RAPID DEACTIVATION OF FRESH CRACKING CATALYST A.
BONDI, R. S . M I L L E R , AND W . G.SCHLAFFER
Shell Development Go., EmeryvillP: Calt'f.
Fresh catalyst particles can reach a sufficiently high temperature for rapid deactivaiion, only if they carry oil from the reactor into the regenerator, and if they are carried into a gas bubble of high oxygen concentration, as can happen only if a few oil-loaded fresh catalyst particles are in a generator bed of comparatively slow-burning equilibrium catalyst. Oil may b e incompletely stripped from the fresh catalyst particles in strippers with appreciable backrnixing, and also in strippers with plug flow, if the residence time is insufficient for oil desorption.
of radioactively tagged fresh cracking catalyst from catalyst samples which had been withdrawn periodically from a full-scale catalytic cracking unit had brought to light that about SOYG or the specific surface area of freshly added catal!.st particles is lost during the first few hours after its introduction into the reactor-regenerator system (19). Considering the great effort \vhich is put into the preparation of such catalyst. this is a rather disappointing performance. Moreover? combinations of all knolvn data on catalyst deactivation rate in typical regenerator atmospheres and a t the nominal regenerator temperatures proved irreconcilable with this rapid deactivation in the full-scale unit. 4 s the product distribution obtained from fresh catalyst is more favorable than that which results from contact with deactivated catalyst. there was considerable incentive to look for means to preserve the fresh catalyst surface for as long as possible. 'The present investigation was undertaken to find the origin of the rapid initial deactivation and. if possible, to suggest means to preserve initial catalyst activity for longer pe r iods . T h e analysis of the problem consisted of three steps: to assess the conditions under which fresh catalyst particles can reach higher than average temperatures in the regenerator, and to learn what factor in the make-up of a catalyst particle contributes to rapid collapse, and how much hydrocabron can be carried by a fresh catalyst particle from the reactor through the stripper to the regenerator. T h e present analysis reached its goal when its results outlined means to test ne\v catalysts and new design ideas. SOLATIOK
I
Pointers
T h e analysis of the problem was guided by the following array of experimental observations: T h e pattern of initial deactivation of fresh catalyst particles introduced into a unit operating on steady-state ("equilibrium") catalyst was that found in the laboratory a t 800' C.-namely. a small change of the ratio of pore volume to specific surface area while the surface area declined sharply. Thereafter, this pattern changed to that characteristic of laboratory steam deactivation at the nominal regeneration temperature. This behavior pattern could be reproduced in small-scale apparatus \\hen 2% fresh catalyst \vas circulated \vith 98y0 equilibrium catalyst through a reactor-regenerator combination. Fresh catalyst contains much more coke after the cracking reaction than the surrounding equilibrium catalyst. as is to be expected from its much higher activity. 196
l&EC
PROCESS DESIGN A N D D E V E L O P M E N T
Such rapid initial deactivation was not found when a unit was started u p with fresh catalyst only ( 4 ) . T'hese facts point to excessive particle temperature for fresh catalyst particles in an environment of equilibrium catalyst and to the possible cause of this high temperature. Temperature
of Catalyst Particles
'4ssuming the availability of sufficient oxygen, the temperature which a particle can reach is the result of a balance between the coke burning rate and the rate of heat transfer from the catalyst particle to its surroundings. Rather accurate burning rate data are available in this laboratory for coke in catalyst particles at temperatures between 350' and 500' C . T h e high quality of the data permitted extrapolation to regenerator temperature ( ?C 600' C.) without misgivings. Heat transfer rates to the average catalyst particle in fluidized beds have been reported (73). However? the "average" particle is of little interest to us. At typical fluidized bed densities (300 grams per liter) the average particle is surrounded by less than 0.01 liter of air per gram of catalyst. At the regenerating temperatures and pressures about 0.1 5 liter of air is required per gram of catalyst for every per cent of carbon in the catalyst. Obviously, only the catalyst particles sojourning in '.bubbles" have enough air for the rapid combustion required to raise the temperature of the particle to the desired level. \Ve therefore assume the heat transfer rates for single spheres. T h e rate expressions. heat transfer