I n d . Eng. Chem. Res. 1992,31, 1589-1597 Faraday Trans. 1 (Faraday Symposium 21),1987b,83,2193. Fiolitakis, E.; Hofmann, H. Dependence of the kinetics of the lowtemperature water-gas shift reaction on the catalyst oxygen activity as investigated by wavefront analysis. J. Catal. 1983,80, 328. Froment, G. F. Reversed flow operation of fixed bed catalytic reactors. In Unsteady State Processes in Catalysis; Matros, Yu. Sh., Ed.; VPS B V Utrecht, 1990. Kagan, Yu. B.; Liberov, L. G.; Slivinskii, E. V.; Loktev, S. M.; Lin, G. I.; Rozovskii, A. Ya; Bashkivov, A. N. Mechanism of methanol synthesis from carbon dioxide and hydrogen. Dokl. Akad. Nauk SSSR 1975a,221,1093(in Russian). Kagan, Yu. B.; Rozovakii, A. YR; Liberov, L. G.; Slivinski,E. V.; Lin, G. I.; Loktev, S. M.; Bashkirov, A. N. Mechanism of methanol synthesis from carbon dioxide and hydrogen. Dokl. Akad. Nauk SSSR 1975b,224,1081. Lee, C. T.; Bailey, J. E. Diffusion waves and selectivity modifications in cyclic operation of a porous catalyst. Chern. Eng. Sci. 1974,29, 1157. Matros, Yu. Sh. Unsteady Processes in Catalytic Reactors; Elsevier: Amsterdam, 1985. Matros, Yu. Sh. Catalytic Processes under Unsteady State Conditions; Elsevier: Amsterdam, 1989. Neophytides, S. G.; Marchi, A.; Froment, G. F. Unpublished results, LPT Ghent, 1991a. Neophytides, S. G.; Ochoa, F.; Froment, G. F. Unpublished results, LPT Ghent, 1991b.
1589
Padberg, G.; Wicke, E. Stable and unstable behavior of adiabatic tubular reactor as,for example, in catalytic CO oxidation. Chem. Eng. Sci. 1967,22, 1305. Rozovakii, Va. A. New data on the mechanism of catalytic reactions with the participation of carbon oxides. Kinet. Katal. 1980,21, 97 (in Russian). Saussey, J.; Lavalley, J. C. An in situ FT-IR study of adsorbed species on a Cu-ZnA1204methanol catalyst under 1 MPa pressure and at 525K effect of hydrogen-carbon monoxidecarbon dioxide feed stream composition. J. Mol. Catal. 1989’50, 343. Silveston, P.L. Periodic operation of chemical reactors. A review of the experimental literature. In: Reactions and Reaction Engineering; Maskelkar, R. A., Kumar, R., Eds.;Indian Academy of Sciences: Bangalore, India, 1987. Ueno, A.; Omishi, T.; Tamaru, K. New dynamic approach for elucidating the mechanism of catalytic reactions. The mechanism of the decomposition of methyl alcohol on zinc oxide. Trans. Faraday SOC. 1970,66,756. Van Herwijnen, T.; De Jong, W. A. Kinetics and mechanism of the CO shift on Cu/ZnO. I. Kinetica of the forward and reverse CO shift reactions. J. Catal. 1980,63,93. Van Herwijnen, T.; Guczaleki, R. T.; De Jong, W. A. Kinetics and mechanism of the CO shift on Cu/ZnO. 11. Kinetics of the decomposition of formic acid. J. Catal. 1980,63,94.
Received for review November 15, 1991 Accepted April 7, 1992
Effect of Nitrogen Compounds on Cracking Catalysts Teh C. €Io* Exxon Research and Engineering Company, Annandale, New Jersey 08801
Alan R. Katritzky and Stephen J. Cat0 Department of Chemistry, University of Florida, Gainesville, Florida 32611
In a paper of the same title, Fu and Schaffer reported on the poisoning effecta of more than 30 individual nitrogen and aromatic compounds on cracking catalysts. A significant outcome of their study was a database on the relative poisoning potency of a variety of nitrogen compounds. On the basis of the database, this study was aimed a t correlating the poisoning power of nitrogen compounds with their structures. For each compound, we determined 24 structural variables; of these, the dominant ones were identified by a chemometric technique. This provides a basis for developing a simple nonlinear correlational model for practical applications. It is shown that the poisoning power of a nitrogen or aromatic compound is primarily determined by a balance between ita heaviness/size and basicity. The former may be measured by molecular weight, while the latter by proton affinity.
