Search Documents

Statistics is essentially a study of variability, the use of some suitable mathematical model representative of such variability, and the application of this inferred pattern of behaviour to practical problems. Probability theory is the mathematical structure devised for providing models for chance happenings. Perhaps the simplest example of a chance happening is the result obtained in tossing a coin. Although the result of a single toss can never be predicted with certainty, there is no reason why in repeated tosses the expectancy of heads and tails should not be equal. In such a case the outcomes of the experiment are said to be equally likely, so that the probability of obtaining heads (or tails) is 1 in 2, that is, 0,5. This simple probability .model refers to a 'mathematical' or 'unbiased' coin. Whether such probabilities are meaningful for actual coins tossed in any particular way is a matter for experience to determine. Probability models have also provided the basis for representing observed variability in cases where the actual under- lying probabilities are only partly known or defy analysis. A typical example of the latter case is the variability observed in the values obtained from gold or other ore samples. The interacting natural forces which gave rise to this variability are obviously very complex and are unlikely ever to be unravelled completely. In spite of this, probability theory and the more recent geostatistical theories have provided us with models which can represent this variability on a reasonable basis. Applied statistics and geostatistics must therefore never be accepted as exact mathematical sciences. Furthermore, a basic and essential concept is that in the type of applications covered in these notes, no model must ever be accepted as necessarily the final and exact answer to the problem; thus, any model must prove and continue to prove its appropriateness in practice, preferably by follow-up comparisons.

Jan 1, 1981

By A. D. Engelbrecht

An investigation was undertaken to ascertain the suitability of four selected low grade, South African coals for gasification in a bubbling fluidized bed for production of synthesis gas and for the development of integrated gasification combined cycles (IGCC). This study consisted of the characterization of the coals, laboratory evaluation of intrinsic reactivity, and experimentation with a pilot-plant fluidized bed gasifier. Results of the characterization experiments show that the selected coals are high in ash, rich in inertinites, very dense (low porosity), with low caking indices and high ash fusion temperatures. Reactivity measurements with a thermogravimetric analyser (TGA), under reaction rate controlling conditions with carbon dioxide, showed that the reactivity of the coal chars decreases with increase in rank of the coal, as expressed by the vitrinite random reflectance and carbon content of the parent coals. The fixed carbon conversion achieved in the fluidized bed gasifier also correlates well with the rank parameter of the coal, with higher conversions being obtained with the lower rank coals. Thermal shattering and attrition of the coal particles produce significant amounts of fines, which correlate with the grindability indices, and no agglomeration (non-caking) was observed. It is concluded that fluidized bed gasifiers are able to utilize typical low grade, high ash South African coals for synthesis gas production and for inclusion in integrated gasification combined cycles for power generation.

Jan 1, 2010

By N. Simpson

Low carbon 11.5% chromium stainless steels are finding increasing use in industry as square or rectangular tubing material for the construction of structures by welding. During processing, resistively welded circular pipes are bent into square or rectangular shapes. During this process longitudinal cracks can sometimes develop atone of the inner corners of the section. An investigation has shown that the processing of round into square tubing with very sharp corners can cause excessive cold working at the inner corners of the squared tube. This, together with the high tensile residual stresses and a susceptible microstructure due to the presence of grain boundary carbides, can result in brittle cleavage cracking. Measures that can be used to reduce the problem are described.

Jan 1, 2003

By D. K. Chibwe, P. Taskinen

"This investigation consists of a numerical and physical modelling exercise on flow patterns, mixing, solid-liquid mass transfer, and slag-matte phase distribution in a 0.2-scale cold model of an industrial Peirce-Smith converter (PSC). Water, kerosene, air, and sintered benzoic acid compacts were used to simulate matte, slag, injected gas, and solid additions into the PSC. The 2D and 3D numerical simulations were carried out using volume of fluid (VOF) and realizable k-e (RKE) turbulence models to account for the multiphase and turbulence nature of the flow respectively. These models were implemented using the commercial computational fluid dynamics numerical code FLUENT.Numerical and physical simulations were able to predict, in agreement, the mixing and dispersion characteristics of the system in relation to various blowing conditions. Measurement of mass transfer indicated that fluid flow in the PSC is stratified. Blowing configurations and slag volume both had significant effects on mixing propagation, wave formation, and splashing.As a potential process alternative to increase conversion efficiency, we propose a combined blowing configuration using top lance and lateral nozzles. The numerical simulations were conducted on combined as well as lateral blowing conditions, and the results of the combined concept are encouraging."