coefficients, and temperature rise calculations are described in the Appendix. The above rate data were then used to calculate the transient temperature behavior of a particle for several combinations of coke and oxygen concentrations. In addition, calculations were made using multiples of the extrapolated laboratory burning rates and fractions of the calculated heat transfer coefficients. In all cases the calculated temperature rise was negligible. This unexpected result is due to the high heat transfer rates from very small particles which prevent particle overheating at burning rates for coke. I t may be suggested that particles with so much coke might stick together to form what is effective1)- a much larger particle \vith a much smaller heat transfer rate. Hotvever. a spent fresh catalyst particle Ivould probably not have an opportunity to agglomerate with other spent fresh catalyst because of the very small amount of such material present at any time. If the fresh particle
did form an agglomerate with other particles, these particles would be equilibrium catalyst with a much smaller amount of coke and hence would quench any runaway. The part of these calculations most open to question is the use of laboratory coke burning rates. The catalyst used for such experiments has been exhaustively stripped and held a t a high temperature long enough to permit any remaining oil to crack off. The remaining material has a low hydrogen content and an appreciable fraction of a graphitic nature. The percentage of hydrogen in coke reported by the refineries on the basis of regenerator oxygen balances indicate hydrogencarbon atom ratios of 0.9: 1 to 1.5: 1. The material burned off in the laboratory has much less hydrogen. Therefore, i t is not unlikely that fresh catalyst. with its high surface area and small average pore diameter. will contain appreciable amounts of hydrogen-rich material. In fact. the hydrogen contents reported by the refineries would require an oil to be present to a large extent. Extrapolation of surface oxidation rates of lubricating oils to regenerator temperatures indicates burning rates many orders of magnitude higher than the laboratory coke burning rates. When this condition obtains in a catalyst particle, the burning rate should be determined by the rate at which oxygen diffuses into the particle. The model to be used for the calculation of particle temperature rise is now modified. All of the combustion takes place at a spherical zone which advances into the particle as fast as material is consumed. Therefore, oxygen must diffuse through a growing spherical shell of porous gel, no\\
emptied of combustible material, to the burning zone where it is used. The calculation of the burning rate reduces to the calculation of the rate of diffusion of oxygen to the burning zone for combustion. This is the problem of unsteady-state absorption in a spherical drop with a rapid two-component, irreversible reaction, and a nondiffusing component originally in the drop. The solution of the problem for the semi-infinite slab is presented by Sherwood and Pigford ( 7 3 ) for both components diffusing. The differential equations for the spherical case were written. but could not be solved analytically. However, if the period of high temperature occurs before the burning zone has advanced very far into the particle-say one tenth of the radius-the solution for the semi-infinite slab is adequate. The appropriate differential equations and their solution appear in the Appendix. l h e resultant burning rate was then used in the differential equation for the transient temperature of the particle, which is given, with its solution, in the Appendix. The temperature histories of a particle for three combinations of carbon and oxygen concentrations are presented in Figure 1. The particle reaches its maximum temperature in about 4 milliseconds. The calculations were continued to 10 milliseconds, a t which time the burning zone had advanced 12.5% of the radius into the particle for the case of 570 carbon and 20% oxygen. although less than 10% in the other t ~ v ocases. This solution assumed a uniform temperature in the particle, a condition which is not likely. Therefore? the more general
500
I
I
I
I
I
-1 I
450
\
1
400
L
\
i 350
Lo
*
.'. 3
ol
-1 I
I I
5
300
~
i
250
200
c
I
1
,I
-__
4
h
h
I
n
>
I
I
I
I
1
?
4
6
8
10
Tlrne, m i l l i s e c o n d s
Figure 1 .
Particle temperature rise
Diffusion-controlled burning, no gradient in particle
T i m e , milliseconds
Figure 2.
Particle temperature rise
Diffusion-controlled burning, gradient in particle Carbon 5%. Oxygen 2070
VOL. 1
NO. 3
JULY
1962
197
I milliseconds
*io
-
a . 400
-
b.
7 milliseconds
n
2 ,a
a D
5
15"
-
1
250
L 0.2
0.4
0.6
0.8
1.0
Fractional Distance From center
Figure 3.
Temperature gradient in particle Diffusion-controlledburning Carbon 5%.
