Vapor Flow Variations on Liquid Holdup

Appendix 34.1 Impact of Vapor Flow Variations on Liquid Holdup 

In chapter 16 the liquid dynamics for a distillation column were derived. In section 16.8 it was shown that the response of the bottom hold-up to vapor flow changes can be written as  

Bottom level control using H is slowed down by the X effect, if X 0.5, which is clear from the following approximation. The closed loop transfer function with proportional control is  

After approximation of the last term by a dead time nti, the oscillation period and the closed loop gain on the limit of stability can be foimd. For simplicity reasons is assumed to be unity. If A = 0.5 it is found that  

For X= Eqn. (34.6) reduces to the equation for bottom level control using the reflux, which is  

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