Page 264 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

10.3 Packed column 265

When k , k , P(x AL ,y AG ) are known, construction of the driving force line PM allows us to deter-
0
0
x
y
mine the corresponding interphase concentration x Ai and y Ai at point M on the equilibrium curve. As an
are
iM iM
engineering assumption, the system may be considered dilute and ð1 x A Þ and ð1 y A Þ
nearly unity if the concentration is below 10%. In this case, the line can be straightaway drawn through

P with its slope as ( k k ).
0
0
x y
The following iterative procedure is needed to draw the line PM for concentrated systems as the
expression of slope contains the interphase concentrations (x Ai and y Ai ) that are not known initially
iM value to be unity as the first trial
ð1 y A Þ
(i) Assume f ¼
iM
ð1 x A Þ
k 0
x
k y
(ii) Draw line PM with slope 0 and locate M on the equilibrium curve
k 0
x 0 which is used to
k y
(iii) The coordinates of M (x Ai ,y Ai ) are used to recalculate f and the slope f
refine the location of M. Three trials usually suffice.
10.3.3 Overall mass transfer coefficient
Overall mass transfer coefficient is obtained from the individual coefficients by addition of interphase
resistances
1 1 m 0
(10.9)
¼ þ
K y k y k x
1 1 1
(10.10)
¼ þ
K x k x m k y
00
In Eqs. 10.9 and 10.10, m and m are the slope of the chords (Fig. 10.4B). They are equal only for a
00
0
linear equilibrium curve.
If k x z k y , the slope of equilibrium curve (m ), at the point in question, decides the rate of mass
0
1
1
transfer. If m is small, 1 z and when m is very large, 1 z .
0
0
K y k y K x k x
When k x z k y the relative size of (k x /k y ) and m determines the location of mass transfer resistance.
0
Since superficial mass velocities vary slightly throughout the tower, mass transfer coefficients also
vary slightly. Fig. 10.3 shows that the smallest driving force occurs at the (column) top. Therefore, the
mass transfer coefficients are calculated for rates at top of the column as a conservative estimate.
The designer needs to know whether the mass transfer in the system is gas-phase or liquid-
phase controlling. Usually, for commercial processes, absorption
is gas-phase controlling, especially for highly soluble gases or
when the gas reacts with the liquid. Since the resistance to mass
Mass transfer coefficient transfer essentially resides in the gas film, calculating only the gas-
phase mass transfer coefficient is sufficient. For stripping, the
liquid phase is usually controlling, and only the mass transfer
coefficient in the liquid phase is calculated.
In most diffusion operations, e.g., in packed and spray towers, the estimation of available inter-
facial area for mass transfer is not possible. It is also difficult
to measure the film coefficients k and k and K and K .In
0
0
0
0
x y x y
such cases it is customary to report experimentally observed
Volumetric mass transfer coefficient
rates of transfer in terms of transfer coefficients based on unit
volume of bed (volumetric mass transfer coefficient) rather