Ind. Eng. Chem. Process Des. Dev. 1986, 25,
the effective light path length instead of the film thickness, S, agree well with the experimental results as shown in Figures 7 and 8. The relative volumetric rate of light absorption can also be determined from the correlation for a correction factor based on the diffuse light model shown in Figure 10. Acknowledgment We are grateful to the students at the University of Tokushima, Mitsuyoshi Hara, Makoto Etoh, Masahiro Yokota, Kazuo Shiramizu, and Makoto Takahashi for their assistance in the experimental work. Nomenclature
207-210
207
L = liquid phase S = single phase T = two-phase w = at reactor wall Greek Letters a = molar absorptivity, L-' M-l ,f3 = parameter defined by eq 9
0 = angle of rotation with coordinate center at radial position r , radian X = wavelength, 1 I.L q5
= attenuation coefficient, I-' = quantum yield of ferrous production, mol einstein-'
+ = correction factor defined by eq 10
Registry No. Potassium ferrioxalate, 14883-34-2.
C = concentration, M or mol L-' Co = initial concentration, M DT = diameter of reactor, 1 E(X) = relative radiant energy = light intensity, einstein t 2t-' I = average light intensity over reactor cross-sectionalarea, einstein t-l ( I ) = volumetric light intensity, einstein t-' ( I a ) = volumetric rate of light intensity, einstein 1-3 t-l Le = effective light path length, 1 r = radial distance, 1 R = radius of reactor, 1 RL = liquid holdup S = liquid film thickness, 1 T(X)= transmittance U = velocity, I t-l z = axial distance, 1 Az = axial length of optical window, 1 Subscripts dif = diffuse light model Fe3+ = ferric ion Fez+ = ferrous ion
Literature Cited Akehata, T.; Itoh K.; Inokawa, A. Kagaku Kogaku Ronbunshu 1976, 2 , 583. Cassano, A. E.: Silveston, P. L.; Smith, J. M. Ind. Eng. Chem. 1967, 5 9 , 19. Governale, L. J.; Clarke, J. T. Chem. Eng. Prog. 1956, 5 2 , 281. Hill, F. E.; Reiss, N.; Shendalman, L. H. AIChE J . 1968, 74, 798. Itoh, M.; Hara, Y. Jpn Patent, 3925041, 1964. Matsuura, T.; Smith, J. M. AIChE J . 1970, 76.321. Otake, T.; Tone, S.;Kono, K.; Nakao, K. J . Chem. Eng. Jpn. 1979, 72, 289. Otake, T.; Tone, S.;Higuchi, K.; Nakao, K. Kagaku Kogaku Ronbunshu 1981, 7, 57. Otake, T.; Tone, S.;Higuchi, K.; Nakao, K. Int. Chem. Eng. 1963, 2 3 , 288. Parker, C. A. Proc. R . SOC.London, Ser. A 1953, A220, 104. Ramage, M. P.; Eckert, R. E. Ind. Eng. Chem. Fundam. 1975, 14, 214. Shlrotsuka, T.; Sutoh, M. Kagaku Kogaku Ronbunshu 1978, 4 , 502. Spadoni, G.; Bandini, E.; Santarelii, F. Chem. Eng. Sci. 1978, 3 3 , 517. Tomida, T.; Yoshida, M.; Okazaki, T. J . Chem. Eng. Jpn. 1976, 9 , 464. Tomida, T.; Yusa, F.; Okazaki, T. Chem. Eng. J . 1978, 16, 81. Tomida, T.; Tabuchi, F.; Okazaki, T. J . Chem. Eng. Jpn. 1982, 75, 434. Troniewski, L.; Ulbrich. R. Chem. Eng. Sci. 1984, 3 9 , 751. Yokota, T.; Iwano, T.; Deguchi, H.; Tadaki, T. Kagaku Kogaku Ronbunshu 1981a, 7 , 157. Yokota, T.; Iwano, T.; Saito, A,; Tadaki. T. Kagaku Kogaku Ronbunshu 198lb, 7, 164. Williams, J. A. AIChE J . 1978, 2 4 , 335. Zolner, W. J.; Williams, J. A. AIChE J . 1971, 77, 502.
