Ind. Eng. Chem. Res. 2008, 47, 9183–9194
9183
Ethylbenzene Dehydrogenation into Styrene: Kinetic Modeling and Reactor Simulation Won Jae Lee† and Gilbert F. Froment* Artie McFerrin Department of Chemical Engineering, Texas A&M UniVersity, College Station, Texas 77843-3122
A set of intrinsic rate equations based on the HougensWatson formalism was derived for the dehydrogenation of ethylbenzene into styrene on a commercial potassium-promoted iron catalyst. The model discrimination and parameter estimation was based on an extensive set of experiments that were conducted in a tubular reactor. Experimental data were obtained for a range of temperatures, space times, and feed molar ratios of steam to ethylbenzene, styrene to ethylbenzene, and hydrogen to ethylbenzene. All the estimated parameters satisfied the statistical tests and physicochemical criteria, and the kinetic model yielded an excellent fit of the experimental data. The model was applied in the simulation of the dehydrogenation in industrial multibed adiabatic reactors with either axial or radial flow and accounting also for thermal radical-type reactions, internal diffusion limitations, coke formation, and gasification. 1. Introduction Styrene (ST) is one of the most important monomers in the chemical industry. More than 2.5 × 107 MT/year of styrene monomer is produced worldwide.1 The dehydrogenation of ethylbenzene (EB) on iron oxide catalysts promoted by potassium accounts for 85% of the commercial production.2 Benzene (BZ), toluene (TO), methane, and ethylene are the main byproducts.3 The dehydrogenation of EB is an endothermic and reversible reaction with an increase in the number of moles, so that high conversion requires high temperatures and a low EB partial pressure. Potassium promotes the catalyst activity and enhances the selectivity to ST. The role of potassium is attributed to the existence of an active phase, potassium ferrite (KFeO2).4–10 Potassium also promotes the gasification of the carbonaceous deposits on the catalyst and would maintain the catalyst activity, even at relatively low steam-to-hydrocarbon ratios (i.e., below a molar ratio of 11.8:1).5,11,12 High steam-to-hydrocarbon ratios favor the selectivity to ST but also the lifetime and stability of the catalyst by decreasing the undesired carbon production. Devoldere and Froment13 studied the influence of the formation of coke on the catalyst and of its gasification by steam on the operation of ST plants and introduced the notion of a “dynamic equilibrium coke content”. The kinetics of EB dehydrogenation have been widely investigated14–18 but seldom in a fundamental way, generating empirical polynomial correlations for the optimization of the commercial unit.19–21 Furthermore, the reaction rates reported in most of the papers are not intrinsic, but rather are effective (i.e., including the effects of diffusional limitations).14,16,22 Recently, however, Schu¨le et al.23 derived a mechanistic model using a single-crystal unpromoted iron oxide film. It includes EB dehydrogenation into ST, but it does not consider BZ and TO formation and thermal reactions. The redox reactions on the catalyst and coke formation were included in the model that contains 31 parameters, 13 of which were estimated from overall kinetic measurements, whereas the others (such as adsorption * To whom correspondence should be addressed. Tel.: +1-979-8453361. Fax: +1-979-845-6446. E-mail:
[email protected]. † Present address: Corporate R&D, LG Chem, Ltd./Research Park, Moonji-Dong, Yuseong, Daejeon, 305-380, Korea.
and desorption parameters) were determined by specific experimentation. To accurately predict the reactor performance, the development of an intrinsic HougensWatson type kinetic model, i.e., accounting for the adsorption and desorption of the reacting species, is indeed required. This was attempted in the present work starting from an extensive set of kinetic experiments. The intrinsic kinetic model is inserted into a heterogeneous reactor model, accounting for diffusion limitation inside the catalyst particles and also for the thermal reactions, to simulate industrial axial and radial flow multibed adiabatic reactors. The kinetic model for the main reactions is also combined with that for the coke formation and gasification to calculate the dynamic equilibrium coke content of the catalyst for different steam-tohydrocarbon feed ratios and to investigate the influence of the coke formation on the reactor performance. 2. Experimental Unit Two liquid feeds, i.e., hydrocarbon mixture (EB and ST) and water, were separately pumped and controlled by two Harvard precise syringe pumps. N2 was used as a diluent for the reaction and as an internal standard for the gas chromatography (GC) analysis. The flow rate of N2 was controlled by an Omega mass flow controller. Great care was taken to have the liquids and gases well-mixed through two preheaters in series before they were fed to the reactor. The reactor was fabricated from a stainless steel tube and had an internal diameter of 1 in. and a length of 18 in. The inner surface of the reactor was plated with chromium, to suppress coke formation on the walls. The reactor was heated by an electric furnace surrounding the reactor tube. Three Omega type-K thermocouples were located on the surface of the internal wall of the furnace. The temperature inside the reactor was monitored by a Omega type-K thermocouple that slid inside a thermowell. No temperature gradient was observed over the catalyst bed. The commercial iron catalyst was crushed to a particle size of 0.25-0.42 mm, to avoid internal diffusion limitations, and was mixed with the same particle size of R-Al2O3 (Saint-Gobain NorPro, D-99) in a weight ratio of 1:6. Because the ratio of tube diameter to catalyst pellet diameter is .10, the flow pattern inside the reactor can be considered to be of the plug-flow type. The catalyst-inerts mixture was placed in the middle section
10.1021/ie071098u CCC: $40.75 2008 American Chemical Society Published on Web 02/06/2008
9184 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
of the reactor, and its bed depth varied between 3 and 5 cm, depending on the amount of catalyst. The upper and lower sections of the reactor were filled with R-Al2O3 beads to serve two functions: preheating and mixing of reactants and decreasing the free volume in the reactor. A small fraction of the exit gas was sent to a Shimadzu 17A gas chromatograph with a thermal conductivity detector (TCD), followed by a HewlettsPackard (HP) 5890 gas chromatograph with a flame ionization detector (FID) for online analysis. Two gas chromatographs were connected in series, and helium was used as a carrier gas. The Shimadzu 17A gas chromatograph was equipped with two valves to inject the gaseous products and switched the valves by means of a timing program stored in the gas chromatograph. The oven temperature programs of the Shimadzu 17A and HP 5890 gas chromatographs and valve switching timing program were matched to accomplish the desired separation of all compounds. Three capillary columns were used: HP PLOT Molecular Sieve 5A column (Agilent, 0.53 mm ID × 25 µm × 15 m), for the separation of H2 and N2; GS-Q capillary column (J&W, 0.53 mm ID × 30 m), for the separation of N2, CO, CO2, CH4, C2H4, and H2O; and a HP-5 capillary column (Agilent, 0.53 mm ID × 1.5 µm × 30 m), for the separation of aromatic compounds. N2 was used as a primary internal standard for the TCD analysis. EB was chosen as a secondary internal standard, because it appeared on both TCD and FID as one of the major compounds and could be used to “tie” the analyses on the two detectors. EB conversion, conversions of EB to product j, and selectivities to product j were calculated using the following definitions: EB conversion (%) ) 100 ×
Figure 1. Effect of temperature on the ethylbenzene (EB) conversion to styrene (ST) for T ) 600, 620, and 640 °C; PT ) 1.04 bar; PN2 ) 0.432 bar; H2O-to-EB molar ratio ) 11 mol/mol; ST-to-EB molar ratio ) 0; H2to-EB molar ratio ) 0.
