Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 995-999
Literature Cited
995
Huff, 0. A., Jr.; Satterfieid, C. N. I n d . Eng. Chem. Process D e s . Dev. i m a , 23,696. 0, A., Jr,; satterfield, c, N. J , catel, 1884b, B5, 370. Zwolinski, B. J.; Wiiholt, R. C. "Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds"; Thermodynamics Research Center: College Station, TX, 1971.
Anderson, R. B. "Catalysis IV"; Emmett, P. H., Ed.; Reinhold: New Y o k , 1956; Chapter 2. Anderson, R. 6.; Karn, F. S.:Shuitz, J. F. Bull-U. S . Bur. Mines lSS4, No. 614, 1. Dictor, R. A.; E d , A. T I d . Eng. Chem. Process Des. D e v . 1883, 2 2 , 678. Dry, M. E. I n "Catalysis--Science and Technology 1"; Anderson, J. R., Boudart, M., Eds.; Springer-Verlag: New York. 1981; Chapter 4. Huff, G. A,, Jr. Sc.D. Thesis, M.I.T., Cambridge, MA 1982.
Received f o r review June 25, 1984 Accepted December 17, 1984
Techniques for Evaluating Heavy Oil Cracking Catalystt George W. Young* and Kuppuswamy Rajagopalan W. R. Grace & Company, Davlson Chemical Division, Columbla, Maryland 21044
The influence of matrixdiffusion resistance in heavy oil cracking was investigated experimentally and theoretically for vapor and liquid reactants. Experimental results suggest that matrix diffusion is not the rate-limiting step in the cracking of heavy oil components by commercial catalysts. A commercial feedstock was cut into three fractions with differing boiling ranges. Cracking of the feed cuts by four commercial catalysts was then studied. Chromatographic simulated distillations of heavy oil feeds and cracked products were also examined. All commercial catalysts used in the experiments cracked the heavier fraction of the feed more rapidly than the lighter fraction. Relative activity for cracking the heavier fraction of the feed with respect to the llghter fraction as well as selectivity for the production of coke and H, can be correlated with the surface area of the catalyst matrix.
With the ever increasing cost and difficulty of obtaining high-quality crude for FCC operations,' some 37% of US refineries were processing resid and other heavy oil stocks in their FCC feed by 1982 (Thiel, 1983). The presence of the heavy oil can present several problems for the catalyst. Some of the actual observations of commercial operations are documented by Thiel, and these indicate a significant drop in equilibrium catalyst activity combined with a 4fold increase in contaminant metals such as nickel and vanadium (Table I). Other consequences of processing heavy oil include an increase in Conradson carbon and basic nitrogen, both of which will have adverse effects on catalyst performance caused by increased coke loads and poisoning of acid sites. In face of such problems, both catalyst user and supplier are faced with trying to predict how a catalyst will perform under these unusual conditions and to devise catalysts that will give an economic advantage to the processing of heavy oil. From the processing point of view, several different options are available. One of the earliest successful attempts at processing heavy oils was that of Phillips Petroleum who, in cooperation with M. w. Kellogg, developed the HOC process which has been in operation at Phillip's Borger, Tx,refinery since the early 1960s. Since that time, Ashland Oil has developed their RCC process and after successful pilot plant demonstration constructed a 40 000 B/D unit in Catlettsburg, KY, which went on stream in 1983 (Zandona et al., 1982). Other innovative processing methods have recently been reported by Total Petroleum (Dean et al., 1982) at their Adrmore, OK, refinery. The main features of their approach are to use high regenerator and reactor temperatures along with improvements in feed nozzles and a two-stage regenerator design. A different
Table I. Summary of Catalyst Usage Rates and Quality (Resid Operations)" atm vac bottoms bottoms DAO HGO tot catal additns, lb/bbl 0.412 0.423 0.228 0.231 0.347 Equilibrium Catalyst Quality microactivity V % 64.5 68.7 66.9 72.0 66.5 Ni, ppm 1550 1400 1250 650 1350 v, PPm 2200 2100 1700 900 1950 Cu, ppm 60 40 40 50 45 Fe, wt % 0.64 0.62 0.51 0.57 0.60 Na, w t % 0.59 0.64 0.50 0.58 0.58 aSource: Thiel, P. G. "Davison Resid Survey"; 1983; W. R. Grace & Co.: Baltimore, MD Catalgram no. 66.
