REGENERATION OF COKED CATALYST IN ADIABATIC FIXED BEDS AT LOWER TEMPERATURES Y U l C H l
O Z A W A
Mobil Research & Development Corp., Paulsboro, N . J . 08066 Simulation of the adiabatic regeneration process in fixed beds at lower temperatures was studied. At lower temperatures, the burning rate is controlled by the intrinsic chemical kinetics, which has a much higher activation energy than the mass transfer-controlled regime. The higher temperature dependence of the rate constant causes a significant difference in the temperature and concentration profiles compared to the conventional regeneration process, such as the existence of minimum in the coke concentration profile. An implicit semianalytical solution for the quasi-steady-state burning regime was obtained and shown to approach the unsteady-state solution asymptotically for larger times. This semianalytical solution greatly reduces the numerical solution time required for simulating the entire burning period,
IN
most chemical processes in the petroleum industry, carbonaceous deposits accumulate on the solid catalysts and the activity decreases. This coke has to be removed periodically to restore the activity of the catalysts. This regeneration process for a fixed bed is usually conducted in an adiabatic fashion. On initiation of burning, a sharp temperature peak is observed in a transient period and this peak travels through the bed, after which the concentration and temperature profile changes little with timei.e., quasi-steady state. T o retain the catalyst activity, the temperature in a bed should not exceed a fixed value depending upon the nature of the catalyst. Conventional silica-alumina catalysts may be able to withstand higher temperature, while zeolite catalysts are more sensitive to heat. Therefore, in the regeneration of these zeolitic catalysts, extra caution has to be taken not to damage the catalyst. The simulation of the unsteady-state behavior of an adiabatic fixed-bed reactor has been studied by many investigators. Material and heat balance equations can be expressed in terms of a set of first-order quasilinear partial differential equations, assuming no radial transport of heat or mass. Approximate analytical solutions have been presented by van Deemter (1953, 19541, Johnson et al. (1962), and Zhorov et al. (1967). A numerical solution was developed by Schulman (1963). Gonzalez and Spencer (1963) also proposed a numerical solution, using a secondorder polynomial approximation. Liu and Amundson (1962) treated a similar problem in their stability analysis of an adiabatic packed-bed reactor. The Runge-KuttaGill method was used by Olson et al. (1968) to solve the system equations. Weekman (1964) obtained dynamic solutions for the moving-bed process. Theory
The following assumptions, made to establish the mathematical model, have been used by several investigators. 1. There are no temperature differences between the catalyst particle and the gas due to an infinite heat transfer rate. 378
I & E C PROCESS D E S I G N A N D DEVELOPMEN7
2. There are no radial temperature gradients, since the process is considered to be adiabatic. Liu and Amundson (1962) demonstrated that the interphase temperature difference is negligible in the region under consideration. 3. Heat transfer occurs only in the direction of flow by convection. 4. Gas velocity is uniform over the cross section and length. Gas density variations due to the chemical reaction and temperature changes are negligible. Two distinct limiting models for the coke-burning kinetics have been proposed by Weisz and Goodwin (1966). The coke-burning reaction is controlled by the “intrinsic” chemical kinetics a t temperatures below around 950” F., where the burning rate is essentially uniform through the catalyst pellet. At temperatures above 950°F., the burning rate is controlled by the mass transport of oxygen to the reaction shell. The latter is characterized by a “shell-progressive” burning. In both cases, the burning rate can be expressed in terms of the fraction of carbon remaining and the oxygen partial pressure and the reaction rate constant follows an Arrhenius function of temperature (Zhorov et al., 1967). The activation energy of the Arrhenius expression is estimated in the range of 4000 to 16,000 B.t.u./lb. mole in the mass-transport-controlled region (Gonzalez et al., 1963; Johnson et al., 1962; Schulman, 1963). The assumption of a temperature-independent rate constant can be justified in this region, since the activation energy is rather small compared with that for the chemical reaction. In the intrinsic chemical reaction-controlled region, the activation energy is 67,500 B.t.u./lb. mole (Weisz and Goodwin, 1966), which is much larger than that of the mass-transport-controlled region. In the case of the regeneration of the zeolite catalyst, the process has to be conducted in the intrinsic reactioncontrolled region because of its sensitivity to the heat, while the most conventional silica-alumina catalyst can be regenerated in a shell-progressive burning region. Considerable differences are observed, especially in the coke profile through a reactor for the lower temperature regeneration due to the larger dependency of a rate con-
stant on temperature. Material and heat balance equations under these assumptions are: Oxygen Balance. ps ax + -
M, a7
T=Toatz=Ofort>O where
-G_ax = M , at
B = kot, with x = 0 at
7
= 0 for L 2
xo
-
Yo
1
2 0
D = koxoRt,ps[ 1
x = x O a t t = O f o r r >0
1 t
AE
(z(13) )
P A + PSCS]
Coke Kinetics.
ay = -ko a7
t, = Lpgt J G
exp(-aE/Re) x ( y / y o )
with
L0
y = yoat7 = OforL 2 Heat Balance. a0
[tpgCg+
(1- t ) p s ~ ~]
ae = + Gcg at
a7
AH(1 - e ) psko exp(-AEIRO) x ( y / y o )
(3)
with
L
0 = Boat 7 = 0 for L 0 = Boat = 0 for
T
L0
L0
Equations 1, 2, and 3 with initial and boundary conditions are then normalized by introducing the following reduced variables: = x/xo
Transient-State Model. A numerical solution for the unsteady state was obtained by the method of characteristics (Acrivos, 1956; Liu and Amundson, 1962). Characteristic directions are found for each equation along which the original partial differential equations are converted to ordinary differential equations readily solved by a numerical method. The gas bulk velocity and the heat propagation velocity along the characteristics are as follows: Gas bulk velocity:
Uo7= F L / V t Oxygen transit time (required for oxygen front to reach end of reactor): to, = L / U Q 2= V t J F = t ,
LFP&
x y
= Y/Yo
= [EPgCg
+ (1- t)pscs]V
Heat transit time (required for heat front to reach end of reactor) :
T = RoJAE z =
(14)
Heat propagation velocity:
[/L
t = rG/Lpgt
To give an example, the following operating conditions were chosen:
Oxygen Balance.
ax + dz ax = - A e x p ( - l / T )
-
at
XY
with
X
= O a t t = Ofor 1 L z L 0
X
= 1 . 0 a t x = 0 fort
xo = 0.0175 yo = 0.06 00 = 800" F. ps
>0
= 1.0 g./cc.
pg =
4.52 x
g./cc.
Coke Kinetics. t
dY _ - -B e x p ( - l / T ) XY
= 0.35
M , = 12 g./g. mole
at
with
M g = 28 g./g. mole
Y = 1 . 0 a t t = Ofor 1 2 z
20
Heat Balance.
D
dT
at
aT
+ H- az
cs = 0.292 cal./g. ' C.
c, = 0.294 cal./g. ' C.
= exp(-l/T)
XY
AE= 37,500 cal. Jg. mole VOL. 8
NO. 3 JULY 1969
379
AH = 83,100 cal./g. mole Izo = 1.80 x 10" hr.-'
V = 300 CC.
