Electrodialysis / EDI simulation

Governing equations

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

$\dot{n}_{salt}$

salt transported out of the diluate [mol/s]

$\xi$

current utilisation — leakage, co-ion transport and splitting all reduce it [-]

$i$

applied current density [A/m^2]

$i_{lim}$

limiting current density: the boundary layer cannot deliver ions faster [A/m^2]

$i_{eff}$

the current density that actually moves salt [A/m^2]

$A_{cell}$

membrane area per cell pair [m^2]

$N_{cp}$

number of cell pairs in the stack [-]

$z$

charge number of the transported ion [-]

$F$

Faraday constant, 96485 C/mol

$k$

diluate-side mass-transfer coefficient — a measured stack property [m/s]

$c_d$

diluate concentration; i_lim falls with it, which is why ED stalls near pure water [mol/m^3]

$t_m$

counter-ion transport number in the membrane [-]

$t_s$

counter-ion transport number in solution [-]

$U$

stack voltage [V]

$U_{el}$

electrode-reaction overpotential [V]

$r_{cp}$

area resistance of one cell pair [ohm m^2]

$r_{mem}$

membrane contribution to that resistance [ohm m^2]

$\delta$

compartment thickness [m]

$\kappa_d$

diluate conductivity — collapses as it is stripped, unless resin-filled [S/m]

$\kappa_c$

concentrate conductivity [S/m]

$\Lambda$

molar conductivity of the salt [S m^2/mol]

$P$

stack power [W]

Parameters

cell_pairs [-, REQUIRED], cell_area [m^2 per cell pair, REQUIRED], current_density [A/m^2, REQUIRED — stack size and drive cannot be inferred from the feed]; optional current_efficiency [-, default 0.9], concentrate_fraction [-, default 0.1, the share of the feed sent to the concentrate loop], salt [component id, default 'nacl'], charge [-, default 1], resin_filled [bool, default false — true makes it EDI: the resin carries the current and lifts the limiting-current cap], mass_transfer_coefficient [m/s, default 2e-5], transport_number_membrane / transport_number_solution [-, defaults 0.98/0.5], cell_pair_resistance [ohm m^2, default 5e-4], cell_thickness [m, default 5e-4], molar_conductivity [S m^2/mol, default 0.0126 for NaCl], resin_conductivity [S/m, default 0.05], electrode_voltage [V, default 2], water_splitting_overpotential [V per cell pair, default 0 -- with it omitted the reported energy is a FLOOR, since a real EDI stack's voltage is dominated by it], hydration_number [-, default 0 = no electro-osmotic water drag]. Outlets in order: diluate, concentrate.

Example flowsheets that use it