2,6-Xylenol from phenol methylation

Liquid-phase methylation of phenol with methanol at 250°C/150 bar over a selective ortho-methylation catalyst, per US Patent 3,707,569. At 50% single-pass phenol conversion the reported selectivity is 70% to o-cresol and 25% to 2,6-xylenol (the further-methylated product) — modeled here as two sequential fixed-conversion reactors (phenol -> o-cresol, then o-cresol -> 2,6-xylenol) approximating that split, followed by a distillation separating the light methanol/water from the phenolics, with an o-cresol side draw. The column is solved with the side draw as a real MESH withdrawal (rigorous_draws) on Soave-Redlich-Kwong: every other combination plateaued — the default carve (side draw cut from a distillate/bottoms profile) on PR, SRK or a Ge-mixing-rule package sat at a 2e-3 temperature residual, the rigorous draw on PR at 7e-5; on SRK it closes to 1e-8 with the component balance at 1e-7. Read the phenolic split for what it is: 20 stages at R=2 between three ortho-substituted phenols nine kelvin apart is a screening cut, and a cubic with van der Waals mixing carries no hydrogen-bonding non-ideality for the methanol/water/phenol top section (PSRK now has the phenolic UNIFAC groups, but a genuine PSRK evaluation of this column takes minutes per solve).