approach by Englehard attempts to upgrade the feed by means of their ART process in which it is claimed that contaminant metals and high Conradson carbon can be reduced by a precracking contact with a low cracking activity scavenging material (Bartholic and Haseltine, 1981). Despite these process improvements, the key to profitable FCC operations is the catalyst used in the process, and there exists almost no information in the literature on how typical cracking catalysts will perform with the heavy oil feeds. The evaluation of cracking catalyst performance for commercial viability has traditionally been accomplished by cracking a midboiling-range (600-900 O F ) gas oil. The catalyst performance is then determined by measuring, at specific conditions (temperature, WHSV, c/o), the quantities of useful liquid products, gas, and coke generated. Since a refiner is usually interested in gasoline, gas, and coke, anything leftover is considered to be unconverted feed. From this "unconverted" feed, distillation can recover a light cycle oil (LCO, 430-640 O F ) for diesel fuel and a heavy cycle oil (HCO, 640-t-O F ) for no. 6 fuel oil. Ciearly the performance of a cracking catalyst is based on how
Based on a paper presented at the 186th National Meeting of the American Chemical Society, Washington, DC, Aug, 1983. 0198-4305/85/ 1124-0995$01.SO10
0
1985
American Chemical Society
996
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
i11
lo
C3 Zeolite Particulates
Figure 1. Commercial cracking catalyst.
much gasoline, gas, and coke can be produced from a given feedstock at specified conditions. While this is an oversimplification and ignores such things as quality of product (octane, API gravity, etc.), from a refiner's point of view, the economics of his business can be sufficiently condensed with data of these kind. From a technical point of view, this analysis of catalyst performance can also be acceptable since it is common practice to use lumping techniques with complex, multicomponent systems (Weekman, 1979). The above approach represents the simplest model for the cracking reaction; the oil feed is a single reactant lump. Thus, a complex reacting system has been reduced to simple terms and classical kinetic, mechanistic, and evaluation techniques can be used to gain understanding and predict performance for engineering scale up. There has been some work that reports on feed effects (Nace et al., 1971; Upson and Sikkan, 1982),and there has been a substantial amount of work that addresses the influence of nitrogen poisoning and the effects of contaminant metals on zeolitic cracking catalysts (see, for example, Venuto and Habib, 1979; Mitchel, 1980; Letzsch and Wallace, 1982). We intend to focus this discussion specifically on the crackability of heavy oils and the role of catalyst properties in heavy oil cracking. Experimental Methods Catalysts chosen for these studies were all commercial catalysts; some of the testing for diffusion-limiting effects was performed on equilibrium samples of a catalyst from a commercial FCC, but the majority of the testing used a variety of laboratory steam-deactivated catalysts. The deactivation conditions were 1350 O F in 2 atm of steam pressure for 8 h. All the activity testing was performed in fixed-bed microactivity test units as described in the ASTM D3907 procedure. Liquid syncrude analyses were handled by using simulated distillation (ASTM D2887) as implemented on the Hewlett-Packard HP5880A gas chromatograph. We modified the H-P software to permit us to monitor the 900+ O F lump on syncrudes and feeds. Coke analyses were done with a Leco WR12 instrument; gas analyses were handled by routine gas chromatography. Nitrogen porosimetry was performed by using a Micromeritics DigiSorb 2500, and mercury penetrometry data were obtained with a Quantachrome scanning porosimeter (60000 psi range). Distillation data were obtained by using ASTM D1160 and D2887 procedures. Evaluation of Heavy Oil Diffusion in Commercial Catalysts Commercial cracking catalysts are microspheroidal (40-120-pm diameter) particles containing zeolite particulates (about 1 pm diameter) dispersed in a porous amorphous matrix as illustrated in Figure 1 (Venuto and Habib, 1979). The conversion of crude feedstock to the desired lighter boiling products in a commercial catalytic cracker involves diffusion of the reactant through the matrix to the active sites within a catalyst particle. High molecular weight reactant molecules in heavy oil diffuse through the cracking catalyst at a slower rate than reac-
10
100
1000
10000
Pore Diameter A
Figure 2. Differential pore volume distribution of an equilibrium cracking catalyst.
