Hydrometallurgy & Electrochemical Refining, Copper SX-EW Tankhouse Faraday Balance
Copper Electrowinning Tankhouse Harvest & kWh/t Formula
Calculate Daily LME Grade-A Copper plated per Electrolytic Cell (kg/day), Total Tankhouse Cathode Harvest (t/day), Rectifier DC Bus Load (MW), and Specific DC Energy (kWh/t Cu).
Ferric iron Fe³⁺ carryover from solvent extraction parasitic-redoxes copper cathodes—dropping current efficiency from 92.5% to 78% and spiking power cost +31%!
In **Solvent-Extraction Electrowinning (`SX-EW`)** copper hydrometallurgy, rich `CuSO_4 - H_2SO_4` pregnant electrolyte circulates through **`N_{cell}` Polymer-Concrete Electrolytic Cells wired electrically in series** at **Rectifier DC Current `I`** (`kA`), plating `99.99%` LME Grade-A copper (`M_{Cu} = 63.546` g/mol, `n = 2` electrons per `Cu²⁺` ion, Faraday constant `F = 96,485.332` C/mol) onto `316L` stainless-steel mother blanks opposite `Pb-Ca-Sn` oxygen-evolving anodes (`Cell Voltage V_{cell} ~= 1.95–2.25` V vs `0.89` V thermodynamic decomposition)! By Faraday’s Law scaled by **Cathodic Current Efficiency `eta_I%`** (lost to `Fe³⁺ + e⁻ -> Fe²⁺` parasitic iron shuttle and stray short circuits), each cell plates **`m_{cell} = ((I * 1,000) * 86,400 * 63.546 * (eta_I / 100)) / (2 * 96,485.332 * 1,000)`** (`kg Cu/day`), totaling **`M_{tot} = (m_{cell} * N_{cell}) / 1,000`** (`t Cu/day`) at **Specific DC Energy `E_{spec} = (V_{cell} * 2 * 96,485.332 * 1,000) / (3,600 * 63.546 * (eta_I / 100))`** (`kWh/t Cu`)!
Verify on an `84`-Cell Commercial SX-EW Tankhouse Section—Rectifier_DC_Current `I` = 34.0 kA (B2), Series_Electrolytic_Cells `N_{cell}` = 84 (B3), Cathodic_Current_Efficiency `eta_I` = 92.5% (B4), and Mean_Cell_Voltage `V_{cell}` = 2.02 V (B5): Copper Plated per Cell equals `894.81` kg/day (E2), Total Section Harvest equals **`75.16` t Cu/day** (E3), Rectifier DC Bus Load equals `5.769` MW (E4), and Specific Energy equals **`1,842.1` kWh/t Cu** (E5)!
| SX-EW Tankhouse Faraday KPI (34 kA, 84 Series Cells: Clean Electrolyte vs High-Fe³⁺) | Formula | Verified Output |
|---|---|---|
| Daily Copper per Cell (kg/day) | (I_kA*1e3 * 86400 * 63.546 * CE) / (2 * 96485.332 * 1e3) | 894.81 kg/d (754.54 kg/d @ 78% CE!) |
| Tankhouse Cathode Harvest (t/day) | (Daily_Cu_Cell_kg * Series_Cells_N) / 1000 | 75.16 t/d (63.38 t/d = -11.8 t/d lost!) |
| Rectifier DC Bus Power (MW) | (Current_kA * Series_Cells_N * Vcell_V) / 1000 | 5.769 MW (6.397 MW @ scaled anodes) |
| Specific DC Energy (kWh/t Cu) | (Rectifier_MW * 24 * 1000) / Harvest_t_d | 1,842.1 kWh/t (2,422.4 kWh/t = +31.5%!) |
Faraday Divalent Cu²⁺ Electrowinning Mass Balance & Specific Energy Formula
Validate `Rectifier_Current I` in `[1, 100]` kA, integer `Series_Cells N_{cell}` in `[1, 500]`, `Current_Efficiency` in `[40%, 100%]`, and `Cell_Voltage V_{cell}` in `[1.50, 3.50]` V!
=LET(ik_a, B2, nc_s, B3, ce_p, B4, vc_v, B5, mc_k, (ik_a * 1000 * 86400 * 63.546 * (ce_p / 100)) / (2 * 96485.332 * 1000), mt_t, (mc_k * nc_s) / 1000, mw_d, (ik_a * nc_s * vc_v) / 1000, IF(OR(ik_a < 1, ik_a > 100, nc_s < 1, nc_s > 500, ce_p < 40, ce_p > 100, vc_v < 1.5, vc_v > 3.5), "Invalid EW Input", ROUND((mw_d * 24 * 1000) / mt_t, 1)))High Ferric Entrainment + Anode Scale (`CE = 78%`, `V_cell = 2.24` V) Power-Penalty Check
Let crud carryover spike electrolyte `Fe³⁺ > 3` g/L (`CE` drops to `B4 = 78%`) while aged lead anodes climb to `B5 = 2.24` V: Daily Harvest E3 loses `11.78` tonnes/day (`75.16 -> 63.38` t/d) even as Rectifier Power E4 rises to `6.397` MW—driving Specific Energy E5 up **`+31.5%` to `2,422.4` kWh/t Cu**!
=IF(ISTEXT(E5), E5, LET(mc_k, (B2 * 1000 * 86400 * 63.546 * (B4 / 100)) / (2 * 96485.332 * 1000), ROUND((mc_k * B3) / 1000, 2)))Try the example
Use the original values or change them to test your understanding.