Use of Tracers in Refinery Studies
E. SINGER, D.
B. TODD,
and V.
P.
GUINN
Shell Development Co., Emeryville, Calif.
Catalyst Mixing Patterns in Commercial Catalytic Cracking Units
THE
fluid process of catalytic cracking is chemically and mechanically complex. The microspheroidal catalyst, in addition to serving its catalytic function, acts as the heat transfer medium as it circulates through the unit by the fluidizing action of oil vapors or air. Coke is continuously deposited on the catalyst during its passage through the reactor and is continuously burned off the catalyst in the regenerator. The rate of coke laydown and the- activity of each catalyst particle in the reactor is a function of the time that the particle has been in the reactor since its last regeneration. The rate of coke burning in the regenerator is a function of the time that the catalyst particle has been in the regenerator, since its last deactivation in the reactor. Because of this interrelationship, it is essential to know the distribution of times spent in each of these vessels in order to gain a complete understanding of the system. Unlike the situation in a fixed bed process, a given catalyst particle entering the fluid bed system normally loses its identity in the mass of particles of varying ages and properties and cannot be traced in its individual history. However, with the aid of recently developed radioactive tracer techniques described here, much information about the catalyst flow patterns is revealed. The detailed knowledge of these flow patterns is necessary for any rational correlation of industrial reactor and regenerator performance, as well as for the correlation of industrial systems with small scale pilot plants or laboratory units. Another part of the over-all problem, the gas mixing characteristics of commercial-scale fluid beds, is reported in a companion paper (7). With the aid of tracer-tagged catalyst, the catalyst circulation patterns have been determined in three different catalytic cracking units-the Shell Oil re-
fineries in Houston, Tex., and Norco, La., and a t the Shell Oil Co. of Canada refinery in Vancouver (Shellburn), B. C. These tests were a joint effort of Shell Development Co. and Shell Oil Co. personnel. Catalyst Tagging
Choice of suitable radioisotopes for use in these studies was dictated by two requirements : 1. The isotopes must adhere to the catalyst surface under the high oxidizing temperatures ( ~ 1 1 0 0 "F.) of the regenerator, the high reducing temperatures (-900' F.) of the reactor, and the high steam temperatures (-900" F.) of the stripper. 2. For maximum sensitivity of detection they should be gamma emitters. These two points are developed later. The first criterion is chemical and essentially limits the choice to radioisotopes of elements which do not vaporize as the free element, hydride, carbonyl, or oxide at the high temperatures encountered in a catalytic cracking unit. There are a number of elements which satisfy this criterion and which also have gamma-emitting radioisotopes of reasonable half life (weeks to months) available a t low cost from the Oak Ridge National Laboratory and the British and Canadian counterparts. From this group of available and possibly suitable isotopes, scandium-46 (Sca) and cerium144 (CeI4*) were studied in some detail and found to be satisfactory. The radioactive decay paths are somewhat complex but are essentially as follows : scandium-46 decays with an 85-day half life to stable titanium-46, emitting one beta particle (0.36 m.e.v. maximum energy) and two gamma ray photons (0.89 and 1.12 m.e.v. energies) per disintegration. I t is available from Oak Ridge at a cost of $3.00 per millicurie.
Cerium-144 decays with a 275-day half life, emitting one beta particle (0.17 m.e.v. Emax,) and one gamma ray photon (0.13 m.e.v.) in each of about 407, of its disintegrations. In the other 607, it emits only beta particles (0.30 m.e.v. E m a x ) . The daughter of Ce144is Pr144 which is also radioactive and decays with a 17-minute half life to stable Nd144 and emits primarily beta particles (3 m.e.v. Emax,).Cerium-144 is available from Oak Ridge at a cost of $1 per mc. Scandium-46 is adsorbed strongly by equilibrium silica alumina cracking catalyst when the latter is stirred in a slightly acidic (pH = 4) aqueous solution of scandium chloride containing ScW13. The tagged catalyst did not lose radioactivity when heated for 2 hours in a muffle furnace at 1800'F., showing that the scandium is not volatile under high temperature oxidizing conditions, even during the process of burning off the 1% carbon on this catalyst. Cerium-I44 is similarly strongly held when adsorbed by equilibrium catalyst from an acidic aqueous solution of CeC13 containing Ce*@C13. The requirement that the radioisotopes be gamma emitters is not necessarily rigid, but their use definitely simplifies the counting of the samples. If one employs gamma-emitting isotopes, it is possible to utilize large samples effectively without the severe limitation of sample self-absorption encountered in beta counting. For example, if 1- liter samples of material of about unit density, containing an isotope which emits one 1-m.e.v. gamma ray photon per disintegration, are counted with a scintillation dip counter with a 2-inch sodium iodide (Tl) crystal, it is found experimentally that about 77, of the gammas emitted by the sample are counted. For 0.1-m.e.v. gammas the efficiency is about 9%. Thus, if 1 mc. (the amount of radioisotope that gives 2.22 X I O 9 disVOL. 49, NO. 1
JANUARY 1957
11
Figure 1. Catalytic crackirShell Oil Co., Houston, Tex.
