Page 267 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

268 Chapter 10 Absorption and stripping

" #
L dx
Z Z
h bed x 1
iM
ð1 xÞ
h bed ¼ dz ¼ (10.16)
0 k aA t ð1 xÞ ðx i xÞ
0
y
av x 2
" #
Z Z
h bed y 2
G ð1 yÞ M dy
h bed ¼ dz ¼ (10.17)
0
0 K aA t ð1 yÞ y 1 ðy y Þ

y
av
x
h
Z bed Z 1
L dx
M
ð1 xÞ
h bed ¼ dz ¼ (10.18)

0
x
K aA t ð1 xÞ av ðx xÞ
0 x 2
Additionally, for a dilute system, the operating line is nearly straight, and the log mean driving
force is used:
y 2
Z
dy ðy 1 y 2 Þ ðy 1 y i1 Þ ðy 2 y i2 Þ
M
¼ ; where ðy y i Þ ¼ (10.19)
M ln½ðy 1 y i1 Þ=ðy 2 y i2 ފ
y 1
ðy y i Þ
ðy y i Þ
and

Z
dy ðy 1 y 2 Þ y 1 y 1 y 2 y 2
y 2
(10.20)
M
¼ ; where ðy y Þ ¼

ln y 1 y = y 2 y
y 1 ðy y Þ ðy y Þ M 1 2
For relating the performance of packed towers with tray towers, the packing performance is defined
in terms of the height equivalent to a theoretical plate (HETP).
Although the HTU concept is theoretically
more correct for packed towers in which mass
transfer is accomplished by a differential action
Height equivalent to a theoretical plate (HETP) rather than a series of discrete stages, the concept
of HETP is more convenient.
For linear equilibrium and operating curves,
the two concepts are related as
H TOG mðG=LÞ 1
(10.21)
HETP lnðmðG=LÞÞ
¼
Where G and L are the respective molar flow rates of the gas and liquid phase, and m is the slope of the
equilibrium curve.
For the special case when the equilibrium and operating lines are parallel (mG/L ¼ 1),
H TOG ¼ HETP and bed height h bed may be estimated from either HTU or HETP concepts, i.e.,
h bed ¼ H TOG N TOG ¼ HETP N (10.22)
where N is the number of theoretical plates (stages).
10.3.5 Design based on liquid-phase resistance
The number of liquid-phase transfer units (N TOL ) is not the same as the number of gas-phase transfer
units (N TOG ) unless the operating and equilibrium lines are straight and parallel. For absorption, the
operating line is usually steeper than the equilibrium line, which makes N TOG > N TOL , but this