tants present in light gas oil (Reid et al., 1977). Equilibrium cracking catalysts exhibit porosity over a wide range of pore radii from less than 10 to 5000 8, (Figure 2). Nitrogen sorption has routinely been used for the determination of pore size distribution for pores in the radius range 10-300 A, while mercury intrusion can cover the radius range (in 40-120 pm particles) 20-5000 A. A combination of the methods can be used to measure specific pore volume (V) and the pore volume distribution function (dV/dr) for an equilibrium catalyst particle. Fractional void space t in a catalyst particle is expressed in terms of skeletal density p and specific pore volume. PV
e = -
1
+pv
The fraction of porosity, f(r) dr in the range of pore radius between r and r + dr can be derived as
Since the pore volume associated with the zeolite is in the pore radius range below 10 A and can be considered small compared to the total pore volume, the pore volume averaged radius (r,) of the matrix of a cracking catalyst can be defined as r, = J y r f ( r ) dr
(3)
The limits have been chosen to exclude zeolite contribution and inter-particle void space. Molecular diameters of asphaltenes in resid can vary from 10 to 100 A, and the diffusion of large molecules through pores of a cracking catalyst can be hindered (Spry and Sawyer, 1975). The ratio of the cross-sectional area of the reactant molecule to that of a pore of radius r is a measure of this hindrance caused by the pore wall. The fraction of open area available for diffusion, ( H ( r ) )is given, for a molecule of diameter Q, by eq 4.
z) 2
H(r) = (1 -
(4)
Effective diffusivity De, of vapor-phase reactants through the matrix of an equilibrium catalyst can be estimated by the method described by Satterfield (1970). Effective diffusivity depends on molecular diffusivity, DAB, and Knudsen diffusivity, DK,both of which can be calculated for model reactant and product compounds. The Satterfield expression can be corrected for hindered diffusion by using eq 4 to yield
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 997
Particle Size Experiments on Commercial Catalysts Screening a catalyst into different size fractions and testing them on a commercial midcontinent heavy feed can detect matrix diffusion limitations, since increasing the catalyst particle size from 40 to 120 pm results in increasing the diffusion resistance defined as the square of the Thiele modulus by a factor of 9. Different particle size fractions of commercial catalysts were obtained by micromesh screening and were characterized as shown in Table 11. The catalyst fractions were tested on two different feedstocks (A and B, Table 111) selected to detect possible matrix diffusion limitation during either predominantly vapor-phase cracking or during dominant liquid-phase cracking. The vapor-phase test was performed by microactivity testing (ASTM D3907) each particle size on catalyst A, using feed A (Table 111), at the following test condition: T = 930 O F , weight hourly space velocity (WHSV) = 16, catalyst-to-oilratio (c/o) = 2. The results (Table IV) show no systematic increase in conversion with decreasing particle size which indicates the absence of vapor-phase diffusion limitations. The liquid-phase test was similar except feed B was used at a reactor temperature of 800 O F , WHSV = 16, c/o = 2 and 3. Results (Table V) again showed no systematic increase in conversion with decreasing particle size for any of the three catalysts tested. This experimental result suggests the absence of diffusion limitation for commercial cracking catalysts in the liquid phase and is contrary to our theoretical expectation. Conversion of reactants in heavy oil cracking results in molar expansion and reduction in partial pressure of the heavier portion of the feed (e.g. TBP >900 OF). Vaporization of the heavier feed improves as the feed is converted during the process as illustrated by thermodynamic calculations by using the Soave-Radlich-Kwong method. These calculations suggest that none of the feed is vaporized at the reactor inlet under the conditions of the liquid-phase experiment. However, at 65 w t % conversion, 74 wt % of the unconverted feed is vaporized. Therefore, the liquid-phase diffusivity expression may not represent diffusivity of the heavier portion of the feed throughout the cracking reactor. Under these conditions, the effective diffusivity of the heavier portion of the feed could be higher than that predicted by eq 6, and this could be the cause of the disagreement between theoretical prediction and experimental results. Inspection of eq 6 suggests that if diffusion of heavy oil reactants was rate-limiting, then the effect is minimized by increasing the pore volume, V ,and volume average pore radius, rv, defined by eq 3.
Table 11. Experimental Test of Diffusion Control catal properties type matrix vol av pore diam, 8,
catal
A, A2 B1
equilib lab-steamed" lab s t e a m e e
450 450 80
'Steamed 8 h at 1350 O F , 30 psia steam.
