Gao Ninghan; Tang Xiaojin; Zhou Zhenhuan; Xu Jian

(1. SINOPEC Research Institute Of Petroleum Processing, Beijing 100083;2. China Uniνersity of petroleum-Beijing, Beijing 102249)

Abstract: Reactor models were developed to describe the isomerization reaction process of C8 aromatics by applying a sixcomponent sequential reaction network. Lab-scale experimental data were used in an axial bed reactor model, and dynamic parameters were fitted by simulated annealing algorithm. In addition, industrial data and calculated dynamic parameters were used to determine the six-component concentration distributions using a radial reactor model. The influence of backmixing on reaction performance was investigated. It was found that the model considering back-mixing was much closer to the real industrial reaction process.

Key words: Isomerization of C8 aromatics; reactor model; radial bed reactor

1 Introduction

The isomerization of C8aromatics is a reaction process in whicho-xylene,m-xylene, or ethylbenzene are converted top-xylene under the action of catalysts. In industrial applications, radial bed reactors are widely used in the isomerization of C8aromatics units. An accurate radial bed reactor model is beneficial to the in-depth study of the isomerization process, and it plays a key role in the design and scale-up of the reactor.

A reaction network is very important to radial bed reactor models. Some researchers have suggested thatm-xylene is an intermediate in converting fromo-xylene top-xylene[1-3]. Chen et al.[4]established a sequential reaction network to investigate the isomerization dynamics of xylene on modified molecular sieve catalysts and determined the experimental conditions to maximized thep-xylene yield. It is also assumed that the reactions of producing the byproducts which main are toluene and tritoluene are irreversible[5-6]. Rbschger et al.[7]proposed a reaction network that contained ethylbenzene. Wu et al.[8]suggested that octane naphthenes should be included as an isomerization component of C8aromatics. Xu et al.[9]proposed a six-component isomerization reaction network, and eight-carbon naphthene and eight-carbon straight chain alkane in reaction network were regarded as one aggregate component. Ramage et al.[10]suggested that the C8aromatic isomerization reactions could be regarded as pseudo-first-order reactions when the content of light hydrocarbons is relatively large and the partial pressure of hydrogen have a little chang in the reactor.

A reactor model can be developed to describe the isomerization reaction process of C8aromatics by applying a reaction network, and then a mathematic method can be used to solve the model. Himmelblau et al.[11]used an iterative method to obtain the reaction rate constants of a complex reaction network. To estimate the dynamic parameters of C8aromatic isomerization reactions, Dai et al.[12-13]used a trial difference matrix method. Hu et al.[14]used the Quasi-Newton optimization algorithm. Shen[15]used an eigenvector and eigenvalue method, and Chen[16]used the least squares method. The calculation costs of the above-mentioned methods are quite large, and the model parameters are difficult to obtain. From this point of view, an effective method that could be used to solve the model is quite essential. The simulated annealing algorithm has been widely used in recent years, as it is simple and flexible in calculating dynamic parameters[17].

In this study, a radial bed reactor model is established.The simulated annealing algorithm is used to obtain the apparent activation energy and pre-exponential factor.Using this model, the six-component concentration distributions in the reactor can be obtained.

2 Modeling

2.1 Reaction Network

A six-component sequential reaction network is used in this study. Besides ethylbenzene (EB),p-xylene (PX),o-xylene (OX),m-xylene (MX), eight-carbon naphthene,and eight-carbon straight-chain alkane are aggregated into component C8(N+P)[9], and the total byproducts of the reaction network are regarded as component A6. The sequential reaction network of the six components is shown in Figure 1.

Figure 1 Six-component sequential reaction network

2.2 Reaction Dynamics

According to the reaction network shown above, the dynamic equation of each component can be deduced as follows:

For the six-component sequential network, the rate constant matrix can be written as:

wherekmnis the rate constant of reaction A(n)→A(m) in the reaction network.

2.3 Reactor Model

In the experiments[9], the lab-scale experimental device was a miniature axial fixed bed. According to the characteristics of the device, a one-dimensional homogeneous axial bed reactor model is established as Equation 3, ignoring the effect of back-mixing:

whereaiis the content of each component,his the axial position of the catalyst bed (m),LHSVis the liquid hourly space velocity of the feed (h-1), andVcis the packing volume of the catalysts (m3).

