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Transient changes in the temperature and conversion of a single coked catalyst pellet during its burning regeneration
The Chemical Engineering
Journal, 29 (1984)
85
85 - 96
Transient Changes in the Temperature and Conversion of a Single Coked Catalyst Pellet during its Burning Regeneration KENJI HASHIMOTO,
Department (Received
KOUJI
TAKATANI
of Chemical Engineering, March
22,1984;
and TAKAO
Kyoto
in final form
University,
August
Kyoto
606 (Japan)
22, 1984)
ABSTRACT
A model is presented that predicts the transient changes in both the temperature and the conversion of a single coked catalyst pellet during its burning regeneration. The following assumptions are made in developing the model. The coke, consisting of carbon and hydrogen, is dispersed in fine particle form within the catalyst pellet. The hydrogen is first oxidized at a sharp interface in the coke particle and then the carbon remaining outside the interface is gradually oxidized to yield simultaneously CO and CO,. The temperature in the pellet is uniform and the pellet is in a pseudo steady state. In addition the in trapellet diffusion effect is taken in to account. Transient profiles of both the temperature and the conversion in the catalyst pellet were measured during the burning regeneration of coked silica-alumina catalysts. The experimental results were in good agreement with the results predicted by the model.
1. INTRODUCTION
The temperature inside catalyst pellets increases during the burning regeneration of coked catalysts. This accelerates sintering of the catalyst, leading to loss of activity of the regenerated catalyst. To minimize this deactivation, it is necessary to predict the temperature rise during the burning regeneration accurately. Several methods have been presented for computing the transient change in temperature within a single catalyst pellet and throughout fixed bed reactors. Most of these are based on the mathematically simple un0300-9467/84/$3.00
MASUDA
reacted core model. Luss and Amundson [ 11 and Sohn [ 21 presented methods for predicting the maximum temperature rise for a diffusion-controlled unreacted core system. Shettigar and Hughes [3] developed a modified unreacted core model which assumed that the reaction occurs in a narrow zone between the product zone and the unreacted core. They also measured transient temperature profiles in a single catalyst pellet during its burning regeneration and found that their model gave predictions closer to the experimental results than did the original unreacted core model [ 41. Other useful models are based on the particle-pellet model (or the grain model [5]). These models assume that the solid component comprises coherent aggregates of relatively non-porous particles of uniform size and that the reaction proceeds by diffusion of gaseous reactant through the pellet to the reactive surfaces of the particles. Sampath et al. [6] presented two models based on the particle-pellet model. They examined extensively the effects of various parameters on the maximum temperature rise in the pellet but did not attempt to verify either of the models experimentally. All the models reviewed above assume that the coke is composed only of carbon. However, several investigators, including Massoth [ 71, have clearly shown that the coke produced in most cracking processes has the composition CH,, where n has a value between 0.4 and 2. It is important to take account of this hydrogen from two points of view: firstly, the heat of reaction for oxidation of the hydrogen contributes appreciably to the temperature rise; secondly, steam, some of which is produced by the oxidation of the hydrogen, causes a significant reduction in the 0
Elsevier Sequoia/Printed
in The Netherlands
86
surface area within the catalyst pellet [ES]. Thus the burning regeneration of coked catalysts must be analysed non-isothermally, with the fact that the coke consists of hydrogen as well as carbon taken into account. Although Massoth [7] presented a model which considers the oxidation of both carbon and hydrogen, he was not concerned with the non-isothermal situation. Ramachandran et al. [ 91 proposed a model for the non-isothermal burning off of coke consisting of carbon and hydrogen. They assumed that the hydrogen in the coke reacted with oxygen at a sharp interface within the coked pellet, whereas the carbon reacted in the zone between the hydrogen interface and the outer surface. To simplify the analysis they also assumed that the concentration of the carbon varied linearly with the radial position in the outer carbon zone. This assumption, however, is valid only in the initial stage of the oxidation, and this model would only be useful for predicting the maximum temperature rise which may occur in the initial stage of the reaction. Over the whole course of the reaction, the agreement between the calculated transient temperature profiles and the experimental data was unsatisfactory. This may have resulted from the nature of the model itself as well as from uncertainties in the kinetics parameters used for the calculations. In a previous paper [lo], we presented a kinetics model for the burning of coke under isothermal and chemical-reaction-controlled conditions. This model considers the oxidation of both carbon and hydrogen in the coke. The rate parameters for these oxidations were estimated by means of a simple procedure. In this paper the model is extended to the more general situation where the intrapellet diffusion and the temperature effects are also taken into account. The validity of the proposed model is examined experimentally for the burning regeneration of coked silica-alumina catalyst.
,camyst
OF THE
MATHEMATICAL
coke
nreacted
0
_..-.2L__!
R Ro
(a)
(b)
Fig. 1. Model for the simultaneous carbon and hydrogen (a) in a coked and (b) in a coke particle.
oxidation of catalyst pellet
spherical catalyst pellet of radius R, and a typical coke particle located at the radial position R in the pellet. The coke particles are assumed to be uniform spheres of radius r. and to consist mainly of carbon and hydrogen. The reaction kinetics in the coke particle were developed in the previous paper [lo]. The hydrogen in the coke is oxidized faster than the carbon and hence a sharp reaction interface appears, the radius rH of which shrinks with the progress of the reaction. Two zones are thus formed within the coke particle, as shown in Fig. l(b): an inner unreacted core and an outer zone consisting only of carbon, Figure l(b) also illustrates the concentration profiles Cc’ and Cn’ of carbon and hydrogen respectively within the coke particle. The oxidations of both carbon and hydrogen in the coke are assumed to proceed simultaneously according to the following stoichiometry and reaction kinetics [lo] : c+~o,-co c + 0, -
co2
H+$O,2. FORMULATION
pellet
+H,O
rl = klCc’PA
(14
r2 = WCrPA
(lb)
r3 = kn,Cn,‘p,
(Ic)
MODEL
The reaction rate rc of carbon is expressed by using the equations for the two rates r, and r2, yielding
2.1. Reaction model Coke is finely distributed within the catalyst pellet. Figure l(a) illustrates a
-rc
= (k, + k,)Cc’p, = kcC,‘p,
(2)
87 where
k, = k, + k, The dependences of the rate constants k,, and kc on the temperature were found [lo] to be represented by the Arrhenius equations (3)
On the basis of the model shown in Fig. 1, the local conversions X, and Xc for both the hydrogen and the carbon at any radial distance in the catalyst pellet are respectively equal to the average conversions for both components in the coke particle, which were derived in the previous paper [lo]. Therefore we have Xn=1--&3
(5) dt
Xc = 3jg’r, and two correlations were presented for kc and k&r, (Table 1). Since the radius r. of the coke particle is difficult to evaluate, it is combined with the rate constant kHs. The diffusional resistance of oxygen through the outer zone in the coke particle is assumed to be negligibly small [lo]. However, interphase and intrapellet diffusional resistances are not neglected; the profile of the oxygen pressure PA in the catalyst pellet is schematically shown in Fig. l(a). The oxygen partial pressure within the coke particle is uniform and equal to that in the pellet at the radial position at which the coke particle is located. TABLE
;dI$;C,F
Numerical values of several computations
parameters
=
x 10’
X 10 exp
R. = 2.4 x lOa
-
s
1.403
x 105
-
3
mo3Cco’A c exp
XPAVH-Xc)
Pa-’
dr
X
s-l
RF.T kH8 = 7.526 r0
ro kcpAC&r2
'H
used in the
Pa-’
and xc= l-
4nro2CHo’AH eXp
4
1.562
-
X 103exp
EH =rH/rO
x pA( 1 - A&)“~
=
kc= 1.516
=r/rO,
The reaction rates rnp and rep for hydrogen and carbon based on the single coke particle can be formulated by combining the kinetics model and eqns. (3) - (6) as follows:
-rep =
1
(6)
EH
s-l
&z* m
(8)
The reaction rate r&, for the oxygen can be easily derived on the basis of the stoichiometry and the reaction kinetics represented by eqns. (1) and (2) as follows:
e = 0.9 cp = 1.50
kJ kg-‘K--l
AH,
$
= -393.70
kJ mol-’
AH,
Mo = -110.58
kJ mol-’
&CZ,wo = -241.94
kJ mol-’
2.2. Mass balance equations In this section and Section 2.3, mass and heat balance equations are developed for a single spherical catalyst pellet placed in the reaction tube.
