Mineralogical Modelling: Rule of Thumb vs Probability Methods (Part 1)

This is the first of two blog posts on mineralogical modelling where we highlight some of the terminology used and misconceptions made.  Part 2 will further develop the theme by comparing the value of using rule-of-thumb and probability -based particle modelling principals.

Liberation

Many users of mineralogical analysis focus only on elementary concepts such as grain size.  Yet there are many levels of depth available to analyse liberation data.  In this section we focus on using liberation data in a simulation model.  Critical to understanding mineralogy is the concept of ‘liberation’.  A particle is considered liberated if it consists of only one mineral.  Conversely a particle is considered ‘barren’ if it contains no valuable mineral.  There are a few issues with ‘liberation’ defined in this way.  For a start is it really important if a particle is say 99% valuable mineral rather than 100% mineral?  Because the purest definition (particles consisting of only valuable mineral) is of limited value, the word ‘liberation’ has become generalised, and to some extent over-used.  Yet when discussing ‘liberation’ generally we are simply referring to how distinct the valuable mineral is from the associated gangue.

Fig 1. Various definitions of particle types (Liberated, Binary, MultiMineral)

For the ‘Binary particle’ consider the yellow area as being the mineral of interest.  The issue arises as to whether we would like to float the particle as is, or grind the particle further  (in order to reduce the non-valuable mineral component in the particle).  Clearly there is a trade-off; float particle as is (and decrease grade), or grind particle to smaller sizes (and increase energy costs).

One of the important issues about mineralogical analysis is the use of jargon words rather than terms that have more general statistical meaning.   This means that there is disconnect between statistical analysis and mineralogical analysis where there shouldn’t be. For example the expression ‘liberation distribution’ is often used to represent the distribution of mineral within particles, however this can be misleading.  Rather than use this term, it is more precise if one calls this distribution the ‘mineral composition distribution’ as this is far more consistent with established statistical terminology.

Multimineral particles

The third particle in Figure 1 is a multimineral particle.  If the particle were ‘multimineral’  and the original mineral were also valuable, the decision as to whether to float or regrind is rendered more difficult.  Here the word ‘multimineral’ is used and is sometimes called ‘ternary’.  When a particle is multimineral; and say there are two valuable minerals, and one nonvaluable mineral; we cannot just lump the two valuable minerals together and describe them as a single valuable mineral.  Why?  Because the value of the minerals and the processing properties of the minerals could be very different.  For example galena is targeted for recovery in the lead circuit and chalcopyrite is targeted in the copper circuit.  Yet if a particle contains both chalcopyrite and galena, where will it report?– the copper product or the lead product.  Only a detailed analysis of the circuit (inclusive of mineralogical analysis) can answer this question, and by understanding how particles are behaving in the circuit can we improve the process with a view to increasing profit.  Hence we can consider an ore types as ‘simple’ or ‘complex’.

A ‘simple ore’ is one in which there are only two minerals of interest.  That is a valuable mineral of interest and an associated gangue mineral.  Generally, although not exclusively, iron ore and coal are considered ‘simple’.  A complex ore is one in which there are numerous minerals.

Because the information obtained from mineralogical analysis is potentially detailed, the user must decide whether to use simple rule-of-thumb approaches; i.e. ‘grain-size indicates grind size’; or whether to use thorough mineralogical analysis linked to simulation.  Recently, software for detailed mineralogical analysis for simulation has been developed (such as that by Stephen Gay); and here we discuss some of the concepts of simulation briefly.  These concepts include particle based modelling, stereology and probability methods.

Stereology

Thus far I have used the word ‘particle’ often; yet when we perform mineralogical analysis we reveal particle sections; not particles.  In order to accurately estimate the multimineral compositions of particles we need to apply a ‘stereological’ adjustment.  The word ‘stereology’ has multiple meanings: and therefore leads to some confusion.  Here stereology is defined as relating information from various dimensions.  An alternative definition of stereology is the spatial structure of particles (which is a very different definition).

For example we estimate particle multimineral composition (three-dimensional information) from linear intercepts (one dimensional information) or particle sections (two dimensional information).  Methods to perform stereological adjustment are necessarily mathematical, but are available from the author (Stephen Gay).  Figure 2 indicates the stereology problem.  Even though the particle is composite it can appears liberated, barren or composite.  What this means in practise is the number of liberated particles is always larger than there really is.  Also, the number of intercepts does not mean that stereological error is reduced.  The only way to remove the error due to the stereological effect is to apply what is called a stereological correction or stereological adjustment.

Fig 2. Three Linear Intercepts through a binary particle. The first intercept indicates the 2D particle is the ‘red’ mineral. The second intercept intercept indicates the yellow mineral. The third intercept indicates the 2D Particle is composite

References and Bibliography

The life of Ludwig Boltzmann  http://en.wikipedia.org/wiki/Ludwig_Boltzmann.
Gay S.L 2004  A liberation model for comminution based on probability theory, Minerals Engineering. Vol. 7, No. 4: pp. 525-534.
Gay  S.L. 1994 Liberation Modelling using particle sections (1994) PhD thesis.  Julius Kruttschnitt Mineral Research Centre, The University of Queensland.
Gay S.L.  2014 MMPlantMonitor.  A new software system for monitoring processing plants http://circlepad.com/MathsMet/MMPlantMonitor
Gay SL  & Vianna S 2002 Mass Balancing – Considerations for reconciling mineralogical data. AusIMM Value Tracking Symposium, Brisbane pp. 131-140.
Jaynes E.T. 1995 Probability Theory: The Logic of Science , Available directly from the internet:  http://shawnslayton.com/open/Probability%20book/book.pdf
Keith J.M.  2000 A Stereological correction of multimineral particles.  PhD thesis.  . Julius Kruttschnitt Mineral Research Centre, The University of Queensland.
Latti D. 2006 The Textural Effects of Multiphase Mineral Systems in Liberation Measurement.  PhD thesis.  Julius Kruttschnitt Mineral Research Centre, The University of Queensland.
Shannon  C.E. , Weaver W.. 1949 The Mathematical Theory of Communication. Univ of Illinois Press, 1949. ISBN 0-252-72548-4.
A full list of JKMRC PhDs is available at: https://www.jkmrc.uq.edu.au/Publications/PostgraduateTheses.aspx