1185
I n d . Eng. Chem. Res. 1989, 28, 1185-1190
Simulation of the Xylene Isomerization Catalytic Reactor Subhash Bhatia,* Sudeep Chandra, and Tathagata Das Department of Chemical Engineering, Indian Institute of Technology, P.O. Z.Z.T., Kanpur 208016 (U.P.),India
A steady-state simulation model of the xylene isomerization catalytic reactor, using octafining I1 catalyst, was developed. T h e main isomerization reactions along with other side reactions such as hydrogenolysis, disproportionation of xylene, and ethylbenzene isomerizations were considered in the model. The mathematical model predicts the concentration, temperature, and pressure profiles of a n industrial fixed bed catalytic reaction for a given feed input and operating conditions. T h e simulated results of a n adiabatic reactor model were found t o be in good agreement with existing plant data. A sensitivity analysis of the model was performed to predict the optimum operating conditions of the reactor. Considerable interest has been developed in recent years for the isomerization of xylenes, mainly because of the greatly increased demand for p-xylene as an intermediate in the manufacture of polyester fibers and films. Because of the possibility of separating desired isomers and increased p-xylene demand, xylene isomerization processes are expected to become more attractive economically. The octafining I1 process of xylene isomerization developed by Engelhard Industries, Murray Hill, NJ, and Atlantic Richfield Company, Philadelphia, PA, has been considered in the present study. The reactor used in this process is an adiabatic fixed bed catalytic reactor. The octafining I1 catalyst used in this process is a silica-alumina catalyst, containing 0.5 wt 70platinum in the mixture. The main advantage of octafining I1 catalyst is it can convert ethylbenzene to p-xylene and o-xylene, as a considerable amount of ethylbenzene is always present in the feed to a xylene processing unit. A mathematical model considering different physical and chemical processes in the reactor has been given in the present work. A one-dimensional plug flow model has been proposed to represent the catalytic fixed bed isomerization reactor. The simulated results were compared with the plant data, for adiabatic operation of the reactor. An attempt to establish the optimum operating conditions on the basis of a sensitivity analysis of the simulated model was made.
Reactor Modeling Reaction Rates. During the xylene isomerization reaction, there are a number of side reactions that take place in the reactor besides the main isomerization reaction. These are represented as follows. Main Reaction. (i) Xylene Isomerization: p -Xylene m-Xylene o-Xylene. Cortes and Corma (1978, 1979) have shown that the isomerization over silica-alumina catalyst proceeds through consecutive and reversible reactions by intermolecular 1,2 shifts of the methyl group so that o-xylene and p-xylene cannot be directly interconverted through each other but they are interconverted through the meta isomer. Cortes and Corma (1980) have also reported that in xylene isomerization the main reaction is represented by a single-site surface reaction mechanism as
1 + CKiPi
(1)
i=l
-rM = ( ( k - 1
+ k 2 ) K M P M - klKpPp k-zKoPo)
1 1 + CKiPi
(2)
i=l
1
-ro = (k-zKoPo - ~ z K M P M ) 1 CKiPi
+ i=l
(3)
Side Reactions. (ii) Hydrogenolysis
-
+ H, k3 toluene + CHI o-xylene + Hz toluene + CHI m-xylene + H, toluene + CHI -rH = (kBPp + k4Po + k$M)PH p-xylene
k4
k5
(4)
(iii) Ethylbenzene Isomerization ethylbenzene
ks
o-xylene or p-xylene or m-xylene
ethylbenzene
kd
toluene
+ methane
The rate equation for ethylbenzene isomerization is given as (based upon the reaction order to be first order) (5) -rEBZ = k6pEBZ + k,'PEBZ (iv) Disproportionation k
2@-xylene) 1,toluene k-7
2(o-xylene)
+ trimethylbenzene
k 2 tcluene + trimethylbenzene k, k
2(m-xylene) & toluene k--a
2(toluene)
km
+ trimethylbenzene
o-xylene + p-xylene
Assuming a second-order reaction with respect to xylene partial pressure, the rate expression can be written as -rTMB = (k-7 + k-8 + ~-~)PTMBPT (k7Pp2 + K&0 ' 2 + K,PM') (6) -rT
* To whom the correspondence should be addressed.
