Grade-tonnage Curves Research Articles

THE PERFORMANCE OF ESTIMATION TECHNIQUES FOR NICKEL LATERITE RESOURCE MODELING

The choice of estimation technique according to geological conditions and mineralization character is the main problem in estimating block grade of nickel laterite. CV (coefficient of variance) and variogram determine the choice of estimation technique for nickel laterite resource classification. This study aims to evaluate various techniques for estimating block grades and to select the appropriate method for the classification of nickel laterite resources. The basic statistical analysis is to find out the description of the data, while the variography is to find out the spatial correlation between the data. Nickel grade estimation results are based on Near Neighbor Polygon (NNP), Inverse Distance Weighting (IDW), and Ordinary Kriging (OK) techniques to determine the classification of nickel resources. Accuracy levels are based on cross-sectional visualization comparisons, plan views, probability plots and linear regression analysis. The OK technique were not superior in grade estimation, especially in nickel laterite deposits. The results showed that the IDW technique was suitable to be applied to the limonite zone, while the NNP technique was suitable to be applied to the saprolite zone. Based on the performance of the estimation technique, the weighted average method can be applied for the classification of inferred, indicated, and measurable resources. The grade-tonnage curve shows the nickel laterite resource potential in the study area.

Assessing geological uncertainty of a cement raw material deposit, southern Vietnam, based on hierarchical simulation

Resource modeling plays a crucial role in raw material quality management for cement manufacturing. Research has shown that geological uncertainty in resource modeling is inevitable and results in risk to future extraction planning and operations of the cement plant. This study aims to assess the geological uncertainty and associated risk in modeling a cement raw material deposit in southern Vietnam. For this deposit, soil, clay, laterite, and limestone are the four primary rock types, controlling the occurrence and spatial distribution of chemical grades. In this study, hierarchical simulation method was used to evaluate the uncertainty. Rock types were first simulated, and the chemical grades conditioning to the rock types were then generated. The results demonstrated the capability of the hierarchical simulation approach to incorporate the uncertainty of rock types in resource modeling and to allow evaluating the risks in providing the desired raw material for the cement plant in the form of grade-tonnage curves.

Constrained Kriging: An Alternative to Predict Global Recoverable Resources

In most NI-43-101 resource assessment reports the prediction of global in situ resources is performed by either inverse distance weighting, ordinary kriging (OK) or uniform conditioning (UC). These methods have known drawbacks: OK estimates are oversmoothed, and UC necessitates an additional step to localize resources within panels. An alternative, named constrained kriging (CK), enables to circumvent the smoothing issue of OK by imposing the desired theoretical variance to the interpolated variable. CK is not used in NI-43-101 reports, possibly due to a lack of real application examples and little detailed study of its properties. This paper seeks to fill the gap by comparing the prediction performance for global resources of OK, UC and CK on a synthetic lognormal dataset and two real datasets, the Walker Lake and a gold deposit. Results indicate that CK, although being slightly less precise than OK, provides better predictions of grade-tonnage curves than OK and predictions comparable to UC, a remarkable achievement considering that UC is a widespread nonlinear method specifically designed to predict recovery functions. CK is also shown to provide resource estimates more robust than UC with respect to the variogram model specification. Hence, CK appears as a valuable tool allowing simultaneously to localize resources and easily account for change of support in resources estimation.

A method for optimal cut-off grade policy in open pit mining operations under uncertain supply

Cut-off grade controls the movement of materials among mining, processing and refining stages of an open pit mining operation. The cut-off grade policy constitutes a schedule of cut-off grades and the associated quantities of materials that flow through various stages over the life of operation. This flow of materials in the system relies on the grade-tonnage curve of the mineral resource and given that the variation in grade-tonnage curve is inevitable, it is crucial that the methods that define the cut-off grade policy must consider this grade uncertainty. However, with few exceptions, a majority of these methods ignore this uncertainty in the supply of materials. This paper shares a two-stage stochastic linear programming based cut-off grade optimisation model that accounts for the grade uncertainty and maximises the net present value (NPV) subject to the production capacity constraints over the life of operation. An application of the proposed method at hypothetical and realistic cases promises higher NPV as compared to the traditional heuristic approach.

Forecasting the grade-tonnage curves and their uncertainty at the Mehdiabad deposit-Yazd, central Iran

Forecasting the grade-tonnage curves and their uncertainty at the Mehdiabad deposit-Yazd, central Iran

A test of the appropriateness of the LUC technique in high-nugget Birimian-style gold deposits

'=:17<7 The localized uniform conditioning (LUC) technique was proposed by Marat Abzalov in 2006. The technique converts conventional uniform conditioning (UC) grade-tonnage curves into single grade values attached to each smallest mining unit (SMU). This is achieved by ranking the SMUs within a panel in increasing order of their grade (based on the direct kriging of SMUs). This ranking is then used to localize the conventional UC grade-tonnage curves for each panel by dividing them into classes and computing their mean grades, which are assigned to the SMUs. The quality of this localization process will depend heavily on the validity of the grade patterns predicted by the direct kriging of the SMUs. Abzalov noted that where the distribution of data available for the direct kriging of the SMU is characterized by strong short-range variability, the advantages of using the LUC approach may be more limited. Consequently, a study was undertaken to determine how valid the predicted grade patterns of a typical Birimian-style gold deposit (with high nugget effect and strong short-range variability) might be expected to be. This was determined by comparing the direct SMU kriging ranking (based on sparse data) with the grade control model ranking (based on close-spaced data and the best available estimate of the deposit). The results showed a satisfactory correlation between these rankings and it was concluded that, although the grade patterns predicted by the direct kriging of the SMUs may be less meaningful for deposits exhibiting strong short-range continuity, there is nevertheless a convincing relationship with the actual (or best available) rankings. Therefore, the LUC technique is still considered to be useful for this style of deposit.

Integration of different-quality data in short-term mining planning

AbstractDecisions, from mineral exploration to mining operations, are based on grade block models obtained from samples. This study evaluates the impact of using imprecise data in short-term planning. The exhaustive Walker Lake dataset is used and is considered as the source for obtaining the true grades. Initially, samples are obtained from the exhaustive dataset at regularly spaced grids of 20 × 20 m and 5 × 5 m. A relative error (imprecision) of ±25% and a 10% bias are added to the data spaced at 5 × 5 m (short-term geological data) in different scenarios. To combine these different types of data, two methodologies are investigated: cokriging and ordinary kriging. Both types of data are used to estimate blocks with the two methodologies. The grade tonnage curves and swath plots are used to compare the results against the true block grade distribution. In addition, the block misclassification is evaluated. The results show that standardized ordinary cokriging is a better methodology for imprecise and biased data and produces estimates closer to the true grade block distribution, reducing block misclassification.

Choice of a methodological approach for the estimation of recoverable resources with Uranium deposits in Central Jordan

Choosing a resource estimation approach for uranium deposits central Jordan needs to consider various issues; the particular geological context of these deposits, the varying degree of reliability of input data and the level of selectivity that can be reasonably envisaged at a production stage. These issues make this resource estimation challenging from a geostatistical perspective. Here, we provide details of the approach used during resource estimation for the surficial part of uranium deposits in central Jordan; as a more standard approach has been applied to the deeper parts of these deposits. The workflow is as follows:(i) Interpolation of the geometry of the mineralised formation. Kriging with external drift is applied to model hangingwall and footwall surfaces.(ii) Estimation of global resources by 2D estimation of layer thicknesses and uranium accumulation using channel samples within delineated areas.(iii) Accounting for vertical selectivity and development of grade tonnage curves using uniform conditioning (UC) followed by localised post-processing (called LUC) delivering, a 3D block model at the selective mining unit support scale.A description of the UC/LUC approach and the adaptations made in order to account for the variable thickness is presented in this paper. This approach involves performing UC on each panel in turn with a thickness varying from panel to panel. This leads to a specific change of support coefficients for each panel. The illustrations of this approach are taken from one specific zone within the Central Jordan deposits.

