Ind. Eng. Chem. Res. 1993,32, 577-583
577
KINETICS, CATALYSIS, AND REACTION ENGINEERING Tracer Studies on a Riser Reactor of a Fluidized Catalyst Cracking Plant Pekka I. Viitanen V T T (Technical Research Centre of Finland), Reactor Laboratory, P.O.Box 200 (Otakaari 3 A ) ,
SF-02151 Espoo, Finland
Tracer studies performed on a riser reactor of a fluidized catalyst cracking plant are presented including some of the raw data. The tracers used were 41Arand I4OLa. Axial and radial dispersion coefficients have been determined for modeling purposes.
Introduction The dynamics of fluidized beds has been a subject of intensive study over the past decade as the importance and use of fluidization techniques have increased. A major question is defining the regime of fluidization, which depends on many parameters and greatly affects the dynamic behavior of the particles. Extreme cases of fluidization regimes are a fixed bed and a dilute-phase flow of particles (Matsen, 1988). In this paper the distribution of different phases in a riser reactor at a fluidized catalyst cracking (FCC) plant, which is used in the oil refinery industry, has been studied. The work was mainly based on measurements with radioactive tracers. The measurements provided essential parameters for the mathematical models presented. The flow in the riser reactor consists of steam, hydrocarbons to be cracked, and the cracking catalyst. The hydrocarbons are introduced to the riser as liquid, but in the heat of the reactor they are vaporized almost immediately. Thus, the flow in the riser is a multiphase flow but can also be referred as a two-phase flow consisting of a vapor phase and a particulate phase. Most flows met in practice are turbulent. The modeling of turbulence demands a statistical approach, and even when considering one-phase flow in a simple geometry, the problem of turbulence is a very difficult one. Even laminar flows can be solved only in simple idealized cases. This makes it easy to understand that the modeling of two-phase or multiphase turbulent flows is far from exact. However,when experimental correlations are made, many practical tasks can be solved satisfactorily. The model described in this paper is of a statistical nature and uses the random-number generator of a computer. The very simple idea of the model is to present the effect of turbulence and the particle-particle interactions as a random component added to the particle convective movement.
The Riser of an FCC plant Catalytic cracking is a process in which partially refined oil products are converted into more valuable products, e.g., gasoline. This process is one of the most profitable in the oil refinery industry. The main sections of an FCC plant are the riser in which the cracking takes place, the disengager in which the cracked hydrocarbons and catalyst are separated by OSSS-5SS5/93/2632-Q577$04.00/0
cyclones, and the regenerator, which is used to regenerate the spent catalyst before it is introduced into the riser again. When fluidized catalyst cracking is used, the hydrocarbons to be cracked are injected into ariser reactor where the fluidized catalyst flow upward. The catalyst is fluidized by steam injected through a porous distributor a t the riser bottom. When the hydrocarbons and the catalyst are in contact, the cracking takes place. The FCC cracking catalyst is a ceramic powder-like substance containing lanthanum-exchanged zeolite. Commercially available catalysts differ slightly in size distribution and density. The catalyst here had a mean particle diameter of about 70 pm as mass fractions are used and a bulk density of about 640 kg/m3. The riser is a vertical tube reactor. The riser studied in this paper has an inner diameter of 1.0 m a t the lower section of the riser. The diameter widens at the height 9.5 m to 1.3 m. The oil inlet nozzles shoot at the height 2.8 m measured from the riser bottom, and the total height of the riser is 39 m. Data needed in calculations done in this paper, e.g., the operation conditions of the riser during the measurements, are listed in Table I.
