REGENERATION OF ADIABATIC FIXED BEDS K. E. OLSON,' DAN LUSS,zAND NEAL R. AMUNDSON University of Minnesota, Minneapolis, Minn. 55455
A model is presented for the diffusion-controlled combustion of coke during catalyst regeneration in an adiabatic packed-bed reactor. Numerical solutions indicate that during startup a rapid premature heating may occur, leading to high temperatures which can damage the catalyst. All the reaction occurs in a combustion zone which remains fixed with time with respect to a moving coordinate system which moves through the b e d at a rate determined solely by the stoichiometry of the process. Concentrating the coke in the external surface of the pellets causes a decrease in the length of the combustion zone. The temperature and concentration profiles are compared to those obtained with other models.
HE
packed-bed regeneration of catalyst with coke deposited
T on its internal porous surface is carried out by preheated flue gas containing approximately 27, oxygen. T h e gas flows through the packed bed and establishes a shallow combustion zone, which slowly travels up the bed, burning off the coke in one pass (Ciapetta et al., 1958; Nix, 1957). T h e maximum temperature attained must be controlled to prevent deactivation of the catalyst. Methods for estimating transient temperature profiles during fixed-bed regeneration have been proposed by van Deemter (1953, 1954) and Johnson et al. (1962). Both assumed temperature independence of the reaction rate, which is a reasonable assumption when the process is diffusioncontrolled. However, the forms of their reaction rates were somewhat oversimplified and as a result neither analysis can be expected to predict temperature and concentration profiles adequately in the combustion zone or the length of this zone. However, the expressions for the regeneration time, the asymptotic maximum temperature attained, and the profiles outside the combustion zone are independent of the reaction rate, so that models give a reasonable qualitative description of the process. Gonzalez and Spencer (1963) used a similar type of kinetics and assumed the reaction to be temperaturedependent. They discussed in detail the numerical difficulties of solving the nonlinear differential equations. T h e aim of this work is to use a more refined rate expression for the case of low oxygen concentration and diffusion-controlled combustion of coke to obtain the temperature profiles in the bed and compare them with the simpler models.
where
T h e temperature change of each pellet (assuming that each pellet has a uniform temperature) is given by
The gas phase is described by
T h e transient terms of Equations 4 and 5 which represent the accumulation of heat and oxygen in the gas phase have been neglected, the justification being that these terms are negligible in comparison with the convective flow. T h e boundary conditions are
Mathematical Model, Model C
Bowman (1955), Johnson et al. (1962), Dobychin and Klibanova (1959), and Weisz and Goodwin (1963) presented evidence that at temperatures above 540' C. the combustion of coke deposited upon a catalyst is diffusion-controlled. The combustion occurs in a very narrow zone and the rate of movement of this reaction zone is controlled by the diffusion and mass transfer of the oxygen to the reaction shell. Yagi and Kunii (1953) were the first to devise a pseudo-steadystate model for such a reaction, and the approximations involved in this model were shown to be negligible (Bischoff, 1965). The work of Weisz and Goodwin (1963) presents experimental evidence for the adequacy of the shell progressive model. T h e differential equation describing the movement of the dimensionless coked zone radius, s( = rc/R),is 1
2
96
Present address, American Cyanamid Co., Stamford, Conn. Present address, University of Houston, Houston, Tex. l&EC PROCESS D E S I G N A N D DEVELOPMENT
x,
= xpo
atz = 0
(6)
T,
=
T,,
atz = 0
(7)
s
= 1
ate = 0
(8)
Ts = Too
ate = 0
(9)
The concentration profile of the coke in the catalyst was taken as TV = W* [ b
+ (i)*]
which reduces to a uniform distribution of carbon for very large values of b. Equations 1, 3, 4,and 5 can be rewritten as bS
b 7', --
=
a4(Ts
- To)
where
a5 =
3MIl'* c,(TO) -
R
xo0
cs(T0)
T h e equations were solved numerically using the RungeKutta-Gill method. The computations were continued until the profile for long regeneration times became evident or the combustion zone reached the end of the bed. T h e change of properties with temperature was included in the computed example. T h e details of the computer program are described by Olson (1962).
Example.
P To
The following operating conditions were chosen :
1 "" I"
= = =
3 atm. 300' C. 0.02
+
(;>'I
Jt7
=
0.06[0.067
ps
=
R
=
-AH =
1.10 gram/cc. l/16 inch 0.00957 gram,/'sq. cm. sec. 5.55 sq. cm./sec. 0.2132 0.0851 X l o p 3 T,cal./g. K . 0.2194 0.065 T,cal./g. K . 30 g./g. mole 0.38 11.83 g. coke/g. mole 0 2 93851 - 0.398 T,cal./g. mole O2
h
2.023 .