Received for review October 1, 1984 Accepted June 24, 1985
Ethylbenzene Dehydrogenation Reactor Model Charles M. Sheppard' and Edward E. Maler USS Chemicals, Monroevlile, Pennsylvania 15 746
Hugo S. Caram Department of Chemical EnQheerhQ, Lehigh University, Bethlehem, Pennsylvania 180 15
A model of an industrial catalytic dehydrogenation reactor was developed. Several kinetic models were calibrated by using catalyst manufacturers data. The calibrated Langmuir-Hinshelwood models did not represent the data well, so an empirical model was selected and a comparison was made between simulated and actual industrial operations for two different plants. The optimum operating conditions were explored for one- and two-bed reactor configurations by using two industrial catalyst systems.
The purpose of this work was the development of a model to simulate an industrial ethylbenzene dehydrogenation reactor and the use of this model to perform economic analyses of different operating conditions, reactor configurations, and catalysts systems. 0196-4305/86/1125-0207$01.50/0
Styrene is commercially produced by the dehydrogenation of ethylbenzene over an iron oxide catalyst in the presence of steam. Steam is used to supply heat for this endothermic reaction, to inhibit coke formation, and to reduce the partial pressure of the products and thus in0 1985 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1 , 1986
208
Table I. Summary of the Kinetic Models Investigated av absolute deviation between the predicted and manufacturer's data styrene toluene benzene
kinetic const for the
model 1 2
author Wenner
inhibitor none
Carra
PEB
+
ZPSTY
3 36
Lebedev
(1 +
Sheppard PEB+
(ZPSTY)'
5'
Sheward PEB+
(ZPSTY)'
az
styrene A E,
calibrated models toluene benzene A E, A E,
z
PEB- (PSTYPHZ/ PEBPHZPEB 11.5 24.1 16.6
31.3 13.2
33.2
9.6
2.4
0.6
KeJ PEB- ( P S T Y ~PEB HZ/
46.8 18.9
45.2 8.0
4.0
0.8
0.6
14.4 16.02
34.1 u
3.1
2.0
0.5
51.4 18.3
37.8 u
2.7
1.3
0.6
PEB 18.3 38.2 20.6
Keq)
PEB- ( P S T ~ P H PEBPH, Z/ PEB 17.5 30.6 9.1 ~PsTY)' Keq) PEB- (PSTYPHZ/ PEB PEB 17.2 30.2 16.9 (1 + rPSTY)2
4
driving force for the reaction generating styrene toluene benzene
Keq)
PEB - (PSTYPHZ/ PEB
PEB
87.4 39.9
74.9 100
2.3
0.9
0.6
Keq) PEB- (PSTYPHZ/ PEB
PEB 42.3 74.5 61.4 115.5 61.6
114.4 100
2.0
0.6
0.7
38.1 65.9 47.9
Keq)
= (0.0218 atm) exp(T/6995 K). bToluene reaction driving force modified. 'Model 4 fit for Shell 015 catalyst.