Introduction The poisoning effects of nitrogen compounds on cracking catalysts are of considerable interest to workers in catalytic cracking as well as in hydroprocessing. Most early studies (in the 1950s) were conducted on amorphous silica-alumina catalysts. Recently, a few studies were performed on zeolite-containing catalysts using model compounds (Young,1986;Corma et al., 1987). The most comprehensive study perhaps is that of Fu and Schaffer (1985). They investigated the effects of 28 nitrogen compounds and three aromatic compounds on cracking of a gas oil and of a hydrotreated vacuum resid over modem zeolitic catalysts. The experiments were carried out by adding each of the pure compounds (or poison additives) to the feed which was cracked in a fluidized-bed reactor over a metal-free or metal-contaminated equilibrium catalyst. The 28 nitrogen compounds were chosen to study the following effects: (1) basicity, (2) type of heterocyclic nitrogen (pyridinic vs pyrrolic), (3) length and location of alkyl substituents in the heterocyclic rings, (4) number of attached benzene rings, ( 5 ) hydrogenation of the nitrogen I
compounds, and (6) the presence of more than one nitrogen atom in the heteroring. The results showed that these nitrogen compounds exhibited widely different poisoning tendencies. Some of the results are not intuitively obvious. For instance, a less basic compound (measured by pK,) can be more harmful than a more hasic compound, and a sterically hindered nitrogen heteroatom can be more damaging than a completely accessible nitrogen heteroatom. One should be able to gain a better understanding of the nitrogen effecta if Fu and Schaffer’s data can be correlated with some intrinsic structural properties of the nitrogen compounds. Fu and Schaffer did not discuss this point, except to mention that the most important property, based on a subset of the data, appeared to them to be the gase-phase basicity as measured by the proton affinity. Corma et al. (1987)have also reached the same conclusion. This is hardly surprising. After all, cracking catalysts are solid acids. The basicity of nitrogen compounds enables them to interact with the acidic sites on catalysts in one of two ways: they can accept surface protons (Bronsted
Q888-5885/92/2631-1589$03.OO/Q0 1992 American Chemical Society
1590 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
acidity) or donate unpaired electrons to surface electrondeficient sites (Lewis acidity). In the latter, steric hindrance plays an important role (Ho, 1988). These types of acid-base interactions have often been used to obtain information on the total number and/or the distribution of acidic sites. We present below a detailed analysis of Fu and Schaffer's data. The analysis is carried out as follows. First, for each of the poison additives, we determine a set of 24 structural variables (or descriptors) describing various physicochemical, topological, and electronic properties of the poisons. These variables are then linearly combined to form a small number of independent aggregates by means of the partial least squares (PLS) method (Lindberg et al., 1983;Frank et al., 1983;Wold et al., 1987). The key here is to select a minimum number of such aggregates to capture the maximum amount of information about the possible relationship between the poisoning power and the structure of the poison molecules. We find that the basicity of nitrogen compounds (measured under nonreacting conditions) is not the dominant factor in determining the extent of poisoning. To a first approximation, the poisoning power of a nitrogen or aromatic compound is determined by a balance between ita heaviness/size and basicity. This result provides a basis for constructing a nonlinear correlational model based on molecular weight and proton affinity.
