mining reserve estimation
Over my years of working on and reviewing mining studies, ore dilution often seems to be one of the much discussed issues.  It is deemed either too low or too high, too optimistic or too pessimistic.  Project economics can see significant impacts depending on what dilution factor is applied.  They are numerous instances where mines have been put into production, and excess dilution has subsequently led to their downfall.  Hence we need to take the time to think about what dilution is being applied and the basis for it.

Everyone has a preferred dilution method.

I have seen several different approaches for modelling and applying dilution.   It seems that engineers and geologists have their own personal favorites and tend to stick with them.   Here are some common dilution approaches that I have seen (and used myself).
1. Pick a Number:
This approach is quite simple.  Just pick a number that sounds appropriate for the orebody and the mining method.  There might not be any solid technical basis for the dilution value, but as long as it seems reasonable, it might go unchallenged.  Possibly its a dilution value commonly seen in numerous other studies.
2. SMU Compositing:
This approach takes each percent block (e.g.  a block is 20% waste and 80% ore) and mathematically composites it into a single Selective Mining Unit (“SMU”) block with an overall weighted average grade.  The SMU compositing approach will dilute the ore in the block with the contained waste.  Ultimately that might convert some highly diluted ore blocks to waste once a cutoff grade is applied.   Some engineers may apply an additional dilution percentage beyond the SMU compositing, while others will consider the blocks fully diluted at this step.
3. Diluting Envelope:
This approach assumes that a waste envelope surrounds the ore zone.  One estimates the volume of this envelope on different benches, assuming that it is mined with the ore.  The width of the waste envelope may be linked with the blast hole spacing used to define the ore and waste contacts for mining.  The diluting grade within the waste envelope can be estimated or one may simply assume a more conservative zero-diluting grade.   In this approach, the average dilution factor can be applied to the final production schedule to arrive at the diluted tonnages and grades sent to the process plant.
4. Diluted Block Model:
This dilution approach uses complex logic to look at individual blocks in the block model, determine how many waste contact sides each block has, and then mathematically applies dilution based on the number of contacts.  A block with waste on three sides would be more heavily diluted than a block with waste only on one side.   Usually this approach relies on a direct swap of ore with waste.  If a block gains 100 m3 of waste, it must then lose 100 m3 of ore to maintain the volume balance.   The production schedule derived from a “diluted” block model usually requires no subsequent dilution factor.
5. Using UG Stope Modelling
I have also heard about, but not yet used, a method of applying open pit dilution by adapting an underground stope
modelling tool.  By considering an SMU as a stope, automatic stope shape creators such as Datamine’s
Mineable Shape Optimiser (MSO) can be used to create wireframes for each mining unit over the entire
deposit. Using these wireframes, the model can be sub-blocked and assigned as either ‘ore’ (inside the
wireframe) or ‘waste’ (outside the wireframe) prior to optimization.   It is not entirely clear to me if this approach creates a diluted block model or generates a dilution factor to be applied afterwards.


When is the Cutoff Grade Applied?

Depending on which dilution approach is used, the cutoff grade will be applied either before or after dilution.   When the dilution approach requires adding dilution to the final production schedule, then the cutoff grade will have been applied to the undiluted material (#1 and #2).
When dilution is incorporated into the block model itself (#3 and #4), then the cutoff grade is likely applied to the diluted blocks.
The timing of when the cutoff grade is applied to the ore blocks will have an impact on the ore tonnes and had grade being reported.

Does one apply dilution in pit optimization?

Another occasion when dilution may be used is during pit optimization.  In the software, there are normally input fields for both a dilution factor and an ore loss factor.   Some engineers will apply dilution at this step while others will leave the factors at zero.  There are valid reasons for either approach.
My preference is use a zero dilution factor for optimization since the nature of the ore zones will be different at different revenue factors and hence dilution would be unique to each.   It would be good to verify the impact that the dilution factor has on your own pit optimization by running with a factor to see the result.


My personal experience is that, from a third party review perspective, reviewers tend to focus on the value of the  dilution percentage used and whether it seems reasonable.   The actual dilution approach tends to get less focus.
Regardless of which approach is being used, ensure that you can ultimately determine and quantify the percent dilution being applied.  This can be a bit more difficult with the mathematical block diluting approaches.
Readers may yet have different dilution methods in their toolbox and I it would be interesting to share them.
There is another blog post that discussed dilution from an underground mining perspective.  This discussion was written by another engineer who permitted me to share their paper.    You can read that at “Ore Dilution – An Underground Perspective“.
The entire blog post library can be found at this LINK with topics ranging from geotechnical, financial modelling, and junior mining investing.
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2 thoughts on “Mining Dilution Prediction – Its Not That Simple

  1. hardrockminer

    Hi Ken, It’s been a while since I’ve visited your site. Nice to see you’ve continued your blog.

    Dilution is difficult to measure in most mines, particularly in open pits, and this is why (I think) there are so many different ways to put a decent estimate on it for the resource or reserve models. Add to this the fact that reserve models can be highly inaccurate on an annual measurement basis, or even on a life of mine basis, which means any attempt to measure dilution is highly subjective.

    Nevertheless, everyone knows that some estimate is required, else they will be questioned by their superiors as to why they didn’t include it. At the end of the month no one wants to see less metal produced than predicted by the plan. Positive surprises are always good but negative ones cause VP’s to issue directives to sort the problem out.

    When I do pit optimizations I usually include a small percentage for dilution and ore loss. My numbers are probably pie in the sky wrong but I know they will occur at some level so why not acknowledge their reality? Models are most reliable when they are at least close to reality.

    I’ve bookmarked your site and will try to get caught up on some of your blog posts. Being recently retired, I have a bit of time on my hands!

  2. Ken Kuchling Post author

    Thanks for the comments. Its been awhile since I wrote a blog since I ran out of topics to write about (and motivation). I have a small backlog of topics but sometimes the motivation isn’t there to work on them. I’m semi-retired and now have some time, so starting to go through my old blogs, modernizing them, making a few edits here and there, fixing missing links.

    Dilution is a funny one, everyone has opinion when the number is obviously wrong but tougher to come up with the correct number that should be used.

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