Mineral Processing & Smelter Offtake
Mining Net Smelter Return (NSR) & TC/RC Formula
Calculate Concentrate Mass Pull, Minimum-Unit-Deducted Payable Copper Grade, Smelter Value per Dry Metric Tonne of Concentrate after Treatment/Refining/Freight Charges, and Mine-Mouth NSR per Tonne Milled.
Price sulfide concentrate offtake contracts accurately with unit deductions and TC/RCs!
Base-metal copper, zinc, and lead mines rarely pour pure cathode at the mine site—their flotation mill ships a Dry Metric Tonne (dmt) of sulfide concentrate of Concentrate Grade g_conc (e.g., 25.0% Cu = 0.25) to an overseas custom smelter! Under standard international copper smelter terms: (1) Payable Metal Fraction deducts the greater of a Percentage Haircut OR a Minimum Unit Deduction u_ded (typically 1.0% = 0.01 copper unit for slag losses, so g_pay = MAX(0, MIN(g_conc * f_pay_pct, g_conc - u_ded))); (2) Gross Payable Value per dmt concentrate is g_pay * 2204.62 * P_lb (or g_pay * P_mt where P_mt is $/MT LME Copper); (3) Smelter deducts Treatment Charge TC_dmt ($/dmt concentrate), Refining Charge RC_mt_metal * g_pay, and Concentrate Freight F_dmt; and (4) Multiplying Net Concentrate Value ($/dmt) by Mass Pull (g_ore * Rec_mill / g_conc) gives Mine-Mouth Net Smelter Return ($/t milled ore)!
Verify on Ore_Head_Grade g_ore = 0.010 (1.00% Cu, B2), Flotation_Recovery Rec_mill = 0.90 (90.0%, B3), Concentrate_Grade g_conc = 0.25 (25.0% Cu -> Mass Pull = (0.010 * 0.90) / 0.25 = 0.0360 = 3.60% or 27.78:1 concentration ratio, B4), Unit_Slag_Deduction u_ded = 0.01 (1.0% unit -> Payable Grade = 25% - 1% = 0.24 = 24.0% Cu = 240 kg/dmt, B5), LME_Copper_Price P_mt = $9,000/MT (B6 -> Gross Payable Value = 0.24 * $9,000 = $2,160.00/dmt), Treatment_plus_Freight_dmt TC_frt = $140.00/dmt ($80 TC + $60 ocean freight, B7), and Refining_Charge RC_mt = $800/MT payable Cu (~$0.36/lb -> 0.24 * $800 = $192.00/dmt, B8): Net Concentrate Value is 2,160.00 - 140.00 - 192.00 = $1,828.00/dmt (E3), and Mine-Mouth NSR per Tonne Milled Ore is 1,828.00 * 0.0360 = $65.81/t ore (E4, representing 0.8124 = 81.24% Smelter Realization of the $81.00 contained recovered metal in E5)!
| Copper Concentrate Offtake Metric (1.0% Ore, 90% Rec, 25% Conc, 1% Ded, $9k/MT Cu) | Formula | Verified Output |
|---|---|---|
| Concentrate Mass Pull Ratio | (g_ore * Rec_mill) / g_conc | 0.0360 dmt conc / t ore |
| Net Value per dmt Concentrate ($) | g_pay * (P_mt - RC_mt) - TC_frt | $1,828.00 / dmt conc |
| Mine-Mouth NSR per Tonne Ore ($/t) | Net_Conc_Value * Mass_Pull | $65.81 / t milled ore |
| Net Smelter Realization Factor | NSR_ore / (g_ore * Rec_mill * P_mt) | 0.8124 (81.24% Realized) |
Mine-Mouth Net Smelter Return (NSR $/t Ore) Formula
Validate 0 < g_ore < g_conc <= 1, 0 < Rec_mill <= 1, 0 <= u_ded < g_conc, and positive metal prices!
=LET(g_or, B2, rc_m, B3, g_cn, B4, u_dd, B5, p_cu, B6, tc_f, B7, rc_u, B8, IF(OR(g_or <= 0, rc_m <= 0, rc_m > 1, g_cn <= g_or, g_cn > 1, u_dd < 0, u_dd >= g_cn, p_cu <= 0, tc_f < 0, rc_u < 0), "Invalid Smelter Schedule", LET(ms_p, (g_or * rc_m) / g_cn, g_py, g_cn - u_dd, nv_c, g_py * (p_cu - rc_u) - tc_f, ROUND(nv_c * ms_p, 2))))Smelter Payable Realization Ratio Formula
Track NSR / Gross_Recovered_Metal_Value to see why shipping low-grade dirty concentrate (say g_conc = 15%) gets crushed by per-dmt TC + ocean freight!
=LET(ms_p, (B2 * B3) / B4, nv_c, (B4 - B5) * (B6 - B8) - B7, IF(ISTEXT(E4), E4, ROUND((nv_c * ms_p) / (B2 * B3 * B6), 4)))Try the example
Use the original values or change them to test your understanding.