Relationship Between Boilup and Column Pressure Drop

So far we have assumed that there is negligible lag in vapor flow between adjacent trays. This means that we treat the acoustic impedance Zcol between the bottom and top trays as a pure resistance approximately equal to where the subscripts s and r refer to the stripping and rectification sections of the column. The validity of this assumption has been shown by tests run by Stanton and Bremer1 on a 90-tray column and by the computer studies of Williams, Harnett, and Rose.2

If, however, we are interested in the high-frequency behavior of the column, then we must treat the impedance as that of an RC chain as shown in Figure 17.16. Here each RC section represents one tray, the resistance is that of the tray and layer of liquid to vapor flow, and the capacitance is the acoustic capacitance of the space between the trays. The terminal impedance, ZT(s), is simply P^(s)/Qc(s). Mathematically the entire network may be studied by the methods of transmission-line analysis.

If the individual RC sections are equivalent, or nearly so, then the impedance looking up from the reboiler is approximately:

Zj{s) + Zk(s) tanh nl Zk(s) + ZT(s) tanh nl where lR

where R and C are the resistance and capacitance, respectively, for each tray and vapor space, and / is the total number of trays. Two cases are now of primary interest.

If ZT = 0, as would be true for an atmospheric column or for a column with tight overhead pressure control, then:

d ID

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