Biomedical Engineering Reference
In-Depth Information
TABLE 5.2
Reaction Space Time Requirement and Concentration Profile for Single Reactions in an
Isothermal Constant Density Plug Flow Reactor (PFR) with Simple Kinetic Models
1. Zeroth-order: A
/
Products,
r
¼
k
s
¼ð
C
A
0
C
A
Þ=
k
C
A
¼
C
A
0
k
;
s
Q
Q
V
V
= 0 :
= 0 :
C
A
=
C
A
=
C
A0
,
C
B
=
C
B0
,
C
C
=
C
A0
,
C
B
=
C
B0
,
C
C
=
2. First-order: A
/
Products,
r
¼
kC
A
C
C0
,
C
D
=
C
D0
,
C
R
=
C
R0
,
C
C0
,
C
D
=
C
D0
,
C
R
=
C
R0
,
s
¼ lnð
C
A
0
=
C
A
Þ=
k
C
A
¼
C
A
0
expð
k
s
Þ
;
A, B,
C, D,
R
A, B,
C, D,
R
Products,
r ¼ kC
n
A
3. Power-law kinetics: A
/
h
C
1n
i
1
1n
C
1n
C
1n
A
A
0
s
¼
;
C
A
¼
A
0
ð1 nÞk
s
ð
1
n
Þ
k
V
V
=
=
V
V
:
:
C
A
,
C
B
,
C
C
,
C
D
,
C
R
,
C
A
,
C
B
,
C
C
,
C
D
,
C
R
,
4. Bimolecular: A
þ
B
/
Products,
r
¼
kC
A
C
B
1
C
A
1
k
1
C
A
0
Q
Q
s
¼
;
C
A
0
C
A
¼ C
B
¼
if
C
A
0
¼ C
B
0
1
þ
kC
A
0
s
ρ
ρ
= constant
Q = constant
= constant
Q = constant
1
kðC
B
0
C
A
0
Þ
ln
C
A
0
ð
C
A
þ
C
B
0
C
A
0
Þ
_
_
V
V
s
¼
;
τ
τ
= ― =
= ― =
t
t
C
A
C
B
0
Q
Q
Q
Q
C
A
0
ð
C
B
0
C
A
0
Þ
C
A
¼
C
A
0
;
C
B
0
exp½
k
ð
C
B
0
C
A
0
Þ
s
C
B
¼
C
B
0
C
A
0
þ
C
A
5. Autocatalytic: A
þ
R
/
2R
þ
products,
r
¼
kC
A
C
R
1
kðC
A
0
þ C
R
0
Þ
ln
C
A
0
ð
C
A
0
þ
C
R
0
C
A
Þ
C
A
C
R
0
s
¼
;
C
R
0
Þ
C
A
0
þ C
R
0
exp½kðC
A
0
þ C
R
0
Þ
s
;
C
A
0
ð
C
A
0
þ
C
A
¼
C
R
¼
C
A
0
þ
C
R
0
C
A
kC
A
K
A
þ
6. Unimolecular catalytic: A
/
products,
r
¼
C
A
K
A
ln
C
A
þ C
A
0
C
A
1
k
C
A
0
s
¼
kC
2
A
K
A
þ
7. Unimolecular catalytic: A
/
products,
r ¼
C
A
ln
C
A
0
1
k
K
A
C
A
K
A
C
A
0
s
¼
C
A
þ
(
Continued
)
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