simulation of ozone decomposition. Chemical Engineering Science 63, 2811–2823. Hou, B.L., Li, H.Z., 2010a. Relationship between flow structure and transfer coefficients in fast fluidized beds. Chemical Engineering Journal 157 (2–3), 509–519. Hou, B.L., Li, H.Z., Zhu, Q.S., 2010b. Relationship between flow structure and mass transfer in fast fluidized bed. Chemical Engineering Journal 163 (1–2), 108–118. Li, H., Xia, Y., Tung, Y., Kwauk, M., 1991. Micro-visualization of clusters in a fast fluidized bed. Powder Technology 66 (3), 231–235. Mears, D.E., 1971. Tests for transport limitations in experimental catalytic reactors. Industrial & Engineering Chemistry Process Design and Development 10 (4), 541–547. Ouyang, S., Li, X.G., Potter, O.E., 1995. Circulating fluidized bed as a catalytic reactor: Experimental study. A.I.Ch.E. Journal 41 (6), 1534–1542. Patankar, S.V., 1980. Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing Corp., New York. Scala, F., 2007. Mass transfer around freely moving active particles in the dense phase of a gas fluidized bed of inert particles. Chemical Engineering Science 62, 4159–4176. Venderbosch, R.H., Prins, W., van Swaaij, W.P.M., 1999. Platinum catalyzed oxidation of carbon monoxide as a model reaction in mass transfer measurements. Chemical Engineering Science 53, 3355–3366. Voltz, S.E., Morgan, C.R., Liederman, D., Jacob, S.M., 1973. Kinetic study of carbon monoxide and propylene oxidation on platinum catalyst. Industrial & Engineering Chemistry Process Design and Development 12 (4), 294–301. Wang, W., Li, J., 2007. Simulation of gas-solid two-phase flow by a multi-scale CFD approach—of the EMMS model to the sub-grid level. Chemical Engineering Science 62 (1–2), 208–231. Yang, N., Wang, W., Ge, W., et al., 2003. CFD simulation of concurrent-up gas-solid flow in circulating fluidized bed with structure-dependent drag coefficient. Chemical Engineering Journal 96 (1–3), 71–80.