Principles of the Tracer Methods Residence Time Distribution. Radioactive tracers are widely used in industry and environmental measurements. Typical applications are the study of material flow and dispersion, flow measurement, leak detection, and wear studies. Over 30 years ago, e.g., by DeMaria and Longfield (19621,tracers were used to study the behavior of fluidized beds. Recently Lakshmanan and Potter (1987) have used tracers to verify the results of a mixing model for a fluidized bed. Hypphen (1989)has described tracer behavior in a fast-circulating fluidized bed for coal combustion with a dispersion model. Bernard et al. (1989) have used tracers to study an FCC plant. A basic property of a continuous process is its residence time distribution, which tells how much time a particle of process material is likely to spend in the process. The measurement of the residence time distribution is a task which can be done using radioactive tracers. A small amount of the tracer is fed suddenly, optimally as a &peak, into the main material flow at the process entrance. The mean residence time is calculated using discrete measurement data, such as 1993 American Chemical Society
578 Ind. Eng. Chem. Res., Vol. 32,No. 4, 1993 Table I. Operation Conditions and Geometrical Data for the Riser Reactor Studied in This Work process characteristics value or dimension height of riser 39 m inner diam of riser 1.0 m (lower 9.5m) 1.3 m (upper section) wall thickness of riser 16 mm (steel) 75 mm (lining) 250 "c temp of inlet oil temp at rieer top 529 O C press. at riser top 2.58 bar (absolute) mass flow of hydrocarbons 181 tlh molar mass of hydrocarbons 400-440 g/mol mass flow of steam 4 tth mass flow of catalyst 1380 t/h catalyst particle load 488 kg/(m28) (lower 9.5 m) 289 kg/(m*s) (upper section) 640 kg/m3 (bulk) catalyst density 2400 kg/m3 (true) mass fraction (%) catalyst particle size (pm) 0-20 1 20-40 4 40-80 56 20 80-105 105-149 12 >149 7 ~
~
m
istni i=-t, =m
where At is the measurement interval and ni is the number of counts measured at a certain measurement interval. The index m refers to measured resid_ence time. An estimate of the measurement error for tm can be made using the fact that radioactive decay is a statistical process obeying the Poisson distribution. The mean deviation of a measured number of counts n is un = d 2 . Taking this into account it is quite easy to calculate that the mean deviation of 1, is
where N is the total number of counts, Le., N = Ci",-,ni,and the indexing is such that i = 0 at the time t. In an open system some of the injected tracer may be backmixed and, thus, be delayed entering the region of interest. In this case mean residence time measured has to be corrected in order to obtain the true mean residence time. The measured residence time Zm is (van der Laan, 1967;Nauman and Buffham, 1983)
(4)
which becomes identical with the true residence time in a uniformly open case, i.e., DA = DE. Axial mean velocity u can be determined by measuring the time delay between two measuring points having a known distance L. If several measuring points are provided, the axial velocity profile can be approximated. The axial velocity profile together with the knowledge of mass flow can be used to estimate the axial density profile inside the riser. Determination of Axial and Radial Dispersion Coefficients. Axial dispersion models are often used to describe the results of tracer experiments. The axial dispersion coefficient can be determined from the measured residence time distribution by calculating the mean and the variance of the measured curve and evaluating the dispersion coefficient from an equation relating these factors. Axial dispersion models represent the plug flow when the dispersion coefficient D = 0. With small values of D (or high Pe) the model can represent a highly turbulent flow. When dispersion is very large, the physical basis of the model becomes questionable. The Peclet numbers calculated below indicate high dispersion in the studied case. Peclet numbers below 8,a value referred to as the minimum allowable Peclet number in a dispersion model, are observed. However, the dispersion model provides a convenient way to preliminary analysis of the measurementa. The open axial dispersion model was reasoned to correspond to the situation of the measurements, since the measuring locations were not at extreme ends of the riser and, thus, backmixing was possible. The variance for the measured tracer distribution according to the open axial dispersion model is (van der Laan, 1957) (5)
