On the "Old", but relevant drill hole spacing analysis and drilling optimisation workflows
Mesh of 3D Drill holes

On the "Old", but relevant drill hole spacing analysis and drilling optimisation workflows

Drillhole spacing studies aim to quantify the confidence gained from increased drilling density. This can be measured in terms of improved theoretical estimation quality or enhanced predictability in mine production (https://www.mining-plus.com/post/drillhole-spacing-studies#:~:text=A%20drillhole%20spacing%20study%20based,grid%2C%20and%20comparing%20the%20results.). Typically, these studies support Mineral Resource Classification but also inform infill drilling programs for resource definition or grade control drillhole design. All studies rely on well-defined domains and a reliable variogram model.

Common workflows for drillhole spacing studies

Several drillhole spacing workflows have been proposed by different practitioners and some of the most frequently used three are:

  1. Estimation Quality Studies

Estimation quality studies involve producing grids of artificial drillholes with increasing grid dimensions, running theoretical estimates based on each drilling grid, and comparing the results. The statistics used to compare the quality of estimates are typically the slope of the regression (SR) or kriging efficiency (KE)

2. Single Block Kriging Studies

The single block kriging method assesses the variability of grade estimation over various production periods for various drillhole grids.

3. Conditional Simulation Studies

Conditional simulation-based DHS studies aim to quantify the reduced risk resulting from increased drilling. This may be quantified using the production rate and the “15% error at 90% confidence interval” rule or related to specific value drivers such as net smelter return, the thickness of the transitional zone, or the presence of deleterious elements.

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Currently, in our geometallurgy and machine learning research group, we have 4 MSc students working on developing alternative practical methods for drill hole spacing analysis and optimisation. One of the techniques currently explored by the candidates at the Wits School of Geosciences is Dual drillhole spacing optimisation considering workflow parameter uncertainty. The reason for writing this short brief is to call for comments from academics and industry practitioners that can help our students improve their workflows. The workflow involves:

It all starts from the drill core and uncertainty on logging techniques:


Example of virtual drill core logs

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Then.....

  • Composite Boreholes: Combine borehole data to create composite samples that represent continuous intervals of geological interest.


Systematic quantification of ideal composite length


  • Calculate Data Distribution: Determine key statistical measures of the composite data: Mean (??) Variance (??2) Percentiles (25th, 50th, and 75th) Kurtosis Skewness Coefficient of Variation (CV)


Example of descriptive statistics


  • Cell Decluster Exploration Drillhole Data: Apply declustering techniques to correct for sampling bias in the spatial distribution of exploration drillholes.


Example of Cell Declustering

  • Model a Normal-Score Variogram for the Element and Area of Interest: Transform the data to normal scores.


Example of Normal Score transformation

  • Calculate Experimental Variogram and Fit Spherical Models: Calculate the experimental variogram. Fit spherical models to the experimental variogram to capture spatial continuity.


Example of auto-fitted variogram models

  • Perform Quantitative Kriging Neighbourhood Analysis (QKNA): Optimize discretization points, number of informing samples, search range and the number of discretisation points for a particular block size. One can also optimise the block size depending on the objective.

Example of optimal min/max search samples

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Iteratively adjust parameters to improve the accuracy and precision of kriging estimates.

Parameters for QKNA are:

Kriging Efficiency (KE), which measures the effectiveness of the kriging estimate to reproduce the local block grade accurately. A low kriging efficiency indicates a high degree of over-smoothing. Conversely, a high kriging efficiency indicates a low degree of over-smoothing (https://docs.dataminesoftware.com/Supervisor/Latest/G-Kriging-Neighbourhood-Analysis/Kriging-Neighbourhood-Analysis.htm).

The slope of regression (KSOR) (or conditional bias slope), which summarises the degree of over-smoothing of high and low grades. A slope close to 1 indicates that the regression between the estimated and the actual grades is likely to be very good, meaning there is limited over-smoothing. Conversely, low slope values indicate that there is over-smoothing and hence a poor relationship between the estimated and the actual block grades (https://docs.dataminesoftware.com/Supervisor/Latest/G-Kriging-Neighbourhood-Analysis/Kriging-Neighbourhood-Analysis.htm).

KNA is performed by calculating the KE and Slope of regression for varying combinations of estimation parameters. The resulting graph is then used to help in selecting which parameters result in the least over-smoothing


QKNA example outcomes

  • Run Sequential Gaussian Simulation (SGS): Use parameters and statistical distribution from steps 1 to 5. Perform SGS from the exploration drillholes to produce????realizations that reproduce input parameters. Outputs of this step become the “target” for comparison of optimal drill spacing configuration.