1
-rp = (klKpPp - k-1KMPM)
=
(12-7
+ k-8 + k-B)PTMBPT (k,pp2
-
+ K8P02 KJ'M') + kip^' (7)
0888-588518912628-1185$01.50/0 0 1989 American Chemical Society
1186 Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989 Table 11. Conversion (x),Heat of Reaction (AH298.18), and Effectiveness Factor ( v ) for Different Reactions
Table I. Arrhenius Parameters Estimated for Different Reactions (ko)t, kmol/ (kghaatm)
reaction
E,,
m298.16,
kcal/ mol 22.8 22.3 20.0
reaction" p-Xyl
X
em-Xyl
kcal/ kmol
0.9
-170.00
0.9
-420.00
k-1
17.4
k2
20.0 20.0 20.0 -0.11 20.0 20.0 17.4 22.5 22.8 22.3 22.5 5.0
o-Xyl=
m-Xyl
k-2
+ H,
p-Xyl
O-Xyl+ H,
-
ke
EBZ
material balance equation:
ka
T + CH4
1.0
-10256.07
k4
T + CHd
1.0
-10256.07
2T + C H ~
1.0
-10256.07
or m-Xyl
1.0
-2836.670
1.0
-2836.67
1.0
-530.00
1.0
-530.00
1.0
-530.00
+
m - X y l + H~
The Arrhenius parameters estimated for xylene isomerization (Cortes and Corma, 1980), hydrogenolysis (Cortes and Corma, 1980), ethylbenzene isomerization (Pitts et al., 1955), and disproportionation of xylenes (Haag et al., 1984) are reported in Table I. In xylene isomerization, the influence of temperature on the adsorption constants of the three xylenes reported by Cortes and Corma (1980) was very small (activation energy of adsorption = 4 kcal/mol). Therefore, the temperature dependency of the adsorption constants was neglected in the present study. The values of the adsorption constant were taken as 1.333,1.237, and 0.4767 for m-, p - , and o-xylenes, respectively. P p , Po, PM, P H ,PT, PTMB, and PEBz are the partial pressures of p-xylene, o-xylene, m-xylene, hydrogen, toluene, trimethylbenzene, and ethylbenzene, respectively. Model Development. The purpose of the reaction is to develop a suitable mathematical model that expresses the behavior of the reacting system under various operating conditions. Data obtained from the process plant are useful in building a mathematical model. The kinetics and transport phenomena of the process are needed in addition to the data and must be included in the model. The simulation of fixed bed reactors depend upon the simultaneous solution of sets of differential equations. Most industrial fixed bed reactors are designed as adiabatic reactors. A good insulation (-99%) around the reactor vessel usually provides complete isolation and adiabaticity. The xylene isomerization reactor at the plant is operated as an adiabatic fixed bed gas reactor. The simplest model of an adiabatic gas reactor is the one-dimensional plug flow model (Orhan Tarhan, 1983) with the following equations:
0 - , p-,
EBZ
CH+ ~T
2(p-Xyl)
eT + TMB
k7
k-7 k8
2(0-Xyl)
e T + TMB k4 kg
2(m-Xyl) G T
2T
km
0-
+ TMB
k-8
and p-Xyl
partial pressure is always kept at a high value, catalyst deactivation is therefore assumed to be practically absent. In the present model, the activity of octafining I1 catalyst has been taken to be equal to 1.0. The global rates of reactions for different components are given as follows: -Rp
= Vi(kiKpPp - k-iKMpd
+ q5(k$p2
The thermodynamic and transport properties calculated for different reactions are tabulated in Table 11. A t higher values of hydrogen partial pressure, the catalyst deactivation rate is very slow. Since in the plant the hydrogen
~&~PH -PP
- k-7PTMBPT) - 0.5ki$~'
(11)
+ V&APHPO -
i=l
O . ~ ~ V ~ ~ & ' EfBr/5(kgPo2 Z - k-8PTMBPT) -
(12)
-RH = ~3(k3Pp-k kJ'o
(13)
tfb((k-7
=
174k6PEBZ
k5PM)PH
(14)
+ k~'PEBZ
+ k-8 + ~ J P T M B-P T (k7Pp2 f k8P02 + k$M'))
+ k-g)&MBPT
(k7Pp'
(10)
f
1 + CKiPi
1 -Ro = ~z(k-2KOPo- ~ ~ K M P M ) 1 + CKiPi
-RT = v ~ ( ( h - 7+ k-8 Combining eq 8 and 9 gives
1 i=l
0.217&,PEBZ
-RTMB=
energy balance equation:
1.0
Xyl is xylene, T is toluene, EBZ is ethylbenzene, and TMB is trimethylbenzene.
