Page 265 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

266 Chapter 10 Absorption and stripping

than unit interfacial area. The volumetric mass transfer coefficient (K x a, K y a, etc.) is the product of the
mass transfer coefficient and the specific area of mass transfer per unit volume of tower packing. This
can be defined for

(i) equimolar mass transfer for the gas and the liquid phases, as k y a and k x a
(ii) component A diffusing into a stagnant B in liquid and the gas phases as k a and k a
0
0
x y
(iii) overall mass transfer coefficient K a and K a based on the liquid and the gas phases
0
0
x y
It may be noted that for stripping and absorption, the mass transfer is one component diffusing into
a stagnant phase, and therefore, coefficients k a and k a, as well as K a and K a are used in the design
0
0
0
0
x y x y
equations.
3
The volumetric mass transfer in each case will have the unit (kg mole of A transferred)/(s. m of
packing. mol fraction difference of A as driving force).
The mass transfer coefficients of each phase are estimated from available correlations reported
in literature. In packed beds, the coefficients have
been reported to increase with square root of
mass velocity and two-thirds power of diffusivity.
Estimation of individual mass transfer coefficients
Nevertheless, correlations proposed by different
researchers differ appreciably. As the coefficient is
related to turbulence and fluid properties, these are
usually correlated in terms of Sherwood number, Reynolds number, and Schmidt number.
10.3.4 Estimation of active bed height
The design equation for the bed height h bed (m) may be obtained from any of the following expressions
Z Z
h bed y 2
G$dy
(10.11)
h bed ¼ dz ¼ 0
0 y 1 k aA t
y
ð1 yÞðy y i Þ
ð1 yÞ iM
L$dx
h bed y 2
Z Z
(10.12)
h bed ¼ dz ¼ 0
0 y 1 k aA t
x
ð1 xÞðx i xÞ
ð1 xÞ iM
using film coefficients and
G:dy
h bed y 2
Z Z
(10.13)
h bed ¼ dz ¼ 0
0 y 1 K aA t
y

ð1 yÞðy y Þ
ð1 yÞ M
Z Z
L:dx
h bed y 2
(10.14)
h bed ¼ dz ¼ 0
0 y 1 K aA t
x

ð1 xÞðx xÞ
ð1 xÞ M
using overall coefficients.