Your supervisor decides to test the newly hired engineer with a problem that you have not seen before. Recover p-xylene as the center cut (Figure 13-6) from a feed that is \(50.0 \mathrm{wt} \% \mathrm{o}-\mathrm{xylene}, 30.0 \mathrm{wt} \% \mathrm{p}-\) xylene, and \(20.0 \mathrm{wt} \% \mathrm{~m}\)-xylene. Solvent 1 ( \(\beta, \beta^{\prime}\)-thiodipropionitrile) and solvent 2 (diluent, n-hexane) are immiscible. Solvent 1 is added to both columns-there is no solvent 3 . Operation is at \(25^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm}\). Equilibrium data are \(\mathrm{K}_{\mathrm{d}, \mathrm{m}-\mathrm{xy}}=0.050, \mathrm{~K}_{\mathrm{d}, \mathrm{o}-\mathrm{xy}}=0.150\), and \(\mathrm{K}_{\mathrm{d}, \mathrm{pxy}}=\) 0.080 where \(\mathrm{K}_{\mathrm{d}, \mathrm{A}}=\mathrm{y}_{\mathrm{A}}\) (in solvent) \(/ \mathrm{x}_{\mathrm{A}}\) (in diluent) (Perry and Green, 1984). We want \(98+\%\) recovery of o-xylene in the extract product from the first column and \(95+\%\) recovery of \(p\)-xylene in the raffinate product from column 1. Column 1 is operated with \(\mathrm{E}_{1} / \mathrm{R}_{1}=9.1\). Feed rate \(\mathrm{F}_{1}.\) of meta in stream \(\mathrm{R}_{\mathrm{N}}\) (raffinate product) of column 1.] In other words, the solvent-free purities in the raffinate of column 1 equal the purities of the feed to column 2, which has no solvent in the stream. Column 2 is operated with \(E_{2} / R_{2}=15.8\). We want a \(95+\%\) recovery of \(\mathrm{p}\)-xylene compared to the feed to column 2 in the extract product of column 2 and a \(97 \%\) recovery of m-xylene compared to the feed to column 2 in the raffinate product of column 2.

Figure 13-6

Column 1. Determine the following: Integer values for \(\mathrm{N}\) and \(\mathrm{N}_{\mathrm{F}}\) that meet the recovery requirements; recovery of ortho, para, and meta xylenes in extract and raffinate products; solvent-free purities of ortho, para, and meta xylenes in extract and raffinate products.

Column 2. Determine the following: Integer values for \(\mathrm{N}\) and \(\mathrm{N}_{\mathrm{F}}\) that meet the recovery requirements; recovery of ortho, para, and meta xylenes in extract and raffinate products; solvent-free purities of ortho, para, and meta xylenes in extract and raffinate products.

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Solvent 2 A+ Solvent I Solvent 2 Solvent 3 or 1+B A+B+C Solvent 3 or I Solvent I Solvent 2+ C B+C+Solvent 2