different classes of alcohols generated in this work, it is now possible to predict reverse osmosis separations of many alcohol solutes from data on membrane specifications given in terms ~ NaCl only. This predictability is illusof A and D A M / Kfor trated in this paper for the C1 to C g alcohols using cellulose acetate membranes of different surface porosities. This prediction technique can be extended to a wide variety of organic solutes in aqueous solutions where reverse osmosis separations are governed by polar, steric, and/or nonpolar effects and preferential sorption of water at the membrane-solution interface. This possibility opens new areas of reverse osmosis investigations involving a wide variety of organic solutes many of which are of practical interest from the point of view of water pollution control.
Matsuura, T., Bednas, M. E., Dickson, J. M., Sourirajan, S., J. Appl. Polym. Sci., 18, 2829 (1974a). Matsuura. T., Bednas, M. E., Sourirajan, S., J. Appl. Polym. Sci., 18, 567 (1974b). Matsuura, T., Dickson, J. M., Sourirajan, S., lnd. Eng. Chem.,Process Des.Dev., 15, 149 (1976). Matsuura, T., Pageau, L., Sourirajan, S., J. Appl. Polym. Sci., 19, 179 (1975). Matsuura, T.. Sourirajan, S., J. Appl. Po/ym. Sci., 15, 2905 (1971). Matsuura, T., Sourirajan, S., J. Appl. Polym. Sci., 16, 2531 (1972). Matsuura. T., Sourirajan, S., J. Appl. Polym. Sci., 17, 1043 (1973a). Matsuura. T., Sourirajan, S., J. Appl. Polym. Sci., 17, 3661 (1973b). Matsuura, T., Sourirajan, S..J. Appl. Polym. Sci., 17, 3683 (1973~). Pageau, L., Sourirajan, S., J. Appl. Polym. Sci., 16, 3185 (1972). SOUrirajan, S., "Reverse Osmosis," (a) Chapter 1; (b) Chapter 3, Academic Press, New York, N.Y., 1970. Taft, R. W., Jr.. in "Steric Effects in Organic Chemistry." M. S. Newman. Ed., pp 556-675, Wiley. N.Y.. 1956.
Received for review January 28,1976 Accepted August 6,1976
Literature Cited Duvel, W. A,, Jr., Helfgott, T., J. Water Poll. Conk Fed., 47, 57 (1975). Kesting, R. E., Eberlin, J., J. Appl. Polym. Sci., 10, 961 (1966).
Issued as NRC
No. 15671.
A Kinematic Model for an Adiabatic Transfer Line Catalytic Cracking Reactor Y. T. Shah, G. P. Hullng, J. A. Paraskos,' and J. D. McKinney Gulf Research and Development, Harmarville, Pennsylvania 15230
This paper presents a kinematic mathematical model for an adiabatic commercial transfer line fluid catalytic cracking reactor in which both catalyst and reacting fluid move at the same velocity under plug flow conditions. The model assumes that the catalyst activity is a strong function of contact time but that it is essentially independent of temperature. The model includes a single heat parameter which involves the endothermic heat of reaction. It is shown that the nature of the conversion function, l l y 1, where y is the reactant or gas oil fraction within the reactor, vs. flowing space time plot as reported earlier by Paraskos et al. (1976) remains unchanged by the heat parameter. The value of l l y 1 at given space time is, however, changed considerably by nonisothermal operation if the activation energy for the gas oil and gasoline reactions are different. The validity of the model is examined using data obtained from a 99 ft long commercial adiabatic transfer line reactor.
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Introduction In a recent paper, Paraskos et al. (1976) presented a kinematic model for an isothermal transfer line reactor for fluid catalytic cracking. The transfer line reactor is a moving bed reactor in which catalyst particle size is very small and gas velocity sufficiently high, so that both catalyst and gas move at essentially the same velocity and in the plug flow regime. The model outlined by Paraskos et al. (1976) assumed an exponential decay in catalyst activity with respect to flowing space time. For a given reactor temperature, gas oil conversion was assumed to be a unique function of the flowing space time, which is a product of the contact time and catalyst-to-oil ratio. The commercial transfer line reactor is operated under adiabatic conditions. Cracking is an endothermic reaction so that the temperature of the fluid in the reactor decreases with an increase in space time. In this paper we outline a kinematic model for the adiabatic transfer line reactor. The importance of the key independent parameters appearing in this model under prevailing commercial reaction conditions is evaluated and discussed. An approximate solution to the model is presented. The model is then applied to data taken in a commercial, adiabatic transfer line reactor.
