How to simulate wet-process phosphoric acid: electrochemical removal of copper and cadmium
Wet-process phosphoric acid (about 42 wt% H₃PO₄, 10 kg/s) carries the metals its phosphate rock brought in: iron, zinc, nickel, copper and the cadmium that limits how the acid may be used in fertilizer. Two flow-through electrochemical cells remove the two noble enough to plate from strong acid. The first holds its cathode at -0.05 V vs SHE: copper's Nernst potential sits far above that, so copper plates at its mass-transfer limit (plug-flow law, 99% removed) while zinc, nickel, iron and cadmium, whose potentials lie below the cathode, stay dissolved. The second cell runs at -0.55 V and is told that only cadmium plates: mass transfer alone would take 99.4% of it, but at that potential and 323 K the Nernst floor holds about 2.6e-5 mol/L in solution, so the solver reports the equilibrium-limited 91% instead. Each cell's current comes from the metal's partial current and the current efficiency you give it; the copper and cadmium currents regenerate phosphoric acid (one proton per dihydrogen-phosphate counter-ion), and the rest of the charge evolves hydrogen beside the anode's oxygen, which the cell gas reports, with a flammability warning.
- 1Open the ready-made model
Open the "Wet-process phosphoric acid: electrochemical removal of copper and cadmium" 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 water, phosphoric_acid, fe2, zn, ni, cu, cd, o2, h2 — already selected, so the phase equilibrium and enthalpy are physically consistent from the first run.
- 3Review the flowsheet
The flowsheet chains 2× EW CD. 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
- water, phosphoric_acid, fe2, zn, ni, cu, cd, o2, h2
- Unit operations
- 2× EW CD
Opens live on the canvas — free, no install.
Explore the model & flowsheetModeling assumptions & limitations
What this model captures, and what it deliberately does not — from the engineers who built it.
- 1The impurity levels are illustrative inputs, not a measured acid analysis
- 2Iron-group metals (Fe, Ni) are thermodynamically able to plate at -0.55 V but deposit from strong acid only with large kinetic overpotentials that a thermodynamic ordering cannot see, so the second cell is restricted to cadmium by the user, not by the model
- 3The mass-transfer coefficient, cathode area, current efficiencies and cell voltages are illustrative inputs for a three-dimensional flow-through cathode, to be replaced with measured cell data
- 4Real wet-process acid holds its iron mostly as Fe(III), whose reduction to Fe(II) at the cathode consumes current, and that shuttle is represented only through the low current efficiencies given; and
- 5Activity coefficients are taken as one, so the Nernst potentials order the metals rather than fix their electrode potentials.
Frequently asked questions
- What does the Wet-process phosphoric acid: electrochemical removal of copper and cadmium model simulate?
- Wet-process phosphoric acid (about 42 wt% H₃PO₄, 10 kg/s) carries the metals its phosphate rock brought in: iron, zinc, nickel, copper and the cadmium that limits how the acid may be used in fertilizer. Two flow-through electrochemical cells remove the two noble enough to plate from strong acid. The first holds its cathode at -0.05 V vs SHE: copper's Nernst potential sits far above that, so copper plates at its mass-transfer limit (plug-flow law, 99% removed) while zinc, nickel, iron and cadmium, whose potentials lie below the cathode, stay dissolved. The second cell runs at -0.55 V and is told that only cadmium plates: mass transfer alone would take 99.4% of it, but at that potential and 323 K the Nernst floor holds about 2.6e-5 mol/L in solution, so the solver reports the equilibrium-limited 91% instead. Each cell's current comes from the metal's partial current and the current efficiency you give it; the copper and cadmium currents regenerate phosphoric acid (one proton per dihydrogen-phosphate counter-ion), and the rest of the charge evolves hydrogen beside the anode's oxygen, which the cell gas reports, with a flammability warning.
- Which thermodynamic method does it use?
- The BRINE property package, over water, phosphoric_acid, fe2, zn, ni, cu, cd, o2, h2 — already selected. You can switch the method on the canvas before running.
- Which unit operations are in the flowsheet?
- It chains 2× EW CD. 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. Wet-process phosphoric acid: electrochemical removal of copper and cadmium 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.
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.
PEM fuel-cell CHP with cathode water management
A PEM fuel-cell stack (real Butler-Volmer + Nernst polarization model, not an efficiency shortcut) runs on H₂ with a compressed cathode air supply — the reaction water genuinely splits between vapor (carried out in the exhaust air) and condensed liquid via a real (T,P) VLE flash, not a fixed assumption. A downstream cooler + knockout drum recovers additional water from the exhaust before venting.
Green urea synthesis
Green ammonia and captured CO₂ react over a single-pass stoichiometric reactor (2NH₃ + CO₂ ⇌ CO(NH₂)₂ + H₂O) at synthesis-loop conditions — the fertilizer step downstream of green ammonia. Screening fidelity: a real plant recycles the unconverted carbamate/excess ammonia to push per-pass yield well above this single-pass conversion; that recycle isn't modeled here.
Battery cobalt recovery: leach, neutralize, D2EHPA Mn SX, Cyanex 272 Co SX, electrowinning
Spent NMC111 black mass is leached in sulfuric acid with the acid consumption tracked (lithium as Li₂SO₄, each transition metal as its sulfate), so the pregnant leach solution carries the residual free acid a real leach leaves. A neutralizer then titrates that liquor with 20 wt% caustic to pH 4.0 on the aqueous speciation: the caustic dose is solved, not assumed, and the heat of neutralization (55.8 kJ per mole of acid neutralized) warms the liquor; the caustic header is the supply, and what the titration does not take is returned. Two solvent-extraction circuits on the pH-isotherm chemistry follow, the common NMC arrangement: D2EHPA at pH 4.0 takes manganese into the organic while cobalt and nickel stay behind, and Cyanex 272 at pH 5.0 then takes cobalt and rejects nickel and lithium to the raffinate. The Cyanex 272 isotherms are one published measurement (Liu et al., Metals 11 (2021) 401: 0.4 M in ShellSol D70, 40 C, sulfate; pH50 cobalt 4.15, nickel 6.06), and the 1.9 pH-unit gap between them is why the cobalt organic carries about 0.6% of the nickel, against about 3% with D2EHPA at the same cobalt recovery. The loaded cobalt organic is stripped into a dilute sulfuric strip liquor, and that advance electrolyte goes to cobalt electrowinning: Faraday's law at a 90% current efficiency, 90% of the cobalt plated as cathode cobalt, the anode's oxygen and the 10% of the charge that evolves hydrogen reported as cell gas, and one mole of sulfuric acid regenerated per mole of cobalt plated.