F = 24.0 S.C.F./hr. Under these conditions, the oxygen and heat transit times are: to, = 0.20 second
tr = 13.7 minutes The heat transit time is much longer than the oxygen transit time because of the greater density of a catalyst particle compared with a gas. This results in two widely divergent characteristic directions, which require small mesh size to attain numerical convergence. Oxygen, coke, and temperature profiles for unsteady state are shown in Figures 1, 2, and 3. The coke profile has a minimum in the z-direction, caused by a maximum in the rate
of coke burning. This maximum occurs in the axial direction, because the effect of temperature on the burning rate increases while the oxygen contribution decreases, leading to a maximum in the burning rate. Quasi-Steady-StateModel. A transient temperature peak travels through the bed after one heat transit time and the temperature and concentration profiles approach with time the characteristic quasi-steady-state asymptotically. In the numerical solutions it was found that the contribution of the first term (time derivative term) in Equations 5 and 10 becomes smaller as time increases after a certain period. The quasi-steady-state solutions asymptotically approach the solutions of a set of partial differential equations without the first term in Equations 5 and 10. I t is important to know the temperature and concentration profiles for longer times, in order to evaluate the time required to reduce the amount of coke to the desired level. A moving coordinate was used in the combustion zone by Beveridge (1963) and Olson et al. (1968) for the quasisteady-state model, and the partial differential equations were converted to the ordinary differential equations. However, this method is not applicable to the present case, since the combustion zone does not travel through the bed with a constant velocity. Asymptotic solutions for the quasi-steady-state model are the solutions of the following partial differential equations:
dX
--82
-A e x p ( - l / T ) X Y
X = 1.0 a t z = 0 for t 0.1
0
0.2
0.5 0.6 0.7 0.8 L. DIMENSIONLESS REACTOR LENGTH
0.3
0.9
0.4
I
I
I
I
1
dT
I
I
-=
T
I 0.1
1
I
1
I
I
0.2
0.3
0.4
0.5
0.6
z,
I 0.7
I 0.8
I
1
0.9
1.0
DIMENSIONLESS REACTOR L E N G T H
Figure 2. Unsteady-state oxygen concentration profiles 1.00,
I
I
I
I
I
I
I
I
(16) (17)
Y = 1.0 a t t = 0 for 1.0 2 z L 0 dZ
0
>0
dY- -B e x p ( - 1 / T ) X Y at
1.0
Figure 1. Unsteady-state temperature profiles I
(15)
I
I
C exp(-l/T) X Y
= T a a t z = Ofort
(18) (19)
>0
(20)
where C = 1/H. Equations 15, 17, and 19 can be solved easily by a numerical method. However, it may take a considerable amount of computer time to obtain the temperature and concentration profiles for longer times, since the computation must always be started a t the initial points. The semianalytical solutions have great significance, since almost instantaneously they can provide the temperature and concentration profiles a t any time. Combining Equations 15 and 19 and solving them lead to:
T
=
C To +- (1.0 - X ) A
(21)
By introducing the following variables: u = X / A andv = Y / B
0'g2*L++H+J0 Equations 15, 17, and 19 can be reduced to the following two partial differential equations:
0.90
L,
DIMENSIONLESS REACTOR LENGTH
Figure 3. Unsteady-state coke concentration profiles 380
I & E C PROCESS D E S I G N A N D DEVELOPMENT
u, = -ABuv exp [ - I / ( To
+xC
-
CU)] (22)
u= l/Aatz=Ofort>O
(23)
[I
vt = -ABuv exp -1/ ( TO+
c - Cu)]
v = 1 / B a t t = 0 for 1.0 2 z 2 0
(25)
(
F ( u )= J
c
-Cu)] A
du ) Cl T~+--CCU A
where
w = l / ( T o + C I A - CU) .$ = -1/To
+ ATo)
{ = -A/(C
du A B u exp
(-
A B u (u - 1 / A ) exp
(38)
Flu) = 1 / B [bEE i ( w + 5 ) - e-< Ei(w + {)] qb (28)
- t/A + const. =
-J
(37)
where
Integrating Equation 28 with respect to z with Boundary Condition 23 gives: $J
F [ ( u- l/A)/BV + l / A ] - F ( u )
Integration in Equation 38 can be evaluated in terms of the exponential integral (Prater and Wei, 1957) as follows:
Substituting Equation 27 into 22 gives:
[
t=
(24)
where subscript indicates partial differentials. Since U, - ut = 0, a new function, 4, can be introduced, so that u and u can be written as:
u2= -ABu exp -1/ To+
Integration of Equation 36 with Initial Condition 25 yields:
(29)
(- To + cl - CU )
e” -du
- m
A
u
Equation 37 can now be written:
The Legendre transformation was applied, which introduced a new function, 9, provided that the Jacobian did not vanish (Courant and Hilbert, 1962).
