Copper Electrorefining Anode Cycle, Scrap & Slime Formula

Pushing copper electrorefining current density to 410 A/m² passivates impure anodes with CuSO4·5H2O crust—forcing 19% anode scrap recycle back to the anode furnace!

Unlike copper *electrowinning* (`insoluble Pb-Sn-Ca anodes evolving O_2 at ~2.0 V`), **Electrolytic Copper Refining** (`99.5%` fire-refined blister/anode copper -> **`99.99%` LME Grade-A ISA/Kidd stainless-blank cathodes** at just `0.28–0.35` V cell voltage!) electrochemically dissolves cast **Copper Anodes (`Mass M_{an}` kg)** while leaving **`12%–16%` Undissolved Anode Scrap (`s_{scr}` %)** so lug ears never snap and drop `50` kg plates through polymer-concrete tankhouse floors! By **Faraday’s Law (`M_{Cu} = 63.546` g/mol, `n = 2`, `F = 96,485.332` C/mol)** across Two-Sided Active Blank Area `A` (`m²`), Current Density `j` (`A/m²`), and Cathode Current Efficiency `eta_c` (`%`), **Daily Copper Plating Rate equals `m_{day} = ((A * j) * 86,400 * 63.546 * (eta_c / 100)) / (2 * 96,485.332 * 1,000)`** (`kg/d`), fixing **Total Anode Life `t_{an} = (M_{an} * (1 - s_{scr} / 100)) / m_{day}`** (`days`, typically **two `9–10`-day cathode pulls per `18–21`-day anode cycle**), while insoluble **Gold, Silver, Platinum, Selenium & Lead Sulfate (`R_{slime}` kg/t dissolved)** settle to cell sumps as high-value **Anode Slime**!

Verify on a Modern `ISA-Process` Tankhouse Electrolytic Cell—Cast_Anode_Mass `M_{an}` = 380 kg (B2), Target_Anode_Scrap `s_{scr}` = 14.0% (B3), Two-Face_Cathode_Area `A` = 2.05 m² (B4), Current_Density `j` = 310 A/m² (B5), Current_Efficiency `eta_c` = 96.5% (B6), and Specific_Slime_Fall `R_{slime}` = 5.80 kg/t dissolved (B7): Dissolvable Anode Copper equals `326.8` kg (E2), Daily Cathode Gain equals `17.45` kg/d (E3), Total Anode Residence Cycle equals `18.73` days (`two 9.36-day ~163 kg cathode pulls!` E4), and Precious-Metal Bearing Slime Yield equals `1.895` kg per anode (E5)!

Faraday Copper Electrorefining Anode Cycle, Scrap Margin & Slime Balance Formula

Validate `Anode_Mass` in `[150, 600]` kg, `Anode_Scrap` in `[8, 35]`%, `Cathode_Area` in `[1.0, 3.6]` m², `Current_Density` in `[150, 480]` A/m², `Current_Efficiency` in `[80, 99.8]`%, and `Slime_Rate` in `[0.5, 30]` kg/t!

=LET(ma_k, B2, sc_p, B3, ac_m, B4, cd_j, B5, ce_p, B6, sl_r, B7, md_k, ma_k * (1 - sc_p / 100), IF(OR(ma_k < 150, ma_k > 600, sc_p < 8, sc_p > 35, ac_m < 1, ac_m > 3.6, cd_j < 150, cd_j > 480, ce_p < 80, ce_p > 99.8, sl_r < 0.5, sl_r > 30), "Invalid Refining Input", ROUND((md_k / 1000) * sl_r, 3)))

High-Intensity Overdrive (`j = 410` A/m², `Scrap = 19%`, `Eff = 92%`) Nodulation & Passivation Check

Push rectifier density to `B5 = 410` A/m² on high-nickel/antimony anodes where sulfate passivation forces `B3 = 19.0%` scrap pull and dendritic short-circuits drop efficiency to `B6 = 92.0%`: Daily Plating E3 rises to **`22.00` kg/d**, compressing Anode Replacement Cycle E4 to **`13.99` days** (`+34%` crane-handling congestion and anode-furnace remelt fuel) while Slime Capture E5 drops to `1.785` kg/anode!

=IF(ISTEXT(E5), E5, LET(md_k, B2 * (1 - B3 / 100), kd_d, ((B4 * B5) * 86400 * 63.546 * (B6 / 100)) / (2 * 96485.332 * 1000), ROUND(md_k / kd_d, 2)))

Further reading

• Arte Sheets Lesson — Copper Electrowinning Tankhouse Efficiency & Specific kWh/t
• Arte Sheets Lesson — Aluminum Sulfuric Anodizing Rule-of-720 Oxide Build Formula