Theoretical As assumed by Paraskos et al. (1976), the kinetics of the cracking reaction can be modeled by a three-component system, namely gas oil, gasoline (430 OF T B P end point), and C4 and lighter gases plus coke. The reaction mechanism is gas oil
hi
a 1(gasoline)
gasoline
+ C4 and lighter hydrocarbons plus coke
k1
(1)
C4 and lighter hydrocarbons plus coke (2)
The feed conditions in the present analysis are assumed to be the same as the ones assumed by Paraskos et al. (1976). Unlike the isothermal reactor, in an adiabatic reactor the temperature of the catalyst-fluid mixture drops with an increase in contact time due to the endothermic nature of the reaction. The rate constants k 1 and k z will decrease with an increase in contact time. We assume that the catalyst activity for both reactions is the same at all temperatures. The catalyst activity decays exponentially with respect to the flowing space time. The dependence of catalyst activity on the temperature is, however, not clearly understood. Weekman and Nace (1970) reported that their catalyst activity increases slightly Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
89
Coke W t 96
3
1
0
a
with an increase in temperature. Paraskos et al. (1976), however, reported that the deactivation rate of their catalyst increased with temperature. The activity of the catalyst should be largely dependent upon the coke content of the catalyst. Data obtained in this study (see Figure 1)indicate that, a t least within the limited range considered, the temperature has an almost neglibible effect on the coke deposition on the catalyst. The charge stock and the catalyst used in the present study were considerably different from the ones used by Paraskos et al. (1976). The ammonia production in the present experimental study was considerably smaller than that found by Paraskos et al. (1976). Therefore, for simplicity, we assume that the catalyst activity is independent of temperature in this study. With this assumption, the steady-state mass balances for gas oil and gasoline can be expressed in dimensionless form as
(3)
where
Here h i 0and k Z Oare the kinetic constants for reactions 1and 2 at the reactor inlet where the flowing space time, 7 = 0. The quantity a 1 is the weight of gasoline produced per unit weight of gas oil reacted. The ratio pvlpvi can be rigorously correlated to the weight fractions of various components as shown by Paraskos et al. (1976). In an adiabatic reactor, the factor pvlpvi also varies somewhat with space time due to a variation in temperature. As shown by Weekman (1968),the variation in density due to volume expansion is accounted for by using second-order kinetics for the conversion of gas oil. In eq 5 , V R is the volume of the empty reactor, G,, Goand G Fare the mass flow rates of catalyst, oil, and fluid, respectively, while y and y ( ; are the instantaneous weight fractions of gas oil and gasoline, respectively. The activation energy for reactions 1and 2 are E and EG, respectively; T is the temperature of the catalyst-fluid mixture a t any position, and Ti is the temperature of the catalyst-fluid mixture a t the reactor inlet while R is the universal gas constant. The light gases, Cq and lighter, plus coke is given by an overall material balance on the oil feed as Yc = Yi -3’ - Y G 90
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
(6)
I t should be noted, as in Paraskos et al. (1976), that solids in the reactor are assumed to move in plug flow a t the same rate as the gas. The average particle size of the catalyst used in this study is about 68 F. The gas velocity in the commercial riser is 50-60 ftls. In this velocity range, pneumatic flow conditions prevail according to Davidson and Harrison (1971). T o the authors’ knowledge, there are no data available on solids backmixing and/or slip velocity under pneumatic flow conditions. The small particle size implies that backmixing may not be too significant in the reported experiments. Weekman (1968) and Weekman and Nace (1970) have analyzed the effect of solids backmixing on gas oil conversion. According to their analysis, if backmixing were very significant, the theoretical curve of l / y - 1vs. 7 would not correlate as well as the data shown later in Figure 6. (In this regard, two printing errors in Paraskos et al. (1976) should be noted. Column 7 of Table I should be titled l l y - 1and the ordinate of Figure 12 should read 1.0, 2.0 etc.) Furthermore, using Weekman’s (1968) analysis, it was estimated that the difference in the gas oil conversions in most of our experiments for the cases where solids move in plug flow vs. completely backmixed flow were less than 5%. Thus, the assumption of no backmixing of solids is believed to be quite reasonable for the present purposes. Unlike an isothermal reactor, eq 1 and 2 cannot be solved without knowledge of the temperature distribution within the reactor. An energy balance on the adiabatic reactor can be expressed in dimensionless form as
where
Here AH is the endothermic heat of reaction and it is taken to be positive. In practice, the specific heat of fluid, C,,, would be a function of temperature and the composition of the reacting mixture. In the present study, however, for simplicity we assumed it to be constant. An integration of eq 7 leads to the relation -0 = r(i - Y)
(8)
As shown in Figure 2 , the validity of eq 8 was verified in the present experiments. Combining eq 8 with eq 3 and 4 and making the assumption that is most practical cases % E , an increase in reactor temperature will reduce the selectivity for gasoline and when E > E,, the converse will be true. A solution to eq 15 under some typical reaction conditions is illustrated in Figure 4. These results indicate that when E , > E , an adiabatic reaction operation further reduces the gasoline selectivity and once again when E > E,, the converse will be true. When E > E , the maximum gasoline concentration will be larger and it will occur a t a higher value of gas oil conversion in an adiabatic reactor than in an isothermal reactor operating a t the same inlet temperature. The converse will be true when E
