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By J. A. Herbst

Until the past decade, the energy-size reduction relationship was the dominant form of mathematical model used in the description of tumbling mill grinding processes (1,2). Typically, in these models some single measure of product fineness (e.g. the 80% passing size, the size modules, the specific surface area) is chosen as the dependent variable and the energy input per unit mass of material being ground acts as the independent variable. In some instances these models have been useful for the correlation of experimental data, but, invariably, they have been found to be inadequate for meaningful process simulation. During the last decade considerable advances have been made in the development of phenomenological grinding models derived from population balance considerations (3-7). In these models a set of dependent variables is employed, corresponding to the set of mass fractions which constitute the product size distribution, and energy input is abandoned in favor of "time in the mill" as the independent variable. The phenomenological models have been shown to provide accurate simulations of the entire size distribution of ground products produced in batch (8-10), locked cycle(11)and steady and unsteady state, open and closed circuit continuous grinding(12,13).

Jan 1, 1973

By Shoji Taniguchi, Lifeng Zhang, Kaike Cai

"In the present paper, based on the two-phase (Eulerian-Eulerian) model, the 3D fluid flows in gas-stirred systems, i.e., air-stirred water vessel and argon-stirred liquid steel ladle, are simulated. In the Eulerian-Eulerian two-phase model, gas and liquid are considered to be two different continuous fields. The phases are assumed to share space in proportion to their volume fractions. The exchange between the phases is represented by source terms in conversation equations. Turbulence simulated by the k- e model is assumed to be the property of the liquid phase. The following effects of mathematical treatments and operational factors on the fluid flow are discussed, such as interphase drag force, turbulent model, the size of bubble, and gas injection mode.Some interesting results are derived. Except the interphase drag force, the interphase lift force should be taken into accounted in order to exactly simulate the fluid flow in gas-stirred systems. Suitable turbulent model and drag coefficient have effect on the mathematical simulation. Injecting small bubbles can realize a well mixing flow condition. The distance between the two gas-injection nozzles has effect on the fluid flow."

Jan 1, 2000

By Saul Garcia Hernandez

The research work objective is to study a new ladle shroud internal design to reduce the slag emulsification in the tundish during ladle transient periods. A 3D mathematical model of the tundish was created to solve the fundamental equations, a turbulence model, and a multiphase model. The results show that using a conventional ladle shroud, the fluid is delivered with an excessive amount of kinetic energy being dissipated inside the tundish bath, generating strong mixing flow patterns and entrapping a massive amount of slag. In the other hand, the proposed ladle shroud dissipates the kinetic energy before the fluid enters the tundish promoting less intense mixing patterns; thus, the amount of slag emulsification is reduced significantly. Consequently, if the internal design of the ladle shroud is able to dissipate the kinetic energy before the fluid enters the tundish, it shall be possible to reduce considerable the slag emulsification and the slag opening area.

Aug 17, 2017

By A S. Kurilko

For mines located in the cryolitic zone, thermal conditions are an important factor for all kinds of mining works, especially for ventilation of workings. In the present paper, some models of mine air heat transfer considering air distribution in a net of mine workings are developed. A combined solution is suggested for heat transfer and air distribution problems in mine workings and other underground structures located in the cryolitic zone. A software package is also presented for calculating temperature conditions in an underground refrigeration plant and for optimisation of ventilation conditions. This software uses a special 3D mathematical model to describe heat transfer in a freezing chamber between surrounding rock massif and stored product as well as between atmospheric air and the daylight surface of rock massif. A problem requiring strengthening of a backfill material and its thermal interaction with surrounding rocks during underground deposit mining by horizontal layers in conditions of the cryolitic zone is also discussed. The developed program takes into account cement consumption, geometrical dimensions of workings filled and a sequence of deposit mining.

Jan 1, 2005

By S. Sarac

In this study, graphical and mathematical methods used to determine operating points in single or multiple fan ventilation systems are summarized. The problem is mathematically formulized for parallel connected fans in which analytical solutions are not possible. For n number of parallel connected fans, a non-linear equation system that consists of n number of non-linear equation sis derived. The Newton-Raphson method, which is a numerical analysis method, is adapted to solve this non-linear equation system and the solution steps are given as an algorithm. A computer program based on this algorithm is written and its applicability is proved.

