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The next two equations concern the total tray material balance:

This last equation must be used with caution and only after a test made for inverse response (see Chapter 13) shows that response to a change in boilup is neutral.

Terms in the preceding equations not already defined have the following meanings:

Fand L = mols/hr x = mol fraction low boiler (light key) in liquid y — mol fraction low boiler (light key) in vapor

In linearizing and Laplace transforming equation (18.1), we get: M„sx„(s) + x„sM„(s) = Ln+1xn+1(s) + xn+1Ln+1(s)

- Lnx„(s) - x„L„(s) + TV^-iM (18.6) + - V„y„(s) - y„Vn(s)

Then since the vapor composition y„ is a function of both x„ and _y„_i (for any tray efficiency less than unity), we can write:

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