where A= - kz (10) hi +kz Mass balance equations for the hydrogen and carbon in the single coke particle are written under non-isothermal and intrapellet diffusion-limited conditions as follows: ax, -=
at
3 AH r.
(12)
Next, we formulate the mass balance equation for a spherical catalyst pellet. Employing the pseudo-steady-state assumption shown to be justified in most gas-solid reactions [ 11, 121, we can derive the following material balance for the oxygen in the spherical pellet: - 41rR~N,(-r,,)
41rD,, -&
= 0
The rate qt of heat release from the catalyst pellet is represented by qt = 4rR,2(h(T
- Tg) + 5.674
Y 10e8e(T4
- Tw4))
where NC is the number of coke particles per unit volume of the pellet. The boundary conditions for eqn. (13) are R=(-J
dCA -~0
De,
dCA z
- T,) + 5.674
X
- To4)}
X lo-se(T4
(18)
A heat balance equation for the single catalyst pellet can be derived from eqn. (18):
(14)
dR
R = R,
(17)
Substitution of eqn. (16) into eqn. (17) eliminates T, and T,, which are difficult to measure accurately, and yields an equation for qt in terms of the pellet temperature T and T,: qt = 4nRo2{h(T
(13)
X
=
kct@Ag--PAS)
(15) XNc4rR2dR
2.3. Heat balance equations
The oxidation of coke is such a highly exothermic reaction that some of the heat evolved may be accumulated within the pellet and may increase its temperature to above that of the surrounding gas phase. This temperature rise consists of temperature gradients within the pellet and across the fluid film surrounding the pellet. The temperature gradient for most gas-solid reactions occurs primarily across the gas film and not within the pellet [ 131. In the following analysis, therefore, we consider the transient change in the catalyst temperature, which is assumed to be uniform throughout the pellet at any reaction time. Before the reaction starts, the catalyst pellet temperature is assumed to be in thermal equilibrium with that of the ambient gas, which is heated through the reactor wall by the electric furnace. Therefore the following equation holds: 5.674 X 10-8e(7’W4 - To4) = h(T, - Tg)
(16)
where T,, Tg and T, are the temperature of the pellet at the start of the reaction, the temperature of the ambient gas and the temperature of the inner wall respectively.
-44nR,2{h(T-To)
+ 5.674 X lo-se(T4
t
- To4)}
(19)
where AH, is the heat of reaction for the oxidation of atomic hydrogen and AHC represents the overall heat of reaction for the oxidation of carbon to CO and C02. The stoichiometric relationships of these reactions are given by eqn. (1). The basic equations derived above (eqns. (13), (ll), (12) and (19)) can respectively be transformed into the following dimensionless forms, in which the subscript zero represents the start of the reaction:
= 9Hg2\i(l
+ 0)
YH0
X exp i 1+0 X
exp
;fl(l
-Xn)2’3
x
1+x +2(Xn-&)x
I
rc6 i 1+e iI
(20)
89
axH = 3$(1 -Xn)2’3exp au
-
aXc
= cyo$(X,
au
i
s
1
YC0
exp i 1+8 1
-Xc)
(21)
d$ dr)
17’1
-=
Sh*U - ti,) 2
(26)
where (22) Sh*=
2W’RokG
_
The initial conditions for eqns. (20) - (23) are Xn=Xc=e=O
u=o X
J
’$/(l
(27)
The overall conversion Xt for the single catalyst pellet is calculated from
-XH)2’3q2 drj +
0
$4X,
-Xch*dr7
-
l-xt=
&-$1--R,)+
1
-3s#
-3s2{(l
+ e)4-l}
(23)
where $=PA
i++%)
(28) where Xn and Xc are respectively the Overall conversions of hydrogen and carbon in the catalyst pellet and are calculated from the following equations:
PAg
T-T, To
e=
*=
u=
X,=3
t 7 to
r0 kHsoPAe
exp(-_yH)
(24)
Ro
Q
3 =
(-MH)CHokHsoPAg
H w,roTo Q
=
(29a)
drj
(29b)
0
kco=&=M--_yc)
Hg=
‘X,7j*d?J
Xc = 3Jx,q*
to
k HsO=AH
s
0
(-‘%)‘%okcoPAg
C Cp~pTo
S2 = 5.674 X lo-‘e The boundary conditions (eqns. (14) and (15)) can also be converted into dimensionless form : (25)
An equivalent radius R, (the radius of a sphere with the same ratio of volume V, to external surface area S,) is employed as an approximation for non-spherical catalyst pellets. This is based on the approximate treatment for developing the generalized modulus to calculate the effectiveness factor for all shapes [ 141; thus the equivalent radius R, is represented by 3 VP/&, . 2.4. Numerical solution These basic equations were solved numerically. The pellet radius R. is divided into N, equal radial increments, and the two local conversions at the ith mesh point (qi = iA7) are represented by Xni and Xci where the subscript i varies from 0 to s. The temperature at any mesh point is represented by 8. Partial derivatives with respect to q in eqn. (20) were approximated at each mesh point by central differences, leading to a set of IV, + 1 algebraic equations, which is represented in the following matrix form: A9=B
(30)
90
where \k is the unknown vector of the normalized oxygen pressure in the pellet, B is a vector containing only one non-zero element. (when i = s) and A is a tridiagonal matrix of dimension N, + 1. The elements corresponding to the ith mesh point in A and B include XHi, X,i and 8, which change with the elapsed time. To solve eqn. (30) it is necessary to assign values to these dependent variables. Furthermore, partial derivatives with respect to the dimensionless time u are replaced by ordinary derivatives at each mesh point in the pellet, leading to a set of nonlinear ordinary differential equations consisting of 2(N, + 1) + 1 equations that include $. In this way, the basic equations were converted into a set of linear algebraic equations (eqn. (30)) and a set of differential equations. These two sets of equations are not independent of each other, but they can be approximately solved separately as shown below. (1) Initially, an oxygen pressure profile is assumed to exist in the pellet. This is expressed as the following analytical solution obtained by solving eqn. (20) under the initial conditions given in eqn. (27): sinh(h,qi) tii =
I&()=
eqn. (30), which is solved for ‘@to give the oxygen pressure profiles at u = Au. (4) In this way, the radial distributions of XH and Xc at u = Au were calculated. The overall conversions _j?, and it, can be calculated from eqns. (29) using Simpson’s rule and xt from eqn. (28). (5) The repetition of the cycle of steps (2) - (4) gives transient distributions of the conversions and pellet temperature. The convergence of the computing scheme outlined above was examined for the ranges lO
i=l,2,
WVi
!
