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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 M. J. Daly

Historically, engineers and scientists, particularly those involved in the coal-mining industry, have been slow to adopt statistical methods. However, the need to obtain the maximum information .from expensive exploration and development programmes, and the current focus on total quality management, have led to a change in perceptions if classical statistical and geostatistical methods and their application as planning tools. Some if the underlying issues associated with the generally poor communications between statisticians and engineers/physical scientists, which contribute to some if the misconceptions relating to statistical methods, are discussed The potentially profitable application if a number if statistical techniques in the fields if geological evaluation and mine planning! development is also reviewed, with specific reference to the coal industry.

Jan 1, 1995

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

By S Taylor, B Lumsden, G Long

Statistical metallurgical plant trials are becoming more widespread, as a valuable tool for increasing plant profitability. Generally, a single parameter like metal recovery varies under the trial condition while all other variables such as average metal feed grade or average metal concentrate grade are equal for the two test conditions during the period of the test. Metal recovery is usually the measured variable because concentrate grade is fixed by smelter terms, and plants operate to maximise recovery at the required concentrate grade. However, in all flotation plants there is a relationship between concentrate grade and metal recovery, and under the same conditions increasing one results in a decrease in the other. At MMGÆs Rosebery Mine the zinc concentrate produced is generally above smelter specifications, so zinc concentrate grade can vary during a test. During trialling of magnetic conditioning in the Rosebery zinc circuit, the difference in both zinc recovery and zinc concentrate grade were analysed. The analysis of changes in zinc grade and recovery during the trial raised some interesting questions about the relationship between concentrate grade and recovery. A paired statistical method was developed and tested to combine in each pair the change in concentrate grade and recovery in a single result that could be analysed by a paired t test. This method was found to be very sensitive to combined, varying changes in concentrate grade and/or metal recovery. It was also evaluated on plant test results from another flotation plant to verify its applicability in other plants. CITATION:Long, G, Taylor, S and Lumsden, B, 2012. Statistical plant trials - Efficiently combining concentrate grade and metal recovery results, in Proceedings 11th AusIMM Mill OperatorsÆ Conference, pp 355-362 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Oct 29, 2012

By E. Barsky

Physical principles of two-phase flows with a polyfractional solid phase have not received a sufficient theoretical interpretation as yet. Two-phase flows in the separation mode with a counter-flow of particles are even more complicated. Only statistical methods give an insight into general regularities of such processes. These processes can be interpreted best by analogy with the statistical model of an ideal gas developed by L. Boltzmann, although here a number of difficulties arise. The notion of a statistical system for such flows is substantiated. A mathematical estimation of a statistical system is presented. New notions are introduced, namely, potential extraction of a system and lifting factor. A relationship having the physical meaning of entropy is derived for a two-phase flow in the separation modes. The connection of this new entropy with flow parameters, such as the number of particles, separation factor and chaotizing factor, is established. Properties of this entropy are analyzed, as well as the analogy and difference between this entropy and Boltzmann?s entropy. The notion is formulated and the definition of the chaotizing factor of a process is suggested. In the framework of a statistical approach to two-phase flows in the separation mode, the notion of flow mobility has been formulated. Principal regularities of mass transfer in zone/apparatus sys-tem are analyzed. Principal ideas of a cellular model of the process are formulated, and main relationships for its description are derived. Proceeding from the cellular model, a dependence describing the degree of fractional separation of a narrow size grade is found. The analysis of this dependence makes it possible to reveal the crucial role of the Froude criterion for gravitational separation processes. It is found empirically that this parameter is a basis for the affinization of separation curves (Barsky E, Barsky M, 2006; Barsky, 1980).

Jan 1, 2014

By E. L. Schrader

Statistical Process Control (SPC) is a cooperative arrangement between a component or raw materials supplier and a manufacturing customer. The supplier must analyze his own manufacturing process and determine, predict, and control those variable elements in the circuit which affect finished product characteristics according to the customer's specifications. The results include: control of fluctuations in product characteristics to a narrow range, close communication between supplier and customer, and an increased responsibility for quality control placed on the supplier. In the mining and. processing of airfloated kaolin some unique problems arise with the SPC concept: 1) The SPC system was designed for manufacturing facilities that did not have to deal with natural variations in their raw material; 2) The airfloat process is relatively simple and offers limited opportunity to change processing steps or "fine tune" a circuit for special product needs; 3) Determining adequate sampling frequency for a plant which processes hundreds to thousands of tons per day is statistically difficult; and, 4) Due to the variety of customer industries served, different SPC programs must be set up to deal with widely varying specifications. For airfloated kaolin, SPC is "in line" process control, not after the fact "quality" control. The emphasis must be on statistically valid sampling of the kaolin ore and complete monitoring of its path through the beneficiation circuit.