The function F(r) depends on the molar expansion due to cracking as well as the ratio of molecular-to-Knudsen diffusivity and is given by Satterfield (1970). Porosity c and fractional porosity distribution f(r) dr can be calculated by using eq 1 and 2; T is the tortuosity, and a value of 3 is reported by Satterfield as typical for cracking and catalysts. Dm was estimated to be of the order at the integral to be of the order of lo-' for a commercial equilibrium catalyst. Hindered diffusion of hydrocarbon liquid molecules through amorphous silica-alumina catalyst pores was measured by Satterfield et al. (1973). Based on their empirical correlation, we can derive an expression for effective diffusivity, Del, of a liquid reactant through a cracking catalyst matrix as
Del =
D 7
5000 012
10-('/r)f(r) dr
where Do is the bulk diffusivity which depends on the liquid molecular weight, molecular diameter and temperature and is catalyst-independent. Procedures described above were used to obtain order of magnitude estimates for the diffusivity of vapor and liquid reactants through a typical commercial cracking catalyst matrix at 950 O F as and lo-' cm2/s, respectively. The same procedure cannot be used to determine diffusivity within the zeolite channels; zeolite diffusivity, however, is expected to be several orders of magnitude lower than diffusivity through the matrix. A cracking reaction rate of lo4 g mol/cm3 of catalyst/s was observed in the laboratory with a commercial catalyst and feedstock at 950 O F . Variations in observed reaction rates among commercial catalysts were less than an order of magnitude; the particle diameter range of commercial catalysts is 40-120 pm. When these values were used the Weisz-Prater parameter (Weisz and Prater, 1954), 8, was calculated to be of the order of for vapor-phase reactants and 10 for liquid reactants. Calculated values of 0 suggest that cracking of vapor-phase reactants in heavy feeds is not matrix diffusion limited, whereas matrix diffusion may be a rate-determining step for conversion of liquid reactants. Table 111. Feedstock Distillation ASTM D1160
F Gulf Coast feed
IBP 5V% 10 20 30 40 50 60 70 80 90 95 FBP
APIO
A vap test, OF 399 572 634 707 763 827 897 964 982 (64%) distil stopped
23.9
B liq teat, OF 658 883 908 925 931 953 970 990 1005 1025 (78%) distil stopped 21.7
C light cut, O F 381 467 497 527 555 581 604 624 643 666 699 732 771 28.7
D mid cut, 632 703 720 742 763 782 800 819 833 856 879 895 902 22.8
O F
E heavy cut, OF 678 913 928 951 971 980 (39%) distil stopped
15.0
feed, O F 359 516 568 648 709 756 802 847 909 969 982 (85%) distill stopped 24.8
998
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985
Table IV. Vapor-Phase Test with Feed A" part size, Km catal A, std. convers, V %
126 67
68 64
90 65
53 63
" T = 930 OF, WHSV = 16 h-l, c/o = 2. Table V. Liauid-Phase Test with Feed Bo
catal A,* std. convers, V % catal A2 std. convers, V % catal B std. convers, V %
" T = 800
OF,
126 54 75 72
part 90 54 68
0
size, Mm 68 53 51 69 71 72
37 52 69 76
WHSV = 16 h-,, c/o = 3. *Tested a t c/o = 2.
65
-
7 OOY900 'F 9000+ Feed Cut Portion Figure 3. Conversion vs. feed cut range: catalysts of various zeolite/matrix ratio. IEP-7OO0 F
Table VI. Feed Cut Crackability. Catalyst Properties" 0 15
catalvst zeolite area, m2/g matrix area, m2/g avmatrixpore diam, A
w
x
Y
Z
185 32 450
44 75 187
21 100 160
35 200 81
"Catalysts steamed: 8 h, 1350 O F , 30 psia steam pressure.
