Electrowinning / electrochemical metal removal simulation

1 electrolyte -> spent electrolyte (regenerated acid), cathode metal, cell gas

Governing equations

The exact equations the solver works for a electrowinning / electrochemical metal removal — the same math shown in the app's "Theory" panel, not a black box.

$\dot n_M$

metal deposited at the cathode [mol/s]

$\eta_{CE}$

current efficiency — fraction of the current that plates metal [0..1]

$I$

cell current [A]

$z$

charge of the metal ion

$F$

Faraday constant [C/mol]

$V_{cell}$

cell voltage [V]

$E_{rev}$

reversible decomposition voltage from the CRC standard potentials [V]

$\eta_a$

anode overpotential [V]

$\eta_c$

cathode overpotential [V]

$j$

current density I/A [A/m^2]

$\delta$

anode-cathode gap [m]

$\kappa$

electrolyte conductivity [S/m]

$V_{hw}$

contact and bus-bar voltage [V]

$P$

electrical power drawn [W] (reported as duty)

$E_{sp}$

specific energy per kg of metal [J/kg]; also shown in kWh/kg

$M_M$

molar mass of the metal [kg/mol]

$c_{in}$

metal-ion molarity entering [mol/L]

$c_{out}$

metal-ion molarity leaving [mol/L]

$k_m$

mass-transfer coefficient to the cathode [m/s]

$A$

cathode area [m^2]

$Q$

electrolyte volumetric flow [m^3/s]

$E_c$

cathode potential [V vs SHE]

$E^\circ$

standard reduction potential of M^z+/M [V vs SHE]

$R$

gas constant [J/mol/K]

$T$

cell temperature [K]

Parameters

Faraday's-law electrowinning (cathode M^z+ + ze- -> M; anode 2H2O -> O2 + 4H+ + 4e-; the protons leave as regenerated acid); outlets in order spent (electrolyte), cathode (solid metal), gas (O2 + H2); exactly one of: current [A], current_density [A/m^2, with cathode_area], recovery [0..1 of target_metal, current solved], cathode_potential [V vs SHE, with mass_transfer_coefficient and cathode_area: potentiostatic mass-transfer-limited impurity removal; every allowed metal whose Nernst potential is above it plates at its limiting current and never below the Nernst floor]; cathode_area [m^2], mass_transfer_coefficient [m/s], reactor_model ['cstr' or 'plug_flow'], target_metal [metal id]; current_efficiency [0..1 or {metal: share}; REQUIRED, no default], side_reaction ['hydrogen' (default, H2 at the cathode) or 'redox_shuttle' (e.g. Fe3+/Fe2+, no net chemistry)]; cell voltage: cell_voltage [V] or built from CRC standard potentials plus anode_overpotential [V], cathode_overpotential [V], electrolyte_conductivity [S/m], electrode_gap [m], hardware_voltage [V] (none defaulted); optional metals [list of ions allowed to plate; ag cu pb sn ni co (cobalt) cd fe2 (ferrous) zn mn], acid_component [default h2so4 / phosphoric_acid / hno3 if present], protons_per_acid [2 / 1 / 1], temperature [K, isothermal; default feed T]; reports power [W, = duty, electrical work], specific_energy_kwh_per_kg, reversible_voltage, voltage_efficiency, current_efficiency_effective, acid_generated_mol_s, o2_rate, h2_rate

Example flowsheets that use it