Jan 1, 1987

By Henry Eyring, Jay W. Fredrickson

MANY theories have been advanced to explain the phenomena of elastic and plastic deformation. The object of this report is to present a mechanism for deformation, not radically differing from existing theories, but embodying certain principles and concepts of these theories. This proposed theory cannot be the complete answer to the age-old problem of deformation but it is believed that it will be a step further in the proper direction. The plastic properties of solids have recently been reviewed by Seitz and Read.1 Zener2 has reviewed and correlated the existing work on the anelasticity of metals. With these and othersa3,4,5 present theories of deformation are well-known. Of the many theories now extant, those receiving most attention have been proffered by Griffith,6 Becker,7 Smekal,8 Polanyi,9 Orowan10 and Taylor.11Although differing quite widely in details, these theories are based more or less on a common principle of flaws or dislocations that exist in the crystal lattice. The effect of stress concentrations surrounding a flaw or crack has been treated most recently by Fisher and Hollomon.12 The various authors differ as to the exact nature of the flaws or dislocations, the causes of their appearance, or the manner in which they initiate slip. All of the theories agree that the number of dislocations increases with progressing deformation. It is universally agreed that the shearing process is not a simple gliding of ideally perfect atomic lattice planes. It is also agreed that the "macroscopic process of gliding, or slip, is brought about by the spreading of a large number of locally initiated "glide steps" through the whole crystal. The occurrence of these "glide steps" is closely related to the presence of some kind of deviations from the "ideal" lattice structure, even in the undeformed crystal. These deviations are overcome "one at a time," in a manner of speaking, due to some stress-concentrating effect." PROPOSED THEORY Many solids show a continuously increasing deformation if subjected to a constant load of suitable magnitude in an extended range of temperature for a sufficient time. This deformation, or flow, may be said to be due, in general, to the tendency of the atoms or molecules in an elastically stressed body to readjust themselves in such a way that if the deformation were kept constant, a release of stress would take place. If rupture does not occur, this process of relaxation causes the rate of flow to obtain a final constant value, as shown in the curve (Fig I) obtained by Taylor and Quinney.14 In. this state the release of stress by relaxation exactly counterbalances the increase due to the elastic strain on the test pieces. .

Jan 1, 1948

By D. N. Cleaver

Like other influence function methods, the SWIFT subsidence prediction program, developed within the Mineral Resources Engineering Department at the University of Nottingham, requires calibration to regional data in order to produce accurate predictions of ground movements. Previously, this software had been solely calibrated to give results consistent with the Subsidence Engineer's Handbook (NCB, 1975). This approach was satisfactory for the majority of cases based in the United Kingdom, upon which the calibration was based. However, in certain circumstances within the UK and, almost always, in overseas case studies, the predictions did not correspond to observed patterns of ground movement. Therefore, in order that SWIFT, and other subsidence prediction packages, can be considered more universal, an improved and adaptable method of regional calibration must be incorporated. This paper describes the analysis of a large database of case histories from the UK industry and international publications. Observed maximum subsidence, mining geometry and Geological Index for several hundred cases have been statistically analysed in terms of developing prediction models. The models developed can more accurately predict maximum subsidence than previously used systems but also, are capable of indicating the likely range of prediction error to a certain degree of probability. Finally, the paper illustrates how this statistical approach can be incorporated as a calibration system for the influence function program, SWIFT.

