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By D. Rucker

Flow models are used to predict the extraction efficiency of metals in rock piles. These models typically use hydraulic parameters obtained through column studies, which assume that the material in the column wholly represents the entire pile and the parameters can be upscaled several orders of magnitude for model evaluation. This assumption fails for parameters that are spatially variable or scale dependent. To overcome these issues, measurements made directly on the heap at the appropriate model scale can be made with the electrical resistivity method. The method aims to map the variations in the electrical resistivity, which can be associated with moisture content, degree of fines, metal content, and leachate concentration. We present an example of calibrating the resistivity with borehole measurements of moisture using geostatistics to show how the resistivity method can be used to obtain a spatial moisture distribution. It was shown that cokriging the resistivity and moisture together gives a more reliable distribution.

Jan 1, 2010

By Michael J. Friedel

As part of a study aimed at understanding the hydrology of in situ leach mining (ISLM), the Bureau of Mines, in cooperation with the Cyprus Casa Grande Corporation and the University of Arizona, is investigating dynamic transmissivity conditions during ISLM of a copper oxide ore deposit. Spatial and temporal variations in ore zone transmissivity during two years of ISLM operations at the Cyprus Casa Grande mine are evaluated during sixteen intervals of steady-state injection and recovery well operation. Direct inversion of an analytical hydrologic model is used to obtain estimates of transmissivity at 58 well locations during these intervals. Univariate statistical and geostatistical methods are used to describe the temporal and/or spatial relationships that exist between transmissivity and other ISLM parameters, including average well injection pressure, average sulfuric acid concentration in leach solution, and the relative configuration of injection and recovery wells. Average transmissivity during the sixteen steady-state time intervals varies between 6.00 x 10-6 m2/min. (6.46 x 10-5 ft2/min.) and 3.61 x 10-8 m2/ min. (3.89 x 10-7 ft2/min.). A trend toward decreas¬ing transmissivity is evident during two year of ISLM operations. This decreasing trend is found to correlate with a decreasing sulfuric acid concentration in injected leach solution, and suggests increasing geochemical precipitation within the deposit. Geostatistical analyses reveal a dynamic and anisotropic transmissivity structure within the target ore zone, that is dependent upon spatial and temporal changes in injection pressure and well configuration.

Jan 1, 1992

By R. Cao

Geostatistics was initially developed in the mining sector, but has been extended to other geoscience applications, including forestry, environmental science, soil science, and petroleum science and engineering. This paper presents methods, workflows, and pitfalls in using geostatistics for hydrocarbon resource modelling and evaluation. Examples are presented of indicator variogram analysis of categorical variables, lithofacies modelling by sequential indicator simulation and hierarchical workflow, porosity modelling by kriging and stochastic simulation, collocated cokriging for integrating seismic data, and collocated cosimulation for modelling porosity and permeability relationships. These methods together form a systematic approach that can be effectively used for modelling natural resources.

Jan 1, 2014

By Royle A. G

The paper describes a geostatistical structural analysis of an 80 square mile lease of the Athabasca tar sands. Each step of the analysis is presented with the ultimate objective of condensing the principal structural characteristics of the chosen regionalised variables into the opera- tional form of the variogram model. The variogram model is then used to form kriged local and global estimates, with the corresponding estimation errors.

Jan 1, 1977

By R. C. Bryan, D. B. Jamison

This paper describes a procedure for minimizing the operational costs associated with blending sodium in coal at a surface mine in the Powder River Basin. Mine site blending is performed by adjusting daily production rates for high- and low-sodium pits. These adjustments are designed to produce a consistent sodium value called the blending target. The mine's contractual limit for sodium is sufficiently close to the field average value that any decrease in the sodium blending target may result in an opportunity cost, if the number of potentially minable tons is reduced. Conversely, any increase in the blending target may result in a higher sampling cost if more information is required to keep the blend within contractual limits. Blending parameters were defined using a geostatistical block model of sodium content that was based on analyses of hundreds of in-pit sample holes. Variograms for these data were used to compute the marginal costs of opportunity and sampling for a series of hypothetical in-pit drilling patterns. These marginal costs provided a basis for selecting optimum values for key parameters such as the blending target, production variance and in-pit sampling density. The benefit of implementing these optimized parameter values is that operational costs of sodium blending will be minimized over the long-term. At the mine where this procedure was developed, each dollar spent to increase the sampling density to the optimum value was shown to generate a $10 savings in opportunity cost.