Laboratory Methods for Evaluating Heavy Oil Crackability We have presented a discussion on the role of diffusion in heavy oil cracking and described the direction in catalyst properties that will tend to minimize the influence of diffusion. We can now turn our attention to the question of feed crackability and the task of predicting how real-life catalysts will perform in the face of high proportions of high-boiling heavy oil. In this section, we discuss two techniques for the determination of heavy oil cracking by commercial catalysts. In the first technique, we tested several different commercial catalysts by the conventional microactivity test (MAT) but used, as feeds, different distillation cuts from a whole Gulf Coast heavy feed. The feed cuts had boiling ranges of IBP-700,700-900, and 900-FBP O F , feed properties are given in Table I11 (feeds C, D, and E). The catalysts chosen for testing were steam-deactivated and were selected to represent a wide range of physical properties and zeolite content after steaming (Table VI). W was a high zeolite content catalyst with a low-matrix surface area. Catalysts X and Y had similar total surface area but Y contained less zeolite and slightly greater matrix surface area than X. Z contained a zeolite level intermediate to X and Y but had a very high matrix surface area. When tested by standard MAT (standard Davison microactivity), W had the highest activity and x, Y, and Z were of equal, but lower, activity. These catalysts were tested at a reactor temperature of 930 O F , WHSV = 32, c/o = 3, with each of the feed cuts. Conversion to gasoline-range products (as defined in ASTM D3907), yields of hydrogen, and yields of coke were monitored, and the results are shown in Figures 3-5. On the lightest feed fraction (feed C), catalyst W had the highest activity and highest coke yield. X and Z (similar zeolite level) had the same conversion and coke, but Z showed higher hydrogen. Y, the lowest zeolite content catalyst, had the lowest conversion. On the intermediate feed cut (feed D), the most striking results were the significant decrease in activity of all catalysts especially W. Coke and hydrogen yields increased generally. The results with the 900 OF plus feed (feed E) indicate a surprising reversal of activity ranking. W, the high zeolite content catalyst, showed the lowest activity and the lowest hydrogen and coke yields. On the other hand, catalysts
Legend:
s
0 Catalyst W
9 0.10 Iy >
-
Catalyst X OCatalyst Y .Catalyst 2
2 0.05 I
0.00 L IBP-700°F
I
700-900°F Feed Cut Portion
1
900" 4
Figure 4. Hydrogen vs. feed cut range: catalysts of various zeolite/matrix ratio. 12 10
2 0
IEP-700" F
I
700-9OOoF Feea Cut Portion
j 900".
Figure 5. Coke vs. feed cut range: catalysts of various zeolite/ matrix ratio.
X, Y, and Z all showed similar, very high conversion (catalyst Y may be marginally lower than X or Z). Hydrogen and coke yields were all increased. These observations can be qualitatively explained in terms of the known catalyst properties. Increasing the zeolite content (W) appears to maximize the gasoline conversion from the lighter feeds; however, as the feed gets heavier, diffusion in the zeolite becomes rate-limiting and activity can decline. The hydrogen-transfer rate should also be higher with the higher zeolite level and thus give rise to lower hydrogen yields. Judging from the results with feed E, a modest increase in the matrix surface area (catalysts X and Y) is very effective for the conversion of the heavy oil. When a high-volume average diameter for matrix pores is maintained, not only is the possibility of diffusion limitation in the matrix minimized, but stripping of hydrocarbons from the spent catalyst is facilitated. The influence of the matrix area is most clearly seen from the results on feed E where the three higher matrix area catalysts gave higher conversion than W. But it is not enough to just provide the proper matrix (surface area, pore diameter) since the ratio of zeolite-to-active matrix will greatly influence the selectivity characteristics of the
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 4, 1985 999
._ Standard Conversion X,
Figure 6. Selective bottoms conversion comparison o f catalyst families: Gulf Coast feed.