Experimental determination of the radial dispersion coefficient can be made by measuring the amount of spreading of the &inputof tracer. Different constructions for the measuring system are possible depending on the geometry of the studied vessel. The principle of the method is to measure the radiation intensity by at least two detectors. The maximum count rates measured are fitted to the solution of the dispersion equation without convection. This solution has the form of the standard normal distribution
c(x,t)=
-t , = L +Din + Dout U
U2
-)
1 + 1 =t 1+pein 'eout
-(
1
e-x=/4Dt
(47rDt)'/' In a more thorough analysis,the dispersion equation should be solved with the boundary conditions a t the wall. (3)
where D is the dispersion coefficient, L is the length from the injection point to the measuring point, and u is the average flow velocity. Pe = uL/D is the Peclet number. When the tracer concentration is measured in two points, say A and B, the true measured residence time between these points is
Making the Measurements Tracers. The measurement of the residence time of the riser reactor was done separately for the gas phase and the particulate phase. An attempt to separately measure the behavior of hydrocarbons was made, but this was not successful because no suitable tracer was available. The measurement of the gas phase was made using a radioactive isotope of argon (41Ar) as tracer. 41Ar was
Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993 679 obtained by irradiating natural argon in the thermal neutron flux of a 250-kW research nuclear reactor. The nuclear reaction which occurs in the irradiation process is 40Ar(n,y)41Ar.41Arhas a half-life of 1.83 h and radiates y-quanta with an energy of 1.29 MeV. As a noble gas, argon does not react with the process material. The effects of different density when compared to the fluidizing vapor and gaseous hydrocarbons are considered to be minor. The residence time distribution of the particulate phase was measured using irradiated catalyst. The FCC catalyst contains lanthanum, which can be activated by thermal neutrons. The nuclear reaction that occurs is 139La(n,r)140La. The reaction cross section is quite low. This makes it necessary to use a long activation time and a relatively large amount, about 100 g, of catalyst to achieve a detectable amount of radiation. 140Laradiates 8-radiation and y-radiation of several discrete energies. The y-energies are quite low, which decreases the efficiency of radiation detection. The half-life of 140Lais 40.2 h. Measurement Facilities. The tracer pulses were fed into the riser with the purge steam, which is used to clean up the output of the oil inlet nozzles. Since the flow rate of the purge steam is quite low, the initial momentum of the tracer after the injection is almost completely due to drag by the vertical main flow inside the riser. The propagation of tracer pulses was detected using 15 thallium-activated sodium iodide NaI(T1) scintillation detectors. The signal of these detectors is linear up to a count rate of about 10 000 cps, as the dead-time effects become noticeable. The information from the detectors was gathered using two eight-channel measuring systems based on a personal computer. A detailed description of the equipment has been presented by Kiimiiriiinen et al. (1990). The detectors were located at seven different heights along the riser. At four levels, three detectors were collimated side by side in such a way that information about the radial distribution of the different phases could be obtained. The accompanying detectors were checked with a standard radiation source to give equal signals within a range of about *5%. At other levels, only one detector was used. The heights and horizontal location of the detectors, when the level of the oil inlet nozzles is taken as zero, are indicated in Figure 1.