Jan 1, 1991

By C. Özgen Karacan

The formation of the gas emission zone in longwall mining and the potential amount of gas in this zone are factors of local geology and spatial variability within this geology. Therefore, geostatistical methods can be used for modeling and prediction of gas amounts and for assessing its uncertainty in the gas emission zone of longwall mines. This study used core data obtained from 64 exploration boreholes drilled from the surface to the bottom of the Pittsburgh coal seam in a mining district in the Northern Appalachian basin. After identifying important coal layers for the gas emission zone, semivariogram modeling was conducted for different coal seams to define the distribution and continuity of various attributes. Sequential simulations were performed for stochastic assessment of these attributes to calculate gas-in-place (GIP) in each coal seam. GIP calculations for coals of various gas emissions zones were combined and ranked for their cumulative distribution function to find GIP in the caved zone and in the fractured zone at the 5%, 50%, and 95% quantiles. Fifty percent quantile results were later used to isolate a panel from the whole area and create a mosaic representation corresponding to the daily advance rate of the longwall face. This approach helped to estimate the daily emissions of this panel from the caved zone and from the fractured zone. Results showed that gas-in-place in the Pittsburgh coal seam, in the caved zone, and in the fractured zone showed spatial correlations that could be modeled and estimated using geostatistical methods. This study showed that gas-in- place volumes in the study area may be as high as 12.3 Bscf and as much as 3.5 MMscf per acre of mining.

Jan 1, 2012

Knowledge of true block grades is obtained from a mathematical model of an orebody, simulated with sample grades normally distributed and spatially correlated according io a spherical semi-variogram model.The superiority of kriging to the polygonal method of estimation is demonstrated on this modelled deposit by comparing the true values with the kriged and polygonal estimates obtained from sampling the deposit. Finally, selection of blocks of the deposit on the basis of the estimated values, shows that if kriging is used, what is predicted is largely mined, whilst if the polygonal method is used large biases can occur depending on the position of the cut-off grade.

Jan 1, 1978

During a programme to determine the suitability of the UK site for deep disposal of radioactive wastes, geostatistical methods were used to characterise rock heterogeneity on the basis of seismic and wireline acoustic-impedance data. The data were analysed to yield semi-variogram models that quantified the three-dimensional spatial heterogeneity of acoustic impedance. These models were reconciled with geological interpretations of the area and used to generate simulations of acoustic impedance, with wireline acoustic impedance as conditioning data. The three-dimensional simulated images were compared with actual seismic acoustic impedance. The variography confirmed a vertical zoning effect in the Borrowdale Volcanics, showing that it is caused by preferential clusters of high acoustic impedance values corresponding to regions of relatively low porosity. The method provided realistic three-dimensional models from sparse, one-dimensional wireline data

Jun 19, 1905

By G. Pan

A geostatistical approach is proposed for the design of infill drilling programs. The method is consisted of three major steps: developing geological favorability models, delineating mineralization and ore envelopes, and classifying reserves or resources. Geological modeling aims at developing favorable geological zones in which drilling is designed. Modeling mineralization and ore envelopes establishes criteria on potential blocks to be drilled. Top target blocks should be those included within ore envelopes. The framework of resource categories includes five types: probable reserves, indicated reserves, indicated resources, possible resources, and barren. Indicated reserves or resources are the top priority to be drilled for the definition of minable reserves. Possible resources may be considered as targets for further exploration. The algorithms involved in the analysis include indicator favorablity analysis, ordinary kriging, and indicator kriging. A case study presented here involves a gold deposit of Carlin type. The deposit was delineated by a sparse drilling program with 230 feet of average spacing. The infill drilling program designed by the new method suggests a significant reduction on the number of holes from a regular-grid infill drilling pattern.

Jan 1, 1995

By J. A. McLennan

Geological uncertainty is an unavoidable characteristic of all mining projects since only limited information is available from sampling. Mine planning and development decisions with significant economic consequences are made when the geological heterogeneity is inherently uncertain. Geostatistical simulation is preferred over kriging because the methodology provides alternative property realizations that can be combined into a model of geological uncertainty. Geological uncertainty can be transferred into production uncertainty, which can help characterize the economic risk of the project. This paper presents a case study for the Pogo property, being prepared for development near Fairbanks, Alaska. The exact dimensions, grades and production predictions have been modified; however, the methodology is illustrative. The geostatistical methodology consists of (1) assembling the relevant drillhole data and establishing a suitable coordinate system, (2) calculating the target distribution, (3) creating a model of spatial correlation, (4) generating multiple realizations at a small scale and (5) linearly averaging all the realizations to the chosen selective mining unit (SMU) support size. The geostatistical model is then used to calculate production uncertainty.