F0EB - FEB F0EB
Conversion of EB to product j (%) ) 100 ×
Selectivity to product j (%) ) 100 ×
Fj - F0j F0EB
Fj - F0j F0EB - FEB
Prior to conducting the experiments, the fresh iron catalysts were activated. The temperature was increased to 620 °C under a N2 flow for 12 h. A typical partial pressure of N2 was 0.432 bar. Water was injected to the preheater 1 or 2 min before the EB was added. A typical H2O-to-EB feed ratio was 11 mol/mol. Several days were required for the catalyst to be fully activated. During the night, the feed of EB and water was always shut off, while the temperature was maintained at 620 °C under N2 flow. Kinetic data were collected at various temperatures, space times, and feed molar ratios of H2O and EB, ST and EB, and H2 and EB. Space time is defined as the weight of catalyst divided by the feed molar flow rate of EB. Space time was in the range of 6-70 g-cat h/(mol EB). Experiments were performed at three different temperatures: 600, 620, and 640 °C. The kinetic experiments were always conducted at relatively low conversions, far away from equilibrium. A reference reaction condition was used to check whether the catalyst was not deactivated by coke accumulation, potassium loss, or reduction before conducting kinetic experiments. If any loss of activity was detected, the catalyst was replaced. The standard activity was easily reproduced. Interfacial gradients of temperature and partial pressure were negligible in all experiments reported here.
Figure 2. ST selectivity as a function of EB conversion for T ) 600, 620, and 640 °C, PT ) 1.04 bar; PN2 ) 0.432 bar; H2O-to-EB molar ratio ) 11 mol/mol; ST-to-EB molar ratio ) 0; H2-to-EB molar ratio ) 0.
3. Experimental Results Experimental data were collected by injecting the exit sample 6-10 times into the online GC setup under the same reaction conditions. The data plotted in the following figures are averages of those values. The standard deviation of each point is ∼1% of the average value. For all the temperatures, the EB conversion did not increase appreciably when the space times exceeded 70 g-cat h/(mol EB), because the reactions approach equilibrium at high space time. The solid lines in the following figures are drawn to fit the data. Figure 1 shows the effect of temperature on the EB conversion to ST for a molar steam-to-EB ratio of 11. The rate of formation of ST from EB decreased as the space time increased. The calculated equilibrium conversions of EB to ST are 80.4%, 85.0%, and 88.8% at T ) 600, 620, and 640 °C, respectively. 0 The corresponding experimental values at W/FEB ) 62 g-cat h/mol shown in Figure 1 were 60.0%, 71.6%, and 79.1%, respectively, i.e., well below the equilibrium values. Figure 2 shows the ST selectivity as a function of the EB conversion for the complete temperature range. The ST selectivity evolves in an opposite way to the EB conversion. The ST selectivity has a tendency to decrease as the temperature increases, because the competitive reactions that produce byproducts become pronounced with increasing temperature. Figures 3 and 4 show the BZ and TO selectivity, as a function of EB conversion. The rate of BZ formation is only slightly affected by the EB conversion (or space time), but the rate of TO formation is significantly enhanced as the EB conversion (or space time) increases.
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9185
Figure 3. Benzene (BZ) selectivity as a function of EB conversion for T ) 600, 620, and 640 °C, PT ) 1.04 bar; PN2 ) 0.432 bar; H2O-to-EB molar ratio ) 11 mol/mol; ST-to-EB molar ratio ) 0; H2-to-EB molar ratio ) 0.
Figure 6. Effect of ST-to-EB feed ratio on (a) the EB conversion and (b) the ST selectivity for T ) 620 °C; PT ) 1.04 bar; H2O-to-EB molar ratio ) 11; H2-to-EB molar ratio ) 0.