1 + 2.51 X lo3 exp -
5
5.19 x lo4 W
(33)
W
The heats AH, and AHc of reaction for the oxidation of atomic hydrogen and of carbon respectively were calculated from the following equations:
where 3
gs(h, coth
h, - 1)
(32a)
AHH = 0.5{AH,,,”
+ (T - 298.2)(C,+w (34)
- % H, - 0.5G. *)I h, = f (30) l12Hg
-l
(32b)
AHc = XAHf, ,,O+ (1 - h)AHf, Mo+ f (T - 298.2){cPq,
(2) The profile of the oxygen pressure is assigned to rl/ in the set of differential equations corresponding to eqns. (21) - (23), and the resulting equations are integrated for a short time interval Au using the RungeKutta-Gill routine. This computation gives the profiles of X, and Xc in the pellet and the uniform pellet temperature at the dimensionless time Au. (3) These new values of X,, Xc and 8 are substituted into the elements of A and B in
+ (1 - h)cP,,
0.5(1 + X)C,, A}
-&!-
(35)
The initial concentrations cHO and Cc, of hydrogen and carbon respectively in the coked catalyst pellet are computed from wpp x lo3 cc0 =
12 +n (36) wp,n
CHO
=
x
12 +n
lo3
91
where pP refers to the apparent density of the catalyst pellet, which was measured as 1200 kg mP3. The value of n was estimated from ref. 10, Fig. 4. The value of the effective diffusivity DeA of the catalyst pellet was calculated by means of a parallel pore model which utilizes the pore volume distribution and neglects the variation in the diffusivity with gas composition because of its small effect [ 161. The tortuosity factor was taken as 3.0. The intraphase heat coefficient h and the mass transfer coefficient ko were calculated from the correlations of Ranz and Marshall [ 171 by taking the Nusselt and the Sherwood numbers to be approximately equal to 2. The original shape of the catalyst pellet is cylindrical (4.8 mm in diameter and 4.8 mm in height), and its equivalent radius R, (2.4 mm) (the radius of a sphere with the same ratio of volume to external surface area) was employed in the numerical calculations. The values of several parameters used in the numerical calculations are listed in Table 1.
3. EXPERIMENTAL
4. RESULTS
AND DISCUSSION
4.1. Uniform coke deposition Figure 2 shows the effect of pellet size on the net coke deposition over a wide range from 0.16 to 2.4 mm in equivalent radius, indicating clearly no dependence of the coke deposition on the pellet size. This is evidence for the absence of diffusion effects, and hence the coke deposit is distributed uniformly inside these catalyst pellets including the cylindrical catalyst (R, = 2.4 mm) used mainly in the regeneration experiments in this work. 4.2. Comparisons of temperature distribution Figure 3 illustrates the transient changes in the pellet temperature for three different initial temperatures. In all cases, the temperature rises rapidly in the initial stage of the reaction and then gradually decreases. The
DETAILS
The experimental apparatus and procedure for both the coking in the cracking of cumene and the regeneration are almost the same as those in the kinetics runs described in the previous paper [lo] except for the following points. First, experiments to measure the changes in catalyst weight and in temperature were carried out separately. The catalyst weight was measured using a reactor equipped with a balance. To monitor the catalyst temperature, the balance was removed from the reactor and the top of the reactor was sealed with a silicon rubber cup through which a very fine thermocouple (0.3 mm in diameter) was admitted into the reactor. The junction of the thermocouple was embedded in a cylindrical catalyst pellet in the bucket. Second, air was mainly used undiluted in order to give large changes in temperature. Third, the concentration of water vapour evolved inside the reactor was measured at the reactor exit by gas partition chromatography, yielding the overall conversion of hydrogen for the catalyst pellet.
t Cminl
Fig. 2. Effect of the pellet size on the net coke deposition (T = 873.2 K; Cne = 2.56 mol mp3): 0, R, 2.4 mm; CL,R, = 0.55 mm; 0,R, = 0.16 mm.
=
Fig. 3. Comparison of calculated (proposed model; - - -, one-component coke model) and experimental distributions of temperature for three different initial temperatures (w = 3.05%;~~~ = 21.3 kPa; R, = 2.4 mm): 0,run 20, To = 637.4 K;n, run 24, To = 884.1 K; 0, run 26, 7’0 = 934.2 K.
92
maximum rise in temperature increases with an increase in the initial temperature, reaching 45 K for the highest initial temperature shown (run 26). Thus the reaction must be treated non-isothermally. The computed results based on the proposed model, shown by the full curves, are in close agreement with the experimental results. In addition, the broken curves represent the calculated results based on a onecomponent coke model which regards the coke as consisting only of carbon (Appendix A). A number of previous models are based on this kind of treatment. The temperature rises calculated by means of the onecomponent coke model are lower than those calculated by means of the proposed model, and their agreement with the experimental results is clearly poor. Although the differences in the maximum temperature rise between the two models are of about the order of 10 K under the experimental conditions in this figure, a larger difference occurs for higher values of the atomic ratio n of hydrogen to carbon in the coke, as shown in Fig. 4. Thus the proposed model predicts more accurately the transient temperature profile during the burning off of coke than does the one-component coke model. Figure 5 shows that an increase in the oxygen partial pressure resulted in a rapid rise in the catalyst temperature (run 24), while a decrease in the oxygen partial pressure resulted in an almost isothermal reaction (run 21). In the kinetics runs this approximate isothermal situation was realized by reducing the oxygen pressure. The maximum temperature rise above the temperature of the ambient gas was about 0.3 K for a kinetics run using the crushed catalyst pellet (R, = 0.16 mm) under
Fig. 4. Effect of the initial atomic ratio n of hydrogen to carbon on the transient profile of the catalyst temperature (2’0 = 893.2 K; w = 3%;p,, = 21.3 kPa; Ro = 2.5 mm; e = 0.9).
P c
*501,, , I,,
0
(1,,
/,
200
100
j
300
I [sl
and experiFig. 5. Comparison of calculated ( ---) mental distributions of temperature for two different partial pressures of oxygen (Z’s = 883.8 K; w = 3.05%; R, = 2.4 mm): A, run 21, pAg = 7.98 kPa; 0, run 24, pAg = 21.3 kPa.
0
100
200
300
I Csl
and experiFig. 6. Comparison of calculated ( -) mental distributions of temperature for three different coke levels (To = 879.4 K; pAg = 21.3 kPa; Ru = 2.4 mm): 0, run 22, w = 1.94%;/\, run 23, w = 2.84%; 0, run 25, w = 4.42%.
the conditions TO = 873.2 K, PAg = 7.98 kPa and w = 0.0317 [lo]. Figure 6 demonstrates that higher coke levels lead to higher temperature rises during the reaction. 4.3. Comparisons of conversion distribution The three full lines in Fig. 7 show the calculated transient profiles of the three conversions xc, gH and xt. The computed profile of 1 -x, is in good agreement with
Fig. L Transient profiles of three conversions Xc, XH and X, under the conditions To = 873.2 K, PAs = 21.3 kPa, w = 4.42% and R, = 2.4 mm: __ , proposed model; - -, one-component coke model.
93
the experimental data represented by the open circles. In addition, the broken curve shows the profile of 1 -x, calculated by means of the one-component coke model, which clearly gives poorer agreement with the experimental results. A special feature of the proposed model is that it takes into account the contribution of the oxidation of hydrogen in the regeneration of coked catalysts. Direct measurement of the conversion of hydrogen, rather than the overall conversion, allows a stricter examination of the model. Figure 8 illustrates the results of such an examination, which reveal good agreement between the calculated and the experimental conversions of the hydrogen in the coke. Figure 9 shows comparisons of the computed and the experimental overall conversions for three different coke levels and indicates good agreement between them. An
0
IO00
500 t Csl
Fig. 8. Comparison of calculated () and experimental (- - 0 - -) conversions ZH of hydrogen (run 21; T, = 823.2 K; R, = 2.4 mm; w = 3.05%; p& = 21.3 kPa).
0
200
600
400 I
CSI
Fig. 10. Comparison of calculated (proposed model; - - -, one-component coke model) and experimental overall conversions X, for two partial pressures of oxygen (To = 873.2 K; w = 2.83%; R, = 2.4mm):0,run16,pAg=10.6kPa;~,run17,P&= 21.3
kPa.
increase in the coke level requires a longer reaction time. Figure 10 illustrates the effect of the oxygen pressure on the overall fraction of unreacted coke. The full curves are calculated by means of the proposed model, whereas the broken curves are calculated by means of the one-component coke model. Clearly the proposed model simulates more accurately the transient change in 1 - _%;,than does the one-component coke model. Semilogarithmic plots of 1 - x, against the reaction time are linear for isothermal conditions in the later period of the reaction [lo], whereas under non-isothermal conditions they deviate from the straight line, as shown in Figs. 9 and 10.
