Resource Model Dilution and Ore Loss: A Change of Support Approach

Abstract

The estimation of ore dilution and ore loss factors is critical for the evaluation of mining projects, with the proper estimation of these effects essential for Ore Reserve Estimation. Unplanned ore dilution occurs when excessive amounts of waste are mined with ore, and such dilution may result in the processing of lower than economic cut-off grade material with the ore. Unplanned ore loss occurs when material that is above the economical cut-off grade is hauled to waste stockpiles, due to poor mining practices and/or poor information regarding the local grade of the critical components.

The sources of dilution and ore loss in mining operations are many. This study focuses on the assessment of the ore dilution and loss in a Mineral Resource model, specifically, the proportion and average grade of blocks that are misclassified as ore and waste, which can be referred to as Resource Model Ore Dilution and Model Ore Loss, respectively. Unlike the well-established geostatistical conditional simulation approach for assessing model dilution and loss, in this study analytical expressions are derived that are defined under the theoretical framework of the discrete Gaussian method for change of support to quantify the expected model dilution and ore loss. Practical application of this method is demonstrated through a case study from an Iron Ore deposit in Australia.

Appendix

The tonnage associated with blocks correctly classified as waste is

$$ P\left( Z(v)< z/{Z}^{*}(v)< z\right)=( F( y)+ F\left({y}^{*}\right)+{H}_{\rho}\left( y,{y}^{*}\right)-1)/ F\left({y}^{*}\right) $$

and corresponding expected metal is

$$ E\left( Z(v){1}_{Z(v)< z}/{Z}^{*}(v)< z\right)=\frac{1}{F\left({y}^{*}\right)}{\displaystyle {\sum}_n{\phi}_n{r}^n}{\displaystyle {\sum}_k{\rho}^k}\left[{\delta}_{n k}-{U}_{n, k}(y)\right]\left[{\delta}_{0 k}-{U}_{0, k}\left({y}^{*}\right)\right] $$

The tonnage associated with blocks correctly classified as ore is

$$ P\left( Z(v)\ge z/{Z}^{*}(v)\ge z\right)={H}_{\rho}\left( y,{y}^{*}\right)/\left(1- F\left({y}^{*}\right)\right) $$

and corresponding expected metal is

$$ E\left( Z(v){1}_{Z(v)\ge z}/\ {Z}^{*}(v)\ge z\right)=\frac{1}{1- F\left({y}^{*}\right)}{\displaystyle {\sum}_n{\phi}_n{r}^n}{\displaystyle {\sum}_k{\rho}^{k\ }}{U}_{n, k}(y){U}_{0, k}\left({y}^{*}\right) $$