Figure 4. Toluene (TO) selectivity as a function of EB conversion for T ) 600, 620, and 640 °C, PT ) 1.04 bar; PN2 ) 0.432 bar; H2O-to-EB molar ratio ) 11 mol/mol; ST-to-EB molar ratio ) 0; H2-to-EB molar ratio ) 0.
results at 600 and 640 °C are not included. The increase in the H2O-to-EB feed ratio did not result in an increase of the EB 0 conversion or the ST selectivity for W/FEB < 30 g-cat h/mol. 0 Even for W/FEB > 30 g-cat h/mol, the effect of increasing the H2O-to-EB feed ratio on the EB conversion was insignificant. The effect of the H2O-to-EB feed ratio on the styrene selectivity, however, becomes pronounced as the EB conversion increases. Effect of the Styrene-to-Ethylbenzene Feed Ratio. Figure 6 shows the effect of the ST-to-EB feed ratio on the EB conversion and the ST selectivity at 620 °C. As the ST-to-EB ratio in the feed increases, the EB conversion decreases, because of the competitive adsorption of ST and the approach to equilibrium. Furthermore, the adsorbed ST on the surface changes to a carbonaceous deposit, which causes catalyst deactivation. As the ST-to-EB feed ratio increased, the ST selectivity decreased. Effect of Hydrogen-to-Ethylbenzene Feed Ratio. Figure 7 shows the effect of hydrogen addition on the EB conversion and the ST and TO selectivity at 600 °C. Hydrogen is involved in the formation of TO from ST, so that when the H2-to-EB feed ratio is increased, the TO selectivity is favored, while the ST selectivity suffers from side reactions. The addition of hydrogen further reduces the iron catalyst from hematite (Fe2O3) to magnetite (Fe3O4), which has a lower activity. 4. Reaction Scheme and Rate Equations
Figure 5. Effect of H2O-to-EB feed ratio on (a) the EB conversion and (b) the ST selectivity for T ) 620 °C; PT ) 1.04 bar; ST-to-EB molar ratio ) 0; H2-to-EB molar ratio ) 0.
Effect of the Steam-to-Ethylbenzene Feed Ratio. Figure 5 shows the influence of the H2O-to-EB feed ratio on the EB conversion and the ST selectivity at 620 °C. The experimental
4.1. Thermal Reactions. Thermal radical-type reactions cannot be ignored in the derivation of the kinetic model for EB dehydrogenation. They occur in the zones without catalyst or in the voids of zones that contain only inert solids or in the void fraction of the catalyst bed itself. These reactions involve free-radical mechanisms; however, given the low thermal conversions, they were approximated in the present work by a simple molecular scheme.24,25 The kinetic parameters for these reactions are given in Table 1. They were obtained by matching simulations based on the detailed radical scheme shown by the following molecular mechanism:
9186 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
(
kt1
EB {\} ST + H2 rt1 ) kt1 PEB kt1 - 1
PSTPH2 Keq
)
Scheme 1. Catalytic Reaction Scheme of Ethylbenzene (EB) Dehydrogenation
kt2
EB 98 BZ + C2H4 rt2 ) kt2PEB kt3
EB + H2 98 TO + CH4 rt3 ) kt3PEB By way of example, the conversion of EB to ST that results from thermal reactions was simulated for a typical bench-scale experiment at 620 °C, as reported in Figure 1. Using the kinetic parameters given in Table 1 and accounting for the temperature profiles or levels in the preheater, catalytic, and bottom sections of the reactor, the thermal conversion of EB to ST amounted to 5.7%, whereas the measured EB conversion to ST shown in Figure 1 was 62.4%. 4.2. Catalytic Reactions. Scheme 1 shows the catalytic reaction scheme that is generally accepted for EB dehydroge-
nation. The reaction ST + H2 f BZ + C2H4 in Scheme 1 was dropped early in the kinetic modeling procedure of the present work. The selected rate equations are k1KEB[PEB - (PSTPH2 ⁄ Keq)]
rc1 )
(1 + KEBPEB + KH PH 2
2
(1)
+ KSTPST)2
k2KEBPEB (1 + KEBPEB + KH2PH2 + KSTPST)2
rc2 )
(2)
k3KEBPEBKH2PH2
rc3 )
(1 + KEBPEB + KH PH 2
2
(3)
+ KSTPST)2
k4KSTPSTKH2PH2
rc4 )
(1 + KEBPEB + KH PH 2
2
(4)
+ KSTPST)2
These rate equations correspond to the rate-determining steps on dual sites and involve an adsorbed hydrocarbon and a molecularly adsorbed hydrogen, confirming the earlier conclusions of Devoldere and Froment.26 Twenty-four rival models based in Scheme 1 and comprised of models with ratedetermining steps that could be single-site or dual-site adsorption, desorption, or reaction and with molecular or atomically produced hydrogen in the reaction step proper were tested. The discrimination was based on the F-test and the confidence intervals of the parameters. A nonsignificant value of the adsorption equilibrium constant for water was obtained, reflecting what was reported in the section on the influence of the steam-to-EB feed ratio. Nonsignificant values were also obtained for the parameters related to the conversion of ST to BZ, which is the reason why this reaction does not appear in Scheme 1. 5. Parameter Values 5.1. Continuity Equations for the Reacting Species. Kinetic analysis of the data obtained in the integral reactor with plug flow previously described requires a set of continuity equations for the reacting species, accounting for both catalytic and thermal reactions in the catalyst bed and voids. For steady-state operation, the following can be written for Scheme 1: dXEB W ⁄ F0EB
d(
)
) η1rc1 + η2rc2 + η3rc3 + (rt1 + rt2 + rt3) dXST
Figure 7. Effect of H2-to-EB feed ratio on (a) the EB conversion, (b) the ST selectivity, and (c) the TO selectivity for T ) 600 °C; PT ) 1.04 bar; H2O-to-EB molar ratio ) 11; ST-to-EB molar ratio ) 0.