@=tu+zv-qJ
Ei(w)=S
(30)
+ E ) - e& Ei(w’ + {)] [e-€ Ei(w + E ) - e-{ Ei(w + {I]}
t = 1 / B { [e-t Ei(w’
(39)
where
Then,
t = *u
(31)
z = a”
(32)
Differentiating Equation 29 with respect to u gives:
1
d U - *.,/A = A B u exp
(33)
(- To + Cl ) - CU
z(= a”) = l / B ([e-‘$
A
Since 4 = &u
+ a.,u - 0,4” takes the form: 4” = @ u u u +
(34)
@“UV
aUu +
= 1
A B u exp
e-cJ
w’ Ei(w’+ {) CWt2
+ (1 cwr2
w’ Ei(w’
dw’]-
dw’ -
u - 1/A
[e-€ Ei(w’ + tj -
e& Ei(w’ + {)I} + g ( v ) (40)
Substituting Equation 34 into 33 (U - 1 / A )
The exponential integral can be readily evaluated numerically or the tabulated values can be found in the mathematical tables (Abramowitz and Stegun, 1964; Weast and Selby, 1967). Similarly, z can be expressed in terms of w and w‘ by integrating Equation 39 with respect to u and differentiating with respect to u.
(35)
(- To+--Cu cl
where g ( v ) is an arbitrary function of v and can be determined by Boundary Condition. Integrating by parts and using the Boundary Condition 16, Equation 40 takes the form:
)
A
Equation 35 is a quasilinear partial differential equation with respect to (or t ) and can be converted to the ordinary differential equation as follows:
du u-l/A
dv = -v = -ABu exp
(
1
c
To + - - CU
) dt
(36)
A
VOL. 8 N O . 3 J U L Y 1 9 4 9
381
u and u cannot be explicitly expressed in terms of z and
t , since the right-hand side of Equations 39 and 41 cannot be analytically inverted. The following computing scheme was used to obtain the concentration and temperature profile numerically for a given time. Equation 39 was solved for w', given a set of values of t and w, by using the Newton-Raphson method. The value of w' obtained was then substituted into Equation 41 and a value of z was determined. The oxygen and coke concentration and temperature profiles obtained by solving Equations 15 through 20 are compared to those obtained by solving the original Equations 5 through 12 for longer times in Figures 4 and 5. The quasi-steady-state solution agrees well with the unsteady-state solution after 7.5 heat transit times (103 minutes in actual time). At greater heat transit times, the quasi-steady-state solution asymptotically approaches the unsteady-state solution. If the quasi-steady-state solution, uq,$,, is substituted into Equations 5 , the last two terms vanish, since uq,*, satisfies Equation 15. auq,s,/ a t is obtained by differentiating Equation 29 with respect to t and takes the form:
au at
q.~. =
1 To + C / A - CU ) (42)
-ABu(u - 1 / A ) exp (
The right-hand side of Equation 42 approaches zero with time, since u approaches 1/A as time goes to infinity. Conclusions
When adiabatic regeneration in a fixed bed is conducted a t lower temperature, the coke concentration profile has the minimum point along the axial direction of the bed because of the higher activation energy of burning reaction. This minimum point moves toward the end of the reactor and the combustion zone does not travel with a constant velocity as in higher temperature regeneration.
UNSTEADY 0
.a
STATE S O L U T I O N
QUASI-STEADY
840
./"
0.2
..-y , 0.1
I
I
0.2 1.
1
I
0.5
0.6
1
I
0.7 0.8 DIMENSIONLESS R E A C T O R LENGTH
0.3
0.4
9 I
-820
*-/@
0
z
-860
STATE SOLUTION
I 0.9
IC'
800 1.0
Figure 4. Unsteady-state and quasi-steady-state solutions of temperature and oxygen Concentration profiles
The effect of accumulation terms in the oxygen balance and heat balance equations became smaller for longer times after the quasi-steady state was established. The solutions of the complete unsteady-state equations converged to the solutions of the quasi-steady-state equations asymptotically. These semianalytical solutions for larger burning times are useful in evaluating the approximate regeneration time required to reduce the coke concentration to a desired level. Acknowledgment
The author thanks the Mobil Research and Development Corp. for permission to publish this work. He also expresses appreciation to J. C. W. Kuo and S. Liu, Central Research Division, Mobil Research and Development Corp., for their advice and encouragement. Nomenclature
A, B C, D, H = dimensionless constants c = heat capacity, B.t.u./lb. F. AE = activation energy of coke burning reaction, B.t.u./lb. mole F = gas flow rate, cu. ft./hr. G = gas m a s flow rate, lb./hr. sq. ft. AH = heat of combustion, B.t.u./lb. coke ko = rate constant, defined by Equation 13, l i h r . L = height of packed bed, ft. M = molecular weight, lb./lb. mole R = ideal gas law constant T = dimensionless temperature, defined by Equation 4 t = dimensionless time, defined by Equation 4 t, = contact time, defined by Equation 14, l / h r . to* = oxygen transit time, defined by Equation 14, l/hr. tr = heat transit time, defined by Equation 14, l/hr. U = propagation velocity, defined by Equation 14, ft./ hr. u = X/A V = reactor volume, cu. ft. v = Y/B w = 1/(To+ CIA - CU) W' = 1 / ( To + C/A - C [ ( U- ~ / A ) / u 1+/ A ] } X = dimensionless oxygen concentration, defined by Equation 4 x = mole fraction of oxygen Y = dimensionless coke concentration, defined by Equation 14 y = coke concentration, lb. cokeilb. catalyst t = dimensionless distance, defined by Equation 4
GREEKLETTERS (Y
= stoichiometric coefficient, lb. moles On/lb.
= 0 = e
= = = @ = t = I = p
T
01
0
I 0.1
I
0.2 1 ,
I
I
0.3
0.4
I 0.5
I
I
I
I
1
0.6
0.7
0.8
0.9
1.0
DIMENSIONLESS R E A C T O R L E N G T H
Figure 5. Unsteady-state and quasi-steady-state solutions of coke concentration profiles 382
I & E C PROCESS D E S I G N A N D DEVELOPMENT
moles coke void fraction of bed temperature, O F . density, lb./cu. ft. time, hr. function, defined by Equation 30 function, defined by Equations 26 and 27 -1/To -A/(C+ATo)
SUBSCRIPTS c = coke g = bulk gas phase
= oxygen s = catalyst phase T = temperature U.S. = unsteady state q.s. = quasi-steady state 0 = initial value 0 2
Literature Cited
Abramowitz, M., Stegun, I. A., “Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables,” National Bureau of Standards, 1964. Acrivos, A., I d . Eng. Chem. 48, 703 (1956). Beveridge, G. S. G., Symposium on Chemical Engineering in the Metallurgical Industries, Edinburgh, Sept. 25-26, 1963, p. 87. Courant, R., Hilbert, D., “Methods of Mathematical Physics,” Vol. 11, p. 32, Interscience, New York, 1962. Gonzalez, L. O., Spencer, E. H., Chem. Eng. Sci. 18, 753 (1963). Johnson, B. M., Froment, G. F., Watson, C. C., Chem. Eng. Sci. 17, 835 (1962).