Jan 1, 1995

By H. McLeod

Introduction In the period from 1939 to the present, Canada has experienced a remarkable industrial expansion, rising to probably seventh in rank amongst world countries. In the early part of this period, the desperate need for military supplies unloosed tremendous amounts of capital for building new factories and for expanding and converting existing facilities. Mines, factories, and other divisions of the industrial economy bent every energy toward greater and greater output. The result was an 80 per cent increase in the volume of the nation's production within a period of four years, a truly remarkable accomplishment and one in which the mining industry had a very vital part. After the critical year, 1944, the tempo of industry eased off a bit, dropping approximately 20 per cent by 1946. At this time the prospects or post-war industry were clouded by monetary and political chaos in overseas countries, by trade restrictions, and by market uncertainties. There was, of course, a pent-up demand, both at home and abroad, for civilian goods that had been curtailed during the war and for capital equipment that had been destroyed. In the midst of this world-wide uncertainty, if anyone had ventured to predict that by the end of 1950 Canada's industrial output would be back to the 1944 level and humming along at nearly twice the best pre-war pace, he would have been considered rash indeed. Yet this has been the case.

Jan 1, 1951

By Richard M. Crowell

"As thorough sampling is usually expensive, the cost of a complete job is often unwarranted, and a cheaper approximation must be substituted. The engineer should, however, weigh the situation thoroughly before subscribing to an alternative other than an accurate assay basis on which to build his conclusion." Examination and Valuation of Mineral Property. R. Parks, 1949

Jan 1, 1994

By A. M. Elmahdy

An amphoteric collector was tested for dolomite removal from phosphate ore. The effects of some operating parameters and their significance on the flotation of dolomite were studied using statistically designed experiments. The parameters studied were impeller speed, pH and collector dosage. Analysis of the results showed that pH is the most significant parameter. Moreover, a concentrate containing 0.53% MgO and ~31.1% P2O5 with a recovery of ~ 90% can be achieved at optimum values of studied parameters, i.e., a pH of 12, an impeller speed of 1,000 rpm and a collector dosage of 2.5 kg/t.

Jan 1, 2007

By Silvia H. M. Grimaldi, Afonso H. Martins

The scope of this experimental work was to study the yttrium extraction and stripping behaviour in a solvent extraction system with mono(2-ethylhexyl)2-ethylhexylphosphonic acid (IONQUEST 801) in a chloride system The study was performed for only one contact between organic and aqueous phases The experiments were carried out according to a factorial design. Due to the statistical analysis and its experimental proof, the optimum conditions for maximum yttrium loading into the organic phase of the extraction stage were 16 minutes for time of contact between phases, 980 rpm of stirring intensity and pH=2.3 for the aqueous phase of the sovent extraction system. The optimized experimental conditions by the statistical approach for the stripping stage were: time of contact between phases equal to 20 minutes, 1050 rpm of stirring intensity and 1.75 M HCI into the stripping aqueous solution.

Jan 1, 1995

By d&apos, Kathleen J. Amico

THIS summary appears in Minerals Yearbook volumes I and III, which cover mineral production in the United States, its island possessions, the Canal Zone, and the Commonwealth of Puerto Rico, as well as the principal minerals imported into and exported from the United States. The several commodity and area chapters contain further details on production. A summary table comparing world and U.S mineral production also is included.

Jan 1, 1964

This chapter summarizes data on crude mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Included also are tables that show the principal mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume n of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in this chapter is what is normally termed "mine output!' It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the production of auxiliary processing at or near the mines.

Jan 1, 1979

This chapter summarizes data on crude mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Included also are tables that show the principal mineral commodities exported from and imported into the United States, and that compare world and U.S. mineral production. Except for the mineral fuel commodities, the detailed data from which these tables were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume II of this edition of the Minerals Yearbook. In October 1977, responsibility for the collection of data on mineral fuels-coal, petroleum, natural gas, and natural gas liquids-was transferred to the newly created Department of Energy. Although chapters covering these commodities will no longer appear in Volume I of the Minerals Yearbook, quantity and value data have been included in most of these summary tables to maintain statistical consistency in State and national value of overall crude mineral output. This shift in responsibility has also resulted in changes to the composition of the "Nonmetals? and "Mineral Fuels" groups in table 1 and table 2. The commodities-asphalt and related bitumens (natural), carbon dioxide (natural), helium, and peat-have been removed from the ?Mineral Fuels" group, and are now included under the "Nonmetals" group. There has been no change in the components of the "Metals" group.

Jan 1, 1981