W ⁄ F0EB
d(
dXBZ
Table 1. Pre-exponential Factors and Activation Energies for the Thermal Reactions i
Ati [kmol/(m3 h bar)]
1 2 3
2.2215 × 10 2.4217 × 1020 17 3.8224 × 10 16
)
) η1rc1 - η4rc4 + rt1
W ⁄ F0EB
d(
Eti [kJ/mol]
dXH2
272.23 352.79 313.06
W ⁄ F0EB
d(
)
)
) η2rc2 + rt2
B FB
(5b)
B FB
) η1rc1 - η3rc3 - 2η4rc4 + (rt1 - rt2)
with initial conditions
B (5a) FB
(5c) B FB
(5d)
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9187 Table 2. Parameter Values and Statistical Tests Derived from the Data at 620 °C 95% Confidence Interval parameter
unit
estimate
standard deviation
t value
lower value
upper value
KEB KST KH2 k1 k2 k3 k4
bar-1 bar-1 bar-1 kmol/(kg-cat h) kmol/(kg-cat h) kmol/(kg-cat h) kmol/(kg-cat h)
8.466 34.00 3.091 0.2725 0.00544 0.0184 0.0302
1.01 1.51 0.447 0.0171 0.000504 0.00874 0.00565
8.37 22.6 6.91 15.9 10.8 2.11 5.66
6.460 31.02 2.204 0.2385 0.00444 0.001095 0.0190
10.47 36.99 3.977 0.3065 0.00644 0.03571 0.0413
Table 3. Values of the Kinetic Parameters Derived from the Estimation Based on the Data at All Temperatures symbol
value
Pre-exponential Factor of Catalytic Reaction i [kmol/(kg-cat h)] 4.594 × 109 1.060 × 1015 1.246 × 1026 8.024 × 1010
A1 A2 A3 A4
Pre-exponential Factor of Adsorption Species j [bar-1] 1.014 × 10-5 2.678 × 10-5 4.519 × 10-7
AEB AST AH2
Figure 8. Effect of temperature on (a) the rate coefficients ki and (b) the adsorption equilibrium constants Kj. Symbols represent estimated values per temperature; lines represent calculated values from estimates at all temperatures.
Activation Energy [kJ/mol] E1 E2 E3 E4
175.38 296.29 474.76 213.78 Adsorption Enthalpy [kJ/mol] -102.22 -104.56 -117.95
∆Ha,EB ∆Ha,ST ∆Ha,H2
Xj ) 0 at
W )0 F0EB
Small catalyst particles were used to eliminate internal diffusion limitations and, thus, obtain intrinsic kinetics. In that case, the effectiveness factors (ηi) are equal to 1. The thermal reactions inside the pores of the catalyst were not taken into account. 5.2. Parameter Estimation. The parameter estimation was based on the integral method as described by Froment and Bischoff27 and Froment.28 The set of stiff differential equations (eqs 5a-d) were integrated numerically using Gear’s method.29 The parameters were estimated through the minimization of the multiresponse objective function, which was performed by means of the Marquardt algorithm. The minimization of the sum of squares of residuals can be represented by n
S(β) )
∑ [y - f(x , β)] i
i
2
β
98 Min
(6)
i)1
The parameter values, the statistical tests, and the approximate 95% confidence intervals derived from the experimental data at 620 °C are given in Table 2. The parameter values obtained from the data at all temperatures simultaneously are shown in Table 3. The agreement between the two sets of parameters can be observed in Figure 8, which shows the temperature dependence of the adsorption equilibrium constants and rate coefficients. The symbols represent the values of the kinetic parameters estimated from various sets of data collected at a given temperature, whereas the lines correspond to the values estimated from the complete set of data at all temperatures. The
Figure 9. Comparison of calculated and experimental conversions, as a function of space time. Symbols represent experimental data; lines represent calculated values using the estimates of the kinetic parameters obtained from all temperatures simultaneously. T ) 620 °C; H2O-to-EB molar ratio ) 11 mol/mol; PT ) 1.044 bar; PN2 ) 0.432 bar.
kinetic parameters lead to an excellent fit of the experimental data. By way of example, Figure 9 compares the experimental and calculated conversions, as a function of space time at 620 °C. 5.3. Physicochemical Tests on the Model Parameters. Boudart and coauthors30–32 proposed several rules for validating kinetic parameters. The following test procedure was guided by the work of Mears and Boudart,33 Van Trimpont et al.,34 Xu and Froment,35 and Froment and Bischoff.27 (1) For an endothermic reaction, the thermodynamics require the activation energy of reaction (Ei) to exceed the heat of reaction (∆Hr,i): Ei > ∆Hr,i
(7)
The activation energies for reactions of EB to ST and EB to BZ, which are endothermic reactions, are given in Table 3. They are indeed larger than the corresponding heats of reaction at 893.15 K, which amount to 124.8 and 101.5 kJ/mol, respectively, as calculated from the thermodynamics.
9188 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 4. Adsorption Entropies and Standard Entropies for Ethylbenzene (EB), Styrene (ST), and Hydrogen (H2) component
0 -Sa,j [J/(mol K)]
0 -Sg,j [J/(mol K)]a
51 - 0.0014∆Ha,j [J/mol]
ethylbenzene, EB styrene, ST hydrogen, H2
95.61 87.53 121.5
361.65 346.25 186.1
194.1 197.4 216.1
a
Values are obtained from Stull et al.36
(2) The heat of adsorption (-∆Ha,j) must be positive, because the adsorption is exothermic. All the estimates of the heats of adsorption satisfy this constraint. (3) The adsorption entropy must satisfy 0 < -∆Soa,j < Sog
∆Soa ) Soa - Sog
For cylindrical packings, the coefficients a and b are 1.28 and 458, respectively.38 The pressure drop between the catalyst beds is neglected. 6.2. Continuity Equations for the Components Inside the Porous Catalyst. The continuity equations for the components inside a porous catalyst that account for the thermal reactions occurring in the void space inside the catalyst particle are given as follows:
(
)
RgT 1 d 2 dPs,BZ r )(F r + srt2) 2 dr dr De,BZ s c2 r
(15c)
(
B dT ) F0EB -∆Hr1 η1rc1 + rt1 0 F d(W ⁄ FEB) B j)1 B B - ∆Hr3 η3rc3 + rt3 - ∆Hr4η4rc4 (12) ∆Hr2 η2rc2 + rt2 FB FB
(
)
]
and the momentum equation is given as -
dPt d(W ⁄ F0EB)
) fR
usGF0EB FBdpΩ
(
)
(
)
)
RgT 1 d 2 dPs,H2 r )[Fs(rc1 - rc3 - 2rc4) + s(rt1 - rt3)] 2 dr dr D r e,H2 (15d) with boundary conditions Ps,j ) Pj at r ) R dPs,j ) 0 at r ) 0 dr
(11)
6.1. Continuity, Energy, and Momentum Equations. A multibed industrial adiabatic reactor with axial flow was simulated, based on a heterogeneous reactor model (i.e., accounting for internal diffusion limitations). The steady-state continuity equations for the reacting species have already been given in eqs 5. With the catalyst particle sizes used in industrial production units, the effectiveness factors ηi are different from 1. For the simplified pseudohomogeneous reactor model in which diffusion limitations are not taken into account, ηi ) 1. With the set of rate equations used here, there is no analytical expression for the calculation of the effectiveness factors, in terms of a modulus, so that the solution can only be obtained by explicitly considering the transport equations inside the catalyst particle. The energy equation is written as
)
(14)
(15b)
6. Simulation of a Three-Bed Adiabatic Reactor with Axial Flow
[ ( ) (
]
(9)
Table 4 shows that this rule also is satisfied.