5. CONCLUSION
1.0 6 4 Iz
2
-
10-I 6 4 2 10’ 0
200
400
600
Fig. 9. Comparison of calculated ( -) and experimental overall conversions xt for three coke levels (To= 873.2 K;JJA,= 21.3 kPa; R, = 2.4 mm): 0, run 17, w = 2,84%;A, run 18, w = 4.42%;0, run 19, w = 5.75%.
The new model presented predicts accurately the transient changes in temperature and conversion during the burning regeneration of coked catalysts. This model considers the combustion of both the carbon and the hydrogen in the coke. The rapid temperature rise in the initial stage of the reaction is attributable mainly to the preferential burning of hydrogen in the coke. The transient temperature profiles predicted by this model are in good agreement with the experimental results for the burning regeneration of coked silica-alumina catalyst pellets. The oxidation rate constants obtained in the previous paper
94
were successfully used in the calculation. Thus the model was found to be valid for predicting the temperature rise as well as the conversion change during the burning regeneration of coked catalysts.
cording to the kinetics represented by eqns. (la) and (lb). Basic equations may be obtained by replacing Xu in eqns. (20) - (23) by 1 .O. Furthermore, the initial profile of oxygen pressure can be calculated from the equations in which the parameter h, is replaced by h,’ where h,’ is given by
ACKNOWLEDGMENT
&?
The support of the Ministry of Education through a Grant-in-Aid for Scientific Research (number 56470095) for part of the work is gratefully acknowledged.
APPENDIX
AH
1 D. Luss and N. R. Amundson, AIChE J., 15 (1969) 194. J., 19 (1973) 191. 2 H. Y. Sohn,AlChE 3 U. R. Shettigar and R. Hughes, Chem. Eng. J., 3 (1972) 93. 4 U. R. Shettigar and R. Hughes, Chem. Eng. J., 4 (1972) 208. 5 J. Szekely and J. W. Evans, Chem. Eng. Sci., 26 (1971) 1901. P. A. Ramachandran and R. 6 B. S. Sampath, Hughes, Chem. Eng. Sci., 30 (1975) 125. 7 F. E. Massoth, Ind. Eng. Chem., Process Des. Dev., 6 (1967) 200. 8 W. G. Schlaffer, C. 2. Morgan and J. N. Wilson, J. Phys. Chem., 61 (1957) 714. M. H. Rashid and R. 9 P. A. Ramachandran, Hughes, Chem, Eng. Sci., 30 (1975) 1391. K. Takatani, H. Iwasa and T. 10 K. Hashimoto, Masuda, Chem. Eng. J., 27 (1983) 177. 11 C. Y. Wen, Ind. Eng. Chem., 60 (9) (1968) 34. 12 D. Luss, Can. J. Chem. Eng., 46 (1968) 154. Ind. Eng. Chem., Fundam., 14 13 J. J. Carberry, (1975) 129. 14 R. Aris, Chem. Eng. Sci., 6 (1957) 262. 164. 15 J. R. Arthur, Trans. Faraday Sot., 47 (1951) M. Teramoto, K. Miyamoto, T. 16 K. Hashimoto, Tada and S. Nagata, J. Chem. Eng. Jpn., 7 (1974)
116. 17
W. E. Ranz and W. R. Marshall, 141,173.
(Pa-’
CP CA
cBO
cc’ cCO> cHO
C co ’ CHO' 3
cp. i D eA
Jr., Chem. Eng.
Prog., 48 (1952)
e
Ec,E, APPENDIX
A
A.1. The parameter h, for the one-component coke model The one-component coke model regards the coke as consisting only of carbon and its oxidation as proceeding homogeneously ac-
B: NOMENCLATURE
frequency factor of the reaction rate of oxidation of carbon defined in eqn. (2) (Pa-“ ss’) frequency factor of the reaction rate r3 defined in eqn. (lc)
AC REFERENCES
h
(AlI
SC’)
specific heat capacity of the catalyst pellet (J kg-..‘) concentration of oxygen at any radiaI position in the catalyst pellet (mol rne3) concentration of cumene at the reactor inlet in the coking reaction (mol m-“) concentration of carbon at any radial position in the coke particle (mol me3) initial atomic concentrations of carbon and hydrogen in the catalyst pellet (mol me3) initial atomic concentrations of carbon and hydrogen in the coke particle (mol m- 3, average molecular heat capacity over the temperature range from 298.2 K to the pellet temperature (J mol-’ K-‘) effective diffusivity of oxygen in the catalyst pellet (m2 s- ‘) emissivity (blackness) of the coked catalyst pellet (dimensionless) activation energies of the combustion of carbon and atomic hydrogen (J mol-‘) gas-film heat transfer coefficient (J m-* s-’ Km-’) modified Thiele modulus defined in eqn. (24) (dimensionless)
95
AHc
Mf.i
kc kG
k HS
k,
9 k2
n
NC
PA PAg 4t
rc
F-0 w-2
r3
R
4 R*
overall heat of reaction for the oxidation of carbon to produce CO and CO,, defined in eqns. (la) and (lb) (J mol-‘) the standard heat of formation of the ith component at 298.2 K (J mol-‘) heat of reaction for the oxidation of atomic hydrogen, defined in eqn. (lc) (J mol-‘) k, + k, (PaWIF1) gas-film mass transfer coefficient for oxygen (mol m-* s-l Pa-‘) rate constant for the oxidation of atomic hydrogen (m Pa-’ s-l) second-order rate constants for the oxidation of carbon to CO and CO2 (P~-‘s-~) initial atomic ratio of hydrogen to carbon in the coke (dimensionless) number of coke particles per unit volume of the catalyst pellet (mm3) partial pressure of oxygen (Pa) partial pressure of oxygen in the ambient gas (Pa) rate of heat removal from the catalyst pellet (J s-l) reaction rates based on a single coke particle for oxygen, carbon and hydrogen (mol s-l) reaction rate of carbon based on the volume of coke (mol m-3 s-l) radius of the coke particle (m) reaction rates for carbon based on the volume of coke, defined in eqns. (la) and (lb) (mol me3 s-l) reaction rate for atomic hydrogen based on the surface area of the reaction interface, defined in eqn. (lc) (mol me2 s-l) radial distance in the catalyst pellet (m) 8.314, gas constant (J mol-’ K-l) equivalent radius of the pellet (equal to the radius of a sphere with the same ratio of volume to external surface area) (m)
t
radius of the catalyst pellet (m) 2RgTROkG/DeA, modified Sherwood number (dimensionless) reaction time of regeneration
to*
ro/kH&pAg, time at which the
Ro Sh*
(s)
Tci
unreacted core disappears at the temperature To (s) temperature of the catalyst pellet (K) temperature of the ambient gas
TW
(K) temperature
T
To
U W
xc
xc,
XH
xC,xH
of the reactor
wall
(K) temperature .of the catalyst pellet at the start of the reaction (K) t/to* 9 dimensionless time mass ratio of coke to uncoked catalyst (dimensionless) conversion of carbon at any radial distance in the coke particle (dimensionless) conversions of carbon and hydrogen at any radial distance in the catalyst pellet (dimensionless) overall conversions of carbon and hydrogen in the catalyst pellet (dimensionless) overall conversion of coke in the catalyst pellet (dimensionless)
Greek symbols kc#Ag to* (dimensionless) a0 n/a, (dimensionless) P E,/R,T, (dimensionless) YC EHfRgTO (dimensionless) YH R/R,, dimensionless radial posi77 tion in the catalyst pellet e (T - To)/To, dimensionless temperature of the catalyst pellet k2/(kl + k,) (dimensionless) r/To, dimensionless radial dis: tance in the coke particle apparent density of the catalyst PP pellet (kg mm3) PA/PA~(dimensionless) ti Subscripts
A C D
oxygen carbon co2
96
& H H2
M
ambient gas atomic hydrogen molecular hydrogen co
surface of the catalyst reactor wall steam (gaseous water) start of reaction
pellet
Journal, 29 (1984)
85
85 - 96
Transient Changes in the Temperature and Conversion of a Single Coked Catalyst Pellet during its Burning Regeneration KENJI HASHIMOTO,
Department (Received
KOUJI
TAKATANI
of Chemical Engineering, March
22,1984;
and TAKAO
Kyoto
in final form
University,
August
Kyoto
606 (Japan)
22, 1984)
ABSTRACT
A model is presented that predicts the transient changes in both the temperature and the conversion of a single coked catalyst pellet during its burning regeneration. The following assumptions are made in developing the model. The coke, consisting of carbon and hydrogen, is dispersed in fine particle form within the catalyst pellet. The hydrogen is first oxidized at a sharp interface in the coke particle and then the carbon remaining outside the interface is gradually oxidized to yield simultaneously CO and CO,. The temperature in the pellet is uniform and the pellet is in a pseudo steady state. In addition the in trapellet diffusion effect is taken in to account. Transient profiles of both the temperature and the conversion in the catalyst pellet were measured during the burning regeneration of coked silica-alumina catalysts. The experimental results were in good agreement with the results predicted by the model.
