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Exercise 12.1
Subject:
Revision of ratebased equations to account for entrainment and occlusion.
Given:
. Ratebased model Eqs. (124) to (1218).
Find:
Modified equations
Analysis:
Entrainment:
Let
φ
j
= ratio of entrained liquid (in the exiting vapor) that leaves Stage
j
to the liquid leaving
Stage
j
,
y
y
i n
i n
,
,
and
I
. Then, the entrained component liquid flow rate leaving Stage
j
=
φ
j
x
i,
(1
)
L
j
j
r
L
+
.
Correspondingly, the entrained component liquid flow rate entering Stage
j
=
φ
j+1
x
i,j
+1
(
)
1
1
1
+
+
+
r
L
j
L
j
.
Occlusion:
Let
θ
j
= ratio of occluded vapor (in the exiting liquid) that leaves Stage
j
to the vapor
leaving Stage
j
,
(
)
1
+
r
V
j
V
j
. Then the occluded component vapor flow rate leaving Stage
j
=
θ
j
y
i,j
(
)
1
+
r
V
j
V
j
.
Correspondingly, the occluded component vapor flow rate entering Stage
j
=
θ
j
1
y
i,j

1
(
)
1
1
1
+


r
V
j
V
j
.
The liquidphase component material balance, Eq. (124), and vaporphase component
material balance, Eq. (125), become, respectively,
M
r
L x
L
x
r
L
x
f
N
i
C
i j
L
j
L
j
j
i j
j
i j
j
j
L
j
i j
i j
L
i j
L
,
,
,
,
,
,
(
)
(
)
,
≡
+
+


+


=


+
+
+
+
1
1
0
1
1
1
1
1
1
φ
φ
= 1, 2, .
..,
M
r
V y
V
y
r
V
y
f
N
i j
V
j
V
j
j
i j
j
i j
j
j
V
j
i j
i j
V
i j
V
,
,
,
,
,
,
(
)
(
)
,
≡
+
+


+

+
=
+
+




1
1
0
1
1
1
1
1
1
θ
θ
i
C
=
1 2
,
, ....
,
The liquidphase energy balance, Eq. (126), and vaporphase energy balance, Eq. (127),
become , respectively,
E
r
L H
L
H
r
L
H
j
L
j
L
j
j
j
L
j
j
L
j
j
L
j
j
L
≡
+
+


+


+
+
+
+
(
)
(
)
1
1
1
1
1
1
1
1
φ
φ
,
1
0
C
LF
L
L
L
j
i j
j
j
i
H
f
Q
e
=

+

=
1
1
1
1
1
1
,
1
(1
)
(1
)
0
C
V
V
V
V
V
V
VF
V
V
V
j
j
j
j
j
j
j
j
j
j
j
j
i j
j
j
i
E
r
V H
V
H
r
V
H
H
f
Q
e
+
+




=
≡
+
+ θ

θ
+

+
+
=
The total phase material balances, Eqs. (1216) and (1217), become, respectively,
M
r
L
L
r
L
f
N
T j
L
j
L
j
j
j
j
j
L
j
i j
L
i
C
T j
,
,
,
(
)
(
)
≡
+
+


+


=

+
+
+
=
1
1
0
1
1
1
1
1
φ
φ
M
r
V
V
r
V
f
N
T j
V
j
V
j
j
j
j
j
V
j
i j
V
i
C
T j
,
,
,
(
)
(
)
≡
+
+


+

+
=
+



=
1
1
0
1
1
1
1
1
θ
θ
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View Full DocumentExercise 12.2
Subject:
Revision of ratebased equations to account for a chemical reaction in the liquid
phase.
Given:
. Ratebased model Eqs. (124) to (1218).
Assumption:
Perfect mixing in the liquid on a stage.
Find:
Modified equations for:
(a) chemical equilibrium
(b) kinetic rate law
Analysis:
Let the chemical reaction be:
ν
ν
ν
ν
A
B
R
S
A
B
R
S
+
⇔
+
where:
ν
ι
=
stoichiometric coefficient of component
i
where it is (+) for products R and
S, and () for reactants A and B.
Let the change in flow rate of component
i
in the liquid on stage
j
due to reaction be:
Δ
n
M
r
i j
j
i
k
k j
,
,
= 
±
²
³
´
µ
ν
ν
(1)
where:
M
j
= volumetric holdup of liquid on stage
j.
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 Spring '08
 Ofoli
 The Land

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