nit,
integrations per minute) of a I-m.e.v. gamma emitter is.unifody mixed with 500 tons of equilibrium cracking catalyst, a 1-liter sample counted as described above should give a counting rate of about 300 counts per minute (c.p.m.) above a counter badtground of 200 c.p.m. (If a Geiger counter were used instead, the counting rate would amount to only about 5 c.p.m. above a shielded background of 20 c.p.m.) The standard deviation of a single 10-minute count on such a sample, assuming an equal background counting time, amounts to +39& Since in a given refinery-scale mixing experiment the mixing curve is determined by the counting rates of perhaps 20 samples, the shape of the curve is established to a higher degree of accuracy than this. In addition, the peak counting rate obtained in a given vessel, following pulse injection of tagged catalyst into the vessel, is conliderably higher than the completely mixed value, in about the same ratio as the total inventory divided by the vessel inventory,
Figure 2. .~talytic cracking Shell Oil Co., Norco, La.
unit,
Figure 3. Catalytic cracking unit, Shell Oil of Canada, Shellburn Wancwver), B. C.
thus increasing the accuracy of the part
stack. These problems are discussed below for the same typical case described -namely, the use of 1 mc. of a 1-m.e.v. gamma emitter in a 500-ton inventory unit. The radiation intensity, I (millimntgens/hour), at various distances from the Center of a small container (approximating a point source) holding a gamma emitter is given by the approximate relationship :
of the mixing curve of greatest interest.
In each of the mixing tests described, small hatches (5 to 10 pounds) of plantregenerated equilibrium silica alumina catalyst were impregnated with the radioactive solution and the "hot" catalyst was then dried for 48 hours at 150" C. in an air stream to a final water content of about 1%. The various tagged catalysts used are summarized in Table 1. The radioactive material was obtained from the Oak Ridge National Laboratory and permission to conduct such studies at the Shellbum refinery was obtained from the Atomic Energy Control Board of Canada. Safety Conridemlions The safety problems can be grouped into those involved in the preparation of the "hot" catalyst, shipment of the catalyst to the refinery, injection into the unit, and lw of catalyst fines to the atmosphere through the regenerator
Thus, 1 mc. of a 1-m.e.v. gamma emitter gives a radiation level of 5500 mr./hour at a distance of 1 cm. but only 55 mr./ hour at 10 cm. Since the established radiation tolerance level for lifelong repeated expasure is 300 mr./week, it is clear that this amount of activity can readily be handled with safety by the simple use of laboratory tongs or forceps and by minimizing the duration of exposure. Shielding is not necessary.
Table I. Catalyst Mixing Tests Employing Radioactive Tracers Appro.. Activity, Refinery Hotwton
Norco
Shellburn
12
%'easel Regenerator
Reaotor Reactor Regenerator Reactor Regenerator Regenerator
Test I I1 I I1 I 11
m
Isotope
Mc.
