Inte rnatio nal Jo urnal o f Sc ie ntific & Eng inee ring Re se arc h Vo lume 3, Issue 3 , Marc h -2012 1

ISSN 2229-5518

Modeling and Simulation of Styrene Monomer Reactor: Mathematical and Artificial Neural Network Model

Seyed Mahdi Mousavi, Parvaneh Nakhostin Panahi, Aligholi Niaei, Ali Farzi, Dariush Salari

**Abs tract**— A pseudo-homogeneous model w as developed f or f ixed bed catalytic styrene monomer reactor based on the reaction mechanisms and mass and energy balance equations. With the proposed mathematical model, the prof iles of ethyl benzene conversion, styrene yield and selectivity w ere achieved through the length of catalytic bed reactor. Good agreement w as f ound betw een model results and industrial data. The ef f ects of some input parameters such as the molar ratio of the steam to ethyl benzene in the f eed (S/E) and inlet temprature w ere investigated on f inal conversion of ethyl benzene and styrene selectivity using proposed mathematical model. USING THE RESULTS OF mathematical model, a three-layer perceptron neural netw ork w as developed f or simulation of the effects of f eed composition and operation condition on conversion and selectivity. The optimum structure of neural netw ork w as determined by a trial-and-error method and diff erent structures w ere tried.

Inde x Terms— Artif icial Neural Netw ork, Fixed bed catalytic reactor, Mathematical modeling, Styrene monomer

—————————— ——————————

tyr ene is one of the simplest and most important mono- mer s pr oduced wor ldw ide, and finds maj or use in the pr oduction of polystyr ene, acrylonitr ile/butadiene/styr ene

r esins (ABS), and var ious miscellaneous polymers in the p e-

tr ochemical industry [1]. Styr ene pr oduced commer cially by catalytic dehydr ogenation of ethyl benzene, which firstly pr e- sented in 1869 by Berthelst. Recently, optimal design and op- eration of the styr ene r eactor needed, as it is the cr itical equipment in the styr ene manufacturing pr ocess.

Dehydr ogenation r eaction of ethyl benzene is equilibrium,

endothermic r eversible r eaction and ther mally pr oceeds w ith low yield but catalytically w ith high yield such as ir on oxide and supper heated steam [2]. This r eaction str ongly depends on temperatur e and pr essur e conditions and the favor ite con- ditions for it is high tem peratur e and low pr essur e. In addition to dehydr ogenation of ethyl benzene to styr ene r eaction, a set of parallel endothermic r eactions can occur that lead to ben- zene and toluene pr oduction. These competitive endothermic r eactions cause decr ease of styr ene yield. Ther efor e an optimal operating temper atur e must be selected to achieve high con- version of ethyl benzene to styr ene [3]. Additionally, selectivi- ty of catalyst for conversion of ethyl benzene to styr ene must be consider ed. Gener ally, yield and selectivity of styr ene mo- nomer can be influenced by some parameters such as tempera-

———— ——— ——— ——— ———

*Seyed Mahdi Mousavi is PhD student of Applied Chemistry and member of Young Researchers club, Tabriz Branch, Islamic Azad University, Tabriz, Iran, 00984113340191, *

*Parvaneh Nakhostin Panahi is a PhD student of Applied Chemistry in*

University of Tabriz, Tabriz, Iran,

*Aligholi Niaei,is a prof of Chemical Engineering in University of Tabriz,*

Tabriz, Iran,

*Dariush salari is a prof of Applied Chemistry in University of Tabriz,*

Tabriz, Iran,

*Ali Farzi is a prof of Chemical Engineering in University of Tabriz, Tabriz,*

Iran,

tur e, pr essur e, molar r atio of the steam to ethyl benzene in the feed and selectivity of catalysis. Conversion of ethyl benzene and selectivity of the styr ene incr eases with incr easing of tem- peratur e, pr essur e and molar ratio of steam to ethyl benzene in the feed [4].

