How to simulate 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.
- 1Open the ready-made model
Open the "Phosphoric acid concentration: microwave-then-steam hybrid (29 → 42 → 54% P2O5)" model in the MaximaLabs workspace — no install, no license. It loads live on the canvas, ready to edit and run.
- 2Confirm the thermodynamics
This process is modeled with the BRINE property package over phosphoric_acid, water — already selected, so the phase equilibrium and enthalpy are physically consistent from the first run.
- 3Review the flowsheet
The flowsheet chains MW, 2× Flash2, PUMP, HX. Every block is a real, solvable unit op you can reconfigure on the canvas.
- 4Run the simulation
Click Run. The deterministic solver converges the material and energy balances (recycles included) and fills the live stream table — the AI never invents a number.
- 5Read the results and iterate
Inspect the converged streams, tweak a spec, and re-run — or ask the AI copilot to explain a result or diagnose a failed solve in plain English.
- Thermodynamics
- BRINE
- Components
- phosphoric_acid, water
- Unit operations
- MW2× Flash2PUMPHX
Opens live on the canvas — free, no install.
Explore the model & flowsheetFrequently asked questions
- What does the Phosphoric acid concentration: microwave-then-steam hybrid (29 → 42 → 54% P2O5) model simulate?
- 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.
- Which thermodynamic method does it use?
- The BRINE property package, over phosphoric_acid, water — already selected. You can switch the method on the canvas before running.
- Which unit operations are in the flowsheet?
- It chains MW, 2× Flash2, PUMP, HX. Every block is a real, solvable unit operation you can reconfigure, add to, or remove.
- Do I need to install software or buy a license?
- No. Phosphoric acid concentration: microwave-then-steam hybrid (29 → 42 → 54% P2O5) runs entirely in your browser on MaximaLabs — free, no install, no license. Open the model to load it live and run the deterministic solver.
More guides like this
Phosphoric acid concentration: steam evaporator baseline (29 → 54% P2O5)
The conventional wet-process step, at the scale of one Jorf Lasfar concentration line: 138 t/h of 29% P₂O₅ acid, heated by 3.5 bar LP steam in a graphite exchanger and flashed under vacuum (0.12 bar) to 54% P₂O₅, evaporating 64.0 t/h of water. The steam feed is tuned so the concentrate lands on 54.0 wt% P₂O₅ (the user variable p2o5_wt_product), which takes 71.7 t/h of steam — 1.79 t steam per tonne of P₂O₅, 43.4 MW of condensing duty. That is the single-effect ideal; the published plant benchmark of ~2.8 t/t carries exchanger approach, losses and off-design operation on top. The point of the number here is what it costs the site: at Jorf Lasfar this steam is a co-product of the exothermic sulfuric-acid plants, which is the fact any electric alternative has to beat. Compare the two sibling examples, phosphoric-acid-concentration-microwave and -hybrid. 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. The acid heated at 1 atm here partly boils in the exchanger (the model's colligative boiling point at 1 atm); the real acid is kept liquid under static head and flashes in the chamber.
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.
Steam utility island: deaerator, boiler, desuperheater
The three units that stand between raw makeup water and steam a turbine can accept, on the IAPWS steam tables. The deaerator takes 500 mol/s of 300 K makeup and 40 mol/s of LP steam and returns 540 mol/s of saturated liquid at 5 bar (425 K) for 3.23 MW. It is a direct-contact heater, so the heating steam does not leave — it condenses into the feedwater and shows up in the outlet flow. That is the point of the unit: the reason a plant heats feedwater by injecting steam into it rather than through a tube bundle is that boiling the water is what strips the dissolved oxygen out of it. The boiler then absorbs 26.6 MW into the water and fires 31.3 MW to do it — the gap is the stack loss, and it is the number a fuel bill is written against, not the absorbed duty. The desuperheater takes that 720 K steam down to a 660 K target by spraying 25.96 mol/s of water into it. The spray rate is SOLVED, not specified: you state the temperature you want and the unit finds the water that achieves it, which is how an attemperator is actually specified. Note the outlet is 566 mol/s, more than entered it, the spray water becomes steam. Bounded: the deaerator is an equilibrium model, so it reports no rate-based O₂/CO₂ stripping (there is no residual-oxygen ppb number here, which is what a real deaerator is guaranteed on), and the desuperheater assumes the spray fully evaporates.