Lb. Cat.lyst Injected
Av. Catalyst Holding Times.Mi". Reactor Stripper Regenerator Total
Net C.P.M./Kg. Peak Mired
Sc'
2
14.3 14.3
2.8 2.8
21.5 21.5
38.6 38.6
620
2
10 10
1110
SC'6
1350
MH)
ScU
0.5 2
10 10
5.3 5.0
2.7 2.5
18.8 17.8
26.8 25.3
300 650
130 420
0.1 0.4 0.4
5 5 5
2.0
0.9 0.9 1.1
6.7 6.5 5.5
9.7 9.3 8.8
500 850 1250
125 560
SC'E
Gel' CS"'
c.9
INDUSTRIAL AND ENQINEERINQ CHEMISTRY
-
1.9 2.2
660
After drying, the tagged catalyst was carefully transferred to polyethylene bags. The bags were sealed and placed in metal cans, which were in t u m m t e d for shipping. With regard to shipping the “hot” catalyst Via air or rail, the maximum surface radiation level permissible in the United States and Canada is 200 mr./hour. A IO-pound sample of cradring catalyst containing 1 mc. of a I-m.e.v. gamma emitter, packaged inside of a cubical wooden box 2 feet on a side with no shielding, givea a surface radiation level of only about 6 mr./hour, so shipping is quite simple. The labeled catalysts were prepared a t the Emeryville Research Center and were then shipped by air freight to the refineries. Radiation levels were measured with calibrated radiation survey meters (ionization chamber type). The labeled catalyst is handled throughout the period of p r e p amtion, drying, and finally injection into the unit by one or two trained radiochemists SO that no refinery personnel are exposed to any type of radiation or radioactive ingestion hazard. Preparatory to injection, the catalyst was readily transferred from the plastic bags to the injection vessel without loss. Once mixed in a commercial unit the radiation level a t the surface of the unit is negligible, of the order 0.01 mr./hour-lower by a factor of 100 than the radiation level of a typical luminous dial watch. The radioactive concentration of the catalyst in the unit, after mixing, was so low that the catalyst could be handled, transferred, and eventually disposed of just as though no radioactive material had been employed. The body tolerance levels for Sc’ and W4 have been set a t 6 and 5 mc., respectively (2). One would have to retain steadily in his bady all the radioactive material contained in about 3 tons of completely mixed catalyst ( 1 mc. in 500 tons) to reach even momentarily the ingestion tolerance level. With regard to ingestion hy inhalation, the tolerance concentrations for continuous breathing of Sc‘ and cC14LPr’u in air have been set (2) at 7 X 10-8 and 7 X 10’ mc./ml. of air, respectively. If tagged equilibrium catalyst containing 1 mc. of radioactivity were injected into a unit operating with a regenerator stadr effluent rate of 50,000 std. cu.ft./ min., and if 1% of this catalyst were lost during the first hour, the radioactive concentration of the effluent, even before atmospheric dilution, would amount to only 4 X 10-1’ mc./ml. (at the effluent temperature) and would be expected to decline rapidly thereafter. The effluent catalyst is highly diluted with nonradioactive catalyst so that eventual settling to ground level constitutes no contamination problem or health hazard.
C
0 R e g e n e r a t o r Wall T a p A R e g e n e r a t o r Standpipe
2
0
.9
S t r i p p e r Standpipe
1
2
I
E 0
1.5
0
C 0
U Q
.2 c
1.0
Id
d
$ 0
0
I
5
10
15
Time a f t e r Pulse Injection, m i n u t e s Figure 4. Time-concentrotion curves for Houston regenerator test Experimental Procedure Schematic drawings of the three catalytic cracking units are given in Figures 1, 2, and 3, with the associated injection and sampling points. The tagged catalyst, in each case 5 to 10 pounds, was injected from a -vessel pressurized with nitrogen. The injections were completed in less than 15 seconds. Just prior to injection, and continuously for several minutes thereafter, catalyst sampleowere withdrawn from the various sampling ports. The initial samples were taken at intervals of time roughly one fortieth of the average catalyst holding time in the unit (total inventory/ catalyst circulation rate). Additional samples were withdrawn a t greater time
intervals in order to establish the “wellmixed” concentrations of radioactivity. One liter of sample was used for analysis with the counting equipment employed. Counting Procedure. MI samples were counted with a scintillation dip counter employing a Harehaw canned 1.75-inch diameter by 2-inch long thallium-activated sodium iodide crystal sealed to the face of a DuMont 6292 photomultiplier tube with high Viscosity silicone oil. The canned crystal is encased ‘in a dose-fitting thin aluminum case and the photomultiplier tu& is contained in a mu metal magnetic shield and an aluminum light-tight case. A cathode follower circuit is also included in the
2.0(
8 .* u
*Stripper
(I
h u Q
1.5
0
5
U
* .“ u Q
1.
4
0.
-71
p’-/Regenerator
10 15 20 ’ Time a f t e r Pulse Injection, minutes Figure 5. Time-concentration curves for Houston reactor test 5.
VOL. 49, NO. 1
JANUARY 1957
1?
