Laboratory Testing & General Mineral Processing Engineering

Laboratory Testing & General Mineral Processing Engineering

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The Liberation Factor, l (3 replies)

R
Dick
7 years ago
Dick 7 years ago

My interest is in particulate sampling of ores in the minerals industry. The formula for the Fundamental Sampling Error devised by Pierre Gy in the 1950's includes a term we refer to as the Liberation Factor (l), a dimensionless number that varies between 0 and 1 and purports to measure the degree of liberation of target minerals from the gangue. The equation for the Liberation Factor is, l = (dl/dN)^0.5 where dl is the liberation size (in cm) and dN is the nominal top size of fragments in the lot (also in cm). In reading articles in process metallurgy, with a particular emphasis on liberation, I expected to see this equation used quite often as a measure of mineral liberation. I have not found it anywhere and I would like to know if it is currently used or if it is heavily disguised in other formats, but nevertheless used in principle. If it is not used, can I ask if there is there an equation akin to the Liberation Factor that is used in metallurgy?

I plotted a model for the Liberation Factor versus fragment size and got the following:

liberation factor
https://www.911metallurgist.com/wp-content/uploads/2017/04/Liberation-Factor.png
A
AJNeale
7 years ago
AJNeale 7 years ago

Hi Dick - you've raised questions about sampling that I haven't thought about for 20 years.  I did a masters in engineering in the 80s studying digital simulation (in FORTRAN if you can believe that) and advanced process control, so spent a lot of time studying math in general (state-space estimation, Kalman filters, geostatistics, etc.) and sampling theory in particular.  The problem with Guy's work, and some of the other French mathematicians that looked at sampling theory, is that very few of us could get through the math.  If you suffer from insomnia, Guy's book is a great cure - :-).

The problem with sampling is the practical limitations.  If you look at drilling off an ore body, sampling production at an operating mine (underground or open pit), or sampling at an operating plant, the sample size is driven by time & cost concerns (i.e. how many holes can you afford to put in a deposit before you think you fully understand it?), and practical limits on how large a sample you can handle.  At one project we set up the automatic head and tails samples to fill up a 5-gallon pail over the two hour sampling period.  This was something that the operator could carry to the lab every two hours, and the lab guys could process (filter, split, dry, split, pulverize, split, assay) and get the numbers turned around and back to the operator in two hours.  Similarly, in a block cave, when sampling at the draw point, the guys (or gals) will only take the samples that fit into their sample bag, so never sample that 1 m3 rock in the draw point.

So I know I'm getting cynical in my old age (59), but all the sampling mathematics goes out the window when it comes to developing functional sampling procedures - and this coming from a guy who's known as a numbers geek - i.e. I don't dismiss numerical approaches easily.  On the other hand, consultants have made a living going from mine to mine convincing the operator that their sampling methodologies are insufficient, and advising them how to improve them, only to see them fail the minute the consultant leaves the property.

I have been told that Pretium have commissioned a novel sampling approach to deal with their very high grade, very nugget deposit, and internally have quantified great repeatability.  I'm not sure if anything has been published on this, but if you send me an e-mail (andrew.neale@seprosystems.com) I can provide you with a contact.

So bottom line, at the operations level, I'm see very few people talk in terms of liberation factors, but rather in terms of avoiding obvious sampling biases during the primary and secondary sampling procedures, and getting as good a sample as possible to the assay lab.  While a great deal of focus is usually paid to sample handling techniques and assaying procedures inside the lab, in practical terms, all the sampling and sample handling errors occur prior to the sample being delivered to the lab.

Perhaps not the response you were looking for, but hopefully something to put sampling into a context that can assist you with your work.

Best Regards

Andrew

P
Philip Stewart
7 years ago
Philip Stewart 7 years ago

Why bother with a formula, which is little more than a guess, when there is now a proliferation of instruments with the capability of providing direct measurement of the association of one mineral with another - Mineral Liberation Analyser, QEM*SEM, etc.  CSIRO (Australia) are expert in this as are several companies providing services in this area.  The skill comes in providing meaningful samples and deciding which mineral phase associations are the most important in terms of processing and the maths comes in converting what is essentially 2D data to 3D.  Mineral to mineral to mineral interfacial areas are measured unambiguously but other data can require interpretation.

 

M
Marcia
6 years ago
Marcia 6 years ago
1 like by David

I may be mistaken, but today we use in practice tools like QScan or MLA that provide this information coupled with chemical / mineralogical compositions.
We have used these tools a lot. However, attention should be paid to the preparation of samples. We use a preparation (grinding and sorting) that resembles industrial mineral processing.

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