Ind. Eng. Chem. Res. 1987, 26, 1399-1407
There are five carbon atoms in this molecule, so N , = 5. By use of eq 4,the upper flammability limit is estimated to be 11.4 vol %. Sax (1984) reported an experimental value of 9.0 vol 90. Example 111. Calculate the upper flammability limit of dimethylamine i
n,
$i
N CH, H
1 2 1
1/4 2/4 1/4
hi 0.0
-0.9307 -0.5625
Two carbon atoms are in dimethylamine, so N , = 2. By use of eq 4, the upper flammability limit is estimated to be 15.3 vol %. Tyron (1962) reported an experimental value of 14.0 vol %. Registry No. Methyl chloride, 74-87-3; trans-1,2-dichloroethylene, 156-60-5; ethyl chloride, 75-00-3; 2-chloropropene, 557-98-2; 2-methoxyethanol, 109-86-4; trans-crotonaldehyde, 123-73-9; isobutyl alcohol, 78-83-1; ethyl propyl ether, 628-32-0; aniline, 62-53-3; 2,2-dimethylbutane, 75-83-2; 3,3-diethylpentane,
1399
1067-20-5; decane, 124-18-5; toluene, 108-88-3.
Literature Cited Beyer, W. H., ed. CRC Standard Mathematical Tables, 26th ed.; CRC: Boca Raton, FL, 1981. Daubert, T. E.; Danner, R. P. Data Compilation: Tables of Properties of Pure Compounds; American Institute of Chemical Engineers: New York, extant 1985. Nuzdha, L.; Glinkin, M. A,; Rafales-Lamarka, E. E.; Tyupalo, N. F. Soviet Chem. Ind. 1979, 11, 230. Sax. N. I. Dangerous Properties of Industrial Materials, 6th ed.; Van Nostrand Reinhold: New York, 1984. Shebeko, Y. N.; Ivanov, A. V.; Alekhina, E. N.; Barmakova, A. A.; Soviet Chem. Ind. 1983a, 15, 1203. Shebeko, Y. N.; Ivanov, A. V.; Dmitrieva, T. M. Souiet Chem. Ind. 1983b, 15, 311. Tryon, G. H., ed. Fire Protection Handbook, 12th ed.; National Fire Protection Association: Boston, 1962. Zabetakis, M. G. Estimating Techniques for Vapor Flammability; Bureau of Mines: Washington, DC, 1965; Bull. 627, Appendix B. Received for review April 3, 1986 Revised manuscript received March 26, 1987 Accepted April 10, 1987
A Kinetic Modeling Approach to the Design of Catalysts: Formulation of a Catalyst Design Advisory Program James A. Dumesic,* Beth A. Milligan, Leonard0 A. Greppi, Vijay R. Balse, K e n n e t h T. Sarnowski, C h a r l e s E. Beall, T a k u o Kataoka, a n d Dale F.R u d d Department of Chemical Engineering, University of Wisconsin, Madison, Wisconsin 53706
A n d r e s A. T r e v i n o Shanahan Valley Associates, Madison, Wisconsin 53711
We describe an approach to catalyst design that allows the coordination, interpretation, and generalization of theoretical and experimental catalysis studies. Our approach allows for the rapid estimation of catalyst performance from reaction mechanism considerations and serves to direct the catalyst designer toward experiments which are likely to yield the catalytic properties sought. We apply the approach to two test catalyst design problems: that of predicting the reactions of n-hexane and hydrogen on platinum catalysts and that of predicting the conversion of methanol to olefins on a zeolite H-ZSM-5 catalyst. We also show how this simple approach forms the basis for a Catalyst Design Advisory Program capable of being implemented on a computer. Portions of the advisory program have been made available commercially and are being used in industry under the name of CATALYST 11. Background Heterogeneous catalysts are key components of many industrial chemical processes, such as ammonia synthesis, methanol synthesis, cracking of fuel oils to gasoline products, reforming of hydrocarbons to enhance combustion performance,polymerization, and partial oxidation of hydrocarbons. Despite the importance of these catalytic processes, the search for new catalysts or the improvement of existing catalysts has been empirical. Our current understanding of chemical processes occurring on solid surfaces is not yet sufficiently well developed to allow the design of heterogeneous catalysts without extensive experimental studies. This empirical search for new or improved catalysts, however, should be based on fundamental science. Before an experimental program is undertaken, it is important to determine its probability of success in terms of creating the desired catalytic properties. The purpose of the present paper is to formulate a methodology for the evaluation of catalyst performance that incorporates both chemical expertise and experimental work. 0888-5885/ 87 / 2626- 1399$01.50 / 0
A Modeling Approach to t h e Design of Heterogeneous Catalysts An important problem facing the designer of heterogeneous catalysts is how to coordinate, interpret, and generalize the results of experimental studies. The catalyst designer must assimilate the existing experimental data for a given catalytic process to predict how a new catalyst can be formulated or to improve the performance of an existing catalyst. Alternatively, the catalyst designer must extrapolate the results from studies of known catalysts and reactions for use in the generation and performance estimation of a catalyst for an entirely new chemical process. Here we propose a catalyst design approach based on a kinetic model of the reaction/catalyst system to be used in conjunction with experimental studies. Specifically, the performance of a catalyst is simulated by automated modeling of proposed chemical reaction mechanisms, and this modeling is then used in directing experimental work. It is through the combination of modeling and experimental studies that the kinetic model is altered and refined 0 1987 American Chemical Society
1400 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987
to become a useful catalyst design tool. Indeed, modeling in the absence of experimental data may be a mathematical exercise, while experimentation in the absence of a kinetic model may lack direction; however, the combination of these two efforts results in a powerful strategy for catalyst design. (It is important to note that the kinetic model must not only describe the catalyst performance in the reactor, but it must also be consistent with information from independent spectroscopic, physical, and chemical measurements.) It is this strategy that forms the basis of the Catalyst Design Advisory Program. The catalyst design approach that we propose includes three main tasks: (a) postulation of a reaction mechanism, (b) construction and calibration of a kinetic model, and (c) application of the model to catalyst design. These tasks are discussed below. (a) Reaction Mechanism. A fundamental starting point for the interpretation and generalization of experimental studies for catalyst design must involve a description of the main reactions, reaction intermediates, and series of elementary steps that comprise the overall chemical process. While it is true that rigorous reaction mechanisms have been established for only the simplest of chemical reactions, detailed kinetic descriptions have been proposed for many catalytic processes (for example, see recent review articles: Gault, 1981; Biloen and Sachtler, 1981; Grasselli and Burrington, 1981; Madix, 1980; Engel and Ertl, 1979; Temkin, 1979). Furthermore, a wide variety of reaction intermediates adsorbed on catalyst surfaces have been identified by spectroscopic techniques. It is thus possible to construct working mechanisms for a given catalytic process in terms of elementary steps and adsorbed intermediates that have been observed and studied for that or analogous catalytic processes. (b) Kinetic Model. (b.1) Construction. An important step in the analysis of the possible mechanisms for a given catalytic process is to estimate the rate constants for the various elementary steps by an Arrhenius expression. Collision and transition-state theory can be used to make order of magnitude estimates of the preexponential factors for the rate constant (e.g., Boudart and DjBga-Mariadassou, 1984; Somorjai, 1981; Laidler, 1965; Frost and Pearson, 1953). The estimation of activation energies is typically more difficult; however, a three-step procedure of general utility can be followed. First, the enthalpies of the various elementary steps are estimated, assuming that all steps take place in the gas phase. This is accomplished using known or estimated bond dissociation energies and heats of formation of gaseous molecules, radicals, and ions. Second, the estimated gaseous heats of reaction are converted to surface heats of reaction by introducing the heats of adsorption of all surface species. This involves the making and breaking of surface chemical bonds, the energetics of which can be estimated by analogy with other chemical reactions. Indeed, these estimates of surface bond strengths will become the important parameters of the kinetic modeling. Finally, the estimation of activation energies from heats of reaction can be accomplished by linear free-energy correlations, such as Polanyi relations, Hammett equations, or the Bransted catalysis relation (e.g., Boudart and DjBga-Mariadassou, 1984; Somorjai, 1981; Laidler, 1965; Frost and Pearson, 1953). The estimates of rate constants for all possible elementary steps in the catalytic process provide insight into which of these steps are sufficiently fast that they can be assumed to be in equilibrium and which steps are sufficiently slow that they can be assumed to be rate determining or can be neglected. In addition, it is possible to
estimate in this manner the relative coverages of the various adsorbed species and to thereby predict which species are most abundant and which species are present in sufficiently small surface concentration that they can be neglected. (b.2) Calibration. Once the key steps in the proposed reaction mechanism have been identified, the estimates of the rate and/or equilibrium constants for these steps can be refined. The mechanism is then used to predict the activity and selectivity of the known catalytic process under investigation. If the predictions do not agree with experimental results, then the kinetic parameters (e.g., surface bond strengths, parameters introduced by the correlations of activation energies with heat of reaction) must be altered systematically within reasonable physical limits to achieve good agreement. This is done by changing those parameters that are least well-known. If agreement between model predictions and experimental data cannot be achieved, then the reaction mechanism must be altered accordingly. ( c ) Model Applications. Having achieved satisfactory agreement between the predictions of the kinetic model and the results of experimental data, the model is ready to be used to guide the catalyst designer in the search for new catalysts or for improvements on existing catalysts. For example, sensitivity studies can be conducted to determine which of the kinetic parameters have strong effects on catalyst performance, and the designer must then decide how these parameters can in fact be altered by changing the nature of the catalyst. Alternatively, the designer can take a series of proposed catalysts, estimate how the kinetic parameters may differ for these different catalysts, and then use the kinetic model to evaluate the performance of each catalyst for the chemical process of interest. The next section illustrates the application of kinetic modeling to the following two important catalytic processes: reactions of n-hexane over platinum, as a model of catalytic reforming, and methanol conversion to olefins over H-ZSM-5 zeolite, as a model of hydrocarbon production from methanol. The subsequent section is devoted to the problems of developing a generally applicable Catalyst Design Advisory Program. Examples of Kinetic Modeling of Heterogeneous Catalytic Processes Reactions of II -Hexane over Platinum. In general, four classes of reactions take place when n-hexane is brought into contact with a platinum catalyst at temperatures near 600 K in the presence of hydrogen. These reactions are (a) aromatization to form benzene, (b) cyclization to form methylcyclopentane, (c) isomerization to give 2- and 3-methylpentanes, and (d) hydrogenolysis to give smaller hydrocarbons. The objective of this illustration is to demonstrate that the product distributions obtained experimentally over platinum catalysts can be modeled by using published descriptions of reaction intermediates and elementary steps and making reasonable estimates for rate constants. A variety of reaction intermediates and elementary steps have been proposed in the literature. We have selected representative schemes to describe the basic catalytic processes that take place on the platinum surface. In short, aromatization is described by ring closure of a 1,1,6-triabsorbed species (Gates et al., 1979); cyclization to methylcyclopentane and isomerization of 2- and 3-methylpentanes are described by the formation of 1,1,5-triadsorbed species, followed by C-C bond-formation and breaking steps (Gault, 1981; Ponec, 1983; Machiels and
