Page 228 - Introduction to chemical reaction engineering and kinetics

210 Chapter 8: Catalysis and Catalytic Reactions

If kobs, kA, and D, all follow Arrhenius-type behavior,

ace reaction) + E,(diffusion)] 21 i E,(surface reaction) (8.531)

since the activation energy for diffusion (- RT) is usually small compared to the (true)
activation energy for a reaction (say 50 to 200 kJ mol-‘). The result is that, if reaction
takes places in the catalyst particle in the presence of strong pore-diffusion resistance,
the observed EA is about 1/2 the true E,,, for the surface reaction. This effect may be
observed on an Arrhenius plot (In kobs versus l/T) as a change in slope, if conditions
are such that there is a change from reaction-rate control (negligible pore-diffusion
resistance) at relatively low temperatures to strong pore-diffusion resistance at higher
temperatures.

8.5.5 Dependence of q on Temperature

The definition of the particle effectiveness factor r] involves the intrinsic rate of reaction,
( -Y*)~~~, for reaction A -+ products, at the exterior surface conditions of gas-phase
concentration (cAs) and temperature (T,). Thus, from equation 8.55,

(-rz4)obs = d-rA)inr,c&
So far, we have assumed that the particle is isothermal and have focused only on the
diffusional characteristics and concentration gradient within the particle, and their ef-
fect on 7. We now consider the additional possibility of a temperature gradient arising
from the thermal characteristics of the particle and the reaction, and its effect on 77.
The existence of a temperature gradient is illustrated schematically in Figure 8.9 for a
spherical or cylindrical (end-on) particle, and for both an exothermic and an endother-
mic reaction. The overall drop in temperature AT,, from the center of the particle to
bulk gas may be divided into two parts:

AT,, = ATP + ATf (8.533)

where ATP is the drop across the particle itself, and AT, is that across the gas film or the
thermal boundary layer. It is the gradient across the particle, corresponding to AT,, that
influences the particle effectiveness factor, 7. The gradient across the film influences the
overall effectiveness factor, v0 (Section 8.5.6).
Two limiting cases arise from equation 8.5-33:
(1) Rate of intraparticle heat conduction is rate controlling:

ATf -+ 0; T, + T g (8533a)

The result is a nonisothermal particle with an exterior surface at T,.
(2) Rate of heat transfer across gas film is rate controlling:

ATP -+ 0; T(throughout) -+ T, (8533b)

The result is an isothermal particle, but hotter (exothermic case) or colder (en-
dothermic case) than the bulk gas at Tg.