Liu, S., Amundson, N. R., Ind. Eng. Chem. Fundamentals 1, 200 (1962). Olson, K. E., Luss, D., Amundson, N. R., IND. ENG. CHEM.PROCESS DESIGNDEVELOP. 7, 96 (1968). Prater, C. D., Wei, J., Mobil Research & Development Corp., Paulsboro, N. J., private communication, 1957. Schulman, B. L., Ind. Eng. Chem. 55,44 (1963). Van Deemter, J. J., Ind. Eng. Chem. 45, 1227 (1953). Van Deemter, J. J., Ind. Eng. Chem. 46, 2300 (1954). Weast, R. C., Selby, S. M., “Handbook of Tables for Mathematics,” Chemical Rubber Co., Cleveland, Ohio, 1967. Weekman, V. W., Mobil Research & Development Corp., Paulsboro, N. J., private communication, 1964. Weisz, P. B., Goodwin, R. B., J . Catalysis 6, 227 (1966). Zhorov, Yu. M., Panchenkov, G. M., Laz’yan, Yu. I., Zh. Fiz. Khim. 41, 1574 (1967).
RECEIVED for review September 26, 1968 ACCEPTED February 17, 1969
ACTIVE SPECIES ON COKED SILICA-ALUMINA CATALYST F . E . MASSOTH AND P . G . M E N O N ’ Gulf Research & Development Co., P.O. Drawer 2038, Pittsburgh, Pa. 15230 The rapid, initial temperature rise attending oxidation of coked silica-alumina catalysts is due to a highly reactive material residing on the coke surface. The active species is formed in the coking process and is present even after a mild prevolatilization treatment in nitrogen; but it may be removed or rendered inactive by pretreatment under vacuum or in nitrogen a t high temperature. A hydrogen-rich coke layer on the exterior of the basic coke particle is believed to be responsible for the effect observed.
DURING investigation
into the kinetics of regeneration of coked silica-alumina catalysts, several attempts were made to measure the temperature excursions attending initial reactivity (Massoth, 1967). A rapid rise in sample temperature was immediately obtained upon introduction of the oxidizing gas, followed by a moderately rapid decrease in temperature to essentially isothermal conditions for the duration of the oxidation. Since a rapid, initial adsorption of oxygen coincided with the temperature rise, it was thought that the latter was due to the heat of adsorption of oxygen on the coke, which may be high (Haywood and Trapnell, 1964). Recently, a Russian paper ascribed the initial temperature peaks to a combination of the carbon oxidation reaction and heat transfer limitations in the coked silica-alumina catalyst (Zhorov et al., 1966). In light of this work, earlier runs were reviewed and additional experiments were performed to establish if the authors’ initial temperature peaks were attributable to either the oxidation reaction or adsorption. Our results show that neither mechanism is important, but that an active species residing on the coke is responsible for the effect. ‘Present address, Ketjen N.V., Amsterdam, The Netherlands.
Experimental
Fuller details of the coking procedure previously outlined (Massoth, 1967) are given here because of its bearing on the results. A batch reactor under hydrogen pressure was used for the coking instead of the conventional flow reactor at atmospheric pressure, in order to ensure that the coke was evenly deposited throughout the catalyst particle. More importantly, this procedure conveniently permitted obtaining coked catalysts having different hydrogen-carbon ratios by simple changes in operational parameters. The silica-alumina is contained in several wire-mesh steel baskets, arranged one on top of the other in a vertical steel reactor of about 1-liter capacity. The catalyst is given a pretreatment with hydrogen a t atmospheric pressure and 425”C. for 2 hours, followed by cooling in hydrogen to room temperature. Under a hydrogen atmosphere, prepurified FCC furnace oil (or a mixture in n-hexane) is forced up from the bottom of the reactor just to cover all the catalyst. The catalyst is left thus immersed for 5 minutes. The oil is then drained off and the reactor evacuated under a rough vacuum for 15 minutes. Hydrogen pressure is then applied to about 300 p.s.i.g., the reactor heated to the coking temVOL. 8 N O . 3 JULY 1 9 6 9
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