Table I. Descriptor Definitions and Number Designations no. definition 1 molecular weight (MW) 2 proton affinity (PA) 3 PK, 4 boiling point (at 1 atm) 5 no. of atoms 6 no. of carbon atoms 7 no. of nitrogen atoms 8 no. of basic rings 9 no. of ring atoms 10 molecular connectivity environment at nitrogen 11 path 1 molecular connectivity 12 path 1 molecular connectivity corrected for rings 13 path 1 molecular connectivity corrected for rings and heteroatoms 14 path 2 molecular connectivity 15 path 3 molecular connectivity 16 path 4 molecular connectivity 17 cluster 3 molecular connectivity 18 path cluster 4 molecular connectivity 19 sum of absolute values of all u charges 20 angstrom separation of highest positive and negative u charges 21 approximate u electron density for most electronegative atom 22 molar volume 23 surface area 24 molecular volume
Poisoning Power and Structural Descriptors Fu and SchaEfer (1985)presented data for two different experimental conditions. In the first set of experiments (hereafter referred to as set l), the conversion percentages were measured for 18 nitrogen and aromatic additives using a West Texas Refinery equilibrium catalyst. The amount of additive was adjusted to give an overall 0.5 wt % nitrogen in the feed for additives containing one nitrogen atom. For additives containing two nitrogen atoms, the amount added was such as to give an overall 1 wt 90 nitrogen. For additives not containing nitrogen, Le., benzene, naphthalene and anthracene, the amounts added were the same as the corresponding amounts of pyridine, quinoline, and acridine, respectively. The second set (set 2) of experiments was done in a more controlled way; a series of pyridine derivatives and piperidine were used with a metal-free catalyst at 0.3 wt % nitrogen. To use both seta of data in combination, we define a normalized poisoning parameter called y. The normalization was done for each experimental set relative to the run without any additive present; i.e., y for each poison molecule is defined as follows E loo-I' y=1--- loo-E (1) I'
xij, j = 1-24. Most of them were calculated by using the
where [ is the percent conversion to C430 OF products, and 6' is this value in the absence of addtives. Since [/(lo0 - 5) is a widely used activity function (based on secondorder kinetics) in catalytic cracking, the quantity [(lo0 €')/(lo0 - [)p is a normalized activity. Thus y measures the relative poisoning, or degree of inhibition, due to the additive. A large y means severe poisoning. When no additive is present, y = 0. Obviously, 0 Iy I1. For ease of analysis, we denote yias the poisoning power of the ith additive. The collection of all yisforms a vector Y. As mentioned, our task is to quantitatively related Y to the intrinsic properties of the poison additives. At this point it pays to select as many properties as possible, including different basicity measures, geometric indexes, and electron densities. As detailed below, for each poison
additive i (i = 1-32),we obtain 24 structural descriptors ADAFT (automated data analysis via pattern-recognition techniques) program. The calculations were based on the optimized three-dimensional geometries of the molecules concerned. Descriptions of the descriptors and their number designations are given in Table I; for full details the ADAPTdocuments should be consulted (Jura, 1987).
Calculation of Structural Descriptors Here we briefly describe how the 24 descriptors were obtained. Proton Affinity and pK,. Of course, it would be highly desirable if one has information on the basicity under reaction conditions. Unfortunately, such information is not available. For lack of anything better, we use proton affinity PA and pK, (basicity in aqueous solution) as measures of basicity. The PA values were calculated by the method of Dewar and Dieter (1986)using the following equation PA(B) AHf(H+)+ AHf(B) - A"f(HB+) (2) where the AHf terms are the heats of formation calculated for the proton (H+),free base (B), and conjugated acid (HB+). The values of the heats of formation for the bases and their protonated forms were calculated using the AMPAC version of 2.1 (available from the Quantum Chemistry Program Exchange) and the AM1 Hamiltonian (Dewar et al., 1985). Initial geometry optimization was carried out using the PRXBLD program (Wipke et al., 1972)with final optimization within the MAC package using the DavidonFletcher-Powell method (Fletcher and Powell, 1963;Davidon, 1968). As recommended by Dewar and Dieter (1986),the experimental value of 367.2 kcal/mol (Stull and Prophet, 1971)was used for the heat of formation of H+. These results are summarized in Table 11, along with the corresponding yivalues. The pK, values for the compounds were taken from Perrin (1965)where available. In some cases it was necessary to make estimates based on the effects of the substituents. The pK, values are also listed in Table II. Due to the solvent effects (Taft, 1983),the self-consistency of
Ind. Eng.Chem. Res., Vol. 31, NO. 7,1992 1691 Table 11. Poisoning Power and Properties of Nitrogen and Aromatic Compounde no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34
additive none aniline benzene pyrrole pyrrolidine pyrazine pyridine piperidine naphthalene indole quinoxaline quinoline 1,2,3,4-tetrahydroquinoline 5,6,7,8-tetrahydroquinoline anthracene carbazole 1,2,3,4-tetrahydrocarbazole phenazine acridine none pyridine 2-methylpyridine 2-ethylpyridine 2-methyl-5-vinylpyridine 2-vinylpyridine 2,4-dimethylpyridine 5-ethyl-2-methylpyridine 2,3-cyclopentapyridine 2-p-tolylpyridine 2,6-di-tert-butylpyridine 3-methyl-2-phenylpyridine piperidine 1-ethylpiperidine 2-ethylpiperidine
MW
PA
PK,
ref”
93.13 78.11 67.09 71.12 80.09 79.10 85.15 128.18 117.15 130.15 129.16 133.20 133.20 178.24 167.21 171.24 180.21 179.22
211.1 118.9 215.6 216.9 204.1 215.1 219.9 194.6 211.3 215.2 221.0 215.8 221.6 196.3 210.8 209.9 220.2 228.9
4.63 -14.8 -3.8 11.31 0.65 5.23 11.12 -9.3 -2.46 0.56 4.90 5.03 6.65 -7.80 -6.0 -4.9 1.21 5.58
1 1 1 1 1 1 1 1 1 1 1 1 2 1 3 3 1 1
116 115 106 218 254 223 237 249 218 340 355 330 360 346
79.10 93.13 107.16 119.17 105.14 107.16 121.15 119.17 169.23 191.32 169.23 85.15 113.20 113.20
215.0 219.0 219.9 220.5 220.1 221.8 221.0 220.1 223.3 228.6 223.5 219.9 223.8 220.7
5.15 5.94 5.89 5.67 4.98 6.99 6.51 5.84 5.02 5.02 5.0 11.12 10.45 11.25
1 1 1 1 1 1 1 1 1 1 1 1 1 1
115 129 149 187 160 159 178 215 (88 at 11) 305 (180 at 20) 215 (101 at 23) 280 (148 at 16) 106 131 143
Y
bPb
O.OO0
0.206 0.234 0.160 0.279 0.210 0.247 0.302 0.222 0.299 0.458 0.541 0.552 0.592 0.154 0.238 0.288 0.484 0.621 0.0 0.274 0.347 0.363 0.368 0.381 0.401 0.449 0.474 0.491 0.565 0.592 0.331 0.418 0.446
184 80 131 88
‘References: (1)Perrin, D. D. Dissociation Constants of Organic Eases in Aqueous Solutions; Butterworth London, 1972. (2) Epsztajn, E.; Marcinkowski,T. Cycloalkenes Fused with Heterocyclic Rings Part XXX, Basicity of Cycloalkeno[b]and Cycloalkeno[c]pyridines. Pol. J. Chern. 1979, 53, 601. (3) Carmody, M. P.; Cook, M. J.; Nissanke, L. D.; Katritzky, A. R.;Linda, P.; Tock R. D. Aromaticity and Tautomerism V The Basicity and Aromaticity of Pyrrole, Furan, Thiophene, and Their Benzo Derivatives. Tetrahedron 1976,32, 1769. bAt normal pressure. Where value is given in parentheses, this is the value a t reduced pressure corrected by the nomograph (see text).
the pK, values is expected to be poorer than that of the PA values. Molecular Heaviness/Size/Shape.As a yardstick for the heaviness and size of the additives, one may simply u ~ molecular e weight (Mw)or boiling point (bp). Boiling points (“C)at standard pressure were taken from the AMrich Catalog (1989),where available, or from Beilstein’s Handbook of Organic Chemistry (Springer-Verlag,Berlin). The nomograph published in the Aldrich Catalog (e.g., p 2208 of the 1988-1989 catalog) was used to estimate standard pressure boiling points which were quoted at reduced pressures. Table I1 also contains the values of molecular weight and boiling point. We also used the ADAPT program to calculate other properties related to molecular size, such as molar volume, surface area, and molecular volume. Furthermore, quantities related to molecular “skeleton” or “branchingness” were calculated. These include different molecular connectivity indices (see Appendix A for more details; also refer to the ADAPT documents),some of which may reflect the accessibility of the nitrogen atom. Figure 1 gives an illustrative example of how path 1 molecular connectivity is calculated. Electron Density. The ADAPT program was used to estimate some electronic properties, such as the approximate u electron density for the nitrogen atom and angstrom separation of highest positive and negative u charges (see Appendix A). The values of the descriptors generated by ADAPT are given in Table 111. Note that some of the descriptors distinguish nitrogen compounds from pure aromatics.
1
Path 1 Molecular Connectivity 1
-- -+-+-+-
1
1
1
m f i m m
-2.21
Figure 1. Example of path 1 molecular connectivity.
These include the number of nitrogen atoms (descriptor 7), molecular connectivity environment at nitrogen (descriptor lo), and the approximate u electron density for the most electronegative atom (descriptor 21). We may appear to be overly cautious by choosing some descriptors which seem either overlapping or too simple. We do so with the intent to begin with a relatively robust list of variables and then to significantlynarrow them down using PLS without much loss of information.
Partial Least Squares Analysis The resulting data set for the additives’ structural properties forms a 32 X 24 matrix denoted by X,where 32 is the number of additives, each having 24 descriptors. Invariably, many of the descriptors correlate with each other (i.e., they are not orthogonal to each other). To overcome this problem, we use PLS to find new variables, called latent variables (LVs) (or aggregates as mentioned
1592 Ind. Eng. Chem. Res., Vol. 31, No. 7,1992
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1593 Table IV. Information Content of Latent Variables LV1 LV2 LV3 total
x,%
Y,%
57.42 20.57 3.89 81.88
40.35 11.89 9.22 61.46
in the Introduction), which are mutually uncorrelated. The LVs are linear combinations of the original descriptors and constructed to describe the variances present in both X and Y. While the total number of LVs is 24, a main object of the PLS analysis is to select a minimum number of significant LVs to capture the greatest amount of information in X and Y. Thus PLS not only solves the problem of covariations (or “colinearity”)among xu, but also greatly reduces the “dimensionality” of the problem (Le., approximating the matrix X by a much smaller matrix). Note that the LVs are calculated after proper scalings on X and Y: the elements of X and Y are scaled by subtracting the mean value and dividing by the standard deviation. It is pertinent to remark that PLS is closely related to the well-known principal component analysis (PCA) (see, for example, Sharaf et al. (1986)). Each LV is nothing but a linear combination of the principal components (PCs) from PCA. To find the PCs requires information only on X. (It basically amounts to determining the ei envectors and eigenvalues of the correlation matrix X‘k after a proper scaling, where XT is the transpose of X.) By contrast, the construction of the LVs requires information on both X and Y,which is to say PLS is driven by the relationship between X and Y. A brief overview of PLS is presented in Appendix B. Details of this method can be found elsewhere (Lindberg et al., 1983; Frank et al., 1983; Wold et al., 1987).
Results of PLS Analysis A PLS software package provided by the Center for Process Analytical Chemistry at the University of Washington was used to find a possible linear relationship between Y and X. Note that it is the variances present in Y and X that represent the useful information, since we want to correlate variation in yi with the variation among xi’. The 32 X 24 matrix X has a superficial dimensionality od 24. What we need to do is to contract the dimension without much loss of information. The LVs are obtained in order of decreasing information content. Table IV lists the amount of variance, or information, described by the fmt three LVs. This variance information is provided for both Y and X. As can be seen, the information content of the first LV is described by the ordered pair [57.42%, 40.35%], meaning that this LV accounts for 57.42% of the variance in X and 40.35% of the variance in Y. Hence, the majority of the variance in X is indeed correlated to Y. The corresponding information contents of the second and thiid LVs are [20.57%, 11.89%]and [3.89%, 9.22701, respectively. We do not compute successive LVs. Together, the first three LVs account for 82% of the variance in X and 61% of the variance in Y. This is quite good considering the complexity of the problem (e.g., the effects of different catalysts, feedstock properties, and kinetic variables are not considered) and that PLS is just a linear analysis. As mentioned, each LV is a linear combination of the original descriptors. In other words, each descriptor has a “loading”, or weight (or coefficient), which describes its contribution to the particular LV of interest. The higher the loading (+ or -) of a descriptor, the more that de-
e 9 u)
17
0.15 2
10
7
0.05
-0.05
c
20
3
LV1 21
Descriptor
Figure 2. Loading plot for the first latent variable.
