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By S. Al-Thyabat

Conditioning of flotation feed is an important prerequisite for efficient flotation. This process depends on parameters such as conditioning time, slurry concentration and slurry pH. The objective of this paper is to optimize the conditioning process for the flotation feed. This was achieved by first conducting preliminary experiments at constant slurry pH to determine the significant ranges of slurry concentration and conditioning time. Then, factorial experimental design (32 experiments) was used to investigate the significance of the above parameters and their interactions on flotation recovery and grade. Statistical analyses using ANOVA approach showed that flotation recovery (R) and concentrate grade (g) were affected by feed conditioning. It was found that concentrate grade was linearly proportional to the slurry concentration and conditioning time, while flotation recovery was exponentially proportional to the conditioning parameters. A contour plot of the flotation response (recovery and grade) against conditioning parameters showed that the optimum operating parameters for flotation feed conditioning was a conditioning time of 1.5 to 2 minutes and a slurry conentration of 55% to 60%.

Jan 1, 2008

In making any attempts to determine the depositional environments in which coal seams accumulated it would be useful to establish whether there is a pattern, or patterns, of development which the majority of the seams have followed. To this end, the distribution of types of coal seam sequences found in the standard petrographic profiles of about a hundred Australian coal seams of Permian and Triassic age has been examined statistically, using the "chi square test" with the limiting probability set at O·Gl.Results indicate that non-random conditions have probably prevailed during the deposition of most of the seams. More samples are needed for conclusive results.The plants, or some other internal feature of the swamp environment, have been the important controlling factor in the development of the seam sequences.Comparison has been made with some British Carboniferous coals.

Jan 1, 1972

By S Pfaff, R Rajic

In the case when the number of independent variables is greater, a careful design for carrying out tests has to be made in order to obtain, with the smallest possible number of tests, as much as possible neutral information about the influence of independent variables on the dependent ones. Only on the basis of such design and its statistical analysis it is possible to come to right conclusions about the function of the whole system. The influence of pressure, temperature, humidity and granulation of the coal upon the resistance to pressure and the water absorption of the briquettes has been tested, with the aim to examine how each of the two dependent variables changes depending on the values assumed by any of the four independent variables and which of the mentioned independent variables significantly influences the dependent ones. The full factorial design with 16 experiments and the central composite design with 27 experiments have been applied. The influence of the independent variables upon the dependent ones has been examined by applying the analysis of variance. The influence values of individual factors and their interaction upon the dependent variables have been stated as well as coefficients of curvilinear equation.

Jan 1, 2003

INTRODUCTION TO STATISTICAL INFERENCE The intent of the mineral appraiser in collecting samples from a mineral deposit is to arrive at accurate conclusions concerning the size and value of the deposit. In other words, he wants to derive reliable inferences about the total mineral population from the collected sample data, which (he hopes) is representative of the whole. The discussion of sampling theory in Chapter 2 was oriented toward assuring that our sampling techniques and sampling units would indeed be representative of the total mineral population. Chapter 3 described the most common statistical parameters for defining distribution in various populations. Chapter 4 gave some insight into theoretical distributions of random variables and the probabilities associated with them. The intent of this chapter is to derive inferences from the preceding information about the population mean and the population variance. Knowing something about the normal distribution, and assuming our samples represent a roughly normal population, we can make inferences or logical deductions about the estimated interval or the limits of values which can be assigned to a mineral population. ESTIMATION OF POPULATION PARAMETERS In the application of statistics to mineral deposits it is never possible to know the actual values of the parameters or the theoretical distribution of values within the deposit for which our data are samples. Even after the deposit has been mined out it is questionable if the true value of the parameters can be retrieved accurately, due to dilution, mining, and processing losses. Therefore, our problem is to determine what function of our sample values we should use to estimate the unknown parameters of greatest interest to us-namely, the population mean and the population variance of the deposit. Since we cannot know

