Categorization of Mineral Resources Based on Different Geostatistical Simulation Algorithms: A Case Study from an Iron Ore Deposit

Mineral resource classification plays an important role in the downstream activities of a mining project. Spatial modeling of the grade variability in a deposit directly impacts the evaluation of recovery functions, such as the tonnage, metal quantity and mean grade above cutoffs. The use of geostatistical simulations for this purpose is becoming popular among practitioners because they produce statistical parameters of the sample dataset in cases of global distribution (e.g., histograms) and local distribution (e.g., variograms). Conditional simulations can also be assessed to quantify the uncertainty within the blocks. In this sense, mineral resource classification based on obtained realizations leads to the likely computation of reliable recovery functions, showing the worst and best scenarios. However, applying the proper geostatistical (co)-simulation algorithms is critical in the case of modeling variables with strong cross-correlation structures. In this context, enhanced approaches such as projection pursuit multivariate transforms (PPMTs) are highly desirable. In this paper, the mineral resources in an iron ore deposit are computed and categorized employing the PPMT method, and then, the outputs are compared with conventional (co)-simulation methods for the reproduction of statistical parameters and for the calculation of tonnage at different levels of cutoff grades. The results show that the PPMT outperforms conventional (co)-simulation approaches not only in terms of local and global cross-correlation reproductions between two underlying grades (Fe and Al₂O₃) in this iron deposit but also in terms of mineral resource categories according to the Joint Ore Reserves Committee standard.

     

Resource depletion calculated by the ratio of the reserve plus cumulative consumption to the crustal abundance for gold

The magnitude of the world's mineral consumption has increased sharply, and there is no sign that growth is likely to stop in the near future. Currently, new discoveries and technology add to the reserves of varous mineral commodities at a rate that has exceeded depletion. As a result, life expectancies have remained nearly constant. However, it is questionable whether this condition is sustainable in the future. Therefore, most of our attention to the future has been focused on potentially recoverable resources. The potentially recoverable resources for 35 minerals in the Earth's crust were estimated based on the relationship between crustal abundance and the reserve of currently recoverable gold. The ratio of the reserve plus cumulative consumption to the abundance of gold is appropriate for calculating reserves of other mineral resources because gold has the highest profit margin for exploration of reserves. From an economic perspective, the price of gold is 350 times the mean value of 33 other resources for calculating production versus price. New mining technologies and new processing methods have been developed during the last 20 years as a response to high prices. As a result, five times the reserves available in 1970 have now been discovered, and two times the reserves available in 1970 were consumed during the past two decades. It is questionable whether other mineral commodities can reach the ratio of reserve plus cumulative consumption to abundance that gold does. Using this concept, the limit of the Earth's resources under present technology was calculated for 35 mineral resources, based on the ratio of the reserve plus cumulative consumption to abundance for gold. Even though recoverable tonnage of lead, silver, tin, boron, copper, and mercury from ore deposits in the Earth's crust is relatively low, the abundance of these metals is apparently sufficient for future supplies. However, considering the special situation of gold created by its very high price compared to world production, there is anxiety concerning steep increases in the price or depletion of these metals, which have a shorter lifetime from a geochemical point of view.     

Grade and Tonnage Uncertainty Analysis of an African Copper Deposit Using Multiple-Point Geostatistics and Sequential Gaussian Simulation

Spatial uncertainty analysis is a complex and difficult task for orebody estimation in the mining industry. Conventional models (kriging and its variants) with variogram-based statistics fail to capture the spatial complexity of an orebody. Due to this, the grade and tonnage are incorrectly estimated resulting in inaccurate mine plans, which lead to costly financial decision. Multiple-point geostatistical simulation model can overcome the limitations of the conventional two-point spatial models. In this study, a multiple-point geostatistical method, namely SNESIM, was applied to generate multiple equiprobable orebody models for a copper deposit in Africa, and it helped to analyze the uncertainty of ore tonnage of the deposit. The grade uncertainty was evaluated by sequential Gaussian simulation within each equiprobable orebody models. The results were validated by reproducing the marginal distribution and two- and three-point statistics. The results show that deviations of volume of the simulated orebody models vary from ? 3 to 5% compared to the training image. The grade simulation results demonstrated that the average grades from the different simulation are varied from 3.77 to 4.92% and average grade 4.33%. The results also show that the volume and grade uncertainty model overestimates the orebody volume as compared to the conventional orebody. This study demonstrates that incorporating grade and volume uncertainty leads to significant changes in resource estimates.     

Spatial Pair-Copula Modeling of Grade in Ore Bodies: A Case Study

A real-world mining application of pair-copulas is presented to model the spatial distribution of metal grade in an ore body. Inaccurate estimation of metal grade in an ore reserve can lead to failure of a mining project. Conventional kriged models are the most commonly used models for estimating grade and other spatial variables. However, kriged models use the variogram or covariance function, which produces a single average value to represent the spatial dependence for a given distance. Kriged models also assume linear spatial dependence. In the application, spatial pair-copulas are used to appropriately model the non-linear spatial dependence present in the data. The spatial pair-copula model is adopted over other copula-based spatial models since it is better able to capture complex spatial dependence structures. The performance of the pair-copula model is shown to be favorable compared to a conventional lognormal kriged model.     

Uncertainty Estimate in Resources Assessment: A Geostatistical Contribution

For many decades the mining industry regarded resources/reserves estimation and classification as a mere calculation requiring basic mathematical and geological knowledge. Most methods were based on geometrical procedures and spatial data distribution. Therefore, uncertainty associated with tonnages and grades either were ignored or mishandled, although various mining codes require a measure of confidence in the values reported. Traditional methods fail in reporting the level of confidence in the quantities and grades. Conversely, kriging is known to provide the best estimate and its associated variance. Among kriging methods, Ordinary Kriging (OK) probably is the most widely used one for mineral resource/reserve estimation, mainly because of its robustness and its facility in uncertainty assessment by using the kriging variance. It also is known that OK variance is unable to recognize local data variability, an important issue when heterogeneous mineral deposits with higher and poorer grade zones are being evaluated. Altenatively, stochastic simulation are used to build local or global uncertainty about a geological attribute respecting its statistical moments. This study investigates methods capable of incorporating uncertainty to the estimates of resources and reserves via OK and sequential gaussian and sequential indicator simulation The results showed that for the type of mineralization studied all methods classified the tonnages similarly. The methods are illustrated using an exploration drill hole data sets from a large Brazilian coal deposit.     

Probabilistic Estimates of Number of Undiscovered Deposits and Their Total Tonnages in Permissive Tracts Using Deposit Densities

Empirical evidence indicates that processes affecting number and quantity of resources in geologic settings are very general across deposit types. Sizes of permissive tracts that geologically could contain the deposits are excellent predictors of numbers of deposits. In addition, total ore tonnage of mineral deposits of a particular type in a tract is proportional to the type’s median tonnage in a tract. Regressions using size of permissive tracts and median tonnage allow estimation of number of deposits and of total tonnage of mineralization. These powerful estimators, based on 10 different deposit types from 109 permissive worldwide control tracts, generalize across deposit types. Estimates of number of deposits and of total tonnage of mineral deposits are made by regressing permissive area, and mean (in logs) tons in deposits of the type, against number of deposits and total tonnage of deposits in the tract for the 50th percentile estimates. The regression equations (R ² = 0.91 and 0.95) can be used for all deposit types just by inserting logarithmic values of permissive area in square kilometers, and mean tons in deposits in millions of metric tons. The regression equations provide estimates at the 50th percentile, and other equations are provided for 90% confidence limits for lower estimates and 10% confidence limits for upper estimates of number of deposits and total tonnage. Equations for these percentile estimates along with expected value estimates are presented here along with comparisons with independent expert estimates. Also provided are the equations for correcting for the known well-explored deposits in a tract. These deposit-density models require internally consistent grade and tonnage models and delineations for arriving at unbiased estimates.     

Selection of Optimal Thresholds for Estimation and Simulation Based on Indicator Values of Highly Skewed Distributions of Ore Data

This study strives to outline a geostatistics model for estimation and simulation of the Qolqoleh gold ore deposit located in Saqqez, NW of Iran. Considering that this gold deposit contains high-grade values, accurate evaluation of such values is of high importance, and therefore different methods based on indicator values, such as full indicator kriging (FIK) and sequential indicator simulation (SIS), have been employed to improve the accuracy of estimation and simulation of high-grade values. FIK and SIS cover the full range of grades based on several thresholds on the indicator data. The cumulative distribution function (CDF) is typically used for selection of threshold values. Given the highly skewed distribution of gold grade and its intense fluctuations, the number of thresholds is increased using CDF, which in turn results in a whole lot of calculations. To reduce the volume of calculations, the number–size (N–S) fractal model has been used to select thresholds. From such a model, all optimal thresholds are chosen with respect to geology and the unnecessary thresholds are excluded from selection. Thus, a study of the selection of optimal thresholds for estimation and simulation of a gold ore resource by means of FIK and SIS, respectively, based on thresholds selected using the N–S fractal model is presented. Finally, it is proved that results of these geostatistical methods based on thresholds selection from the N–S model appear to be better-positioned to explain ore grade variability compared to thresholds selected from the CDF and threshold selection from the N–S model is more effective for reducing the volume of required calculations.     

Trends in U.S. Recoverable Coal Supply Estimates and Future Production Outlooks

The geological coal resource of the U.S. is abundant and proved coal reserves are listed as the world’s largest. However, the reserves are unevenly distributed and located in a small number of states, giving them major influence over future production. A long history of coal mining provides detailed time series of production and reserve estimates, which can be used to identify historical trends. In reviewing the historical evolution of coal reserves, one can state that the trend here does not point toward any major increases in available recoverable reserves; rather the opposite is true due to restrictions and increased focus on environmental impacts from coal extraction. Future coal production will not be entirely determined by what is geologically available, but rather by the fraction of that amount that is practically recoverable. Consequently, the historical trend toward reduced recoverable amounts is likely to continue into the future, with even stricter regulations imposed by increased environmental concern. Long-term outlooks can be created in many ways, but ultimately the production must be limited by recoverable volumes since coal is a finite resource. The geologic amounts of coal are of much less importance to future production than the practically recoverable volumes. The geological coal supply might be vast, but the important question is how large the share that can be extracted under present restrictions are and how those restrictions will develop in the future. Production limitations might therefore appear much sooner than previously expected.     

An Objective Approach to the Definition of Some Mining Terms: Application to the Hasançelebi Iron Ore Deposit

In the mining industry, definitions of terms such as geologic resource, geologic reserve, mineral resource, mineral, mineral reserve, ore, ore reserve, mineable reserve, and industrial minerals always have been debated, and have caused much confusion. The process of arriving at these definitions requires complicated exploration, calculation, and evaluation. Based on such work, the definitions about the mineral property will be distinctly different. The aims of this paper is to discuss and compare these definitions, and then contrast the differences among them in the example of the Hasançelebi iron are deposit, which is an important source of iron ore in Turkey.     

Monte Carlo Simulations of Product Distributions and Contained Metal Estimates

Estimation of product distributions of two factors was simulated by conventional Monte Carlo techniques using factor distributions that were independent (uncorrelated). Several simulations using uniform distributions of factors show that the product distribution has a central peak approximately centered at the product of the medians of the factor distributions. Factor distributions that are peaked, such as Gaussian (normal) produce an even more peaked product distribution. Piecewise analytic solutions can be obtained for independent factor distributions and yield insight into the properties of the product distribution. As an example, porphyry copper grades and tonnages are now available in at least one public database and their distributions were analyzed. Although both grade and tonnage can be approximated with lognormal distributions, they are not exactly fit by them. The grade shows some nonlinear correlation with tonnage for the published database. Sampling by deposit from available databases of grade, tonnage, and geological details of each deposit specifies both grade and tonnage for that deposit. Any correlation between grade and tonnage is then preserved and the observed distribution of grades and tonnages can be used with no assumption of distribution form.     

基于Surpac的乌山铜钼矿模型优化研究

利用矿业软件Surpac,收集矿山在开采过程中的生产勘探数据和南矿段补勘所采集的钻孔资料,更新了地质数据库;对乌山铜钼矿矿床模型进行了优化研究;为边际品位指标优化提供了地质资源基础;同时也作为储量估算和境界圈定的依据。     

马关都龙曼家寨锡锌多金属矿床经济评价研究

在对马关都龙曼家寨锡锌多金属矿床地质特征进行分析、研究的基础上,应用地质统计学的理论和方法,运用大型矿业专用软件Surpac建立了该矿体的原始资料数据库和三维数学模型.根据不同边界品位多方案圈定矿体,分别计算矿体的盈亏平衡品位、平均品位和综合品位.通过对比以平衡品位和综合品位圈定的矿体块体模型,对该矿床进行技术经济评价研究,得出了有利于矿产资源综合利用、减少资源浪费的以综合品位圈定矿体的结论.     

