Biomedical Engineering Reference
In-Depth Information
Mole balances on A and B in the reactor leads to
d C A
d t ¼r ¼ k S C s K A
C A C B =K C
(E9-4.28)
1
þ K A C A þ K B C B
d C B
d t ¼ r ¼ k S C s K A
C A C B =K C
(E9-4.29)
1
þ K A C A þ K B C B
The solutions from LHHW model can be obtained by solving Eqn (E9-4.28) and
Eqn (E9-4.29) with initial conditions given by C A0 ( Eqn E9-4.27 ) and C B0 ¼
0. Subse-
quently, the fractional coverages can be obtained from Eqn (E9-4.23) and (E9-4.24) . One
should note that the initial conditions set for surface-rate limiting LHHW model must
have taken the adsorption equilibria into consideration.
Instead of having four equations to solve, we now have only two equations to solve.
The solutions to one case consistent with the approximation to the first case discussed
earlier are shown in Fig. E9-4.6 . For comparison purposes, we have plotted the LHHW
approximations as dashed lines and the original solutions with individual rates are shown
as solid lines.
0at t
¼
(a)
(b)
10
10
9
9
C A
8
8
C A
7
7
6
6
5
5
4
4
3
3
2
2
C B
1
C B
1
0
0
0.01
0.1
1
10
100
0.0
0.2
0.4
0.6
0.8
1.0
k S t
k S t
(c)
(d)
1.0
1.0
A
0.8
A
0.8
0.6
0.6
j
j
0.4
0.4
0.2
0.2
0.0
B
B
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.01
0.1
1
10
100
k S t
k S t
FIGURE E9-4.6 Variations of concentrations in the bulk phase and fractional surface coverages as functions of
time for K A ¼
1/ C s . The dashed lines are the predictions from LHHW kinetics assuming that the
surface reaction is the rate-limiting step, whereas the solid lines are for k A C s ¼
1/ C s ; K C ¼
4; K B ¼
10 k S and k B C s ¼
10 k S .
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