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1401 Chart I
*I I
CH2
x
/ /
/H
H
C-*
H2C
I II (2)
*
P
II
+ * (3)
(11)
I
/
/
H3C
H3C
* II (4)
* /
CH2
*
CH-CHz
H
C H ~ C H ~ C H Z C H ~ C Ht ~ C4* H~
CHZCH~CHCHZCH~CH~ -t 2
I
I
* H C H ~ C H ~ C H C H Z C H ~tC H 2 1~
*I
CH3
*
*I
*
I*
I
*
(13)
t
+
CH~CHCHZCHZCH~ 2*
(14)
CH4 t 2*
(15)
*I
H
I
CH3 C
*
*I
H C H ~ C H C H Z C H Z C Ht~
* Hz
Anderson, 1979); and hydrogenolysis is described by the formation of l,&diadsorbed species, followed by C-C bond cleavage (Gates et al., 1979; Machiels and Anderson, 1979). For simplicity, C-C cleavage is assumed to occur at the 1,2-position. The hydrogen adsorbed on the platinum surface is assumed to be atomic (Gates et al., 1979). The elementary steps assumed in the present modeling of n-hexane reactions on platinum are shown in Chart I. This scheme involves 17 elementary reversible steps, 12 adsorbed species, and the formation of 6 stable reaction products. It should be remembered that this sequence of steps is used for illustrative purposes only. Preexponential factors for the forward and reverse rate constants for the 17 elementary steps of the assumed reaction scheme can be estimated from collision and transition-state theories (e.g., Boudart and DjBga-Mariadassou, 1984; Somorjai, 1981; Laidler, 1965; Frost and Pearson, 1953). If only order of magnitude estimates are needed,
I
* t 2x
C H ~ C H Z C H ~ C H ~tC H2*~ (16)
H 21
*
(17)
then two classes of reactions can be distinguished. The preexponential factor for rate constants involving the adsorption of a gaseous species to form immobile surface species should be approximately 102-105 Torr-l s-l, and the preexponential factor for rate constants involving only adsorbed species or desorption processes should be approximately 1012-1016s-l. When these rate constants are multiplied by gaseous pressures (in Torr, where 1Torr = 133.32 Pa) and by fractional surfaces coverages (dimensionless), the calculated rates are expressed in turnover frequencies (molecules reacted per site per second). We and 1013 s-l for the have chosen values of lo5 Torr-l present illustration. The enthalpies of reaction for the 17 steps of the assumed reaction scheme were estimated in two steps as described earlier. First, the heats of formation of the various intermediates were estimated by assuming that the reactions took place in the gas phase and by using tabu-
1402 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987
lations of heats of formation of stable molecules and bond dissociation energies. The carbon-hydrogen bond energy was assumed to be the same for all species, and this value was left as a parameter of the model. Second, the strengths of the Pt-C a-bond, Pt-C r-bond, and Pt-H bond were used to correct the gaseous heats of formation to heats of formation of surface species. These three bond strengths were also left as parameters of the modeling. The parameter values that appeared to represent the experimental data most closely were 100 kcal/mol for the C-H dissociation energy and 40, 25, and 60 kcal/mol for the three surface bond strengths, respectively. Activation energies, E,,,, for the rate constants of the assumed reaction scheme were estimated from the above heats of reaction, H , using the Polanyi expression (Boudart and DjBga-Mariadassou, 1984): Eact= Eo + cyH for exothermic reactions
Eact= E,
+ (1 - a)H
for endothermic reactions
In the present modeling illustration, we have chosen E, and cy to be 15 kcal/mol and 0.5, respectively. Furthermore, for exothermic reactions, we have set Eactto zero whenever the Polanyi expression predicts a negative activation energy (with the activation energy for the reverse rate constant equated to the absolute value of the heat of reaction, H). With the above estimates for rate constants, it is possible to determine the surface coverages of reaction intermediates by solving simultaneously the steady-state equations for these coverages. In general, one steady-state relation is written for each surface species, and these are combined with a relation expressing the conservation of surface sites. Thus, 13 equations must be solved simultaneously for the present example involving 1 2 surface intermediates. It is apparent that these equations also involve the pressures of all gaseous species, and these pressures are additional unknown quantities requiring additional equations, i.e., reactor design equations for the independent chemical reactions. The reactor model used for simplicity in the present illustration was that of a continuously well-mixed reactor. The application to batch or plug flow reactors is a straightforward extension (e.g., a plug flow reactor can be modeled by a series combination of well-mixed reactors). For gas-phase reactions, the well-mixed reactor design equation takes the following form Pf - Pi = (WRTS/ Vo)rToF where Pf and Pi are the effluent and inlet pressures of a given gaseous species, W is the catalyst weight, R is the gas constant, T is the temperature, S is the number of active sites per unit mass of catalyst, Vois the volumetric flow rate to the reactor, and rTOF is the turnover frequency for the production of the gaseous species which can be expressed in terms of rate constants and surface coverages. We have further assumed in the present example that the volumetric flow rate is the same at the reactor effluent and inlet, i.e., that the reactants are fed to the reactor in an inert carrier gas. A typical value of WRTS/ Vofor a single crystal in a laboratory reactor is 1 Torr-s, and this value was used in this illustration. Five different chemical reactions comprise the present illustration, i.e., the formation from n-hexane of (a) benzene, (b) methylcyclopentane, (c), 2-methylpentane, (d) 3-methylpentane, and (e) methane and pentane. If the inlet pressures of all reactants and products are known (the latter assumed to be zero in the present example), then the design equations for each species can be used to relate
