48 ◾  Distillation Control, Optimization, and Tuning
L = liquid flow rate
x = concentration of solute in liquid phase
y = concentration of solute in vapor phase at equilibrium
When dilute solute concentrations are stripped with a pure
vapor, the number of theoretical stages can be calculated by
Equation 6.2.
NTS = Ln[(x F /x B )(1 − 1/S) + 1/S]/Ln S
(6.2)
where:
NTS = number of theoretical stages
x F = concentration of light key solute in liquid leaving
feed stage
x B = concentration of light key solute in bottoms liquid
This model suggests that an infinite stripping factor can
achieve any desired separation, that is, x F /x B , with zero
theoretical stages. Clearly, that is not a good model of mass
transfer at high stripping factors. The mass transfer in a
stripping section becomes mass transfer rate limited in the
liquid phase. In other words, even with an infinite stripping factor with a pure stripping gas, there will still be a
required amount of contact time for desorption of the light
impurity solute out of the liquid phase from x F down to x B .
The liquid phase mass transfer unit based on overall driving force in liquid phase concentrations, N OL , gives a more
realistic model of mass transfer at high stripping factors
(Equation 6.3):
N OL = {Ln[(x F /x B )(1 − 1/S) + 1/S]}/{1 − 1/S}
(6.3)
where:
N OL = number of mass transfer units based on overall
driving force in liquid phase concentrations