MAXIMUM TEMPERATURE RISE INSIDE CATALYTIC PELLETS A method for estimating the maximum temperature difference between the gas and the interior of a symmetric catalyst pellet, in which a single chemical reaction occurs, is presented. The estimate is expressed in terms of directly observable quantities.
W H E N a chemical reaction occurs within porous catalyst pellets, the temperature and concentration differences between the gas and the interior of the pellet may mask considerably the true kinetics when the interpretation is based on externally observable quantities. Damkohler (1937), Thiele (1939), and Zeldowitsch (1939) investigated the effect of mass diffusion. Later Damkohler (1943) and Prater (1958) obtained the following - upper _ _ bound on the maximum temperature deviation between the interior and surface of the pellet,
T, =
(-AH ) Dc,
x
+ H)M +M)HPa
=
DS,dc
(7 1
Defille
R2 dn Dca dt
(8)
'pa=--
in 7 yields
Substitution of Equation
Similarly, one can obtain
By use of Equations 1, 9, and 10 the following upper bound on the maximum temperature in the pellet is obtained,
and
Equation 11 enables the determination of the maximum temperature difference between the gas and the interior of the pellet based on observable ambient quantities. The value of the maximum temperature difference approaches asymptotically the value
where
M
dn _
(1 1
Wei (1966) has shown that this bound may be exceeded during the transient behavior. The surface temperature of a catalyst pellet may largely exceed that of the gas, on account of external heat transfer resistance. This has been demonstrated by Gioia and Green (1967), who analyzed the experiments of Crosser and Fulton (1965). Carberry (1961) and Tinkler and Pigford (1961) considered the combined effects of internal and external resistances on the effectiveness factor. Carberry (1966) used certain simplified assumptions to obtain the following approximate bound on the maximum temperature difference between the interior of the pellet and the gas
Tm --- Ta - (1 Ta (1
The observed reaction rate is equal to
kc R -
D
hR €I = -
x
In this work a technique is developed for estimating the maximum temperature difference between the gas and the interior of a catalyst pellet in terms of observable quantities. This estimate is sharper than the results previously reported. Determination of Upper Bound
For a single chemical reaction proceeding inside a catalyst pellet, the steady-state equations are
D-- d ( 1.2 dr
7.2-
;;)-
3 3+
X--
1.2-
dc
l&EC
T,- Ta Tm - Taw --=Ta Ta
@a&
(14)
3H
as +aa (1/H - 1/M) >> 1 and iM >> H. Carberrv (1966) has shown that under practical conditions M is much ljrger than H and the ratio
&l Xk,
_ = -
H
(15)
hD
(3 )
(-AH)f(c, T ) = 0
(4)
is much larger than unity (usually, 10 < M/H < 50,000). This causes the interphase heat transfer resistance to be more important than the interphase mass transfer resistance and the value of (Tm- T a ) /T , to exceed Pam Comparison of Equations 11 and 2 s h o w that the two predict the same bound only when
(5 )
au= -
k c ( c a - cs) r = R
dT A - = h ( T a - T,) r = R dr 596