Jan 1, 2015

By E. Pizarro, A. Videla, G. Compan

One of the main problems related to mining investment decisions is the use of accurate prediction models. Metallurgical recovery is a major source of variability, and in this regard, the Chuquicamata processing plant recovery was modelled as a function of geomining-metallurgical data and ore characteristics obtained from a historical database. In particular, the dataset gathered contains information related to feed grades, ore hardness, particle size, mineralogy, pH, and flotation reagents. A systemic approach was applied to fit a multivariate regression model representing the copper recovery in the plant. The systemic approach consists of an initial projection of the characteristic grinding product size (P80), based upon energy consumption at the particle size reduction step, followed by a flotation recovery model. The model allows for an improvement in the investment decision process by predicting performance and risk. The final geometallurgical model uses eight operational variables and is a significant improvement over conventional prediction models. A validation was performed using a recent data-set, and this showed a high correlation coefficient with a low mean absolute error, which reveals that the geometallurgical model is able to predict, with acceptable accuracy, the actual copper recovery in the plant.

Jan 1, 2015

By C. Musingwini, A. S. Nhleko

"Since the Global Financial Crisis (GFC) in mid-2008, capital has been more difficult to access. Mining projects must contend with projects from other industries for scarce capital. A decision to invest available capital in mineral projects requires that valuation be conducted to assess the expected return on the projects. The discounted cash flow (DCF) analysis is generally applied for the valuation of mining projects, whereby future cash flows are discounted to present value using an appropriate discount rate. The discount rate significantly affects the outcome of a valuation. Economic and finance theory provides tools to calculate discount rates. The discount rate must account for factors such as the risk and stage of development of the mineral project; hence the appropriate discount rate to utilize in a project is often a subject of debate.The discount rate is the weighted sum of the cost of debt and equity. There are several methods for determining the cost of equity. This study considers the commonly applied Capital Asset Pricing Model (CAPM) and Gordon’s Wealth Growth Model because of their simplicity and availability of parameters required to estimate the cost of equity. This study explores how differences in the cost of equity obtained by these two methods can be explained for a mining environment. Data for empirical analysis were collected from the I-Net Bridge, McGregor BFA, and Bloomberg databases. It was found that Gordon’s Wealth Growth Model provides better estimates of the cost of equity compared to the CAPM under depressed market conditions. Therefore, this research recommends that Gordon’s Wealth Growth Model be used to estimate the discount rates for mining projects during periods of depressed market conditions."

Jan 1, 2016

By Y. -J. Park, K. -H. You, Y. -T. Choi, Lee. H. -W.

Many large caverns are being constructed in great depths in Korea mainly for the storage of oil and LPG. These caverns are mostly located near the port where rock conditions are reasonably good. In some instances, the horizontal stress is very high and endangers the stability of the cavern. The purpose of this study is to assess the stability of large caverns excavated in a rock mass with high horizontal stress where Ko value is close to 3. Result shows that stress exerted in the shotcrete at crown exceeds allowable value when the 3rd bench is excavated. Also found is the tensile failure of shotcrete near the boundaries between benches. In Korea werden viele grosse Kaverne fuer Aufbewahrung vom Oel und Fluessiggas in grosser Tiefe gebaut. Am Meisten befinden sich diese Kaverne in der Naehe von Haefen, wo der Fels gute Verhaeltnisse zum Bauen einer Kaverne besitzt. In einigen Faellen ist die Horizontalspannung sehr gross und dadurch wird die Stabilitaet vom Kaverne gefaerdet. Der Zweck dieser Arbeit ist die Stabilitaet des im Fels gebauten grossen Kavernes mit hoher Horiaontalspannung zu schuetzen, wo Ko-Wert sich auf 3 naehrt. Die Ergebnisse zeigen, dass die Spannung im Spritzbeton an der Krone den zulaessigen Wert ueberschreitet, wenn das dritte Bank ausgegraben wird. Im Bereich des Spritzbetons zwischen Baenke wurde das Zugversagen festgestellt. Des larges cavités nombreuses sont en train d’être construites en grand profondeur en Corée prin-cipalement pour le stocage du pétrole et LPG. Ces cavités sont pour la plupart situées près de la porte oú les conditions des roches sont résonablement bons. En quelques cas, la contrainte hori-zontale est trés haute et met en danger la stabilité de la cavité. L’objet de cet étude est d’estimer la stabilité des large cavités excavées dans une masse de roche ayant une haute contrainte horizontale oú la valeur de Ko est proche à 3. Le résultat montre que la contrainte exercée dans le shotcrete à la couronne dépasse la valeur admissible quand le troisième banc est excavé. En plus une faillite en tension du shotcrete près de la frontière entre des bancs est trouvée.