j pj
b(1 - B) Re
RgT 1 d 2 dPs,ST r )[Fs(rc1 - rc4) + src1] 2 dr dr D r e,ST
Table 4 shows that the rule is satisfied. (4) The last criterion has been applied by Everett,37 Vannice et al.,31 and Boudart et al.30
∑ m˙ c
a+
(8)
(10)
41.8 < -∆Soa,j e 51 - 0.0014∆Ha,j
[
RgT 1 d 2 dPs,EB r ) [F (r + rc2 + rc3) + s(rt1 + rt2 + rt3)] 2 dr dr De,EB s c1 r (15a)
where Sog is the standard entropy of the gas and Soa is the entropy of the adsorbed molecule. For adsorption, Soa is smaller than Sgo, because of the translational contribution to Sgo.33 The gas-phase o standard entropies of EB, ST, and H2 in Sg,j can be obtained 36 o from Stull et al. ∆Sa,j was calculated from the relation ∆Soa,j ) R ln Aj
3
B
The inequality comes from the relation
6
1 - B
f)
(13)
The friction factor (f) is calculated using the Ergun relation:
where Ps,j is the partial pressure of component j inside the catalyst. The effective diffusivities are calculated from the weighted binary molecular diffusivities, the void fraction of the catalyst particle (0.4), and the tortuosity factor (3.0) along the lines explained in Froment and Bischoff.27 The numerical integration of this set of equations yields the profiles of the reacting species inside the catalyst particle at a given position in the reactor and provides insight into the importance of diffusion limitations on the various reactions. These limitations can also be expressed in terms of a single number: the effectiveness factor (ηi). Accounting for the rates of both the catalytic reactions and the thermal reactions in the void space inside the porous catalyst, the effectiveness factors ηi can be calculated from these profiles by means of
∫
V
ηi )
0
[rci(Ps,j)Fs + rti(Ps,j)s] dV [rci(Pj)Fs + rti(Pj)s]V
(16)
6.3. Numerical Procedures. The continuity, energy, and momentum equationsseqs 5, 12, 13, and 14swere solved numerically, using Gear’s method. For each integration step along the reactor length, the set of equations described by eqs 15 was solved by means of the orthogonal collocation method with six internal collocation points, whose coefficients were obtained numerically from the Jacobian orthogonal polynomials. Calculations using nine internal collocation points led to exactly the same results. 6.4. Results and Discussion. The feed conditions and reactor dimension for the simulation of a three-bed adiabatic reactor with axial flow are given in Table 5. The simulation results are given in Table 5 and shown in Figures 10 and 11.
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9189 Table 5. Feed Conditions, Reactor Dimensions, and Simulation Results of a Three-Bed Adiabatic Axial Flow Reactor Using the Heterogeneous Model value parameter
bed 1
bed 2
bed 3
weight of catalyst [kg] space time [kg-cat h/(kmol EB)] length of each bed [m] XEB [%] SST [%] SBZ [%] STO [%] Pin [bar] Tin [K] Tout [K]
72950 103.18 1.33 36.89 98.49 1.000 0.507 1.25 886 811.36
82020 219.19 1.50 65.78 95.10 1.423 3.480 1.06 898.2 845.71
78330 329.98 1.43 83.76 90.43 1.754 7.809 0.783 897.6 873.6
parameter inner radius of reactor [m] feed molar flow rate [kmol/h] EB ST BZ TO H2O total feed molar flow rate [kmol/h]
value 3.50 707 7.104 0.293 4.968 7777 8496.37
Figure 11. Evolution of effectiveness factors in a three-bed adiabatic axial flow reactor for Tin ) 886, 898, and 897 K; Pin ) 1.25 bar; H2O-to-EB 0 molar ratio ) 11 mol/mol; FEB ) 707 kmol/h.
The comparison of simulated profiles of EB conversion and ST selectivity between the pseudohomogeneous model and the heterogeneous model is plotted against the space time in Figure 10. The EB conversion at the exit of the reactor simulated by means of the heterogeneous model was 83.76%, versus 86.82% for the pseudohomogeneous model, ignoring diffusion limitations. The ST selectivity for the heterogeneous model was 90.43%, versus 91.43% for the pseudohomogeneous model. The
Figure 12. Effect of total pressure on (a) the EB conversion and (b) the ST selectivity in a three-bed adiabatic axial flow reactor using the heterogeneous model for isobaric conditions and for Tin ) 886, 898, and 897 K; H2O-to0 EB molar ratio ) 11 mol/mol; FEB ) 707 kmol/h.