Results Data Manipulation. Some of the raw data obtained from the measurements are presented in Table 11. The data are compressed by summing the original data which had a time step 0.1 s. The first task in data manipulation is to subtract the background count rates from the measured count rates. The half-life correction which is often necessary in radioactive tracer experiments is here unnecessary because of the short duration of the measurement. In order to calculate the residence times, the time of the tracer injection can be determined using the distribution measured at the level 0 m. The count rates have a statistical variation, and also, disturbances effected by the tracer moving in the injection equipment outside the riser are seen in the beginning of the data. The effect of these disturbances is minimized by choosing only the peak area to be used in the calculations. After this the mean residence times and their error estimations as well as the variances of the tracer concentration distributions can be calculated. The variances can be used to make the corrections to the mean residence times of an open system.
31.9 m
22.1 m
9.9 m .
7.4 m.
3.3 m 1.3 m. 0 m. \
Figure 1. Location of the detectors along the riser. The positions of the detectors at each measuring level are indicated in the boxes representing a horizontal cross section of the measuring levels. The oil nozzles used in tracer injections are at the level 0 m.
Residence Time Distributions. The tracer concentration curves measured by the uppermost detector are presented in Figure 2. The mean residence times calculated for the uppermost measuring point were about 2.9 s for the gas and 5.3 s for the catalyst. The mean residence times are presented in Table 111. These are averages of four different measurements for the gas phase. As the calculations of the dispersion coefficients presented below indicate that the system is not uniform, the correction described by eq 4 has been made. The errors have been estimated using eq 2. Only two different measurements of the catalyst phase were successful. This happened because the nozzles, through which the tracer was fed, became clogged. Axial Velocity and Density Profiles. The axial velocity profile was estimated from the mean velocity between successive measuring points. This velocity was set to correspond to the velocity in the middle of the two measuring points. The velocity profile obtained using this procedure is presented in Figure 3. The errors were estimated using the data in Table I1 for the error of time determination and a value of 0.1 m for the error of the distance between the measuring points. The error for the gas velocity is noticed to be considerably large since the relative error for the time determination is large. The velocity of the gas phase obtained by the tracer technique can be validated by calculating the gas velocity using the process conditions. The mass flow of steam was 4 t/h and that of the hydrocarbons 181 tlh. If a pressure of 2.6 bar (absolute) and atemperature of 500 OC are used, a value of 2.3 m3/kg is obtained for the specific volume of steam. Furthermore, if the molar mass of the inlet hydrocarbons is 420 glmol, the specific volume of the
580 Ind. Eng. Chem. Res., Vol. 32,
No. 4,1993
Table IL8 Raw Data Obtained from the Measurements channel 1ocation Unit 1 1 Om 2 1.3 m, left 3 1.3 m, middle 4 1.3 m, right 5 3.3 m, left 6 3.3 m, middle 7 3.3 m, right 8 31.9 m 1
2
3
387 205 104 57 54 44 32 43 24 43 35 35 23 37 28 29 16 26 24 32 23 20 30 21 27 36 32 32 25 25 26 31 26 22 26 31 26 24 23 26
1115 821 376 106 53 31 29 28 20 22 29 12 17 17 13 12 16 17 13