Oxygen 20%
partial differential equation for the temperature distribution in the particle was salved for the case of highest temperature rise. An analytic solution was not possible, hut a numerical scheme could be used and is described in the Appendix. T h e two solutions agree in form, the mass average temperature where the temperature gradient is considered being about 30' F. higher than for the simpler case (see Figures 2 and 3). T h e temperature difference between the center and boundary of the particle is about 40' F. These numbers may he taken as proportional to the maximum temperature rise when applied to the other cases. Before the results of the calculations are discussed further, several of the assumptions should be mentioned. T h e Knudsen diffusion coefficient for oxygen was calculated from equations proposed by Wheeler (78). Both the diffusion and heat transfer coefficients were assumed independent of temperature over the temperature range covered here. These quantities are approximately proportional tn the one-half power of the ahsolute temperature, sn vary by only about 10% far the most extreme case considered, The particle was taken to be 80 microns in diameter and to have a high pore volume of 0.95 cc. per gram. A more dense particle with the samc specific surface area should give a higher temperature rise. During the discussion of this paper (at the Chicago ACS meeting) R . A. Van Nordstrand suggested that the change in total surface energy per gram of catalyst caused by lass of surface area might contribute substantially to the temperature rise. A quantitative check of this suggestion, using published data for the surface tension, y, and dy/dT of silica-alumina systems ( 7 7 ) and handbook values far the heat capacity of glassy silica, yields the respectable temperature rise of 30° to 70' C. per 100 sq. meters per gram change in surface area. T h e limits correspond to the uncertainty of dy/d T; the lower limit pertains i r d y / d T = 0 and the uppcr i f d y / d T = -0.25 erg/sq. cm. C. ( 7 7 ) . As perhaps half the total loss in surface area = 500 sq. meters per gram takes place during the initial particle collapse, the contribution to temperature rise from this source might make the deactivation process autocatalytic. 198
We have now arrived a t a mechanism whereby temperature rises of 200' C. over bed temperature can be reached in a regenerator with reasonable concentrations of oxygen and combustible materials. Regenerator gas mixing tests ( 8 ) showed that a zone containing 5% oxygen exists near the air inlets. Such concentrations, or even higher ones, can be expected to occur in bubbles (the most probable place far such a process to take place). There is ample evidence that spent fresh catalyst contains high concentrations of combustible material. This mechanism can also he seen to satisfy the several conditions outlined above. Catalyst can achieve the necessary high carbon levels only when it has a high surface area; hence the high temperatures would be specific to fresh catalyst. There is a high probability that a fresh catalyst particle will reach such combustible concentrations, so it seems reasonable that the process could occur to most of such particles within 24 hours after addition to the unit, There are two reasons why this process can occur only when very small amounts of material of high surface area are present: Fresh catalyst can reach carbon levels so far above the average only when present in small amounts. Also, the mechanism requires the particle to consume a very large amount of oxygen and it will be capable of obtaining this oxygen only if i t is competing with material of low carbon level. The proposed mechanism sets u p two strict requirements: The combustible material must he of a farm which has a n extremely high burning rate, and the strong initial deactivation must occur in extremely short times. The first requirement is met by a material of the nature of a n oil. It is feasible that the coke contains enough hydrogen to be of such a nature. Unfortunately, there is no apparent manner in which a sample of spent fresh catalyst from a mixture with equilibrium catalyst can be obtained far analysis with the coke deposit unaltered. Sufficient information is not in hand a t present to test the second requirement. Also laboratory measurements have shown that deactivation rates at these temperatures are extremely sensitive to the steam concentration. T h e steam concentration in and around a particle undergoing such a process is unknown. Also, the pdrticle is undergoing the severe thermal shock of a temperature rise of several hundred degrees in a few milliseconds. The sintering mechanics involved in rapid catalyst deactivation can only he guessed a t present. Substitution of the known values of surface tension (77), elementary particle size (0, and deactivation time scale into the Frenkel equation for
l&EC PROCESS DESIGN A N D DEVELOPMENT
Figure 4.
