DME synthesis via reactive distillation

Methanol dehydrates to dimethyl ether over the reactive stages of a column — reaction and separation in one shell, pulling DME overhead while unconverted methanol and water leave the bottoms (Peng-Robinson EoS avoids the missing UNIFAC group-decomposition for ethers that blocks this under an activity-coefficient package). The conversion is 78%, not 80%: with the distillate drawing 40% of the feed, an 80% conversion makes exactly the 4 mol/s of DME the distillate takes, so it would demand a perfectly pure DME overhead and DME-free bottoms, a split no finite column makes. The stages near the condenser hold almost no methanol, so the reaction runs where the methanol is, on the feed and stripping trays.