Figure 10. Comparison between profiles predicted by the heterogeneous and the pseudohomogeneous model of (a) the EB conversion and (b) the ST selectivity profiles in a three-bed adiabatic axial flow reactor for Tin ) 886, 898, and 897 K; Pin ) 1.25 bar; H2O-to-EB molar ratio ) 11 mol/ 0 mol; FEB ) 707 kmol/h. Solid line represents the heterogeneous model, dashed line represents the pseudohomogeneous model.
diffusion limitations, expressed in terms of the effectiveness factors (η1, η2, and η3) are shown in Figure 11. At the entrance of the beds, the temperature is high and the intrinsic reaction rate is fast. Accordingly, the effectiveness factors for reactions 1 and 2 (the formation of ST from EB and formation of BZ from EB, respectively) are low, meaning that the process is diffusion-controlled. These effectiveness factors increase along the bed as the intrinsic reaction rates decrease. In contrast, the effectiveness factor for reaction 4 (the formation of TO from ST) is very high at the entrance, because it is a consecutive reaction. Figure 12 considers an isobaric reactor and shows how reducing the pressure from 1.25 to 0.70 bar, while maintaining
9190 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 6. Feed Conditions, Reactor Dimensions, and Simulation Result of a Three-Bed Adiabatic Radial Flow Reactor Using the Heterogeneous Model value parameter
bed 1
bed 2
bed 3
weight of catalyst [kg] space time [kg-cat h/(kmol EB)] catalyst bed depth [m] XEB [%] SST [%] SBZ [%] STO [%] Pin [bar] Tin [K] Tout [K]
72 950 103.18 0.614 36.59 98.43 1.01 0.56 1.25 886 812.04
82 020 219.19 0.708 64.18 93.92 1.53 4.54 1.22 898.2 850.26
78 330 329.98 0.681 81.19 83.24 2.12 14.60 1.21 897.6 890.37
parameter
Figure 13. Simplified radial flow reactor configuration.
a constant steam-to-EB ratio, increases the ST selectivity at the exit from 82.18% to 90.13%. This is a consequence of the shift of the equilibrium conversion to a higher value. 7. Simulation of a Reactor with Radial Flow and Three Adiabatic Beds The pressure drop in a radial flow reactor is much smaller than that in an axial flow reactor, because of the higher crosssectional area of the catalyst bed. It permits one to use smaller particles, which leads to higher effectiveness factors. The differences in the performance of these two types of reactor are discussed below. 7.1. Continuity, Energy, and Momentum Equations. Figure 13 schematically represents a radial flow reactor configuration. Gas flows in a centrifugal direction across the catalyst bed contained in a cylindrical basket. The cross-sectional area of the catalyst bed varies with the radial coordinate r. The continuity equation for the components can be expressed in 0 terms of space time, W/FEB , with W ) πzFB(r2 - r02): dXj d(W ⁄ F0EB)
) ηiRj
inner radius of catalyst bed [m] length of each reactor [m] feed molar flow rate [kmol/h] EB ST BZ TO H2O total feed molar flow rate [kmol/h]
value 1.5 7 707 7.104 0.293 4.968 7777 8496.37
simulations of a radial flow reactor and an axial flow reactor with each of three adiabatic beds, using the heterogeneous model. The operating conditions were identical. In the reactor with radial flow, the EB conversion amounted to 81.19%, compared to 83.76% in the axial flow reactor. The pressure drop in the radial flow reactor, with its large cross-sectional area, was 0.04 bar, whereas the pressure drop amounted to 0.95 bar in the axial flow reactor, as shown in Figure 15. The lower EB
(17)
where Rj is the total rate of reaction of component j. The steady-state energy equation can be written in terms of 0 W/FEB , 6
∑ m˙ c
j pj
j)1
4
∑
dT ) F0EB (-∆Hri)ηiri 0 d(W ⁄ FEB) i)1
(18)
and the momentum equation is given as F0EBFgus2 ) fR 2πzrFBdp d(W ⁄ F0EB) dPt
(19)
The continuity, energy, and momentum equations (eqs 17, 18, and 19, respectively) must be integrated simultaneously. For the radial flow reactor, the cross section of the catalyst bed is dependent on the space time, i.e., radial position, so that the superficial velocity (us) must be adapted in each integration step through the reactor. 7.2. Results and Discussion. The feed conditions and reactor dimensions are shown in Table 6. The length of each reactor and the inner radius of the catalyst bed were assumed to be 7 and 1.5 m, respectively. Table 6 and Figures 14 and 15 compare
Figure 14. Comparison of simulated (a) EB conversion profiles and (b) ST selectivity profiles using the heterogeneous model between a three-bed adiabatic radial flow reactor and a three-bed adiabatic axial flow reactor for Tin ) 886, 898, and 897 K; Pin ) 1.25 bar; H2O-to-EB molar ratio ) 0 11 mol/mol; FEB ) 707 kmol/h.
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9191
Figure 15. Comparison of simulated (a) temperature profiles and (b) pressure drop profiles using the heterogeneous model between a three-bed adiabatic radial flow reactor and a three-bed adiabatic axial flow reactor for Tin ) 886, 898, and 897 K; Pin ) 1.25 bar; H2O-to-EB molar ratio ) 11 mol/ 0 mol; FEB ) 707 kmol/h.
conversion in the radial flow reactor is caused by the lower pressure drop, meaning that the conversion essentially occurs close to the feed pressure. In the axial flow reactor, a substantial fraction of the conversion occurs at lower pressures. The ST selectivity, which is strongly dependent on the pressure, as previously evidenced by Figure 12, was 83.24% for radial flow, versus 90.43% for axial flow. The difference in the TO selectivity (14.60% vs 7.89%) was substantial, but the difference in the BZ selectivity (2.12% vs 1.75%) was insignificant. These results might lead to the conclusion that the radial flow reactor is less favorable than the axial flow version; however, Figure 16 reveals the advantage of the radial flow reactor, which permits operation at much lower feed pressures. At Pin ) 0.70 bar, which is a low value that cannot be used in the axial flow reactor, the ST selectivity amounted to 91.32%, compared to 83.24% at 1.25 bar for essentially the same EB conversion. This result is quite similar to that derived from the simulation of the axial flow reactor for the isobaric condition shown in Figure 12. 8. Simulation of a Radial Flow Reactor with Three Adiabatic Beds Accounting for Coke Formation and Gasification Coke formed on the potassium-promoted iron oxide catalysts is at least partially removed by gasification with steam.2 Previous kinetic investigations have ignored coke formation and coke gasification; however, more recently, Devoldere and Froment13 developed detailed kinetic models for these reactions. The model
Figure 16. Effect of feed pressure on simulated (a) EB conversion and (b) ST selectivity in a three-bed adiabatic radial flow reactor Tin ) 886, 898, 0 and 897 K; H2O-to-EB molar ratio ) 11 mol/mol; FEB ) 707 kmol/h.