::p3
:iI:
3
10
LV2
7
0.2
19
8- 0.1 o.2
1
Lv2 17
0.0
-I
-0.1 -0.2 -0.3
-
t‘ -
11~~1314 15 4 8 9
ia
23
20
22
1
1 1 24,
16
21
scriptor has in common with the LV in question. We next look at what are the major descriptors comprising each of the three LVs in Table IV. Figure 2 is a plot of the descriptor loadings for the first latent variable, LV1. One sees that quite a few descriptors have high loadings. They include molecular weight, path 1molecular connectivity and its variants, molar volume, surface area, and molecular volume. Other high-scoring descriptors are boiling point, number of atoms (total or carbon), and paths 2 and 3 molecular connectivities. Thus, to a first approximation, LV1 merely reflects the size/ heaviness of the poison molecule. This LV alone explains the majority of the variance in Y, This is hardly surprising; a big molecule should block a large area of the catalytic sites and does not easily desorb from the catalyst surface. Fu and Schaffer’s data showed that the extent of poisoning decreases with increasing temperature. Others have made similar observations (Voltz et al., 1972; Young, 1986). Figure 2 also reveals that molecular heaviness/size actually is a more important factor than basicity. Indeed, Fu and Schaffer found that sterically crowded nitrogen, such as 2,6-di-tert-butylpyridine1 does much more damage than completely accessible nitrogen, such as pyridine. Figure 3 is a loading plot for LV2. Here descriptors measuring basicity (descriptors 2,3, and 21) and accessibility of nitrogen (descriptor 10) all have high loadings. Note that the number of nitrogen a t o m (descriptor 7) also has a high loading, indicating that an important feature of LV2 is to “separate out” pure aromatics from the pool of poisoning molecules. The data of Fu and Schaffer showed that nitrogen compounds, regardless of their type, are much stronger poisons than aromatics. These results, taken together, indicate that LV2 reflects the importance of the basicity of nitrogen compounds. The main source of basicity is apparently associated with the nitrogen sp2 lone pair, suggesting an electronic interaction between the
1594 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 Table V. Values of Rzfor One-DescriDtor Models
0.4 0.5
0.3
R* set
-
1
g) 0.2 -
p
0.1 -1
3
0.0 -0.1
-0.3
*
5 6
-
PA
PK.
bP
0.166 0.656 0.217
0.223 0.041 0.220
0.127 0.634 0.111
11 1213 15
8
4
-
-0.2 -
2 1+2
9
E
MW 0.182 0.831 0.262
16
lo
14
7
17
19
Descriptor
Figure 4. Loading plot for the third latent variable.
nitrogen molecule and the catalyst acidic sites. Note that descriptors relating to molecular size/heaviness all score low on LV2, as expectad from the orthogonality of the LVs. As Figure 4 shows, the loading distribution for the third LV is different from those for the preceding LVs: here one finds a single dominant descriptor-the distance of separation between the highest positive and negative u charges (deacriptor 20) in the molecule. It is not obvious to us how to rationalize this, except to say that this quantity is related to the polarity of the poison molecules. To a lesser extent, LV3 is also influenced by descriptors 17-19. Also, LV3 stands in contrast to LV1 and LV2 in that LV3 conveys much more information about Y than about X (9.22% vs 3.89%). The above results are not sensitive to small changes in the descriptor values. For instance, the values of PA and pK, were "perturbed" by about lo%, and essentially the same results were obtained.
Development of Correlational Model Linear Model. Of c o r n , the simplest possible relation between Y and X is linear. One could use PLS to construct such a linear model baaed on the three latent variables computed in the preceding section. However, this approach does not appeal to us. Inatead, we want to develop an even simpler model based on what we learn from the constituents of the LVs. The resulting model should be more useful from a practical point of view, although it is not as mathematically rigorous as the PLS model. Basically, the PLS results give us two main messages. One is that, to a good first approximation, molecular size/heavinese plays the dominant role in determining the molecule's poisoning power. Another is that basicity is also an important factor, which is primarily associated with the environment near the nitrogen atom. These salient features of the data (X and Y)led us to build a simple model as described below. For simplicity, we use molecular weight, the most easily available measure of molecular size, to approximate LV1. And we choose proton affinity as the basicity index to approximate LV2. Other poasible basicity indexes are not chosen for the following reasons: (1)The pK, values are subject to large uncertainties, (2) the number of nitrogen a t o m is not discriminating, and (3) the nitrogen molecular connectivity is less readily available and not applicable to pure aromatics. It must be emphasized that using MW and PA as the two correlating variables cannot convey all the information contained in the data [see data in Table 2-methyl-4I1 for the pairs (2,3-~yclopentapyridine, vinylpyridine) and (2-p-tolylpyridine, 3-methyl-2phenylpyridine)]. Our objective here is to minimize information loss.
