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.
Data used. A variogram is built from spatially-located assay data – every sample (drill-core interval, blast-hole, channel sample, etc.) must carry both a grade value and 3-D coordinates, so that the separation vector between any two samples is known. The richer and more regularly spaced the drilling grid, the more directions and lag distances can be modelled reliably.
How the calculation is made. For a chosen lag distance h (within a lag tolerance) and a chosen direction (within an angular/azimuth and dip tolerance, and a band-width limiting how far off-line a pair may fall), every pair of samples separated by approximately h is found, and the experimental semivariance is computed as $$\gamma(h) = \frac{1}{2N(h)}\sum_{i=1}^{N(h)} \left[z(x_i) - z(x_i+h)\right]^2$$ where N(h) is the number of pairs at that lag. Repeating this for a sequence of lags produces the experimental variogram (a scatter of γ(h) versus h), to which a permissible theoretical model (spherical, exponential, Gaussian, etc.) is then fitted, yielding a nugget, sill and range for that direction. The exercise is normally repeated in several directions to test for anisotropy.
Information the model provides. The fitted model quantifies the deposit's spatial continuity: the nugget reflects short-scale/micro variability plus sampling and analytical error; the sill is the total (a priori) variance of the grade population; the range is the distance beyond which samples are effectively uncorrelated (defining the practical search-neighbourhood radius); and the shape of the rise from nugget to sill describes how quickly spatial correlation decays. These parameters are not academic – they are fed directly into the kriging system as the covariance/semivariance model that determines every block-estimation weight, and they set defensible search-ellipse dimensions and resource-classification (Measured/Indicated/Inferred) criteria.
