Page 263 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

264 Chapter 10 Absorption and stripping

10.3.2 Driving force line
Line PM is termed as the driving force line since it identifies the bulk (x,y) and the corresponding
interface concentrations (x i ,y i ) at a point P in the bed, and the difference (y y Ai ) gives a measure of
the driving force. The slope of the driving force line is a function of the relative diffusional resistance
in the two phases.
The equation for line PM is deduced as follows
Molar flux of A at steady state in case of equimolar counterdiffusion:
(10.6)
N A ¼ k y ðy AG e y Ai Þ¼ k x ðx Ai e x AL Þ
and when A diffuses into nondiffusing B:
k 0
y
(10.7a)
k y ¼
ð1 y A Þ iM
k 0
x
k x ¼ (10.7b)
ð1 x A Þ iM
Where
fð1 y Ai Þ ð1 y AG Þg
ð1 y A Þ iM ¼ (10.7c)
lnfð1 y Ai Þ=ð1 y AG Þg
and

fð1 x AL Þ ð1 x Ai Þg
ð1 x A Þ iM ¼ (10.7d)
lnfð1 x AL Þ=ð1 y Ai Þg
Equating the flux of A in the two phases relates y AG and x AL as-

N A ¼ k y 0 ðy AG e y Ai Þ ¼ k 0 x ðx Ai e x AL Þ (10.8)
iM iM
ð1 y A Þ ð1 x A Þ
Eq. 10.8 relates the bulk and the interphase concentrations and is the equation of the driving force
line passing through P (x AL ,y AG ) and M (x Ai ,y Ai ).
Only a single component diffusing across the interphase is mostly considered in designing for
absorption, as well as stripping columns, and in such a case, the slope of PM in case of only A diffusing
in stagnant B is given by

k
0 0
x
ðy AG e y Ai Þ k =ð1 x A Þ iM x
Slope ¼ ¼ ¼ f (10.8a)
0
y
ðx AL e x Ai Þ k =ð1 y A Þ iM k y 0
where,
iM
ð1 y A Þ
f ¼ (10.8b)
ð1 x A Þ iM

The slope of PM is ( k k ) in case of equimolar counterdiffusion.
0
0
y
x