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Effect of gas distributor on hydrodynamic and the Rochow reaction in a fluidized bed membrane reactor Feng Zhang, Zhihao Zhang, Yefei Liu, Zhaoxiang Zhong, and Weihong Xing Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b02028 • Publication Date (Web): 19 Sep 2016 Downloaded from http://pubs.acs.org on October 3, 2016

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Industrial & Engineering Chemistry Research

Effect of gas distributor on hydrodynamic and the Rochow reaction in a fluidized bed membrane reactor Feng Zhang, Zhihao Zhang, Yefei Liu, Zhaoxiang Zhong, Weihong Xing*

State Key Laboratory of Materials-Oriented Chemical Engineering, National Engineering Research Center for Special Separation Membrane, Nanjing Tech University, Nanjing 210009, China

*Corresponding author: Tel.: +86-25-83172288; Fax: +86-25-83172292; E-mail: [email protected]

Abstract Gas distributor configurations were optimized for the direct synthesis of methychlorosilanes in a fluidized bed membrane reactor. The Syamlal-O’Brien drag model was optimized to allow reasonable prediction of solid volume fraction, and the influences of opening area ratio and the number of holes of gas distributor on hydrodynamics were investigated by CFD simulation. The results indicated that a gas distributor with a 0.53% opening area ratio and 19 holes exhibited a steadier radial solid volume fraction distribution and lower dead zone area ratio. The effects of gas distributor configuration on the Rochow reaction were also tested experimentally, and dimethydichlorosilaneselectivity and Silicon conversion were both increased. This suggested that the hydrodynamic behavior using a gas distributor with Φ=0.53% and n=19 is beneficial for a well-distributed heat transfer coefficient. Consequently, Φ=0.53% and n=19 was proposed as the best gas distributor configuration and the reaction yield was 7.3% higher.

Keywords: Fluidized bed membrane reactor; Gas distributor; Rochow reaction; CFD simulation 1

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1. Introduction The direct synthesis of methychlorosilanes (MC) from the reaction of methyl chloride with Si, also known as the Rochow reaction, was developed by Eugene Rochow for the efficient production of MC monomers for the silicone industry. The most desirable of these monomers to date has been DMDC, which serves as the main raw material of the silicone industry. There are several side reactions in the practical processes and improved activity and selectivity would help maximize the yield of DMDC. The reaction rate and DMDC selectivity depend on many factors, which can be grouped into two classes. The first class includes factors that can affect the reaction performances directly, including catalysts, promoters, and temperature. A lot of work has been done investigating the effects of structure and type of Cu-based catalysts on the Rochow reaction, and results showed that the morphological structure, contents, and surface area all have significant effects on DMDC selectivity and Si conversion.1-3 Wang et al.4 compared different promoters for their ability to stimulate the Rochow reaction and found that Zn enhances the formation of Cu3Si in the stirred bed and Sn accelerates the consumption of Cu3Si in the promotion of reaction rate. Han et al.5 reported that the reaction rate increases with the increase of reaction temperature, DMDC selectivity shows an inverse relationship with temperature, and the optimal temperature is between 280~300 oC. Additionally, contact mass irreversibly loses activity at higher temperatures. The other class of factors includes heat transfer and mass transfer in the reactor. A fluidized bed was found to be more efficient, and is widely used in the direct synthesis of methylchlorosilanes. Both experimental and numerical simulations were performed to measure the mass and heat transfer in the fluidized bed reactor. Fan et al.6 found that the particle material and gas flow rate have significant effects on the solid/bubble motion in a fluidized bed and these rates could be predicted by the correlations from Werther and Darton. Esmaili et al.7 simulated the momentum transfer between phases using several drag models and proposed an optimization 2


