Phosphoric acid concentration: microwave-then-steam hybrid (29 → 42 → 54% P2O5)

The transition path the concept proposes: microwaves take the acid from 29 to 42% P2O5 in a first vacuum flash (29.1 MW absorbed), a pump returns the 42% acid to atmospheric pressure, and the existing steam exchanger and second flash finish it to 54.0 wt% — 23.4 t/h of steam (0.59 t/t) plus 1,120 kWh of electricity per tonne of P2O5 at 65% magnetron efficiency, the same 64.0 t/h of water removed in total. The split is not free: two-thirds of the latent duty moved from a co-product steam to purchased electricity, and nothing about the second stage got easier. What a hybrid does buy is a pilot that can be run beside the existing evaporator without betting the line on it, and the freedom to put the microwave stage where it has a case — the viscous, fouling end — rather than on the dilute feed. Compare phosphoric-acid-concentration-steam and -microwave. Model scope, stated up front. The acid runs on the brine package, which carries phosphoric acid as a non-volatile molecular solute with its CRC liquid heat capacity (145 J/mol/K) — the streams show the real H3PO4/water compositions and the acid's sensible heat is in the balance. What that package does NOT yet carry is the acid's non-ideal water activity: it runs Raoult's law, so the boiling-point elevation is the colligative one, right in sign but about a third of the real value (+9 K at 54% P2O5 here; the real acid runs 20-30 K hotter, and 85 wt% acid boils at 158 °C at atmospheric pressure). The Pitzer fit that closes it is published (Bakher & Kaddami 2018, Braz. J. Chem. Eng. 35(3) 1153, open access) and named in the package as the parameters to transcribe. No heat of dilution is carried. Both omissions move the acid temperatures, not the water removed nor the energy-carrier comparison, which is what the study turns on. The 320 K feed stands in for a hotter plant feed for the same reason.