Biomedical Engineering Reference
In-Depth Information
1
dC
dt
ln
( )
n
m
k
ln[H
2
O]
FIGURE 8.23
Plot of Eq. (8.34) for determination of residence time.
different operating temperatures such as 700
C, 800
C, and 900
C; so, for
each temperature, one k value is obtained.
Now k can be expressed as:
0
1
E
a
RT
@
A
k
5
k
0
exp
2
(8.35)
ln k
0
E
a
RT
ln k
5
This shows that if we plot a graph between ln k and 1/T, the y intercept
will give the value of k
0
and the slope will give the value of (
E
a
/R).
The reaction rate for the steam gasification of biomass is given by:
dC
dt
5
2
½
E
a
RT
n
k
0
m exp
H
2
O
(8.36)
2
This gives the generalized reaction rate that shows the dependence of the
gasification rate on temperature, mass of carbon or char, and concentration
of steam/air/oxygen.
From a knowledge of the reaction rate, the residence time,
θ
, can be cal-
culated as:
C
0
X
r
θ
5
(8.37)
where C
0
is the initial carbon in the biomass particle (kg), X is the required
carbon conversion (
), and r is the steam gasification reaction rate (kg/s).
We can avoid such experiments if there is a suitable expression for the rate
of steam gasification of the designed biomass char (Sun et al., 2007).
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