crease the equilibrium conversion. The three key reactions are EB = STY + H2
+ H2 = TOL + CH, EB = BEN + C2H4
EB
10 9 8
I
I
I
I
-
7
(1)
1
I
LEAST SOUARES FIT
6
0 SHELL -SET 1
(2)
5
0
SHELL -SET 2
(3)
4
0
UNITEDCATALYST -SET 3
In addition, other aromatics present may be dehydrogenated or dealkylated, and coke on the catalyst surface reacts with the steam. Oxidation and the water gas shift reaction also occur; these reactions involve species which are vapor at room temperatures and will be referred to as the gas reactions. The following three reactions adequately represent these reactions and complete the set of reactions for the model:
3
A UNITEDCATALYST-SET5
+ H20 = CO + 3Hz '/2C2H4 + H2O = CO + 2H2 CO + HzO = COZ + H2 CH4
(4) (5)
(6)
A model was written to simulate a plug flow reactor using a published integration package (EPISODE, 1975) to integrate the differential component, momentum, and energy balance down the reactor (Sheppard, 1982). No dispersion effects were included in the component or energy balances. The model can be used to simulate either an isothermal or an adiabatic reactor. Selection of a Kinetic Model In seeking to simulate an ethylbenzene dehydrogenation reactor, the first order of business is to select a kinetic model. The kinetic data in the literature include a simple Arrhenius relationship proposed by Wenner and Dybdal (1948) and Langmuir-Hinshelwood mechanisms proposed by Carra and Forni (1965) and by Lebedev et al. (1978). An empirical model was proposed in order to reconcile the observation of Carra and Forni (1965) that the initial reaction rate was independent of the partial pressure of ethylbenzene and the observation of Lebedev et al. (1978) that the inhibition term was approximately proportional to the partial pressure of styrene squared. These rate expressions (see Table I) were evaluated by using isothermal integral data provided by the catalyst manufactures to see which best describes the kinetic behavior of the catalyst. Data for Shell 105 were used because this catalyst was being employed. Also, both Shell and United Catalyst Inc. supplied information for this catalyst. The computer model was used to simulate the isothermal conditions of the manufactures conversion data. Kinetics taken from the literature for the gas reactions (eq
WlTEDCATALMT-sEI4 V UNITEDCATALYST-SET6
\
kl
SHELL 105CATALYST
kpmol kg-cat hr
1
0.9 0.8 0.7 0.6 0.5
0.4
0.3
0.2
0.1 110
112
114
116
118
120
122
103/T IK ' I
Figure 1. Arrhenius plot of the apparent reaction rate constants for the main reaction of model 4.
4-6) were used in the model (Akers and Camp, 1955; Moe, 1962). The model was used in conjunction with a modified Leverberg-Marquart search algorithm which located the apparent reaction rate constants for the three reactions involving ethylbenzene. The analysis includes the effect of the gas reactions and the inhibition term. These apparent rate constants were used in conjunction with a linear least-squares regression to calculate the Arrhenius constants (see Figure 1). After the four kinetic models were calibrated, they were used to simulate these same manufactures conversion data, and the average deviation between the models and data are summarized in Table I. From this table, it is apparent that model 4 is the best model of those considered. Table I also contains the parameters for the Arrhenius equation and the inhibition term. The activation energies calculated for models 4 and 5 are higher than can be easily justified on physical
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986 209 Table 11. Comparison of Model 4 and Plant Data run no.
temp in, OC
temp out, OC
1. 1 2 2
570.43 593.33 570.10 597.83 569.83 592.62 568.0
555.44 558.33 568.33 571.11 555.37 560.00 559.38 565.56 561.20 562.22
model data model data model data model data
3 3 4 4
649.44 649.44 648.85 648.85 647.18 647.18 649.44 649.44
model data model data model data model data model data
5 5 6 6 7 7 8 8 9 9
617.78 617.78 632.22 632.22 623.33 623.33 628.89 628.89 628.89 628.89
pressure pressure in, atm out, atm styrene Polymer Corporation Data 2.37 1.953 40.63 2.37 2.29 39.80 2.37 1.953 40.71 2.73 40.72 2.31 1.955 40.30 2.37 38.35 2.71 1.795 40.60 2.71 43.22
% conversion
benzene
toluene
styrene selectivity, %
1.91 2.99 1.90 2.99 1.87 2.53 1.89 2.67
4.65 2.29 4.62 3.17 4.50 2.40 4.58 2.79
86.11 87.09 86.18 86.86 86.35 88.60 86.25 88.78
1.77 1.52 1.81 1.43 1.78 1.23 2.16 1.34 2.16 1.87
3.96 3.62 4.48 3.17 4.03 2.13 5.38 2.52 5.70 3.95
88.39 89.23 86.72 89.15 87.99 92.11 86.68 91.67 86.94 89.16
USS Chemicals Data 1.952 1.952 2.429 2.429 1.884 1.884 1.680 1.680 1.816 1.816