青海察尔汗盐湖采卤试验区固体钾矿的应用探析

青海察尔汗盐湖采卤试验区中固体钾矿储量很大，固体钾矿与液体钾矿在静态条件下存在着一定的平衡关系，但单独开采价值不大．应考虑在开采液体钾矿的同时，我钻孔的不同部位从下至上轮流抽卤，使整个钾矿层中的固体钾矿转化到液相中来，则能充分利用其资源。     

Typing Mineral Deposits Using Their Grades and Tonnages in an Artificial Neural Network

A test of the ability of a probabilistic neural network to classify deposits into types on the basis of deposit tonnage and average Cu, Mo, Ag, Au, Zn, and Pb grades is conducted. The purpose is to examine whether this type of system might serve as a basis for integrating geoscience information available in large mineral databases to classify sites by deposit type. Benefits of proper classification of many sites in large regions are relatively rapid identification of terranes permissive for deposit types and recognition of specific sites perhaps worthy of exploring further.Total tonnages and average grades of 1,137 well-explored deposits identified in published grade and tonnage models representing 13 deposit types were used to train and test the network. Tonnages were transformed by logarithms and grades by square roots to reduce effects of skewness. All values were scaled by subtracting the variable's mean and dividing by its standard deviation. Half of the deposits were selected randomly to be used in training the probabilistic neural network and the other half were used for independent testing. Tests were performed with a probabilistic neural network employing a Gaussian kernel and separate sigma weights for each class (type) and each variable (grade or tonnage).Deposit types were selected to challenge the neural network. For many types, tonnages or average grades are significantly different from other types, but individual deposits may plot in the grade and tonnage space of more than one type. Porphyry Cu, porphyry Cu-Au, and porphyry Cu-Mo types have similar tonnages and relatively small differences in grades. Redbed Cu deposits typically have tonnages that could be confused with porphyry Cu deposits, also contain Cu and, in some situations, Ag. Cyprus and kuroko massive sulfide types have about the same tonnages. Cu, Zn, Ag, and Au grades. Polymetallic vein, sedimentary exhalative Zn-Pb, and Zn-Pb skarn types contain many of the same metals. Sediment-hosted Au, Comstock Au-Ag, and low-sulfide Au-quartz vein types are principally Au deposits with differing amounts of Ag.Given the intent to test the neural network under the most difficult conditions, an overall 75% agreement between the experts and the neural network is considered excellent. Among the largestclassification errors are skarn Zn-Pb and Cyprus massive sulfide deposits classed by the neuralnetwork as kuroko massive sulfides—24 and 63% error respectively. Other large errors are the classification of 92% of porphyry Cu-Mo as porphyry Cu deposits. Most of the larger classification errors involve 25 or fewer training deposits, suggesting that some errors might be the result of small sample size. About 91% of the gold deposit types were classed properly and 98% of porphyry Cu deposits were classes as some type of porphyry Cu deposit. An experienced economic geologist would not make many of the classification errors that were made by the neural network because the geologic settings of deposits would be used to reduce errors. In a separate test, the probabilistic neural network correctly classed 93% of 336 deposits in eight deposit types when trained with presence or absence of 58 minerals and six generalized rock types. The overall success rate of the probabilistic neural network when trained on tonnage and average grades would probably be more than 90% with additional information on the presence of a few rock types.     

Effects of fetch and surface texture on aeolian sand transport on two nourished beaches

Aeolian sand transport on two nourished beaches was related to the fetch of the wind over the beach sand and to surface characteristics. Meteorological and hydrological conditions were recorded for 2 months. The fetch of wind over beach sand was estimated from wind direction, water level, wave height and beach topography. Aeolian sand transport was determined with sand traps. Sediment flux was found to increase with fetch, although this relation was especially affected by the variability in surface characteristics. On one of the beaches sediment supply was limited as a result of shells, forming a lag deposit.     

Basic concepts in three-part quantitative assessments of undiscovered mineral resources

Since 1975, mineral resource assessments have been made for over 27 areas covering 5×10⁶ km² at various scales using what is now called the three-part form of quantitative assessment. In these assessments, (1) areas are delineated according to the types of deposits permitted by the geology,(2) the amount of metal and some ore characteristics are estimated using grade and tonnage models, and (3) the number of undiscovered deposits of each type is estimated.Permissive boundaries are drawn for one or more deposit types such that the probability of a deposit lying outside the boundary is negligible, that is, less than 1 in 100,000 to 1,000,000.     