Jan 1, 2003

By R. Webster

"Daniel Krige’s influence on soil science, and on soil survey in particular, has been profound. From the 1920s onwards soil surveyors made their maps by classifying the soils and drawing boundaries between the classes they recognized. By the 1960s many influential pedologists were convinced that if one knew to which class of soil a site belonged then one would be able to predict the soil’s properties there. At the same time, engineers began to realize that prediction from such maps was essentially a statistical matter and to apply classical sampling theory. Such methods, though sound, proved inefficient because they failed to take account of the spatial dependence within the classes.Matters changed dramatically in the 1970s when soil scientists learned of the work of Daniel Krige and Georges Matheron’s theory of regionalized variables. Statistical pedologists (pedometricians) first linked R.A. Fisher’s analysis of variance to regionalized variables via spatial hierarchical designs to estimate spatial components of variance. They then applied the mainstream geostatistical methods of spatial analysis and kriging to map plant nutrients, trace elements, pollutants, salt, and agricultural pests in soil, which has led to advances in modern precision agriculture. They were among the first Earth scientists to use nonlinear statistical estimation for modelling variograms and to make the programmed algorithms publicly available. More recently, pedometricians have turned to likelihood methods, specifically residual maximum likelihood (REML), to combine fixed effects, such as trend and external variables, with spatially correlated variables in linear mixed models for spatial prediction. They have also explored non stationary variances with wavelets and by spectral tempering, although it is not clear how the results should be used for prediction. This paper illustrates the most significant advances, with results from research projects."

Jan 1, 2015

By Lutz Markworth, Wolfram Jaspers, Johannes Kottmann

PNEUFLOT® technology has been applied for the past 20 years in coal, ore and other minerals processing plants. During the last two years this technology has achieved a breakthrough with some 42 units being sold signifying a rising trend. »Humboldt Wedag Coal & Minerals Technology« has performed extensive research and development work over the last five years. The results of which were used to design a new fourth generation aerator. Humboldt Wedag, through its association with EKOF, can offer a holistic solution encompassing both flotation equipment and reagents. It is the only company in the world able to offer such a package. The association with EKOF strengthens the Humboldt Wedag product offering, especially as the company in-troduced pneumatic flotation cells to the South African market in the form of the PNEUFLOT®. Before starting pilot scale test work, a mineralogical analysis has to be carried out to determine the mineral com-position as well as the liberation grade. HW-CMT works together with independent institutes. Different reagent regimes can be tested in laboratory scale. Pilot machines, each packed in a 20? container, are available to carry out extensive test work at customers? processing plants. A group of engineers from HW-CMT is involved in the pilot test work. The flexible pilot machines are designed to cater for coal, ores and other minerals. The small feed rates of 7 ? 12 m³/h only means the pilot machines do not disturb the operation of process plants. Batch tests have to be carried out to determine the numbers of PNEU-FLOT® stages. New applications in iron ore, copper ore, platinum group minerals, rock phosphate and potash were suc-cessfully tested in the last three years. In applications where the feed material is very fine, PNEUFLOT® technology is able to achieve high recoveries with particle sizes where conventional technology failed.

Jan 1, 2007

By TvS. von Moltke

Steel is a highly versatile material due to its low cost and good mechanical properties, but typically needs some or other form of corrosion protection due to its tendency to corrode when exposed to atmospheric conditions. In the case of organic coatings, the corrosion protection and functionality of the final product is critically dependent on the adhesion of the coating to the surface of the steel. In this work the effect of contaminants and the nature of the surface layers present on industrial steel products are investigated by means of paint adhesion tests, Auger electron spectroscopy (AES), and X-ray Photoelectron spectroscopy (XPS). It was found that the presence of sodium species on the surface is very detrimental to paint adhesion under wet conditions, while satisfactory adhesion may be obtained even in the presence of silicon and carbon residues. It was also found that the nature of the Fe-O layer, formed under wet conditions is labile and different from that formed in dry air, and that subtle changes in process conditions, such as changing the oxygen content of the quench water, may change the adhesion of paint to the surface of the steel. Lewis acid-base interactions are discussed as a mechanism that may determine the bonding between the steel and polymer coating.

Jan 1, 2003

By Ö. Erdem

The investment decision making process in the insurance and finance industries is affected by new advances such as simulation techniques. These advances have improved the discounted cash flow method (DCF). In DCF, a dynamic and flexible model construction is not possible because it does not consider uncertain conditions. Each project should be evaluated taking into account the related uncertainties because the related uncertainties determine the characterization of the project. Related uncertainties can be processed in dynamic DCF, which is applicable to both financial and non-financial industries with different kind of uncertainties, such as power generation and petroleum projects. The dynamic DCF method can estimate net present value (NPV) while managing related project uncertainties with a simulation method like Monte Carlo Simulation. The simulation method is preferred because its output is unbiased. Therefore, a more realistic financial evaluation of the project can be concluded. In spite of the improvement of dynamic DCF, this project evaluation method is not used frequently in mining industry. However, the mining industry is ideally suited to this concept because it is highly dependent on estimations such as orebody size and ore grade. During the project evaluation stage, these uncertainties can be included with the dynamic DCF method. This study aims to contribute to increasing the usage of this method in mining projects. A copper reserve in Turkey is selected as a case study to apply uncertainty assessment for the evaluation of NPV.

Jan 1, 2012

By Y. He

Early research showed that the separation of particles based upon their density was not possible in steadily rising air streams. The terminal velocities of moving spheres are determined by their aerodynamic characteristics. This prevents particle separation by density in standard air classifiers. Passive pulsing air classifiers have accelerated airflow in certain regions, which achieves density-dominant separation. Numerical simulation of airflow within passive pulsing air classifiers was done to estimate airflow patterns near a damper. Analysis of those results shows the significant acceleration of the airflow above the damper. Laboratory trial separations have shown that passive pulsing classifiers are superior to standard air classifiers. Keywords: pulsing airflow, passive, simulation of airflow models, acceleration effect, density

Jan 1, 2005

By S. Michael, T. E. Moongo

Electrowinning consumes a substantial amount of electrical energy, and owing to the ever-increasing unit cost of electrical power there is a need to improve current efficiency in the process. This research was carried out to design a continuous quality improvement framework for improving electrowinning current efficiency by applying statistical process control (SPC) on an online industrial copper electrowinning operation. A sequential mixed research methodology was applied and a statistical software package utilized for analysing data. It was concluded that metallurgical short-circuits (hotspots) had the most significant effect on current efficiency. Bringing hotspots under statistical control resulted in a 5.40% improvement in current efficiency, which is equivalent to approximately 74 t of 99.999% pure grade A copper cathode production over a period of 1.5 months.

Jan 1, 2021

By Hao Li, Allan Moss, Richard K. Brummer

At the Palabora Mine, the transition to caving 400 m below the bottom of the 800 m deep pit resulted in a slope failure of the North wall that began in 2003, and is still mobile. This failure can be explained by the daylighting into the cave zone of a prominent joint set. The failure was modelled by the 3-dimensional code 3DEC, which is capable of modelling the nonlinear behaviour of discontinuum materials with large displacement.

