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Ind. Eng. Chem. Res. 1999, 38, 2626-2633
Coke Formation and Gasification in the Catalytic Dehydrogenation of Ethylbenzene Kris R. Devoldere† and Gilbert F. Froment* Laboratorium voor Petrochemische Techniek, Universiteit Gent, Krijgslaan 281, B-9000 Gent, Belgium
A detailed kinetic model for coke formation and gasification on an industrial potassium-promoted iron oxide catalyst during ethylbenzene dehydrogenation is developed. The kinetic parameters are estimated from a set of transient experiments in an electrobalance reactor, operated under differential conditions. The gasification was found to proceed through an edge recession mechanism. The coke formation occurs as a sequence of precursor formation followed by growth. The coupling of this coke formation/gasification model with a detailed model for the main and the side reactions allows an accurate prediction of the amount of CO2 formed in a multibed pilot-plant unit. The model is used to evaluate some recently proposed modifications to the process operation. Introduction The annual production of the styrene monomer exceeds 17 × 106 metric tons. More than 70% is produced by catalytic dehydrogenation of ethylbenzene in the presence of an excess amount of diluent steam over a potassium-promoted iron oxide catalyst in multibed adiabatic units. The production capacity of a single unit can easily exceed 500 000 metric tons/year, which explains the large interest in the development of reliable kinetic models for process simulation and optimization (Carra and Forni, 1965; Lebedev et al., 1978; Liu et al., 1983; Hirano, 1986). These models aim at the prediction of the global conversion and of the styrene selectivity and include the formation of the side products benzene and toluene. Two reactions that have been disregarded so far in the kinetic models are the formation of carbonaceous deposits on the catalyst surface and their subsequent gasification by the diluent steam, leading to the production of small amounts of CO2. The effect of these reactions on the overall conversion and selectivity is twofold. First, ethylbenzene and styrene are irreversibly converted into coke and/or CO2, which represents a loss in selectivity. Second, the presence of CO2 in the reactant mixture strongly affects the catalyst activity (Hirano, 1986; Muhler et al., 1990; Taguchi et al., 1994). Only Grootjans and Schockaert (1992) have accounted for the loss of valuable aromatics using an empirical overall reaction for the formation of CO2 from styrene, which was coupled with the kinetic model of Liu et al. (1983). The influence of the CO2 produced on the catalyst activity and selectivity was not accounted for. The present paper deals with a mechanistic model for the formation and gasification of carbonaceous deposits on an industrial potassium-promoted iron oxide catalyst during the dehydrogenation of ethylbenzene to styrene. The coke formation consists of a precursor formation step, followed by coke growth. The kinetic model for the * Author to whom correspondence should be addressed. Current address: Department of Chemical Engineering, Texas A&M University, College Station, TX 77843-3122. † Current address: VITO (Vlaamse Instelling voor Technologisch Onderzoek), Boeretang 200, B-2400 Mol, Belgium.
gasification is based on an edge recession mechanism. The interaction between coke formation and gasification leads to a dynamic equilibrium coke content on the catalyst. The models, which were validated against a set of pilot-plant data, will be used to evaluate the soundness of some recently proposed modifications in the process operation. Experimental Section The experiments were conducted under differential conditions in an electrobalance reactor. The basket, containing 50 mg of crushed catalyst (L: 0.25-0.40 mm), was suspended in an empty tubular reactor from one arm of a Sartorius 4438 MP8-1 electrobalance. The reactor was heated by means of two infrared heating panels. A thermocouple located just underneath the catalyst basket measured the reactor temperature. The gaseous feed components (N2 as a diluent and as an internal standard for the GC analysis and H2) were fed by means of Matheson thermal mass flow controllers. The liquid components (water and ethylbenzene/styrene mixtures of various composition) were pumped from reservoirs placed on high-precision balances (Sartorius Electronic Toploader 1574 MP 8) using HPLC pumps (Pharmacia High-Precision Pump P-500). The water was evaporated and mixed with the preheated gaseous feed, and the mixture was sent to a second evaporator, where it was mixed with the aromatic feed components. The effluent of the second evaporator is fed at the bottom of the tubular reactor. The bottom section of the reactor was filled with inert Al2O3 beads, serving two purposes: the uniform distribution of the feed over the cross section of the tube and the reduction of the empty volume of the reactor. The gases passed through the catalyst in the basket, reacted, and left the reactor at the top. In order to prevent the exit stream from entering the balance chamber, the latter was kept under a slight overpressure by means of a helium sweep stream. The major part of the gases leaving the reactor was sent to a condenser for separation of the condensables. The other part was sent to a Packard 438A gas chromatograph for on-line analysis. The GC used H2 as a carrier gas and was equipped with two packed col-
10.1021/ie980169+ CCC: $18.00 © 1999 American Chemical Society Published on Web 05/29/1999
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2627
umns: a Porapack Q column (separation of N2, H2O, CO, CO2, CH4, and C2H4) and a 5% AT-1200 + 1.75% Bentone 34 on Chromosorb W-AW column for separation of the aromatic compounds. The detection of the eluting compounds was performed by two detectors in series: a thermal conductivity detector (TCD) followed by a flame ionization detector (FID). N2 was used as an internal standard for the TCD chromatogram. Because the FID is highly sensitive to hydrocarbons, the composition of the hydrocarbon fraction of the effluent was calculated from the FID chromatogram using ethylbenzene as a secondary standard. Before each coke formation experiment, the fresh catalyst was pretreated in a mixture of ethylbenzene and steam (steam/ethylbenzene ) 12 mol/mol) for 1 h at 600 °C. By this pretreatment the catalyst was activated and brought into the correct oxidation state. Data Treatment The determination of the intrinsic rate of coke formation from the experimentally measured curves of the catalyst coke content as a function of the run length was no straightforward matter. The coking experiments were conducted within a range of operating conditions favoring coking (reduced steam to hydrocarbon ratios). To obtain kinetic parameters that are relevant for industrial operation, it is imperative that the oxidation state of the catalyst is identical. The presence of an excess amount of steam diluent under industrial conditions prevents the reduction of the bulk iron oxide phase beyond magnetite (Fe3O4). If all of the steam diluent were to be replaced by an inert during the coking experiments, the reduction of the bulk iron oxide phase to metallic iron by the hydrogen formed could not have been avoided. Besides, there exist strong indications in the literature that the active phase of the catalyst, which most likely consists of potassium ferrite (K2Fe2O4), is subject to a cycle of continuous formation and deterioration under the influence of respectively the steam and the hydrogen present in the reaction mixture (Andrushkevich et al., 1978; Molchanov et al., 1988; Hirano, 1986; Muhler et al., 1990). Therefore, the steam diluent was not completely omitted but only reduced to 1-3 mol of H2O/mol of aromatics (compared to 10-12 mol/mol for industrial operation) during the coke formation experiments. The presence of steam in the reaction mixture leads to a continuous gasification of the deposited coke so that the experimentally measured rate of coke formation is a net rate resulting from both deposition and gasification. During the kinetic modeling of the coke formation, the gasification has to be accounted for. So, the kinetics of the gasification had to be determined before those of the coke formation. The composition of the gas phase surrounding the catalyst basket during the coke formation was not identical to the feed composition at the reactor inlet, due to a certain amount of thermal cracking. The amount of thermal cracking is minimized by short residence times and, therefore, high feed rates. These are also required to ensure the differential operation during the coke formation experiment by keeping the space time low. The presence of inert alumina beads in the bottom section of the reactor reduces the void fraction and the residence time in this section by 50%. The effect of the thermal cracking reactions in the bottom section of the tubular reactor on the gas-phase composition was calculated using the equivalent reactor
Figure 1. Experimental (points) and calculated (line) evolution of the catalyst coke content during the gasification. Operating conditions: T ) 874 K; PH2O ) 0.072 atm.