A Chart for Judging Optimal Sample Spacing for Ore Grade Estimation

Mineral deposit grades are usually estimated using data from samples of rock cores extracted from drill holes. Commonly, mineral deposit grade estimates are required for each block to be mined. Every estimated grade has always a corresponding error when compared against real grades of blocks. The error depends on various factors, among which the most important is the number of correlated samples used for estimation. Samples may be collected on a regular sampling grid and, as the spacing between samples decreases, the error of grade estimated from the data generally decreases. Sampling can be expensive. The maximum distance between samples that provides an acceptable error of grade estimate is useful for deciding how many samples are adequate. The error also depends on the geometry of a block, as lower errors would be expected when estimating the grade of large-volume blocks, and on the variability of the data within the region of the blocks. Local variability is measured in this study using the coefficient of variation (CV). We show charts analyzing error in block grade estimates as a function of sampling grid (obtained by geostatistical simulation), for various block dimensions (volumes) and for a given CV interval. These charts show results for two different attributes (Au and Ni) of two different deposits. The results show that similar errors were found for the two deposits, although they share similar features: sampling grid, block volume, CV, and continuity model. Consequently, the error for other attributes with similar features could be obtained from a single chart.     

中国主要含砷矿产资源的区域分布与砷污染问题

本文分析了我国主要含砷矿资源的区域分布及其开采所带来的环境污染问题。截至2003年底,我国累计探明砷矿资源储量为397.7万t,保有储量279.6万t,其中87.1%的保有储量以共生、伴生砷矿形式存在。砷矿资源分布相对集中于广西、云南、湖南,三省的保有储量占全国保有储量的58.0%;其中广西南丹县和云南个旧市的保有储量最大,分别占全国总保有储量的17.0%和10.2%。我国已经有大量的砷随矿产资源的开采而带至环境中。截至2003年底,全国砷采出量至少高达139.2万t,其中广西、云南、湖南采出量最大,分别达73.3、34.2和15.3万t。在矿产采冶过程中,采出的砷有70%弃留于尾矿中。矿业活动释放的砷已通过土壤及食物链途径威胁到人体健康,尤其是在矿冶活动密集的西南地区问题更加突出。     

Geological Modeling of Gold Deposit Based on Grade Domaining Using Plurigaussian Simulation Technique

Mineral resource evaluation requires defining grade domains of an ore deposit. Common practice in mineral resource estimation consists of partitioning the ore body into several grade domains before the geostatistical modeling and estimation at unsampled locations. Many ore deposits are made up of different mineralogical ensembles such as oxide and sulfide zone: being able to model the spatial layout of the different grades is vital to good mine planning and management. This study addresses the application of the plurigaussian simulation to Sivas (Turkey) gold deposits for constructing grade domain models that reproduce the contacts between different grade domains in accordance with geologist’s interpretation. The method is based on the relationship between indicator variables from grade distributions on the Gaussian random functions chosen to represent them. Geological knowledge is incorporated into the model by the definition of the indicator variables, their truncation strategy, and the grade domain proportions. The advantages of the plurigaussian simulation are exhibited through the case study. The results indicated that the processes are seen to respect reproducing complex geometrical grades of an ore deposit by means of simulating several grade domains with different spatial structure and taking into account their global proportions. The proposed proportion model proves as simple to use in resource estimation, to account for spatial variations of the grade characteristics and their distribution across the studied area, and for the uncertainty in the grade domain proportions. The simulated models can also be incorporated into mine planning and scheduling.     

Peak Minerals: Theoretical Foundations and Practical Application

This article reviews the theoretical foundations for the concept of peak minerals; drawing on similarities and differences with peak oil as modelled using Hubbert style curves. Whilst several studies have applied peak modelling to selected minerals, discussion of the appropriateness of using Hubbert style curves in the minerals context remains largely unexplored. Our discussion focuses on a comparison between oil and minerals, on the key variables: rates of discovery, estimates of ultimately recoverable resources and demand and production trends. With respect to minerals, there are several obstacles which complicate the application of Hubbert style curves to the prediction of future mineral production, including the lack of accurate discovery data, the effect of uncertain reserve estimates, and varying ore quality and quantity. Another notable difference is that while oil is often combusted during use, minerals are used to make metals which are inherently recyclable. Notwithstanding, by using a range of estimates of resources and/or reserves, a period of time can be identified which indicates when a peak in minerals production may occur. This information may then be used to plan for a transition from using a potentially constrained resource, to using substitutes if available, or to reducing demand for that mineral in society.