A Mathematical Description of the Concepts of Theoretical Plate and Transfer Unit

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Abstract
For reasons of simplicity the concepts of theoretical plate and transfer unit are frequently used in books and papers dealing with countercurrent separation processes. The physical validity of these two concepts cannot be deduced from their definitions. Although the two concepts have been discussed many times, an acceptable relation between the two concepts fails. Moreover, the regions of applicability of the concepts cannot be well indicated. In this paper the concepts of theoretical plate and transfer unit have been related with the column equation. The equations obtained show that both the theoretical plate and the transfer unit are satisfactory units of column length when the compounds are difficult to separate or when the concentration of one component is small with respect to the other. When dealing with exchange systems showing an equilibrium constant deviating from unity, the regions of applicability of the theoretical plate and of the transfer unit may be different. Depending on the parameters of the column equation, the theoretical plate may be preferable to the transfer unit or vice versa. The assumption of many authors that the concept of the transfer unit is more satisfactory than the concept of the theoretical plate when dealing with packed columns is not confirmed by the calculations presented.

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