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## Sample Homogenization (4 replies)

A few comments and questions:

- I don't see any issues with monitoring the variogram of the ratio - I expect that MgO and SiO2 are strongly correlated in this type of material?
- Rather than working with SDs (which are not statistically additive) I suggest you standardise your variograms to the (sill variance). So your sill of 0.08^2 is 0.0064(Ni)^2 which when standardised is 1. The nugget of 0.07^2 is 0.004(Ni)^2 so nugget effect 0.625 or 62.5% of the variance. As such the estimated correlation between two repeat samples (in theory) collected at the same location in the belt is 1-0.625=0.375 or 37.5%.
- Can you please explain what you mean by 'blending factor' - how are you calculating this?
- To predict the 2 hr feed variability I would need to know the flow rate on the belt and whether this belt represents the total stream to the plant - this may be confidential (?) but perhaps you could offer some conceptual numbers?

Blending from more pits may help in reducing variability and interim blending of stockpiles can help in front of the plant. I once completed a conditional simulation exercise to demonstrate this in a bauxite mine. This is a lower capital cost approach but does increase operating cost due to the need to re-handle the ore from the interim stockpiles. Again you can evaluate this cost using simulation methods

We implemented some upfront blending from the pit to the ROM pad at a copper mine in the DRC to try and stabilise the plant feed grade. The previous procedure was to blend from up to 9 stockpiles on the ROM pad. Feed grade variation of up to 1% Cu were reduced to 0.5%Cu or less (based on a average feed grade of about 3.5-4% Cu).

It would appear that the indicator you should use for measure should be the indicator of primary commercial interest, be it the ratio SiO2/MgO or one or more of the individual constituents.

Contrary to the common view consider: What is called the nugget variance for a variogram is only the variance of sample preparation and analysis and is easily measured by sample duplication. Keeping in mind that all batches of material that are of practical interest are finite and that there is no variogram sill unless the qualities of the finite population of collected increments are random, which is not at all likely.

It appears that your 6-hour sampling intervals for the blended product may not be sufficient.

The task here for your purpose is to collect the variogram data for the feed material and the varoigram data for the blended material then calculate a measure of the efficiency of blending. To do this you will need to first calculate an equation for each variogram based on the data collected. You will then need to do some math to put the variograms on the same basis in order to determine the effectiveness of the blending. Much of the math to do this is in my paper "Evaluation of Precision Being Obtained by a Three-stage Sampling System for Coal" presented at AusIMM Sampling 2012 conference in Perth. By the way, the variogram data should be for individual sampling increments, not batches of multiple increments.

Using the approach above I have successfully evaluated coal blending being done with off-shore terminals.

Sorry for the delay in answering, I work on this mainly on my "off time".

Yes SiO2 and MgO are strongly correlated, thanks for that it confirms our approach and 3) Actually I am working on Stdev because the required specification for our ore is a stdev of a certain value over 2 hours (which is about 1 000 tonnes of ore, which is the total stream). Also here the "blending factor" = (stdev pre-mixing) / (stdev after-mixing). At the moment they just take a raw standard deviation on sample data, but given our specifications, I'm thinking we should use the squared root of the 2-hour variogram on the after-mixing sample data.

Also my issue is that the pre-mixing sampling is an in-line CNA and the after-mixing is a poor quality sampling analysed in the lab. Hence different analytical qualities, sampling error, sample sizes, etc. Added to that an insufficient frequency on the after-mixing material, the difficulty to answer the question: have we fully homogenized our ore, and if not, how much more can be done ?

At the moment I consider that is the variogram on the after-mixing samples is flat, then according to Pierre Gy's theory on bed blending, my ore has reached maximum homogenization. However if it's not completely flat, then I word it as for example "2-hr standard deviation is 0.1 while it would be 0.06 if fully homogenized".

We have considered this approach but it is not achievable on our site, due to the lack of flat surfaces. As the chief engineer says: "Space is often more important than nickel here !"

I agree that our 6 hour sampling is insufficient given our spécifications. I'd be interested in reading your paper, would you mind forwarding it so I can assess if we can implement your method ?

I am currently working on evaluating the homogenization of our process (currently done with a stacker doing windrows, about 30 layers). For that I have cross-belt sample data (measurement every 20 minutes) before homogenization, and after homogenization a fairly poor quality taken by stopping the conveyor belt (every 6 hour !! even though I have a small dataset every 1 hour). Few questions for the community of experts which would really help us get more certainty: