where ye is the composition of the vapour that would be in equilibrium with the liquid of composition xn actually leaving the plate. This equation gives the efficiency in vapour terms, although if the concentrations in the liquid streams are used then the plate efficiency Emi is given by:
xn+1 xe
where xe is the composition of the liquid that would be in equilibrium with the composition yn of the vapour actually leaving the plate.
The ratio EMv is shown graphically in Figure 11.56 where for any operating line AB the enrichment that would be achieved by an ideal plate is BC, and that achieved with an actual plate is BD. The ratio BD/BC then represents the plate efficiency. The efficiency may vary from point to point on a tray. Local values of the Murphree efficiency are designated Emv and Em1.
The efficiency of the individual plates is expected to depend on the physical properties of the mixture, the geometrical arrangements of the trays, and the flowrates of the two
Mole fraction of more volatile component in liquid (x)
Figure 11.56. Graphical representation of plate efficiency EMr
Mole fraction of more volatile component in liquid (x)
Figure 11.56. Graphical representation of plate efficiency EMr phases. A simple empirical relationship for the overall efficiency, E, of columns handling petroleum hydrocarbons is given by Drickamer and Bradford(58) who relate efficiency of the column to the average viscosity of the feed by:
where: x/ is the mole fraction of the component in the feed, is the viscosity at the mean tower temperature, and is the viscosity of water at 293 K (approximately 1 mNs/m2).
Further work, mainly with larger towers 3 m in diameter, suggested that higher efficiencies were obtained with larger diameters because of the longer liquid path. Thus, compared with a 0.9 m diameter tray, one of 3 m diameter might give up to 25 per cent greater efficiency.
Example 11.20
Component |
Mole fraction |
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