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method to minimize deviation from the experiment data. Hou et al.8 reported that the heterogeneous gas–particles flow structure can exert significant effects on the drag coefficient, the mass transfer coefficient, and the heat transfer coefficient in fast fluidized beds, and developed a model that included flow structure and that could predict the effects accurately. Jie et al.9 discussed the effects of reactor structure on moderate temperature dry desulfurization in a fluidized bed and reported that a gas distributor with large holes reduces desulfurization efficiency due to inefficient bed fluidization. Geldart et al.10 found that light of uniform gas distribution, bubble formation, pressure drop, dead zones, and particle attrition were affected by the design of distributors for gas-fluidized beds. The effects of fluidized bed reactor construction on fluid hydrodynamic behavior especially DMDC selectivity and Si conversion are less studied. Our previous work did not consider the influences of fluidized bed reactor construction on the Rochow reaction, and only catalyst concentration and superficial velocity effects on DMDC selectivity and Si conversion were studied in fluidized bed membrane reactor.11 To more fully understand the effects of gas distributor configurations on the fluid hydrodynamic behavior in the fluidized bed membrane reactor, we developed and validated a 3D computational model of a fluidized bed reactor for the synthesis of methychlorosilanes. The gas distributor configuration was optimized for opening area ratio and the number of holes, and simulation data were used to correlate with the experimental results. The effects of gas distributor configuration on DMDC selectivity and Si conversion were also investigated experimentally.

2. Experimental details A fluidized bed membrane reactor was constructed to synthesize MC directly. Figure 1 shows a schematic representation of the experimental setup, including gas source, fluidized bed membrane reactor, product collection system, and off gas scrubber. The ceramic membrane used in this experimental was a tubular Al2O3 membrane, with a length of 65 mm, an outer diameter of 13 mm, an inner diameter of 8 3



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mm, a nominal average pore size of 3~5 µm, which was provided by Nanjing Jiusi High-Tech Co., Ltd., China. The main parameters of the reaction experiment program as described by Wu et al.11 are listed in Table 1. Additionally, Cu-Cu2O-CuO was used as catalyst and ZnO was used as a promoter. The MC products were mainly comprised of methyltrichlorosilane (MTC), DMDC and trimethylchlorosilane (TMC) which accounted for about 95 wt% of total reaction products. For simplifying the calculation, the other products were not taken into account, hence the DMDC selectivity, Si conversion and DMDC yield were calculated according to the following formulas: weight DMDC × 100% + weight DMDC + weight TMC

(1)

weight reactant before reaction − weight reactant after reaction × 100% weight reactant before reaction

(2)

DMDC selectivity =

Si conversion =

weight MTC

DMDC yield = DMDC selectivity × Si conversion × 100%

Table 1 The main parameters of the reaction experiment program. Parameters

Value

Diameter of Si (m)

2×10-4

Minimum fluidization velocity (Umf, m/s)

1.41×10-2

Superficial velocity (m/s)

1.56×10-2

Mass ratio of reactant (Si:Catalyst:Promoter)

100:4:1

Pressure (MPa)

0.2

Temperature (oC)

315±5

4


(3)

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Figure 1. Schematic representation of the experimentation design.

An experimental apparatus was also constructed to measure the point solid volume fraction at different radial positions, as presented in Figure 2. This was composed of an organic glass fluidized bed, solid volume fraction measurement device (PC6M, provided by Institute of Process Engineering, Chinese Academy of Sciences), and a data acquisition module. The measurement position was located at 0.05 m above the gas distributor, which was just below the maximum initial bed height of 0.177 m.

Figure 2. The test instrument to measure the solid volume fraction. 5



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3. Simulation methods A two-fluid model based on the Euler-Euler approach was employed to investigate the effects of gas distributor configuration on the hydrodynamic behavior of gas-solid flow in a fluidized bed reactor. The gas phase was considered the first phase and the particle phase was considered as the secondary phase.

