Page 242 - Separation process principles 2

6.5 Stage Efficiency 207

using those methods. Except when temperature changes sig-
nificantly from stage to stage, the assumption that vapor and
liquid phases leaving a stage are at the same temperature is
often reasonable. The assumption of equilibrium with re-
spect to mass transfer, however, is not often reasonable and,
for streams leaving a stage, vapor-phase mole fractions are
not related to liquid-phase mole fractions simply by thermo-
dynamic K-values. To determine the actual number of plates,
A Ethylbenzene
the number of equilibrium stages must be adjusted with a
w Benzene
0 Toluene stage eflciency (plate eflciency or tray eficiency).
Stage efficiency concepts are applicable to devices in
which the phases are contacted and then separated, that is,
when discrete stages can be identified. This is not the case
I Number of equilibrium stages
for packed columns or continuous-contact devices. For these,
Figure 6.13 Results of Example 6.2 for stripping of VOCs from the efficiency is imbedded into an equipment- and system-
water with air.
dependent parameter, an example of which is the HETP
(height of packing equivalent to a theoretical plate).
The calculations when carried out with a spreadsheet computer The simplest approach for staged columns, in preliminary
program give the following results: design studies and in the evaluation of the performance of an
existing column, is to apply an overall stage (or column)
Percent Stripped efficiency, defined by Lewis [5] as

1 2 3 4
Component Stage Stages Stages Stages
where Eo is the fractional overall stage efficiency, usually
Benzene 90.82 99.08 99.91 99.99 less than 1.0; N, is the calculated number of equilibrium
Toluene 90.62 99.04 99.90 99.99 (theoretical) stages; and Nu is the actual number of contact-
Ethylbenzene 91.68 99.25 99.93 99.99 ing trays or plates (usually greater than N,) required. Based
on the results of extensive research conducted over a period
The results are quite sensitive to the number of theoretical of more than 60 years, the overall stage efficiency has been
stages as shown in Figure 6.13. To achieve 99.9% removal of the found to be a complex function of the
total VOCs, three theoretical stages are needed, corresponding to
the necessity for a 15% stage efficiency in the existing 20-tray 1. Geometry and design of the contacting trays
tower. 2. Flow rates and flow paths of vapor and liquid streams
It is best to process the exiting air to remove or destroy the
3. Compositions and properties of vapor and liquid
VOCs, particularly the benzene, which is a carcinogen [4]. The
streams
amount of benzene stripped is
For well-designed trays and for flow rates near the capacity
limit, Eo depends mainly on the physical properties of the
vapor and liquid streams.
If benzene is valued at $0.30/lb, the annual value is approximately Values of Eo can be predicted by any of the following four
$100,000. It is doubtful that this would justify a recovery tech- methods:
nique, such as carbon adsorption. It is perhaps preferable to destroy
the VOCs by incineration. For example, the air can be sent to a util- 1. Comparison with performance data from industrial
ity boiler, a waste-heat boiler, or a catalytic incinerator. It is also to columns for the same or similar systems
be noted that the amount of air was arbitrarily given as 3,400 scfm. 2. Use of empirical efficiency models derived from data
TO complete the design procedure, various air rates should be in- on industrial columns
vestigated. It will also be necessary to verify by methods given later
in this chapter that, at the chosen air flow rates, no flooding or 3. Use of semitheoretical models based on mass- and
weeping will occur in the column. heat-transfer rates
4. Scale-up from data obtained with laboratory or pilot-
plant columns
6.5 STAGE EFFICIENCY
These methods, which are discussed in some detail in the
Graphical and algebraic methods for determining stage re- following four subsections, are applied to other vapor-liquid
quirements for absorption and stripping assume equilibrium separation operations, such as distillation, as well as to
with respect to both heat and mass transfer at each stage. absorption and stripping. Suggested correlations of mass-
Thus, the number of equilibrium stages (theoretical stages, transfer coefficients for trayed towers are deferred to Sec-
ideal stages, or ideal plates) is determined or specified when tion 6.6, following the discussion of tray capacity.