466
Chapter 10
Figure 10.10 Plot of the effectiveness factor for a first order process. The effectiveness factor has been
calculated both exactly, using Eq. (10.51) and the Thiele modulus for a sphere (Eq. 10.50), and
approximately using Eq. (10.53) and the generalized Thiele modulus given by Eq. (10.55) with
^
= Rp/3.
As seen from Fig 10.10, the deviation between the exact and approximate solution is small for a
first order reaction, with maximum deviation in the intermediate range (see also Example 10.7).
Example 10.7. Effectiveness factor for a pellet with Monod kinetics
We will now consider a pellet with biomass immobilized uniformly thorughout a pellet to a concentration
of x kg m'3. The uptake rate of glucose is assumed to follow Monod kinetics, i.e.
where
~ 4 s
s
x = k- S
s + K.
S + a
(
1
)
jy’
S =
— -— ,
k = Ya{tnaxx
and
a
= - - -*■■■
T
xs ' max
c
*5
su rfa c e
su rfa c e
(
2
)
The relevant data is summarized in Table 10.11. For a porosity of 0.5 and an assumed tortuosity factor of
1.5,
we find the effective diffusion coefficient for glucose in the pellet by using Eq. (10.43):
D
„*■ =
6-10
10
=
210
'
eff
1.5
(3)