Modelling density for resource estimation often becomes an afterthought, or only when a consultant asks for it which often leaves companies scrambling for a balance. Significant time is devoted to grade modelling as a primary focus, but density is a critical component in converting volumetrics into tonnages and should be considered carefully. Grade, volume, and density form the three pillars that underpin any resource estimation. It is important that each component be sufficiently examined to provide meaningful results.
Figure 1: A block model of the Micromine Raven training dataset showing density being modelled using Ordinary Kriging.
In this article, we will review some current industry practises for modelling density and suggest methods that can be employed to ensure effective modelling of density to robustly support a resource estimation.
To be clear, this article will jump between the use of the term density, which is defined as "mass per unit volume (e.g., Pounds per cubic foot (lbs/ft3) or grammes per cubic centimetre (g/cm3)), and bulk density, which is the density value that accounts for void space and porosity .
Sadly, this term has been used interchangeably used during the resource estimation process with the term specific gravity or relative density, which is a measure of the density of a material in comparison to water (and unitless). Specific gravity does not take into account the void space or porosity and its use may over-state the tonnages. It’s important that users understand the difference between these technical definitions.
The problem is clear: after reviewing competent persons reports, sufficient modelling of bulk density is often lacking. Giles Arseneu's 2013 publication on "Estimation of Mineral Resource Reporting" conducted research into 50 technical reports filed on SEDAR.com, found that only 20% of the reports reviewed, utilised a density-specific data set, with the data being used to estimate the density independently for each block of the block model, while 18% of the reports reviewed did not discuss density at all. Some 58% of these documents reported a simple average density value, not taking the distribution of the data into consideration. Such findings really emphasise the lack of importance attributed to one of the three pillars of resource estimatimation.
Sampling methods for bulk density is well established and should be employed from the very first drillhole. As resource estimation relies on three main inputs: Grade, volume, and density, attempts should be made to balance the collection of grade and density samples. The most commonly used methods for bulk density and specific gravity measurements are summarised below in Table 2. Such methods have advantages and disadvantages and do not necessarily suit all deposit types, so selection criteria should be identified to check suitability. One way is to seek advice from the resource geologist early and avoid issues at a later data. Many projects have been delayed due to the confusion between density and specific gravity measurements.
The interplay between moisture content and density should also be considered for certain commodities and cannot be assessed using the methods below. Samples should be dry before measuring density as mineral resources are typically reported as dry tonnes.
Table 2: A table displaying a commonly used method for density sample collection.
So, what does suitable density modelling, or more accurately, bulk density modelling, look like? We need to ensure the following criteria are assessed: as density is one of the three pillars; sampling must be prioritised at the same level as geochemical sampling from the outset of the exploration programme. The modelling of bulk density should reflect the in-ground variability. Studies should be conducted to better understand how bulk density varies based on lithology, mineralogy and metal content. Often, there is a direct link between grade and density, and this should be one of the first steps in the mineral resource estimate. The scatter plot of iron versus density data from Gümüştaş' Bolkar Project, Türkiye in Figure 3 shows that there is a strong correlation between iron content and density, as one would expect. As part of the study, It would be advisable to investigate further controls and the spatial extent of these kinds of relationships.
Too often, easy and loose-fitting simple averages of the density are assigned per domain; this lazy method can have significant implications for an estimation. But this doesn’t have to be the case and should be the normal default procedure. Having parity between grade and density samples, means the density samples can be interpolated just like a grade item, after all, they are still numbers and numbers love to be Kriged. Twinning the modelling of density and grade provides a much more accurate prediction of in-grade density behaviour. This works well when modelling domains and density closely related to mineralisation. Density can also be modelled independently where sufficient population data supports independent research into in-situ variability.
Figure 3: A scatter plot investigating the relationship between iron content and density for the Gümüştaş' Bolkar Project, Türkiye.
Modelling grade and density concurrently was one of the many methods used for the recently completed modelling work for Esen Maden (Gümüştaş) at the Bolkar deposit. Modelling has been completed by Addison Mining Services (AMS), who were able to draw upon the strengths of robust and plentiful density sampling.
