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We assume that the flows of the species are approximately constant across each section of the column:

${y}_{n}=\frac{L}{V}{x}_{n.-1}+\frac{D}{V}{x}_{\mathrm{D}}$

${y}_{m}=\frac{L\prime }{V\prime }{x}_{m-1}+\frac{W}{V\prime }{x}_{\mathrm{W}}$

The feed to the column is partially liquid. Thus we define the liquid and vapor fraction of the feed as ${\mathit{\Phi }}_{\mathrm{L}}$ and ${\mathit{\Phi }}_{\mathrm{V}}$, respectively:

${\mathit{\Phi }}_{\mathrm{L}}=\frac{L\prime -L}{F}{\mathit{\Phi }}_{\mathrm{V}}=\frac{V-V\prime }{F}$

Thus the q line can be written as follows:

$q=\frac{{\mathit{\Phi }}_{\mathrm{V}}-1}{{\mathit{\Phi }}_{\mathrm{V}}}{x}_{n.}+\frac{1}{{\mathit{\Phi }}_{\mathrm{V}}}{x}_{\mathrm{f}}$

We now ...

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