Mathematical model of the distillation plate

We will now derive the equations necessary to describe the dynamic behaviour of a distillation plate. The modelling procedure for multi-component boiling has strong similarities to the situation of single component boiling condensing already described in Section 12.2. We shall wish to know the masses of all the components in the liquid phase and in the vapour phase, the temperature of the plate, the pressure in the plate, the specific volume of the liquid components and the specific volume of the vapour mixture as a whole. This information is sufficient to allow us to calculate the mole fractions in the vapour and the liquid and the inter-plate flows. 

The choice of state variables follows the example of single component boiling. It is perhaps surprising that we can calculate all the variables listed above from a knowledge of only the component liquid masses in the plate and the plate temperature. These are thus the obvious state variables. It is customary and natural 

Assuming there are n components in the feed, then the mass balance over the liquid yields for the most general case  

Muj is the mass of component j in the liquid phase in plate i (kmol), 

Li is the total liquid flow from plate i to plate i — 1 (kmol/s), 

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