Figure 4: A block model and drillhole display showing bulk density modelling of vein 12 of the Bolkar deposit.
With data kindly provided by Gümüştaş, we have been able to highlight the importance of effective density sampling. The Bolkar deposit has been used to investigate the impact that poor density sampling can have on the resource estimation process. This project has been showcased because of its exemplary density sampling campaign. Just under 5,000 bulk density samples have been collected, which is 20% more than any singular-grade items. Bulk densities were collected during the logging stage and measured using the Archimedes method (Table 2). The abundance of bulk density values also meant that Addison Mining Services was able to run a QAQC report on the bulk density sampling, further improving confidence.
Table 5: Vein report of the Bolkar deposit, including both modelled bulk density and simple average density.
In Table 5, I have attempted to quantify the damage that using a simple average density can have on the resource estimation process. In Table 5, the normal reporting breakdown, which includes the modelled bulk density is presented. For reference, this bulk density has been formulated by Kriging the bulk density values alongside the grade items. This contrasts with the simple average bulk density, which is a mean average value generated from bulk density values in the domain.
Admittedly, there is a large population of density samples; however, domain restrictions during the modelling process have significantly reduced the sample population size for both applicable grade and bulk density samples. Similar to geochemical samples, density samples have to be domained. Ultimately, the available samples were significantly reduced, and this puts further pressure on selecting an appropriate modelling technique.
Table 5 reports the top five largest (by volume) veins of the Bolkar deposit. There are significant fluctuations from -4% to +29% of predicted tonnage based on modelling density using a simple average. Such fluctuations are important and can undoubtedly have substantial implications for any project. In short, having a poor density modelling strategy will result in unreliable tonnage estimates. For the Bolkar deposit, I have shown how this could potentially have resulted in tonnage estimates being up to a third different.
But why is this the case? The answer is very simple: using the simple average doesn’t effectively represent the in-ground variability of the density and produces errors in local estimation. Modelling either independently or twinning with grade provides a much more effective means of estimation. Density in estimation is equally as important as grade and volume.
It should also be noted at this stage that metallurgical properties should not be overlooked. Consideration of bulk density should go hand in hand with efforts to start considering and modelling geometallurgical properties during the resource estimation process. Geometallurgical properties, such as recovery (based on deleterious elements), potential acid consumption and hardness can be interpolated, but this is a topic for another day.
Also related to this topic is core recovery. Often core recovery is a silent partner in the equation and as A. E. Annels &S. C. Dominy 2013 pointed out in their article, Core recovery and Quality. Heavy core losses throughout an ore body intersection can seriously undermine the confidence in a resource estimate. But how if any, do mineral resource estimates account for core loses other than downgrading confidence of samples? And are missing intervals treated as having no grade? Relevant here and as suggested by Annels 2013 is investigating if a relationship exists between grade and core recovery. Poor recovery that can be attributed to geological factors could in theory be modelled and assist with improving the understanding of bulk density and fracture networks.
Density is an important variable and one of the three pillars that support the resource estimation process. There is significant variation in how density modelling strategies are employed, and hopefully this article emphasises the “why?” of bulk density modelling should be seriously considered. With all things mining-related, there isn’t a one-size-fits-all approach. The modelling process is extremely subjective (something the Parker Challenge attempts to define) and can be hugely different based on different types of mineralized deposits. For example, density sampling strategies will be extremely different for a SedEx and placer deposits as opposed to a porphyry copper deposit. The above suggestions attempt to offer ideas but are not prescriptive. The density strategy should evolve with the project, becoming more developed with its advancement. The most important thing is to collect density data early and often!
Acknowledgements
Sincere thanks to Gümüştaş Madencilik A.Ş. ( for permission to use their data from the Bolkar Pb/Zn mine in Türkiye.
Thanks to the assistance and support of Lewis Harvey of Addison Mining Services (addisonminingservices.com), for his help with the writing of this article and arranging access to the data.
References
Arseneau, G.J. 2013. Estimation of bulk density for mineral resource reporting. Internal SRK Report
Annels A. E. & S. C. Dominy 2013 Core recovery and quality: important factors in mineral resource estimation
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