-REBZ
d_T _ -dx F Y d - M ) dz dz Cpmi,
I)
+ kSPo'
(15)
f
kgM2))
+ k,$~*
(16)
From analysis of the data on ethylbenzene isomerization as reported by Pitts et al. (1955), the selectivities of oxylene, p-xylene, and m-xylene are 0.32, 0.21, and 0.47, respectively. In this reacting system, the total number of moles, F , remains always constant. The material and energy balance equations for various components, like p-xylene, o-xylene, hydrogen, ethylbenzene, and toluene, are obtained after the mole fraction
Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989 1187 for hydrogen
Table 111. Input Plant Data inDut data catalyst age, days feed flow rate, kg/h catalyst bed length, m diameter of catalyst bed, m inlet temp, "C inlet pressure, atm feed components p-xylene o-xylene m-xylene hydrogen ethylbenzene toluene benzene methane ethane propane butane pentane hexane C9 aromatic nonaromatics
case I case I1 76 83 21.1277 X lo3 21.514 X lo3 0.96 0.96 3.0 3.0 385.5 381.5 13.10 13.10 mole fractions
where FYOH
w3
0.010 0.005 0.055 0.742 0.030 0.010 0.00 0.030 0.030 0.030 0.025 0.004 0.000 0.000 0.029
0.013 0.007 0.006 0.709 0.028 0.008 0.000 0.044 0.037 0.035 0.021 0.005 0.001 0.000 0.029
=CpmIu
w4
FYOEBZ
='pmix
of all reacting systems and the total pressure are substituted in the equations. These are for p-xylene
where w5
YOT
=CPmu
The overall rate of temperature change along the reactor is obtained by adding the contribution of individual reactions: F(6) = (dT/dz), + (dT/dz), + (dT/dz), + (dT/dz), + (dT/dz), (26) In a packed reactor, the loss of pressure may also be significant. This has been taken into account by using the modified Ergun's equation (Ergun and Cranfield, 1970). The equation is
10-5(1- E)GU,/(~%,,) bar/m (27) Thus, we have following equations constituting the mathematical model: (28) FW) = f G p , Xo, XH, XEBZ,XTMB,T,P, XT) */dz = f b p , xo, XH, XEBZ, XTMB, T, P, XT) (29) where N = 1, ..., 5. Here the boundary conditions are, a t z = 0, x p = 0, xo = 0, X H = 0, xEBZ = 0, xTMB = 0, XT = 0, T = Ti,, and P = Pi, where Ti, and Pi, are the temperature and pressure a t the reactor inlet. In a d i a b a t i c o p e r a t i o n eq 28 and 29 are solved by the fourth-order Runge-Kutta method (Carnahan et al., 1969) to get concentration, temperature, and pressure profiles at different values of the independent variable (2). where
Results and Discussion The simulation model presented has been tested for the xylene isomerization reactor of an existing petrochemical plant. The plant has been operating for years, and steady process data were collected to check the validity of the
1188 Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989 Table IV. Comparison of Simulated Values of an Adiabatic Reactor with Plant Datao case I case I1 calcd actual calcd actual temp, "C 399.70 398.70 395.91 394.10 pressure, atm 13.08 13.00 13.09 13.00 Component Outlet Composition, Mole Fraction p-xylene 0.023 0.018 0.027 0.020 x-xylene 0.015 0.016 0.018 0.016 m-xylene 0.043 0.040 0.060 0.048 hydrogen 0.722 0.738 0.688 0.705 ethylbenzene 0.028 0.023 0.029 0.024 toluene 0.013 0.009 0.007 0.007
13.12 Pressure P r o f i l e
13.081
-
1 5
a
1 1304t
,
13.021
Plant data
u Case I -&-
case 11
13.00b
The change in mole fraction of other components is negligibly small, and therefore, it has not been included for comparison.
iz.ga1 0 Temperature Profile
0 -Plant Data
0
I
1
I
I
20 40 60 80 Catalyst Bed Length (cm)
Plant Data
1( 3
Figure 2. Pressure profile in an adiabatic reactor.