  • Set Up Artificial Drilling Grids at Various Spacings: Populate the artificial drillholes with simulated grades from the target model. Vary the spacing between drillholes to assess the impact on estimation quality.


Example of multiple drill hole spacing grids

  • Perform Block Kriging from the Artificial Drillholes: Conduct kriging for each artificial drilling grid spacing.


Example of 3D regular pattern


Estimate block grades based on the artificial drillhole data.

  • Calculate Kriging Efficiency and Slope of Regression: For each drilling grid, compute Kriging Efficiency (KE) and Kriging slope of regression (KSOR).


Example of optimal search and KEFF/SLOR

  • Compare Results with Target Model: Compare the kriging results for each grid spacing with the target realization obtained in step 7.

Evaluate the accuracy and precision of the estimates.

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Examples of Swath plots in principal directions are used to check the reproduction of trends and the data

  • Assess Risk and Optimal Drill Hole Spacing: Use the results from steps 10 and 11 to assess the risk associated with each drilling grid spacing. Determine the optimal drillhole spacing that balances estimation accuracy and resource confidence.


Example of optimal drill hole spacing


Example of the final block model


Some of these procedures are explained in detail in:https://www.routledge.com/Geostatistics-Notes-for-Practitioners/Nwaila-Tolmay-Burnett/p/book/9781032599267 and its associated hands-on practicals:https://resourcecentre.routledge.com/books/9781032599267?_gl=1*2pvnbh*_gcl_au*MTAyMDgwOTk4LjE3MjI2NzAyOTk.*_ga*MTQ3MDQ0MTE2Ni4xNzIyNjcwMzA0*_ga_0HYE8YG0M6*MTcyMjc5MTU1Ny4zLjAuMTcyMjc5MTU1Ny42MC4wLjA.


Yousef Ghorbani | Mehdi Saffari | Mahlomola Isaac Mabala | Richard Minnitt | Cuthbert Musingwini | Grant Bybee | Julie Bourdeau | Sebastian Avalos | Francky Fouedjio, Ph.D. | Behnam Sadeghi (PhD, RPGeo, FAusIMM, FAIG, FAAG)

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Stefanos Sykiotis

Mine Geologist | Msc in Physics-Geophysics, Uppsala University

5 个月

Geological features often introduce anisotropy in mineralization. It’s important that the variogram models reflect any directional dependencies or anisotropy in mineral distribution. For instance, in a vein-type deposit, mineralization may be highly anisotropic along the strike of the vein, so variogram models and drill spacing should be adjusted accordingly. Conditional Simulation: Students should keep in mind that conditional simulation often provides a better assessment of uncertainty in highly variable or structurally complex deposits than kriging. This method allows for a range of possible realizations rather than a single estimate, which can be crucial when assessing the uncertainty tied to drillhole spacing. Kriging Over-Smoothing: Kriging tends to smooth grades, especially in areas with high variability. This over-smoothing effect can mask the presence of high-grade zones or erratic mineralization. Students must be mindful of this and not rely solely on kriging efficiency or slope of regression without considering alternative simulation techniques in areas of high uncertainty.

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Wendpanga ILBOUDO

Chief Geologist, Discovery, Exploration, Ressource Evaluation, Production, Reconciliation Professionnal

7 个月

Bon à savoir?!

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Wendy Ware

Sustainably unlocking value across mining value chains through full rock understanding

7 个月

I love reading about what your Geometallurgy and Machine Learning Research Group are up to. This is a highly relevant topic - well done to all involved!

Mehdi Saffari

Mineral Processing Specialist l Modelling and Simulation

7 个月

Fantastic work, Glen Nwaila! Thanks for the update.

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Abdoulaye Ngom

Resources Geologist Manager at BARRICK

7 个月

This is a topic a like performing to much because of its important in mineral resources definition but also it FINANCIAL IMPACT in budgeting. The way i question it is, if at a certain drill space the overall grade mean of the deposit or the panel is x g/t, why drilling more if that mean will keep staying to be x g/t. So there is an optimum space.? How much do we gain and how much do we loose if we drill to each of the desired space? So many question that lead to the importance of putting this DHS as part of the FRONT END LOADING. The uncertainty, i would place it before the start of the logging. I mean at the drilling stage. The localisation of the samples is the base of the the whole estimation work. So ACCURATE COLLAR and ACCURATE survey. Very interesting that last. There is the decluster step in the process yes but what if the data are regular and well partitionned from the beginning? There should be a reason for each of these step in the workflow. Having a representative data to calculate a good variogram becomes crucial as this can even help in farther works. Always good to include with the FINANCIAL IMPACTS in the study. It helps to get an approval so quick ?? Thanks Timo, thanks Prof Glen. Exciting!!!

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