Huang Kai　 Lin Sheng　 Zhou Jiancheng

(School of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, China)

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Numerical simulation of diffusion processfor oxidative dehydrogenation of butene to butadiene

Huang Kai Lin Sheng Zhou Jiancheng

(School of Chemistry and Chemical Engineering, Southeast University, Nanjing 211189, China)

Abstract：A comprehensive single particle model which includes the mesoscale and microscale models was developed to study the influence of particle diameter on mass and heat transfer occurring within a ferrite catalyst during the oxidative dehydrogenation of butene to butadiene process. The verified model can be used to investigate the influence of catalyst diameter on the flow distribution inside the particle. The simulation results demonstrate that the mass fraction gradients of all species, temperature gradient and pressure gradient increase with the increase of the particle diameter. It means that there is a high intraparticle transfer resistance and strong diffusion when applying the large catalysts. The external particle mass transfer resistance is nearly constant under different particle diameters so that the effect of particle diameter at external diffusion can be ignored. A large particle diameter can lead to a high surface temperature, which indicates the external heat transfer resistance. Moreover, the selectivity of reaction may be changed with a variety of particle diameters so that choosing appropriate particle size can enhance the production of butadiene and optimize the reaction process.

Key words：multi-scale model; mass and heat transfer; particle diameter; oxidative dehydrogenation of butene to butadiene; single particle model; transfer resistance

Received 2015-01-05.

Biography：Huang Kai (1973—), male, doctor, associate professor, huangk@seu.edu.cn.

Foundation items：The National Science Foundation of China (No.21576049, 21576050), the Fundamental Research Funds for the Central Universities (No. 2242014K10025).

Citation：Huang Kai, Lin Sheng, Zhou Jiancheng. Numerical simulation of diffusion process for oxidative dehydrogenation of butene to butadiene[J].Journal of Southeast University (English Edition),2015,31(4):572-576.[doi:10.3969/j.issn.1003-7985.2015.04.024]

The requirement of butadiene has increased recently because it is an important raw material for manufacturing a large number of chemical products in the petrochemical industries[1]. Although the production of butadiene primarily depends on the extraction of butadiene from crude C4 stream, establishing as additional cracking unit of naphtha cannot meet the rising demand due to the fact that other basic fractions are excessively produced[2]. The oxidative dehydrogenation of butene has attracted much attention as a promising process to produce butadiene. A great number of catalysts such as vanadium-containing catalyst[3], ferrite-type catalyst[4], Bi-Mo based catalyst[1], and Octahedral Molecular Sieves catalyst[5]have been investigated for this reaction system. As Zinc ferrite is the most efficient catalyst, it has been widely employed by researchers[6].

It is well known that diffusion exists within the catalyst particle. Zinc ferrite and its kinetics have been widely studied for the oxidative dehydrogenation of butene to butadiene, but to the best of our knowledge, no paper reports the influence of the catalyst particle diameter on particle mass and heat transfers[6]. Therefore, a model should be developed to study the effect of the diameter.

In this work, a comprehensive single particle model, containing the mass, energy, and momentum balances as well as the gas-state equations, kinetic equations, and multicomponent diffusion equations, is developed to analyze the process of ODOBTB. The single particle model is a multiscale model, which can study the diffusion on the mesoscale and microscale. In addition, the multiscale model can compute the distribution of pressure, species fractions, and temperature so that the influence of particle size to particle transfer can be achieved.

1Single Particle Model and Solution Derivation

1.1　Modeling of particle mass and heat transfer

A comprehensive single particle model contains the mass, energy, and momentum balances as well as the gas-state equations, kinetic equations, and multicomponent diffusion equations[7]. After modeling, three assumptions have been accepted: 1) The Zinc ferrite catalyst is regarded as a spherical particle; 2) The deformation of particle can be ignored; and 3) All particle parameters vary with the radial position only. Thus, the following model equations can be obtained.