May 1, 2004

The theory and practice of sampling of particulate material have been the focus of a continued attention on the part of the mining industry worldwide for almost a century now, because of its critical importance at all phases of a mining project, from exploration (bulk sampling, assaying) to production (grade control) and marketing (quality control). A powerful, complete theory was put together by P. Oy (1968 to i982), but its applications to gold ores have met with limited success to date, due to the inadequacy of its sampling variance and minimum sample mass determination formulae to the challenging case of gold ores. This paper presents a research project completed at Inco Exploration and Technical Services Inc., using a geostatistical approach, to shed light on the results of P.Gy's theory, and adapt them to the case of particulate gold ores. After a reminder of Gy's formulae and a simplified demonstration of the generic form of Gy's and more traditional formulae, an empirical approach, based on sampling experiments from four gold deposits, shows how Gy's formulae must be corrected to adjust to the case of gold ores. The generality of the results formula is then substantiated with a geostatistical analysis of the problem. A parameterized formula results, and indications are given on how to fit its parameters to experimental data. Application guidelines and charts to fit any case and budget are presented, along with a detailed practical example.

Jan 1, 1991

By Armstrong M

The highest grades of the Porgera gold deposit, Papua New Guinea, are contained in Zone 7 due to the presence of the Roamane fault, which acted as channelway of the gold-bearing fluids. Prior to the development and underground mining of this fault-controlled high-grade zone it was critical to provide grade estimates of relatively small mining units, and of the proportion of mining units above cutoff. To be applicable to Zone 7 of Porgera a grade estimation method should account for the following:1. the highly skewed and apparently lognormal distribution of the grades,2. the rapid drop off of the local mean grade and the variance as the distance to the Roamane fault increases,3. the presence of high grade pockets in the footwall, away from that fault, and4. the existence of variograms for the logs with sills parallel to the fault and without sills perpendicular to it.

Jan 1, 1990

By J. M. Ortiz

Mineral resource evaluation requires defining geological domains that differentiate the types of mineralogy, alteration and lithology. Usual practice is to consider the domain boundaries as hard, i.e. data from across the boundaries are disregarded when estimating the grades within a given domain. This practice may hinder the quality of the estimates when a significant spatial correlation of the grades exists across the domain boundaries. In this paper, several geostatistical methodologies to handle soft geological boundaries are compared through a case study on a copper mine in Chile. The estimation methods considered are: ordinary kriging using hard boundaries between geological domains; ordinary kriging omitting the geological boundaries; traditional and standardized ordinary cokriging of the grades assayed in different domains; ordinary kriging within dilated geological domains, that is, incorporating samples from adjacent domains up to a given radius from the boundary of the domain being considered. The estimations are performed using a set of exploration data (drill hole samples) and are validated using a set of production data (blast hole samples collected for grade control). Results indicate that kriging with dilated domains performs better than ordinary kriging using hard boundaries or no boundaries and better than the ordinary cokriging approaches. It therefore appears as a simple alternative to global kriging (without considering the geological domains) and allows accounting for changes in the grade average, dispersion and spatial continuity with the geological characteristics of the deposit, via the use of grade variograms proper to each geological domain. The maximal distance for searching samples from adjacent domains should be chosen according to the spatial correlation of the grades across the domain boundaries, or via a cross-validation at an early stage of the mine or a jack-knife if production data are available. Keywords: Kriging; cokriging; soft boundaries; hard boundaries; geological control; geological domains.

Jan 1, 2006

In the estimation of reserves the known values of the variables of interest from surrounding drill holes are used to compute or estimate the unknown value of the orebody over a given region or at a given point of interest. The classical means of doing this are: 1. The Polygonal Method û where the region is divided into polygons centred on bore holes, each variable is then assumed to have constant value over each polygon. 2. Inverse distance methods, where the variable is assumed to vary linearly with the distance between the known values of the drill holes. 3. Inverse distance squared method û a quadratic variation is assumed for the variables between the bore holes.

