Page 184 - Separation process engineering

use a measure of efficiency.
Many different measures of efficiency have been defined. Two that are in common use are the overall

efficiency and the Murphree efficiency. The overall efficiency, E , is defined as the number of
o
equilibrium stages required for the separation divided by the actual number of stages required:

(4-56)

Partial condensers and partial reboilers are not included in either the actual or equilibrium number of
stages, since they will not have the same efficiency as the stages in the column.

The overall efficiency lumps together everything that happens in the columns. What variables would we
expect to affect column efficiency? The hydrodynamic flow properties such as viscosity and gas flow rate
would affect the flow regime, which affects efficiency. The mass transfer rate, which is affected by the
diffusivity, will in turn affect efficiency. Overall efficiency is usually smaller as the separation becomes
easier (α increases). The column size can also have an effect. Correlations for determining the overall
AB
efficiency will be discussed in Chapter 10. For now, we will consider that the overall efficiency is
determined from operating experience with similar distillation columns.
The overall efficiency has the advantage of being easy to use but the disadvantage that it is difficult to
calculate from first principles. Stage efficiencies are defined for each stage and may vary from stage to
stage. The stage efficiencies are easier to estimate from first principles or to correlate with operating
data. The most commonly used stage efficiencies for binary distillation are the Murphree vapor and liquid
efficiencies (Murphree, 1925). The Murphree vapor efficiency is defined as

(4-57)

Murphree postulated that the vapor between trays is well mixed, that the liquid in the down-comers is
well mixed, and that the liquid on the tray is well mixed and is of the same composition as the liquid in
the downcomer leaving the tray. For the nomenclature illustrated in Figure 4-27A, the Murphree vapor
efficiency is

(4-58)

Figure 4-27. Murphree efficiency; (A) stage nomenclature, (B) McCabe-Thiele diagram for E MV