아세틸렌 전환기의 Hybrid neural model

주 은 정 , 이 상 규, 박 선 원

한국과학기술원 화학공학과

Hybrid Neural Network Model of Acetylene Converter

Eunjung Joo, Sanggyu Lee  and Sunwon Park

Dept. of Chem. Eng., KAIST

Introduction

When the system under consideration is very difficult to identify or complex to model mathematically, the neural network modeling is very attractive if the input/output data can be easily obtained. In reactor operations, the kinetic analysis of complex systems of chemical reactions is a difficult problem. Despite of the fact that significant economical benefits could be derived from optimization of such processes, the complex reaction network that characterizes them makes the development of a detailed understanding of the reaction kinetics difficult, which is the first prerequisite for the optimization procedure. Therefore it is generally thought to be desirable to develop approximate kinetic models which can be used to maximize the yield and selectivity of the desired product, and improve the safety of its production. Many processes involve nonlinear input-output relationships, which can be handled by the nonlinear nature of neural networks. Therefore an increasing number of applications for neural networks is being reported. But despite of the advantages of black box modeling, existing knowledges of the system under consideration are extremely valuable. Previous research into the design of artificial neural networks for process modeling has largely ignored the existing knowledge about the task at hand. To take the advantage of the existing knowledge and the simplicity of artificial neural networks, it is proposed to make use of a neural network model of the process with inputs derived from two sources. One is the available process input and output  measurement data, and the other is the first principles model of the process that embodies those process features that are clearly understood. The use of the first principles model in this way makes the neural network to cope only with less well understood aspects of the system, including any mismatch between the mechanistic model and real world behaviour. This makes maximum use of process insight while at the same time reducing the breadth of problem to be handled by the neural network.

Modeling Problem of Acetylene Converter

In the acetylene converter, there are two main competing hydrogenation reactions: one is acetylene to ethylene, the other is ethylene to ethane. The ethylene forming reaction is the desired reaction and the ethane forming reaction is highly undesired side reaction. They are both exothermic reactions:

[eqn: C_{2}H_{2}+H_{2} &-> C_{2}H_{4} ~~~&Delta H_{298K}=-172 MJ/kmol ~~~~~~~~~~~&(1)# C_{2} H_{4} + H_{2} &->C_{2} H_{6} ~~~~~&Delta H_{298K} = -137 MJ/kmol ~~~~~~~~~~~&(2)]

These reactions are highly affected by some operating conditions, for example, temperature, [eqn: H_{2} / C_{2}H_{2}] ratio, and CO content. To obtain maximum ethylene gain, these operating variables should be adjusted pertinently. In addition to these, there are other side reactions forming c4-cut or green oil and hydrocarbon cracking reactions at higher temperature.

[eqn: C_{2}H_{2}+nC_{2}H_{2}+H_{2} -> C_{2n+2}H_{2n+4} ~~~~~~~~~~~~~~~~~~~~~~&(3)]

But the effect is not great compared to that of the hydrogenation reactions, so those effects will not be considered.

The differential equations for the system are written as follows:

[eqn: {dx_i }over{dz} = (lambda * theta * {r_i}prime )/F ~~~~ i=1,2,3]

For each component,

[eqn: {dx_{C_2 H_2 }}over{dz} &=& -(lambda * theta *({r_1}prime+{r_3}prime) )/F # {dx_{C_2 H_6 }}over{dz} &=& (lambda * theta *{r_2}prime)/F # {dx_{H_2 }}over{dz} &=& -(lambda * theta *({r_1}prime +{r_2}prime +{r_3}prime)/F]

Carbon monoxide is just a selectivity and activity moderator and does not participate in any reactions. If the carbon monoxide concentration is at steady state in the reactor, then the carbon monoxide concentration can be assumed to be varied with respect to the change in the total molar flow of the reactor.

[eqn: d(Fx_{CO}) = x_{CO}dF + Fdx_{CO} = 0 # {dx_{CO}}over{dz}=(-x_{CO}/F)*(dF/dz)]

The total flow across the reactor decreases according to the proceeding reactions.

[eqn: {dF}over{dz}=F*[{dx_1 }over{dz} + {dx_2 }over{dz} + {dx_3 }over{dz}]]

The energy balance can be written as:

[eqn: {dT}over{dz}=H_r /(C_p *V_z )]

By the hydrogenation reactions, the temperature of the bed increases. So the acetylene converter energy balance across an incremental slice is:

[eqn: {dT}over{dz} = ({dx_1 }over{dz} H_{r_1} + {dx_2 }over{dz} H_{r_2} + {dx_3 }over{dz} H_{r_3})/{C_p}]

The rate expressions of this reacting system are :

[eqn: r_{1}={k_{1}K_{a}P_a K_b P_b }over{(1+K_a P_a +K_{CO} P_{CO} ) (1+K_b P_b )}~~ (kmol/kg_s s)]

[eqn: r_{2}={k_{2}K_{b}P_b K_c P_c }over{(1+K_c P_c +K_{CO} P_{CO} ) (1+K_b P_b )}~~ (kmol/kg_s s)]

[eqn: r_{3}={k_{3}K_{a}P_a K_b P_b (A+K_{CO}P_{CO}^{B})}over {(1+K_a P_a +K_{CO} P_{CO} )(1+K_b P_b )}~~ (kmol/kg_s s)]

where

a :    acetylene

b :    hydrogen

c :    ethylene

The catalyst activity at any point in time can be defined as :

[eqn: theta(t) = {rm present~conversion~rate~of~the~reactants}over {rm conversion~rate~of~the~reactants~with~fresh~catalyst}]

By definition, [eqn: 0 leq theta(t) leq 1] that is, [eqn: theta=1] means the fresh catalyst. Mainly the catalyst is deactivated by the green oil formed during the hydrogenation, thus the activity at time t is dependent on the cumulative green oil production from time zero to t. But to calculate the activity at time t, the amount of green oil produced at t is needed. That makes the problem highly complex. However, the deactivation of the catalyst is slow with respect to the reaction dynamics so the pseudo-steady state could be assumed. Thus the activity at time t is dependent on the cumulative green oil simply until t-1 time step. That is, the status at time t can be determined by the history of the bed until time t-1. Therefore the catalyst deactivation model form can be rewritten as:

[eqn: theta(t) = 1/(1+K_E sum_{i=1}^{t-1} rm green~oil~p roduced)]

Quality of this model directly depends on simplifying assumptions and on experimentally determined kinetic parameters and the catalyst activity. To obtain exact values of these  parameters is not easy due to the noisy data of  the actual plant and model-plant mismatch. The uncertainty of first principles modeling can be coped in neural network modeling.

Hybrid Neural Network Modeling

To handle dynamics of this system, a hybrid neural model is proposed which is combined with a mathematical description of  that system. A schematic representation of the proposed hybrid neural model is shown in Fig.1:

Figure 1. Hybrid neural network model structure diagram.

The role of the neural network is the correction of the first principles model, so the neural network output variables should be the variables which need correction by the neural network. They are the outlet concentrations of hydrogen and ethane and temperature. In addition, the outlet acetylene concentration is the most important specification and it should be below 3 ppm. Thus it should be included in the output of the neural network. Therefore the neural network output variables include catalyst bed outlet concentrations of acetylene, ethane and hydrogen, and outlet temperature.

Results and Discussion

In figure 2, the outputs corrected by the neural network show better prediction than that by the first principles model.

Figure 2. Performance comparison between the first principles model and the hybrid model.

The developed first principles model has some weakness in the outlet acetylene concentration prediction. The outlet acetylene prediction is extremely sensitive to the catalyst activity and any deviation in the modelled catalyst activity can easily result in prediction of the outlet acetylene with a large offset.

Conclusion

In this study, a simple hybrid model is proposed which combines the first principles model and a multilayer perceptron neural network. The hybrid model shows better prediction capability than the first principles model and can be used for optimization of the acetylene converter operation.

References

[1] Bos,A.N.R., E.S.Bootsma, Foeth,F., Sleyster,H.J., and Westerterp,K.R., Chem. Eng. Proc., vol. 32, pp.53-63,1993

[2] Brown,M.W., Penlidis,A., and Sullivan,G.R., The Canadian J. of Chem.Eng., vol. 69, No.2, pp.152-164,1991

[3] Joo, E., S. Lee, and S. Park, KIChE Symp. Fall, '96

[4] Zbicinski,I., Strumillo, and P.,Kaminski,W., Comp. chem. Engng vol.20., Suppl., pp.s695-s700, 1996

Acknowledgment

Financial support from the Korea Science and Engineering Foundation through the Automation Research Center at Postech is gratefully acknowledged. This research was also supported by Ministry of International Trade and Industry .