Figure 17. Effect of H2O-to-EB molar feed ratio on dynamic equilibrium coke content profiles in a three-bed adiabatic radial flow reactor for Tin ) 0 886, 898, and 897 K; Pin ) 1.25 bar; FEB ) 707 kmol/h.
for the coke formation was based on a two-step mechanism: coke precursor formation and coke growth.39 Coke gasification was assumed to occur at the edges of the carbon, which were oxidized by water.40 The effect of the operating conditions (particularly the steam-to-EB feed ratio) on the dynamic equilibrium coke content along the three-bed adiabatic reactor and the effect of coke formation on the reactor performance are discussed below. 8.1. Model Equations. 8.1.1. Rate Equation for the Formation of Coke Precursor. The formation of an irreversibly adsorbed coke precursor from EB and ST, both adsorbed up to equilibrium with the gas phase, is assumed to be the ratedetermining step.27
9192 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
rs )
dCCP ) δrs0ΦCp ) dt kEB,pKEBPEB + kST,pKSTPST × (1 - RpCCP)ns(20) δ (1 + KEBPEB + KSTPST)ns
The values of δ, ns, Rs, kEB,p, and kST,p were estimated by Devoldere and Froment.13,41These values were obtained on a catalyst that was not the same as that used in the work reported here. Nevertheless, their insertion in the present model leads to useful insight and reliable trends. 8.1.2. Rate Equation for Coke Growth. Further dehydrogenation of the coke precursor forms the sites on which the coke accumulates. The intrinsic rate of coke growth can be expressed as the product of three factors: the intrinsic rate of coke growth per active site, the total number of active sites on the growing coke, and a deactivation function: 0 CtgrΦgr rgr ) rgr
dCgr ) dt kEB,grPEBnEB + kST,grPSTnST
(1 + KH OPH O ⁄ PH 2
2
2
+ KH2√PH2
{(
W ⁄ F0EB
d(
)
) η1rc1 + η2rc2 + η3rc3 + (rt1 + rt2 + rt3)
dXST
) η1rc1 - η4rc4 + rt1
W ⁄ F0EB
d(
)
dXBZ W ⁄ F0EB
d( dXH2 d(
)
)
n3
)
PH2
1 - RgrCgr)ngr(22)
n2 (
k2PH2O
1 + K3√PH2 [(PH2 ⁄ K1) + (k2 ⁄ k1)] + PH2O
)
}
CtG (23)
The parameter values in eq 23 were also obtained from the work of Devoldere and Froment.13,41 8.1.4. Coke Formation and Gasification: Dynamic Equilibrium Coke Content. The EB conversions in the main reactions decrease until the coke content of the catalyst reaches a steady state. The stabilization process is very fast, so that the deactivation of the catalyst is limited to a very early stage of the operation. After it is reached, the coke content, which is called the dynamic equilibrium coke content and is dependent only on the temperature and the compositions, remains constant.13 No deactivation effect is observed from then onward. At dynamic equilibrium, the rate of formation of coke precursor and the rate of coke growth are compensated by the gasification, so that the dynamic equilibrium coke content can be obtained from dCCP ) δrs0ΦCP - rG ) 0 dt
(24a)
dCgr 0 ) rgr CtgrΦgr - rG ) 0 dt
(24b)
These equations also express that coke formation, like any catalytic reaction, is subject to deactivation, but gasification is not.
B rc(ST) FB 8
) η2rc2 + rt2
B FB
) η1rc1 - η3rc3 - 2η4rc4 + (rt1 - rt2)
(
21 Ccn1
B rc(EB) + FB 8 (25a)
W ⁄ F0EB
The values of nEB, nST, n1, n2, n3, ngr, Rgr, kEB,gr, and kST,gr were estimated by Devoldere and Froment13,41 and are used in the present work. The intrinsic rate of coke formation, accounting for the coke precursor formation and coke growth, can be expressed as the summation of eqs 20 and 22. 8.1.3. Rate Equation for Coke Gasification. The rate equation for coke gasification was developed under the assumption that the rate-determining step is the irreversible decomposition of an oxidized carbon complex to CO and free carbon.13 Using the pseudo-steady-state approximation for the surface intermediates, the rate of coke gasification is given by rG )
dXEB
(21)
The model for the rate of coke growth is rgr )
The kinetic model for coke formation and gasification was coupled to the kinetic model for the main reactions in the simulations of a three-bed adiabatic reactor with radial flow, using the heterogeneous model. Equations 25a-d show the continuity equations for the components, accounting for the coke formation from both EB and ST.