Jan 1, 2006

A well known rock mass classification system has been altered slightly to address the issues found under remnant mining conditions. By detail study of the expected fracture patterns and local geology, the rock mass is classified to indicate the condition of the hanging wall prior to mining. The risk level of each mining step is evaluated by calculating input parameters for computer simulations from the actual rock mass condition. Seismic activity is catered for by the understanding that large event rates and large magnitude events reduce the quality of the local rock mass and that the rock mass stiffness should be adapted accordingly. A case study is presented to test parts of the protocol. Un système connu de classification des masses rocheuses a été légèrement modifié pour faire face aux questions posées par les conditions d’extraction de débris. Une étude détaillée des diagrammes de fragmentation et de la géologie locale permet de classer la masse rocheuse pour indiquer la condition du toit avant l’extraction. Le niveau de risque de chaque étape minière est évalué en calculant les paramètres d’entrée pour simulation par ordinateur à partir de la condition réelle de la masse rocheuse. L’activité sismique est prise en compte avec la réalisation que les taux de larges évènements et les évènements de large magnitude réduisent la qualité de la masse rocheuse locale et que la raideur de la masse rocheuse doit donc être adaptée. Une étude de cas est présentée pour tester des sections du protocole. Ein sehr bekanntes Gesteinsmassenklassifikationssystem wurde abgeändert um die Probleme zu behandeln die unter Restabbaukonditionen angetroffen werden. Durch detaillierstes Studium der der zu erwartenden Bruchmuster und der lokalen geologischen Verhältnisse wird die Gesteinsmasse in Hinblick auf die Konditionen der Flözoberseite klassifiziert. Das Risikoniveau für jeden Abbauschritt wird durch die Eingabeparameter aktuellen Gesteinsmassenkondition für die Computersimulation evaluiert. Für die Seismische Aktivitäten wird Sorge getragen durch das Verständnis, daß große Ereignisraten und Ereignisse hoher Größenklassen die Qualität der lokalen Gesteinsmasse reduzieren und daß die Gesteinsmassensteifheit entsprechend adaptiert werden sollte. Eine Fallstudie um Teile des Protokolls zu testen wird präsentiert.

Jan 1, 2003

By M. Saghaeian, R. Hejazi, L. Hosseini, M. V. Sheikhzadeh

Blaine number has long been used to evaluate the pelletising ability of iron concentrate in the industry. Much information and practical data are available about the effect of Blaine number on pelletising efficiency of different concentrate types. But not many researchers have focused on the effect of Blaine increasing method on pelletising behaviour of coarse concentrates. In this paper the effect of two different grinding methods (i.e. HPGR and Ball Mill) on physicochemical properties of coarse magnetic concentrate green and fired pellets were investigated. Microstructural studies by Field Emission Scanning Electron Microscope (FESEM) showed that the concentrate for which the Blaine number had been increased through HPGR grinding, has flake-like morphology. In contrast, increasing the Blaine number through ball mill grinding results in more granular particles. Two samples were prepared using HPGR and ball mill. The Blaine number of the HPGR product and ball mill product were 900 cm2.gr-1 and 1200 cm2.gr-1 respectively. The results revealed that pellet properties of this HPGR product are comparable to that of the ball mill product; this is due to the fact that the flake-like morphology leads to enhanced pelletising performance of coarse magnetite concentrates. Keywords: Iron pelletising, Blaine number, HPGR, ball mill, coarse particles

Jan 1, 2020

By J. Daraisme

Société le Nickel (SLN) exploits the Dôme lateritic nickel orebody at its Tiébaghi operations in New Caledonia. The site geology has an obvious bearing on recovery and metallurgical performance, and the controls are extremely complex at all scales: lithology, oxidation-reduction conditions, mineralogy, and multivariate geochemistry. In that context, establishing an adapted recoverable resource estimation method that is efficient and transparent proves an interesting challenge. The method must address the key notions of: ? Support effect: the exploration data-set can only warrant the estimation of large panels 20×20×3 m3, which are much larger than the selective mining units (SMUs) of 5×5×3 m3 ? Information effect: the selection at production stage uses estimates based on information much denser than that available for mine planning. The problem is rendered more complex in this type of deposit by the fact that the additive variables used for any estimation process (metal accumulation and ore tonnage) are not the ones used to establish the selection at mining stage (i.e. the nickel grade of SMUs, which is the ratio of accumulation on tonnage). Eventually, the selection criteria involve not only Ni grades but also other constituents such as Al2O3, Fe2O3, MgO, and SiO2. The solution presented in this paper is the construction of a platform of SMU multivariate simulations in the saprolitic horizon, together with efficient post-processing aimed at producing the multivariate recoverable resource estimates. The efficiency constraints imposed by the number of blocks to be simulated (1.5 million) lead to resorting to direct block simulations. The underlying multivariate discrete Gaussian model (DGM), the validity of which is tested beforehand, is put to good use to mimic the selection process at the mining stage, by offering the ability to simulate in each block a composite value located at random within the block. Finally, the paper presents the application of a scenario reduction algorithm to pick a representative subset of a few simulations to help appraise the risk attached to the downstream phases (reserve optimization, mine sequencing) of the project. The implementation presented here is for the first generation of the Scenario Reduction plugin built in Isatis software, where measuring the distance between the initial set of scenarios and the reduced set is based on Ni quantities only. Research is under way to adapt the measure to the true multivariate nature of the problem.