Table I. Reactions of n-Hexane on Pt(ll1): Comparison of Model with Experimental Results ( T = 573 K, HJHC = 10, P,,, = 220 Torr) rate of reaction, selectivity, molecules/(Pt atom-s) mol % reaction exptl calcd exptl calcd 4.9 X 5.9 X 15 15 aromatization cyclization 11 x 10-3 12 x 10-3 35 32 7.9 X 8.1 X 24 22 isomerization 8.7 X 12 X hydrogenolysis 26 31 Table 11. Reactions of n -Hexane on Pt( 111): Comparison of Model with Experimental Results (T= 638 K, H2/HC = 10, P,,, = 220 Torr) rate of reaction, molecules/(Pt selectivity, mol atom-s) % reaction exptl calcd exptl calcd 0.03 0.10 33 17 aromatization 0.17 13 30 cyclization 0.01 0.01 0.14 14 25 isomerization 0.04 0.16 40 28 hydrogenolysis
the effluent pressures to the surface coverages and rate constants of the assumed reaction mechanism. The result is a series of (NS NP + 1)equations and unknowns that must be'solved simultaneously, where NS is the number of surface intermediates and N P is the number of gaseous species. (For the present example, NS = 12 and N P = 8.) A number of studies of reactions of n-hexane on Pt have been reported. For instance, Davis et al. (1984) have studied the effects of temperature, inlet hydrogen to hydrocarbon ratio (H,/HC), and catalyst surface structure on product selectivities. They found that on a Pt(ll1) surface (T = 573 K, H2/HC = lo), the reaction products contained 35% methylcyclopentane (MCP), 26 % hydrogenolysis products, 24% isomerization products (2- and 5-methylpentane), and 15% benzene. A well-dispersed Pt/ Si02 catalyst also favored methylcyclopentane over isomerization products (Santacessaria et al. 1978). In contrast, van Schaik et al. (1975) found that on larger Pt particles supported on Si02,the products contained 48% isomerization products, 43% hydrogenolysis products, 7% methylcyclopentane, and 2 % benzene. Davis and others have concluded that isomerization via C,-cyclization requires metal atoms with few nearestneighbors and/or with weak metal-support interactions. In addition, Davis concluded that the aromatization reaction must occur via a 1,6 ring closure rather than through the C5-cyclization mechanism. Since our kinetic model uses a 1,6 ring closure mechanism for aromatization and a C,-cyclization mechanism for isomerization, the experimental data of Davis et al. (1984) on single-crystal Pt surfaces seem well-suited for comparison with our model. The results of the kinetic model and experimental data for Pt(ll1) in a batch reactor at 573 and 638 K are shown in Tables I and 11. The model is a good predictor of both the activity and the selectivity of the Pt catalyst at lower temperatures. For both the model and the experimental data, methylcyclopentane and hydrogenolysis products dominate. Also, both the model and the data show that during isomerization, 3-methylpentane is favored over 2-methylpentane. A t higher temperatures, the model predicts a higher activity than the experimental data exhibit. Also, the model does not predict the significant change in selectivity with increasing temperature shown by the experimental data. Experimentally, the selectivity toward benzene and hydrogenolysis products is increased at 638 K. The decreased activity and altered selectivity
+
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1403 at higher temperatures can be explained by experimentally observed, unreactive carbon deposits that cover the Pt surface. As many as 90% of the surface atoms are covered by these deposits at 638 K (Davis et al., 1982). The presence of these carbon deposits was not included in the present model. One way to improve the model predictions is to modify the mechanism. The aromatization mechanism used in this model was based on dehydrogenation of adsorbed cyclohexane. However, the hexane-hexene-hexadiene stepwise mechanism may be more reasonable (Paal, 1980). Similarly, it may be more appropriate to use a 1,1,3- or 1,3,3-adsorbed species as the hydrogenolysis intermediate (Gault, 1981; Davis et al., 1984; Sinfelt, 1973). Also, better accuracy may be obtained by including the bond-shift isomerization pathway (Gault, 1981). Reactions of Methanol over H-ZSM-5Zeolite. Much attention has focused on ZSM-5 zeolites since it was reported that these materials were effective for the production of hydrocarbons from methanol (Chang and Silvestri, 1977). Depending on reaction conditions and Si/Al ratio of the zeolite, for example, the selectivity can be controlled to favor the production of olefins or the production of aromatics. The unique pore structure of the zeolite precludes the formation of hydrocarbons containing more than about 10 carbon atoms. The present paper will address for simplicity the production of light olefins (lower than C,) from methanol. The mechanism for the formation of olefins can be divided into three important processes: (a) formation of dimethyl ether (DME), (b) production of the first olefin, and (c) the further syntheses of higher olefins. In the first process, dimethyl ether is formed by the interaction of methanol with a Bransted acid site, leading to a surface methyloxonium species; the latter species subsequently reacts with a gaseous or weakly adsorbed methanol molecule to form a dimethyloxoniumion species which desorbs from the surface, giving gaseous dimethyl ether and regenerating the Bransted acid site (Kaeding and Butter, 1980). The mechanism for the formation of the first olefin (ethylene) from methanol is not well understood. For example, carbenoid species (Chang and Silvestri, 1977; Venuto and Landis, 1968) and carbenium ions (van den Berg et al., 1980) have been suggested to be intermediates in this process. We have selected a mechanism involving oxonium ion species (van den Berg et al., 1980; Espinoza and Mandersloot, 1984). In particular, a dimethyloxonium ion is imagined to react with dimethyl ether to give a trimethyloxonium ion, which then undergoes a Stevens rearrangement to give an ethylmethyloxonium ion. The latter ion may then decompose to give ethylene and methanol, or it may react further with dimethyl ether to give an ethyldimethyloxonium ion, which then undergoes a Stevens rearrangement to give a methylpropyloxonium ion. Finally, the latter oxonium ion decomposes to give propylene and methanol. The mechanism chosen for the formation of higher olefins was that of Kaeding and Butter (1980), involving the reaction of a gaseous or weakly adsorbed olefin molecule (containing N carbon atoms) with a surface methyloxonium species to give a surface carbenium ion (containing ( N + 1) carbon atoms) and water. We also included reactions of olefin molecules (containing N carbon atoms) with surface carbenium ions (containing A4 carbon atoms) to give larger surface carbenium ions (containing ( N + M) carbon atoms) (Gates et al., 1979). The elementary steps chosen to model the formation of olefins from methanol over H-ZSM-5 zeolite are shown in Chart 11. It should be noted that we have assumed steps