Assumingl = h/H, Equation 4 is obtained[9]:

whereMHSVis the mass hourly space velocity (h-1),Ris the reactor radius (m),ρis the density of six-component gas phase (kg/m3), andρcis the packing density of the catalysts (kg/m3).

For a radial industrial reactor, a one-dimensional homogeneous radial bed reactor model is established as Equation 5, ignoring the effect of back-mixing:

Assumingl = r/R, Equation 6 is obtained:

If the effect of back-mixing is considered, Equation 7 is obtained:

With the simulated annealing algorithm, the dynamic parameters of the reaction could be obtained by regressing the experimental data. The object function of the regression is shown as Equation 8; with the optimized values of the reaction dynamic parameters, the concentration distributions of all the components in the reactor could be calculated:

wherea2iis the calculated values of the outlet contents,a1iis the experimental values of the outlet contents, andnis the number of components in the reaction network.

3 Results and Discussion

The lab-scale experimental data[16]are used in the axial bed reactor model (Equation 5) to calculate its dynamic parameters (apparent pre-exponential factors and activation energies). The calculated pre-exponential factors and apparent activation energies are shown in Table 1.

It can be seen that the reaction rate of EB to PX is higher than that of PX to EB, which indicates that EB is beneficial to increase the yield of xylene. The apparent activation energies of cinverting PX and MX to C8are negative, which illustrates that the reactions are exothermic, and that the reaction rates decrease with an increase in temperature[18].

According to the apparent activation energies and preexponential factors in Table 1, the reaction performances under different operating conditions are obtained, as shown in the Figures 2-5.

Figure 2 Comparison between calculated results and experimental values of product distribution at 360 ℃

It can be seen that the calculated results of product distributions at different temperatures are consistent with the experimental values. In addition, the model is more accurate at high temperatures and high space velocities.With industrial data[16]and the dynamic parameters obtained above, the radial bed reactor model that ignoresFigure 3 Comparison between calculated results and experimental values of product distribution at 380 ℃back-mixing (Equation 6) is used to calculate the concentration distributions of all the components in a real industrial radial reactor. The concentration distributions are shown in Figure 6, and the inlet and outlet contents of the reactor are shown in Table 2.

Table 1 Calculation results of dynamic parameters of the axial bed reactor model

Figure 4 Comparison between calculated results and experimental values of product distribution at 400 ℃

Figure 5 Comparison between calculated results and experimental values of product distribution at 420 ℃

Figure 6 Concentration distributions of a radial bed reactor model without back-mixing

Table 2 Comparison between actual values and calculated results of outlet content

From Figure 6 and Table 2, it can be seen that there are obvious differences between the actual outlet values and the calculated outlet results. Therefore, the radial bed reactor model that ignoring back-mixing dose not accurately provide the concentration distributions in the reactor.

Next, the back-mixing model (Equation 7) is used to describe the isomerization reaction process of C8aromatics. The dispersion coefficient calculated using the simulated annealing algorithm is 0.0897 m2/h. The concentration distributions are shown in Figure 7, and the inlet and outlet contents of the reactor are shown in Table 3.

Table 3 Comparison between actual values and calculated results of outlet contents

Figure 7 Concentration distributions of a back-mixing model

From Figure 7 and Table 3, it can be seen that the actual outlet values agree very well with the calculated outlet content. Therefore, it is determined that the backmixing model can accurately provide the concentration distributions in the reactor.

4 Conclusion

For the isomerization reaction process of C8aromatics,reactor models were established based on a six-component sequential reaction network. Lab-scale experimental data were used to calculate the dynamic parameters of the reaction network using a simulated annealing algorithm. The results showed that the accuracy of the model was good.

Then, industrial data and reaction dynamic parameters were used in a radial bed reactor model, that considered back-mixing. The concentration distributions of all the components were obtained. It was found that back-mixing was an important factor that affected the isomerization reaction process of isomerization of the C8aromatics.