-
Plant Data
4001
E
i
0 A
,
.-5
$i
p-xylene 0-xylene
'\
1
i \
m-xylene
,I
I
380
0
I
I
I
I
20 40 60 80 100 Catalyst Bed Length (cm)
Figure 1. Temperature profile in an adiabatic reactor.
model. At steady state, the temperature and pressure remained almost constant, whereas there observed to be a variation in the feed composition resulting in the variation of outlet concentration from the reactor. The plant operating data are available at two different days for two different feed compositions and inlet temperatures as given in Table 111. The simulated values of reactor outlet temperature, pressure, and composition have been calculated from mathematical models for different modes of operation of the reactor. Simulated results obtained from isothermal and nonisothermal nonadiabatic conditions were compared with results obtained under adiabatic conditions. The mathematical model proposed was solved numerically by using the fourth-order Runge-Kutta technique on a DEC-10 computer and holds good for a reactor operating under adiabatic conditions and a t the given feed composition.
Adiabatic Operation Temperature, pressure, and concentration profiles for case I and case I1 data were obtained by solving energy balance, pressure drop, and mass balance equations (eq 28 and 29) for an adiabatic reactor. The reactor outlet composition values have been compared with the plant data in Tables IV for both case I and case 11. Figure 1 shows the temperature profile of the reactor for both case I and case 11, whereas Figure 2 shows the pressure profile for both cases. It is clear from the figures that the temperature and pressure profiles are in good agreement with the plant data. Temperature rises almost linearly with bed length, and the pressure decreases with bed length. The deviation in outlet temperature is less than 1% ,whereas in the outlet pressure
0.005
0
20 40 60 80 Cotalyst Bed Length (cm)
100
Figure 3. Concentration profile in an adiabatic reactor (case I).
it is less than 0.2% between plant data and calculated results. Since plant data of the pressure drop and temperature are not available in the middle section of the reactor, a comparison could not be made. Figures 3 and 4 show the concentration profiles of m-, 0-,and p-xylene in the reactor against bed length for case I and case 11, respectively. Plant data are compared with simulated results in both figures. The agreement between plant data and simulated values of the concentration profile is fairly good. a t a reactor temperature of about 390 "C, the equilibrium concentration of p-xylene is always lower than o-xylene, and below 390 "C the p-xylene concentration is higher than the o-xylene concentration. The reactor operating temperature in both cases falls within this range of temperatures, Le., around 390 "C. It is observed that simulated values of the temperature in both cases are more than that of plant values and the difference is of the order of 1 "C. The discrepancy between plant and simulated values is probably due to some loss in the reactor since absolute adiabaticity does not exist and a loss of 1% is practical. The simulated concentration values of m-xylene and p-xylene were observed to be little more than plant values but o-xylene concentration was close to the actual value.
Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989 1189 On the basis of a sensitivity analysis carried out on a DEC-10 varying the various parameters, we can suggest the optimum operating conditions of the isomerization reactor. The suggested optimum conditions are as follows: (i) The feed inlet temperature should be around 400 "C. (ii) The reactor inlet pressure should be in the lower range, Le., 13-15 atm. (iii) The WHSV should be reasonably high, 4-5 kgh/k mol. (iv) The feed should contain a reasonably high concentration of m-xylene compared to the o-xylene or ethylbenzene concentration. Thus, the one-dimensional plug flow model adequately represents the behavior of the xylene isomerization reactor.
b
0.005
I
I
I
I
40 60 80 Catalyst Bed Length ( c m l
20
1
Figure 4. Concentration profile in an adiabatic reactor (case 11).