I
2.5
0 S t r i p p e r Standpipe A Regen. Standpipe
2.0
-P e r f e c t
E: 0
c
.rl
Mixing
Ld
&
4
c
1.5
Q)
20 U Q)
>
‘
1.0
.rl c
Ld +
0.5
0 T i m e a f t e r P u l s e Injection, minutes Figure 6.
radioactivity existing at the end of each test. These normalized concentrations are plotted against time (corrected for the small time lag of the sampling lines) in Figures 4 through 11. The discussion of the results of the circulation tests is illuminated by comparing the data with a simple theoretical model which incorporates the concept of a perfect mixing stage. “Perfect” mixing means that the catalyst which enters a particular region mixes uniformly and instantaneously with the entire inventory of catalyst in that region or, more precisely, that the probability that a given catalyst particle will leave the region is the same as that for any other particle regardless of the respective times that these particles have spent in that inventory. Under these circumstances, the model for three perfect mixing stages in closed series is governed by the follo~vingdifferential equations :
Time-concentration curves for Norco reactor test
counter. One-liter samples were counted with the crystal immersed in a reproducible manner to the approximate center of the sample. A Tracerlab 1000 Scaler was used, and the counter was operated at a voltage at the center of the plateau of the counting rate versus voltage curve--1200 volts for Sc46, 1500 volts for Ce144. Sample and counter were surrounded by 2 inches of lead shielding, giving a counter background of about 200 c.p.m. Counting times were 10, 20, and 5 minutes, respectively, in the tests at Houston, Norco, and Shellburn, with background similarly determined about once per hour. Data from Circulation Tests
The piece of information which emerges most quickly from the data taken during the circulation tests is the calcu-
lation of the total inventory in the catalytic cracking system. Since the concentration of radioactive material on the tagged catalyst is known and the amount of tagged catalyst introduced into the system is accurately measured, it is possible to calculate the amount of dilution of the tagged catalyst after a period of time long enough for complete mixing in the entire inventory to occur but short enough for the stack loss to be insignificant-generally within three nominal catalyst turnover times. These calculations were made for each of the circulation tests and each of the commercial units. I n each case the inventory calculated from the radioactivity measurements checked within 2% those calculated from pressure drop measurements. All the concentration data were normalized against the completely mixed
The material balance equation is OACA
+
OBCB
+
ODCD
= OncF
(5)
For a pulse injection of tagged catalyst into vessel A of the closed series, the initial and steady state conditions are
at t =
m,
CA =
Cg
= CD = Q
(6)
The solution of these equations is
2.0
Regen. D e n s e Bed
A Regen. Standpipe
0
0 S t r i p p e r Standpipe
-P e r f e c t
ll+-*
Mixing
where
m =
h
+d
h n k
2
(10)
1.0
1
”:
AI
0.5E 0 0
v
Figure 7.
14
>
5
I I I A V\ 20 25 T i m e after P u l s e I n j e c t i o n , m i n u t e s I
I
10
15
Time-concentration curves for Norco regenerator test
INDUSTRIAL AND ENGINEERING CHEMISTRY
If m and n in these equations involve complex roots? the solutions take the form I 60
U S E O F T R A C E R S IN R E F I N E R Y S T U D I E S
G-
\n
hi ...
s i n 2g -cos$]
(15)
Test I
cD(t+ eD) = cB(t)
h
I n j e c t i o n I n t o Reactor
Reactor Bed
Stripper
When, for example, the third vessel is in plug flow and the other two are perfect mixing stages, the differential equations would be
-
0 Spent Cat. Standpipe A Regen. Cat. Standpipe
-
Solid L i n e s R e a c t o r and R e g e n . W e l l Mixed, S t r i p p e r P l u g Flow
I
\o
(20)
The solution of this set of equations is best obtained by numerical procedures. In Figure 4 (representing the Houston regenerator study), the upper solid curve for the regenerator and the lower solid curve for the stripper indicate the concentrations expected if all three vessels behaved as perfect mixing stages in closed circuit, with pulse injection into the regenerator. Experimental data for two sample points in the regenerator, a wall tap and the regenerated catalyst standpipe, are shown by the circles and triangles. The agreement between these two sample points is good, with no time lag between them, showing that the regenerator, by this criterion, corresponds to a well-mixed stage. However, theagreement between the data and the theoretical curve is less satisfactory, indicating some departure from the well-mixed, three-vessel model. For the stripper sample, the data precede the theoretical curve by 2 to 4 minutes. A plausible explanation is that some of the catalyst short circuits part of the volume in the reactor-stripper system. Figure 5 illustrates the data obtained in the Houston reactor test. In this figure the solid curves, as in the preceding figure, are for the three perfect mixing stages. All three of the dashed experimental curves precede the corresponding theoretical curves by several minutes. Also the peak in the stripper concentration is higher than that given by the theoretical curve. These factors point to catalyst moving through the system more rapidly than is predicted by the model. In other words, some of the catalyst appears to be bypassing some region or regions in the system. This bypassing must be occurring in the reactor, since it is the first vessel in the sequence, and its curve precedes the theoretical by about the same time as the precession time for the stripper. The next two figures, 6 and 7, depict the data obtained in the Norco circulation studies. Once again the solid
I
A 2 Figure 8.
