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 (29.6 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% — 24.2 t/h of steam (0.61 t/t) plus 1,140 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 — and a water activity fitted to measured data: binary boiling points (Li 2017, NIST TRC ThermoML Archive) and 20 °C vapour pressures up to 85 wt% (Kirk-Othmer), with a held-out error of 2% in water activity. The boiling-point elevation is therefore the fitted one, 23.5 K at 54% P2O5 and 0.12 bar (the ideal, Raoult's-law activity this replaced gave 9 K). Checked against a boiling point the fit never saw, it puts 85 wt% acid at 164 °C at atmospheric pressure against a measured 158 °C. Above 18 mol% acid the temperature dependence rests on one coefficient and that single check, so read the concentrate temperature to within a few kelvin. No heat of dilution is carried (about 1.5% of the latent duty at 54% P2O5). The 320 K feed stands in for a hotter plant feed.