Application of joint conditional simulation to uncertainty quantification and resource classification

Identifying and quantifying grade uncertainty is important in mineral resource classification from an economic perspective. Conditional simulation techniques can be used to this end. In multi-element deposits, for which spatial correlations are important, techniques such as principal component analysis and minimum/maximum auto-correlation factors can be used to transform the multivariate simulation problem into a series of univariate problems. In this study, a methodology is presented for classifying mineral resources and for assessing the uncertainty in grade–tonnage curves, with an application to a porphyry copper deposit located in the central part of Iran with three correlated variables (grades of Cu, Mo, and Ag). The resources are classified based on the simulated copper grades, considering the so-called 15 % rule. This means that the estimated grade, tonnage, and metal content in a production period will have at most 15 % error at 90 % confidence level.

Application of median indicator kriging in the analysis of an iron mineralization

This paper presents an application of median indicator kriging in the analysis of iron mineralisation data from the Chadormalu iron mine in Yazd province, Iran. The sample data used in this study consist of exploration drilling data, suitably composited. The data set is sparse, irregularly spaced, and has a bimodal distribution. It is important to use an estimation method that deals with the nature of the distribution appropriately. Since none of the grade distributions are normal or log-normal, a non-linear estimator is ideal. The indicator kriging method is considered to provide a better way of estimating an element with a bimodal distribution. Indicator semivariograms were modelled for nine cut offs, the deciles. Semivariograms were standardised by dividing each semivariogram by the total sill, and a single spherical structure plus nugget was fitted in each case. All data were treated as point data in three-dimensional space rather than block data. The grade tonnage curves were calculated on the assumption that each estimate is representative of a block of size 20 m by 20 m by 12.5 m centred on the location of the datum.

Quantifying multi-element and volumetric uncertainty, Coleman McCreedy deposit, Ontario, Canada

Traditional geostatistical modelling of orebodies and estimation of grade–tonnage curves do not account for the uncertainty of the orebody grades and tonnages. Geological interpretations of complex shapes are often over-constrained, and therefore do not properly identify the location of the ore. In these situations, tonnage is often under-estimated and grade is over-estimated, resulting in orebody models used for mine planning that lead to costly financial decisions. This paper presents an approach aiming to better assess the uncertainty in an orebody model. The approach is applied to Vale's West Orebody of the Coleman McCreedy Mine, a poly-metallic deposit containing nickel, copper, gold, platinum and palladium. To encapsulate the orebody's variability and uncertainty, the nickel–copper sulphide mineralized zone is simulated using the single normal equation simulation method. The realizations serve as the orebody models from which the grades of multiple elements are jointly simulated using Min/Max Autocorrelation Factors. The final result is a series of equiprobable representations of the mineralization that incorporates both grade and tonnage uncertainty. The case study indicates that had conventional orebody estimations been used, there would have been a 10% over-estimation of orebody volume, along with significant over-estimation of low-grade material and under-estimation of high-grade material.

Optimal production scale of open pit mining operations with uncertain metal supply and long-term stockpiles

An open pit mining operation consists of various stages, and the calculation of the production capacities of these stages depends upon the available supply of ore (mineralized material of economic value) and waste material. Cutoff grade is the criterion that specifies the amount of ore and waste. The material with grade equal to or higher than the cutoff grade is classified as ore. The material with grade less than the cutoff grade is considered waste. While this explains the link between cutoff grade theory and the calculation of production capacities, the majority of optimization models for finding production capacities not only disregards this relationship but also ignores expected variations and uncertainty in metal content or the available supply of ore and waste material.An extension to an established theory of cutoff grade is proposed herein to determine the optimal production capacities based on a stochastic framework relying on multiple grade-tonnage curves derived from a set of simulated orebody realizations. The proposed model (i) maximizes the net present value of cash flows over the life of an operation; (ii) offsets the initial investment in developing the constituent stages of an operation; and (iii) explores the impact of creating a long-term stockpile on the designed operational capacities. Application on an actual copper deposit demonstrates the benefits of the proposed model.

