Adjacent keys, constant overflow

This system for evaluating multicomponent adjacent key systems, assuming constant relative volatility and constant molai overflow, has proven generally satisfactory for many chemical and hydrocarbon applications. It gives a rigorous solution for constant molai overflow and volatility, and acceptable results for most cases which deviate from these limitations. 

Heat Balance—Adjacent Key Systems with Sharp Separations, Constant Molal Overflow... 

Underwood [39] derived Equations 6.27.3 and 6.27.4 for estimating the minimum reflux ratio for a specified separation of two key conponents. These equations assume constant molar overflow and relative volatility. Underwood showed that at minimum reflux the value of 0 in Equations 6.27.3 and 6.27.4 must lie between the relative volatility of the heavy and light key components. If the key components are not adjacent, there will be more than one value of 0. This case is illustrated in an example by Walas [6]. Here, we will assume that the key con5)onents are adjacent. As has been pointed out by Walas [6], the minimum reflux ratio calculated by the Underwood equations could turn out to be negative, which means that the equations do not apply for the given separation. 

The classical McCabe-Thlele method can be applied for the preliminary design of columns separating quasi-ideal binary mixtures in products with moderate purity when the volatility is larger than 1.5. It is also suitable for multi-component mixtures when the key components are adjacent. The method is based on the assumption of constant molar overflow. 

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