Enthalpy balances below feed plate

To obtain a relation between Ln and Lm, it is necessary to make an enthalpy balance over the feed plate, and to consider what happens when the feed enters the column. If the feed is all in the form of liquid at its boiling point, the reflux Lm overflowing to the plate below will be Ln + F. If however the feed is a liquid at a temperature Tf, that is less than the boiling point, some vapour rising from the plate below will condense to provide sufficient heat to bring the feed liquor to the boiling point. 

Assume Hr = Hs, hr = hs. where these are the vapor and liquid enthalpies which appear in the enthalpy balance enclosing the feed plate and any number of plates above or below it. 

Equal-molal overflow could be assumed, but if the calculations are done by computer, an enthalpy balance would probably be made and the change in pressure from stage to stage would also be allowed for. The calculations are continued in this fashion, alternating the use of equilibrium and material-balance relationships, until the composition is close to that of the feed. Similar calculations are carried out for the lower section of the column starting with an estimated reboiler or bottoms composition. The next step is to match the Compositions at the feed stage for the two sets of calculations. Based on the differences for individual components, the product compositions are adjusted and the calculations repeated until all errors fall below a specified value. In some procedures, the number of plates and the feed plate are fixed beforehand, and the calculations are repeated for different reflux ratios until the desired match is obtained at the designated feed plate. 

The value of p is best obtained by an enthalpy balance around the feed plate. However, when the molal enthalpy of the overflow from the feed plate and the plate above is essentially the same and the enthalpy of the vapor from the feed plate and the plate below is also the same, then, by Eqs. (7-6) and (7-6o), — p becomes approximately the heat necessary to vaporize 1 lb. mol of the feed divided by the latent heat of vaporization of the feed. Thus, an all-vapor feed at its boiling point would have a value of p = 0, for an all-liquid feed at its boiling point, p would equal — 1 p would be less than —1 for a cold feed, between — 1 and zero for a partially vaporized feed, and greater than zero for a superheated vapor feed. 

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See also in sourсe #XX -- [ ]

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