24-MMP-A4 Mine Valuation and Mineral Resource Estimation · December 2018
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, 2018-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 1.1–1.8); candidates then select THREE of the five optional Questions 2–6 (20 marks each) to complete the paper.
Reference texts: Isaaks & Srivastava, An Introduction to Applied Geostatistics (variogram modelling, kriging, anisotropy); Hustrulid, Kuchta & Martin, Open Pit Mine Planning and Design (mine valuation, NPV/IRR and cut-off grade methodology); Gentry & O'Neil, Mine Investment Analysis (smelter/refining contract terms, net smelter return, taxation and risk); Guilbert & Park, The Geology of Ore Deposits, and Evans, Ore Geology and Industrial Minerals (VMS/SEDEX and porphyry deposit models); SME Mining Engineering Handbook, 3rd ed. (mineral exploration/evaluation stages, ore reserve classification); CIM Best Practice Guidelines and NI 43-101 (Canadian Securities Administrators).
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.
Method of sections began as hand-drafted cross-sections spaced along a vein or tabular body, with the geologist planimetering each section's ore area by hand and averaging grade between adjacent sections by the trapezoidal or prismoidal rule — a purely manual, drafting-table process. Calculators sped up the volume/tonnage arithmetic once section areas were measured, and computer-aided design (CAD) later automated both the area measurement (digitized polygons) and the inter-section volume integration, but the method's logic — interpolate between parallel geological sections — is unchanged and remains the natural choice for narrow, steeply dipping, structurally continuous bodies (veins, tabular VMS lenses) where a geologist's interpreted section is more reliable than a statistical grid.
Method of polygons assigns each drill hole its own area of influence (a polygon, often constructed by perpendicular bisectors between neighbouring holes) and applies that hole's grade uniformly across its polygon. Manually this meant drafting polygons on a plan with a protractor and planimeter; calculators allowed polygon-area and tonnage summation by hand-entered coordinates; GIS/mine-planning software (e.g. Voronoi/Thiessen polygon routines) now generates and areas the polygons automatically. It suits early-stage, widely and irregularly spaced drilling in a reasonably homogeneous, low-nugget orebody, but gives a blocky, non-smooth grade model and no explicit estimation-error measure.
Inverse-distance-squared (IDW) weights nearby samples by 1/d² to estimate a point or block grade, smoothing the polygon method's abrupt boundaries. By hand this required tedious repeated distance and weight calculations per block; calculators made routine grids feasible; computers made full 3-D block-model IDW (searching hundreds of composites per block) standard practice from the 1970s–80s onward. It works well for moderately continuous disseminated deposits without strong directional anisotropy.
Geostatistics supplants all three by first quantifying spatial continuity objectively (the experimental and modelled variogram) rather than assuming it, then using that model to derive statistically optimal, minimum-variance weights (ordinary/simple kriging) that also honour anisotropy and provide an explicit estimation-variance map — the basis for modern NI 43-101 resource classification (Measured/Indicated/Inferred), which sections, polygons and IDW cannot themselves produce.
