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KINETICS, CATALYSIS, AND REACTION ENGINEERING Analysis of Fundamental Reaction Rates in the Methanol-to-Olefins Process on ZSM-5 as a Basis for Reactor Design and Operation Tae-Yun Park† and Gilbert F. Froment*,‡ SABIC Technology Center, 1600 Industrial Boulevard, Sugar Land, Texas 77478, Chemical Engineering Department, Texas A&M University, College Station, Texas 77843-3122
The paper reports on work aiming at collecting more insight into the methanol-to-olefins process and its product distribution and, more generally, into the behavior of carbenium ion elementary steps of methylation, olgomerization, and β scission on zeolite catalysts. The single-event concept for the rate coefficient, derived from transition-state theory and statistical thermodynamics, and the Evans-Polanyi relationship for the activation energy drastically reduced the number of parameters to be derived from the experimental data from 726 to 33. The number of single events and the heats of formation required for this approach were calculated from the reacting structures and ab initio molecular orbital calculations. The kinetic parameters were inserted into a reactor model to generate sets of rate and yield profiles in an isothermal fixed-bed reactor in the range of 380-480 °C. Finally, for commercial applications, a multibed adiabatic reactor concept was explored. Introduction “Methanol-to-olefins” (MTO) is a catalytic process for the production of ethylene (O2) and propylene (O3) that is on the verge of competing with the thermal cracking of light hydrocarbons and naphtha to adapt the propylene/ethylene ratio to market demands. The catalyst is a zeolite of the SAPO or ZSM-5 type.1-4 The reaction scheme shown in Figure 1 essentially consists of two parts, the first dealing with the conversion of methanol (MeOH) into dimethyl ether (DME) and the primary products propylene, ethylene, and, to a minor extent, methane and the second with the production of higher olefin.5-7 At conversions below 75%, the product spectrum almost exclusively consists of olefins. The steps leading from the primary products ethylene and propylene, formed out of MeOH and the intermediate DME, to the higher olefins are methylation, oligomerization, and β scission. These elementary steps proceed on the acid sites of the catalyst and involve carbenium ions. (De)protonation, hydride shift, methyl shift, and branching protonated cyclopropane (PCP) isomerization are also involved, of course. In previous papers,6,7 the kinetics of the MTO process on a ZSM-5 catalyst were modeled on the basis of a detailed mechanistic reaction scheme. The number of olefins with a carbon number below 9 amounts to 142, the number of carbenium ions to 83, and the number of elementary steps to 726. To reduce the number of rate parameters, the latter were modeled using transitionstate theory. The introduction of the single-event con* To whom correspondence should be addressed. Tel.: +1-979-845-0406. Fax: +1-979-845-6446. E-mail: g.froment@ ChE.tamu.edu. † SABIC Technology Center. Tel.: +1-281-207-5517. Fax: +1-209-844-2561. E-mail:
[email protected]. ‡ Texas A&M University.
Figure 1. Reaction scheme. bs: basic site of the catalyst.
cept8 accounted for the effect of the carbenium ion structure on the change of entropy associated with the transformation, while the linear relationship between activation energy and reaction enthalpy of EvansPolanyi9 accounted for the effect of the structure on the activation energy. The basic parameters, i.e., the singleevent preexponential factor or frequency factor, A ˜ , the intrinsic activation barrier, E°, and the transfer coefficient, R, are considered to be identical for the methylation and oligomerization elementary steps and applicable also to β scission, which is the reverse of oligomerization. The other stepss(de)protonation, hydride and methyl shift, and the PCP branching isomerization stepsall reach equilibrium. Relationships between the rate parameters, in particular for those of deprotonation of carbenium ions into olefins, derived from thermodynamic restrictions, further reduced the number of independent rate parameters to 33. These were determined in reparametrized form from a set of experimental data obtained in the temperature range of 360-480 °C.6,7 The present paper focuses on the elementary steps of carbenium ion chemistry of the process. They account
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for 11 of the 33 independent parameters: one singleevent frequency factor, two parameters related to the activation energies of methylation and oligomerization steps, one entropy of protonation, and seven heats of protonation or “stabilization” of the carbenium ions on the acid sites of the catalyst. To get more insight into the relative importance of the various carbenium ion elementary steps and on their influence on the product distribution, the reparametrized single-event rate parameters are converted into the elementary step level parameters. By doing so, the structure dependency of the rate coefficients of the various methylations, oligomerizations, and β scissions is explicitly indicated. The reactor model equations containing the detailed kinetic model generates the evolution of the rates of the elementary steps and of the product distributions through the reactor, thus providing insight for the conceptual design of an MTO reactor and for the selection of the reactor configuration and operating conditions. Single-Event Concept
( ) (
)
kBT ∆S°q ∆H°q exp k′ ) exp h R RT
(1)
The standard entropy that enters into the frequency factor of the rate coefficient contains translational, vibrational, and rotational contributions. The latter can be split into internal and external contributions, but both consist of an intrinsic term, S°rotq, and a term containing the symmetry number of the species, σ, that reflects the structure of the species:
˜ °rotq - R ln σ S°rotq ) S
(2)
When chirality is accounted for through the introduction of a global symmetry number, the change in the standard entropy due to symmetry changes associated with the transformation of the reactant into the activated complex is given by
∆S°symq ) R ln(σrgl/σqgl)
(3)
where σrgl and σqgl are the global symmetry numbers for the reactant and the transition state, respectively.10 When the symmetry contribution (3) is factored out, eq 1 for the rate coefficient of a monomolecular elementary step, e.g., becomes
k′ )
()
Evans-Polanyi Relation for the Activation Energy Whereas the single-event concept accounts for the effect of structure on the frequency factor of an elementary step, the linear relationship between the activation energy and the reaction enthalpy of Evans and Polanyi9 accounts for the effect of structure and chain length upon the enthalpy contribution to the rate coefficient through
Ea ) E° - R|∆Hr|
The rate coefficient for the transformation of a reactant into a product via an intermediate, the activated complex, contains entropy and enthalpy contributions:
σrgl σqgl
Hence, the rate coefficient of an elementary step, k′, is a multiple of that of a “single event”, k˜ . The number of single events, ne, is the ratio of the global symmetry numbers of the reactant and transition state.11 The calculation of the global symmetry numbers of the reacting and produced carbenium ion and of the activated complex requires their configuration. These can be determined by means of quantum chemical packages such as MOPAC, GAMESS, and GAUSSIAN.
( ) ( )
k BT ∆S ˜° exp h R
q
exp -
q
∆H° RT
(4)
A “single-event” frequency factor that does not depend on the structure of the reactant or activated complex and is unique for a given type of elementary step can be defined as
( )
k BT ∆S ˜ °q A ˜ ) exp h R
(5)
Equation 1 can also be written as
k′ ) nek˜ , with ne ) σrgl/σqgl
(6)
(exothermic reaction)
Ea ) E° - (1 - R)|∆Hr|
(endothermic reaction) (7)
Indeed, it permits the calculation of the activation energy, Ea, for any elementary step or single event pertaining to a certain type, provided the R coefficient and E° of a reference step of that type are available. Use of modern quantum chemical packages, such as GAUSSIAN, is essential for the calculation of ∆Hr. Written according to Arrhenius, the temperature dependency of the single-event rate coefficient becomes
k˜ ) A ˜ exp(-Ea/RT)
(8)
in which A ˜ is a modified or “single-event” frequency factor, “modified” because the structure effect on the entropy change has been accounted for by factoring out the number of single events, ne. The Polanyi parameters E° and R take on unique values for a given type of elementary step or single event so that there are only two independent rate parameters for this step. The single-event concept and the Evans-Polanyi relation drastically reduce the number of rate coefficients to be determined from experimental data. From these independent parameters, the complete set of rate coefficients can then be calculated using eqs 1-8. From Single-Event to Elementary Step Rate Coefficients By way of example, the rate parameter for the methylation of propylene by a methoxycarbenium ion R1+ can be written as t kMe(O3;R1+) ) CH +k′Me(O ;R +) 3 1
k′Me(O3;R1+) ) ne,Me(O3;R1+)k˜ Me(O3;R1+)
(
k˜ Me(O3;R1+) ) A ˜ exp -
)
E° - R|∆HMe(O3;R1+)| RT
(9)
t where CH + represents the total acid concentration, ne,Me(O3;R1+) the number of single events in the elementary step, k′Me(O3;R1+) the rate coefficient of the elementary step, and k˜ Me(O3;R1+) the corresponding single-event
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rate coefficient. The structures of the reactant and of the transition state were determined by means of the quantum chemical package MOPAC, followed by Bartels nonlinear least-squares minimization, McIver-Komornicki’s norm minimization, and the Eigenvector Following routine of Baker. As a final step, internal reaction coordinate calculations were carried out to determine and verify the structure. The number of single events, ne, is then obtained from the ratio of the global symmetry numbers of the reactant and the transition state. Values of ne were calculated for 91 methylations, 53 oligomerizations, and 25 β scissions. Even within a given type of elementary step, ne was found to vary significantly, depending upon the structures. For methylation, ne is mostly 2.00; for oligomerization, ne is also mostly 2.00, although values up to 12 were calculated. For β scission, values ranging from 0.25 to 6.00 were obtained and these were always half the value of the corresponding oligomerization.
Table 1. ∆H°f Values (kcal/mol) of Various Carbenium Ions: Comparison between Experimental and Calculated Values for Various Types and Structures
Calculation of the Heat of Formation of Carbenium Ions The heat of reaction of the elementary step, required for the application of the Evans-Polanyi relation, depends on the thermodynamic properties of the olefin and of those of the surface-associated carbenium ions. The thermodynamic properties of the olefin isomers were calculated using Benson’s group contribution method,12 and those of the surface-associated carbenium ions were obtained in two steps. In the first, the properties of free carbenium ions were estimated by means of quantum chemical packages. The second step dealt with the calculation of the properties of surfaceassociated carbenium ions. Thermodynamic Properties of Free Carbenium Ions. Until now, computational means do not permit consideration of really representative configurations of the acid sites of the zeolite, so that the calculation of the number of single events is based upon the configuration of the gas-phase reactant and transition state. Kazansky13 concluded from ab initio calculations and high-resolution 13C MAS NMR that alkyl carbenium ions are rapidly converted into surface alkoxy ions, which are covalently bonded to the surface oxygen ions. The global symmetry number of such a configuration is reduced by a factor of 2 from that of the gas-phase carbenium ion, but because of additional chirality on the C atom carrying the positive charge, the loss of 2-fold axes for tertiary carbenium ions with more than four atoms, and the loss of external symmetry, the global symmetry number for the surface-associated activated complex is also reduced by a factor of 2. Consequently, the number of single events is the same as that obtained from gas-phase configurations, for which far more information is available and calculations are easier. The stability difference between carbenium ions is mainly determined by (1) the type of cation (methyl, primary, secondary, tertiary); (2) the size of the cation, defined by its number of C atoms; and (3) the number of C-C bonds of the carbon atom in the R position with respect to the C atom carrying the positive charge, nCR-C. The most stable ion is the tertiary ion, and the stability decreases as the number of C-C bonds on the charge-bearing C atom decreases. For a given type of carbenium ion, those ions with a larger number of C atoms are more stable. For a given type of carbenium
ion and with the same number of C atoms, the stability is mainly determined by nCR-C: the larger the number of these bonds, the higher the stability, i.e., the lower ∆H°f.14 The semiempirical method MOPAC predicted the right trends for (1) and (2) but led to substantial deviations between the predicted and experimental stability behavior of the ions with respect to (3), i.e., the effect of nCR-C. Therefore, an ab initio molecular orbital method, GAMESS, was used. Among the various possible basis sets, the STO-3G set was found to be optimal. The ab initio calculation provides the total energy of a molecule, Etot, which is the sum of the electronic and nuclearnuclear repulsion energies for molecules isolated in a vacuum, without vibration, and at 0 K. To obtain the absolute values of ∆H°f, additional calculations based upon statistical thermodynamics are required.
∆H°f ) Etot + E′(T) +
∑{-Eel(atom) + ∆H°f (atom)}
(10)
Table 1 shows the agreement reached between the experimental data and the values of ∆H°f calculated in this way. From a comparison of A-C, it is seen how ∆H°f significantly decreases from primary to tertiary ions. A comparison within the group of primary ions of group A shows that the ∆H°f also decreases with increasing chain length. The same is true for the secondary carbenium ions of group B and for the tertiary carbenium ions of group C. The effect of the chain length may cause some overlapping of ∆H°f values for different types of R+ (viz., secondary and tertiary R+ in B and C). For the same number of C atoms and the same
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Figure 2. Single-event rate coefficients for the methylation and oligomerization of linear olefins at 440 °C as a function of the C number of the product. Methylation labels: C number of olefins. Oligomerization by ethyl R+ labels: C number of olefins.
Figure 4. Single-event oligomerization rate coefficients. Carbenium ion: ethyl. Effect of the olefin structure. (a) 1, propylene; 2, 1-butene; 3, 2-Me-2-butene; 4, 2-Me-3-pentene. (b) 1, 2-Me-4pentene; 2, 2-hexene; 3, 2-Me-3-pentene.
∆q(2-butyl R+) ) q(H+) - q(isobutyl R+), where isobutyl R+ is the reference R4+, introduced to reduce the number of independent rate parameters. ∆q(isobutyl R+) is accessed through the protonation of propylene: ∆HPr(O3) ) ∆Hf,g(isobutyl R+) - ∆Hf(O3) - ∆Hf,g(H+) + ∆q(isobutyl R+). The quantity ∆HPr(O3) was estimated by Park and Froment7 from their experimental data, ∆Hf,g(isobutyl R+) and ∆Hf,g(H+) were calculated by ab initio quantum chemical calculations, and the heat of formation of O3 is available in the literature. ∆q(R1+) is accessed via the protonation of MeOH and the hydration of R1+:
Figure 3. Single-event methylation rate coefficients. Effect of the reacting olefin structure. (a) Labels: number of C atoms in the olefin. Produced R+: 2-Me-2-butyl; 2,3-diMe-3-butyl; 2,2,3-triMe3-butyl; 2,2,3-triMe-3-pentyl. (b) All C7 olefins. Produced R+: 2-Me3-heptyl; 4-Me-3-heptyl; 3,3-diMe-4-hexyl; 2,2,4-triMe-3-pentyl. (c) All C7 olefins. Produced R+: 2,3-diMe-2-hexyl; 2,5-diMe-3-hexyl; 2,3,4-triMe-3-pentyl.
MeOH + H+ h MeOH2+
(12)
R1+ + H2O h MeOH2+
(13)
From eq 12
∆HPr(MeOH) ) ∆Hf,s(MeOH2+) - ∆Hf(MeOH) ∆Hf,s(H+) (14) and from eq 14
type of carbenium ion, the effect of the degree of branching is small (group D). The higher nCR-C, the lower ∆H°f. The same trends were also obtained for C8 ions, but these are not shown here. Thermodynamic Properties of Surface-Associated Carbenium Ions. The second step in the calculation of the thermodynamic properties of the surfaceassociated carbenium ions involves correction terms called heats of stabilization on the surface for both the reacting and the produced carbenium ion. Consider, by way of example, the methylation of propylene by the methylcarbenium ion, represented by R1+ and leading to 2-butyl R+. The heat of methylation can be written as
∆HHyd(R1+) ) ∆Hf,s(MeOH2+) - ∆Hf(H2O) -
∆HMe ) ∆Hf,g(2-butyl R+) - ∆Hf,g(R1+) - ∆Hf(O3) +
Rate Coefficients for the Various Elementary Steps It now becomes possible, using eqs 1-7 and the values of the independent parameters, to calculate the 88 elementary step rate coefficients of methylation of the various olefin isomers and, in an analogous way, the 52 rate coefficients of oligomerization and the 21 rate
q(R1+) - q(2-butyl R+) (11) The last two terms in eq 11 are equivalent to ∆q(2-butyl R+) - ∆q(R1+), where ∆q(2-butyl R+) ) q(H+) - q(2butyl R+) and ∆q(R1+) ) q(H+) - q(R1+). In addition,
∆Hf,s(R1+) (15) where the heats of formation of H+ and R1+ on the surface can be explicitly indicated as ∆Hf,s(H+) ) ∆Hf,g(H+) - q(H+) and ∆Hf,s(R1+) ) ∆Hf,g(R1+) - q(R1+). Subtracting eq 15 from eq 14 leads to an equation for ∆q(R1+), in which the values for ∆Hf of MeOH and water are known from the literature, while the ∆Hf,g of H+ and R1+ can be calculated by means of quantum chemical ab initio methods and ∆HPr(MeOH) and ∆HHyd(R1+) were determined by Park and Froment7 from their experimental data.
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length and/or nCR-C. From curve b, corresponding to C6 olefins, branched or straight, it follows that the effect of branching is very weak. Figure 5 compares k˜ for the β scission of various octyl R+. The order of the curves reflects the sequence k˜ (s;t) > k˜ (t;t) > k˜ (s;s) > k˜ (t;s), generally observed in carbenium ion chemistry. The difference in k˜ values within one type of elementary step, β scission, is really striking. The ne values are also quite different. The k˜ values are seen to take off from 460 °C onward. Figure 5 also compares the evolution with the temperature of k˜ for an oligomerization, which is the reverse of one of the β scission. The curves cross around 460 °C. Figure 5. Single-event rate coefficients for elementary cracking steps. (a) 2,2-diMe-4-hexyl R+ into 1-butene and 2-Me-2-propyl R+. (b) 2,2,4-triMe-4-pentyl R+ into isobutylene and 2-Me-2-propyl R+. (c) 3,4-diMe-5-hexyl R+ into 2-butene and 2-butyl R+. (d) 3,5-diMe5-hexyl R+ into isobutylene and 2-butyl. (e) Single-event rate coefficient for the oligomerization step, which is the reverse of the cracking step of curve b.
coefficients of β scission. Figure 2 shows the effect of the chain length on the single-event rate coefficients for methylation of linear olefins and on those for their oligomerization by means of ethyl R+ at 440 °C. The produced R+ are all linear and secondary. The single-event rate coefficient significantly increases with chain length. Because, by virtue of the single-event concept, there is only one frequency factor in this model,6,7 this effect solely results from the enthalpy contribution to k˜ . Figure 3 illustrates the effect of branching, expressed in terms of nCR-C in the produced R+, and of the nature of R+ on k˜ for methylation. A comparison of curves a and b, corresponding to R+ that are respectively all tertiary and all secondary, reveals that the effect of the nature of R+ is far more pronounced than that of branching. Curve c, derived for C7 olefins, like curve b, essentially confirms that conclusion. Figure 4 deals with oligomerization by means of the ethyl R+ and producing secondary R+. Curve a shows how k˜ increases with chain
Conceptual Design of a Reactor for Maximum Propylene Production With these rate coefficients and the appropriate rate equations,6 the process behavior in a fixed-bed reactor with plug flow can be investigated by simulation. The reactor model is of the pseudohomogeneous type with plug flow, and the pressure drop equation is that of Ergun. The equations are given by Froment and Bischoff.15 Exploratory simulations of isothermal operation were performed at temperatures ranging from 380 to 480 °C. Rate profiles in an isothermal reactor operating at 460 °C are shown in Figure 6. The rate of disappearance of MeOH monotonically drops to zero, but the net rate of production of DME becomes negative at W/F°MeOH ) 0.25. All of the other rates start from zero. They correspond to secondary reactions of the process. At low temperatures, the net rate of production of ethylene exceeds that of propylene, but this is reversed from 400 °C onward. The location of the maximum of the rate profiles shifts to higher space times or MeOH conversions as the carbon number increases. The properties of the rate profiles are reflected in the yield profiles, examples of which are shown in Figure 7a,b for operation at 460 °C. The yields, expressed in kilograms of product i per 100 kg of MeOH fed, decrease in the order O3 > O4 > O2 > O6 > O5 > O7 ≈ O8. The
Figure 6. Rate profiles in an isothermal reactor at 460 °C (space time based upon the molar feed rate of MeOH).
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Figure 7. (a and b) Yield profiles in an isothermal reactor at 460 °C (yield in kilograms of product formed per 100 kg of MeOH fed).