4-9,12,14,16, and 18 involving oxonium ion reactions and olefin reactions with adsorbed methoxide species to be irreversible. It can be seen that 27 reactions have been included, involving 13 intermediates and 8 reaction products. Thus, kinetic modeling using the scheme requires the simultaneous solution of 13 steady-state equations, 8 reactor design equations, and 1site conservation equation, i.e., a total of 22 equations. Preexponential factors for the forward and reverse rate constants of the 27 reactions of the assumed reaction sequence were estimated as discussed previously in this paper. In particular, a preexponential factor of lo2 Torr-' s-' was used for reactions involving adsorption of a gaseous species, corresponding to the formation of immobile surface species, and a preexponential factor of lOI3 s-' was assumed for reactions involving adsorbed species only or for desorption processes. The activation energies for the rate constants of the elementary steps were estimated from the enthalpy changes of the various steps using the Polanyi relations presented previously. For this illustration, we found that values for Eo and a equal to 5 kcal/mol and 0.5 provided good simulations of experimental data, as presented below. Estimation of the enthalpy changes of the steps in the proposed reaction scheme, required for the calculation of activation energies, was carried out according to the procedure described previously. As a first step, the enthalpies of formation of the various intermediates and reaction products were estimated assuming all species to be in the gas phase. This was accomplished using tabulations of thermodynamic heats of formation and proton affinity data (Dean, 1979; Bowers, 1979; Cox and Pilcher, 1970). (The proton affinity of a molecule is the heat released when that molecule reacts with a proton in the gas phase.) For cases where several isomers of a given species were possible, we used the thermodynamic properties of the most stable isomer. In several cases, thermodynamic data were not available and estimates for heats of formation were made. Specifically, the proton affinity of methyl propyl ether was estimated by analogy from the proton affinities of dimethyl ether and ethyl methyl ether. In addition, the heats of formation of the trimethyl- and ethyldimethyloxonium ions were assumed to be 5 kcal/mol lower than those of the ethylmethyl- and methylpropyloxoniumions, respectively. The values were then used to estimate enthalpy changes for the various elementary steps in the gas phase, and these enthalpy changes were converted to surface enthalpy changes using one adjustable parameter: the proton affinity of the active sites on the H-ZSM-5 zeolite. A value for this parameter of 170 kcal/mol was found to be reasonable for the kinetic modeling of the present example. In these calculations, we also assumed that the strength of hydrogen bonding was 6 kcal/mol. We have attempted to simulate experimental data for the conversion of methanol to hydrocarbons for cases where the production of aromatics was negligible. One such experimental study was that of Chang and Silvestri (1977). For simplicity, we did not attempt to distinguish between aliphatics and olefins in the experimentally observed product distribution; instead, we grouped together hydrocarbons with the same carbon number and treated these as olefins. Furthermore, the experimental data were collected in a plug flow reactor, while we modeled the reactor for simplicity as a well-mixed reactor; therefore, we must expect only qualitative agreement between experimental and kinetic modeling results. A typical laboratory value for a high surface area catalyst of 100000 Torrms was used for WRTSI V , in the model.
1404 Ind.
Eng.Chem. Res., Vol. 26, No. 7, 1987
Chart I1
+ CH3OH t H t C CH3OH2 CH36H2 t CH30H
= CH36CH3 I /I
CH3C=CHCH3
I
t H20
t
- I
C H B O C H ~t CH30CH3
I H
CH3tCH2CH2CH3
CH3
CH3C=CHCH2CH3
+
CH30CH3
I
CH3
-
CH30CH2CH3 t CH3OCH3
I
+
CH30CH2CH3 H
+
CH30CH2CH3
---
t
CH3CHCCH2CH3 t Hfl
I 1
I I CH3CH3
CH3zH2
t
CH30CH2CH3 t CHsOH
I I CH3 CH3
+
6 7 -=CH2
CH3CCH2CH2CH3
+
CH3
t
CH30CH2CH2CH3
I H
CHz =CH2
+
CH3CCH2CH3 CH3
+
+ CH2=CHCH3 CH3dHCH2CH3 ===
CHaCH=CHCH3
-
(10) (11)
H+
CH3dHCH2CH3 t H20
CH3CH=CHCH3
t CH36H2
-
CH3
CH3CCH2CH3
+
H+
CH3&H2CH3
t H20
(13)
(25)
CH3CH3
(12) CH3CH=CH2
t
t
t CH3CHCHEH3
CH3CHCCH2CH3
(26)
I I CH3 CH3
(14)
= H30C
H20 t H t
t He
+
CH3CHCCH2CH3
I I
I
CH3C=CHCH3
(24)
CH3 t
CH3CHCH3 t CH3CH=CHCH3
CH3 CH3&CHzCH3
+
C
c
+
(23)
I
t H
= CH&H=CH2
(22)
t
t CH3CHCH3
CH3CH2 t CH3CH=CH2
+
t CH3CH2
I
I H
CH30H2
+
c
C H ~ C C H ~ C H Z C H ~ CH3CH=CHCH3
+
CH3dHCH3
(21)
CH3
CH30H t CH3CH2
-=CH2=CH2
(20)
I
CH30CH2CH2CH3 -.-- CH30H t CHjCHCH3
+
(19)
t
CH3CHCH3 t CH3CH =CH2
+
H+
CHzHCH2CH3
t
CH3
CH3
CHaCH2
+
CH3CHECH2CH3 t CH3C=CCH2CH3
I
(18)
CH3CH3
H
H
-
CH3
CH30CH2CH3
t
t CH30H2
I
CH3
(17)
I
CH3
CH30CH3 t CH3OH
t H+
CH3C=CHCH2CH3
I
c
t
I
CH3
t
H
t
CHaCCH2CH2CH3 t H20 (16)
CH3
CH30CH3 t H +
CH$CH3
-
+
t CHaOH2
(27)
(15)
CH3
Table 111. Methanol Conversion to Olefins: Comparison of Model with Experimental Results Dartial Dresaure, Torr exDtl calcd 12.5 15.5 ethylene 23.0 23.2 propylene 14.1 19.8 butylene 13.9 4.62 pentene 1.81 3.85 hexene 3.29 0.32 heptene 147 147 dimethyl ether 401 403 water
L C 6
0
We had difficulty simulating the experimentally observed catalytic activity and selectivity using only the adjustable parameters described above, i.e., the Polanyi parameters and the proton affinity of the active sites. However, if we decreased the forward rate constant for step 1 by a factor of 2 and increased the forward and reverse rate constants for step 2 by a factor of 20, then good agreement between the experimental and calculated partial pressures of the eight reaction products was obtained. These results are summarized in Table 111. The utility of kinetic modeling is that after the model has been adjusted to achieve good agreement with experimental results, the model can be used to predict catalyst behavior under other reaction conditions or to predict
I 1
2
3
4
5
Flow Rate (em3/,)
Figure 1. Variation of predicted olefin distribution with flow rate.