3.1. Conversion equations and drag models The mathematical model applied in the numerical study is based on two principles of fluid dynamics, mass and momentum conversion for the gas and solid phases. Table 2A lists the details of the model. The Kinetic Theory of Granular Flow is used to describe the properties of solid phases. The drag force between phases is one of the dominant forces in a fluidized bed. Three widely used drag models in gas-solid flow, including the Wen-Yu drag model, the Huilin-Gidaspow drag model, and the Syamlal-O’Brien drag model, are summarized in Table 2B. In all drag correlations, the drag force depends on the local relative velocity and the void fraction. In the derivation of these general empirical drag correlations, some other factors are not considered, such as particle size distribution or particle shape. Void fraction is very difficult to determine for conditions other than a packed bed. However, there is specific information on minimum fluidization velocity for particular materials. Syamlal12 introduced a feasible optimization method, listed in Table 2B, to modify the original drag law using minimum fluidization velocity to include commonly available experimental information for a specific material.

Table 2 Summary of Euler-Euler governing equations and drag model correlations. A. Governing equations (a) Continuity equations for gas (g) and solid (s) phases uur ∂ (α g ρ g ) + ∇ • (α g ρ gν g ) = 0 ∂t 6


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uur ∂ (α s ρ s ) + ∇ • (α s ρ sν s ) = 0 ∂t (b) Momentum conversation equations for gas and solid uur uuruur uur uur ∂ (α g ρ gν g ) + ∇ • (α g ρ gν gν g ) = ∇ • τ g − α g ∇p + α g ρ g g + Κ sg (ν s −ν g ) ∂t uur uur uur uur uur ∂ (α s ρ sν s ) + ∇ • (α s ρ sν sν s ) = ∇ • τ s − ∇ps − α s ∇p + α s ρ s g + Κ sg (ν s − ν g ) ∂t (c) Stress-strain tensor for gas and solid uur uur uur 2 τ g = α g µ g (∇ν g + (∇ν g )T ) − α g µ g ∇ • ν g I 3 uur uur T uur 2 τ s = α s µs (∇ν s + (∇ν s ) ) + α s (λs − µs )∇ • ν s I 3 (d) Solid pressure Ps = α s ρ s Θ s + 2 ρ s (1 + e)α s2 g 0 Θ s

α 1 3 g 0 = 1 − ( s ) 3  5  α s ,max 

−1

13

B. Drag model correlations (a) Wen-Yu drag model14

Κ sg =

CD =

3 ρ gα g α s 4d s

uur uur C D ν s −ν g α g−2.65

24 1 + 0.15(α g Re s )0.687  α g Re s uur uur

Re s =

ρ g d s ν s −ν g µg

(b) Huilin-Gidaspow drag model15

K sg = (1 − ϕsg ) K sgErgun + ϕ sg K sgWu − yu K

Ergun sg

α s2 µ g α g ρ g uur uur ν s −ν g , α g ≤ 0.8 = 150 + 1.75 α g d s2 ds

K sgWu − yu = Κ sg =

3 ρ gα s 4d s

uur uur C D ν s −ν g α g−2.65 , α g ≥ 0.8

7



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 24 1 + 0.15(α g Re s )0.687  , Re s < 1000  CD = α g Re s 0.44, Re ≥ 1000 s  uur uur ρ g d s ν s −ν g Re s =

µg

ϕ sg =

Arc tan 150 ×1.75 ( 0.2 − α s ) 

π

+ 0.5

(c) Syamlal-O’Brien drag model16

Κ sg =

Re s uur uur 3 α sα g ρ g C ( ) ν −ν D ν r ,s s g 4 ν r2, s d s 2

    4.8   CD = 0.63 +  Re    ν r   1 ν r =  A − 0.06 Re+ (0.06 Re) 2 + 0.12 Re(2 B − A) + A2   2

A = α g4.14 C2α 1.28 g , α g < 0.85  C B = α g 1 , α g ≥ 0.85  C1 = 2.65, C2 = 0.8 (d) Optimization method12

υr , s =

Ret A + 0.06 B Re s = Re s 1 + 0.06 Re s

Ret =

υt d s ρ g α g µg

  4 Ar  4.82 + 2.52 − 4.8  3  Re s =    1.26      

2

8


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(ρ Ar =

s

− ρ g ) d s3 ρ g g

µ g2

A = α g4.14 B = C2α 1.28 g C1 = 1.28 +

log ( C2 ) log ( 0.85 )

