Question 23 of 27

Question 4.4 O’Hara mine-life rule (4 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.

The O’Hara rule. O’Hara (1980, CIM Bulletin) observed that, across a large database of built mines, milling/mining RATE scales as a power law of total ore reserves rather than being chosen independently: $$\text{Mill rate (short tons/day)} = 0.014 \times T^{0.75}$$ where T is total ore reserve tonnage (short tons). Implied mine life follows directly: Life (years) = T ÷ (rate×365). Illustrating with T=50 million short tons: $$\text{rate} = 0.014 \times (50{,}000{,}000)^{0.75} \approx 8{,}324\text{ stpd}$$ $$\boxed{\text{implied life} \approx 16.5\text{ years}}$$ (illustrative example; the paper supplies no specific reserve tonnage).

Accuracy for feasibility studies with time value of money. The rule is a useful ORDER-OF-MAGNITUDE sanity check — it reflects the real industry tendency for larger deposits to be mined at proportionally larger daily rates (larger deposits justify larger, more capital-intensive plants, and a too-slow rate on a huge deposit leaves capital idle for decades) — but it is empirical and BACKWARD-looking (fitted to already-built mines’ historical choices, not to a discounted-cash-flow optimum), and it embeds no metal price, cost, or discount-rate information at all. For a genuine NPV-based feasibility study, the OPTIMAL mining rate is the one that MAXIMISES discounted cash flow given the specific project’s price deck, cost structure and discount rate — which can differ substantially from O’Hara’s reserve-only regression, particularly for unusually high-grade, high-margin deposits (where NPV strongly favours mining FASTER than the historical-average rate, since a high margin makes accelerating cash flow very valuable at any realistic discount rate) or very low-margin deposits (where the historical rate may already be too aggressive). O’Hara’s rule is therefore best used as an initial screening/sanity-check figure early in a study, not as a substitute for an explicit NPV-optimised rate-sizing exercise.