6
I 8
I
”
A
I
10 15 Time A f t e r I n j e c t i o n , m i n u t e s
4
I 25
Time-concentration curves for Shellburn reactor test
curves are those predicted for three wellmixed stages. In the reactor test, Figure 6, the experimental stripper curve lags the theoretical curve by 2 to 3 minutes at the beginning, which is evidence that there is a plug flow region in the reactor-stripper system, probably in the baffled stripper. There likewise is a 4minute initial lag in the regenerator standpipe sample relative to the theoretical curve. This represents an additional lag in the system which can only be attributable to the regenerator. The main information for the regenerator system is obtained from Figure 7. In this figure the regenerated catalyst standpipe sample lags the dense phase sample by
about 4 minutes during the initial and peak periods. Thus, the regenerator behavior does not a t all correspond to the model with three well mixed stages. Furthermore, the lag between the outlet and the wall sample shows that the catalyst follows a lengthy and perhaps indirect circulation path through the vessel, reaching the wall sample point before reaching the drawoff weirs. The lag between the stripper standpipe and the theoretical curve is in approximate agreement with the sum of the lag found in the regenerator and the plug flow lag indicated for the stripper on Figure 6. A third kind of behavior for catalyst circulation systems is illustrated in
Injection i n t o Reactor
0 . Y ,-I
(d
W e l l Mixed I I I
I
0.I
0
1
2
I 3
I
4 Time A f t e r I n j e c t i o n ,
I
I
I
5
6
7
minutes
Figure 9. Detail o f time-concentration curve for Shellburn stripper reactor test VOL. 49, NO. 1
during
JANUARY 1957
15
0 Regen. Bed (Top) Regen. Bed (Bottom) ARegen. C a t . Standpipe C 0
u
T e s t I1 Injection I n t o Regen.
I
1.:
.L(
. A.
m
L.
Solid L i n e s - R e a c t o r and Regen. W e l l Mixed, S t r i p p e r Plug Flow
1
C
u 0
C
l3> 0
l.OI
c
.r(
m
d
u g 0.:
0 0
6
2
8
20
10
0
Time A f t e r Injection, m i n u t e s Figure IO. Time-concentration curves for Shellburn regenerator a t high inventory ity a t the stripper outlet, relative to that predicted by either the well mixed or plug flow model, indicates that some short circuiting from the reactor may be occurring. In Figure 10 the data for the regenerator show that there is a small but probably significant time lag between the experimental points and the perfect mixing curve. This might be caused by a small zone of inactive catalyst in the vessel. However, the data for thepmple points a t t h e places in the regenerator agree among themselves fairly well, showing that quite rapid mixing is occurring in most of the regenerator. Figure 11 shown data similar to those in Figure 10 but a t a lower inventory level in the regenerator. These are in fair agreement, so that the general pattern is the same a t these two inventorv levels.
Figures 8 through 11. At Shellburn it was known beforehand that the stripper would act more nearly like a plug flow region than a well-mixed stage, and the solid linea in this case are those which would be predicted on the basis of the reactor and the regenerator being perfectly mixed stages and the stripper being in plug flow. In Figure 8 the reactor data appear to give quite good agreement with the theoretical cusve, attesting that a well-mixed model is a good representation. The stripper concentration starts earlier than shown by the plug flow model but fails to reach the peak plug Bow concentration. Figure 9 shows the stripper data more clearly. The peak concentration approaches but fails to attain the plug flow peak, indicating that some axial mixing occum in the stripper. The early appearance of activ2.0-
0 Regen
DL.U
1 ear 111
\ Io p i
Regen Bed (Bottom) A Regen C a t Standpipe
Injection into Regenerator
Solid L i n e s - R e a c t o r and Reg-Well mixed, S t r i p p e r Plug FI
".Stripper Stand? I
0
6
I
Figure 11.