Catalyst particles tusea ~y rlasn aeacnvanon
Particle oreorwhich did not absorb red dye closed by furion
sintering by a viscous flow mechanism (70) yields a maximum permissible viscosity of the order of 10’ to 108 poises. Observed viscosities of silica-alumina systems (5) extrapolate to values which are several orders of magnitude larger. However. Yovanovitch’s recent observation of a threefold reduction of the viscosity of silica glass by 200 p.p.m. of water a t 1000° to 1500’ C. (20) indicates that the water vapor evolved during hydrocarbon combustion may reduce the viscositv of the catalyst by several orders of magnitude. A systematic investigation of sintering mechanisms along the lines proposed by Kingery and Berg (70) suggests that mass transfer by an evaporation-condensation process cannot be ruled out. Attack of the catalyst surface by steam from the hydrocarbon combustion may produce volatile species such as silanols, and the driving force-i.e., the ratio of the vapor pressure of the primary particles of the catalyst to that of the bulk catalyst-is about 4. Demonstration
of Rapid Deactivation
Following the above analysis, a simple laboratory experiment was carried out to demonstrate the efficiency of shortterm ‘‘flash’’ deactivation by burning oil rather than carbon .4ir was blown into a quartz tube of 6.4-cm. inner diameter and 68-cm. length at a rate equivalent to 2 cm. per second at GOO” C. About 45 cm. of the tube’s length were a t the nominal temperature of the experiment, the whole tube being inside a n electric furnace. Suitably prepared catalyst particles were dropped countercurrent to the air stream in small slugs. Three sets of experiments were conducted, in all of which the 80- to 100-mesh fraction of fresh, calcined MSA-3 alumina-silica cracking catalyst was used. I n the first experiment the catalyst was coked in a conventional laboratory fixed fluidized bed cracking test into W’est Texas gas oil at 500” C. T h e coked catalyst was not stripped and contained 18% carbon or coke and heavy oil. The coked particles Tvere dropped into the hot tube. At 600” C. about one particle in a thousand was observed to scintillate and a t 750’ C. about one in a hundred. I n the second experiment, the fresh catalyst was impregnated with 0.4 gram of heavy bright stock oil per gram of catalyst. Sow, violent flashes and showers of red-hot catalyst particles were produced when slugs of about 1 to 2 mg. were injected into the furnace. Black and white particles emerged from the tube. Some of the black particles could not be regenerated in a stream of air a t 550’ C., probably because the carbon was occluded in fused silica. Figure 4 shows the methyl redstained particles after the ”flash regeneration.” Only some of the particles took the stain, while others Lvere either totally or partly fused, so that their interior became inaccessible to the staining solution. I n the third experiment. MSA-1 particles were impregnated \vith 0.4 gram of residual catalytically cracked gas oil per gram of catalyst. Then scintillation and flashing were likewise observed when slugs of particles were injected into the tube at GOO” C. However. the flashing occurred only at particle densities in the tube in excess of about 0.05 mg. per cc. Injeciion of single particles did not cause scintillation or flashing. Transport
of Oil
in Fresh Catalyst Particles
The stripper through which all catalyst passes on the way from the reactor to the regenerator should prevent the transport of oil into the regenerator. Mass balances around the regenerator generally sho\v that strippers accomplish their task reasonably successfully for the bulk of the catalyst. Yet: \ v r are postulating that fresh catalyst carries appreciable iirnounts of oil into the regenerator. ‘The folloiving analysis i d 1 sho\v that simultaneous effective stripping of equilibrium catalyst and appreciable oil retention by fresh catalyst arc indeed compatible. We shall first consider the relevant
1
I
0.1
0 .z
Surface C o v e r a g e , B
Figure 5. Relative adsorption on fresh and equilibrium catalysts of dodecylpyrene and phenanthrene
adsorption equilibria and then the appropriate mass transfer rates. Adsorption Equilibria. Two questions have to be answered. Does fresh catalyst adsorb more oil than equilibrium catalyst only by virtue of its larger surface area or does it also attract oil more strongly? How much oil is held in the catalyst in the reactor and in the stripper in thermodynamic equilibrium? The first question is answered in the affirmative. Adsorption of the model compounds phenanthrene and dodecylpyrene out of heptane solution a t room temperature is very much stronger on fresh than on equilibrium catalyst, as is shown by the data of Figure 5. The adsorption constant of 0 1 that figure is defined as K = x -, where 0 is the fractional 1-0 a surface coverage and a is the activity of the solute in the heptane solution. An answer to the second question can be obtained by a fairly crude estimate of the adsorption equilibria under plant operating conditions. O\ving to a fortunate accident of nature. the 0 /I\ adsorption constant I; = X - remains constant over the 1 - 0 p range 0.05 < 0 < 0.5, and the free energy of adsorption AF = --RTIn K for a given system is sensibly constant over a wide range of temperatures. Here p is the partial pressure of the adsorbate and p s is its saturation pressure. For T > T , one obtains pJ by straight-line extrapolation of the vapor pressure curve. just as Hildebrand and Scott (9) suggested for the calculation of the solubility of gases. ‘l’he magnitude of I F can. in turn, be estimated from molecular structure, because i t turns out that the AF increment per carbon atom is constani at about 355 i 25 cal. per mole for thr systems n-butane-silica a t 0’ C. (75) and n-hexanen-heptane-benzene-toluene on cracking catalyst a t 310’ to ~
VOL.
