# Graphical Correlations

When the number of theoretical plates is plotted as a function of reflux ratio, the curve is hyperbolic in type with asymptotes at Nmn and (0/D)min. These two limiting conditions as asymptotes are useful in drawing such a curve, but they would be more helpful as definite points on the diagram. By modifying the variables, they can be made definite points; in fact they can be made the same points for all cases. There are many ways in which the variables can be modified, and one that has been useful (Ref. 6) is shown in Fig. 12-1. The ordinate is OS — Sm)/(S + 1), where 8 is the total theoretical steps including any enrichment in the still and condenser, and Sm is the value of S

for total reflux, O/D « co. The abscissa is ^ — jy^+

At total reflux the ordinate is 0.0 and the abscissa is 1.0, while at the minimum reflux ratio the ordinate is 1.0 and the abscissa is 0.0. As the reflux ratio is increased from the minimum to total reflux, a given design problem will give a curve that goes from 1,0 to 0,1. It was expected that a series of curves between these two points would be obtained, depending on (1) the degree of separation, (2) the relative

P Wmin

Fig. 12-1. Graphical correlation for design calculations.

P Wmin

Fig. 12-1. Graphical correlation for design calculations.

volatilities, and (3) the components lighter and heavier than the key components. The results of plate-to-plate calculations were plotted and gave a narrow band which could be reasonably represented by a single line. It can be shown theoretically that a single line cannot represent all cases exactly, and the correlation can be improved by using more than one line. For example, the position of the line is a function of the fraction of the feed that is vapor. The best line drawn through the all-vapor feed cases on a plot such as Fig. 12-1 is lower than the corresponding line for all-liquid feeds. It is also possible to improve the correlation by changing the variable groups, but it is doubtful whether the increased accuracy justifies the added complications. The accuracy of such a correlation will always be limited by the errors in 8m and (0/Z>)min. It is believed that it is of real value when it is applied as (1) a rapid but approximate method for preliminary design calculation or (2) a guide for interpolating and extra-

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