458
Chapter 10
P =
D a + a -1
(10.40)
The
Damkohler number
can, like the dimensionless groups of Table 10.6, be interpreted and given
a physical meaning. It is the ratio between the maximum rate of substrate consumption by the
reaction and its maximum mass transfer rate. Thus, if Da « 1
the maximum mass transfer rate is
much larger than the maximum rate of reaction (low mass transfer resistance).
SA
is in this case ~ 1
and the conversion proceeds at the same rate as in the bulk phase. When Da » 1, on the other
hand, the mass transfer is the rate-limiting step and the reaction rate is significantly lower than at
bulk phase conditions. These cases can be referred to as a
reaction-limited regime
and a
mass
transfer-limited regime,
respectively.
Note 10.5, Effectiveness factors for film transport
Following the tradition in heterogeneous catalysis, the effect of external mass transfer on the overall
conversion can be quantified by means of the
effectiveness factor for film transport, rtf,
which is defined as
the ratio of the observed reaction rate and the reaction rate that would have occured without external mass
transfer resistance. Thus with Monod kinetics
=
Sa/(Sa+<x)
1
/(
1
+ a )
(
1
)
Consequently,
rjf
< 1, and in general the effect of increasing mass transfer resistance is a reduction of the
effectiveness factor.
For Da approaching zero (very slow reaction compared with the mass transfer process), we find from Eq.
(10.39) that
SA
must approach unity. For the reaction-limited regime we therefore have
jjr =
1
, and the
observed reaction rate is given by
~<lA=Y«M*m.
S*
X
(2)
S A + K ,
i.e., the bulk liquid concentrations can be directly applied in the kinetic expression of the surface reaction.
For very large values of Da,
SA
will be close to zero, and from Eq. (10.39)
1
_
s A
Da
S A + a
which, inserted in Eq. (1) gives
7 / =
(l + a )
D a
(3)
(4)
Here the observed reaction kinetics is given by
- q A = k sasA
(5)