1. INTRODUCTION
The temperature inside catalyst pellets increases during the burning regeneration of coked catalysts. This accelerates sintering of the catalyst, leading to loss of activity of the regenerated catalyst. To minimize this deactivation, it is necessary to predict the temperature rise during the burning regeneration accurately. Several methods have been presented for computing the transient change in temperature within a single catalyst pellet and throughout fixed bed reactors. Most of these are based on the mathematically simple un0300-9467/84/$3.00
MASUDA
reacted core model. Luss and Amundson [ 11 and Sohn [ 21 presented methods for predicting the maximum temperature rise for a diffusion-controlled unreacted core system. Shettigar and Hughes [3] developed a modified unreacted core model which assumed that the reaction occurs in a narrow zone between the product zone and the unreacted core. They also measured transient temperature profiles in a single catalyst pellet during its burning regeneration and found that their model gave predictions closer to the experimental results than did the original unreacted core model [ 41. Other useful models are based on the particle-pellet model (or the grain model [5]). These models assume that the solid component comprises coherent aggregates of relatively non-porous particles of uniform size and that the reaction proceeds by diffusion of gaseous reactant through the pellet to the reactive surfaces of the particles. Sampath et al. [6] presented two models based on the particle-pellet model. They examined extensively the effects of various parameters on the maximum temperature rise in the pellet but did not attempt to verify either of the models experimentally. All the models reviewed above assume that the coke is composed only of carbon. However, several investigators, including Massoth [ 71, have clearly shown that the coke produced in most cracking processes has the composition CH,, where n has a value between 0.4 and 2. It is important to take account of this hydrogen from two points of view: firstly, the heat of reaction for oxidation of the hydrogen contributes appreciably to the temperature rise; secondly, steam, some of which is produced by the oxidation of the hydrogen, causes a significant reduction in the 0
Elsevier Sequoia/Printed
in The Netherlands
86
surface area within the catalyst pellet [ES]. Thus the burning regeneration of coked catalysts must be analysed non-isothermally, with the fact that the coke consists of hydrogen as well as carbon taken into account. Although Massoth [7] presented a model which considers the oxidation of both carbon and hydrogen, he was not concerned with the non-isothermal situation. Ramachandran et al. [ 91 proposed a model for the non-isothermal burning off of coke consisting of carbon and hydrogen. They assumed that the hydrogen in the coke reacted with oxygen at a sharp interface within the coked pellet, whereas the carbon reacted in the zone between the hydrogen interface and the outer surface. To simplify the analysis they also assumed that the concentration of the carbon varied linearly with the radial position in the outer carbon zone. This assumption, however, is valid only in the initial stage of the oxidation, and this model would only be useful for predicting the maximum temperature rise which may occur in the initial stage of the reaction. Over the whole course of the reaction, the agreement between the calculated transient temperature profiles and the experimental data was unsatisfactory. This may have resulted from the nature of the model itself as well as from uncertainties in the kinetics parameters used for the calculations. In a previous paper [lo], we presented a kinetics model for the burning of coke under isothermal and chemical-reaction-controlled conditions. This model considers the oxidation of both carbon and hydrogen in the coke. The rate parameters for these oxidations were estimated by means of a simple procedure. In this paper the model is extended to the more general situation where the intrapellet diffusion and the temperature effects are also taken into account. The validity of the proposed model is examined experimentally for the burning regeneration of coked silica-alumina catalyst.
,camyst
OF THE
MATHEMATICAL
coke
nreacted
0
_..-.2L__!
R Ro
(a)
(b)
Fig. 1. Model for the simultaneous carbon and hydrogen (a) in a coked and (b) in a coke particle.
oxidation of catalyst pellet
spherical catalyst pellet of radius R, and a typical coke particle located at the radial position R in the pellet. The coke particles are assumed to be uniform spheres of radius r. and to consist mainly of carbon and hydrogen. The reaction kinetics in the coke particle were developed in the previous paper [lo]. The hydrogen in the coke is oxidized faster than the carbon and hence a sharp reaction interface appears, the radius rH of which shrinks with the progress of the reaction. Two zones are thus formed within the coke particle, as shown in Fig. l(b): an inner unreacted core and an outer zone consisting only of carbon, Figure l(b) also illustrates the concentration profiles Cc’ and Cn’ of carbon and hydrogen respectively within the coke particle. The oxidations of both carbon and hydrogen in the coke are assumed to proceed simultaneously according to the following stoichiometry and reaction kinetics [lo] : c+~o,-co c + 0, -
co2
H+$O,2. FORMULATION
pellet
+H,O
rl = klCc’PA
(14
r2 = WCrPA
(lb)
r3 = kn,Cn,‘p,
(Ic)
MODEL
The reaction rate rc of carbon is expressed by using the equations for the two rates r, and r2, yielding
2.1. Reaction model Coke is finely distributed within the catalyst pellet. Figure l(a) illustrates a
-rc
= (k, + k,)Cc’p, = kcC,‘p,
(2)
87 where
k, = k, + k, The dependences of the rate constants k,, and kc on the temperature were found [lo] to be represented by the Arrhenius equations (3)
On the basis of the model shown in Fig. 1, the local conversions X, and Xc for both the hydrogen and the carbon at any radial distance in the catalyst pellet are respectively equal to the average conversions for both components in the coke particle, which were derived in the previous paper [lo]. Therefore we have Xn=1--&3
(5) dt
Xc = 3jg’r, and two correlations were presented for kc and k&r, (Table 1). Since the radius r. of the coke particle is difficult to evaluate, it is combined with the rate constant kHs. The diffusional resistance of oxygen through the outer zone in the coke particle is assumed to be negligibly small [lo]. However, interphase and intrapellet diffusional resistances are not neglected; the profile of the oxygen pressure PA in the catalyst pellet is schematically shown in Fig. l(a). The oxygen partial pressure within the coke particle is uniform and equal to that in the pellet at the radial position at which the coke particle is located. TABLE
;dI$;C,F
Numerical values of several computations
parameters
=
x 10’
X 10 exp
R. = 2.4 x lOa
-
s
1.403
x 105
-
3
mo3Cco’A c exp
XPAVH-Xc)
Pa-’
dr
X
s-l
RF.T kH8 = 7.526 r0
ro kcpAC&r2
'H
used in the
Pa-’
and xc= l-
4nro2CHo’AH eXp
4
1.562
-
X 103exp
EH =rH/rO
x pA( 1 - A&)“~
=
kc= 1.516
=r/rO,
The reaction rates rnp and rep for hydrogen and carbon based on the single coke particle can be formulated by combining the kinetics model and eqns. (3) - (6) as follows:
-rep =
1
(6)
EH
s-l
&z* m
(8)
The reaction rate r&, for the oxygen can be easily derived on the basis of the stoichiometry and the reaction kinetics represented by eqns. (1) and (2) as follows:
e = 0.9 cp = 1.50
kJ kg-‘K--l
AH,
$
= -393.70
kJ mol-’
AH,
Mo = -110.58
kJ mol-’
&CZ,wo = -241.94
kJ mol-’
2.2. Mass balance equations In this section and Section 2.3, mass and heat balance equations are developed for a single spherical catalyst pellet placed in the reaction tube.