3.2. Simulation setup Figure 3a shows the simulated fluidized bed reactor. This system is composed of pre-distributor, gas distributor, reaction zone, and expanding section. Si particles enter the reaction zone as bed material and the initial bed height is 0.177 m. The computational domain consists of three parts: pre-distributor, gas distributor, and reaction zone, as shown in Figure 3b. The computational domain has a 0.026 m I.D., is 0.308 m in height, and the gas distributor is 0.003 m thick.

Figure 3. Diagrammatic sketch of fluidized bed membrane reactor. (a) Fluidized bed reactor; (b) Computational domain.

The simulations were carried out in a 3D fluidized bed reactor based on the computational domain in Figure 3b. The gas entered the fluidized bed from the 9



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bottom and traveled through the gas distributor to the gas outlet. Thus, the bottom was set as the velocity inlet and the gas outlet was set as the pressure outlet at atmosphere pressure. The no-slip boundary condition was used at the bed walls. The material properties and the simulation parameters used in this article are listed in Table 3. According to our previous work11, the Rochow reaction has the highest Si conversion when the superficial velocity was 1.56×10-2 m/s as shown in Table 3, which was 1.1 times of critical fluidization velocity (1.41×10-2 m/s).

Table 3 Summary of material properties and the simulation parameters. Parameters

Value

Gas density (kg/m3)

2.22

Gas viscosity (Pa·s)

2.15×10-5

Superficial gas velocity (m/s)

1.56×10-2

Particle density (kg/m3)

2328.3

Mean particle diameter (m)

2×10-4

Restitution coefficient e

0.9

Initial solid packing

0.49

Static bed height (m)

0.177

Inlet boundary condition type

Velocity-inlet

Outlet boundary condition type

Pressure-outlet

4. Results and discussions 4.1. Drag model selection and model validation Several drag models, including the Huilin-Gidaspow drag model, the Syamlal-O’Brien drag model, and the Wen-Yu drag model, were evaluated under the gas distributor as shown in Figure 5b with Φ=5.92% and n=10. In our previous work, we found that the gas-solid flow reached close to steady state within 8 s. Figure 4 shows the snapshots of solid volume fraction distribution profiles at the center slice of 10


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the fluidized bed at 10 s according to different drag models. In the fluidized bed, when calculating the mean residence time, the porosity of about 0.5 should be taken into consideration. Hence, the mean residence time is about 5 second in the bed. So the volume fraction showed little difference between 0 s and 10 s in these three drag models, and the pre-distributors were all filled with solid. Additionally, the magnitude of solid axial velocity was below zero as shown in Figure 5a, indicating that the solid particles were all moving in the opposite direction of gas when the superficial velocity was 1.1 Umf. Consequently, these three commonly used drag models all underestimate the gas-solid interaction.

Figure 4. Solid volume fraction distribution profiles in the fluidized bed for different drag models at 10 s. (a) Huilin-Gidaspow drag model; (b) Syamlal-O’Brien drag model; (c) Wen-Yu drag model; (d) Optimized drag model; (e) experimental snapshot.

The Syamlal-O’Brien drag model was optimized by the method detailed in Table 2B. According to minimum fluidization velocity and other available experiment information for the contact mass in this work, the drag coefficients were changed to C1=38.918 and C2=0.002 from the default values (C1=2.65 and C2=0.8), and the 11



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optimized drag model was incorporated in the simulation by UDF. The optimization method of Syamlal-O’Brien drag model which was used to obtain the modified C1 and C2 was shown in Table 2 B(d). As shown in Figure 4d, the solid volume fraction distribution profile was obviously different when the optimized drag model was used. The magnitude of solid axial velocity shown in Figure 5a was partly above zero, indicating that the particles are fluidized. It can also be seen from the results in Figure 5b that the simulation data of the solid volume fraction at 0.05 m height agreed well with the experiment data. The optimized drag model reasonably predicted the hydrodynamic behavior in the fluidized bed membrane reactor.