Many studies on kinetics, reactor modeling, simulation and optimization of the styrene reactor have been reported. More

than 50 years ago, Wenner and Dybdal [5] obtained rate data from experiments for two types of catalysts. Sheel and Crowe [6] determined rate coefficients and heat of reactions from the industrial data of an adiabatic styrene reactor using a pseudo- homogeneous model. They obtained the best kinetic model by calibrating several models using catalyst manufacturers’ data. The kinetic model proposed by Sheel and Crowe has been widely used by most researchers for simulation and optimiza- tion of industrial reactors [7 -9]. Elnashaie et al. developed a heterogeneous model based on the dusty gas model [9]. They used the model to extract intrinsic kinetic data from industrial data iteratively. In another paper, Abdalla et al. reported in- trinsic kinetics for three promoted iron oxide catalysts using pseudo-homogeneous and heterogeneous models, and com- pared the performance of these catalysts [4].

In the present work, results of mathematical modeling of styrene monomer production process were reported. With this ps eudo-homogeneous model, the profile conversion of ethyl benzene and steam, styrene yield and selectivity, temeperature and pressure were achieved through the length of catalytic fixed bed reactor and were compared with an industrial rea c- tor as a case study. The best molar ratio of the steam to ethyl benzene in feed has been investigated for optimal conversion of ethyl benzene and styrene selectivity. Using results of ma- thematical model, an Artificial Neural Network model has been developed for s imulation of the effects of feed compos ition.

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TABLE1

Kinetic Equation And Frequency Factors And Activation Energy Of Ethylbenzene Dehydrogenation

Num | Reaction | Reaction rate | Ai | Ei×10-5 (j.mol-1 ) |

1 | C6 H5 CH2 CH3 C6 H5 CHCH2 + H2 | 8.32×103 | 0.909 | |

2 | C6 H5 CH2 CH3 C6 H6 + C2 H4 | 4.29×109 | 2.80 | |

3 | C6 H5 CH2 CH3 +H2 C6 H5 CH3 +CH4 | 6.13×102 | 0.915 | |

4 | 2H2 O + C2 H4 2CO + 4H4 | 3.95×102 | 1.040 | |

5 | H2 O + CH4 CO + 3H2 | 1.42×102 | 0.675 | |

6 | H2 O + CO CO2 + H2 | 5.82×1012 | 0.736 | |

In styr ene monomer r eactor fr esh ethyl benzene mixed w ith r ecycled ethyl benzene and steam is pr eheated using the pr oduct str eam fr om the r eactor , and then mixed w ith the s u- perheated steam to r eactor inlet temperatur e of over 875 K befor e inj ecting into the fixed bed catalytic r eactor [10]. Super- heated steam pr ovides the necessary heat of r eaction and pr e- vents coke formation, r educes partial pr essur e of styr ene and hydr ogen to shift the thermodynamic equilibrium in favour of the styr ene production [9, 10]. The r eactor effluent is cooled to quench all r eactions in several heat exchangers, an d then di- r ected to the separ ator to r ecover styr ene.

Six main r eactions occur in styr ene r eactor. Rate equations

and fr equency factor s and activation ener gy of those r eactions

ar e listed in Table 1 [6]. The kinetic constants of the r eactions ar e expr essed by Arr henius equation. Dehydr ogenation of ethyl benzene (Eq. (1)) is an endothermic r ever sible r eaction, and pr oceeds thermally with low yield but catalytically w ith high yield. As it is an endothermic r eaction pr oducing two moles of pr oduct with one mole of r eactant, low pr essur e and high temperatur e favour forwar d r eaction pr oducing styr ene. The competing r eactions, (Equations (2) and (3)) degr ade ethyl benzene to by-pr oducts such as benzene and toluene, thus r educe styr ene yield [6]. As the rate of for mation of by- pr oducts incr eases with temperatur e, an optimal operating temperatur e is necessary to compr omise between conversion of ethyl benzene to the styr ene and by-pr oduct for mation. Mor eover , a selective catalyst is desirable to achieve high sty- r ene yield at the low temperatur e and to minimize side r ea c- tions.

For modeling of styr ene monomer r eactor , assuming a plug flow r eactor was employed. Heat and mass transfer as well as diffusion in catalyst pellets w er e lumped in the rate constants. Catalyst activity is consider ed to be constant because of lack

the available data, even though it varies with time and r eactor length, also steady state conditions ar e consider ed. Thus, the

model is a pseudo-homogeneous model and r eactor is cons i- der ed single phase. Since in the multi-phase r eactor , molar flow rates of component s ar e pr eferr ed rather than molar frac- tions, mass balance equations ar e wr itten based on molar flow rate of components.