Jan 1, 2000

By Boris K. Krstev

INTRODUCTION The flotation process, in the real industrial complexes, is characterized by the existence of the significant number of the close reciprocal interrelationship between the input and output Darameters. Traditional complexity is appeared with regard to absence of the suitable a priori information for the physico-chemical characteristics of the flotation process. It’s led to needful of taking of consideration about the undefinition which have got the place in the real conditions and application of the statistical methods. The identification of the flotation process through statistical methods is conception of the more-stages procedure, including the collection and previous analysis, the choice of the model structure and valuation method, the estimation of the model un- known parameters and the results interpretation. The essential concept for the subject of this paper belongs to the empirical models ("black-box") and deals with optimizing in constant industrial plant process. The offered method envisages the application of process operation data in order to improve the work process or constant accomplishment of better results for the target function in relation to the former achievement. The optimum process solution isn't afixed value under the influence of various factors, but "a moving point" along the response surface and deviates from the scheme solutions. The evolutive planning method constantly "investigates and approaches" the optimum solution for the selected target function. As a matter of fact the expert operates the plant without interrupting the normal work process. The essential concept of method is to attain changes in the standard conditions, but so limited that they will not effect either production or the product. This method is based on statistical concepts and availability of following the risk of error. The possible influental factors for the flotation process (m=l, 2, 3) is following: the metal content in the feed ore; production level (t/h); grinding fineness in the flotation pulp; pH-values; the consumption of collectors and modifiers The possible target functions are: the recovery of plant capacity, metal recovery in the concentration process and concentration quality. The application of the evolutive operativity method in the chalcopyrite flotation- Bucim concentrator, combines the statistical data and the operator's experience in the interpretation and making a decision which adds up to the precise automatic performance of the process. The advantages of this method in relation to the existing procedure for the flotation process are the following: • The method is unexpensive and losses are reduced to the time necessary to collect the data and record them in the computer. This method provides a constant process control and a quality decision which is better than those brought by an ex- pert with great experience ("hit-and-miss method"). • The method also provides incidental data about the effects. • The method should not be considered as a procedure for solving an incidental problem ("crash program"). • The obtained results must be interpreted by an appropriate expert in order to be considered instructive. MATHEMATICAL STATISTICS Taking into consideration the complexity of the enrichment processes it's necessary the application of "black-box" and mathematical modelling. The presence of the indefinite elements compel us towards the both theory of the probability and mathematical statistics. The mathematical statistics by the mineral processing investigation of the valuable raw materials in the last years has had greater signifance and widely spread application. The application of the mathematical statistics methods for the technological pro- cess analysis and the construction of the mathematical models is bound up by the task putting of the automatic control system de- sign (Fisher R. A. 1941, 1949). The statistical analysis in the enrichment processes is applied formerly, especially in the sampling estimation. Contemporary, in the last years is imposed the tendency of mathematical statistics application for the obtaining of quantity characteristics and quantity valuation from the individual influental factors. Above mentioned tendency in the significant level is based by the mathematical statistics development as a mathematical discipline close connected with the technical cybernetics general joining to the investigated object as a "black-box". Another essential factor in the mathematical statistics development is appeared the created mathematical theory of experiments as a new, to some extent, autonomous statistical domain. The theory of experiments has demonstrated exclusively importance for the investigation of the complex more-factorial processes in the chemistry, mineral processing, metallurgy etc. The investigation by the enrichment processes of the valuable raw materials and their management is possible by the statistical method application. In the same time, it's possible to use the wide-spread traditional methods of the statistical analysis, such as the methods of the dispersion, correlation, regression etc. Also, it may be mentioned above all the methods of the statistical planning of the extreme experiments. The more perspective are representatived some cybernetic methods which are based by the probability as an approach in the process analysis, for example, the identify of the ways and forms, the graph application as an additional instrument in the correlation analysis, the dynamic programming etc. The mathematical statistics application in the laboratory investigation scale is connected above all by the experimented material analysis and the compact representation of the obtained results. The mathematical statistics methods are more varrying and may be applied in the investigations of the wide circle of problems