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1962
199
Table 1.
Estimated Amounts of Oil on Catalyst in Reactor and Stripper
(If stripper is well mixed stage for gas and catalyst at 500" C . ) Oil on Catnlyct.
PIP. G. Catalyst Equilibrium 0.04 0.015 Fresh 0.10 Strippers Equilibrium 0.0288 0.013 Fresh 0.088 .4mount of stripping steam, 4 g . i k g . catalyst; steam assumed to be Place
Reactor
a
inert gas.
400' C. ( 7 ) . The required surface area data per molecule are available from van der Waarden's measurements (77). With the aid of this information and the knowledge that most of the adsorbed oil is composed of alkyl phenanthrene-type substances the adsorption equilibria in well mixed reactor and stripper, respectively, have been estimated. I t is apparent from the results in Table I that comparatively little oil is desorbed in well mixed stripper. In actual operation it probably serves mostly to dilute and displace the interstitial oil vapors of the incoming fluidized solids. In true countercurrent stripping less oil would be left on the particles. Diffusion and Mass Transfer. Even countercurrent stripping would not be effective if the mass transfer rate from particle surface to stripping gas or the diffusion rate from the catalyst interior to the surface was insufficient to permit removal of the oil during the residence time in the stripper. T h e first of these, the mass transfer rate from particle surface to stripping gas, can be estimated from recently published correlations (6.73) with some degree of confidence. I n the stripper under consideration the stripping steam velocity was so low that iYSu must have been somewhere between 0.07 [according to the curve of Richardson and Ayers (73)]and 0.02 [according to Frantz' correlation (6)1. T h e diffusion rate inside the catalyst particle is far more difficult to estimate, particularly since the available data suggest that in typical fresh cracking catalyst (with E N 0.68 cc. per cc.: ,4 = 1.26 x IO7 sq. cm. per cc.: and T , of the adsorbate a t 0.7 to 0.8) most of the adsorbate is transported by means of surface diffusion. for the prediction of which there is no theory. T h e only relevant data are the recent measureof the lower paraffins on cracking ments of surface diffusion, D,:: catalyst (2). A series of daring extrapolations, first of log D , U J . TR-l. then from methane to phenanthrene, yields a t best order of magnitude estimates. 'Phe combination of
-
these estimates with .V,u values likely to prevail in commercial strippers lields the oil desorption times shown in Table 11. The assembled numbers indicate that the stripper under consideration. \vith .V,u even loiver than in the table, must have permitted a great deal of oil to remain on the fresh catalyst particles. However, even in the more usual strippers with 60-second residence time and higher gas velocities, mass transfer resistance can (according to the estimates of Table 11) often be high enough to permit passage of oil-laden particles into the regenerator, particularly if the solids flow pattern approximates that of a well mixed bed. a situation often found in practice (75). Conclusions
Aside from the possibly more extensive coke laydown due to chemical activity, fresh catalyst particles can adsorb more oil in a given cracking reactor atmosphere than can equilibrium catalyst particles by a purely physical mechanism. This extensive oil loading is only partly removed from the fresh catalyst particles during their stay in the stripper because of the slowness of diffusion out of the particles and the fluid mechanical deficiencies of typical strippers. \$'hen these oilcontaining particles enter a n air bubble in the entrance zone of the regenerator, the oil burns at a rate limited only by oxygen diffusion. Hence, the particles can acquire temperatures of the order of 800' C. At that temperature part of its fine-grained structure sinters and the specific surface area of the catalyst rapidly acquires the steady-state value characteristic of the reactor-regenerator-catalyst-oil combination at hand. T h e outlined series of events can happen only when comparatively small amounts of fresh catalyst are injected into a system operating with old catalyst, because only then can an oil-laden particle find enough air in the regenerator entrance zone to start selective rapid combustion. If the catalyst charge is fresh. no particle can burn any faster than the test, and one obtains the relatively slow decrease of catalyst activity which has been observed in units charged entirely with fresh catalyst ( d ) . Numerous stripper and regenerator design ideas have been stimulated by this analysis in order to minimize the activity decline rate of fresh catalyst injected into a running unit. However, the main value of this work lies probably in the conditions Ivhich its results suggest for meaningful catalyst life-testing procedures.