16
I
"
8 10 T i m e A f t e r Injection, m i n u t e s 4
~
Time-concentration curves for Shellburn regenerator a t low inventory
INDUSTRIAL AND ENOINEERINS CHEMISTRY
'here is good agreement among the three sample points a t the low inventory level also. Thus, rapid, uniform mixing in the vesel is indicated for both tests, and no pronounced s e c t of inventory level on mixing is found. The data from the three refining units indicate three qualitatively different kinds of behavior. The Shellburn data indicate the c l m t approach to wdlmixed vessels (the reactor and the regenerator), although there is evidence showing that there are regions of inactive catalyst in the regenerator and that some catalyst b y - v the reactor. The Houston data indicate that catalyst travems the system faster than would be predicted hy well-mixed stages; this is what we have termed catalyst by-passing. The Norco regenerator data illustrate the case where tagged catalpt lags behind the curves predicted by the well-mixed stages, which is attributed to the existence of a more or less welldefined drculatiou pattern in the vessel. What these three kinds of behavior mean in terms of the practical operation of the system requires the application of the kinetics of the chemical operations occurring in the reactor and the regenerator. The use of these concentration data in terms of chemical kinetics is much simplified by the translation of the concentration data into distributions of catalyst holding times, which is demonstrated in the next section. Interpretation of Data Although the concentration data have been compared with theoretical curves that would have occurred with perfect mixing and/or plug flow, the re-entry of tagged material into each veasel makes it difficult to separate the behavior of one veasel from the other vesaels. Therefore, it is convenient to transform the raw concentration data to distributions of catalyst holding times. The distrihution function, D, is defined as the derivative of the curve of weight fraction of catalyst younger than age 1. Thus, the integral of D over any interval of time is the weight fraction of material which has a holding time within that interval. The equation describing the dationship between the distribution function and the concentration of tagged catalyst may be derived as follows: Suppox that for a short time, Ai, the catalyst entering a certain portion of the system contained concentration Co of tagged material and that thereafter it contained none. &me that tagged catalyst behaves in every way the same as untagged catalyst despite the means of injection, the taggin process, etc. If the concentraion, CI($ ofta is measured a t some point 1 a t time f after the start of injection, the fraction of catalyst, f, a t that point which had been at the injection point between t and t Ai before is
iT
+
--- Houston -Norco Therefore for very short injection times
In the cases to be considered, however, the catalyst returning h r n the rest of the system contains some tagged catalyst after the initial injection. Since this material is subject to the same distribution as the originally injected material, its effect may he subtracted h m the total in the following way. At time 1, the fraction of material which reentered the system a t time v and a t the sample v) which comsponds to point is j ( t D(r - v)do. The sum of all the concentrations of material a t the sample point a t time t which did not come "firsthand" from the injection is therefore
-
and C,(t) - Jot Cz(u)D(t -
D(t) =
0)dU
(24)
CcAt But C& is given by CcAt = Caea
(25)
and therefore
Note that in Equation 26 function D, which is to be determined for one particular value of the argument ( t ) is required with a different value of the argument (t - D), for its own determination. Nevertheless, the numerical profedure required for the application of this integral equation is not tw difficult because the concentration of tagged material returning from the residual of the system, C,, is 0 a t zem time and therefor the value of the distribution function a t zero time as B(o). This giqes the
e&F
initial condition from which the continuation of the numerical procedure can be made. The u x of this equation permits the isolation of the phenomena occurring in each of the vessels or systems of vessels studied. The isolated behavior of one vessel so determined may thus be compared with any hypothetical model or with the analogous m l of any other unit. The regenerators are compared with each other and with the perfect mixing d e l in Figure 12. The time scale is normalized by dividipg the actual time by the average catalyst holding
Shellburn High Inventory Shellburn Low Inventory .- -......Single Stage Perfect Mixing
1.0
-3 n
0.5
\
U
0.L
0.6
0.4
'.--
".8
t/o
Figure 12.
Catalyst age distributions in three regmerabrs
times in the respective regenerators. The comparisons made earlier about the by-paaping in the Houston vc.4, the lag in the Norco vessel, and the dose a p proach to perfect mixing in the Sbellbum vewl are well demonstrated here. Also the comparison between the distribution functions for the two Shellburn regenerator tests is more readily seen here than between the corresponding concentration curves. Another application of the distribution functions is in the calculation of certain properties. Since behavior of catalyst in any particular region is a function of the time that it spends in that region, we can, when we determine the proper weighting factor (from the chemical kinetics of the phenomena involved), weight the distribution function in order to calculate the average property of the catalyst in that particular region. For example, if the carbou-on-catalyst is proportional to the square mot of the time that the catalyst spends in contact with hydrocarbon vapors (3), then the integral of 0 1 0 . 6 from 0 to a is pmportional to the average carbon-on-catalyst at the place where the D is determined. The distribution functions derived directly from the concentration data may also he compared with those predicted fmm a theoretical model for that vessel without introducing inaccuracies due to guesses about the appropriate models for the other vessels in the system. In order to make this comparison, we must calculate the distribution function corresponding to a particular theoretical model for the vessel. For example, for a reactorstripper system similar to that shown in Figure 1, the mathematical procedure is as follows:
Write a material balance around the reactor cone on material of age t . Therc is no material entering the cone of age greater than zero. The net rate of a p pearance of catalyst of age t in the cone (below the grid) is dD WJDXt - at) - DXt)] = - W e_ dtI 6f (27)
Assume that the fraction by-passing the cone is (1.K) and the fraction by-passing the bed above the grid is (1-L). At steady state the net rate of appearance is equal to the rate of removal: dD (28) KRDe6t = - We*" This equation may be integrated to give D, = D.(O)a
- % I
(29)
we
Since
and if we let
it may be shown that, 1 - l/O. De=-*
(32)
e.