where A= - kz (10) hi +kz Mass balance equations for the hydrogen and carbon in the single coke particle are written under non-isothermal and intrapellet diffusion-limited conditions as follows: ax, -=
at
3 AH r.
(12)
Next, we formulate the mass balance equation for a spherical catalyst pellet. Employing the pseudo-steady-state assumption shown to be justified in most gas-solid reactions [ 11, 121, we can derive the following material balance for the oxygen in the spherical pellet: - 41rR~N,(-r,,)
41rD,, -&
= 0
The rate qt of heat release from the catalyst pellet is represented by qt = 4rR,2(h(T
- Tg) + 5.674
Y 10e8e(T4
- Tw4))
where NC is the number of coke particles per unit volume of the pellet. The boundary conditions for eqn. (13) are R=(-J
dCA -~0
De,
dCA z
- T,) + 5.674
X
- To4)}
X lo-se(T4
(18)
A heat balance equation for the single catalyst pellet can be derived from eqn. (18):
(14)
dR
R = R,
(17)
Substitution of eqn. (16) into eqn. (17) eliminates T, and T,, which are difficult to measure accurately, and yields an equation for qt in terms of the pellet temperature T and T,: qt = 4nRo2{h(T
(13)
X
=
kct@Ag--PAS)
(15) XNc4rR2dR
2.3. Heat balance equations
The oxidation of coke is such a highly exothermic reaction that some of the heat evolved may be accumulated within the pellet and may increase its temperature to above that of the surrounding gas phase. This temperature rise consists of temperature gradients within the pellet and across the fluid film surrounding the pellet. The temperature gradient for most gas-solid reactions occurs primarily across the gas film and not within the pellet [ 131. In the following analysis, therefore, we consider the transient change in the catalyst temperature, which is assumed to be uniform throughout the pellet at any reaction time. Before the reaction starts, the catalyst pellet temperature is assumed to be in thermal equilibrium with that of the ambient gas, which is heated through the reactor wall by the electric furnace. Therefore the following equation holds: 5.674 X 10-8e(7’W4 - To4) = h(T, - Tg)
(16)
where T,, Tg and T, are the temperature of the pellet at the start of the reaction, the temperature of the ambient gas and the temperature of the inner wall respectively.
-44nR,2{h(T-To)
+ 5.674 X lo-se(T4
t
- To4)}
(19)
where AH, is the heat of reaction for the oxidation of atomic hydrogen and AHC represents the overall heat of reaction for the oxidation of carbon to CO and C02. The stoichiometric relationships of these reactions are given by eqn. (1). The basic equations derived above (eqns. (13), (ll), (12) and (19)) can respectively be transformed into the following dimensionless forms, in which the subscript zero represents the start of the reaction:
= 9Hg2\i(l
+ 0)
YH0
X exp i 1+0 X
exp
;fl(l
-Xn)2’3
x
1+x +2(Xn-&)x
I
rc6 i 1+e iI
(20)
89
axH = 3$(1 -Xn)2’3exp au
-
aXc
= cyo$(X,
au
i
s
1
YC0
exp i 1+8 1
-Xc)
(21)
d$ dr)
17’1
-=
Sh*U - ti,) 2
(26)
where (22) Sh*=
2W’RokG
_
The initial conditions for eqns. (20) - (23) are Xn=Xc=e=O
u=o X
J
’$/(l
(27)
The overall conversion Xt for the single catalyst pellet is calculated from
-XH)2’3q2 drj +
0
$4X,
-Xch*dr7
-
l-xt=
&-$1--R,)+
1
-3s#
-3s2{(l
+ e)4-l}
(23)
where $=PA
i++%)
(28) where Xn and Xc are respectively the Overall conversions of hydrogen and carbon in the catalyst pellet and are calculated from the following equations:
PAg
T-T, To
e=
*=
u=
X,=3
t 7 to
r0 kHsoPAe
exp(-_yH)
(24)
Ro
Q
3 =
(-MH)CHokHsoPAg
H w,roTo Q
=
(29a)
drj
(29b)
0
kco=&=M--_yc)
Hg=
‘X,7j*d?J
Xc = 3Jx,q*
to
k HsO=AH
s
0
(-‘%)‘%okcoPAg
C Cp~pTo
S2 = 5.674 X lo-‘e The boundary conditions (eqns. (14) and (15)) can also be converted into dimensionless form : (25)
An equivalent radius R, (the radius of a sphere with the same ratio of volume V, to external surface area S,) is employed as an approximation for non-spherical catalyst pellets. This is based on the approximate treatment for developing the generalized modulus to calculate the effectiveness factor for all shapes [ 141; thus the equivalent radius R, is represented by 3 VP/&, . 2.4. Numerical solution These basic equations were solved numerically. The pellet radius R. is divided into N, equal radial increments, and the two local conversions at the ith mesh point (qi = iA7) are represented by Xni and Xci where the subscript i varies from 0 to s. The temperature at any mesh point is represented by 8. Partial derivatives with respect to q in eqn. (20) were approximated at each mesh point by central differences, leading to a set of IV, + 1 algebraic equations, which is represented in the following matrix form: A9=B
(30)
90
where \k is the unknown vector of the normalized oxygen pressure in the pellet, B is a vector containing only one non-zero element. (when i = s) and A is a tridiagonal matrix of dimension N, + 1. The elements corresponding to the ith mesh point in A and B include XHi, X,i and 8, which change with the elapsed time. To solve eqn. (30) it is necessary to assign values to these dependent variables. Furthermore, partial derivatives with respect to the dimensionless time u are replaced by ordinary derivatives at each mesh point in the pellet, leading to a set of nonlinear ordinary differential equations consisting of 2(N, + 1) + 1 equations that include $. In this way, the basic equations were converted into a set of linear algebraic equations (eqn. (30)) and a set of differential equations. These two sets of equations are not independent of each other, but they can be approximately solved separately as shown below. (1) Initially, an oxygen pressure profile is assumed to exist in the pellet. This is expressed as the following analytical solution obtained by solving eqn. (20) under the initial conditions given in eqn. (27): sinh(h,qi) tii =
I&()=
eqn. (30), which is solved for ‘@to give the oxygen pressure profiles at u = Au. (4) In this way, the radial distributions of XH and Xc at u = Au were calculated. The overall conversions _j?, and it, can be calculated from eqns. (29) using Simpson’s rule and xt from eqn. (28). (5) The repetition of the cycle of steps (2) - (4) gives transient distributions of the conversions and pellet temperature. The convergence of the computing scheme outlined above was examined for the ranges lO
i=l,2,
WVi
!