grounds. The two-site styrene adsorption term dominates the inhibitor. So part of the high activation energies may be the contribution of the styrene adsorption/desorption temperature dependence. It was found that the reactions were relatively insensitive to the kinetics of the gas reactions. However, a possible refinement to the model would be the empirical correction of the kinetics for reactions 4-6, since the predicted gaseous product rate, when simulating plant operating conditions, is about 2.5 times less than the observed rate. Lee (1973) suggested that intraparticle diffusion may be important, but effectiveness factor calculations did not show a significant diffusion effect even when a tortuosity factor of 20 (instead of 3 which is typical) was used (Sheppard, 1982). Testing the Kinetic Model against Plant Data The reactor model was then run by using these kinetic constants to simulate industrial reactors. Plant conditions for the USS Chemicals plant of Houston, TX (Sheppard, 1982), and for the Polymers Corp. of Ontario, Canada (Sheel, 1968), were used in this comparison. As expected, the range of plant operating conditions is narrow. The inlet temperature, pressure, flow rate, and composition were specified for the model as well as adiabatic reactor operation. The pressure drop was calculated by using the Ergun equation and a void fraction of 0.325. Table I1 gives a comparison of the ethylbenzene conversion and selectivity for several representative points. With the exception of the Polymer Corp. conversion to benzene, the predicted ethylbenzene conversions were higher than the actual conversions for all three reactions. The styrene selectivity, however, agrees well. The higher predicted conversions may be due to catalyst deactivation with age. One cause for this deactivation may be the potassium migration as described by Lee (1973) and by Herzog and Rase (1984). For the almost 100 cases simulated, the average difference between the predicted and measured conversions to styrene was less than 10%; this also confirms the model ability to predict plant behavior. Also, 85% of these cases showed an actual conversion lower than the predicted conversion. This again suggests catalyst deactivation. Economic Analysis of Catalysts and Reactor Configurations The styrene industry trend in the U S A . has been to move to multibed reactor systems (to approach isothermal
1.766 1.755 2.231 2.170 1.734 1.721 2.476 1.572 1.621 1.707
43.66 42.59 41.08 41.16 42.61 39.18 49.07 43.17 48.99 47.87
operating conditions) and to higher selectivity catalysts. These high selectivity catalysts typically can be operated with lower steam-to-oil ratios and not experience deactivation problems caused by coke buildup. The lower steam to oil ratio results in an energy savings. The USS Chemicals ethylbenzene dehydrogenation unit employs a single reactor bed and the high activity, lower selectivity, Shell 105 catalyst. An economic analysis to quantify the benefits of using a high selectivity catalyst was performed. This involved using manufacturer’s data to fit the kinetic parameters for kinetic expressions of the same form as those used for Shell 105. Shell 015 was chosen since most of the data available for high selectivity catalysts were for this catalyst. The kinetic parameters calculated which best represent the catalyst behavior are given in Table I under model 5. The economic analysis also involved choosing an objective function. The objective function (also referred to as “profit”) was (the styrene production rate) X (the styrene selling price) - (the styrene production cost). A styrene selling price of 55.l@/kg(25 @/lb)was used. The styrene production cost was calculated based on a fixed cost of $190/h, a material cost of ethylbenzene of 34.6@/kg (15.7t/lb), a vent gas credit of 4.63@/stdm3 (0.131 @/std ft3), and an energy cost of $3.94/billion J ($4.16/million BTU). The vent gas credit was multiplied by a factor of 2.5 in the analysis to account for the fact that the model consistently underpredicted the vent gas production. The plant energy requirements are dominated by the energy lost in condensing the reactor effluent and the steam used in the recycle column reboilers. The design condenser duty was 1000 kJ/kg (945 Btu/lb) of the reactor effluent, and the design recycle columns reboiler duties were a total of 1740 kJ/kg (1650 Btu/lb) of feed. These costs are calculated by scaling the heat duties by the flow rates and using the design values as the base point. A fixed cost of l.O@/kg (0.458@/lb)is used for the B I T column reboiler and the styrene finishing energy costs. The other energy user considered is the steam boiler duty. Mo.e details of this analysis are given by Sheppard (1982). The economic analysis of styrene production in a single-bed reactor (having of the same configuration as the USS Chemical reactor) included investigating three different steam-to-oil ratios for the two different catalysts over a range of reactor inlet temperatures. The results are
210
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 1, 1986 300
7
1
CATALYST
'0s o
'5 0
0
1
1
I
I
1
MOLAR STEAM TOOIL RATIO 741
I
1
1 I-
-
ldoo
100
A
0
600-
200
800-
100
-
700
f
f
E
$
yf
yf
:
0
E
0
600-
500
400
-100
300
200
-200
I 600
I 625
I 650
I 675
I 700
I 725
REACTOR INLET TEMPERATURE,'C
MOLAR STEAM TO OIL RATIO STAGE 1 STAGE 2
-
I
d I 600
I 625
INTERSTAGE HEATING V I A
0
8.0
8.0
HEATEXCHANGER
0
8.0
11.6
STEAM INJECTION
A
11.8
11.8
HEATEXCHANGER
I 650
I 675
I 700
I 725
REACTOR INLET TEMPERATURE, 'C
Figure 2. Profit vs. reactor inlet temperature for a single-stage reactor.