Jan 1, 1980

By H. Stocker, C. E. Makepeace

"This paper presents the statistical analyses of several sets of data acquired in several programs of sampling of radon daughters in uranium mines. The measurements were taken over periods of days or weeks for given locations or location occupations within these mines. Because the sampling applies to specific intervals of time and specific locations, a method is suggested f or the eventual application of a monitoring program which would be suitable on an annual basis for these locations. The present data and analyses thereof are not justifiably applicable to a monitoring regimen on an annualbasis, without a number of additional assumptions.The aim of the present analyses of concentration measurements is the determination of the minimum number of measurements required to achieve an annual radon daughter exposure estimate, for individual workers, having an error no greater than 50% at the 95% confidence level. The criterion of accuracy is taken from a statement in the American National Standard, Radiation Protection in Uranium Mines (ANSI NI3.8-I973), and is currently used, in somewhat modified form, as a guide to uranium mining licensees in Canada. Uncertainties associated with occupancy time are ignored in the present analysis. IntroductionOne of the principal aims of any scheme of radiation protection is that of improving the accuracy of exposure estimation for workers. The example presented here is from the area of radon daughter exposure estimation for uranium miners. The conventional means of estimating workers' exposures is grab sampling of radon daughter concentrations combined with occupancy time weighting in the various work and travel locations. Uncertainties exist in each of these components, and in an environment of highly variable radon daughter concentrations (such as an active uranium mine) one is always uncertain as to the representativeness of the grab sample (compared to the average concentration) unless a sophisticated monitoring scheme has been implemented based on previous experience in such an environment.Improvements in the accuracy and precision of employee radon daughter exposure records depend, primarily, on three factors;"

Jan 1, 1980

By G. B. Gould

EVERY mathematical statement of a measure of anything (as distin-guished from a count) is followed by a qualification always implied if not explicity stated--that the statement is only an estimate, which may vary from absolute accuracy within certain limits, according to the accu-racy of the measuring instrument. This basic fact, so obvious to engineers, is not so well understood by many that make use of laboratory coal tests. The tolerances that must be allowed in measurements of coal quality are very important in both their commercial and engineering applica-tions-and the significance of these tolerances depends upon the use made of the laboratory coal test. Only in recent years has there been any intensive study of this ques-tion of tolerances as applied to measurements of coal quality. There is very little in our published literature on the subject, and what has been published is not, readily comprehended by those who sell coal, or buy coal and use it, unless they happen to have made a study of the subject them-selves. There is great need for more widespread understanding of what has been discovered and how it applies to the use of laboratory coal tests. What follows is an attempt to condense into a few pages the results of the major investigations so far reported, and to explain their meaning in simple nontechnical language, with the addition of some recent illustrative experiments.

Jan 1, 1937

By Arthur W. Rose

Statistical techniques are being widely used in geochemical exploration to answer questions involving sample spacing, analytical and sampling errors, thresholds, data smoothing, and optimum combination of several elements into one measure of favorability. The applications of sampling theory, mean and standard deviation, trend surfaces, moving averages, factor analysis, cluster analysis, discriminant analysis, and regression analysis to these questions are discussed with examples. Although the techniques are very useful as means of handling large amounts of data, they require as much geological and geochemical judgment as any other approach to data interpretation.

Jan 1, 1973

During 1995 a catastrophic accident took place at the No 2 Vaal Reefs shaft in South Africa, when a locomotive fell onto a cage, causing the death of 104 people. The subsequent Commission of Enquiry found that the safety detaching hook had opened when hit by parts of the falling locomotive, detaching the cage from the rope and allowing the cage to drop 400 m down the shaft. It was believed that had the hook not detached, the rope would have been sufficiently elastic not to have failed, implying that many fatalities may have been avoided. In addition, the risk of accidental opening of hooks due to impact with smaller falling objects in shafts became a concern. This paper deals with a comprehensive statistical investigation that was performed to quantify this risk, establish acceptable levels of such risks and to derive criteria for the resistance of detachment hooks against accidental opening caused by impacts. The investigation involved a survey, dynamic finite element analyses and Monte Carlo simulations.

Jan 1, 2005

By John A. Patterson

There are certain data handling techniques used by statisticans that can help one to calculate the size of an orebody and to develop some of the relationships between size, cutoff grade, average grade, mining cost, and profit. Knowing the relationships amongst these factors can help determine the most desirable operating conditions. A statistical technique that we will use is data grouping. This allows us to work with relatively few groups instead of many samples, If we were able to segregate the ore in an orebody into grade groups, add the amounts in each group, and plot the sums as a curve, we would get something like Figure 1. A smooth curve develops when the grade classes are small enough, otherwise a "stair step? histogram results. The area under the curve, being the sum of the tonnages in all of the grade classes, is proportional to the total number of tons in the orebody. If we take the data of a distribution such as Figure 1 and add the tonnages above a specific grade we have in effect a cutoff grade