Jan 1, 1983

By F. A. G. M. Camisani-Calzolari

Approximately 850 groundwater samples were collected over a 29 300 km2 region of the semi-arid Northwestern Cape during the site selection phase of the South African radioactive waste disposal project. The purpose of the geostatistical investigation was primarily to delineate metallogenic occurrences and provinces which might exist below the thin veneer of surficial material and could thus interfere with the suitability of the site, and to quantify the distribution patterns of groundwater parameters in order to establish a relationship to local and regional geology. Up to 34 variables were analysed for each sample. Structural analysis revealed that the study area is statistically uniform. The variables have low correlation coefficients, with the exception of major ions, indicating a general poor degree of interrelationship between the spatial distribution patterns of the different variables. On the other hand, the long semivariogram range of the majority of variables, which reaches 70 km in cases, demonstrates their continuity on a regional scale. Kriging, which was repeated for each parameter, reveals that most variables, particularly trace metals, have distribution trends which are not influenced by local geomorphology or surface lithology. A 50 km wide, 220 km long metallogenic province, defined by kriging, could possibly reflect a broad metallogenic imprint on the basement and could represent a target area for prospecting. Kriging also reveals the possible existence of a wrench faulting system which may well have influenced the Namaqualand coastal graben and the western boundary of the Karoo.

Jan 1, 1987

By A. H. Onur, S. Ural

"The Afsin-Elbistan coal deposit with its 3.4 billion metric tons of reserve is the biggest coal basin and one of the most important resources for electrical energy production in Turkey. The coal deposit is located north of Elbistan, Kahramanmaras Province, in southeast Turkey (Fig. 1).The Kislakoy sub-basin of the Afsin-Elbistan basin was selected as the first open cast mine to feed four power station blocks of 340 MW each. The mine is equipped with six identical bucket wheel excavators of the type Sch Rs (2300/5) 32. The annual coal demand of the power station is 18.5 million metric tons. The Elbistan basin encompasses an area of 900 km2, and its centre lies about 1150 m above mean sea level. The sedimentation took place mainly in the upper Pliocene period. The thickness of the coal bed varies from 20 m to 60 m, respectively. The basal part of the coal beds consists of clay, marl and sandy clay. These formations are overlain by gyttja, which may also occur in the form of calcareous ooze, enveloping coal beds. The thickness of the gyttja is up to 35 m (Otto-Gold, 1969). The coal of Afsin-Elbistan is soft coal and the quality has been found to vary considerably throughout the deposit. The thicknesses of the sterile intercalations vary from 0.50 m to 2.2 m and average 1 m in thickness. From the quality control point of view, the coal seam is regarded as upper seam where the gyttja formation occurs as sterile intercalations, and lower seam where the clay formation occurs instead of the gyttja (Fig. 2). The CaO content of upper Kislakoy coal is very high, grinding resistance is low and base to acid ratio of ash, that is, the ratio of acid oxides of metals to base, is greater than one (Ural and Onur, 2001). Contrary to upper Kislakoy coal, CaO content of lower Kislakoy coal is very low, grinding resistance is high and base:acid ratio of ash is smaller than one. Modified Impact Strength Index (MISI) tests are used to determine the grindability of the Elbistan coals (Ural, 1999)."

Jan 1, 2003

By Y. C. Kim

The results from a retrospective study are described in this gaper in which she past development drilling activities were investigated using geostatistics. The purpose of the study was to determine the amount of savings in drilling cost that could have been realized through the optimal placement of sequential drill holes using geostatistics. Out of 144 DDH's that were in place within the study area, the results showed a possible elimination of 34 DDH's without any reduction on the confidence interval of the global reserve estimates. If the incremental savings from one drilling campaign to the next were considered, however, the amount of percentage savings were even greater. Other interesting results from this study were; 1) tangible demonstration of the importance of a proper geologic delineation within the study zone, and 2) the robustness of the obtained experimental variograms from the rather early stage in development drilling.

Jan 1, 1981

By Jennifer Riefenberg

Ground control hazards, coal quality, ore reserve estimation, and pollution modeling seem unrelated topics from most mining perspectives. However, geostatistical methods can be used to characterize each of these, and more topics. Exploratory drill core data, and continued drilling and field measurements, can provide a wealth of information related to each of the above areas and are often severely underutilized. Recent studies have led to the development of the Multiple Parameter Mapping (MPM) technology, which utilizes geostatistics and other numerical modeling methods, to generate a "hazard index" map, often from exploratory drill core data. This mapping has been presented for ground control hazards relating roof quality, floor quality, numerically modelled stresses due to mining geometry, and geologic features. A review of the MPM method, future directions with the MPM, and a discussion of using these and other geostatistical methods to quantify coal quality, ore reserve estimation, and pollutant modeling are presented in this paper.

Jan 1, 1996

By D. E. Ranta, M. G. Hester

The ore reserve modelling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore-forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high-grade and low-grade drill hole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realtistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1992

By M. G. Hester

The ore reserve modeling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high grade and low grade drillhole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1985