Risk quantification in grade-tonnage curves and resource categorization in a lateritic nickel deposit using geologically constrained joint conditional simulation

The risk quantification in grade-tonnage curves is critical for capital investment in mining projects. Geostatistical simulations for orebodies can be used to obtain grade-tonnage curves, and determine uncertainty and risk assessments. Applying these in multi-element deposits can be a difficult practice, as the related attributes using the traditional co-simulation approaches require intensive computational work and may be impractical for use in the mineral industry. This paper presents the risk assessment for integrating grade-tonnage curves and resources categorization for lateritic nickel deposits in the central region of Brazil, by joint simulation of multiple correlated variables of interest: Ni, MgO and SiO2. The joint simulation of these variables is based on Minimum/Maximum Autocorrelation Factors (MAF). Based on this approach, the resources are categorized honoring Ni joint simulated results by applying the 15 % rule, where it is considered there will be a statistical error < 15 %, with 90 % of a confidence interval per production period.

Geostatistical Modeling of Uncertainty for the Risk Analysis of a Contaminated Site

This work is a study of multivariate simulations of pollutants to assess the sampling uncertainty for the risk analysis of a contaminated site. The study started from data collected for a remediation project of a steel- works in northern Italy. The soil samples were taken from boreholes excavated a few years ago and analyzed by a chemical laboratory. The data set comprises concentrations of several pollutants, from which a subset of ten organic and inorganic compounds were selected. The first part of study is a univariate and bivariate sta- tistical analysis of the data. All data were spatially analyzed and transformed to the Gaussian space so as to reduce the effects of extreme high values due to contaminant hot spots and the requirements of Gaussian simulation procedures. The variography analysis quantified spatial correlation and cross-correlations, which led to a hypothesized linear model of coregionalization for all variables. Geostatistical simulation methods were applied to assess the uncertainty. Two types of simulations were performed: correlation correction of univariate sequential Gaussian simulations (SGS), and sequential Gaussian co-simulations (SGCOS). The outputs from the correlation correction simulations and SGCOS were analyzed and grade-tonnage curves were produced to assess basic environmental risk.

Genetic algorithm-based neural network learning parameter selection for ore grade evaluation of limestone deposit

Ore grade evaluation is a decisive task in mine planning operations. A reliable estimate can represent the deposit close to reality. A neural network (NN) model was used to develop a reliable estimate of ore grades of a study mine. The learning parameters for the NN model were selected by genetic algorithm. The optimum hidden layer nodes were selected based on minimum mean square error of a validation data set. The performance of the model was tested and compared with an ordinary kriging model. The comparative result revealed that the NN model performed better for all four attributes of the case study mine than the ordinary kriging model. The developed NN model incorporates lithological information as input parameters. Therefore, lithological maps of the deposit were generated using sequential indicator simulation. Ten different ore grade maps were generated for calculation of the uncertainty associated with the model. The grade tonnage curve along with uncertainty will help mine management by improving understanding about the deposit.

Revisiting the Cumulative Grade-Tonnage Relationship for Major Copper Ore Types

In order to develop long-term scenarios of copper supply and demand, a grade-tonnage density function model was developed for four major copper ore types. The model was used to create cumulative grade-tonnage curves, representing 1,778 million metric tons (Mt) of mineable copper. These cumulative curves were then validated against 70 years of historical world average ore grade using production input by ore type from 1800 to 2000. Additionally, the curves were used in conjunction with estimates of the ultimate porphyry resource and copper concentration in common rocks to conduct a rough analysis of the validity of the bimodal log-Gaussian distribution hypothesis for the global copper resource base. The resulting analysis did not confirm or refute the hypothesis but did provide guidance as to the way in which data from new resource exploration can be used to address the issue of the ultimate mineable copper resource. As ore deposit grade-tonnage data for other geochemically scarce metals becomes available, the methods described in this paper can serve as a template for further investigations of resource quality.

