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64 3. Heterogeneous Processes and Reactor Analysis

For slurries:

• for porous particles,
S SM s s
Sm s s (3.22)
V L V L

• for nonporous particles,
S
ex (3.23)
V L c
For particles:

• for porous particles,
S SM s s
S p (3.24)
s
V S V S
• for nonporous particles,
S 6
ex (3.25)
V S d p

where:
S s the surface area per unit mass of catalyst
S ex the external surface area of catalyst.
By using these ratios and the relationships (3.18) and (3.19), we can alter the material
balance expressions and the corresponding solutions of the reactor models if we use other
rate expressions. It should be noted that in practice, in fed-beds and slurries of porous ix
particles, the external area of the particle and thus the parameters a u and a c are used,
respectively.
It should be noted that when referring to the reaction rate per unit surface of a porous
icient,
particle or to the corresponding rate coef it should be clarified whether the rate or
f
Then,
the rate coefficient is based on the external or the total surface area. for e in xample,
a slurry reactor where the reaction rate is expressed per unit volume of liquid, the rate
could be
r S m k f C s s () (3.26)
s
u
or
r a k f C () (3.27)
c s
u
These two expressions are equialent only for nonporous particles. For porous particles,
v
S ⋅ m s ferent from is very dif a c as well as the corresponding k v alues.
s
s