Appendix
Table II. Estimated Desorption Time of Polyaromatic Hydrocarbon from Cracking Catalyst in Stripper of Table I Tzmea for 90% of Equil D~rorption.Sec. YhUb = 2 YL,, = 0 i .V,o = 0.77Model Hydro~carbon ai' h n h n b 216 330 550 47 78 130 Phenanthrenr 370 57 135 149 380 945 Chrysene a L'suai residence time tn stripjvrr I S of, oidri of 00 f 30 sec, in stripper under constderation, 500 rec .Vus~rlt number h a r p defined ar Zk, X a / D , , ahere k, and D , arp mas( transfer and diffusion cor8cients gas-phase, respectivel). c Surface dzffusion extrapolaled from Rarrer's data by means of liquid mcortty correlation. and of relation AFa0 6 F , where :Fa = actioation free m e r q y f o r surface difusion, and j F o = R T l n K(b). ~~~
200
~
~
I & E C PROCESS D E S I G N A N D D E V E L O P M E N T
Particle Temperature Rise at Coke Burning Rate. Consider a particle of spent fresh catalyst in a bubble in the regenerator bed. I t is at the bed temperature \Then it enters a region of high oxygen concentration. T h e rate of heat production in the particle will be greater than the average because of its high coke level. This heat \vi11 cause the particle temperature to rise above that of the bed by a n amount determined by the rate of burning. the rate of heat transfer between the particle and the gas, and the heat capacity of the particle. 'The most reliable burning rates available are those determined at Emeryville. 'I'he rate of burning was found to be first-order in carbon and approximately first-order to oxygen. 'l'hus.
S o reliable measurements of the rate of combustion of the hydrogen in the coke have been published. iVe used a n equation identical \virh Equation 1, but Lvith four times the rate constant:
'The rate of heat generation is then given by
'l'he heat transfer coefficient for the particle is best calculated from a correlation for single spheres-e.g., that of Ranz and hfarshall (72). T h e particle velocity was assumed to be the free fall velocity, which gave a Nusselt number of NU = 2
+ 0.6 Re1(2/Pr1!3= 2.127
Oxygen Diffusion in a Catalyst Particle. Consider a porous sphere whose internal surface is covered with a uniform layer of combustible material. I t is assumed that the reaction rate of oxygen with the combustible material is very fast compared to the diffusion rate? so that the combustion occurs only at a n advancing spherical zone. Thus, the concentration of combustible matter (expressed as carbon) is zero in the region through which the oxygen passes and is uniform else\vhere. T h e oxygen concentration varies from the gas phase concentration at the spherical border to zero at the burning zone. If it is further assumed that the diffusion of oxygen follows Fick's "second law." the equations for the concentration of oxygen and for the movement of the burning zone are
(4)
T h e heat transfer coefficient a t 1100" F. calculated by this formula is 354 B.t.u. (hr.)(sq. f t . ) ( " F.). T o this must be added the coefficient for the parallel heat transfer path of radiation. ?l'his gives a n over-all coefficient at 1100' F. of 381 B.t.u. (hr.)(sq. f t . ) ( " F . ) . T h e equation for thc temperature rise of the particle over bed temperature. with the heat transfer coefficient assumed independent of temprrature, is
D -Dc'12 = mCp Dr 1 ,I
l'(0)
x
d r (owvgen balance at burning. front),'
di
= a
'Ihe system of Equations 6 could not be solved. HoLvever, if the burning zone has not advanced very far into the particle, the diffusion rate \vi11 be about the same as for a similar semiinfinite slab. T h e equations for this geometry are
I h e carbon concentration at any time is found by numerical integration of Equation 1. where K is a f~inction of temperature. T h e numerical values used were 2.33 X 10' (sec.-l)(atrn.-')
=
c,, = 0.27 B.t.u./(lb.)('F.) AFT(, = -14,000 B.t.u./lb. M I H = -55,000 B.t.11. 4 h . E , R = 31,500' R.
A
(7)
507 (sq. ft.)/lb. (80-micron particle with purc volume of 0.95 cc. per gram)
=
For 20% oxygen a t 17 p.s.i.g.. 570 carbon. and 0.4% hydrogen on catalyst. and a bed temperature of 1100" F.. Equation 5 reduces to
14,000
LL'C
+ 880
(%)'I
exp
(- 1560
+
1.989 X 10*T (5a)
a n d Equation 1 becomes
T h e maximum temperature rise for each of several cases is given in Table 111. T h e reaction rates are relative to the laboratory data and the heat transfer coefficients are relative to the calculated values.
