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3.9 P article Analysis 241

hence . actor are in the range 2 < alues of the tortuosity f ypical v T < 6 for silica gel and
p p
alumina, 5 < < 65 for acti and 3 < v ated carbon, < 4 for catalyst particles, if no other
p p
v
f,
,
information is aailable (Froment and Bischof 1990). Generally the tortuosity f actor
should be handled as an empirical constant, which is characteristic for each material, and
should be evaluated experimentally (Perry and Green, 1999).
Estimation methods
Depending on the specific pore system, the dif es place in three fusion in a solid particle tak
ranges (Perry and Green, 1999):

• Knudsen diffusion in small pores ( D )
k
• Fick’s or molecular diffusion in large pores ( D ), also called “bulk dif fusion”
F
• Transition range diffusion, which includes both mechanisms ( D )
t
The Knudsen diffusion coefficient D corresponds to the movement of gaseous solutes in
k
small pores and can be estimated by using the following equation (Perry and Green, 1999):
T
D k 9700 r pore (3.600)
MB

Here, D is in cm 2 /s, r the average pore radius (cm), MB the molecular weight of the gas
k pore
(g/mol), and T the temperature in K. In the case of a narrothe a ution, w pore size distrib er- v
age pore radius can be estimated as follows (Froment and Bishof 1990): f,

2
r pore p (3.601)
S
sp
where is the internal porosity of the solid, the particle density of the solid (g/cm 3 ),
p p
and S the specific area of the solid (cm 2 f /g). The bulk diffusion coeficient corresponds to
s
the moement of gaseous or liquid solutes in large pores and can be estimated as follo v ws:

D = D p (3.602)
F f

p
where D is the diffusion coefficient of the molecules in the fluid phase and the tortuos-
f p
ity of the solid structure, which is defined as the ratio of the actual distance a molecule
travels between two points and the shortest distance between these points (F 1999). , ogler
Fogler (1999) adds one more factor to the abo e equation: v

D D pp (3.603)
f
F

p
where
is the constriction f ariation in the cross-sectional area actor that accounts for the v
p
A typical v that is normal to difalue of the constriction factor is 0.8. fusion.