Environmental Engineering Reference
In-Depth Information
Table 7.7: Mass transfer and kinetic data for leaching V (0.66M; 323 K) [From ref.
490
. Reprinted
with permission].
Acetic acid
Malonic acid
Oxalic acid
Diffusion coefficient,
D
(cm
2
/s)
10
5
×
1
.
908
1
.
881
2
.
088
10
7
Effective diffusivity,
D
e
(cm/s)
×
Spent catalyst
2
.
75
2
.
70
3
.
01
After 1
st
stage leaching
23
.
4
23
.
0
25
.
6
After 2
nd
stage leaching
33
.
6
33
.
2
36
.
8
Fresh catalyst
43
.
9
43
.
3
48
.
1
Leaching rate (wt.%/s)
×
10
5
13
.
19
31
.
25
41
.
48
Thiele modulus
1
st
stage leaching
1
.
73
4
.
17
4
.
96
2
nd
stage leaching
0
.
21
0
.
49
0
.
58
catalyst porosity in the course of leaching. As expected, the
D
e
values are higher in the stage 2
than in stage 1. The values also confirm the established efficiency of the acids for leaching, i.e.:
Oxalic acid
>
malonic acid
>
acetic acid
The combined effects of reaction rate and diffusion on leaching process can be examined using
the Thiele modulus defined as the ratio of the reaction rate to diffusional rate, i.e.:
R
c2
k
D
e
R
c2
Reaction rate
(
C
Ao
)
n
ϕ
2
=
=
D
e
×
(7.7)
where
R
c
is the catalyst pellet radius,
k
is the rate constant,
n
is the order of reaction, and
C
Ao
is the initial concentration of leaching agent. The values of Thiele modulus in
Table 7.7
indicate improvement in intraparticle mass transfer due to metal removal. Thus, as leaching
progresses, the intraparticle transfer is gradually improved in the pore network and chemical
reaction becomes rate-controlling. This is confirmed by much higher values of Thiele modulus
for the stage 1 (
Table 7.7
), whereas significantly diminished restriction indicated by low values
of Thiele modulus confirm that in the stage 2, the reaction is chemically controlled. This
situation can be represented by “A” progressing to “B” as it is illustrated in
Fig. 7.15 [491]
and
the mass balance can be expressed as:
2
r
2
r
2
R
2
t
τ
D
=−
R
2
[ln (
R
)
−
(
r
)]
+
1
−
(7.8)
