Numbers of Transfer Units for Multicomponent Systems

When we carry out the multiplications required by Eqs. 12.2.18-12.2.21, we obtain explicit expressions for the elements of the inverse matrices and in terms of 

For ternary systems [N] may be inverted explicitly with the following results (cf. the inversion of [7 ] in Section 8.3.1) 

The numbers of transfer units for each binary pair may be obtained as described in Section 12.1.5 or from experimental data and these binary numbers of transfer units used directly in the estimation of the matrices of numbers of transfer units for multicomponent systems as Example 12.2.3 demonstrates. 

Example 12.2.1 Numbers of Transfer Units for the Methanol-l-Propanol-Water System 

Biddulph and Kalbassi (1988) investigated the distillation of the ternary system methanol(l)-l-propanol(2)-water(3). In separate experiments they determined the numbers of transfer units for each binary pair that makes up the ternary system. Estimate the number of transfer units for the ternary system at total reflux if the composition of the liquid leaving the tray is 

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Correlations of numbers of transfer units developed for binary systems may be used to compute numbers of transfer units for multicomponent systems as described in Section 12.1.5. An alternative method that follows the ideas put forward by Toor in his development of the linearized theory of mass transfer is to generalize binary correlations by replacing the binary diffusivity with the matrix of Fick diffusion coefficients (in much the same way that we generalized correlations of binary mass transfer coefficients in Section 8.8.2). Let the number of transfer units in a binary system be expressed as... 

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