volume concept developed by Hougen and Watson (1947) and further applied by Buekens and Froment (1968, 1971) and Van Damme et al. (1975). The equivalent reactor volume of the entire tubular reactor was estimated from a series of blank experiments at different temperatures. The equivalent reactor pressure was taken to be the reactor pressure. The equivalent reactor temperature was the temperature measured right underneath the catalyst basket. A molecular model for the thermal cracking of ethylbenzene, valid over the range of operating conditions for an industrial dehydrogenation unit, was derived from the fundamental radical reaction scheme of Qi and Froment (1990). Because of the geometry of the tubular reactor, accounting for the presence of the inert Al2O3, and the almost symmetrical axial temperature profile in the reactor relative to the position of the catalyst basket, the partition of the equivalent reactor volume between the bottom and top sections can be taken to be equal to the geometrical partition of both sections. The gas-phase composition of the gas surrounding the basket was then calculated for each coke formation experiment from the feed composition and the equivalent reactor volume of the bottom section using the molecular model for the thermal cracking of ethylbenzene. Results An experimentally observed curve of the catalyst coke content as a function of the run length during a gasification experiment is shown in Figure 1. Two zones can be distinguished: a zone of constant gasification rate, showing a linear decrease of the catalyst coke content with run length, followed by a zone of decreasing gasification rate for the lowest catalyst coke contents. A total of 24 coke content versus run length curves were used to discriminate between the rival gasification models and to estimate the values of the kinetic constants in the rate equation for the gasification. The range of operating conditions used in the gasification experiments is given in Table 1. The rate of gasification increases with increasing steam partial pressure and temperature, while an increase in the hydrogen partial pressure significantly decreases the gasification rate. The rival models for the gasification are, listed in Table 2. The first two rate expressions in this table (G I and G II) are based upon the reaction scheme proposed by Ergun (1962). The first step in the gasification mechanism consists of the oxidation of a carbon
2628 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 Table 1. Range of Operating Conditions Covered by the Gasification and Coke Formation Experiments gasification temperature (K) P0Aro (atm) ST/EB (mol/mol) 0 PH O (atm) 02 PH (atm) 2
coke formation
853-918
853-918 0.060-0.155 0.000-1.425 0.030-0.250 0.000-0.090
0.030-0.250 0.000-0.090
Table 2. Rival Models for the Gasification Reaction
rG )
rG )
rG )
rG )
k2 C 1 + KH2OPH2/PH2O tG
(G I)
k1PH2O
C 1 + k-1/k2PH2 + k1/k2PH2O tG k1PH2O 1 + k1/k2PH2O + KH2xPH2
(G II)
(G III)
CtG
k2PH2O
CtG (1 + KH2xPH2)(PH2/KH2O + k2/k2) + PH2O
(G IV)
atom with a free sp2 orbital (Cf) and is considered to be in equilibrium k1
H2O + Cf y\ z Cf(O) + H2 k -1
KH2O ) k1/k-1
In the following step, the oxidized surface complex decomposes irreversibly through the release of CO and the regeneration of a carbon atom with a free sp2 orbital: k2
Cf(O) 98 CO + Cf Model G I is based on the assumption that the decomposition of the surface complex is the rate-determining step, while model G II is based on the pseudo-steadystate hypothesis for all surface intermediates. Giberson and Walker (1966) attributed the sharp decrease in the gasification rate upon the introduction of hydrogen to a competitive dissociative adsorption of the latter on the active centers: 1
k3
/2H2 + Cf y\ z Cf(H) k -3
KH2 ) k3/k-3
These authors assumed the formation of the oxidized surface intermediates to be irreversible and arrived at model G III by applying the pseudo-steady-state hypothesis for all surface intermediates. Hu¨ttinger and Lietzke (1989a,b) derived a general reaction scheme for the gasification which contains all possible interactions between carbon, steam, and hydrogen with the formation of CO, CO2, and methane. Under the operating conditions relevant for ethylbenzene dehydrogenation, the direct formation of CO2, the gasification by hydrogen, and the molecular adsorption of hydrogen can be neglected. The complete reaction scheme thus reduces to the scheme proposed by Ergun (1962), extended with the competitive dissociative adsorption of hydrogen, as proposed by Giberson and Walker (1962). The pseudo-steady-state hypothesis for all surface intermediates yields model G IV in Table 2. All rate equations in Table 2 still contain the number of active sites for the gasification, CtG. Under steadystate conditions, the number of active sites is invariant
