Constraints ◾  51
This model suggests that a stripping factor of zero can achieve
any desired separation, that is, y F /y D , with zero theoretical
stages. Clearly, that is not a good model of absorption (enriching) mass transfer at low stripping factors. The mass transfer
in a rectification (absorption) section becomes mass transfer
rate limited in the vapor phase. In other words, even with
a stripping factor of zero and a zero concentration of heavy
key solute in the liquid entering the absorption section, there
will still be a required amount of contact time for absorption
of the heavy key impurity solute out of the vapor phase from
y F down to y D . The gas phase mass transfer unit based on
overall driving force in gas phase concentrations, N OG , gives a
more realistic model of mass transfer at low stripping factors
(Equation 6.8):
N OG = {Ln[(y F /y D )(1 − S) + S]}/{1 − S}
(6.8)
where:
N OG = number of mass transfer units based on overall
driving force in gas phase concentrations
When the stripping factor is zero, the number of mass transfer
units can be calculated by Equation 6.9:
N OG = Ln(y F /y D )
(6.9)
When the stripping factor is equal to 1.0, the values of NTS
and N OG are identical (Equation 6.10):
For S = 1.0:
N OG = NTS = y F /y D – 1
(6.10)
In other words, reducing a heavy key solute in the vapor from
1,000 ppm to 1 ppm requires 999 theoretical stages or mass
transfer units when the stripping factor is 1.0. Table 6.2 shows