Figure 5. (a) Solid axial velocity distribution using different drag models and (b) Comparison of solid volume fraction between simulation and experiment.

4.2. Effect of gas distributor configuration on hydrodynamic behaviors 4.2.1. Opening area ratio Gas distributors with opening area ratios of 5.92%, 3.33%, 1.48%, 0.95% and 0.53% were selected for a gradual reduction of the orifice diameter with the same number and position of holes. Figure 6 shows the snapshots of solid volume fraction distribution profiles in the fluidized bed for different opening area ratios. The gas distributor with Φ=0.53% showed the longest jet penetration length, which can be attributed to the increase in orifice velocity with the decrease of opening area ratio at the same superficial velocity. Rees et al.17 also observed this trend experimentally. 12


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However, the gas distributor with Φ=5.92% shows a longer penetration length than that of Φ=3.33%, probably because the leaky particles partly block the orifice causing increased orifice velocity.

Figure 6. Solid volume fraction distribution profiles in the fluidized bed for different opening area ratios at 10 s. (a) 5.92%; (b) 3.33%; (c) 1.48%; (d) 0.95%; (e) 0.53%.

Figure 7a shows the solid volume fraction distribution at 0.05 m above the gas distributor for different opening area ratios. Since the superficial gas velocity used is just a little higher than the critical fluidization velocity, the fluidized bed is quite homogeneous. The solid volume fraction does not change with time obviously. The gas distributor with Φ=0.53% showed the lowest fluctuation frequency and amplitude of the solid volume fraction, which indicates improved gas distributor stability. This is likely because the gas distributor pressure drop increases as the opening area ratio decreases. Lim et al.18 reported that stability enhancement improves heat transfer. Accordingly, 0.53% was selected as the best one of the several simulated opening area ratios, and the simulation results showed good agreement with the experimental data as shown in Figure 7b.

13



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Figure 7. Solid volume fraction distribution at 0.05 m above the gas distributor. (a) Comparison between different opening area ratios; (b) Comparison between simulation and experimental results.

The dead zone area ratio also can affect gas distributor performance. The region of slow-moving or stagnant material near the gas distributor is called the dead zone. Wen et al.19 reported that the dead zone consists of three parts in the axial direction from the surface of gas distributor. The first one is a stagnant volume of material positioned directly on the top of distributor. The second one is a quasi-dead volume, which can occasionally mix into the fluidized particles. The material in the last volume can be intermittently disrupted by bubbles that break away from the jets. The dead zone has poor gas-solid contact and it may constitute the highest solid volume fraction of the fluidized bed reactor. The average solid volume fraction (αs,avg) has been proposed to describe the dead zone, and when αs>αs,avg, the corresponding region on the gas distributor is regarded as a dead zone. Figure 8 shows the dead zone area ratio of gas distributor with different opening area ratios. The dead zone area ratio dramatically increased as the opening area ratio decreased from 5.92% to 1.48%, and did not change further when the opening area ratio decreased below 1.48%. The gas distributor with Φ=0.53% showed a relatively high dead zone area ratio which will cause poor heat transfer, sintering, and defluidization. Next, we attempted to decrease the dead zone area ratio of the gas distributor with Φ=0.53%. 14


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Figure 8. The gas distributor dead zone area ratio for different opening area ratios.

4.2.2. Number of holes The number of holes was increased under the same opening area ratio (Φ=0.53%) by reducing the orifice diameter to investigate effects on the dead zone area ratio. Figure 9 shows the dead zone area ratio for 10, 13, and 19 holes. The dead zone area ratio decreased with the increased number of holes. The gas distributor with n=19 showed the lowest dead zone area ratio, 10% lower than that of n=10. This indicates that the gas-solid contact near the gas distributor was improved, which will weaken sintering and defluidization.

