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60 3. Heterogeneous Processes and Reactor Analysis

icient A look into the rate coef f

Following Carberry (1976), in this book the term “rate coefficient” is used for
the proportionality coef icients f k i in the typical rate expression of the
form: r k f ( C ). wing analysis, irst-order ele- a f o simplify the follo T
i
i
mentary reaction is considered. Then the intrinsic reaction rate can be
expressed as
r m k m s C (3.7)

r vs k vs C s (3.8)

k
r C s (3.9)
s
s
where: C S the surface concentration of the reactant, (moles/m 3 )of fluid.
The several rate coeficients have the following units: f

k 1 m fluid 3
m
s kgsolid
k 1 m fluid 3 1
vs 3
s m solid s
k 1 m fluid 3 m
s
s ms 2 olid su o rface s
Then, after some rearrangements:

dN 1 1 M   S M
= r =  S k  C = C k = S k C
n dt t ρ p  n  vs S n s S n m S (3.10)
k k
k t t
t
where, is the particle density. The parameter k has the follo wing units:
p
t
k 1 m fluid 3
t
s n
This rate coefficient corresponds to the reaction rate r , namely, to the reaction rate defined
t
per actie site. This rate coeficient for a specific reaction and a fed catalytic agent and f ix
v
temperature can be considered constant.
In the case of a porous catalyst , where the internal area contributes the most to the total
area, S can be considered to be independent from the catalyst shape and size. Furthermore,
s
the number of catalytic actie sites per unit area v n can be considered a fixed property
S
n
v
for a gien catalyst. Consequently the actie sites concentration can M be also be
v
,
s