Biodiesel: alkali-catalysed transesterification with methanol recovery

Continuous base-catalysed (NaOH/methoxide) transesterification of a refined vegetable oil to fatty acid methyl esters -- the classic FAME biodiesel process. The oil is modeled as a 70/30 triolein/tripalmitin blend (the C18:1 and C16:0 triglycerides that dominate soy, canola and rendered-fat feedstocks); each is transesterified with methanol at a 6:1 molar ratio and 60 C in a two-reactor cascade at 97% conversion per stage, the standard industrial staging that drives the equilibrium toward the esters. Excess methanol is then vacuum-flashed overhead for recycle, and the wash/settling step splits the heavy glycerol phase from the ester product. The FAME product comes out at 96.9 wt% ester content -- just over the EN 14214 minimum of 96.5 wt% -- and the crude glycerin at ~85 wt% glycerol, typical of the crude co-product that goes on to a glycerin refining column.

Honesty note: the deliverable here is the material balance (conversion, ester yield, product specifications, methanol recovery), which is exact. The energy balance is NOT: the triglyceride and methyl-ester records in the databank carry no ideal-gas heat-capacity correlation, so they are injected as pseudocomponents whose Cp comes from the Kesler-Lee petroleum correlation, and their acentric factors (omega ~2.2-2.3) sit far outside the range Peng-Robinson's alpha function was fitted to. Reported duties and any adiabatic mixing temperature are therefore indicative only, which is why every unit here is temperature-specified rather than solved adiabatically, and why the reactor feed is given as one combined specified stream. Two further simplifications: the NaOH catalyst and the soap (sodium palmitate) that free fatty acids would form with it are not carried, so this is a refined, low-FFA feedstock; and the glycerol/ester split is a specified wash-section recovery rather than a rigorous liquid-liquid flash. That is now a modelling choice and no longer a data limit: every species reaching that step -- the methyl esters, glycerol, the unconverted triglyceride and the free fatty acid -- carries a predictive-UNIFAC group decomposition, and a liquid-liquid flash on this stream does split into an ester phase and a glycerol phase with the excess methanol partitioning into the glycerol, as it does industrially. Solving it here rather than specifying it would still inherit the pseudocomponent-Cp caveat above for the phase enthalpies.