Figure 3. Profit vs. reactor inlet temperature for a two-stage reactor packed with Shell 015.
presented in Figure 2. From this figure, it is seen that some gains in profitability for the high activity catalyst can be made by optimizing the steam-to-oil ratio but the gains in profitability by shifting to a higher selectivity catalyst are much greater. For the analysis of a two-bed reactor system, there is also the question of how to perform the interstage heating. Two options are an interstage heat exchanger or interstage steam injection. If steam is to be injected between the stages, then it has been suggested to use a lower steamto-oil ratio in the first bed. These suggestions were investigated over a range of inlet temperature for the Shell 015 catalyst (since the economics favor high selectivity catalyst); see Figure 3. From the graph, it can be seen that the high steam-to-oil ratio case using an interstage heat exchanger is the most profitable. However, this analysis does not consider the capital cost difference between the two options or the possibility of polymer buildup in the heat exchanger. Conclusions A model was developed which simulates an industrial ethylbenzene dehydrogenation reador. Kinetic expressions were calibrated for both a high activity catalyst and a high selectivity catalyst. An e m p i r i d model provided the best fit on manufactures and plant data, but because of the high calculated activation energies, doubt remains about the theoretical foundation of the model. This model was then used to locate the optimum inlet temperature and steamto-oil ratio for a specified styrene selling price and a set of material and operating costs. The model was also used to investigate the economics of installing a two-bed reactor system. The economics of using a high selectivity catalyst
were superior to the high activity catalyst.
Nomenclature A = frequence factor for reaction j .',= activation energy for reaction j , kcal/(kg mol) kj = kinetic constant for reaction j , kg mol/ (kg of catalyst h atm") = exp(A, - EG/RGT) r, = reaction rate constant, kg mol/(kg of catalyst h) = k, (driving force)/ (inhibitor) RG = ideal gas constant styrene conversion or conversion to styrene = (styrene produced)/ (ethylbenzene initially present) styrene selectivity = (styrene produced)/ (ethylbenzene consumed) T = absolute temperature, K z = absorption coefficient t = bed void fraction used in the Ergun equation = 0.325 Registry No. EB, 100-41-4;STY, 100-42-5. Literature Cited Akers, W. W.; Camp, D. P. AIChE J . 1855, 7 , 471. Eng. Chem. Process D e s . Dev. 1965, 4 , 28. Carra, Forni Id. EPISODE (Experimental Package for Integration of System8 of Ordinary Differential Equatlons), June 24, 1975 Version; an Argonne National Laboratory (Chicago, IL) modlfication of an earller version by G. D. Bryne and A. C. Hindmarsh. Herzog, B. D.; Rase H. F. Ind. Eng. Chem. Rod. Res. Dev. 1884, 23, 187. Lebedev, N. N.; Odabashyan, G. V.; Lebedev, V. V.: Makorov, M. G. Kinet Ketal. 1970, 78, 1177-1182. Lee, H. Catel. Rev. 1973, 8, 285. Moe, J. M. Chem. Eng. Prog. 1962. 58(3),33. Sheel, J. G. P. Eng. Thesis, McMaster University, Hamiiton, Ontario, Canada, 1968. Sheppard C. M. M.S. Thesis, Lehigh University, Bethieham. PA, 1982. Wenner R. R.; Dybdai, E. C. Chem. Eng. Prog. 1948, 44 (4). 275.
Received for review January 10, 1985 Accepted June 21, 1985