Table VI. Regression Results for Two-Descriptor Linear Models set B m BPI a R 1 0.163 0.451 -0.264 0.279 2 0.263 0.783 -0.651 0.835 1+2 0.192 0.563 -0.379 0.390
The simplest linear model based on MW and PA is of the form for the ith poison yi = a + + (3) with a and ,Bs being model parameters. - The overbar means normalized quantities, that is, (MW)i (MW),/121.68 and (=Ii (PAIJ217.29 where 121.68 and 217.29 are the average molecular weight and proton affinity for the poison additives tested by Fu and Schaffer, respectively. These two normalized descriptors may be viewed as pseudo latent variables which are "nearly" orthogonal to each other. In this regard we note that benzene, pyrazine, and pyridine have almost the same molecular weights, but their PA values show a much greater variation. On the other hand, the PA values of 2-ethylpyridine, 2,3-cyclopentapyridine, and piperidine are close to each other, but their molecular weights are quite different. Before regressing the above linear model, we first test several one-descriptor models. This was done both separately for the two experimental seta of data and also for the combined set. Table V lists the correlation coefficients R2 for models based on one of the following descriptors: MW, PA, pK,, and boiling point. As can be seen, a onedescriptor linear model in general is unacceptable. The only exception perhaps is with set 2 for which MW provides a relatively high R2 value, suggesting a linear relationship between poisoning and MW. The range of the data is relatively narrow, however. Recall that set 2 contains a series of pyridine derivatives and piperidine. We next carry out multiple linear regression analysis using MW and PA as the descriptors. Again, data seta 1 and 2 were considered separately and in combination. The descriptors were fitted to eq 3. The values obtained for the constant a and the coefficients ,B are shown in Table VI, along with the R2 value. As expected, the two-descriptor model gives a better fit, but the improvement is marginal. For the combined sets, we note an R2 value of 0.390 which is still too low. The advantage of using PLS can be seen as follows. Had we used the three true LVs as the correlating variables, we would have obtained a linear model with an R2 value of 0.615, a significant improvement over 0.390. To obtain a fit better than an R2 value of 0.615, we need to use a nonlinear model. Given the complexity of the problem, there is no a priori reason why a "perfect" linear relation should exist between Y and X. Nonlinear Model. We used a leaps and bounds (Furnival and Wilson, 1974) regreasion analysis, performed by ADAPT,to find the best polynomial models with PA and MW as the descriptors. Terms up to the fourth order were tested. The terms used in various polynomials included: second order, MW2, (MW)(PA), PA2; third order, MW3, (MW2)(PA),(MW)(PA2),and PA3; fourth order, MW',
,BMw(mIi
0.6
-
0.5
-
0.4
-
250.00
I/
0.7
220.w
c
190.00
Y
C LI
2
0.3 -
0.1 0.1
0.2
0.3
0.4
0,s
fl.6
0.7
OBSERVED
Figure 5. Plot of observed vs predicted poisoning for a nonlinear two-descriptor model. R2 = 0.788.
0
1100 30W DO50 00
80 00
1IO
00
l*OOO
17000
zw 00
MDlecular Weight
(MW3)(PA),(MW2)(PA2),(MW)(PA3),and PA4. A total of 63 different polynomials were evaluated. In addition, a power law model of the form
--
y = K(MW~)(PAW)
(4)
was also considered. One requirement here is that we want to minimize the number of parameters while capturing the salient aspects of the data. The best model so found takes the following form y = 0.075 + 0.7351(MW2)(FX2)- 0.4067(MW3) (5) with R2 values of 0.758 and 0.872 for the two data sets 1 and 2, respectively. For the combined set, an R2 value of 0.788 was obtained. A parity plot for this model is shown in Figure 5. Figure 6 is a contour plot of the poisoning values plotted against MW and PA. Elpition 5 and Figure 6 indicate that, a t a constant MW, poisoning always increases with increasing PA. At a constant PA, poisoning increases with MW, but only up to a certain point beyond which poisoning starts to decrease with increasing MW. An obvious explanation is that large molecules will have difficulties penetrating into the zeolite channels. When they do get in, their diffusion rates will be so slow that the interior part of the channels may not be poisoned. Fu and Schaffer's data showed that anthracene, despite its higher basicity, is less damaging (y = 0.154) than benzene (y = 0.234). Also, phenazine (PA = 220.2, y = 0.484) is less harmful than quinoline (PA = 221.0, y = 0.541). As can be seen from Figure 6, the diffusion effect becomes less pronounced for compounds of high PA. In the set 2 experiments, the nitrogen compounds all have relatively high PA values. Summarizing, the nonlinear model represented by eq 5 captures the essential features of Fu and Schaffer's data over a wide range of conditions. The y value may be regarded as a surface coverage by the poison molecule. To a first approximation, it depends on a balance between molecular weight and proton affinity. The former could be loosely argued to reflect the mobility of the poison molecules, while the latter reflects the tightness of the bonding between the adsorbent and adsorbate. LaVopa and Satterfield (1988) in their hydrodesulfurization (HDS) studies found a linear correlation between proton affinity and heat of adsorption.