(1) Wher e i r epr esent components; The ener gy balance equa-

tion for adiabatic operation is given by equation (2). Relation-

ship of par tial pr essur e and molar flow rate of components

with the assumption of ideal gas is given by equation (3).

(2)

(3) The Er gun equation (4) is used to compute pr essur e pr ofiles

along the r eactor.

(4)

(5) Density of gases w ith the assumption of ideal gas is given in equation (5). Viscosity of the mixtur e of gas in catalyst bed is calculated by Chapman-Enskog theory (equation (6)).

(6) The characteristics of the industr ial r eactor at Polymer Cor po- ration, Ontario, Canada ar e given in Table 2 [4].

The differ ential Equations of r eactor model (1 -6) w er e numer i- cally solved using MATLAB. The set of differ ential equation is solved with Runge-Kutta-Verner fourth and fifth or der m e- thod w ith var iable step size. Fig. 1 shows ethyl benzene con- version, styr ene yield and selectivity profiles thr ough the length of the r eactor.

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TABLE 2

Industrial Reactor Specifications, Catalyst Properties And

Feed Conditions

cates that the selectivity for styr ene pr oduction fr om ethyl benzene is 95.85%. Accor ding to this table it is concluded that except in the case of benzene, r esults ar e close to the values of the industrial r eactor, and the err or is negligible.

Ther e have been many attempts to impr ove the pr oductiv i-

ty of the dehydr ogenation r eactor system. Ear ly r esearchers wer e inter ested in the r eaction mechanisms of ethyl benzene dehydr ogenation and mathematical modeling of industr ial dehydr ogenation [10-13]. Pr ediction of r eactor dynamics and var iation of some output against var iation of some inlet para- meter s in industrial sit es is very difficult because observation of r eactor var iables is limited, so trial and err or tests r equir e a lot of time and cost. Mathematical models using plant data ar e inadequate for descr ibing r eactor dynamics [15]. To pr edict some of the outputs against var iation of some input par ame- ter s such as the molar r atio of the steam to ethyl benzene in the feed (S/E) and inlet temperatur e w e pr oposed an alter na- tive hybr id model. This model is composed of pr oposed pseu- do-homogeneous mathematical model and a neural networ k model.

TABLE 3

Comparsion of the Results of Model And Industrial Reactor

45

40 (a)

35

30

25

20

15

X: 1.7

Y: 42.2

10

5

0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Length of Reactor

60

40

20

0

100

(b)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Length of Reactor

Fig. 2 shows the r esults of pr oposed mathematical model for effect of the var iation of S/E in fixed inlet temperatur e (900

°C) on conver sion of ethyl benzene and styr ene selectivity. Accor ding to Fig. 2, it can be seen by incr easing of S/E in fixed inlet t emper atur e; conversion of ethyl benzene incr eases firstly with a shar p slope finally becomes almost constant in the ratio

(c)

50

0

X: 1.7

Y: 95.85

of 100. The effect of the incr easing of S/E on operation of fixed

bed catalytic r eactor can be expr essed in thr ee ways. Fir stly,

steam as a diluting agent r educes partial pr essur e of styr ene and hydr ogen to shift the ther modynamic equilibrium in favor

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Length of Reactor

Fig. 1: a) Ethyl benzene conversion, b) styrene yield and c) selectivity prof ile through the length of the reactor

The r esults of pseudohomogene- ous model and industr ial r eactor ar e compar ed in Table 3. The simulation r esults of the r eactor give ethyl benzene conversion and styr ene yield of 42.11% and 40.41% r espectively. This indi-

of styr ene production. Secondly, superheated steam pr ovides

the necessary heat of endothermic r eactions. Thir dly, super- heated steam pr events coke formation and catalyst deactiva- tion [11].

Fig. 2 shows that the selectivity of styr ene with the var ia- tion of S/E has an optimal value as in the molar ratio 14.2 ma x- imum value of styr ene selectivity can be achieved. Fig. 3 shows the pr ofile of effect of the inlet temper atur e in fixed S/E (14) on conversion of ethyl benzene and selectivity of styr ene.

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91.6

91.4

91.2

91

90.8

90.6

90.4

90.2

90

X: 14.2

Y: 91.55

(a)

cludes one input layer which pr ovides input data to the net- wor k, a hidden layer and an output layer that r epr esents net- wor k r esponse.

