Phosphoric acid concentration: microwave heating (29 → 54% P2O5)

The same duty with the steam exchanger replaced by volumetric microwave heating: 43.4 MW absorbed in the acid, then the same vacuum flash to 54.0 wt% P2O5 and the same 64.0 t/h of water removed — the microwave does not remove water, it supplies the latent heat. At a 65% wall-plug magnetron efficiency (915 MHz industrial units reach ~85%) that is 66.7 MW of electricity, 1,670 kWh per tonne of P2O5 (1,280 at 85%). The comparison that decides it is the energy carrier, not the heating mechanism: at Jorf Lasfar the baseline's 1.79 t/t of steam is a co-product of the sulfuric-acid plants, and the site turns that steam into electricity at roughly 30%. Sending it through a turbine, a magnetron and back into the acid delivers about a fifth of the heat the exchanger delivers directly (0.30 × 0.65 ≈ 0.2), so on this site the microwave route needs roughly five times the primary steam energy of the baseline. Where microwaves do earn their place is not here but at the superphosphoric end (>70% P2O5, viscous, fouling, where the recent literature targets them), and an electric route for the 29-54 step should be compared against mechanical vapour recompression, which reuses the latent heat at a coefficient of performance of 10-30. Sweep the absorbed duty to see the product concentration and the electricity follow it. 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. Microwave penetration depth (about a centimetre in a conductive acid at 2.45 GHz) and the HF attack on quartz windows are equipment questions this model does not carry.