DME yield goes through a maximum at W/F°MeOH ) 0.25. The methane yield is low. The H2O yield is on the order of 50%, which is inevitable in MTO. A number of simulations, all achieving 100% MeOH conversion, showed that the O3 yield increases from 8.1 to 10 wt % between 380 and 480 °C but levels off from 440 °C onward, while the O2 yield drops from 4.8 to 2.1% and the O4 yield from 7.8 to 6.2%. Among the higher olefins, O8 exhibits a maximum in its yield profile for operation above 440 °C, indicating an increasing influence of cracking. The sum of the olefin yields goes through a maximum value of 40.3 wt % at 460 °C. The sum of the O2 and O3 yields is very nearly constant at 13 wt % over the whole range
of 380-480 °C. The maximum O3 yield always occurs at a MeOH conversion of 92% and a DME yield of 2-3%, whatever the temperature. Higher conversions would also generate aromatics and paraffins, which are undesired products in this process. If the design and operating conditions are aiming for maximum propylene yield, the exit conversion should not exceed 92%, meaning that MeOH and DME have to be recycled. Isothermal operation would require a multitubular reactor, the cost of which would be prohibitive for the commercialization of this process. Adiabatic operation is required. The simulation of this type of operation was based again on model equations given by Froment and
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improvements are possible by increasing the number of beds, but the investment sets limits to this. Conclusion Quantitative information was generated on the rate coefficients of carbenium ion elementary steps such as methylation, oligomerization, and β scission, which play an important part in the MTO process. This required in the first place a significant reduction of the number of rate parameters to be determined from the experimental data, made possible by the application of the single-event concept and the Evans-Polanyi relationship for the activation energy. The single-event approach is based upon the modeling of the rate coefficient through transition-state theory and statistical thermodynamics. From ab initio molecular orbital calculations, the effect of the structure of the reactant and activated complex on the frequency factor of the rate coefficient can be explicitly indicated. They also permit the calculation of the heats of formation of the various species, and from these the activation energies of the elementary steps, provided two fundamental parameters, the intrinsic activation barrier and the transfer coefficient, are known for each type of elementary step or can be determined from the experimental data. The effect of the structure and temperature on the rate coefficients of 88 methylations, 53 oligomerizations, and 25 β scissions was quantitatively analyzed, leading to conclusions extending beyond the MTO process. The kinetic information, thus obtained, enabled the investigation of possible configuration and operating conditions for the commercial application of the process. The exothermicity of the process is very high and requires nontrivial solutions to achieve optimal operability and product distribution. Notation
Figure 8. (a-c) Temperature and yield profiles in a three-bed adiabatic reactor. DME and H2O yields in Figure 8c: right ordinate.
Bischoff.15 The exothermicity of the process is such that the simulation of a simple adiabatic reactor led to a temperature rise of more than 250 °C and an unacceptable high methane yield. Such conditions would also cause a rapid deactivation of the catalyst by coke formation and even its deterioration. For this reason, a three-bed adiabatic reactor with an intermediate heat exchanger was studied in greater detail. The results are shown in Figure 8a-c. The MeOH conversion is limited to essentially 90%, and the temperature rise per bed decreases from 147 °C in the first bed, fed at 370 °C, over 134 °C in the second bed, fed at 373 °C, to 110 °C in the third bed, fed at 400 °C. The propylene yield amounts to 8.2%, the ethylene yield to 3%, and the total olefin yield to 34.3%, and the methane yield is only 0.3%. The DME yield at the exit is about 7%. Obviously, the temperature rise in the beds should be reduced. Further