(25b)
(25c) B + FB
) (
)
rc(EB) rc(ST) + 20 (25d) 8 8
where rc(EB) represents the rate of coke formation from ethylbenzene and rc(ST) represents that from styrene. The energy equation is written 6
{ [ ( )] ( )] [ ( )]
B dT ) F0EB -∆Hr1 η1rc1 + rt1 0 F d(W ⁄ FEB) B j)1 B B - ∆Hr3 η3rc3 + rt3 - ∆Hr4η4rc4 ∆Hr2 η2rc2 + rt2 FB FB rc(ST) rc(EB) - ∆HC,ST (26) ∆HC,EB 8 8
∑mc ˙
j pj
[
(
)
(
)}
and the momentum equation is unchanged, with respect to eq 19. The set of continuity, energy, and momentum equationsseqs 25, 26, and 19swas integrated simultaneously along the reactor. 8.2. Results and Discussion. Figure 17 shows the effect of the H2O-to-EB molar ratio on the dynamic equilibrium coke content in a three-bed adiabatic reactor with radial flow. The dynamic equilibrium coke content was low at high H2O-to-EB feed ratios. A high steam-to-EB ratio is not always preferred in industrial operation, because of the cost of steam generation. At this point, optimization is required to obtain the optimum steam-to-EB feed ratio, also accounting for the lifetime of the catalyst. Figure 18 shows the effect of coke formation on the simulated EB conversion and ST selectivity in a three-bed adiabatic reactor with radial flow. Accounting for coke formation from EB and ST leads to a drastic decrease in the ST selectivity but, because of the influence of the equilibrium, a slight increase in the EB conversion. 9. Conclusion The extensive set of experimental data obtained on a commercial catalyst in the experimental part of the work reported here provides a comprehensive basis for a more accurate evaluation of the effect of the various operating parameters on the selectivity of styrene production from ethylbenzene. The detailed and rigorous kinetic model that has been derived from the experimental database also accounted for the background thermal cracking, which strongly increases with tem-
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9193
Figure 18. Effect of coke formation on (a) EB conversion and (b) ST selectivity in a three-bed adiabatic radial flow reactor for Tin ) 886, 898, and 897 K; H2O-to-EB molar ratio ) 11 mol/mol; F0EB ) 707 kmol/h. Solid lines represent the results accounting for the coke formation from ethylbenzene and styrene; dashed lines represent results neglecting this effect.
perature. The optimal operation of today’s large plants also must consider the latter aspect: the kinetic study aimed at deriving intrinsic rate equations. The diffusion limitations encountered with the catalyst particle sizes used in industrial reactors are introduced through the modeling. The catalytic and thermal kinetic models were applied in simulations of the operation of multibed adiabatic commercial configurations with axial or radial flow that also included diffusion limitations and coke deposition and gasification. Therefore, it becomes possible to investigate, under realistic conditions, the complex influence of the various operating variables, in particular, the operating pressure and the steam-to-ethylbenzene ratio, which is an important factor in the economics of the process. Nomenclature Ai ) pre-exponential factor of catalytic reaction i, kmol/(kg-cat h) Aj ) pre-exponential factor for adsorption of species j, bar-1 Ati ) pre-exponential factor of thermal reaction i, kmol/(mf3 h bar) CCP ) coke precursor content, kg coke/kg-cat Cl ) molar concentration of vacant active sites l of catalyst, kmol/ kg-cat Cp ) specific heat of fluid, kJ/(kg K) De,j ) effective diffusivity of component j, mf3/(mr s) dp ) catalyst equivalent pellet diameter, mp Ei ) activation energy of catalytic reaction i, kJ/mol Eti ) activation energy of thermal reaction i, kJ/mol Fj ) molar flow rate of j, kmol/h Fjo ) feed molar flow rate of j, kmol/h f ) friction factor in momentum equation
G ) superficial mass flow velocity, kg/(mr2 h) -∆Ha,j ) adsorption enthalpy of adsorbed component j, kJ/mol -∆Hr ) heat of reaction, kJ/mol Kj ) adsorption equilibrium constant of component j, bar-1 Keq ) equilibrium constant, bar ki ) rate coefficient of catalytic reaction i, kmol/(kg-cat h) kti ) rate coefficient of thermal reaction i, kmol/(mf3 h bar) l ) vacant active site on the catalyst m ˙ j ) mass flow rate of component j, kg/h Pj ) partial pressures of component j in bulk fluid, bar Ps,j ) partial pressure of component j inside the catalyst, bar Pt ) total pressure, bar R ) radius of catalyst particle, mp Rj ) total rate of reaction of the component j, kmol/(kg-cat h) Re ) Reynolds number based on particle diameter; Re ) dpusFg/µ r ) radial coodinate of reactor, mr ro ) inner radius of catalyst bed in a radial reactor, mr rc ) rate of coke formation, kg coke/(kg-cat h) rci ) rate of catalytic reaction i, kmol/(kg-cat h) rG ) rate of coke gasification, kg coke/(kg-cat h) rgr ) rate of coke growth, kg coke/(kg-cat h) 0 rgr ) initial rate of coke growth per active center, kg coke/(kg mol h) rs ) rate of site coverage, kg coke/(kg-cat h) rs0 ) initial rate of site coverage, kg coke/(kmol h) rti ) rate of thermal reaction i, kmol/(mf3 h) S(β) ) objective function 0 -∆Sa,j ) standard entropy of adsorption of component j, J/(mol K) Sg0 ) standard entropy of the gas, J/(mol K) Sa0 ) standard entropy of the adsorbed molecule, J/(mol K) T ) temperature, K Tr ) average temperature, K us ) superficial velocity, mf3/(mr2 s) V ) catalyst pellet volume, mp3 W ) weight of catalyst, kg-cat XEB ) conversion of ethylbenzene Xj ) conversion of ethylbenzene into component j Z ) length of radial flow reactor, mr Greek Letters R ) conversion factor in momentum equation β ) model parameter δ ) conversion factor in the rate of coke site coverage, kmol/kgcat B ) void fraction of bed, mf3/mr3 s ) catalyst internal void fraction, mf3/mp3 ΦCP ) deactivation function for coke precursor Φgr ) deactivation function for coke growth η ) effectiveness factor FB ) bulk density of bed, kg-cat/mr3 Fg ) gas density, kg/mf3 Fs ) catalyst pellet density, kg-cat/mp3 Ω ) cross section of reactor, mr2
Acknowledgment The authors are grateful to Dr. R. G. Anthony, Artie McFerrin Department of Chemical Engineering, Texas A&M, for support and stimulating discussions. Literature Cited (1) Product Focus: Styrene. Chem. Week 2002, (May 15), 36.
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ReceiVed for reView August 8, 2007 ReVised manuscript receiVed December 12, 2007 Accepted December 14, 2007 IE071098U
