Page 260 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

10.3 Packed column 261

and in the case of stripper,
(10.5)
N ¼ log½ðx 1 y 1 = mÞ = ðx Nþ1 y Nþ1 = mފ=logð1 = AÞ
where, A[ ¼ L/(m.G)] is the absorption factor.
When the equilibrium line is in the linear approximation of a curve with the value of m
being m 1 and m 2 at the column bottom and the top conditions, A 1 ¼ L/(m 1 .G), A 2 ¼ L/(m 2 .G)and
A¼ (A 1 .A 2 ) 1/2 is used in Eqns. 10.4 and 10.5.
The problem shown in Fig. 10.2 can also be solved using Eq. 10.4. After constructing tangents
at the top and bottom of the equilibrium curve, the slopes are: m 1 ¼ 20 and m 2 ¼ 43; also
L ð¼ L =A t Þ¼ 333 and G ð¼ G =A t Þ¼ 5:18; A 1 ¼ L/(m 1 .G) ¼ 3.21, A 2 ¼ L/(m 2 .G) ¼ 1.5 and
0
0
0
0
1/2
A ¼ (A 1 .A 2 ) ¼ 2.19;
Using Eqn.10.4, N ¼ 2.59, which is slightly different from 2.4, the value found from the graphical
procedure described earlier.
10.2.2 Absorption factor
The Absorption Factor (A ¼ L/(m.G)) in Eqns. 10.4 and 10.5 is the ratio of the operating line slope to
the equilibrium curve slope. For A<1, there is limited absorption of solute even for an infinite number
of theoretical trays. For A>1, any degree of separation is possible if a sufficient number of trays are
provided. When A is unity, i.e., the equilibrium and operating lines are parallel, Eqns. 10.4 and 10.5
become indeterminate, and the number of stages is the overall concentration change per unit driving
force, which is a constant.
In absorbers, where the solute concentration is not very dilute, heat of solution causes a rise in
temperature, and the value of m is greater at the column bottom than at the top. When the L/(m.G)
value is not constant for this reason or for others, the choice of L/G ratio is more difficult. The con-
ditions at the dilute end are usually more important for the design since, in case of nearly complete
absorption, most of the transfer units are required in the dilute region.
In the case of packed columns, the absorption factor is needed to decide the height of a transfer unit,
the number of transfer units, and also the column diameter.

10.3 Packed column
The operating line in the case of packed bed relates the bulk concentrations (y and x) of the gas and
liquid phases at any section of the column between which the
mass transfer takes place. Figs. 10.3A and B show the typical
operating line and the equilibrium curve for absorbers and
Absorption/Stripping in packed bed strippers, respectively. They also show the operating line cor-
responding to the minimum required liquid flow for absorber,
and the minimum required gas flow for stripper. This line
touches the respective equilibrium lines at a point termed as the pinch point. As pinch point is
approached, the concentration difference (driving force) tends to zero. Thus an infinite number of
contacting stages is required to approach the concentration at pinch point. This then represents the
limiting L/G ratio denoted as (L/G) min .