By similar reasoning we can derive the differtntial equation describing Db, the distribution function for the dense phaX region above the grid: KLRD.
- LRD,
=
Wb
%
(33)
If we let
a -- & wk
VOL. 49, NO. 1
-
JANVARY 1957
(34)
17
0.07
0. 0 4
I
E
'Z n
0.02
0.01
0.007
10
0
Figure 1 3. I. 11.
Ill. IV.
30
40
Figure 1 4. Age distribution functions, Houston reactor
Age distribution functions, Houston regenerator
Data, regenerator standGpe Single region, no bypassing Two regenerator regions, no bypassing Two regenerator regions, cone bypassing = 0.6, bed bypassing = 0
then by combining Equations 32 and 33, integrating, and normalizing
20
A g e , minutes
Age, minutes
K ( l - L)RD,
I. Data, top of dense bed II. Single reactor region, no bypassing Ill. Two reactor regions, n o bypassing IV. Two reactor regions,cone bypassing = 0.85, bed bypassing = 0.14
+ LRDb - RD, =
W , dD edt
(37)
(1 - K)B, - @b e eb(ec- 6,)
- t/@b
(35)
Then at point X in Figure 1 the distribution function for all ages except zero is D, = LDb K ( l - L)D, (36) and the fraction of zero age catalyst at Xis (1 - K ) (1 - L ) . Similarly, the differential equation describing D,.the distribution function for the stripper, is
which after substituting for D , from Equation 32 and Db from 35, integrating and normalizing gives D, = G e-t/& f H
+
0s
e-t/&
+
[ l - e,G - BbH]e-'/@,
(38)
where
e
9
-3
-
R
(39)
There is no material emerging from the stripper which is of zero age. The procedures outlined have been carried out for the data from the Houston test and are illustrated in Figures 13 through 15 for the regenerator, reactor, and reactor-stripper. Shown on these figures are the distribution functions calculated from the observed concentrations (those curves marked I) while
0
Top of Reactor Dense Bed Standpipe
A Regenerator --Calculated
c
E
"I,"
- 1.2 0
10
20 Age, minutes
30
40
Figure 15. Age distribution functions, Houston reactor-stripper I. 11. 111. IV.
18
Data, stripper standpipe Single reactor region, n o bypassing Two reactor regions, no bypassing Two reactor regions, cone bypassing = 0.85, bed bypassing = 0.14 INDUSTRIAL AND ENGINEERING CHEMISTRY
Time, minutes
Figure 1 6. reactor test
Calculated vs. observed concentrations, Houston
USE OF TRACERS IN R E F I N E R Y STUDIES the theoretical distributions are those marked 11, 111, and IV. Excellent agreement of the data with the theoretical models is obtained with the indicated fractions of bypassing used for curves IV. Prediction of Concentration Data Since the theoretical models that were proposed in the preceding section are successful in predicting the distribution functions for each of the two main vessels of the Houston system, we can with some degree of confidence combine the two theoretical models to predict the concentration-time graphs for each of the two tests. There is one first-order linear differential equation corresponding to each of the well-mixed regions of the complete model. Each of these equations is of the general form
where C, is concentration in i’th region C, is concentration in j’th region N is the number of perfect mixing stages aii are coefficients which depend on the size of catalyst streams and the bypassing fraction I t is in principle possible to obtain an explicit solution from this system of linear differential equations but in any of the practical cases it turns out that a numerical solution with perhaps the aid of an automatic computing machine is much simpler. The latter procedure was employed for analyzing the Houston data, and the results of these calculations are illustrated in Figure 16 for the test with injection into the reactor. In making these calculations, it was assumed that there is negligible holdup time in the risers and standpipes of the system. Figure 16 shows that it is possible to predict the concentrations quite well but that the agreement is not as good as that shown for the distribution function (Figure 14). The poorer agreement results because the inadequacies of the hypothetical models are compounded when dealing with the concentrations and there actually is a finite holdup time in the standpipes. The latter fact is manifested by the observed concentrations in the returning streams lagging behind the calculated concentrations.