The number of input and output nodes is governed by fun c-

tional r equir ements of ANN. The number of input neurons

corr esponds to the number of operational condition that con- tains the S/E and inlet temper atur e. The number of output neur ons corr esponds to the numb er of r esponse that contains conversion of ethyl benzene and selectivity of styr ene. A si g- moid transfer function used for the hidden layer and output transfer function was a linear function.

Training of designed ANN was per formed using r esults of pr oposed mathematical model in changes of S/E and inlet temperatur e. Since used transfer function of hidden layers is

0 20 40 60 80 100 120

Water/Ethylbenzene

Fig. 2: a) Ethyl benzene conversion, b) Styrene selectivity prof ile against

70

(b)

sigmoid, w e scaled all input vector s in the interval [0, 1]. The data wer e split in thr ee subsets: tr aining, validation and test set. Splitting of samples plays an important r ole in evaluation of an ANN per formance. The training set is used to estimate the model parameters and the test set is used to check the ge- ner alization ability of the model. In this w or k, 480 data w er e

65

pr epar ed w ith changing of S/E and inlet temperatur e using

60 mathematical mode. The training, validation and test sets in-

55 clude 288 data (60% of total data), 96 data (20% of total data)

and 96 data (20% of total data), r espectively.

50

45

105

40

100

35

(a)

30 95

0 20 40 60 80 100 120

Water/Ethylbenzene

S/E

Accor ding to Fig. 3 with the incr ease of inlet temper atur e, the rate of the endothermic r eaction such as dehydr ogenation of ethyl benzene will be incr eased. Consequently the conversion of ethyl benzene w ill be incr eased with incr easing of inlet temperatur e. Accor ding to Fig. 3 it can be seen that the selec- tivity of styr ene in temper atur e range of 500 – 750 °C is fixed at the maximum amount. How ever the selectivity of styr ene will be r educed in the higher inlet temperatur e. Consequently, an optimum value of the inlet temper atur e should be selected to obtain the highest conversion of ethyl benzene and styr ene selectivity. Accor ding to the r esults of mathematical model, inlet temperatur e between 850 °C to 950 °C is the best temper- atur e to get the highest conversion and selectivity.

In r ecent years, the concept of neural networ ks has gained

wide popularity in many fields of chemical engineer ing such

as dynamic modeling of chemical pr ocesses [15, 16], design of catalysts [17], modeling of chemical r eactors [18, 19 , 20] and modeling of t he complex chemical pr ocess [ 21, 22, 23]. In this r esearch, in or der to simulate the styr ene monomer pr oduc- tion r eactor and pr edict the r esponse of the r eactor against changes of operation condition such as S/E and inlet tempera- tur e, the arr ays of appr opriate thr ee-layer neur al netw or ks have been designed w ith differ ent number of in hidden layer neur ons and netw or k tr aining algor ithm. The networ k i n-

85

80

75

500 550 600 650 700 750 800 850 900 950 1000

Inlet Temperature

70

(c)

60

50

40

30

20

10

0

500 550 600 650 700 750 800 850 900 950 1000

Inlet Temperature

Fig. 3: a) Ethyl benzene convers ion, b) Styrene s electivity profile agains t inlet temprature

It is r ecognized that the selection of neur ons in the hidden layer and training algorithm can have a significant effect on networ k per formance. In this paper, w e tr ied two steps to ob-

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tain the optimum model of ANN. In first step, w e test differ ent number of neur ons in the hidden layer and then, the best d e- sign of layer s of ANN was consider ed for the var iation of training algorithms such as gr adient descent backpr opagation (gd), gr adient descent w ith adaptive lear ning r ule backpr opa- gation (gda), gradient descent with momentum backpr opaga- tion (gdm) and Levenber g-Mar quardt backpr opagation (lm). The mean squar ed err or (MSE) for test set was used as the er- r or function.

In the fir st step, many netw or ks w ith differ ent neur ons in hid- den layer w er e trained with the Levenber g-Mar quar dt back- pr opagation algorithm. Table 4 shows the per formance (MSE for training and test sets) of designed netw or k w ith differ ent neur ons in hidden layer. It was found that the networ k w ith thr ee neur ons in hidden layer has the MSE less than other trained networ ks. The MSE was 3.48e-10 for training set and

4.63e-8 for test set.