1 + 2.51 X lo3 exp -
5
5.19 x lo4 W
(33)
W
The heats AH, and AHc of reaction for the oxidation of atomic hydrogen and of carbon respectively were calculated from the following equations:
where 3
gs(h, coth
h, - 1)
(32a)
AHH = 0.5{AH,,,”
+ (T - 298.2)(C,+w (34)
- % H, - 0.5G. *)I h, = f (30) l12Hg
-l
(32b)
AHc = XAHf, ,,O+ (1 - h)AHf, Mo+ f (T - 298.2){cPq,
(2) The profile of the oxygen pressure is assigned to rl/ in the set of differential equations corresponding to eqns. (21) - (23), and the resulting equations are integrated for a short time interval Au using the RungeKutta-Gill routine. This computation gives the profiles of X, and Xc in the pellet and the uniform pellet temperature at the dimensionless time Au. (3) These new values of X,, Xc and 8 are substituted into the elements of A and B in
+ (1 - h)cP,,
0.5(1 + X)C,, A}
-&!-
(35)
The initial concentrations cHO and Cc, of hydrogen and carbon respectively in the coked catalyst pellet are computed from wpp x lo3 cc0 =
12 +n (36) wp,n
CHO
=
x
12 +n
lo3
91
where pP refers to the apparent density of the catalyst pellet, which was measured as 1200 kg mP3. The value of n was estimated from ref. 10, Fig. 4. The value of the effective diffusivity DeA of the catalyst pellet was calculated by means of a parallel pore model which utilizes the pore volume distribution and neglects the variation in the diffusivity with gas composition because of its small effect [ 161. The tortuosity factor was taken as 3.0. The intraphase heat coefficient h and the mass transfer coefficient ko were calculated from the correlations of Ranz and Marshall [ 171 by taking the Nusselt and the Sherwood numbers to be approximately equal to 2. The original shape of the catalyst pellet is cylindrical (4.8 mm in diameter and 4.8 mm in height), and its equivalent radius R, (2.4 mm) (the radius of a sphere with the same ratio of volume to external surface area) was employed in the numerical calculations. The values of several parameters used in the numerical calculations are listed in Table 1.
3. EXPERIMENTAL
4. RESULTS
AND DISCUSSION
4.1. Uniform coke deposition Figure 2 shows the effect of pellet size on the net coke deposition over a wide range from 0.16 to 2.4 mm in equivalent radius, indicating clearly no dependence of the coke deposition on the pellet size. This is evidence for the absence of diffusion effects, and hence the coke deposit is distributed uniformly inside these catalyst pellets including the cylindrical catalyst (R, = 2.4 mm) used mainly in the regeneration experiments in this work. 4.2. Comparisons of temperature distribution Figure 3 illustrates the transient changes in the pellet temperature for three different initial temperatures. In all cases, the temperature rises rapidly in the initial stage of the reaction and then gradually decreases. The
DETAILS
The experimental apparatus and procedure for both the coking in the cracking of cumene and the regeneration are almost the same as those in the kinetics runs described in the previous paper [lo] except for the following points. First, experiments to measure the changes in catalyst weight and in temperature were carried out separately. The catalyst weight was measured using a reactor equipped with a balance. To monitor the catalyst temperature, the balance was removed from the reactor and the top of the reactor was sealed with a silicon rubber cup through which a very fine thermocouple (0.3 mm in diameter) was admitted into the reactor. The junction of the thermocouple was embedded in a cylindrical catalyst pellet in the bucket. Second, air was mainly used undiluted in order to give large changes in temperature. Third, the concentration of water vapour evolved inside the reactor was measured at the reactor exit by gas partition chromatography, yielding the overall conversion of hydrogen for the catalyst pellet.
t Cminl
Fig. 2. Effect of the pellet size on the net coke deposition (T = 873.2 K; Cne = 2.56 mol mp3): 0, R, 2.4 mm; CL,R, = 0.55 mm; 0,R, = 0.16 mm.
=
Fig. 3. Comparison of calculated (proposed model; - - -, one-component coke model) and experimental distributions of temperature for three different initial temperatures (w = 3.05%;~~~ = 21.3 kPa; R, = 2.4 mm): 0,run 20, To = 637.4 K;n, run 24, To = 884.1 K; 0, run 26, 7’0 = 934.2 K.
92
maximum rise in temperature increases with an increase in the initial temperature, reaching 45 K for the highest initial temperature shown (run 26). Thus the reaction must be treated non-isothermally. The computed results based on the proposed model, shown by the full curves, are in close agreement with the experimental results. In addition, the broken curves represent the calculated results based on a onecomponent coke model which regards the coke as consisting only of carbon (Appendix A). A number of previous models are based on this kind of treatment. The temperature rises calculated by means of the onecomponent coke model are lower than those calculated by means of the proposed model, and their agreement with the experimental results is clearly poor. Although the differences in the maximum temperature rise between the two models are of about the order of 10 K under the experimental conditions in this figure, a larger difference occurs for higher values of the atomic ratio n of hydrogen to carbon in the coke, as shown in Fig. 4. Thus the proposed model predicts more accurately the transient temperature profile during the burning off of coke than does the one-component coke model. Figure 5 shows that an increase in the oxygen partial pressure resulted in a rapid rise in the catalyst temperature (run 24), while a decrease in the oxygen partial pressure resulted in an almost isothermal reaction (run 21). In the kinetics runs this approximate isothermal situation was realized by reducing the oxygen pressure. The maximum temperature rise above the temperature of the ambient gas was about 0.3 K for a kinetics run using the crushed catalyst pellet (R, = 0.16 mm) under
Fig. 4. Effect of the initial atomic ratio n of hydrogen to carbon on the transient profile of the catalyst temperature (2’0 = 893.2 K; w = 3%;p,, = 21.3 kPa; Ro = 2.5 mm; e = 0.9).
P c
*501,, , I,,
0
(1,,
/,
200
100
j
300
I [sl
and experiFig. 5. Comparison of calculated ( ---) mental distributions of temperature for two different partial pressures of oxygen (Z’s = 883.8 K; w = 3.05%; R, = 2.4 mm): A, run 21, pAg = 7.98 kPa; 0, run 24, pAg = 21.3 kPa.
0
100
200
300
I Csl
and experiFig. 6. Comparison of calculated ( -) mental distributions of temperature for three different coke levels (To = 879.4 K; pAg = 21.3 kPa; Ru = 2.4 mm): 0, run 22, w = 1.94%;/\, run 23, w = 2.84%; 0, run 25, w = 4.42%.
the conditions TO = 873.2 K, PAg = 7.98 kPa and w = 0.0317 [lo]. Figure 6 demonstrates that higher coke levels lead to higher temperature rises during the reaction. 4.3. Comparisons of conversion distribution The three full lines in Fig. 7 show the calculated transient profiles of the three conversions xc, gH and xt. The computed profile of 1 -x, is in good agreement with
Fig. L Transient profiles of three conversions Xc, XH and X, under the conditions To = 873.2 K, PAs = 21.3 kPa, w = 4.42% and R, = 2.4 mm: __ , proposed model; - -, one-component coke model.
93
the experimental data represented by the open circles. In addition, the broken curve shows the profile of 1 -x, calculated by means of the one-component coke model, which clearly gives poorer agreement with the experimental results. A special feature of the proposed model is that it takes into account the contribution of the oxidation of hydrogen in the regeneration of coked catalysts. Direct measurement of the conversion of hydrogen, rather than the overall conversion, allows a stricter examination of the model. Figure 8 illustrates the results of such an examination, which reveal good agreement between the calculated and the experimental conversions of the hydrogen in the coke. Figure 9 shows comparisons of the computed and the experimental overall conversions for three different coke levels and indicates good agreement between them. An
0
IO00
500 t Csl
Fig. 8. Comparison of calculated () and experimental (- - 0 - -) conversions ZH of hydrogen (run 21; T, = 823.2 K; R, = 2.4 mm; w = 3.05%; p& = 21.3 kPa).
0
200
600
400 I
CSI
Fig. 10. Comparison of calculated (proposed model; - - -, one-component coke model) and experimental overall conversions X, for two partial pressures of oxygen (To = 873.2 K; w = 2.83%; R, = 2.4mm):0,run16,pAg=10.6kPa;~,run17,P&= 21.3
kPa.
increase in the coke level requires a longer reaction time. Figure 10 illustrates the effect of the oxygen pressure on the overall fraction of unreacted coke. The full curves are calculated by means of the proposed model, whereas the broken curves are calculated by means of the one-component coke model. Clearly the proposed model simulates more accurately the transient change in 1 - _%;,than does the one-component coke model. Semilogarithmic plots of 1 - x, against the reaction time are linear for isothermal conditions in the later period of the reaction [lo], whereas under non-isothermal conditions they deviate from the straight line, as shown in Figs. 9 and 10.