Figure 9. The gas distributor dead zone area ratio for different numbers of holes.

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Figure 10a illustrates the solid volume fraction distribution at 0.05 m above the gas distributor for different numbers of holes. The fluctuation frequency and amplitude of the solid volume fraction became lower as the number of holes increased, which indicates that gas distributor stability was increased. This can be attributed to the increase in the gas distributor pressure drop with the increased number of holes. The simulation results are in good agreement with the experimental data (Fig 10b). Hence, the gas distributor with Φ=0.53% and n=19 shows both high stability and a low dead zone area ratio, showing the best performance of the tested gas distributors.

Figure 10. Solid volume fraction distribution at 0.05 m above the gas distributor. (a) Comparison for different numbers of holes; (b) Comparison between simulation and experimental values.

4.3. Effect of gas distributor configuration on reaction performance Reaction experiments were performed to evaluate the effects of different gas distributor configurations (including Φ=5.92% and n=10, Φ=0.53% and n=10, and

Φ=0.53% and n=19) on DMDC selectivity and Si conversion. Screen mesh was used to avoid slight leakage for the gas distributor with Φ=5.92% and n=10. Figure 11a shows the total product mass versus reaction time for the three different gas distributor configurations. Figure 11b shows the Si conversion under three different gas distributor configurations with the reaction time of 420 min. It is evident from the results in Figure 11a that the total product mass increased with 16


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reaction time, and the slowdown of growth rate of the total product mass can be attributed to the generated by-product carbon that blankets the active site of the reaction. The gas distributor with Φ=0.53% and n=19 showed higher product mass during the whole reaction process. This can be attributed to the excellent mass and heat transfer and low dead zone area ratio and high stability under this condition. The corresponding Si conversion in Figure 11b shows an increase in Si conversion from 42% (Φ=0.53% and n=10) to 51.5% (Φ=0.53% and n=19).

Figure 11. Effects of gas distributor configurations on the (a) total product mass and (b) Si conversion.

The DMDC selectivities for different gas distributor configurations are presented in Figure 12. In the first 200 min, the gas distributors with Φ=0.53% all show a relatively high DMDC selectivity. The gas distributor with Φ=0.53% showed the lowest fluctuation frequency and amplitude of the solid volume fraction, and the radial distribution of particle volume fraction was more uniform which indicated improved gas distributor stability. The radial heat transfer coefficient distribution was consistent with the solid volume fraction profile.20,21 Consequently, the gas distributor with higher stability showed a better heat transfer, the side reactions were suppressed, and the reactions showed higher DMDC selectivity. After 200 min, gas distributors with

Φ=5.92 % and n=10 and Φ=0.53 % and n=19, showed steady DMDC selectivity. This can be attributed to the low dead zone area ratio of these two gas distributors. The dead zone shows poor heat transfer and the dead zone share of the reactants rises with 17



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the reaction time. Accordingly, the Rochow reaction in a gas distributor with a lower dead zone area ratio suffers much less effect from the dead zone, allowing maintenance of DMDC selectivity. Hence, the gas distributor with Φ=0.53% and

n=19 exhibited both high stability and a low dead zone area ratio and showed the highest DMDC selectivity in the whole reaction process.

Figure 12. DMDC selectivity for different distributor configurations.

A comparison of data of the DMDC selectivity reported here and that reported previously is presented in Table 4. The Rochow reaction as studied in this work shows a higher DMDC selectivity than that published previously for both the same reactor type and a stirred bed reactor with superior mass and heat transfer. Additionally, the DMDC selectivity observed here is higher than other reports using the same catalyst. Thus, the optimization of gas distributor configuration can efficiently promote DMDC selectivity.