Figure 2. Experimental (points) and calculated (line) evolution of the catalyst coke content during the coke formation. Operating conditions: T ) 873 K; PEB ) 0.059 atm; PST ) 0.0005 atm; PH2O ) 0.035 atm; PH2 ) 0.0005 atm. Table 3. Residual Sum of Squares (RSSQ), Degrees of Freedom (DF), and Calculated F Values Relative to the Best Model for the Four Rival Gasification Models (F0.95: Tabulated F Value) (G I) (G II) (G III) (G IV)
RSSQ
DF
Fcalc
6.9941 × 10-9 2.8990 × 10-4 1.1250 × 10-3 2.6479 × 10-4
459 457 457 455
2.6184 1.0900 42.301 1
F0.95(459,455) ) 1.0850 F0.95(457,455) ) 1.0853
and is normally incorporated into the rate constant. Because the current model is based on transient experimental data, this procedure would result in an equation incapable of predicting the experimentally observed decrease of the rate of gasification at low coke contents. This decrease is mainly due to gasification occurring at the edges of the carbon (see the Discussion section). At very low coke contents, the number of edge carbon atoms sharply decreases. The dependency of the number of active sites for gasification on the catalyst coke content is introduced through the semiempirical relationship
CtG ) CCnG in which the value of nG is estimated together with the values of the kinetic and adsorption constants. The optimum parameter values were determined by the minimization of the sum of squares using a Levenberg-Marquardt technique. The residual sum of squares (RSSQ) and the degrees of freedom (DF) for each rival model are shown in Table 3. Because all of the parameter values in the models were found to be statistically significant at the 95% confidence level and satisfied the physicochemical constraints (Boudart et al., 1967), the model discrimination was based on the F test. Confrontation of the calculated F values, using the model with the lowest residual sum of squares as a reference, with the tabulated F values at the 95% confidence level indicates that models G I, G II, and G III show a statistically significant inferior agreement with the experimental data than the reference model G IV (Table 3). The excellent agreement between the predictions with model G IV and the experimental data is shown in Figure 1. Figure 2 shows an example of the evolution of the catalyst coke content with the run length. The evolution
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2629 Table 4. Deactivation Functions Considered for the Models of the First Type (Φ ) ΦC; r ) rC) and for the Coke Growth (Φ ) Φgr; r ) rgr) Φ ) exp(-RCC) Φ ) (1 - RCC)n Φ ) 1/(1 + RCC) Φ ) 1/(1 + RCC)2
Figure 3. Experimental evolution of the net rate of coke formation as a function of the catalyst coke content for the experiment shown in Figure 2.
of the net rate of coke formation as a function of the catalyst coke content is shown in Figure 3 for the same experiment. As can be seen from Figure 3, the net rate of coke formation changes in a nonmonotonical way with the catalyst coke content. For sufficiently large coke contents, the net rate of coke formation reaches a value of zero, indicating a dynamic equilibrium between the coke formation and the gasification. Within the range of operating conditions (Table 1), the net rate of coke formation increased with increasing aromatics partial pressure and temperature. An increase of the styrene content of the feed sharply increased the net rate of coke formation. Increasing the hydrogen partial pressure results in a drastic decrease of the net rate of coke formation. The kinetic modeling of the intrinsic rate of coke formation is accomplished along the approach of Froment (1982, 1984, 1991). In a first series of rival models, the intrinsic rate of coke formation at a given coke content is obtained as the product of the initial intrinsic rate of coke formation, r0C(pj,T), reflecting the influence of the operating conditions, and a deactivation function for the coke formation, ΦC(CC), which is a function of the catalyst coke content only:
rC(pj,T,CC) ) r0C(pj,T) ΦC(CC) This type of model can only predict a monotonically decreasing intrinsic rate of coke formation with increasing coke content of the catalyst. Therefore, the approach of De Pauw (1975), Beeckman and Froment (1979, 1980), Marin et al. (1986), and Beyne and Froment (1990, 1993), considering the coke formation as a twostep mechanism of coke precursor formation followed by growth, has been adopted. The intrinsic rate of coke precursor formation is obtained as the product of an initial rate of precursor formation (initial rate of site coverage), r0s (pj,T), reflecting the influence of the operating conditions, and a deactivation function for the precursor formation, ΦCp(Cp). Because in this phase only coverage of active sites is involved, this deactivation function can only be of the linear type, where ns represents the number of active sites deactivated by the formation of the coke precursor:
rs(pj,T,Cp) ) δr0s (pj,T) (1 - RpCp)ns The coke precursor dehydrogenates further, and sites
active for coke growth are formed. Upon further coke growth, the sites active for coke growth become covered with coke. Therefore, the intrinsic rate of coke growth is obtained as the product of three contributions: the intrinsic rate of coke growth for an active center, r0gr(pj,T), reflecting the influence of the operating conditions; the total number of active sites on the growing coke, Ctgr; and a deactivation function for the coke growth, Φgr(Cgr), which only depends on the amount of coke formed in the growth phase:
rgr(pj,T,Cgr) ) r0gr(pj,T) CtgrΦgr(Cgr) Because the sites active for coke growth are formed by dehydrogenation of the precursor, the total number of active sites on the growing coke can be obtained by considering the equilibrium of the global reaction
CC h CC(2n2l) + n2H2 where l represents a site active for coke growth. This yields the following expression for the total number of sites on the coke that are active for coke growth:
Ctgr ) CCn1/PH2n2 Only a fraction of the active centers on the coke are accessible from the gas phase, and this is accounted for by the exponent n1. Four possible expressions were considered for the deactivation function in the models of the first type and for the deactivation function for coke growth (Table 4), leading to eight rival models for the coke formation. The parameters in the intrinsic coke formation models are estimated from the confrontation with the experimentally measured data of the catalyst coke content as a function of the run length. Because the cumulative catalyst coke content is the result of a varying net rate of coke formation over the run length, the intrinsic rate of coke formation and the gasification rate have to be considered simultaneously. For the models of the first series (CF I to CF IV), this requires the integration of the following differential equation:
dCC ) r0C(pj,T) ΦC(CC) - rG(pj,T,CC) dt For the models considering a precursor formation/ growth sequence (CF V to CF VIII), the following differential equation needs to be integrated:
dCC ) δr0s (pj,T)(1 - RsCp)ns + dt CCn1 r0gr(pj,T) ΦCgr(Cgr) - rG(pj,T,CC) PH2n2 The electrobalance was operated under differential conditions and the reactor temperature and feed composition were kept rigorously constant during each
2630 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 Table 5. Model Discrimination between the Eight Rival Models for the Intrinsic Rate of Coke Formation without Expressing the Dependence of the Initial Rates on the Operating Conditions: Residual Sum of Squares (RSSQ), Degrees of Freedom (DF), and Calculated F Values Relative to the Best Model for the Eight Rival Coking Models (F0.95: Tabulated F Value) CF I CF II CF III CF IV CF V CF VI CF VII CF VIII
RSSQ
DF
Fca1c
0. 0440 0.0446 0.0483 0.0497 0.0211 0.0168 0.0188 0.0185
1244 1243 1244 1244 1214 1213 1214 1214
2.5538 2.5886 2.8034 2.8846 1.2549 1 1.1181 1.1003
F0.95(1244,1213) ) 1.0453 F0.95(1214,1213) ) 1.0458
experiment. As a result, the initial rate of coke formation (r0C) in models CF I to CF IV and the initial rate of site coverage (r0s ) and the intrinsic rate of coke growth on an active center (r0gr) in models CF V to CF VIII do not vary with the run length of the experiment and can be determined for each experiment separately. These rates can be expressed as a function of the operating conditions afterward. A total of 26 coke content versus run length curves are available for the estimation of the kinetic parameters in the coking model. This means that 27 parameters (26 r0C and RC) need to be estimated for the models CF I to CF IV and 57 parameters (26 r0s , 26 r0p, Rs, ns, n1, n2, and Rp) for the models CF V to CF VIII. From the confrontation of the calculated F values, using the model with the lowest residual sum of squares as a reference, with the tabulated F values at the 95% confidence level, only one model, CF VI, could be withheld for the intrinsic rate of coke formation (Table 5). A model discrimination, also based on the F test, between four rival models for the initial rate of site coverage (r0s ) and eight rival models for the rate of coke growth for an active center (r0gr) finally yielded the following model for the intrinsic rate of coke formation:
dCC (kEB)s(KEB)sPEB + (kST)s(KST)sPST (1 )δ dt (1 + (K ) P + (K ) P )ns EB s EB
RsCp)ns +
ST s ST
(kEB)grPEBnEB + (kST)grPSTnST
CCn1
n (1 + KH2OPH2O/PH2 + KH2xPH2)n3 PH2 2
(1 -
RgrCgr)ngr
From the confrontation of this modelwith the 26 experimental curves of catalyst coke content versus run length, it followed that a number of exponents in this model could be given fixed values without affecting the fit, as can be seen from Table 6. The accuracy of the model is illustrated in Figures 2 and 4. Discussion Before the parameter values obtained for the coke formation and gasification reaction are discussed, it is useful to discuss more in detail the mechanism of the alkali-catalyzed gasification. It is but until recently that a somewhat consistent mechanism for the (un)catalyzed gasification emerged out of the wide variety of data that