Jan 1, 1996

By D. O. Ehrenburg

DURING the earlier period of electrical prospecting, the search for orebodies was by far the most important application of this method of geophysical prospecting. In the past few years, however, increasing attention has been paid to the possibilities of this method in the investigation of subsurface structures. Not only have fault zones been located, but attempts have been made to determine the depth to certain strata and thus contouring on some bed which proves to be a good "electrical marker." Many workers have published the results of field tests showing how their particular interpretations have agreed with the actual field conditions, but very few have stated their method of interpretation. Weaver, Hummel and Stefanesco and Schlumberger1 have given a more theoretical discussion of the resistivity methods. Hummel and Stefanesco and Schlumberger have published mathematical solutions for the flow of electricity in a medium involving four layers. In this paper the authors present a solution for the flow of electricity in a medium of any number of horizontal strata. By means of this solution, curves showing the relationship between the apparent resistivity and the electrode spacing can be computed for ideal cases.

Jan 1, 1931

By Paul L. Russell

Numbers, arithmetic, mathematics. Where did it all come from? Who needs it? We all do, but many school children would not agree. Engineers, physicists, accountants, tax collectors, and most of the general public are well aware that modern society in large part is founded on mathematics and could not exist without it. Mathematics developed over thousands of years as part of the everyday life of man. No one area, tribe, or race can claim discovery. In fact, from the records that do exist, it is evident that many facets of mathematics were discovered independently of others who made similar discoveries. While proof may be lacking, the earliest concepts of mathematics may be some 250,000 to 300,000 years old. The first use of numbers as written records is unknown. However, a bone of a young wolf deeply cut with 55 notches-arranged in two rows, one of 25 notches, the other of 30-was found in Czechoslovakia. Dated to be about 30,000 years old, it is perhaps an early record of some kind of counting system. It is assumed that mathematics was developed as an answer to man's practical needs, but anthropological studies suggest that the art of counting may have developed in connection with the needs of primitive religious ceremonial rites. Fingers probably were first used to designate sets of from one to five objects. Using both hands, up to 10 items could be indicated. As civilization developed, so did the need for more flexible systems to record items of trade, measure land, and figure taxes. Aristotle noted that the development of the decimal system comes from the fact that most people are born with 10 fingers and 10 toes. In spite of this obvious fact many early civilizations used binary, ternary, and quinary systems while vigesimal systems (with 20 as a base) and even sexagesimal systems (with 60 as a base) were used by others. A form of writing was in use in both the Mesopotamian and Nile valleys as early as 3000 to 4500 B.C. In Mesopotamia, wedge-shaped marks were impressed upon soft clay tablets that were hardened in ovens or by the sun. Many thousands of such tablets have survived. When the tablets were finally deciphered, some were found to be records of items shipped in trade, inventories, tax accounts, and mathematics exercises for teaching. Mesopotamia is also the source of an interesting board game dating back to about 2500 B.C. Its buttonlike men and triangular dice were apparently used with squares of shell, inlaid with lapis lazuli and red sandstone. Unfortunately, rules of play were not found. In Egypt, record preservation was somewhat better. Discovery of the Rosetta Stone in 1799 eventually led to deciphering the Egyptian hieroglyphics that included a numbering system at least 5,000 years old. These records show a competence in counting and numbering. A calendar of good accuracy may have been in existence as early as 4,200 years ago. Mathematics, as practiced today, developed when the Greeks added logic and proof to arithme-

Jan 12, 1982

By H. G. Wang

The production process of a coal mine can often be interrupted by all kinds of events scheduled or unscheduled and thus often needs gas drainage for a temporary or long-term sealed area. Gas drainage has a relatively high risk, therefore attention must be paid to its design to keep the process safe. Based on the conservation laws of mass and constituents, and under the conditions of the allowable gas concentration limit in the return air route, the relationship between gas concentration and gas drainage flow rate as a function of time during the drainage process is discussed in detail to build a mathematical model of gas drainage from a sealed area. With respect to the gas drainage process, two different conditions need to be considered: one with a methane free fresh air supply, the other with a low gas concentration. This paper presents the derived mathematical models for these situations and then shows that they can be incorporated into one model with some modification. This combined model can be employed to determine the optimum gas drainage flow rate with the shortest drainage time. The application is coded using the C# programming language within the .NET framework. Finally, the application program developed by the author is used to validate the mathematical model through an example of gas drainage with varying rate.