Table 4 Comparison of DMDC selectivity observed in this study and data published previously. Reference

Reactor type

Temperature

DMDC selectivity

(oC)

(%)

Catalyst

Zhang et al.22

Fluidized bed reactor

Cu

300

79

Han et al.5


CuCl

310

83

Wang et al.23

Stirred bed reactor

CuCl

320

83

18


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Liu et al.3

Fixed bed reactor

Cu-Cu2O-CuO

325

82

Wu et al.11


Cu-Cu2O-CuO

310

85

Fluidized bed reactor Cu-Cu2O-CuO

315

88

This work

5. Conclusions The optimized drag model can reasonably predict hydrodynamic behavior in the fluidized bed membrane reactor and the CFD simulation results showed good agreement with the experimental data. The decrease in the opening area ratio can promote gas distributor stability but also can increase the dead zone area ratio. However the increase in the number of holes decreases the dead zone area ratio, leaving the stability unchanged. The experimental results indicate that the increase of gas distributor stability and the decrease of dead zone area ratio promote both DMDC selectivity and Si conversion. The gas distributor with Φ=0.53% and n=19 was the best of the gas distributors examined here. This distributor allows both high stability and a low dead zone area ratio, and DMDC selectivity and Si conversion were maintained at 88% and 51.5%, respectively.

Acknowledgement Financial supports of this work are from the National Natural Science Foundation of China (U1510202, No.21306079, 21276124), the Innovative Research Team Program by the Ministry of Education of China (No. IRT13070), the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) of China, and the Jiangsu Province Scientific Supporting Project (No. BE2015695, BE2014717), the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (13KJB530005).

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Notation A

constant in Syamlal-O’Brien drag model (-)

Ar

the Archimedes number (-)

B

constant in Syamlal-O’Brien drag model (-)

CD

drag coefficient (-)

Cn

drag factor on multi-particle system (-)

ds

diameter of solid particle (m)

e

restitution coefficient of solid phase (-)

g

the gravitational acceleration (=9.81) (m s-1)

g0

the general radial distribution function (-)

I

the unit tensor (-)

Ksg

drag factor of phase solid in phase gas (kg m-3 s-1)

P

pressure (Pa)

Ps

solids pressure (Pa)

Re

the Reynolds number (-)

t

time (s)

n

number of holes

Greek letters

α

volume fraction(dimensionless)

ρ

density (kg/m3)

µ

viscosity (kg m-1 s-1)

λ

bulk viscosity (kg m-1 s-1)

Θ

granular temperature (m2 s-2)

υr,s

the relative velocity correlation (-)

r

ν

velocity (m/s)

τ

shear stress of gas or solid phase (Pa)

Φ

opening area ratio 20


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Subscripts X

gas or solid phase

s

solid phase

g

gas or fluid phase

Max

maximum

t

terminal

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51, 1264. (2) Jin, Z.; Li, J.; Shi, L.; Ji, Y.; Zhong, Z.; Su, F. One-pot hydrothermal growth of raspberry-like CeO2 on CuO microsphere as copper-based catalyst for Rochow reaction. Appl. Surf. Sci. 2015, 359, 120. (3) Liu, S.; Wang, Y.; Zhu, Y.; Wang, G.; Zhang, Z.; Che, H.; Jia, L.; Su, F. Controllably oxidized copper flakes as multicomponent copper-based catalysts for the Rochow reaction. RSC Adv. 2014, 4, 7826. (4) Wang, C.; Liu, T.; Huang, Y.; Wang, G.; Wang, J. Promoter Effects of Zn and Sn in the Direct Synthesis of Methylchlorosilanes. Ind. Eng. Chem. Res. 2013, 52, 5282. (5) Han, L.; Luo, W.; Liang, W.; Wang, G.; Wang, J. Effect of Reaction Temperature on Synthesis of Methylchlorosilane. Chem. React. Eng. Technol. 2002, 18, 187. (6) Fan, X.; Parker, D. J.; Yang, Z.; Seville, J. P. K.; Baeyens, J. The effect of bed materials on the solid/bubble motion in a fluidised bed. Chem. Eng. Sci. 2008, 63, 943. (7) Esmaili, E.; Mahinpey, N. Adjustment of drag coefficient correlations in three dimensional CFD simulation of gas–solid bubbling fluidized bed. Adv. Eng. Softw.

