Page 34 - Gas Purification 5E

The kmser equation is useful in the preliminary design of plate columns for physical
absorption processes, such as the dehydration of natural gas with glycol solutions (see Chap-
ter 11) and the absorption of C02 and H2S in nonreactive solvents (see Chapter 14).
As mentioned previously, the number of actual plates in an absorber is related to the num-
ber of theoretical plates by a factor known as the “plate efficiency.” In its simplest definition,
the “overall plate efficiency” is defined as “the ratio of theoretical to actual plates required
for a given separation.” For individual plates, the Murphree vapor efficiency (Murphree,
1935) more closely relates actual performance to the theoretical-plate standard. It is defined
by the following equation:

E,, = Yp - Yp+l (1-21)
Ype - Yp+l

Where: yp = average mole fraction of solute in gas leaving plate
yp+ = average mole fraction of solute in gas entering plate (leaving plate below)
yp = mole fraction of solute in gas in equilibrium with liquid leaving plate

Murphree plate efficiency values can be used to correct the individual steps in graphical
analyses of the number of plates requid. The overall efficiency, on the other hand, can only
be used after the total number of theo~tical plates has been calculated by a graphical or ana-
lytical technique. When operating and equilibrium lines are nearly parallel, the two efficien-
cies can be considered to be equivalent. Under other conditions they may vary widely.
A third version of the plate efficiency concept is the Murphree Point Efficiency, which
can be defined as the Murphree efficiency at a single point on a tray. The point efficiency is
the most difficult to use but is the most useful in theoretical analysis of tray performance.
The Murphree vapor tray efficiency and point efficiencies on the tray are related primarily
by the degree of mixing that occurs on the tray. The two are equal if mixing is complete;
while the tray efficiency can be appreciably higher than the point efficiency if no mixing
occurs. Actual trays fall between the two extremes.
A computer model relating point and tray efficiencies is described by Biddulph (1977). In
this model the calculations for a tray are started at the outlet weir, where the liquid composi-
tion is known, and move progressively through thin slices of the liquid against the liquid
flow to the inlet weir. At each increment, the liquid composition and temperature, and the
gas composition above the point are calculated, based on an assumed point efficiency for
each component and the gas composition below the tray at that point. An eddy diffusion
model is used to define mixing in a comparison of the computer simulation with actual com-
mercial plant data from a distillation column.
For simple physical absorption, the principal factors affecting tray efficiencies are gas sol-
ubility and liquid viscosity, and a correlation based on these two variables has been devel-
oped by O’Connell(194.6). His correlation for absorbers is reproduced in Figure 1-7. Unfor-
tunately, other factors such as the absorption mechanism, liquid depth, gas velocity, tray
design, and degree of liquid mixing also influence tray efficiency, so no simple correlation
can adequately cover all cases. A more detailed study of bubble tray efficiency has been
made by the Distillation Subcommittee of the American Institute of Chemical Engineers
(1958). The Bubble Tray Design Manual resulting from this work provides a standardized
procedure for estimating efficiency which takes the following into account: