where i is any component and r is an arbitrarily selected reference component in the definition of relative volatilities.
The particular value of a is the effective value used in Eqs. (13-36) and (13-34) defined in terms of values for each stage in the column by a = ayay-1■
Equations (13-31) and (13-32) are rigorous relationships between the splits obtained for components i and r in a column at total reflux. However, the correct value of ai must always be estimated, and this is where the approximation enters. It is usually estimated from a = (atopabottom)1'2 (13-35)
A reasonably good estimate of the separation that will be accomplished in a plant column often can be obtained by specifying the split of one component (designated as the reference component r), setting Nm equal to from 40 to 60 percent of the number of equilibrium stages (not actual trays), and then using Eq. (13-32) to estimate the splits of all the other components. This is an iterative calculation because the component splits must first be arbitrarily assumed to give end compositions that can be used to give initial end-temperature estimates. The atop and abottom values corresponding to these end temperatures are used in Eq. (13-35) to give ai values for each component. The iteration is continued until the ai values do not change from trial to trial.
The Underwood minimum-reflux equations of main interest are those that apply when some of the components do not appear in either the distillate or the bottoms products at minimum reflux. These equations are
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