Environmental Engineering Reference
In-Depth Information
This form of equation enables the use of the relative carbon concentration (e.g.,
C
/
C
o
) instead
of absolute carbon concentration
[396]
. After further rearrangement, this equation can be used
to follow the carbon removal in the high-rate burn-off region (
C
1
) and low-rate burn-off region
(
C
2
), i.e.:
C
1
C
10
e
−
k
1
t
=
(6.3)
C
2o
e
−
k
2
t
C
2
=
(6.4)
where total carbon content
C
=
C
1
+
C
2
and relative carbon concentration with time:
C/C
o
=
C
1o
/C
o
e
−
k
1
t
+
C
2o
/C
o
e
−
k
2
t
(6.5)
f
2
)e
−
k
2
t
f
2
e
−
k
2
t
C/C
o
=
(1
−
+
(6.6)
where
f
2
is the fraction of initial carbon associated with
C
2
at
t
=
0. Then, after all
C
1
carbon
was removed, the equation becomes:
f
2
e
−
k
2
t
C/C
o
=
(6.7)
To be used for kinetic measurements, this set of equations requires determination of the carbon
content in spent catalyst at different time intervals during burn-off. To get a realistic
description of regeneration process, such estimate would have to be done for different stages
conducted at gradually increasing temperatures, until most of the carbon was removed from
spent catalyst. Such approach was undertaken by Alwarez et al.
[46]
who studied several spent
catalysts varying widely in the level of deactivation. Their experimental data could be
correlated using two parallel first order independent power laws (Eqns
(6.5) and (6.6)
)upto
90% conversion of coke. However, for the spent catalyst containing 4.1 wt.% V and about
36 wt.% of coke, the second order kinetic law gave the best fit of the experimental results.
Established information (e.g.,
Figs 6.9 and 6.11
) shows that on an industrial scale,
regeneration process has to be conducted in at least two stages. For safety reasons, the first
stage has to be conducted either with a diluted or in air but under all precautions taken to avoid
temperature excursions due to the presence of highly reactive components of coke. For this
stage, the removal of hydrogen from coke is much more important than that of carbon. Based
on the above sequence of the equations, this process may be described by the following
equation:
H
o
e
−
k
3
t
H
=
(6.8)
where
k
3
is the rate constant for the burn-off of hydrogen, whereas
H
and
H
o
are the hydrogen
content in coke at
t
and
t
0, respectively. Then, the following kinetic equation may apply for
the overall coke removal during the chemically controlled first stage:
=
H/H
o
e
−
k
3
t
C
1o
/C
o
e
−
k
1
t
Coke removed
=
+
(6.9)