A ˜ ) preexponential factor of a single-event rate coefficient, s-1 or s-1‚bar-1 t CH+ ) total concentration of acid sites, mol/gcat E° ) intrinsic activation barrier in the Evans-Polanyi relation, J/mol Ea ) activation energy, J/mol h ) Planck constant, 1.841 × 10-37, J‚h kB ) Boltzmann constant, 1.381 × 10-23, J/K k′ ) rate coefficient of an elementary step i, s-1 or s-1‚bar-1 k˜ ) single-event rate coefficient, s-1 or s-1‚bar-1 ne ) number of single events q(i) ) heat of stabilization for species i, J/mol Ri+ ) carbenium ion with carbon number i (i ) 1, 2, ..., 8) Greek Letters R ) transfer coefficient in the Evans-Polanyi relation ∆H°f(i) ) standard enthalpy of formation for species i, J/mol ∆Hi ) heat of reaction of an elementary step i, J/mol ∆Hr ) heat of reaction of an elementary step, J/mol ∆S°q ) standard entropy of activation, J/mol‚K ∆q(i) ) difference in the heat of stabilization between proton and species i, J/mol σigl ) global symmetry number of species i Subscripts bs ) basic site Cr ) cracking De ) deprotonation Me ) methylation Ol ) oligomerization
Ind. Eng. Chem. Res., Vol. 43, No. 3, 2004 689 Pr ) protonation r ) reaction s ) surface sr ) surface reaction sym ) symmetry Superscripts r ) reactant t ) total
Literature Cited (1) Eng, C. N.; Arnold, E. C.; Vora, B. V.; Fuglerud, T.; Kvisle, S.; Nilsen, H. Integration of the UOP/HYDRO MTO Process into Ethylene Plants. AIChE Spring National Meeting, New Orleans, LA, 1998; Session 16. (2) Marchi, A. J.; Froment, G. F. Catalytic Conversion of Methanol to Light Alkenes on SAPO Molecular Sieves. Appl. Catal. 1991, 71, 139. (3) Dehertog, W. J. H.; Froment, G. F. Production of Light Alkenes from Methanol on ZSM-5 Catalysts. Appl. Catal. 1991, 71, 153. (4) Quann, R. J.; Green, L. A.; Tabak, S. A.; Krambeck, F. J. Chemistry of Olefin Oligomerization over ZSM-5 Catalyst. Ind. Eng. Chem. Res. 1988, 27, 565. (5) Hutchings, G. J.; Hunter, R. Hydrocarbon Formation from Methanol and Dimethyl ether: A Review of the Experimental Observation Concerning the Mechanism of Formation of the Primary Products. Catal. Today 1990, 6, 279. (6) Park, T.-Y.; Froment, G. F. Kinetic Modeling of the Methanol to Olefins Process. Model Formulation. Ind. Eng. Chem. Res. 2001, 40 (20), 4172-4186.
(7) Park, T.-Y.; Froment, G. F. Experimental Results, Model Discrimination and Parameter Estimation. Ind. Eng. Chem. Res. 2001, 40 (20), 4187-4196. (8) Baltanas, M. A.; Van Raemdonck, K. K.; Froment, G. F.; Mohedas, S. R. Fundamental Kinetic Modeling of Hydroisomerization and Hydrocracking on Noble-Metal-Loaded Faujasites. Ind. Eng. Chem. Res. 1989, 28, 899. (9) Evans, M. G.; Polanyi, M. Inertia and Driving Force Chemical Reactions. Trans. Faraday Soc. 1938, 31, 11. (10) Pollak, E.; Pechukas, P. Symmetry Numbers, not Statistical Factors Should Be Used in Absolute Rate Theory and Bronstedt Relations. J. Am. Chem. Soc. 1978, 100, 2984. (11) Vynckier, E.; Froment, G. F. Modeling of the Kinetics of Complex Processes based upon Elementary Steps. In Kinetic and Thermodynamic Lumping of Multicomponent Mixtures; Astarita, G., Sandler, S. I., Eds.; Elsevier Science Publishers BV: Amsterdam, The Netherlands, 1984; p 131. (12) Benson, S. W.; Cruickshank, R. F.; Golden, D. M.; Haugen, G. R.; O’Neal, H.; Rodgers, A. S.; Shaw, R.; Walsh, R. Additivity Rules for the Estimation of Thermochemical Properties. Chem. Rev. 1969, 69, 279. (13) Kazansky, V. B. Memorial Boreskov Conference; Institute of Catalysis: Novosibrisk, 1997; part I. (14) Martens, J. A.; Jacobs, P. A. Conceptual Background for the Conversion of Hydrocarbons on Heterogeneous Acid Catalysts. In Theoretical Aspects of Heterogeneous Catalysis; Moffat, J. B., Ed.; Van Nostrand Reinhold: New York, 1990; p 52. (15) Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design, 2nd ed.; Wiley: New York, 1990.
Received for review February 12, 2003 Accepted September 16, 2003 IE030130R
