Parametric Transfer-Functions For Packed, Binary Distillation Columns

Using similar assumptions to those adopted in a companion paper (1) for tray column analysis, a parametric transfer-function (T.F.M.) is here derived completely analytically for packed, binary distillation columns.For simplicity, the method of calculation is illustrated for a column that is symmetrical statically and dynamically i.e. having a rectifier vapour/stripping section liquid capacitance ration c=1.0. This produces a completely diagonal T.F.M. between the sum and output composition changes and the circulating and product take-off flow rates. The T.F.M. is also presented for c=1.0 and although no longer diagonal at all frequencies, analysis and simulation show that the column behaviour is not greatly affected by changes in this parameter. Long packed columns are shown to produce novel nonminimum phase effects when twin product control is attempted, whereas, serious travelling-wave phenomena can limit controller performance in short columns. The possibility of zero separation-gain is also revealed. The computed shapes of inverse Nyquist loci are confirmed by analysis and by numerical time-domain simulation. The chief cause of discrepancy between tray and packed column behaviour is shown to result from the continuous equilibrium assumption for theoretical trays.