TABLE 4

Comparison of the Performance of Different Designed Network

num | topology | Number of epoch | Training algorithm | MSE for training set | MSE for test set | R2 |

1 | 2-1-2 | 1000 | lm | 2.4×10-5 | 1.8×10-4 | 0.9801 |

2 | 2-2-2 | 1000 | lm | 1.2×10-6 | 2.5×10-6 | 0.9745 |

3 | 2-3-2 | 1000 | lm | 3.48×10-10 | 4.63×10-8 | 0.9908 |

4 | 2-4-2 | 1000 | lm | 2.1×10-8 | 4.1×10-6 | 0.9815 |

5 | 2-5-2 | 1000 | lm | 4.7×10-5 | 1.3×10-5 | 0.9600 |

6 | 2-6-2 | 1000 | lm | 3.4×10-3 | 5.87×10-3 | 0.9026 |

7 | 2-3-2 | 1000 | gd | 1.56×10-6 | 4.16×10-5 | 0.8794 |

8 | 2-3-2 | 1000 | gda | 1.4×10-5 | 2.8×10-4 | 0.9178 |

9 | 2-3-2 | 1000 | gdm | 1.89×10-5 | 1.63×10-5 | 0.8165 |

70

Mathematical Model

ANN Model

65

14

y=x

train data

12 test data

60

10

55

8

50

6

45

4

40

35 2

30

0 20 40 60 80 100 120

Water/Ethylbenzene

0

0 2 4 6 8 10 12 14

Measured Values

Fig. 4: Co mparsion betw ean results of mathematical model and ANN prediction of Ethyl benzene conversion

91.6

91.4

91.2

91

90.8

14

Mathematical Model

ANN Model

12

10

8

y=x

train data test data

90.6 6

90.4

4

90.2

2

90

0 20 40 60 80 100 120

Water/Ethylbenzene

0

0 2 4 6 8 10 12 14

Measured Values

Fig. 5: Co mparsion betw ean results of mathematical model and ANN prediction of Styrene selectivity

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In second step, an ANN with thr ee neur ons in hidden layer was consider ed for the variation of the tr aining algor ithm. In Table 5, the per formances (MSE for tr aining and test sets) of designed networ k w ith the differ ent training algor ithm ar e listed. It was found that a networ k w ith t he Levenber g- Mar quar dt backpr opagation algor ithm has the MSE less than other trained netw or ks. To test the accuracy of ANN model, a comparison is made between mathematical model and ANN r esults. Figs. 4-5 show a compar ison betw een mathematical model r esults and pr edicted values of the r esults, using the optimum neural networ k model with thr ee neur ons in the hidden layer and Levenber g-Mar quardt backpr opagation a l- gor ithms. These r esults confir m that the neural networ k model can pr edict adequately the conver sion of ethyl benzene and selectivity of the styr ene in the styr ene r eactor under differ ent feed conditions.

The pseudo-homogeneous model of styr ene monomer pr oduc- tion r eactor was for mulated and numerically was integrated with Runge-Kutta-Ver ner four th and fifth or der method using MATLAB. The pr ofile of effects of some impor tant parameters in the r eactor was found by pseudo-homogeneous mathemat i- cal model. The r esults of the proposed model compar ed to an industr ial r eactor that was very similar. Th e pr oposed mathe- matical model was used for calculation of the output of the r eactor against var iation in S/E and inlet temperatur e. Accor d- ing to the r esults of the pr oposed model, with incr easing of S/E, the conversion of ethyl benzene incr eases but the selectivi- ty of styr ene decr eases. The selectivity of styr ene has an op- timal value in S/E =13.5 -14.5 and inlet temper atur e betw een

850 °C to 950 °C is the best temper atur e to get the highest con-

version and selectivity. THEN a thr ee-layer per ceptron neural

networ k, with two input nodes, thr ee neur ons in hidden layer and two neur ons in output layer and Levenber g–Mar quar dt training algorithm, was developed for simulation of the effect of feed composition and oper ation condition on conversion and selectivity. These r esults confir m that the designed neural networ k model is able to pr edict the conversion of ethyl ben- zene and selectivity of styr ene in the styr ene r eactor under differ ent conditions.

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