G De
=
c
= = = = =
EY
=
cd co
M
=
+ +
T h e high initial rate produces a rapid premature development of a temperature peak which traveled a short distance into the preheating zone as shown in Figure 1. After this initial period heat dissipation by convective flow caused the temperature of this peak to drop below the normal maximum, which is always near the front of the combustion zone. Thus the dashed line follows two different peaks of the temperature and should not be construed as suggesting the existence of a discontinuity. In this example one unit of 7 equals about 0.5 seconds. Once the combustion zone is fully developed, the maximum temperature in the bed rapidly approaches a constant level which is independent of P D , / s - T h i s usually happens after a few centimeters of the bed have been regenerated. the transient However, a t sufficiently low values of P De/* maximum temperature might considerably exceed the asymptotic maximum value. This fact is clearly demonstrated in Figure 2. This effect might be severe enough to damage the catalyst. T h e reason that an increase in the flow rate. G, causes a higher initial maximum temperature, is that initially the rat? of combustion is proportional to K , the mass transfer coefficient, which varies as Even though in this case the temperature peak moves faster out of the combustion zone, the initial rate is sufficiently greater to cause a higher temperature to be reached before the dissipation starts. Figures 3 and 4 show the development of the maximum bed temperature for several values of the initial coke concentration and oxygen levels. Upon a redefinition of the dimensionless time, the abscissa of the point corresponding to the complete regeneration of the catalyst a t 2 = 0 becomes nearly the same for all cases. This implies the expected result that the time for the total combustion of the first catalyst is directly proportional to the initial coke content and inversely proportional to the oxygen mole fraction. T h e initial effects seem to be more important a t lower asymptotic temperatures. I t was shown by van Deemter (1953) and Johnson et al. (1962) that the asymptotic maximum temperature can be estimated from an over-all heat balance without using a reaction rate term. For the low oxygen concentration case in which the transport velocity exceeds the combustion zone velocity
de.
Figure 1 describes the movement of the combustion zone through the reactor. T h e end of the combustion was determined by the point a t which the oxygen concentration, X,, equaled 10 -5. After a short initial time the combustion zone moves at a constant velocity as predicted by van Deemter (1953, 1954) and Johnson et a / . (1962).
Y 0.
P
,
325-
cm
w 601
LOCATION OF MAXIMUM PARTICLE TEMPERATURE-
E
c
-
300-
ASYMPTOTIC
w
MAXIMUM
3
t
2
275-
F W
250
1
25
75
50
DIMENSIONLESS DIMENSIONLESS TIME
Figure 1.
,T
Movement of combustion zone through b e d
Figure 2.
1
I
125
150
~
I00 TIME, T
Initial maximum temperature transients Diffusion-mars transfer ratio as parameter
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NO. 1
JANUARY 1 9 6 8
97
For the standard example this corresponds to an error of 0.02%. If we denote the moving coordinate by z*, the differential equations can be immediately obtained from Equations 1, 3, 4, and 5 by the transformation
COMPLETION OF COKE BURN-OFF AT BED ENTRANCE
X
For computational convenience the equations were written in terms of the dimensionless terms like Equations 11 to 14. T h e independent variable is 60
30
120
90
DIMENSIONLESS
Figure 3.
I50 TIME,
210
180
240
T,
Including the two transient terms of Equations 4 and 5 had a negligible effect on the profiles, as one might expect.
Transient maximum temperature
Initial coke content as parameter
Numerical Procedure
-1 _I
I I
-k, Y /xG0=003
500-
T
I
T h e equations were integrated backwards by the RungeKutta-Gill method from the boundary of the combustionpreheating zone. T h e assumed initial values were p
T,
=
(22)
= 1.0
T , = T,,,
x, = 6 150
Comparison of Johnson’s model with model C
in Figure 9 seems to be that the leading and trailing portions of the combustion zone, where the reaction rate is slow but still significant, are much longer in Johnson’s model. Johnson’s assumption about gas-solid temperature equilibrium did not cause any major differences in the profiles because the reaction rate is practically temperature-dependent. Conclusions
During fixed-bed regeneration all reaction occurs in a combustion zone whose profile remains fixed with respect to a moving coordinate system which passes through the bed a t a constant rate determined solely by the stoichiometry of the process. T h e highest rate of combustion in the diffusioncontrolled case occurs a t the start of the regeneration, when flue gas containing the high inlet oxygen concentration comes in contact with coke-filled pellets in which a diffusion-retarding burned-out shell has not yet been formed. This may cause a rapid premature heating, often leading to temperatures above
100
= =
I h E C PROCESS DESIGN A N D DEVELOPMENT
SUBSCRIPTs = coke g = bulk gas phase S = catalyst phase 0 = initial value Overbar indicates average C
literature Cited
Bischoff, K. B., Chem. Eng. Sci. 20, 783 (1965). Bowman, W. H., 111, Sc.D. thesis, Massachusetts Institute of ‘Technology, 1955. Ciapetta, F. J., Dobra, R. M., Baker, R. W., “Catalysis,” Vol. VI, pp. 632-87, Reinhold, New York, 1958. Dobychin, D. P., Klibanova, T. M., Z h . Fiz. Khim. 33, 869 (1959). Gonzalez, L. A., Spencer, E. H., Chem. Eng. Sci. 18, 753 (1963). Johnson, B. M., Froment, G. F., Watson, C. C., Chem. Eng. Sci. 17, 835 (1962). Nix, H. C., Petrol. Eng. 29, No. 6, c-13 (1957). Olson, K. E., Ph.D. thesis, University of Minnesota, 1962. Schulman, B. L., Znd. Eng. Chem. 5 5 , No. 12, 44 (1963). van Deemter, J. J., Znd. Eng. Chem., 45, 1227 (1953). van Deemter, J. J., Znd. Eng. Chem. 46, 2300 (1954). Weisz, P. B., Goodwin, R. D., J . Catalysis 2, 397 (1963). Yagi, S., Kunii, D. J., J . Chem. SOC.(Japan), Znd. Chem. Sec. 56, 131 (1953). RECEIVED for review April 17, 1967 ACCEPTEDAugust 16, 1967 Work supported by the National Science Foundation.
