Biomedical Engineering Reference
In-Depth Information
Residence-Time-Based Design Approach
A bubbling fluidized bed must be sufficiently deep to provide reactants the
time to complete the gasification reactions. This is why residence time is an
important consideration for determination of bed height. An approach based
on residence time, developed primarily for coal gasification, can be used for
biomass char gasification, which gives at least a first estimate of the bed
height for a biomass-fueled bubbling fluidized-bed gasifier.
The residence time approach is based on the assumption that the conver-
sion of char into gases is the slowest of all gasifier processes, so the reactor
should provide adequate residence time for the char to complete its conver-
sion to the desired level. Here is a simplified method.
Given the following assumption:
1. The reactivity factor f
o
5
1).
2. The solid is in a perfectly mixed condition (i.e., continuous stirred-tank
reactor, CSTR).
1 (which lies between 0
f
o
#
,
Then,
the volume of
the fluidized bed, V,
is calculated using the
equation:
W
out
θ
ρ
b
V
(8.32)
5
where W
out
is the char moving out; kg/s
(1
X) W
in
; X is the fraction of
5
2
the char in the converted feed;
ρ
b
is the bed density, which can be estimated
theoretically from fluidization hydrodynamics and regime (kg/m
3
); and
θ
is the residence time of the char in the bed or reaction time (s).
The residence time approach assumes that
the water
gas reaction,
(C
H
2
), as written in
Eq. (8.33)
is the main gasification reac-
tion, where the char is consumed primarily by the steam gasification reaction
for nth-order kinetics:
H
2
O
-
CO
1
1
1
m
dC
dt
5
n
k
½
H
2
O
(8.33)
where m is the initial mass of the biomass and C is the total amount of car-
bon gasified in time, t. Taking a logarithm of this:
5
1
m
dC
dt
ln
ln
ð
k
Þ
1
n ln
½
H
2
O
(8.34)
Experiments can be carried out taking a known weight of the biomass
and measuring the change in carbon conversion at different time intervals for
a given temperature, steam flow, and pressure. Using these data, graphs are
plotted between ln((1/m)(dC/dt)) and ln[H
2
O]. The y intercept in this graph
will give the value of k, and the slope will give the value of n. An example
of such a plot is shown in
Figure 8.23
. The experiment is carried out for
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