the behavior of different catalysts. The former case is illustrated in Figure 1for the effect of gaseous volumetric flow rate through the reactor on the conversion of methanol to light olefins. In agreement with expectations, ethylene is the primary product at high flow rates (high space velocities) and propylene production passes through a maximum, while heavier olefins are produced at lower flow rates. Catalyst Design Advisory Program We now describe a prototype Advisory Program which
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1405 Define T a r g e t Overall Reaction
t
1
Propose C a t a l y s t t h a t can D e l i v e r t h e Requlred Parameter: I
CATALYST D E S I G N ADVISORY PROGRAM C a t a l y s t Module CATALYST EXPERTISE
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Figure 2. Approach to catalyst design.
is evolving to assist the designer at various stages of the design process. The details of this program, CATALYST 11,will be reported in future publications (Dumesic et al., 1987). A Catalyst Design Advisory Program must respond to the needs of the catalyst designer by providing access to information, concepts, data, and computational power to solve equations, optimize, integrate, and fit experimental data. The Catalyst Design Advisory Program enables rapid access to relevant observations from within the catalyst design laboratory and allows the designer to generalize and expand those facts to direct further experimental explorations in catalyst development. Figure 2 shows the proposed catalyst design approach to be followed by the catalyst designer and the required interaction with a Catalyst Design Advisory Program. The design tasks are still performed by the designer, but a series of support advisory modules is available through the advisory program to facilitate the design. The design approach is parallel to that used in the examples above. It includes (a) the postulation of a reaction mechanism, (b) construction and calibration of the kinetic model, and (c) model applications. The Advisory Program consists of six modules that are utilized at various stages during the design process. Each module consists of two units: (a) a Knowledge Unit containing pertinent databases, algorithms, and computation programs and (b) an Expertise Unit capable of handling and learning conceptual information about the data. For each module, the absence of the Expertise Unit results in the direct use of the stored information, such as physical properties of numerical algorithms. The interaction of each module with the catalyst design approach is described below. (a) Reaction Mechanism. The postulation of a reaction mechanism requires mainly access to published mechanisms for the reaction of interest or for analogous reactions. With existing software, a database can be constructed that is capable of organizing this information so that it can be readily retrieved given a predefined set of cues. The addition of conceptual expertise to the module allows access to concepts contained in the data-
base. For example, such a module would allow the designer to retrieve information on similar reactions, catalysts, or reaction/catalyst systems. The ability to recognize the concept of similarity is built into the Expertise Unit of the Mechanism Advisory Module. The concept itself requires a judicious classification of reactions and catalysts, such as oxidations, hydrogenations, aromatizations, etc., for the reactions and zeolites, supported metals, transition metal oxides, etc., for the catalysts. Notice that the availability of such expertise in the Mechanism Module is not required to complete the design task. Initially, the conceptual capability of the Mechanism Expertise Unit may be nonexistent, and the Mechanism Module in Figure 2 would provide direct access to reaction mechanism publications as do existing computer search services. (b) Kinetic Model. In the construction of the kinetic model, the Advisory Program is used to assemble the kinetic equations, estimate rate and equilibrium constants, solve systems of equations, and compare the results of the model to experimental data. Each of these functions requires a separate module in the Advisory Program. (b.1) Assembly of Kinetic Equations. The kinetic equations are assembled autamatically from the statement of the reaction mechanism. This is accomplished by computer-aided symbol manipulations. This frees the researcher from the errors associated with algebraic formulation of the kinetic model. (b.2) Estimation of Rate Constants. The rate constants are estimated by using the Physical Properties Module shown in Figure 2. This module contains a collection of thermodynamic data, bond strengths, activation energy correlations, and results from collision and transition-state theories for the estimation of kinetic parameters for the reactions and intermediates. The Expertise Unit in the module guides the designer in choosing what physical property estimation equations are more appropriate for the reaction system under study. (b.3) Solution of Equations. For even the simplest chemical processes, multiple, reversible reactions are possible and the active sites for the reactions may involve more than a single surface atom. In this case, one must solve a large set of algebraic nonlinear and differential and integral equations, with one equation for each surface intermediate (i.e., a steady-state relation for each intermediate) and one reactor design equation for each independent reaction involving a product that may readsorb on the surface. Even for relatively simple catalytic processes, it is not possible to obtain analytical solutions for the catalytic activity and selectivity in terms of the kinetic parameters of the model, and numerical solutions must be sought. A variety of general solution algorithms that can be used to solve the resulting equation systems is contained in the Knowledge Unit of the Numerical Methods Module. However, the straightforward application of these numerical algorithms is often plagued by convergence problems. This is specially true in cases involving chemical equilibrium and reaction rate constants. For the specific case of a system of nonlinear algebraic equations, existing algorithms typically fail to find a solution, making empirical and pseudotheoretical modifications to the algorithms necessary (Shacham, 1985; Chen and Stadtherr, 1981). The main goal of these modifications is to make the numerical algorithm recognize a fault when it occurs and apply corrective actions until successful convergence to a meaningful solution is achieved. The Expertise Unit of the Numerical Methods Module includes an arsenal of corrective actions to be used when the algorithms encounter difficulties.