Figure 4. Experimental (points) and calculated (line) evolution of the catalyst coke content during the coke formation. Operating conditions: T ) 904 K; PEB ) 0.093 atm; PST ) 0.0038 atm; PH2O ) 0.112 atm; PH2 ) 0.0130 atm. Table 6. Optimum Value and Approximate 95% Confidence Intervals for Some of the Semiempirical Parameters in the Model for the Intrinsic Rate of Coke Formation, together with the Fixed Value of the Semiempirical Parameter
ns nEB nST ngr n1 n2 n3
lower limit
optimum value
upper limit
6.9406 × 10-1 8.9947 × 10-1 1.9955 1.4946 × 10-1 6.2052 × 10-1 5.2751 × 10-1 3.2648 × 10-1
1.0084 9.6253 × 10-1 2. 1476 1.1233 6.7965 × 10-1 5.4496 × 10-1 3.3635 × 10-1
1.3228 1.0256 2.2997 2.0972 7.3878 × 10-1 5.6240 × 10-1 3.4623 × 10-1
selected value 1 1 2 1 2/
3
1/
2
1/
3
have been published in the literature. The oxidized surface intermediates for both the alkali-catalyzed and the uncatalyzed gasification were shown to be identical by means of spectroscopic and methylation/13C NMR experiments (Freriks et al., 1981; Mims and Pabst, 1983). Semichinon and carbonyl structures at the edges of the carbon substrates have been proposed as active surface intermediates. In the case of the alkali-catalyzed gasification species like CdO-K+ or CdOsK would be formed. The activation energy of the gasification was found to be identical for both the alkali-catalyzed and the uncatalyzed gasification, indicating an identical rate-determining step for both reactions (Kelemen and Freund, 1986; Moulijn and Kapteijn, 1986; Cerfontain et al., 1987; Chen and Yang, 1993). CAEM experiments pointed out that the gasification starts at the edges of the carbon substrate (Mims et al., 1984). By means of molecular orbital calculations, Chen et al. (1993) and Chen and Yang (1993) attribute the promoting effect of the alkali catalyst to two phenomena: a substantial weakening of the C-C bonds at the edge of the carbonaceous deposits and an increase of the rate of dissociative adsorption of CO2 and H2O, generating a flux of active oxygen atoms to the active centers. The value for the exponent nG, expressing the relationship between the total number of active sites for gasification and the catalyst coke content, was found to be close to 1/3. This corresponds to a perimeter to volume ratio, justifying the edge-regression mechanism adopted for the alkali-catalyzed gasification. Moreover, 1/ is obtained independently as the exponent for the 3 adsorption group in the expression for the coke growth rate (n3 in Table 6). Indeed, according to the gasification mechanism, only active centers on the edges of the
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2631
growing coke can be occupied by oxygen or hydrogen. The values of the adsorption constants for steam and hydrogen in the expression for coke growth are taken from the gasification model. The exponent n1, expressing the relationship between the number of active sites on the growing coke and the catalyst coke content, has a value of 2/3. This corresponds to a surface to volume ratio, indicating that only centers at the surface of the growing coke are accessible for the gas-phase molecules. The exponents of the partial pressures of ethylbenzene and styrene in the rate expression for the coke growth can be confronted with the mechanism derived by Dumez and Froment (1976). These authors considered the coke formation as a conversion of lower (Il) into higher (Ih) intermediates by dehydrogenation and/or addition of molecules from the gas phase:
Ill + (nA)l f Ihl + (1 - n)H2l A higher intermediate has a lower H/C ratio than a lower intermediate. The parameter n expresses the contribution of the addition reactions, while 1 - n is the contribution of the dehydrogenation/dehydrocyclization to the coke formation. This mechanism yields the following rate expression for coke formation out of A:
rC ) k′APAn+1/N2 The exponents of the partial pressures of ethylbenzene and styrene in the rate expression for coke growth indicate that dehydrogenation/dehydrocyclization is the rate-determining step for the coke growth from ethylbenzene (nEB + 1 ) 1):
Ill + l f Ihl + H2l while the addition is the rate-determining step for the coke growth from styrene (nST + 1 ) 2):
Ill + (ST)l f Ihl It has already been mentioned that the addition of hydrogen sharply decreases the net rate of coke formation in ethylbenzene dehydrogenation. De Pauw and Froment (1975) and Dumez and Froment (1976) observed the same effect of hydrogen on the rate of coke formation in n-pentane isomerization on Pt/Al2O3 and n-butene dehydrogenation on Cr2O3/Al2O3, respectively. A close inspection of the finally withheld mechanism for the coke formation reveals a twofold effect of hydrogen on the rate of coke growth. First, the presence of hydrogen causes a decrease in the number of active sites on the growing coke, formed by dehydrogenation/dehydrocyclization. Second, there is a strong competitive adsorption of hydrogen on the active sites for coke growth located on the edges of the carbon ensembles. As mentioned above and experimentally verified (Figures 2 and 4), the coke content of the catalyst reaches an asymptotic value after a certain run length. At this specific coke content, the intrinsic rates of coke formation and of gasification are in dynamic equilibrium and there is no net coke formation. This asymptotic coke content is called the dynamic equilibrium coke content and depends only on the temperature and the gas-phase composition. For a given set of operating conditions, the dynamic equilibrium coke content can be calculated from the following set of nonlinear equations:
dCp ) δr0s (pj,T)(1 - RsCp) - rG(pj,T,Cp) ) 0 dt (Cp + Cgr)2/3 dCgr 0 ) rgr(pj,T) (1 - RgrCgr) dt P
x
H2
rG(pj,T,Cgr) ) 0
The influence of the operating conditions on the dynamic equilibrium coke content is illustrated in Figures 5 and 6. The sharp increase of the dynamic equilibrium coke content at low conversions to styrene and hydrogen reflects the growing number of active sites for coke growth, resulting from the low hydrogen partial pressure. The increase of the dynamic equilibrium coke content at higher conversions is due to the higher rate of coke growth from styrene. From these figures, it is clear that high temperatures in combination with low water to aromatics ratios in the feed lead to high dynamic equilibrium coke contents on the catalyst surface. Because the generation and condensation of the diluent steam is the most important cost factor during the operation of an industrial unit, there is an interest in reducing the water to aromatics ratio of the feed. The results of the present work indicate that there is a limit beyond which the water to aromatics ratio can no longer be decreased. The continuous formation and gasification of carbonaceous deposits also exert an influence on the overall conversion and the selectivities of an industrial unit. CO2 is the main gaseous reaction product of these reactions. The CO initially produced is almost completely and immediately converted into CO2 by the water-gas shift reaction. Indeed, potassium-promoted iron oxide is used industrially as a catalyst for this reaction. The formation of CO2 is also favored by the high steam partial pressure, the low hydrogen partial pressure, and the range of operating temperatures of an industrial ethylbenzene dehydrogenation unit. The detrimental influence of the addition of CO2 to the feed on the global conversion and the styrene selectivity has been clearly established in the literature (Hirano, 1986; Muhler et al., 1990; Taguchi et al., 1994), and kinetic models have been constructed to account for the presence of CO2 in the feed (Hirano, 1986). None of the above authors has accounted for the generation of CO2 by the continuous formation and gasification of the carbonaceous deposits. The increase of the CO2 yield with increasing global ethylbenzene conversion and its influence on the rates of the dehydrogenation and of the benzene and toluene formation reactions should be accounted for in a reactor simulation. The above-derived kinetic model for the coke formation and gasification has been coupled to a detailed kinetic model for the dehydrogenation and the benzene and toluene formation reactions. This coupled model, in which both parts were derived separately and in the absence of diffusional limitations, was applied to the simulation of a threebed pilot-plant unit operated under industrial operating conditions with catalyst particles of industrial size. This requires accounting for the influence of the diffusional limitations within the catalyst particles. Solution of the coupled differential equations, both in the bulk gas phase and within the catalyst particles, leads to the evolution of the CO2 yield and of the average dynamic equilibrium coke content of the particles as a function of the dimensionless distance in each of the catalyst beds
2632 Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999
Figure 5. Influence of the temperature and the conversion to styrene and hydrogen on the dynamic equilibrium coke content of the catalyst at a total pressure of 1 atm and a water to aromatics molar ratio of 10 mol/mol. ‚‚‚: 843 K. - - -: 873 K. s: 903 K.
Figure 8. Influence of the amount of hydrogen removed from the exit stream of the first bed on the global ethylbenzene conversion (s) and the CO2 selectivity (‚‚‚) at the exit of the second bed. Inlet conditions bed 2: Tln ) 901 K; Pln ) 0.83 atm; Xln ) 40%.
