A case of ‘AND’ – partially overlapping high grade copper and gold regions in a porphyry copper. Source: Mike O’Brien using Leapfrog Geo 3.01

Author: Mike O’Brien, Senior Principal Consultant, P.Geo., Pr.Sci.Nat.

‘AND’ is a logic gate that sneaks up on mineral projects and destroys their value.

‘AND’ is a logical conjunction and, to grossly simplify, it implies the outcome of applying a series of factors in combination is only positive if each of the series of factors is positive. This logic gate controls a lot of things that we do.  For example, (Exam passed by Jane) = (Jane goes to school) AND (Jane goes to exam venue) AND (Jane obtained pass mark). All three conditions have to happen for Jane to pass the exam. (In lieu of political correctness, feel free to substitute John or any other suitable name to achieve gender neutrality).

Example: simple mineral project

Consider a hypothetical simple mineral project:

The chance of obtaining the breakeven grade in the ground is 70% and the chance of controlling the mining dilution to the required minimum is 70% (and neglecting all other factors).  The estimation geologist may feel that there is a good chance that the grade will be higher than the breakeven. The mining engineer may feel that there is a good chance of controlling the overbreak. On the face of it each believes there is a 70% chance of success; better than two out of three isn’t bad.  Independently they are happy guys based on correct independent assumptions and data. Party time. But the combination (probability of obtaining the breakeven grade in the ground) AND (probability of controlling the mining dilution) means that there is less than an even chance (49%) of getting both things right at the same time. (This simplistic treatment assumes both factors are independent, which is not necessarily true.)

The mining value chain consists of a series of well-meaning and usually expert specialists producing ‘best fit’ outputs which serve as inputs for the next  guy in line.  Not outrageously, add a 90% chance of obtaining the minimum necessary level of metallurgical recovery and add an 80% chance of obtaining the minimum necessary metal price to the grade and dilution probabilities in the hypothetical case.  Now we have only a 35% probability of achieving overall financial success.  Panic now. Sensitivity (‘spider’) diagrams are often used to illustrate the level of risk due to separate components of a project, but they do not convey the additive level of risk from multiple factors to the investor or the poor guy who has to build the mine.

In reality, each and every mineral project is beset with a multitude of assumptions applied to uncertain data and often combined by the dreaded ‘AND’. Individual parts of the process are carried out in good faith and with professional judgement, but it is not easy to combine the information  from different disciplinary silos to produce a meaningful outcome from very different perspectives on the world. Class 1, 2 and 3 engineering estimates do not easily reconcile with order of magnitude geology curve balls that nature loves to throw at the geologist. We walk a precarious path between engineering design drawings and the ‘unknown unknowns’ (to quote Donald Rumsfeld).

As we cannot rely on having the best quality mineral projects or the best prices, we need to organize and measure how we deal with the chain of uncertainty that binds and blinds us. Knowing the chain is there is only the first step. 


The illustration shows overlapping high grade probability regions for copper and gold (red and yellow respectively) generated using Leapfrog Geo™ 3.01. This graphical three dimensional example of ‘ ND’ shows a largely positive relationship in the upper portion of a porphyry copper deposit. For the full model go to https://youtu.be/yfKhgxi_CCw

About Mike O’Brien

Senior Principal Consultant, P.Geo., Pr.Sci.Nat. ARANZ Geo Limited – Expert Services (formerly QG Consulting)

For three decades Mike has been making a difference to Mineral Resources and mines. On the technical front, he has extensive experience in Mineral Resource estimation and geological modelling. He has managed technical teams to achieve results in mining companies and in consultancies. While the majority of his experience has been in gold deposits, he has expertise in the uranium, base metals and multi-product environment. A qualified geologist and geostatistician, he has been a team member and reviewer of due diligence and feasibility exercises in South Africa, Brazil, Ghana, Namibia, DRC, Russia, Kazakhstan, Uzbekistan, Colombia, Peru and the United States. Specialties: Mineral Resource estimation, geostatistics, Mineral Resource classification, Mineral Resource reporting codes, SAMREC, JORC.

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