1406 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 C a t a l y s t ' s Technical P e r f o r m a n c e Da:d
I
fields of catalysis is conceptually possible but not practical at the current state of the art. To maximize the usefulness of the Catalyst Design Advisory Program proposed here, it must be field-specific and capable of running on a personal computer. Such a program provides a valuable hands-on tool that the researcher can tap at will. The Catalyst Design Advisory Program contains elements of an expert system for catalyst design. In fact, it could be classified as an Expert Assistant program. As the catalyst designer works with more catalysts and catalytic reactions, a collection of useful reaction intermediates, elementary chemical steps, rate constants, equilibrium constants, and bond energies is accumulated in the Catalyst Design Advisory Program for use in future catalyst design problems. Furthermore, as the predictions of kinetic models are compared with experimental data, correlations are obtained of kinetic parameters with catalyst structure and composition. It is information of this type that gives direction to the catalyst designer for the preparation of new catalysts from the predictions of kinetic models. The various modules can be updated and expanded either by the catalyst designer or by an automatic learning mechanism. The overall system becomes a more powerful tool for catalyst design with repeated use. The types of catalysts and processes of interest to one catalyst designer are likely to be quite different from those of interest to another individual. Thus, the ability of the modules to learn from the catalyst designer is vital. Accordingly, these modules must be developed with the structure required to execute their basic functions, but they must have the flexibility to be adaptable to the needs of the catalyst designer. A computer system, CATALYST 11, is commercially available to execute the kinetic modeling portions of Figure 2.
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Figure 3. Assessment of catalyst economic performance.
(b.4) Calibration. To compare the results of the kinetic model with experimental data, optimization algorithms and statistical analysis methods are required. The optimization algorithms are used to vary systematically the parameters of the model. Statistics are required to measure the goodness-of-fit of the model to experimental data. A simple preliminary approach is to conduct kinetic modeling simulations over a range of conditions and fit the results to a power-law rate expression, which can then be compared to experimental data. It is important to repeat the following statement made earlier: the kinetic model must not only simulate catalyst performance in the reactor, but it must also be consistent with results of other independent measurements. ( c )Model Applications. The Catalyst Design Advisory Program also provides a valuable function by linking kinetic models for different catalytic processes, thereby allowing information learned for one process to be used in the evaluation of similar processes. Furthermore, the comparison of kinetic parameters from different models provides an important test of the consistency of the models. For example, if two different kinetic models both involve a parameter such as the strength of bonding a particular hydrocarbon fragment to a particular metal surface, then this parameter should be the same in both models. As more experimental data are explained in terms of kinetic models involving the same or related parameters, more confidence is gained in the validity of the models and the values of the parameters. The Catalyst Module provides the basis for this task. The Knowledge Unit contains experimentally obtained correlations of kinetic parameters with catalyst structure and composition, while the Expertise Unit accrues the relevant concepts to be used in applying these correlations to a new design. Once a catalyst that meets the desired technical goals has been designed, it should be evaluated in terms of its potential economic benefits, as illustrated in Figure 3. This can be done by developing a preliminary process design and determining the process economics. The potential acceptance of the new process can be assessed by using adequate technology assessment methods (Rudd et al., 1981). The Process Economics Module contains a Knowledge Unit with the necessary process design and economic data and alternate ways to evaluate the economic potential of a chemical process and an Expertise Unit with advice as to which of these evaluations to use for the specific case on hand. Closing Remarks The Catalyst Design Advisory Program encompasses a set of modules that support the design approach, providing the designer with pertinent raw and conceptual information and with computational capabilities to manipulate this information. The Catalyst Design Advisory Program must be constrained to the specific field of interest of the researcher. A general advisory program encompassing all
Acknowledgment The two examples of kinetic modeling in this paper were carried out as part of an elective course in Catalysis in the Department of Chemical Engineering. We thank the following members of that class for their important contributions to these examples: P. Hanratty, H. Hong, J. LaFord, T. Spielbauer, P. Weninger, M. Amiridis, B. Bischoff, N. Cardona-Martinez, M. Eiseman, S. Goddard, and T. Srnak. Registry No. Pt, 7440-06-4; H3C(CH2)&H3,110-54-3;C,H,, 71-43-2; H3CCH(CH,)(CHZ)zCH,, 107-83-5;H&CH&H(CH3)CHZCH,, 96-14-0;CH4,74-82-8; H&(CHz),CH,, 109-66-0;CHSOH, 67-56-1; H2C=CH2, 74-85-1; H2C=CHCH3, 115-07-1; butylene, 25167-67-3; pentene, 25377-72-4; hexene, 25264-93-1; heptene, 25339-56-4; methylcyclopentane, 96-37-7.
Literature Cited Biloen, P.; Sachtler, W. M. H. Adu. Catal. 1981, 30, 165. Boudart, M.; DjBga-Mariadassou, G. Kinetics of Heterogeneous Catalytic Reactions; Princeton University Press: Princeton, 1984. Bowers, M. T., ed. Gas Phase Ion Chemistry; Academic: New York, 1979; Vol. 2. Chang, C. D., Silvestri, A. J. J . Catal. 1977, 47, 249. Chen, H. S.; Stadtherr, M. A. Comp. Chem. Eng. 1981,5', 3. Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds; Academic: New York, 1970. Davis, S. M.; Zaera, F.; Somorjai, G. A. J. Catal. 1982, 77, 439. Davis, S. M.; Zaera, F.; Somorjai, G. A. J . Catal. 1984, 85, 206. Dean, J. A., Ed. Lange's Handbook of Chemistry, 12th ed.; McGraw-Hill: New York, 1979. Dumesic, J. A.; Trevino, A. A.; Rudd, D. F. "Catalyst Design and Experiment Planning: A Guide to the CATALYST I1 Program", 1987; Shanahan Valley Associates, Madison, WI.
Ind. Eng. Chem. Res. 1987, 26, 1407-1412 Engel, T.; Ertl, G. Adu. Catal. 1979,28, 1. Espinoza, R. L.; Mandersloot, W. G. B. J. Mol. Catal. 1984,24, 127. Frost, A. A.; Pearson, R. G. Kinetics and Mechanism; Wiley: New York, 1953. Gates, B. C.; Katzer, J. R.; Schuit, G . C. A. Chemistry of Catalytic Processes; McGraw-Hill: New York, 1979. Gault, F. G. Adu. Catal. 1981, 30, 1. Grasselli, R. K.; Burrington, J. D. Adu. Catal. 1981, 30, 133. Kaeding, W. W.; Butter, S. A. J . Catal. 1980, 61, 155. Laidler, K. J. Chemical Kinetics; McGraw Hill: New York, 1965. Machiels, C. J.; Anderson, R. B. J. Catal. 1979, 58, 268. Madix, R. J. Adu. Catal. 1980, 29, 1. Paal, Z. Ado. Catal. 1980, 29, 273. Ponec, V. Adu. Catal. 1983,23, 149. Rudd, D. F.; Fathi-Afshar, S.; Trevino, A. A.; Stradtherr, M. A. Petrochemical Technology Assessment; Wiley: New York, 1981.
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Santacessaria, E.; Gelosa, D.; Cara, S.; Adami, I. Ind. Eng. Chem. Prod. Res. Dev. 1978, 17, 68. Shacham, M. Comp. Chem. Eng. 1985,9, 2. Sinfelt, T. Adu. Catal. 1973, 23, 92. Somorjai, G. A. Chemistry in Two Dimensions: Surfaces; Cornel1 University Press: Ithaca, NY, 1981. Temkin, M. I. Adu. Catal. 1979, 28, 173. van den Berg, J. P.; Wolthuizen, J. P.; Van Hooff, J. H. C. Proceedings of the 5th International Conference on Zeolites, Naples; Rees, L. V. Ed.; Heyden: London, 1980; p 649. van Schaik, J. R. H.; Dressing, R. P.; Ponec, V. J . Catal. 1975, 38, 273. Venuto, P. B.; Landis, P. S. Adu. Catal. 1968, 18, 259. Received for review July 3, 1986 Accepted April 13, 1987
A Comparative Study of Zeolite and Resin Adsorbents for the Separation of Fructose-Glucose Mixtures Cecilia Ho, Chi Bun Ching, and Douglas M. Ruthven* Department of Chemical Engineering, National University of Singapore, Kent Ridge, Singapore 0511
T h e kinetics and equilibria of sorption of fructose and glucose on Ca2+ion-exchange resins and Ca2+-exchangedzeolite adsorbents have been studied experimentally by pulse and step chromatographic methods. The best of the resin adsorbents shows a higher equilibrium separation factor than Cay zeolite, but this advantage is largely offset by the greater resistance to mass transfer. Under practical operating conditions in a simulated countercurrent chromatographic separation unit, the resin and zeolite adsorbents show little difference in performance, although the flow conditions required for the two adsorbents are significantly different. The separation of fructose-glucose mixtures in the production of high fructose syrup is generally carried out by simulated countercurrent adsorption using as the adsorbent either a cation-exchange resin in Ca2+ form (Mitsubishi and Illinois Water Treatment Processes) or a CaY synthetic zeolite (UOP process). Both of these adsorbents are fructose selective, but at least from the open literature, it is not clear whether one or the other has any intrinsic advantage, either in terms of fundamental factors such as capacity, selectivity, or adsorption kinetics or in terms of less obvious but equally important factors such as cost and service life. In order to provide comparative data on the intrinsic properties of these adsorbents, a series of experimental studies was undertaken in which breakthrough curves were measured, over a range of liquid flow rates, for two different resin adsorbents and samples of CaY and CaX zeolites. The CaX zeolite showed virtually no selectivity between fructose and glucose, but the selectivity and capacity of the CaY zeolite were found to be similar to the Ca2+resins. The kinetic properties of the CaY zeolite are superior although the equilibrium selectivity is somewhat less favorable. The comparative performance of these two adsorbents is therefore very sensitive to the extent to which the adsorber is affected by masstransfer resistance.
Experimental Section Breakthrough curves were measured in a small column packed with the test adsorbent and surrounded by a water jacket through which water from a thermostat was circulated to maintain a constant temperature. Effluent con-
centrations were monitored with the aid of an on-line refractive index detector. At the start of an experiment, a controlled flow rate of pure water was passed through the column to establish the detector base line, and at time zero the inlet stream was switched to a solution containing either fructose or glucose at the desired concentration level. The flow was continued until the breakthrough was complete and the steady detector signal corresponding to the inlet stream composition was established. Most of the measurements were carried out at low concentrations (- 1%wt) to ensure linearity of the equilibrium. However, a series of measurements was also performed with concentration up to 30% wt in order to establish the form of the equilibrium relationship at higher concentration levels. The moments of the response were calculated from the experimentalbreakthrough curves by integration according to the expressions (see, for example, Ammons et al., 1977) / . m i .
I =J, (:-l)dt
u2=
lm(l-d)tdt-P
In the earlier experiments, measurements were made also by the pulse response method. The first and second moments of the pulse response were calculated according to
* Author to whom correspondence should be addressed. Permanent address: Department of Chemical Engineering, University of New Brunswick, Fredericton, N.B., Canada E3B 5A3. 0888-5885/87/2626-1407$01.50/0
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0 1987 American Chemical Society