2011, 42, 375. (8) Hou, B.; Li, H. Relationship between flow structure and transfer coefficients in fast fluidized beds. Chem. Eng. J. 2010, 157, 509. (9) Jie, Z.; Changfu, Y.; Haiying, Q.; Bo, H.; Changhe, C.; Xuchang, X. Effect of operating parameters and reactor structure on moderate temperature dry desulfurization.

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Scientific Reports 1966, 100. (15) Lu, H.; He, Y.; Gidaspow, D. Hydrodynamic modeling of binary mixture in a gas bubbling fluidized bed using the kinetic theory of granular flow. Chem. Eng. Sci. 2003,

58, 1197. (16) Syamlal, M.; O'Brien, T. J. Simulation of granular layer inversion in liquid fluidized beds. Int. J. Multiphase Flow 1988, 14, 473. (17) Rees, A. C.; Davidson, J. F.; Dennis, J. S.; S Fennell, P.; Gladden, L. F.; Hayhurst, A. N.; Mantle, M. D.; Müller, C. R.; Sederman, A. J. The nature of the flow just above the perforated plate distributor of a gas-fluidised bed, as imaged using magnetic resonance. Chem. Eng. Sci. 2006, 61, 6002. (18) Lim, J. H.; Lee, Y.; Shin, J. H.; Bae, K.; Han, J. H.; Lee, D. H. Hydrodynamic characteristics of gas–solid fluidized beds with shroud nozzle distributors for hydrochlorination of metallurgical-grade silicon. Powder Technol. 2014, 266, 312. (19) Wen, C. Y.; Krishnan, R.; Kalyanaraman, R. Particle Mixing near the Grid Region of Fluidized Beds. In Fluidization, Grace, J.; Matsen, J., Eds. Springer US: 1980; pp 405. (20) Ma, Y.; Zhu, J. X. Heat transfer between gas–solids suspension and immersed surface in an upflow fluidized bed (riser). Chem. Eng. Sci. 2000, 55, 981. (21) Qi, C.; Farag, I. H. Radial particle flux and momentum transfer in the circulating fluidized bed. Chem. Eng. Commun. 1993, 124, 15. (22) Zhang, P.; Duan, J. H.; Chen, G. H.; Wang, W. W. Effect of Bed Characters on the Direct Synthesis of Dimethyldichlorosilane in Fluidized Bed Reactor. Scientific 23



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Figure Captions Figure 1. Schematic representation of the experimentation design. Figure 2. The test instrument to measure the solid volume fraction. Figure 3. Diagrammatic sketch of fluidized bed membrane reactor. (a) Fluidized bed reactor; (b) Computational domain.

Figure 4. Solid volume fraction distribution profiles in the fluidized bed for different drag models at 10 s. (a) Huilin-Gidaspow drag model; (b) Syamlal-O’Brien drag model; (c) Wen-Yu drag model; (d) Optimized drag model; (e) experimental snapshot.

Figure 5. (a) Solid axial velocity distribution using different drag models and (b) Comparison of solid volume fraction between simulation and experiment.

Figure 6. Solid volume fraction distribution profiles in the fluidized bed for different opening area ratios at 10 s. (a) 5.92%; (b) 3.33%; (c) 1.48%; (d) 0.95%; (e) 0.53%.

Figure 7. Solid volume fraction distribution at 0.05 m above the gas distributor. (a) Comparison between different opening area ratios; (b) Comparison between simulation and experimental results.

Figure 8. The gas distributor dead zone area ratio for different opening area ratios. Figure 9. The gas distributor dead zone area ratio for different numbers of holes. Figure 10. Solid volume fraction distribution at 0.05 m above the gas distributor. (a) Comparison for different numbers of holes; (b) Comparison between simulation and experimental values.

Figure 11. Effects of gas distributor configurations on the (a) total product mass and (b) Si conversion.

Figure 12. DMDC selectivity for different distributor configurations.

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