501 434 225 68 51 34 24 25 27 19 12 25 18 20 15 17 14 10 8 14 9 11 11 12 7 7 12 12 10 13 8 6 6 14 11 11 11 12 10 13
265 1786 436 122 87 42 47 49 42 40 36 30 21 21 23 37 26 8 9 6 12 11 12 14
167 155 240 104 50 36 20 30 25 21 18 22 19 21 15
11 6 15 10 9 9 15 17 11 11 15 9 3 10 11 7 9 9 7 12 13
11
15 12 16 14 22 18 10 12
127 248 535 139 68 30 22 29 20 20 23 23 13 16 28 19 17 9 11 11 10 13 20 14
channel
location Unit 2 7.4 m, left 7.4 m, middle 7.4 m, right 9.9 m 22.1 m, left 22.1 m, middle 22.1 m, right
9 10 11 12 13 14 15 16
Om
4
5
6
7
8
9
10
11 12 13 Catalyst Injection to the Leftmost Nozzle 1. Measured Count Rates (At = 0.5 s)
14
180 144 79 45 33 26 18 11 19 14 14 15 16 17 10 13 14 15 18 14 14 7 11 9 15 13 20 9 11 6 13 14 12 13 9 16 12 12 8 8
85 135 129 74 59 37 26 18 19 10 11 5 4 5 0 3 5 3 5 5 2 4 3 2 5 2 2 3 3 2
115 267 202 115 50 44 14 14 18 17 10 3 6 4 1 3 2 4 6 4 5 2 0 1 2 0
306 348 209 90 42 26 28 15 18 14 8 9 8 8 6 4 5 7 5 4 7 6 6 2 2 1 2 2 2 4
1 0 0 17 110 162 190 164 176 153 130 116 94 65 83 45 46 40 41 24 29 16 23 14 15 12 17 13 15 7 5 8 11 9 3 6
3 4 5 0 63 118 94 61 50 41 37 15 15 14 16 17 15 13 10 4 5 0 2 2 2 3 4 2 0 0 6 0 3 2 2 3
3 3 5 0 154 235 248 117 79 70 58 30 26 19 16 13 13 12 15 8 8
0 0 3 0 0 0 46 92 94 78 44 47 40 30 24 27 30 15 8 11 9 6 7 8 6 3 4 1 2 6 2 3 2 6
3 2 3 3 169 239 226 172 125 70 30 44 31 31 19 15 8 4 9 7 10 2 3 4 6 5 4 4 7 1 2
7 0 8 0 1 9 2 3 4 152 2 408 430 33 335 59 183 82 157 54 106 32 26 63 21 64 49 25 17 50 19 40 13 32 24 13 17 32 12 9 11 6 1 8 13 4 5 10 5 5 14 4 3 10 4 4 9 1 3 8 1 6 0 9 2 1 5 2 3 1 5 0 3 1 3 1 2 02 2 4 1 5 7 1 6 0 2 1 0 2 6 3 1 3 3 3 1 5 1 3 2 8 6 5 3 3 2 6 2 1 3 0 3 1 4 6 0 1 1 4 4 4 2 6 3 2 3 3 0 1 1 3 2 2 5 3 2 1 4 1 1 1 4 3 2 1 0 1 2 2 Argon Injection to the Rightmost Nozzle 3. Measured Count Rates ( A t = 0.2 s) 147 20 10 27 0 2 4 1 7 0 12 491 9 20 2 0 1 2 1 1 124 149 805 236 3 4 0 1 0 1 171 118 168 160 0 60 160 178 9 0 45 51 56 63 0 86 158 193 532 0 28 35 23 44 0 48 110 111 674 1 16 18 19 32 9 2 42 52 384 0 22 29 3 7 11 1 25 222 34 15 15 18 10 8 7 2 27 128 14 57 12 24 8 3 7 4 20 23 81 64 18 7 5 4 79 2 24 15 73 98 17 8 6 1 146 8 15 13 41 36 20 3 2 190 2 7 8 37 23 9 2 26 3 137 2 3 2 4 28 19 17 6 4 8 126 2 4 22 8 23 14 4 1 94 2 6 1 7 21 18 17 3 9 11 87 9 6 I 14 13 3 4 84 6 4 6 1 9 10 11 11 4 57 3 1 1 2 9 19 7 44 2 3 5 2 4 0 5 20 6 6 46 3 4 1 4 0 3 5 11 7 11 1 1 33 1 1 5 6 .6 1 2 23 3 8 0 1 2 4 8 2 10 5 1 1 35 2 2 4 3
1 1 2 0 0 3 0 2 2 0 2 2
15
16
1
353 335 441 506 273 152 60 60 49 36 45 30 31 40 36 28 34 24 31 22 22 26 25 33 18 24 25 27 30 36 34 29 16 31 19 34 32 19 25 33
0 0
1 0 0 30 37 44 27 16 13 19 11 19 9 13 9 5 8 3 2
1 1 3 3 3 0 1 0 0 4 3 0 3 2 0
1 1 3 2 2 1
1 0 0
1
1
21 83 89 50 53 25 29 27 20 9 10 5 5 7 4 10 5
11
45 57 41 32 31 17 15 12 2 7 2 4 7
1 5 3
265 1683 551 126 88 42 48 51 42 38 38 32 20 21 23 33 29 10 9 6 10 12 13 12
Ind. Eng. Chem. Res., Vol. 32,No. 4,1993 581 Table I1 (Continued)
1 8 14 18 12 10 16 15 15 18 9 9 14 10 11 13 9 13 20 6 15 11 14 12 10 12 11
2 11 11 12 13 14 20 22 13 16 14 18 9 16 7 17 12 16 17 14 12 12 13 10 19 16 14
3 13 8 12 14 12 17 8 12 13 11 12 6 11 14 15 13 12 13 11 18 12 5 9 12 5 12
4 9 8 9 6 9 7 8 6 8 10 8 10 8 8 6 9 8
5 0 3 2 1 4 7 3 3
6 3
7 0
0 1 1 1 3 4 0 1 2
7 2 4 5 2 2 3 3 3 3 4 2 2 2 3 5 2 3 4 3 5 2 4 1 7
8 17 26 12 10 13 9 13 9 9 9 8
9
10 1 0 0 0 0 0 1 2 2 0 1 1 0 1 1 3 0 0 1 2 2 0 1 1 0 1
5
2 2 1 2 1 1 0 1 0 1 0 1 1 1 1 0 2 0 0 0 0 0 0 1 1
11 0
12 3
1
0 3
14
13 3 0 1 2 3 1 0 0 1 1 1 0 1 0 0 0 1 0 1 2 1 0 0 0 1 0
3 1 4 2 1 2 2 1 3 1 1 1 1 1 1 3 1 4 1 3 0 0 1 0
15 2 4 3 0 2 0 1 0 0 0 0 0 2 0 0 0 0 0 0 1 0 0 0 0 1 0
3
1 0 1 3 2 1 3 0 0 0 0 1 0 0 1 2 1 1 1 0 0 1 0 0 0
16 9 14 18 13 9 15 16 15 17 9 11 12 10 13 13 8 14 18 7 16 10 15 9 13 12 10
1 3 0 0 1 7 1 2 0 3 1 1 1 1 7 0 1 0 3 6 3 1 2 8 6 3 6 0 1 3 4 2 0 3 9 0 4 5 0 5 0 2 8 6 6 3 10 2 0 6 2 12 2 0 4 2 5 3 3 4 1 13 1 2 3 1 4 11 3 5 1 16 3 2 4 0 7 4 2 3 1 a Two separate measuring units were used. Measuring location at 0 m (channels 1 and 16)can be used to determine the time of the tracer injection. 24 300 r--
m
2
-$
0
Y
?
