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24-MMP-A4 Mine Valuation and Mineral Resource Estimation · May 2013

Question 13 of 13: Net Smelter Return for a Blast-Hole Sample

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2013-May. 3 hours duration; one handwritten 8.5×11 in reference sheet permitted (not an open-book exam); only approved Sharp or Casio calculators allowed. Question 1 is compulsory (40 marks, parts 1.1–1.7); candidates then select FOUR of the six optional Questions 2–7 (15 marks each) to complete the paper.

Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging estimators, volume–variance relations); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV and cut-off grade methodology, mineable reserves, selective mining units); Gentry & O'Neil, Mine Investment Analysis (Canadian mining taxation, smelter/refining contract terms, net smelter return); SME Mining Engineering Handbook, 3rd ed. (mineral exploration and evaluation stages, ore reserve classification).

Question 7: Net Smelter Return for a Blast-Hole Sample (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

MetalPriceConc. gradeTreatment/transport costSmelter recovery
CuCAD 2,500/t20% CuCAD 185/t concentrate60%
ZnCAD 1,875/t52% ZnCAD 350/t concentrate80%
AgCAD 28/troz— (no charge)—14%
AuCAD 1,600/troz— (no charge)—55%

Blast-hole assay: 0.2% Cu, 0.8% Zn, 0.30 g/t Ag, 0.02 g/t Au (1 troy ounce = 31.1035 g).

Find. The NSR contributed by each metal, and the total NSR, per tonne of ore for this blast-hole sample; then how the mill-gate NSR is modified to represent broken rock at the pit face.

Approach. For a metal with a treatment charge quoted per tonne of concentrate (Cu, Zn), express the treatment charge per unit of contained/recovered metal by dividing by the concentrate grade, then net the per-tonne-of-ore revenue against the per-tonne-of-ore treatment cost. For Ag and Au (no smelting/transport charge, recovered directly in the concentrator) NSR is simply the recovered-metal revenue.

  1. Copper. Metal recovered per tonne of ore = grade × recovery = 0.2% × 60% = 0.0012 t Cu/t ore. Revenue = 0.0012 × 2,500 = 3.00 (CAD/t ore). Concentrate produced per tonne of ore = recovered metal / conc. grade = 0.0012/0.20 = 0.0060 t conc./t ore. Treatment cost = 0.0060 × 185 = 1.11 (CAD/t ore). $$NSR_{Cu} = 3.00 - 1.11 = \boxed{1.89\ \text{CAD/t ore}}$$
  2. Zinc. Metal recovered = 0.8% × 80% = 0.0064 t Zn/t ore. Revenue = 0.0064 × 1,875 = 12.00 (CAD/t ore). Concentrate produced = 0.0064/0.52 = 0.01231 t conc./t ore. Treatment cost = 0.01231 × 350 = 4.31 (CAD/t ore). $$NSR_{Zn} = 12.00 - 4.31 = \boxed{7.69\ \text{CAD/t ore}}$$
  3. Silver. Convert grade to troy ounces per tonne: 0.30 g/t ÷ 31.1035 g/troz = 0.009646 troz/t ore. Metal recovered = 0.009646 × 14% = 0.0013504 troz/t ore. No treatment charge (recovered directly in concentrator), so NSR is pure revenue: $$NSR_{Ag} = 0.0013504 \times 28 = \boxed{0.038\ \text{CAD/t ore}}$$
  4. Gold. Convert grade: 0.02 g/t ÷ 31.1035 g/troz = 0.0006431 troz/t ore. Metal recovered = 0.0006431 × 55% = 0.0003537 troz/t ore. $$NSR_{Au} = 0.0003537 \times 1{,}600 = \boxed{0.566\ \text{CAD/t ore}}$$
  5. Total NSR. Summing all four metal contributions: $$NSR_{total} = 1.89 + 7.69 + 0.038 + 0.566 = \boxed{10.19\ \text{CAD/t ore}}$$
MetalNSR (CAD/t ore)
Copper1.89
Zinc7.69
Silver0.038
Gold0.566
Total NSR10.19

Modifying NSR to value broken rock at the pit face. As defined, NSR nets the mill-gate value of the ore's contained metal against the smelting/transport charges downstream of the mill – but it still implicitly assumes the ore has already been mined, hauled and processed through the mill (milling and G&A costs are not yet subtracted). To give a mining engineer or grade-control geologist the cash value of BROKEN ROCK sitting at the pit face, ready to be loaded and hauled but not yet committed to the mill, the NSR must be further reduced by every cost still ahead of that rock at the point of the loading decision: $$\text{Mining Cash Value (MCV)} = NSR - C_{mill} - C_{G\&A} - C_{haul}$$ where C_mill is the ore-processing (milling/flotation) cost per tonne, C_haul is the incremental haul cost to the mill (versus to a waste dump, which is typically shorter/cheaper), and C_G&A is an allocated share of general and administrative overhead. The blast-hole/loading-unit decision then reduces to a single, directly comparable number: if MCV > 0 (or, more precisely, if MCV exceeds the avoided cost of instead hauling to waste), the material is loaded as ore; otherwise it is waste (or low-grade stockpile, per Question 4's Category 2/3 logic).

Value of the modification. This conversion is invaluable precisely because the loading/dispatch decision happens in real time at the shovel, using blast-hole assay results, long before the material ever reaches the mill – a mill-gate NSR alone cannot be used at that point because it doesn't yet reflect the cost of getting the rock from the pit to the mill and through it. Expressing value as a single MCV number per blast-hole sample or block lets a dispatch system route each truckload to mill, low-grade stockpile, or waste dump purely by comparing MCV against the relevant cut-off, directly maximizing the realized value of every tonne mined rather than relying on a coarser, resource-model-based ore/waste boundary.

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