The vapor efficiency E°uv is much more commonly used than E°uh. This preference is justified in view of the derivation of the latter.
As an illustration of these relationships, consider the separation of a benzene-toluene mixture with (0/F)n = 0.7 and (0/F)m = 1.2 for Emv — 0-6. The flow conditions correspond to Case III.
The feed-plate region was arbitrarily chosen to make K = 1.0. This corresponds to a liquid composition of about 40 per cent benzene.
The values given for E°MV would be higher than actually obtained because of the liquid mixing on the plate. It is interesting to note that E°/E°mv is near to 1.0 at all positions, and the use of E° = E°MV would be a reasonable approximation. The values of Ke are larger than K except at the bottom of the column. For usual cases, Ke/(0/V) is greater than 1.0, and E°ML will be between E°MV and 1.0.
From the calculational viewpoint, E° is the easiest to apply, but E°mv and E°ml can be used without much additional effort either in algebraic or graphical design calculations. Thus in algebraic calculations, the usual theoretical plate calculations will give y* for a known yn-1, and yn = t/n-i + E°MV(yt — 2/n-i). Thus the values of yn can be calculated, if E%v is known and the calculation is repeated for the next plate. The efficiencies can also be applied to the graphical calculation for binary or multicomponent mixtures. This is illustrated in Fig. 17-5. The use of E°MV is illustrated on the upper operating line: yn~i is the actual vapor composition entering plate n and by material balance the composition xn is fixed on the operating line; the vapor in equilib rium with xn is y* and the actual increase in vapor composition is 2/n — which is obtained by a vertical step of a height equal to E%v(y* ~ yn~i); i.ea fraction of the theoretical plate increase equal to E%v is taken. The use of E°ML for plate m is shown on the lower operating line. In this case a fractional horizontal step equal to E°ML times the theoretical plate change is used.
Effect of Entrainment on Efficiency. Entrainment can lower the apparent plate efficiency because the vapor-liquid mixture carried to the plate above will have a lower average concentration of the more volatile components than the vapor alone. Colburn (Ref. 6) has given an equation relating the measured efficiency with entrainment to that for a plate giving the same change in vapor composition but without entrainment.
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