200
c
2 150
I
I
I
-Catalyst ---Gas
ia -
T
16 -
.-
P)
+
El
I
14x 12 c 8 lo -
C
+d
I
20
250
Q
I
22
2
100
2 0
a 6 -
0
4 -
50
2 -
0 0
10
5
15
Time [ s ]
Figure 2. Tracer concentrations measured at 31.9 m. Table 111. Mean Residence Times of the Gas Phase and the Catalyst in the Riser8 height (m) gas residence time ( 8 ) catalvst residence time ( 8 ) 1.3 0.2f 0.1 0.6f 0.2 1.4f 0.3 3.3 0.3f 0.1 2.3 f 0.3 7.4 0.7 f 0.2 2.4f 0.3 9.9 0.9f 0.2 4.0f 0.4 22.1 1.7f 0.3 31.9 2.9 f 0.4 5.3f 0.4 a
The errors are estimated according to eq 2.
hydrocarbons at the lower part of the riser is 0.6 m3/kg. The total volumetric flow at lower part of the riser is then about 20 000 m3/h, which corresponds to a gas velocity of about 7 m/s. The axial velocity profile of the gas has two noticeable details. First is a deceleration at about the 5-m level. This is explained by the expansion in the riser diameter. Second, a deceleration at about halfway up the riser appears quite unnatural and is probably due to the
0
5
10
15
20
25
30
Height [ m ]
Figure 3. Axial velocity profiles of the gas and solid phase in the riser.
inaccuracy of the calculation, which is indicated by the large error estimations. Also, the fact that the catalyst phase does not decelerate a t this point should confirm this. Using the axial velocity profile of the catalyst presented above and a mass flow of 1380 t/h, the density profile presented in Figure 4 is obtained. For most of the riser an apparent density of about 50 kg/m3is estimated. This corresponds to a particle volume fraction of about 2 % . Dispersion Coefficients. The Peclet numbers and respective axial dispersion Coefficients obtained for the other measuring points are presented in Table IV. The calculation was based on eq 3. The calculation proved to be meaninglessfor the gas phase at the lowest measurement locations, since the measured variance was mainly due to the broadening of the injected tracer peak. The values presented in Table IV indicate that the dispersion coefficient increases as the flow gas upward in the riser. The Peclet numbers obtained are of same order of
582 Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993 250
120
L
I
I
I
-D=0.1
H
Y
100 80
C 0
.c
Z
c
60
C
aJ U C 0
\
0
\
50 -
0
0
40
\
20
t a 0
5
15
10
20
25
30
Figure 4. Average density of the catalyst in the riser calculated using data from Table 111and Figure 2. Riser ~ll5cm
7 7
Nozzles
mators u
u
.o
-0.5
0.0
0.5
1 .o
Distance [rn]
Height [rn]
-50cm
0 -1
u
Detectors Figure 5. Detector arrangement at the 1.3-mlevel.
Table IV. Peclet Numbers and Axial Dispersion Coefficients Obtained from the Model Fittings height (m) Peclet no. dispersion coeff (m2/s) Gas Phase 1.3 3.3 8 9.3 7.4 11.0 9 9.9 14 16.0 22.1 14 23.0 31.9 Catalyst Phase 5 0.3 1.3 6 0.8 3.3 7 3.3 7.4 8 5.0 9.9 13 10.0 22.1 13 15.5 31.9
magnitude as the values reported by Bernard et al. (1989). These were also obtained for a commercial FCC riser and varied from 4 to 25 for the gas phase and from 1to 10 for the catalyst. Li and Weinstein (1989) have reported axial dispersion coefficients in a small scale model for the gas phase with gas velocities up to 5 m/s while particle load was nearly the same as in the upper section of the riser studied in this paper. Their values varying from near 0 to 0.8 m2/sare considerably lower compared to the values in Table IV. The radial dispersion coefficient was determined for the catalyst phase at the lower section of the riser. The detector arrangement at the 1.3-m level is presented in Figure 5. Tracer was fed through the oil inlet nozzle, from which the radial distance to the detection angle of the rightmost detector was about 0.5 m. The mean residence time at the 1.3-m level was 0.6 s, and the solution to the
Figure 6. Solution to the dispersion equation after 0.6 s following a &input at I: = 0.