Total mass balance in a particle:

(1)

Momentum balance in a particle:

(2)

Component material balance in a particle:

(3)

Heat balance in a particle:

(4)

Whenr=0,

ji,0=0,Qr=0

(5)

(6)

whereki,gis the mass transfer coefficient, W/(s·K);hi,gis the heat transfer coefficient, W/(m2·K), and they can be computed via the next equations:

(7)

(8)

(9)

(10)

(11)

Nui=2+0.6Pr1/3Re0.5

(12)

(13)

wheredpis the catalyst average diameter, m;Shiis the Sherwood number of thei-th component;Scis the Schmidt number;Pris the Prandtl number;Reis the Reynolds number;fis the fanning coefficient;μis the mixture fluid viscosity, Pa/s;uis the apparent gas velocity, m/s.

1.2　Reaction kinetics

A kinetics model derived by Ding et al.[8]is used to describe the ODOBTB process based on the Mars-van Krevelen mechanism. The kinetics equations are shown as follows:

(14)

(15)

(16)

(17)

r1,r2andr3represent the reaction rates of the chemical equations for Eqs.(14) to (16), respectively. More details about kinetics parameters are listed in Tab.1[8].

Tab.1　Kinetic parameters for kinetic model

1.3　Solution derivation

The above equations are discretized by the orthogonal collocation method and then the equations can be converted into a set of differential equations. The ODE23S function in the Matlab soft is utilized to compute these differential equations. The model solution and the relationship of the sub-model are shown in Fig.1. All the simulations are performed on a workstation with four

Fig.1　The whole flow-sheet for solving the single model

4.10 GHz Pentium CPUs and 8 GB memory. Modeling with 3, 4, 6, 8, and 10 points are first executed to confirm whether the results are dependent on the number of collocation points or not. The result is that four points can obtain adequately accurate results. Consequently, the simulations are based on four collocation points. The parameters of simulation are listed in Tab.2[9-12].

Tab.2　The parameters for the model

2Results and Discussion

2.1　Model validation

In order to validate the model, the effectiveness factor between the simulation and experiment are compared based on the butene reaction (reaction steps (14) and (15)). The effectiveness factorηcan be calculated by

(18)

As shown in Fig.2, the experimental data and simulated data are similar, indicating that the model is valid. Therefore, the model can effectively predict the effect of particle diameter to diffusion.

Fig.2　The comparison between simulation result and experimental data

2.2　Effect of particle diameter to particle transfer

The single model was validated in the above section. Thus, it can be used to study the distribution of pressure, species concentration, and temperature along a radial direction when changing particle diameter.

2.2.1Distribution of species concentration

Fig.3 depicts that the species concentration gradient increases with the increase of the catalyst diameter. When

Fig.3　Effect of the particle diameter on the intraparticle species mass fraction along the radial direction

2.2.2Distribution of temperature

Fig.4　Effect of particle diameter on the intraparticle temperature along the radial direction

2.2.3Distribution of pressure

Fig.5 shows the pressure distribution profiles within the particle along the radial direction at different particle diameters. Under the steady state condition, an ideal gas law is derived as

(19)

Fig.5　Effect of particle diameter on the intraparticle pressure along the radial direction

3Conclusions

Based on the equations of transfer process, the gas-state equations, kinetic equations and multicomponent diffusion equations, a comprehensive single particle model is established to study the effect of particle diameter on mass and heat transfer occurring within a ferrite catalyst during the ODOBTB reaction process. The simulation demonstrates that the mass fraction gradients of all species, temperature gradient and pressure gradient increase with the increase in the particle diameter. This paper gives new insights into the ODOBTB reaction process. The advanced model can describe the effect of particle diameter after model validation and the conclusions are listed as follows:

1) With the increase in the particle diameter, all species mass fractions gradient, temperature gradient, and pressure gradient increase, which indicates that the transfer resistance increases and an obvious diffusion phenomenon exists with a large particle size.

2) Since the mass transfer coefficientki,gis a constant, the particle diameter hardly affects external mass transfer resistance. When using a smaller catalyst, the external surface temperature of the particle decreases, suggesting the decrease of external heat transfer resistance.

3) The particle diameter is also related to the selectivity of the ODOBTB reaction. It is of great significance to choose appropriate particle size for enhancing the production of butadiene and optimization of the reaction process.

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doi:10.3969/j.issn.1003-7985.2015.04.024