In the present simulation model, deactivation of catalyst has not been taken into account because of the fact that the rate of deactivation of the catalyst a t high hydrogen partial pressure is very slow and it can be assumed to be practically absent during the reaction. This information has been confirmed from the plant operating under hydrogen atmosphere. In the present study, no distinction has been made between the catalyst activities at different intervals of time. The catalyst activity of the fresh catalyst had been incorporated in the model.
Sensitivity Analysis Temperature and pressure are important parameters in the reactor operation, because these parameters affect the rate of reaction, selectivity, and deactivation of the catalyst. In the development of the simulation model, it is important to study the effect of important parameters, namely, feed temperature, reactor inlet pressure (hydrogen partial pressure), feed flow rate, and feed composition, over the product yield. The effects of temperature and pressure for the isomerization reaction are as follows. If the reactor pressure is changed, the maximum change will be for hydrogen partial pressure. The change of hydrogen partial pressure has some remarkable effects. An increase in hydrogen partial pressure will prolong the catalyst life and give a higher ethylbenzene approach to equilibrium, but a t the same time xylene loss will also increase because of more hydrogenolysis. The change in reactor temperature will change the reaction velocity and the equilibrium composition. The operation of the reactor at a lower temperature prolongs the catalyst life and increases the ethylbenzene approach to equilibrium, but this leads to higher xylene loss. Conversely, an increase in temperature will lower the ethylbenzene approach to equilibrium and reduce the loss of xylene. To conserve the life of the catalyst, the temperature should be held a t the minimum required to give reasonable yield. This is particularly important when starting with new or freshly regenerated catalyst that can quickly deactivate by cracking of ethylbenzene to styrene and by the coke forming reaction, if the reactor is operated at high temperature.
Conclusions A simulation model of the catalytic reactor based on the one-dimensional plug flow model has been found to be the most suitable to represent the performance of the industrual xylene isomerization reactor under adiabatic conditions. The optimum conditions of the reactor operation predicted from the model match the industrial conditions. This computer analysis holds for any reactor under any design, feed, and operating conditions. Nomenclature A , = cross-sectional area of the catalyst bed C, = concentration of the gas phase Cp = change in specific heat in the reaction Cpi = specific heat of component i C, = specific heat of the gas mixture dp = effective diameter of the particle Dp = diameter of the pellet DT = diameter of the reactor Ei= activation energy of the ith reaction F = molal flow rate of feed F(1) = factor defined by eq 17 F(2) = factor defined by eq 19 F(3) = factor defined by eq 21 F(4) = factor defined by eq 23 F(5) = factor defined by eq 24 F(6) = factor defined by eq 26 g, = force to mass conversion factor G = mass flow rate of fluid h = heat-transfer coefficient of the film AHT = heat of reaction at temperature T , K "298.16 = standard heat of reaction (at 298.16 K and 1atm) -AH = heat evolved by the reaction; (-AH)l for p-xylene isomerization, ( - A H ) 2 for o-xylene isomerization, ( - A H ) 3 for hydrogenolysis of xylene (para, ortho, and meta), (-AH)4 for ethylbenzene isomerization, (-AH)5 for disproportionation of xylene (para, ortho, and meta) ki = forward rate constant for the ith reaction; kl for p-xylene isomerization, k2 for m-xylene isomerization, k3 for p-xylene hydrogenolysis, k4 for o-xylene hydrogenolysis, k5 for mxylene hydrogenolysis, k6 for ethylbenzene isomerization, k7 for p-xylene disproportionation, k8 for o-xylene disproportionation, k g for m-xylene disproportionation k+ = backward rate constant for the ith reaction; k-, for p-xylene isomerization, k-2 for m-xylene isomerization, k-, for p-xylene disproportionation, k-e for o-xylene disproportionation, k-9 for m-xylene disproportionation = preexponential factor of forward rate constant for the ith reaction (k& = preexponential factor of backward rate constant for the zth reaction K = Boltzmann constant Ki= adsorption constant of the ith component; Kp for pxylene, KO for o-xylene, K M for m-xylene M = molecular weight; Mi of component i, M j of component j