Jan 1, 2014

By R. J. Jewell

The storage capacity of any given tailings storage facility (TSF) is a function of the volume available for the tailings, for which the geometry of the final upper surface of the tailings is most important. One of the advantages that can be obtained from thickening tailings prior to discharge is that the tailings can be stacked at a steeper beach angle than is obtainable with conventional low-density slurries. However, there is at present no universally accepted method available for the accurate prediction of tailings beach slopes. This paper examines the current situation with the objective of putting the quest for a method for the accurate prediction of beach slopes into perspective. The paper references published reviews of the best-known beach slope prediction methods. However, there do not appear to be any independently verified projects or published references to projects on which a Class A prediction has been validated for any of these approaches, and in those instances where projects have been implemented correlation of actual with predicted slopes has been poor - often due to differences between the properties of the tailings assumed in the design and those actually achieved in the field. The author also concludes that flume-scale testing cannot be taken as a reliable indicator of full-scale performance, and suggests that the outcome of any current predictive method should be used by experienced practitioners as only one of a range of indicators in order to suggest a range of slope angles likely to result for any given operation. Practice has shown that it is possible to manipulate beach slopes by changes to the disposal technique, such as limiting the rate of discharge per discharge point and by increasing or decreasing yield stress, but the impact of these changes cannot readily be predicted. There are also newly emerging technologies, such as the injection of a polymer into the tailings at discharge, that will enhance the dewatering of tailings and hence expedite the consolidation of the tailings, that could well facilitate the development of steeper beach slopes. The overall conclusion is that with the current state of knowledge, the accurate prediction of beach slopes is not possible. Furthermore, in view of the inherent variability of the tailings parameters from any operation, it may well be of more value to concentrate on developing an understanding of the means by which the tailings parameters may be manipulated by the operators to achieve a given beach slope than to concentrate wholly on developing a generic beach slope prediction model.

Jan 1, 2012

By R. Altindag

Engineers and researchers need to estimate the mechanical properties of rocks from P-wave velocity. In previous studies, the researchers have investigated either the limited values or all the data belonging to sedimentary, igneous, and metamorphic rocks together in the same statistical analysis. In this study, the raw data pertaining to only sedimentary rocks was taken from previous studies and evaluated. For this purpose, a total of 97 samples of sedimentary rock types were subjected to statistical analysis. First, the relationships between P-wave velocity and physical-mechanical properties were investigated by simple regression analysis. All the data were then subjected to multi-regression analysis. Some empirical equations with high correlation coefficients were derived for rock engineers. The equations obtained from the analyses are compared with previous equations found in literature.

Jan 1, 2012

By F. Habashi

The first documentary evidence for the use of fire to extract a metal was furnished by the wall paintings of the ancient Egyptians showing workers using the blowpipe and bellows to increase the temperature to melt gold in a crucible. Furnaces grew in size and complexity, coke replaced charcoal in the blast furnace, and the Industrial Revolution took place in England that gradually spread worldwide. More metals became known and new techniques were introduced for their extraction. Among these, metallothermic reactions became prominent in the nineteenth century immediately after the discovery of the electric current and its use to liberate the alkali metals from their salts. Once these metals became available, they were used to produce aluminium from alumina that resisted all other methods of attack. Aluminium, now available on a large scale, was used to decompose the most stable compounds and liberate more metals that became the basis of modern civilization.

Jan 1, 2004