finished catalyst. This is partially demonstrated by comparing hydrogen yields. On the lighter feeds (Cand D), hydrogen yield is directly related to the amount of active matrix in the catalyst. On the heavy feed (E), catalyst Y, which has the lowest zeolite content, produced the highest hydrogen. At a high zeolite/matrix ratio, gasoline is expected to be favored but heavy oil cracking is not maximized. At some intermediate ratio (Catalyst X), the benefits of high heavy oil cracking and maximum liquid products (gasoline plus LCO) can be realized while minimizing the risk of unstripped hydrocarbons adding to the coke load in the regenerator. While the results obtained above give important insight to crackability, the experimental technique is very timeconsuming, especially when one is interested only in the heavy oil crackability. We have developed a simpler, alternative technique which uses a whole feed and an extended simulated distillation (ASTM D2887) to monitor the 900+ O F lump in the feed and product. Thus, the standard conversion, X,, as well as the bottoms conversion, Xb (defined as W% conversion of the 900+ O F lump), can be measured. With this method, catalyst families can be identified by plotting Xbagainst standard conversion for family members. Here we define a family to be a series of catalysts with the same composition matrix and zeolite but differing in zeolite/matrix ratio. Typical results of this technique are shown in Figure 6 for two different families tested on a Gulf Coast heavy gas oil (feed F, Table 111) at T = 930 O F , WHSV = 16, c/o = 3. While both catalysts clearly converted the heavy oil portion of the feed selectively (bottoms conversion greater than standard conversion), family B showed the higher bottoms activity. These results also show that as the standard conversion decreases, the difference between catalyst families increases. Using this technique, we can rapidly screen catalysts for heavy oil crackability. When differences in Xb at a given standard conversion are small, then emphasis can be placed on testing for other selectivity differences such as gasoline, coke, dry gas, etc.
Conclusions Despite theoretical predictions that diffusion limitations may exist in liquid-phase cracking, experiments designed to exaggerate liquid-phase cracking indicated a diffusionfree regime. This implies that improvement in cracking catalyst activity for resid applications cannot be obtained by merely adjusting the pore size distribution of the catalysts tested. On the other hand, experiments with catalysts exhibiting a wide range of zeolite and amorphous activity indicate that the heavy end of a resid feed is more easily cracked with active amorphous catalyst than with zeolite alone. The interpretation is that cracking within zeolite crystallites is diffusion-limited. Test results also suggest that while some amorphous activity is beneficial for "bottoms" conversion, too much results in a degradation of product selectivities. Nomenclature DAB= binary molecular diffusivity, cm2/s De, = effective diffusivity of reactant in liquid phase, cm2/s D , = effective diffusivity of reactant in vapor phase, cmz/s Do= bulk diffusivity of liquid reactant, cmz/s T = reactor temperature, O F V = specific pore volume of catalyst, cm3/g r = radius of pore, 8, rv = pore volume averaged pore radius, A Greek Letters t = catalyst porosity u = molecular diameter of reactant, A p = skeletal density of the catalyst, g/cm3 T = tortuosity factor for the catalyst
Literature Cited Barthoiic, D. B.; Haseltine. R. P. National Petroleum Refiners Association Annual Meeting, Am-81-45, March 1981. Dean, R. E.; Mauleen, J. C.; Letzsch, W. S. Oil Gas J. 1982, 80 (40), 75. Letzsch, W. S.;Wallace. D. N. 011 Gss J. 1982, 80 (48), 58. Mitchel. 6. Ind. Eng. Chem. Process Des. D e v . 1980, 19, 209. Nace, D. M.; Voltz, S. E.; Weekman, V. W. Ind. Eng. Chem. Process Des. Dev. 1071, 70 (4), 530. Reid, R. C.; Prausnltz, J. M.; Sherwood, T. K. "The Properties of Gases and Liquids"; McQraw-Hili: New York, 1977. Satterfield, C. N. "Mass Transfer in HeterogeneousCatalysis"; M.I.T. Press: Cambridge, MA, 1970. Satterfieid, C. N.; Cotton, C. K.; Pitcher, W. A,, Jr. AIChE J. 1973, 79, 628. Spry, J. C.; Sawyer, W. H. Paper presented at the 68th Annual AIChE Meeting, Los Angeies, CA, Nov 1975. Thiei, P. G.;"Resid Survey", W. R. Grace & Co., Davison Chemical Division: Baltimore, MD, 1983 Catalgram no. 66. Upson, L.; Sikkan, R. Appl. Catal. 1982, 2 , 87. Venuto, P. 6.; Habib, E. T. "Fluid Catalytic Cracking with Zeolite Catalysts"; Marcel Dekker: New York, 1979. Weekman, V. W. "Lumps, Models, and Kinetics in Practice"; AIChE Monogr. Ser. 1979, No. 7 5 , 11. Weisz, P. 6.; Prater, C. D. Adv. Card. 1954, 6 , 143. Zandona, 0.J.; Hettinger, W. P.; Busch, L. D. Paper presented at the 47th API Refining Meeting, New York, May 13, 1982.
Received for review M a y 21, 1984 Accepted December 7, 1984
