Tray Efficiency for Multicomponent Systems

In this section we show how the matrix generalization of the binary tray efficiency equation (Eq. 13.2.3) may be obtained. 

We differentiate Eq. 13.3.5 with respect to w (assuming the matrix [E] is constant) to get 

In order to proceed further we must say something about how the composition of the vapor below the tray varies with coordinate w. In the so-called Lewis Case /, the vapor entering the tray is assumed to be well mixed d(y )/dw = (0) in which case Eq. 13.3.7 simplifies to 

To eliminate the equilibrium vapor composition (y ) we use the linear equilibrium relationship 

We have replaced the problem of not knowing the gradient of (y ) with the more easily 

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