Concluding Remarks As allued to earlier, many investigators in catalytic cracking have used proton affinity as the most important
Figure 6. Contour plot of predicted poisoning values using eq 5.
measure of nitrogen compounds' poisoning potency (Fu and Schaffer, 1985; Corma et al., 1987). A similar conclusion has also been reached in HDS catalysis (Nagai et al., 1986; LaVopa and Satterfield, 1988). This type of poisoning is basically chemical in origin because of an acid-base interaction. Our analysis of Fu and Shaffer's data identifies another more important factor which is primarily physical in nature; that is, the size/heaviness of the poison molecule. A large molecule can block a large area of the acidic sites on zeolite and does not easily desorb. Of course, a very large molecule, no matter how basic it is, will not be able to diffuse into the zeolite pores. (But it might still cause some damage by choking or encapsulation of the pores.) In the HDS experiments carried out by Nagai et al. (1986) and LaVopa and Satteflield (1988),the effects of pore diffusion are most likely insignificant because the pores are much larger than those in zeolites. One implication of the present results for process modeling is that it may pay to characterize and consider the different nitrogen compound classes in commercial feedstocks.
Acknowledgment We are grateful to S. L. Soled and K. Osmialowski for their help in using the software and organizing the database in Table 111.
Nomenclature
A = coefficient matrix in the linear model defined in eq B3 bp = boiling point B = intercept matrix in the linear model defined in eq B3 i = index to label poison molecules, i = 1,2, ..., 32 j = index to label structural descriptors, j = 1, 2, ..., 24 MW = molecular weight MW = normalized molecular weight PA = proton affinity PA = normalized proton affinity PCA = principal component analysis PLS = partial least squares LV1 = first latent variable LV2 = second latent variable LV3 = third latent variable nx = molecular connectivity index order
1596 lnd. Eng. Chem. Res., Vol. 31,No. 7, 1992
volves summing the occupied volume of each atom in the molecule. This is designated in Table I as descriptor 22. Molecular surface area and volume descriptors are calculated by the SAVOL program. This is the version of a program developed by Pearlman and available as QCPE program No. 413 (Pearlman, 1981). Atoms are considered as spheres of the appropriate van der Waals radius, taking into account all overlaps between spheres. These two descriptors are designated in Table I as 23 and 24.
P = projection (or loading) matrix, eq B1
Q = projection (or loading) matrix, eq B 2 X = data matrix composed of descriptor values x . . = components of X = matrix from projection of x onto a lower dimension space, eq B1 XT = transpose of matrix X Y = vector or matrix composed of dependent variables (e.g., poisoning power) xi = poisoning power of the ith poison molecule Y = matrix from projection of Y onto a lower dimension space, eq B2
B
Appendix B: Overview of the PLS Method The purpose of PLS is to contract the dimension of the problem (with minimal loss of information) and to build a linear model relating Y and X. Suppose that X is an n X p matrix, with p < R. The contraction of ita dimension is done by a projective transformation. By this we mean that X is multiplied by a projection, or “lumping” matrix P (with dimension p X q and q < p ) to form a new matrix X of lower dimension ( n X q). That is, X=XP (B1)
Greek Symbols intercept in the linear model, eq 3 = coefficient for M W in the linear model, eq 3 BPA = coefficient for PA in the linear model, eq 3 y = exponent of M W in the power law model, eq 4 AHf = heats of formation, eq 2 K = coefficient in the power law model, eq 4 [ = percent conversion to