lyst mixing studies in commercial fluid catalytic cracking units. These elements do not vaporize from the catalyst surface even at the high catalyst surface temperatures encountered. By the use of a large crystal scintillation dip counter and large counting samples (1 liter) a high sensitivity of gamma ray detection is achieved. The sensitivity of detection of gamma radiation is approximately 50 times that attainable with Geiger counters. With the use of this scintillation dip counter method mixing experiments are readily carried out in units with catalyst inventories of the order 500 tons, employing only 1 mc. of gamma-emitting isotope. This amount is both inexpensive (approximately $1 .00) and easily handled with safety. This tagging technique has been used to determine the catalyst mixing patterns in three of Shell’s catalytic cracking units, Samples of catalyst were taken rapidly from the various vessels immediately following pulse injection of the tagged catalyst. The well-mixed final dilution permits a precise measurement of the total inventory of the entire unit. The curves of radioactivity-concentration versus time allow determination of the distribution of catalyst holding times within the different vessels. The distributions thus determined indicate that the dense beds in the regenerators and reactors approach perfect mixing, but that there are deviations from perfect mixing attributable to catalyst by-passing, regions of relatively immobile catalyst, and/or elements of plug flow. These studies also indicate that when catalyst is introduced into a dense bed via a riser, there is a strong possibility that some of the catalyst bypasses the dense bed and does not become intimately mixed with the inventory. They also show that no bypassing occurs when catalyst is introduced into a vessel by means of a dense phase standpipe. Furthermore, when catalyst is introduced from a dense phase standpipe into a rather large vessel, there is strong possibility that it does not mix intimately with the entire inventory. I t has also been shown that the flow of catalyst approaches plug flow in strippers which contain baffles in the horizontal plane (Norco and Shellburn). These are to be distinguished from the stripper in the Houston unit, which has no horizontal baffles.
Conclusions
Acknowledgment
A suitable method has been devised for tagging equilibrium cracking catalyst with certain radioisotopes. Two gamma-emitting isotopes of suitable properties, scandium-46 and cerium144, have been used successfully in cata-
The authors acknowledge tbe participation in these tests of their colleagues from the Shell organizations-from the refinery staffs, the Houston Research Laboratories, and the Emeryville Research Center. Special acknowledg-
ment is due J. D. Leslie and R. B. Olney for their part in the interpretation of the data and E. J. Hall for valuable technical assistance. Nomenclature C = radioactivity concentration,c.p.m./ ton D = distribution function, min.-l E = energy, m.e.v. G = constant as defined in Equation 40, min. H = constant as defined in Equation 41, min . I = radiation intensitv. ,, mr./hr. K = 1 - fraction bypassing reactor cone L = 1 - fraction bypassing reactor bed N = number of stages Q = amount of radioactivity, mc. R = catalyst circulation rate, tons/min. W = inventory, tons a = coefficient in Equation 42 d = distance from point source, cm. f = fraction of catalyst a t a given age g = constant as defined in Equation 17, min. h = constant as defined in Equation 12, min .--I k = constant as defined in Equation 13, min.? m = constant as defined in Equation 10, min.-’ n = constant as defined in Equation 11, min.--’ t = time, age, min. u = time, min. e = average holding time ( W / R ) ,min.
Subscripts
A B
1
= vessels
D I = final, total F b c
!
3
1
= =
=
o
=
s
= =
x
1
=
reactor bed reactor cone regions in the system in entering stream during injection stripper position in system, Figure 1 positions in the system
literature Cited (1) Handlos, A. E., Kunstman, R. W., Schissler, D. O., IND.ENG. CHEM.
49,25 (1957).
( 2 ) National Bureau of Standards, Wash-
ington 25, D. C., Handbook, 52: p. 15 (1953). “Maximum Permissible Amounts of Radioisotopes in the Human Body and Maximum Permissible Concentrations in Air and Water. (3) Voorhies, A., Jr., IND.END.CHEM.37, 319 (1945). for review December 17, 1955 RECEIVED ACCEPTED May 29, 1956 Division of Petroleum Chemistry, 129th Meeting, ACS, Dallas, Tex., April 1956. VOL. 49, NO. 1
JANUARY 1957
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