Claus sulfur recovery unit (SRU): the 2:1 ratio that sets the ceiling

The back end of the amine train, and the unit that keeps a refinery's sulfur out of the atmosphere. Acid gas off an amine regenerator (60% H2S, 36% CO2) is part-burned in a reaction furnace, then reacted over two catalyst beds with sulfur condensed between them. The whole design follows from one number. The furnace burns a fraction phi of the H2S to SO2 (H2S + 3/2 O2 -> SO2 + H2O); the Claus reaction then consumes them at 2:1 (2 H2S + SO2 -> 3 S + 2 H2O). Burn exactly one third and the effluent arrives at precisely 2 H2S per SO2, so neither reagent is left over -- which is why air demand, not catalyst, is the manipulated variable in every real Claus plant. Off-ratio, the excess reagent walks straight through to the tail gas and recovery is capped by a stoichiometric ceiling min(3*phi, 3*(1-phi)/2) that no amount of catalyst can beat. Run the built-in combustion-fraction sweep to see it: recovery peaks at 95.3% at phi = 1/3 and falls away symmetrically -- 85.8% at phi = 0.30 and also 85.8% at phi = 0.40, 71.5% at phi = 0.25 and also at phi = 0.50, because the ceiling's two branches cross at one third. Air demand is not symmetric though (128.6 vs 171.4 mol/s at those same two points), so over-firing costs blower duty on top of the lost sulfur. At the design point the unit makes 57.17 mol/s of liquid sulfur from 60 mol/s of H2S against a 142.9 mol/s air demand, and the 2.84 mol/s of sulfur reaching the tail gas is still at exactly 2:1 H2S/SO2 -- the unconverted reagents leave in the ratio they were fed, which is what a tail-gas treating unit downstream is sized for. The sulfur atom balance closes exactly (60.000 mol/s S in, 57.165 as liquid sulfur + 2.835 in the tail gas). Staging is why two beds get to 95%: each converts a fraction of what is left, so X_total = 1 - (1-X_thermal)*prod(1-X_i) -- 0.65 thermal then 0.70 and 0.55 catalytic. Honesty notes (see flowsim/solver/unitops/claus.py): per-stage conversion is an input, not a prediction -- the Claus equilibrium runs through S2/S6/S8 allotrope speciation whose free energies this tree does not carry, and a designer takes those numbers from the licensor's equilibrium chart or a measured approach, so inventing a correlation would fabricate exactly the data that decides the answer. What is exact: the air demand, the ratio, the ceiling, the staging arithmetic and the sulfur atom balance. Not modelled: furnace flame temperature and waste-heat-boiler duty, NH3/BTEX destruction (flagged if present, since they set the minimum furnace temperature), COS/CS2 formation and hydrolysis, sulfur dew point, and the tail-gas treating unit that takes ~95% to ~99.9%. The front end is the companion 'mixed-amine-acid-gas-treating' showcase, whose stripper produces exactly this kind of acid gas. Refs: GPSA Engineering Data Book S22; Kohl & Nielsen (1997), Gas Purification ch. 8.