Prior to discussing scaleup, the factors that affect tray efficiency need to be addressed. These factors are addressed in Sees. 7.3.1 to 7.3.3. Considerations relevant to the effect of flow regime were previously discussed in Sees. 6.4.4 and 6.4.5.
7.3.1 Effect of errors In Vapor-Liquid Equilibrium (VLE) on efficiency
Errors in relative volatility are the most underrated factor that affects both tray and packing efficiency. The effects are direct when VLE errors affect separation stage requirement at a constant reflux ratio, and indirect when VLE errors affect the reflux ratio requirement (which in turn affects the stage requirement). Since higher relative volatility lowers both stage and reflux requirements (and vice versa), the direct and indirect effects complement each other and do not counteract each other. The discussion below applies to both tray and packed towers.
Direct effects. Figure 7.6 was derived (154,155) from the Fenske equation (Sec. 3.2.1) for total reflux as follows:
where
Differentiating Eq. (7.29) gives dN^" -S^-1- (7.31)
Since
% Error in efficiency
% Error in efficiency
and assuming a constant number of trays, Eq. (7.32) becomes dE -da 1
-"apparent ti
Now let E ~ Etrae, a = a^, dE = £apparent - E^, and da = a*pparent
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