Table 111. BPd Temfi.. O
F.
1100 1100 1100 1200
Particle Temperature Rise with Coke Burning Relntiz,e Relatioe Heat Reaction Transfer T , .\lax., Rate Copflcient O F. 1 1 0.5 7 1 2.5 1 0.1 5.0 1 1 1.6
x'(0) = 0
T h e small change in the physical properties of the material balances (Equations 6 and 7) over the temperature range considered permits the material and energy balances to be separated. ~ I h eenergy balance, or temperature equation, is treated below. I n Equations 6 and 7 the diffusional resistance outside the pellet is neglected. This is justified. since the diffusion coefficient outside the pellet is about 50 times that on the inside. I n the temperature equation. the dominant resistance is outside the pellet. since now the outside conductivity is lo\v relative to that on the inside. I'he system of Equations 7 is easily solved by the methods outlined by Sher\tood and Pigford (74) for the problem with both components diffusing to the reaction zone. T h e results are
Ivhere a is given by the equation
and
VOL.
1
NO. 3
JULY
1962
201
Particle Temperature Rise, Oxygen Diffusion-Controlled. The transient temperature of the particle can be calculated in the same manner as in the coke burning case, except for thr change in the rate of heat generation. The new source term is given by
CgAAHcB
(a ~
- x ' ) ~dx' de
a2
(11)
We take the value of x ' from Equation 9,
Hrre. f-
and
dt
=
(a
- 7)* 4cr
1
The solution was constructed from the solution for the impulsive input of heat on a spherical surface. If the solutions for the source at a series of radii are then added with the time delay for each radius as given by Equation 9: the proper solution results. The solution of the impulsive heat input problem is given by Carslaw and Jaeger (3)as
If the heat transfer coefficient is assumed independent of temperature, the temperature equation is
This is a linear, first-order equation; hence the solution is (with the initial condition of T = 0 at t = 0)
Jt
[-"2
-4 a;2 -
+ y]exp
(g
r ) dr
4"
where
cot
pn
+ (2 - 1)
= 0
and for our problem, (14)
Q = - Cc'AHCH
4*a2y '2ff1,2r-1,2
PCP
The desired temperature distribution then becomes
S o w set
Then Equation 14 becomes
The integral is further complicated by the relationship between y ' and 7 : This form is convenient, because values of the function e-z2[
eE2dE are available.
T h e time-temperature relationship for three sets of carbonoxygen concentrations (see Table IV) have been calculated from Equation 15 a n d appear in Figure 1. The maximum temperature is reached in about 4 milliseconds and at 10 milliseconds the burning zone has advanced inward by only 12.5, 6.3: and of the radius for the three cases. The hydrogen concentration was taken as 8% of the carbon concentration and the total pressure was 17 p.s.i.g. An average value of 400 B.t.u.1 (sq. ft.)(hr.)(' F.) was used for the heat transfer coefficient. The preceding calculation assumed no temperature gradient in the particle. a situation not likely in this case even with the small particle radius. The temperature equation for the particle now becomes a partial differential equation for the transient temperature distribution in the particle. The equation and boundary conditions are
-k
dT ar 1
-
1
r = o
= hT(a, t )
lim T ( r , t ) is finite r-0 T(7,0)
202
= 0
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
This relationship restricts the validity of the results to small penetrations in the particle, hence small values of T . The integration was performed numerically for several values of the radius and for several values of time up to 10 milliseconds for the case of 5% carbon on catalyst and 2 0 7 , oxygen in the gas phase. The particle thermal conductivity was estimated to be 0.3 B.t.u./(sq. ft.)(hr.)/(' F./ft.). The temperature distributions in the particle a t several times are plotted in Figure 2, and the temperatures at several radii as a function of time are compared with the solution for no gradient in the particle in Figure 3. The lengthy calculations were not extended to other reactant concentrations, but it is reasonable to assume that the gradient in the particle and the difference between the mean temperature for the two solutions are proportional to the maximum particle temperature. The simpler solution for no gradient in the particle with the estimated corrections is considered adequate in view of the other uncertainties.
Table IV. Carbon and Oxygen Concentrations yo Carbon % Oxygen (a/D)X lo4
Case
1 2 3
5
20
10
3
3
5
?.9 1.o 2.0
Nomenclature
U
a ;Z
= particle radius = specific external surface area of catalyst considered as
1.1
= specific heat of catalyst =
initial concentration of carbon
= concentration of oxygen (,',:?
initial concentration o r oxygen diffusion coefficient Arrhenius activation energy heat transfer coefficient enthalpy of combustion of carbon enthalpy of combustion of hydrogen enthalpy of combustion of carbon plus its hvdroqen . = thermal conductivity of catalyst = stoichiometric factor? moles of oxygen consumed per atom of carbon with its hydrogen = Susselt number = partial pressure of oxygen = Prandtl number = rate of heat production by combustion = strength of heat source, defined after Equation 17 = radial variable in spherical coordinates = radial position of burning zone = gas constani = Reynolds number = bed temprrature = critical temperature =
I1 = E = ii = AHc = AH, = .lHclr =
= = =
= =
= = =
= = = = = = = = =
= =
=
T/TC velocity temperature variable in Equation 17 Lveight fraction carbon on catalyst initial weight fraction carbon on catalyst weight fraction hydrogen o n catalyst initial weight fraction hydrogen on catalyst distance from edge of semi-infinite slab distance from edge of semi-infinite slab reduced radial variable, r 'a reduced radial position of burning zone, r ' , a variable defined after Equation 14 parameter, defined by Equation 10 constant in Equation 17 diameter of ultimate particles in a catalyst pellet void fraction in catalyst particle integration variable, defined after Equation 17 fraction of catalyst surface covered with adsorbatc first-order constant for combustion of carbon
-E constant in Arrhenius equation, K = ~ o e x p R! To 7')
= catalyst density
= surface tension = integration time variable
Acknowledgment
sphere (,';
7
+
The authors are indebted to many colleagues for advice and rooprration. specifically io .John Farrar for the liquid-phase adsorption measurements. to L. J. Tichacek for analyses of stripper mechanics, to H. H. \.age and C:. i V . Bittner for advice on coke burning kinetics. to R. M. Barrer for making surface diffusion d a t a available prior to publication, and to many colleagues in the Shell Oil Co. for their ready cooperation. literature Cited
(1) Adams, C. R., Voge, H. H., J . Phys. Chenz. 61, 722 (1957). (2) Barrer. R. M., Gabor, T., Proc. Roy. Sor. (London) A256, 26119601. (3)' Carglaw, H. C., Jaeger, T. C.. "Conduction of Heat in Solids," p. 307, Oxford Univ. Press. London, 1947. (4) Conn. A. L., Mahan, \V. E.: Shankland, R . V., Chem. Eng. Progr. 46, 176 (1950). (5) ~, Eitel. \I-.. "Phvsical Chrmistrv of the Silicates." L'niversitv Press. Chicago. 1952. (6) Frantz, J. F., Chem. EnS. P r o g r . 57, 35 (July 1961). (7) Good. G. M.. Shell Development Co.. private communication. (8) Handlos. A. E.. Kunstman, R. \ V . > Schissler: D. O., IND.ENG. CHEM.49, 25 (1957). (9) Hildebrand, J . H.: Scott, R. L.. '.Solubility of Non-Electrolytes," Reinhold. New York, 1950. (IO) Kingery. \'V. D.: Berg, M., J . A$$. Phys. 26, 1205 (1955). (11) Popel, C. I.. Esin, 0.A , , J . Znor~y. Chem. C.S.S.R. 2, 632 (1957). (12) Ranz, W. E.: Marshall. \V. R., Jr., Chem. En,?. P r o p . 48, 141, 173 (1952). (13) Richardson, R. F., Ayers. P.: Trans. Znst. Chem. Engrs. 37, 314 (1959). (14) Sherwood, T. K.: Pigford. R . L.. "Absorption and Extraction." McGraw-Hill p. 332, New York. 1952. (15) Singer, E., Todd, D. B.. Guinn, V. P.. IND.ENG.CHEM.49, 11 (1957). (16) Smith, W. R.. Beebe. R . A , , Zbid.. 41, 1431 (1949). (17) van der \Vaarden, M.: J . Colloid Sci.6, 443 (1951). (18) TVheeler, -\., AdDan. Catalysis 3, 264 (1951). (19) TVilson, \V. B., Good, G. M., Deahl. T. J., Brewer. C. P., Appleby, \t7.G., IND.EKG.CHEM.48,1982 (1956). (20) Yovanovitch, .I. Compt. Rend. 253, 853 (1961). RECEIVED for review September 1, 1961 ACCEPTED April 12, 1962 Division of Petroleum Chemistry, 140th Meeting, ACS. Chicago. Ill., September 1961.
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