Jan 1, 1958

By Milton Barbosa Landim, Denise de La Corte Bacci

Statistical methods of multiple regression analysis, trend surface analysis and principal components analysis were applied to seismographic data recorded during production blasting at a diabase quarry in the urban area of Campinas (SP), Brazil. The purpose of these analyses was to determine the influence of the following variables: distance @), charge weight per delay (W), and scaled distance (SD) associated with properties of the rock body (orientation, frequency and angle of geological discontinuities; depth of bedrock and thickness of the soil overburden) in the variation of the peak particle velocity (PPV). This approach yielded variables with larger influences (loads) on the variation of ground vibration, as well as behavior and space tendency of this variation. The results showed a better relationship between PPV and D, with D being the most important factor in the attenuation of the ground vibrations. The geological joints and the depth to bedrock have a larger influence than the explosive charges in the variation of the vibration levels, but frequencies appear to be more influenced by the amount of soil overburden.

Jan 1, 2002

Six simulations by the Mpnte Carlo method employing both classical and geostatistical techniques are presented for the determination of the probability distribution of the in situ value of a coal seam. To avoid the problem of qualitative estimation of parameter variability in the calculation of an arbitrary seam value, only data values from borehole information were used to quantify the variation in four coai seam parameters.The method which is suggested as being the most appropriate is a particular geostatistical approach that employs the best linear unbiased estimate and the error of estimation for a number of two dimensional blocks. The results indicate that the variance of the coal seam unit value may be much higher than that indicated by the classical approach because of the spatial variability that is properly incorporated in the geostatistical approach.The model used in the Monte Carlo simulation to determine the economic value of a coal seam can be extended to incorporate all those parameters which are necessary for a true estimation of the probability distribution of the coal seam value. A time value concept for discounting can also be incorporated to optimize the economic return of a coal mining project.

Jan 1, 1983

By F. P. Agterberg

"IntroductionTHE KNOWLEDGE about the mineral resources in a region ranges from relatively precise ore-reserve estimates for known deposits to probabilistic estimates concerning the speculative resources which may be discovered in future at greater depths and in the less-explored parts of the region. Previously developed probabilistic methods for regional resource evaluation (1) are based on the following two assumptions.(1) The probability that a specific block of rock, or part of a region close to the topographic surface, contains undiscovered deposits can be estimate d by weighting selected geological, geophysical or geochemical parameters for that block. The weights are computed by considering similar environments which are known to contain deposits.(2) Some of the characteristics of the undiscovered deposits, such as ore tonnages and average grades of metals contained in the ore, can be evaluated by considering probability distributions f or known deposit data. These methods were initially applied to Precambrian deposits in the Abitibi Volcanic Belt of the Canadian Shield (1).Since 1972, statistical methods for quantitative resource evaluation have been applied to the occurrences of the mainly Paleozoic base metal deposits in t he Canadian Appalachian Region. The objectives of this project (Project Appalachia) have been discussed by Leech (2) in a paper that introduces 8 papers with results of the exploratory data analysis. Project Appalachia represents an effort to develop and apply methods of combining information and concepts from regional geology, metallogeny and geomathematics for computer- aided regional mineral resource evaluation."

Jan 1, 1977

Statistical frequency distributions may be used to characterize the overall variation of grade in orebodies. Special types of distribution (e.g. lognormal, log-type A) are necessary to describe skewness inthe case of rare metals. Also needed (but for the most part hitherto neglected) is the serial correlation function which describes the tendency for grades near together in an orebody to be closer together than grades at points relatively far apart.The sampling problem for orebodies is interpreted in statistical terms. Different methods are reviewed, and the effect of serial correlation discussed.A discussion is given, based on experiments and observations made by the author, of biases arising in the minei:l material by such methods as chip sampling and grab sampling due to such causes as nonrepresentative selection by the sampler.INTRODUCTIONMiners have always recognized the large element of chance in their operations. Chance is the raw material of statistical theory and, provided there is some recognizable pattern or underlying regularity in a set of data arising from the operation of chance events, statisticians are able to formulate mathematical models to study them. Mining engineers, geologists, and statisticians have gone a long way between them towards finding general statistical rules which describe the distribution of minerals and metals in orebodies, and even the distribution of orebodies over the earth's surface.These rules do not have the force of physical laws, though they obviously derive from them and have been used to throw light on them. From statistical theory it is possible to find methods of estimating from sampling some of the characteristics of orebodies which are of importance to...

Jan 1, 1962

By V. M. Lsoitko

Statistical methods of technological mineralogy are used to model processing flowsheets in order to improve ore dressing efficiencies. The procedure involves determining geological and mineralogical characteristics of ores, classifying ore types and metallurgical procedures, and developing computer programs to interpret essential mineralogical parameters from on-stream analysis data. The on-stream analysis data include magnetism, radioactivity, luminescence and assays. The data are interpreted by computer and appropriate adjustments are made automatically in the plant.

