Modelling the distillation column as a whole

The vapour flow will depend on both the difference in vapour-space pressure in adjacent plates and the head of liquid above the point of vapour entry into the plate above. For a sieve plate or valve-cap plate, the point of vapour entry is the bottom of the tray, but for a bubble-cap plate the point of entry is the lower edge of the bubble-cap. For a sieve or valve-cap plate, the vapour flow will have the form  

Here wj is the molecular weight of component j, and kij is the mole fraction of component j on plate 1  

Normally design calculations or plant data will be available from which Ci can be calculated. 

The theory developed in Section 12.6 assumed that the plate acts as a perfect equilibrium stage for separation. However, in practice it is found that this is only an approximation. While the temperature of the vapour leaving the plate is likely to be the same as that of the liquid leaving the plate, the difference in compositions of the vapour and the liquid is often not as great as implied by equation (12.63), and the plate has therefore not been such an efficient separation stage. The deviation from equilibrium is accounted for partly by gross physical phenomena such as carryover of liquid droplets in the vapour leaving the plate, but a more fundamental reason is the restricted rate of mass transfer between the vapour and liquid phases. A column efficiency, r/r, may be defined as the ratio of the number of plates needed in theory. Nr, to the number needed in practice, Np, to achieve the desired separation  

A typical efficiency figure is 70%, although the efficiency can fail as low as 40%. The model may account for this less-than-perfect separation by using a reduced number, t)cNp, of plates, but with the height of each plate and each weir upgraded by a factor of /r)c in order to maintain the overall volumes constant. 

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