O-109 Is early response a useful predictive factor in neoadjuvant chemotherapy

Traditional geostatistical modelling of orebodies and estimation of grade–tonnage curves do not account for the uncertainty of the orebody grades and tonnages. Geological interpretations of complex shapes are often over-constrained, and therefore do not properly identify the location of the ore. In these situations, tonnage is often under-estimated and grade is over-estimated, resulting in orebody models used for mine planning that lead to costly financial decisions. This paper presents an approach aiming to better assess the uncertainty in an orebody model. The approach is applied to Vale's West Orebody of the Coleman McCreedy Mine, a poly-metallic deposit containing nickel, copper, gold, platinum and palladium. To encapsulate the orebody's variability and uncertainty, the nickel–copper sulphide mineralized zone is simulated using the single normal equation simulation method. The realizations serve as the orebody models from which the grades of multiple elements are jointly simulated using Min/Max Autocorrelation Factors. The final result is a series of equiprobable representations of the mineralization that incorporates both grade and tonnage uncertainty. The case study indicates that had conventional orebody estimations been used, there would have been a 10% over-estimation of orebody volume, along with significant over-estimation of low-grade material and under-estimation of high-grade material.

Localised Uniform Conditioning (LUC): A New Approach for Direct Modelling of Small Blocks

Recoverable mineralisation at a given mining selectivity is traditionally modelled from sparse data grids by non-linear geostatistical techniques such as Uniform Conditioning. This method estimates the tonnage and grade of mineralisation which can be extracted as small selective minable blocks from large blocks (panels), whose grade is modelled by Ordinary Kriging. Uniform Conditioning technique estimates the proportions of recoverable mineralisation in each panel without specifying the actual locations of the economically extractable blocks. This inability to predict a spatial location of the recoverable mineralisation is a major disadvantage of the conventional Uniform Conditioning method. A new approach, called Localised Uniform Conditioning, has been developed to overcome this limitation. This method applies the grade–tonnage relationships modelled by the Uniform Conditioning technique to the spatial grade distribution patterns approximated by direct kriging of the small blocks from the sparse data grid. This approach estimates localised selective mining units grades conforming to the proper grade–tonnage curves obtained by the Uniform Conditioning method as well as maintaining the relative spatial grade distribution pattern indicated by the directly kriged small block grades. The advantage of this approach is essentially dependent upon the data available for ranking the small blocks within a panel in increasing order of their grade. Ordinary Kriging of the small blocks can be used for their ranking providing the kriged estimates produce a meaningful indication of the relative grade pattern. Where the data is sparse and not close to a panel, or their distribution is characterised by a strong short-range variability, the advantages of using the Localised Uniform Conditioning approach are more limited.

Improvements in Grade Tonnage Curve Prediction via Sequential Gaussian Fractal Simulation

An application of sequential Gaussian fractal conditional simulation is presented, using actual sparse, irregularly spaced open cut gold data, to predict the grade tonnage curve associated with a single mining bench. It is shown that this constitutes an improvement over the prediction of the grade tonnage curves obtained via standard sequential Gaussian simulation and median indicator simulation. The fractal conditional simulation method uses the model of the covariance of increments of fractional Brownian motion together with the fractal co-dimension derived from a truncated power semivariogram model to create conditional simulations from irregularly spaced data. The grades and tonnages above several discrete cut offs are calculated for each of one hundred simulations, and the mean and variance of the grade and tonnage values for each cut off are computed to give an average grade tonnage curve with associated confidence limits.

Geostatistical Case Studies

Computing Variograms on Uranium Data.- The Comparison Between the Gamma Logs and the Grades in the Estimation of a Uranium Deposit.- Geostatistical Estimation of a Section of the Perseverance Nickel Deposit.- Multipurpose Geostatistical Modelling of a Bauxite Orebody in Sardinia.- Application of Kriging to the Mapping of a Reef from Wireline Logs and Seismic Data A Case History.- Study of a Gas Reservoir Using the External Drift Method.- The Grade-Tonnage Curves for a Zinc Mine in France.- Conditioning by the Panel Grade for Recovery Estimation of Non-Homogeneous Orebodies.- Recoverable Reserves Estimation at an Australian Gold Project.- Comparing Estimated Uranium Grades with Production Figures.- Global Recoverable Reserves: Testing Various Changes of Support Models on Uranium Data.- Calculating Ore Reserves Subject to Mining Constraints, for a Uranium Deposit.