Ethylene glycol plant: closed water loop + multi-effect evaporator dehydration
The water-integrated evolution of the fiber-grade MEG plant. Two changes turn the once-through EO/glycol chain into a real, water-economical process: (1) the recovered process water is RECYCLED back to the hydration reactors through a purge splitter. A pure recycle is inventory-singular (reactors are keyed on the shrinking EO pool, so water consumption is fixed regardless of how much water circulates), so an 8% purge pins the loop and makes it well-posed, cutting fresh water makeup from 10 to ~1.75 mol/s (a >80% reduction). (2) The bulk dehydration is done by a genuine TWO-EFFECT EVAPORATOR TRAIN (forward-feed, real steam economy: effect 1's low-temperature vapor is the heating steam for effect 2) doing rigorous (P,H)-flash water removal, rather than a single spec-based split. The recycle converges through the solver's Wegstein tearing (~15 outer passes) and MEG still comes out fiber-grade (>=99.9%). HONEST SCOPE: the reaction chemistry is rigorous stoichiometry (real atom balances, ~90/9/1 selectivity) and the evaporators are real energy-balanced flash effects — but flash evaporation CANNOT reach glycol dryness without slipping glycol into the overhead vapor (MEG has a real vapor pressure at 90 C), so the evaporators run cool and only pre-concentrate. An overhead knockout returns the ~1-2% slipped glycol to the product (no yield loss), and a final vacuum-refining polish (still a spec-based split, representing the refluxed dehydration column a flash cannot replicate) removes the last water. This mirrors a real MEG plant's multi-effect-evaporator + vacuum-refining dehydration section. The product columns remain spec-based (a converged 99.9% fiber-grade MEG column is not tractable under Peng-Robinson here — the MEG/DEG relative volatility is too narrow for the wide-boiling MESH path).
Pressure-swing ethanol dehydration (Gᴱ mixing rule)
Ethanol–water is the classic azeotrope, and pressure-swing distillation breaks it without an entrainer: the azeotrope moves with pressure, so a low-pressure column and a high-pressure column pass each other's azeotropic distillate and each recovers a pure product. The whole process only works if the property package tracks that shift — which is exactly where a conventional package choice falls between two chairs. This flowsheet runs the high-pressure column at 15 bar on pr-mhv1: Peng-Robinson with an MHV1 excess-Gibbs mixing rule, so the cubic equation of state gets its attraction parameter from NRTL's excess Gibbs energy instead of from a single binary interaction constant. Switch the thermo package (Solver menu) and compare the predicted azeotrope: | package | 1 atm | 15 bar | valid at 15 bar? | |---|---|---|---| | NRTL | 0.891 | 0.802 | no — γ-φ is a low-pressure formulation (~10 bar) | | Peng-Robinson (kij) | 0.586 | 0.613 | yes, but a kij cannot represent this azeotrope | | pr-mhv1 | 0.949 | 0.798 | yes | (mole fraction ethanol; the repo's DECHEMA-validated 1 atm anchor is 0.894.) At 15 bar pr-mhv1 lands within 0.005 of NRTL while remaining a genuine equation of state, whereas plain Peng-Robinson is off by ~0.19 and puts the azeotrope in the wrong place entirely. Selecting nrtl here also trips the applicability guard, which warns that the activity model is past its pressure ceiling and names the fix. The flowsheet demonstrates the mechanism on itself. Drop the column pressure to 1 atm and re-run, changing nothing else: the solve fails with SPEC_THERMODYNAMICALLY_IMPOSSIBLE, because at atmospheric pressure the requested bottoms purity sits beyond the azeotrope and no column can reach it. At 15 bar the same specification converges and the bottoms leaves at x_EtOH ≈ 0.924 — past the atmospheric azeotrope of 0.894, which is precisely the composition an atmospheric column cannot cross.
Industrial water reuse: RO + membrane distillation to near-ZLD
A chemical-site water-reuse train of the kind large industrial water users build when the intake is salinising and freshwater is getting scarce: reverse osmosis makes reuse-grade water, the RO concentrate is warmed by low-grade waste heat and pushed further by membrane distillation, and the MD concentrate is crystallised to salt. Overall water recovery comes out at 94.9%. The point of the flowsheet is why MD is there at all. RO is pressure-driven, so its ceiling is osmotic pressure — and this feed hits that wall hard: at 25 bar the same 75% recovery is infeasible, and the model says so with a number rather than a shrug (osmotic pressure 27.2 bar against a 25 bar feed, a structured SPEC_THERMODYNAMICALLY_IMPOSSIBLE error, which is why the feed here runs at 45 bar). Membrane distillation is driven by a vapour-pressure difference instead, so only vapour crosses and there is no osmotic ceiling at all: it takes the RO concentrate from 2.0 mol% to 9.7 mol% salt, recovering 81% of the water RO had to leave behind, and its distillate is solvent-only. The waste-heat coupling is not decoration. At the RO concentrate's own 25 C the MD flux is about 1 kg/m2/h and the module is pointless; warmed to 60 C it runs at 21.5 kg/m2/h, inside the 10-50 kg/m2/h band real DCMD modules achieve. That is the entire commercial case for MD — it is a heat-driven process, so it is only cheap where low-grade heat is already being vented.