Environmental Engineering Reference
In-Depth Information
6.6.2
General HTU-NTU method
The height of the packing in a particular column for a given separation can be calculated
with the HTU-NTU method. This method is based on mass transfer between the vapor
and liquid phases.
Assuming constant molar overflow,
L
V
is constant and the assumption of equi-
molar counterdiffusion is valid, so that the flux of one component across the vapor-
liquid interface is equal and opposite to the flux of the other component (
N
A
=−
/
N
B
).
Foradifferential height d
z
in a packed column, the mass transfer rate is:
N
A
aA
c
d
z
=
k
y
a
(
y
A
−
y
A
I
)
A
c
d
z
,
(6.16)
where
N
A
is the flux of solute
A
, and
A
c
is the column cross-sectional area. The mass
transfer rate in terms of changes of solute concentration in the liquid and vapor phases is:
N
A
aA
c
d
z
=−
V
d
y
A
=
L
d
x
A
(
L
and
V
are constant)
.
(6.17)
The last two equations may be combined to give:
V
k
y
aA
c
(
y
A
I
−
d
z
=
y
A
)
d
y
A
.
(6.18)
=
=
Integrating from
z
0to
z
(where
is the total height of packing in a stripping/enriching
section):
y
A
out
V
k
y
aA
c
d
y
A
y
A
I
−
=
y
A
.
(6.19)
y
A
in
This equation is often written as:
=
H
G
N
G
,
(6.20)
where
V
k
y
aA
c
=
H
G
=
height of a gas-phase transfer unit (HTU)
and
y
A
out
d
y
A
y
A
I
−
N
G
=
y
A
=
.
number of gas-phase transfer units (NTUs)
y
A
in
The number of transfer units is a measure of the difficulty of a separation. The higher
the purity of the product, the larger the number of transfer units. This is analogous to the
need for more equilibrium stages in distillation to obtain a higher-purity product. The
height of a transfer unit is a measure of the efficiency of a particular column packing and
configuration to perform the separation. The smaller the value of HTU, then the higher
the effectiveness of the separation for a given transfer unit.
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