1190 Ind. Eng. Chem. Res., Vol. 28, No. 8, 1989
MAv = average molecular weight of the gas mixture P = pressure, atm AP = pressure drop Pi = partial pressure of component i; Pp for p-xylene, Po for o-xylene, P M for m-xylene, PEBZ for ethylbenzene, PTfor toluene, P T M B for trimethylbenzene r’ = rate of reaction per unit volume of catalyst -rv = intrinsic rate of reaction; -rp for p-xylene, -ro for oxylene, -rM for m-xylene, -rH for hydrogen, -rEBZfor ethylbenzene, -rTMB for trimethylbenzene R = universal gas constant -R = global rate of reaction; -Rp for p-xylene, -Ro for o-xylene, -RH for hydrogen, -REBZ for ethylbenzene, -RTMB for trimethylbenzene T = absolute temperature, K U,,, = superficial fluid velocity based on empty reactor cross section x = fractional conversion; x1 for p-xylene isomerization, x 2 for o-xylene isomerization, x g for p-xylene hydrogenolysis, x4 for o-xylene hydrogenolysis, x5 for m-xylene hydrogenolysis, x 6 for ethylbenzene isomerization, x7 for p-xylene disproportionation, x8 for o-xylene disproportionation, x9 for m-xylene disproportionation Xp = total conversion of p-xylene Xo = total conversion of o-xylene X E B Z = total conversion of ethylbenzene XH = total conversion of hydrogen X T M B = total conversion of trimethylbenzene XT = total conversion of toluene Y,, Y, = mole fraction of components i and j Yoi = initial mole fraction of component i, Yop for p-xylene, Yo0 for o-xylene, YoM for m-xylene, YOH for hydrogen, Yomz for ethylbenzene, Yw for methane, Ym for toluene, Y ~ M B for trimethylbenzene z = length of reactor G r e e k Symbols q = effectiveness factor; q1 for p-xylene isomerization, q2 for
o-xylene isomerization, q3 for hydrogenolysisof xylene (para, ortho, and meta), q4 for ethylbenzene isomerization, 75 for disproportionation of xylene (para, ortho, and meta) c~ = gas viscosity kmix= viscosity of the gas mixture pc = bulk density of the catalyst bed c = fractional void volume
Appendix A The mole fraction of all the reacting components at any instant is given by
where the suffixes P, 0, M, H, EBZ, T, C, and TMB represent p-xylene, o-xylene, m-xylene, hydrogen, ethylbenzene, toluene, methane, and trimethylbenzene, respectively, Yoiis the initial mole fraction of component i, and Yi is the mole fraction of component i at any instant. Again, Pi = YiP where Pi is the partial pressure of component i at any instant and P is the total pressure. xp = X I + x g + x7 - 0.21-x~ YOEBZ - 0.5-x~ YOT YOP
XEBZ
XH
=
y0Px3
+
=
x6
+
yOG4
YOP
x6‘
+
YOMx5
YOH XTMB
=
y0Px7
+
yOOx8
+
YOMX9
YOT
Registry No. Pt, 7440-06-4; xylene, 1330-20-7;ethylbenzene, 100-41-4;p-xylene, 108-38-3; m-xylene,95-47-6; toluene, 108-88-3.
Literature Cited Carnahan, B.; Luther, H. A.; Wilkes, J. 0. Applied Numerical Methods; Wiley: New York, 1969.
Cortes, A.; Corma, A. J . Catal. 1978, 51, 338. Cortes, A.; Corma, A. J . Catal. 1979, 57, 444. Cortes, A.; Corma, A. Znd. Eng. Chem. Process Des. Deu. 1980, 19, 263.
Ergun, B. J.; Cranfield, R. R. Br. Chem. Eng. 1970, 190, 481. Haag, W. 0.; Olson, D. H.; Weisz, P. B. Chemistry for the Future; Pergamon Press: Oxford, 1984. Hanson, K. L.; Engel, A. J. AIChE J. 1967, 13, 260. Pitts, P. M.; Connor, J. E.; Leum, Znd. Eng. Chem. 1955, 47, 4. Prasada Rao, T. S. R.; Halgeri, A. B. Second Refinery Technology Conference, Madras, 1986. Tarhan, 0. M. Catalytic Reactor Design; McGraw Hill: New York, 1983.
Received for review March 11, 1988 Accepted January 13, 1989
