Chemical Engineering October 2011 - 69

packing efficiency data in various services.
Measured HTUOG values are
more applicable to other designs and
columns than are HETP values. Because
absorption HETP values contain
corrections for poorly quantified mass
transfer tasks, they are not useful in
other columns unless they replicate
the error too!
Liquid and Vapor FiLm
resistances
Discussion of liquid stripping will require
considering the individual film
resistances of vapor and liquid, and
their relative contribution to overall
mass transfer.
Two-film theory of mass transfer
divides the mass transfer process into
two resistances: the liquid phase resistance
and the vapor phase resistance.
It says that the phase interface resistance
is negligible, so that equilibrium
is reached at the interface. There is a
concentration gradient of x in the liquid
phase, an equilibrium between x
and y at the interface, and a concentration
gradient of y in the vapor phase.
The concentration gradients can be
expressed in terms of resistance to
mass transfer in each phase.
HTU values can be broken into individual
phase components:
HTUOG = HTUG + λ HTUL
(17)
HTUOL = HTUL + (1/λ) HTUG (18)
Note that in the extreme of low-relative-volatility
distillation, λ = 1 and
HETP = HTUOG = HTUOL
= HTUG + HTUL
(19)
In distillation, the value of HTUG is
usually greater than HTUL. This implies
that the liquid phase spreads
thinly over the packing, it turns over
quickly, and it builds little gradient
between the interface and the bulk
liquid. The vapor phase, however, does
not quickly saturate the interface, so
there is a larger concentration gradient
between the bulk vapor and the
interface, and more packed height is
needed for mass transfer.
The low-relative-volatility distillation
database says more about HTUG
values than HTUL values. The observation
about consistent low-relativevolatility
HETP values over various
rates and systems must apply to
HTUG values too, because HTUG is
the largest component of HETP. But
the consistency of low-relative-volatility
HETP values does not necessarily
apply to HTUL values. HTUL values
could vary within the database with
little effect on HETP values, because
HTUL contributes little to HETP.
HigH-reLatiVe-VoLatiLity
distiLLation - stripping
section
The above high-relative-volatility distillation
discussion focused on the rectification
section only. The stripping
section involves similar concepts and
equations, but uncertainty over HTUL
values makes calculations more uncertain.
Figure
4 illustrates one theoretical
stage of the stripping section of a highrelative-volatility
distillation. The
driving force (x-x*) is the horizontal
distance between the equilibrium and
operating lines. As in the rectification
case, the driving force is large at the
beginning of the stage, but it declines
as mass transfer occurs and the liquid
moves down the operating line.
As with y values in rectification,
the number of transfer units (NTUOL)
can be evaluated with x compositions
of the light key component as it is
stripped from the liquid. Possible techniques
include using an equilibrium
stage simulation and a spreadsheet
as described above, or using Table 1
again, or evaluating λ on each stage
and applying the λ correction factor in
Equation (20).
NTUOL = NTS λ (ln λ) / (λ-1)
(20)
For high-relative-volatility rectification,
direct application of HETP values
from low-relative-volatility test data
as high-relative-volatility HTUOG
values was really a minor conservative
approximation. A more exact approach
is to use HTUG and HTUL values
to recalculate HTUOG in Equation
(17). The value of HTUOG will decline
slightly, as λ could decrease from near
unity in low-relative-volatility rectification,
to a value well below one for
high-relative-volatility rectification.
Because the individual HTUG and
HTUL values are unknown, the exact
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