Jan 1, 1989

By K. R. Long

Until it was defunded in 1995, the U.S. Bureau of Mines maintained a Cost Estimating System (CES) for prefeasibility-type economic evaluations of mineral deposits and estimating costs at producing and non-producing mines. This system had a significant role in mineral resource assessments to estimate costs of developing and operating known mineral deposits and predicted undiscovered deposits. For legal reasons, the U.S. Geological Survey cannot update and maintain CES. Instead, statistical tools are under development to estimate mining costs from basic properties of mineral deposits such as tonnage, grade, mineralogy, depth, strip ratio, distance from infrastructure, rock strength, and work index. The first step was to re-estimate ?Taylor?s Rule? which relates operating rate to available ore tonnage. The second step was to estimate statistical models of capital and operating costs for open pit porphyry copper mines with flotation concentrators. For a sample of 27 proposed porphyry copper projects, capital costs can be estimated from three variables: mineral processing rate, strip ratio, and distance from nearest railroad before mine construction began. Of all the variables tested, operating costs were found to be significantly correlated only with strip ratio.

Jan 1, 2011

By Wignall. T. K., J. De Geoffroy

Statistical models are fitted to the observed distributions of eighteen characteristics of the population of commercial porphyry deposits of North and South America. The statistical base required for the formulation of the statistical models includes 58 commercial porphyry-copper-molybdenum deposits of the Cordilleran Belt from which geological, geometric and economic data were collected. Predictive and composite models are derived from the statistical study to assist explorat10n. planning, engineering studies and fmanc1al analyses as required for the development of new porphyry deposits in the Cordilleran Belt.

Jan 1, 1973

By J. Z. Cui

In this paper a statistical multi-scale method for the mechanics parameter prediction of the rock mass with random distribution of multi-scale cracks/joints is presented. First the micro-structure of the rock mass with random distribution of multi-scale cracks/joints is represented. Then the statistical second-order two-scale method for the mechanics performance predictions of the rock mass structure with random cracks/joints distribution is presented, including the statistical second-order two-scale expression on the vector-valued displacement, strain tensor and stress tensor, and the algorithm procedure of statistical multi-sale computation for the mechanics parameters. Finally some numerical results for mechanical parameters for the rock mass with random distributions of multi-scale joints/cracks by statistical multi-scale method are shown.

May 1, 2009

By L. Yacher

Most metallurgical plants already have sophisticated control systems as well as a process-historian that manage thousands of real-time and historical variables. There exists a huge potential for operational improvement through the inference of patterns, correlations and cause-effect relationships within these records. The ability to run online and offline advanced multivariate statistical analyses represents a great potential for the mining industry, in various areas such as cathode quality improvement in an SX/EX plant, the analysis of the correlation between the ore characteristics and the mill throughput, the determination of early failure alerts for major equipment, etc. The background theory is described, as well as some practical experiences of operations in Chile and Peru. Cu2007

Jan 1, 2007

By F. Romero, L. Yacher, M. Orchard

Specific software tools for Statistical Multivariate Analysis combined with real time process data were applied to Concentrator Plant at Compañía Minera Doña Inés de Collahuasi SCM in Chile, basically to two Mill Lines, each one with one SAG mill (32’x15’8MW)and one Ball mill (22’x36’9.7MW). The main objective was to empower the operator actions using process patterns references instead of process variable set-points. Pattern clustering and the analysis of pattern deviations regarding normal or desired pattern, allows for improvements in process control and the further implementation of soft sensors for those variables not included in the initial model.

Jan 1, 2003

By G. Reed Marchant

The control systems engineer is often faced with the problem of designing tests or experiments where the cost of obtaining information is expensive. This is true in aerospace as well as in process industries. In these situations the details of test design should be carefully evaluated before any test is executed so that the maximum amount of information is obtained for the effort expended. In recent years there has been a steady trend towards increased automation, In the process industries this has resulted in extensive review of process variables and, instrumentation techniques, development of more accurate system mathematical models, and extensive investments in complex control system as well as completely automated plants. When planning and developing these systems, where each measure of a process variable is usually expensive, it behooves the design engineer to give considerable thought to the details of test design before instrumentation is procured and installed so that the maximum amount of information can be obtained for the expense incurred.

Jan 1, 1968