dispersion equation with a &function input at x: = 0 while t = 0 is plotted in Figure 6. The measured count rates from the rightmost and leftmost detectors, which had the same measurement geometry, were 41 counts/O.l s and 303 counts/O.l s, respectively. These values give a ratio of 13% for the count rate of the rightmost and the maximum count rate for the leftmost detector. A value between 0.03 and 0.06 m2/scan be estimated for the radial dispersion coefficient from Figure 6. At the 3.3-m measuring level where the mean residence time was about 1.4 s, a similar analysis gave a radial dispersion coefficient about 0.02 m2/s. Taking into account the error estimations for the mean residence times, deviations for the measured count rates, and the measurement geometry,the estimatesfor the radial distribution coefficients can be considered very rough. Application of the Determined Coefficients in a Simulation Model. The axial and radial dispersion coefficients were used in a simulation model, which could be considered as a learning model. The purpose of the model was to demonstrate the increased accuracy of dispersion models, when the axial variation of the axial dispersion coefficient is taken into account and, also, the radial dispersion is taken into account. Disadvantages of the axial dispersion models are considered in more detail by Nauman and Buffham (1983). The axial dispersion coefficient varied as shown in Table IV. Several runs of the model were made varying the radial dispersion coefficient within the determined limits. A value of 0.05 m2/s was used for the result presented in Figure 7. The main points of the model are listed as follows: 1. The passes of 10 OOO single particles through the riser are simulated. 2. The basic particle fluid interactions on the particle are Newtonian drag by the fluid and gravity. The effect of turbulence is described rn dispersion. 3. The fluid velocity profile is described by Prandtl's one-seventh power law. 4. A random displacement obeying the Gaussian distribution with variances corresponding to the measured dispersion coefficients is added to the particle location after each time step.
Conclusions When describing a single particle under the basic fluid particle interactions, it had to be assumed that the catalyst
Ind. Eng. Chem. Res., Vol. 32, No. 4, 1993 683 --Model
. - Tracer 1 7 0
The simulation model presented here was to take into account some of the omissions of one-dimensionalmodels. Figure 7 indicates a quite good fit.
r
Amount of t r a c e r i n the 50 riser output [counts/0.2 s ] 60
particles in the riser output (total 300 10000)
10
0
5
15
10
Flight time of a particle
[SI
Figure 7. Residence time distribution of the catalyst according to the simulation model.
flow is a dilute-phase flow. When the density profile in Figure 4 is inspected, it can be noted that the axial density of the catalyst in the riser is almost constant after 5 m up from the oil inlet nozzles. This fact indicates, indeed, that the flow of the catalyst is mainly a dilute-phase flow and only a small dense fluidization region exists at the bottom of the riser. Another fact indicated by the measurements in favor of the dilute-phase flow is that no cluster formation could be detected. The effect of clusters on the residence time distribution would be large variations in the tracer concentration at the tail area. However, the variations of the tracer concentration of the catalyst phase do not exceed the normal statistical variations characteristic of radioactive decay.
Literature Cited Bernard, J. R.; Santos-Cottin, H.; Margrita, R. Use of radioactive tracers for studies on fluidized cracking catalytic plants. Zsotopenpraxis 1989,25 (4), 161. DeMaria, F.;Longfield, J. E. Point age distributions of the gas phase in fluidized beds. Fluidization 1962,58 (38),16. Hyppiinen, T. An experimental and theoretical study of multiphase flow in a circulating fluidized bed; Research paper 15;Lappeenranta University of Technology: Lappeenranta, 1989. Klimiuiiinen,V. J.;KBU, L.; K&, A. PC-baeed hardware and software for tracermeasurementsApp1. Radiat. Zsot. 1990,41 (lO/ll),1079. Lakshmanan, C. C.; Potter, 0. E. Cinematic modeling of dynamics of solids mixing in fluidized beds. Znd. Eng. Chem. Res. 1987,26 (2),292. Li, J.; Weinstein, H. An experimental comparison of gas backmixing in fluidized beds across the regime spectrum. Chem. Eng. Sci. 1989,44 (8),1697. Matsen, J. M. The Rise and Fall of Recurrent Particles: Hydrodynamics of Circulation. In Circulating Fluidized Bed Technology ZI; Basu, P., Large, J., E&.; Pergamon Press: Oxford, 1988;Vol. 1, Chapter 1. Naumann, E. B.; Buffham, B. A. Miring in Continuous Flow System; Wiley: New York, 1983;271 pp. van der Laan, E. Th. Notes on the diffusion-type model for longitudinal mixing in flow. Chem. Eng. Sci. 1957, 7, 187.
Received for review March 9,1992 Revised manuscript received July 27, 1992 Accepted January 11, 1993