As shown in Figure 8, this removal increases the exit conversion of the second bed and decreases the CO2 selectivity. The latter is mainly due to a lower average, coke content in the catalyst bed. In the inlet layers of the catalyst bed, the coke content is higher when hydrogen is removed between the beds, because of the high temperature, high styrene partial pressure, and low hydrogen partial pressure. The higher coke content quickly drops below the coke level observed when no hydrogen is removed because the rate of gasification is less hampered by the competitive adsorption of hydrogen (viz., eq G IV, Table 2) while the negative effect of CO2 on the dehydrogenation reaction is reduced. Conclusions Figure 6. Influence of the water to aromatics molar ratio and the conversion to styrene and hydrogen on the dynamic equilibrium coke content of the catalyst at a total pressure of 1 atm and a temperature of 903 K.
Figure 7. Calculated CO2 yield and average dynamic equilibrium coke content as a function of the dimensionless distance in each of the catalyst beds for a three-bed pilot-plant unit. Measured CO2 yields at the exit of the beds. b: bed 1. 9: bed 2. 2: bed 3.
shown in Figure 7. The agreement with the experimentally measured CO2 yields is very good. In recent years, there has been an increased interest in removing the hydrogen in between the beds of multibed adiabatic units by oxidation, thus generating part of the heat required for the dehydrogenation in the next bed and allowing for a higher conversion per pass by shifting the composition away from the equilibrium.
The coke formation and gasification on an industrial potassium-promoted iron oxide catalyst during ethylbenzene dehydrogenation is modeled using a set of transient experiments in an electrobalance reactor. The parameter values of the gasification reaction are in accordance with the generally accepted edge-recession mechanism for alkali-catalyzed carbon gasification. The rate of gasification is significantly reduced by competitive dissociative adsorption of hydrogen on the active sites. Coke formation proceeds by a sequence of precursor formation, precursor dehydrogenation leading to the formation of active sites, coke growth, and finally deactivation of the growing coke. Coupling of the coke formation and gasification model with a detailed model for the dehydrogenation and benzene and toluene formation reactions allows an accurate prediction of the CO2 formation under industrial operation. Simulations using this complete model indicate that the removal of hydrogen by oxidation in between the beds of an industrial unit is beneficial, not only because of the shift of the gas-phase composition away from equilibrium but also because of the lower average coke content of the catalyst leading to lower CO2 yields. Nomenclature A/i ) reparametrized frequency factor A/1 ) A/1 exp(-E1/R/Tav) [kmol/kgcat/h] A1 ) frequency factor [kmol/kgcat/h] A/a,j ) reparamatrized frequency factor for adsorption A/a,j ) A/a,j exp(-∆Ha,j/R/Tav) [1/atm] Aa,j ) frequency factor for adsorption [1/atm]
Ind. Eng. Chem. Res., Vol. 38, No. 7, 1999 2633 CC ) catalyst coke content [kgcoke/kgcat] Cf ) active site for gasification Cp ) precursor content [kgcoke/kgcat] Ctg ) total number of active sites for gasification [kmol/kgcoke] Ctgr ) total number of active sites for coke growth [kmol/kgcoke] E1 ) activation energy [kJ/mol] Il ) lower coke intermediate Ih ) higher coke intermediate k1 ) rate constant [kmol/kgcat/h] Kj ) adsorption constant [1/atm] pj ) partial pressure [atm] r0c ) initial coking rate [kgcoke/kgcat/h] rC ) coking rate [kgcoke/kgcat/h] rG ) rate of gasification [kgcoke/kgcat/h] r0gr ) initial rate of coke growth per active center [kgcoke/kgcat/h] rgr ) rate of coke growth per active center [kgcoke/kgcat/h] r0s ) initial rate of site coverage [kgcoke/kmol/h] rs ) rate of site coverage [kgcoke/kmol/h] T ) temperature [K] Tav ) average temperature [K] Greek Symbols RC ) deactivation constant for coking [kgcat/kgcoke] Rs ) deactivation constant for site coverage [kgcat/kgcoke] Rgr ) deactivation constant for coke growth [kgcat/kgcoke] δ ) conversion factor [kmolsite/kgcat] -∆Ha,j ) adsorption enthalpy [kJ/mol] ΦC ) coking deactivation function ΦCp ) deactivation function for precursor formation Φgr ) deactivation function for coke growth
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Received for review March 26, 1998 Revised manuscript received February 8, 1999 Accepted March 3, 1999 IE980169+