5. CONCLUSION
1.0 6 4 Iz
2
-
10-I 6 4 2 10’ 0
200
400
600
Fig. 9. Comparison of calculated ( -) and experimental overall conversions xt for three coke levels (To= 873.2 K;JJA,= 21.3 kPa; R, = 2.4 mm): 0, run 17, w = 2,84%;A, run 18, w = 4.42%;0, run 19, w = 5.75%.
The new model presented predicts accurately the transient changes in temperature and conversion during the burning regeneration of coked catalysts. This model considers the combustion of both the carbon and the hydrogen in the coke. The rapid temperature rise in the initial stage of the reaction is attributable mainly to the preferential burning of hydrogen in the coke. The transient temperature profiles predicted by this model are in good agreement with the experimental results for the burning regeneration of coked silica-alumina catalyst pellets. The oxidation rate constants obtained in the previous paper
94
were successfully used in the calculation. Thus the model was found to be valid for predicting the temperature rise as well as the conversion change during the burning regeneration of coked catalysts.
cording to the kinetics represented by eqns. (la) and (lb). Basic equations may be obtained by replacing Xu in eqns. (20) - (23) by 1 .O. Furthermore, the initial profile of oxygen pressure can be calculated from the equations in which the parameter h, is replaced by h,’ where h,’ is given by
ACKNOWLEDGMENT
&?
The support of the Ministry of Education through a Grant-in-Aid for Scientific Research (number 56470095) for part of the work is gratefully acknowledged.
APPENDIX
AH
1 D. Luss and N. R. Amundson, AIChE J., 15 (1969) 194. J., 19 (1973) 191. 2 H. Y. Sohn,AlChE 3 U. R. Shettigar and R. Hughes, Chem. Eng. J., 3 (1972) 93. 4 U. R. Shettigar and R. Hughes, Chem. Eng. J., 4 (1972) 208. 5 J. Szekely and J. W. Evans, Chem. Eng. Sci., 26 (1971) 1901. P. A. Ramachandran and R. 6 B. S. Sampath, Hughes, Chem. Eng. Sci., 30 (1975) 125. 7 F. E. Massoth, Ind. Eng. Chem., Process Des. Dev., 6 (1967) 200. 8 W. G. Schlaffer, C. 2. Morgan and J. N. Wilson, J. Phys. Chem., 61 (1957) 714. M. H. Rashid and R. 9 P. A. Ramachandran, Hughes, Chem, Eng. Sci., 30 (1975) 1391. K. Takatani, H. Iwasa and T. 10 K. Hashimoto, Masuda, Chem. Eng. J., 27 (1983) 177. 11 C. Y. Wen, Ind. Eng. Chem., 60 (9) (1968) 34. 12 D. Luss, Can. J. Chem. Eng., 46 (1968) 154. Ind. Eng. Chem., Fundam., 14 13 J. J. Carberry, (1975) 129. 14 R. Aris, Chem. Eng. Sci., 6 (1957) 262. 164. 15 J. R. Arthur, Trans. Faraday Sot., 47 (1951) M. Teramoto, K. Miyamoto, T. 16 K. Hashimoto, Tada and S. Nagata, J. Chem. Eng. Jpn., 7 (1974)
116. 17
W. E. Ranz and W. R. Marshall, 141,173.
(Pa-’
CP CA
cBO
cc’ cCO> cHO
C co ’ CHO' 3
cp. i D eA
Jr., Chem. Eng.
Prog., 48 (1952)
e
Ec,E, APPENDIX
A
A.1. The parameter h, for the one-component coke model The one-component coke model regards the coke as consisting only of carbon and its oxidation as proceeding homogeneously ac-
B: NOMENCLATURE
frequency factor of the reaction rate of oxidation of carbon defined in eqn. (2) (Pa-“ ss’) frequency factor of the reaction rate r3 defined in eqn. (lc)
AC REFERENCES
h
(AlI
SC’)
specific heat capacity of the catalyst pellet (J kg-..‘) concentration of oxygen at any radiaI position in the catalyst pellet (mol rne3) concentration of cumene at the reactor inlet in the coking reaction (mol m-“) concentration of carbon at any radial position in the coke particle (mol me3) initial atomic concentrations of carbon and hydrogen in the catalyst pellet (mol me3) initial atomic concentrations of carbon and hydrogen in the coke particle (mol m- 3, average molecular heat capacity over the temperature range from 298.2 K to the pellet temperature (J mol-’ K-‘) effective diffusivity of oxygen in the catalyst pellet (m2 s- ‘) emissivity (blackness) of the coked catalyst pellet (dimensionless) activation energies of the combustion of carbon and atomic hydrogen (J mol-‘) gas-film heat transfer coefficient (J m-* s-’ Km-’) modified Thiele modulus defined in eqn. (24) (dimensionless)
95
AHc
Mf.i
kc kG
k HS
k,
9 k2
n
NC
PA PAg 4t
rc
F-0 w-2
r3
R
4 R*
overall heat of reaction for the oxidation of carbon to produce CO and CO,, defined in eqns. (la) and (lb) (J mol-‘) the standard heat of formation of the ith component at 298.2 K (J mol-‘) heat of reaction for the oxidation of atomic hydrogen, defined in eqn. (lc) (J mol-‘) k, + k, (PaWIF1) gas-film mass transfer coefficient for oxygen (mol m-* s-l Pa-‘) rate constant for the oxidation of atomic hydrogen (m Pa-’ s-l) second-order rate constants for the oxidation of carbon to CO and CO2 (P~-‘s-~) initial atomic ratio of hydrogen to carbon in the coke (dimensionless) number of coke particles per unit volume of the catalyst pellet (mm3) partial pressure of oxygen (Pa) partial pressure of oxygen in the ambient gas (Pa) rate of heat removal from the catalyst pellet (J s-l) reaction rates based on a single coke particle for oxygen, carbon and hydrogen (mol s-l) reaction rate of carbon based on the volume of coke (mol m-3 s-l) radius of the coke particle (m) reaction rates for carbon based on the volume of coke, defined in eqns. (la) and (lb) (mol me3 s-l) reaction rate for atomic hydrogen based on the surface area of the reaction interface, defined in eqn. (lc) (mol me2 s-l) radial distance in the catalyst pellet (m) 8.314, gas constant (J mol-’ K-l) equivalent radius of the pellet (equal to the radius of a sphere with the same ratio of volume to external surface area) (m)
t
radius of the catalyst pellet (m) 2RgTROkG/DeA, modified Sherwood number (dimensionless) reaction time of regeneration
to*
ro/kH&pAg, time at which the
Ro Sh*
(s)
Tci
unreacted core disappears at the temperature To (s) temperature of the catalyst pellet (K) temperature of the ambient gas
TW
(K) temperature
T
To
U W
xc
xc,
XH
xC,xH
of the reactor
wall
(K) temperature .of the catalyst pellet at the start of the reaction (K) t/to* 9 dimensionless time mass ratio of coke to uncoked catalyst (dimensionless) conversion of carbon at any radial distance in the coke particle (dimensionless) conversions of carbon and hydrogen at any radial distance in the catalyst pellet (dimensionless) overall conversions of carbon and hydrogen in the catalyst pellet (dimensionless) overall conversion of coke in the catalyst pellet (dimensionless)
Greek symbols kc#Ag to* (dimensionless) a0 n/a, (dimensionless) P E,/R,T, (dimensionless) YC EHfRgTO (dimensionless) YH R/R,, dimensionless radial posi77 tion in the catalyst pellet e (T - To)/To, dimensionless temperature of the catalyst pellet k2/(kl + k,) (dimensionless) r/To, dimensionless radial dis: tance in the coke particle apparent density of the catalyst PP pellet (kg mm3) PA/PA~(dimensionless) ti Subscripts
A C D
oxygen carbon co2
96
& H H2
M
ambient gas atomic hydrogen molecular hydrogen co
surface of the catalyst reactor wall steam (gaseous water) start of reaction
pellet