24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Mining and Mineral Processing Engineering, 09-Mmp-A4 Mine Valuation and Mineral Resource Estimation, 2013-Dec. 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, compositing and support); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (NPV/cut-off grade methodology, cost estimating, financing structures); Torries, Evaluating Mineral Projects: Applications and Misconceptions (SME) (mine valuation, cost of capital, inflation treatment); Gentry & O'Neil, Mine Investment Analysis (net smelter return, smelter/refining contract terms); SME Mining Engineering Handbook, 3rd ed. (mineral economics, capital and operating cost estimating).
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.
Why compositing is required. Raw 1 m assay intervals have a much smaller physical support (volume represented) than the 15 m bench that will actually be mined and estimated as a block. Variography and kriging both assume a constant support across the dataset; mixing 1 m raw data directly with 15 m block estimation would violate that assumption and, through the volume–variance relationship, bias the estimated grade variance (raw short-interval data is more erratic/higher-variance than the bench-scale values it is meant to represent). Compositing standardizes support before any variogram or kriging work is done.
How it is done. The hole is divided into fixed-length composite intervals equal to the mining unit – here 15 m – honouring the actual bench elevations so that no composite straddles a bench boundary (compositing normally starts at a fixed datum, e.g. the collar or a bench-floor elevation, and proceeds down-hole in 15 m steps). Within each composite, the grade is calculated as a length-weighted average of the raw 1 m assays it contains: $$\bar{z}_{\text{composite}} = \frac{\sum_i l_i z_i}{\sum_i l_i}$$ For equal-length 1 m raw samples this reduces to a simple arithmetic mean, but length-weighting is essential whenever intervals are unequal (partial core recovery, broken/lost core, or a composite truncated at the bottom of the hole).
Only the composited values – not the raw 1 m assays – are then used to build the experimental variogram and to krige block grades, since the block estimate must be produced on the same support as the composite data feeding it.