Aug 1, 2013

By Robert F. Shurtz

This paper suggests that pre-occupation with the random process model notised by geostatisticians may result in neglect of more promising techniques, especially since the random process model does not appear to be essential to current geostatistical procedures. This point of view is emphasized pictorially. To emphasize the potential of new techniques a simple application of the conventional Brownian function is described. The probabilities estimated in this truly random way are different from those estimated by Kriging

Jan 1, 1980

By R. F. Shurtz

This paper relates geostatistical doctrine to classical statistical and mathematical concepts. It is not a contribution to geostatistics; it is a contribution about geostatistics. It uses descriptive and pictorial arguments to assist interested readers in forming an intuitive grasp of the recondite and difficult mathematical issues involved. The method chosen is to cite authoritative literature references from the two fields and trace connections between them. Four broad conclusions appear: first, geostatistics comprises a relabelled subset of concepts detached from classical statistics and mathematics; second, this relabelling artificially isolates geostatistics from the classical fields and restricts its scope; third, the classical fields still have much to offer to the mining industry but will remain fallow unless artifcial communication barriers are removed; and fourth, the unique advantages asserted for geostatistics are neither unique nor necessarily real. These findings should not be regarded as iconoclastic but rather as Pointing the way to a wider and more productive scope for those who evaluate mineral deposits.

Jan 1, 1983

By R. F. Shurtz

This note calls attention to a contradiction in current eatistical theory and to corresponding difficulties in practice. These are significant concern in evaluating almost all ore deposits. The theoretical contradiction is that the commonly used spherical model for the semivariogram is not consistent with the usual definition of a "regionalized variable" as a mathematical function, the direct study of which "is excluded because its spatial variability is usually extremely erratic, with all kinds of discontinuities. . ." (Journel and Huijbregts, 1978). Specifically, this means a grade function that is too "rough" for interpolation to be useful. The practical difficulty is that the spherical semivariogram interprets the data upon which it is based in a manner that is, more often than not, demonstrably inconsistent with reality. This is attributable to the widely disregarded interaction between the sample pattern and the grade function. Each sample pattern "blurs" the grade function in its own particular way. It is as though the grade structure of the deposit were seen through a lens of poor resolution or reflected in a warped mirror, such as those found in amusement parks. The fitted spherical model embeds this sometimes dangerously blurred and distorted image in the Krige regression. A full analysis of these inconsistencies is to be presented later but, in the meantime, it seems urgent to communicate their effects so that those engaged in estimating ore reserves may be on guard. The spherical semivariogram has a sill and can be replaced by the corresponding covariogram. The equation of the spherical covariogram in normalized form, that is, variance and range both equal to one, is represented as: [ ]

Jan 1, 1984

By Harry C. Swanson

TRANSPORTING concrete from mixer to forms has always been a problem. Twenty-five years ago this task was generally accomplished by means of wheelbarrow or concrete buggy. On large dam jobs, as the number of these projects increased, the gantry crane or highline came into use. Today several methods of handling concrete are employed on smaller surface construction jobs, for example, transit-mix trucks or dumpcrete trucks, which have crawler cranes with buckets for placing concrete into forms. In 1944, during early stages of developing Mather mine A shaft, several large underground concrete jobs were necessary. At this time the Cleveland-Cliffs Iron Co. purchased the first pumpcrete machine, introduced by the Chain Belt Co. of Milwaukee. The machine was used to pour approximately 200 cu yd of concrete for a dam, or bulkhead, located 400 ft from the shaft. Concrete was mixed on surface, lowered down the shaft 1000 ft in a 2-cu yd bucket hung under one skip, spouted into the bowl of the pumpcrete machine from the bucket, and pumped directly into the forms.

Jan 4, 1954

JOHN ALEXANDER MATHEWS, who has been awarded the Hunt Gold Medal for his paper "Austenite and Austenitic Steels," which was pre-sented before the Institute as the Howe Memorial Lec-ture for 1925, was born at Washington, Pa., on May 20, 1872. His interest in metallurgy may be said to be hereditary, as three generations of his Colonial forbears were gold and silversmiths. After graduating from Washington and Jefferson College in 1893, he entered Columbia University where he was successively assistant in assaying and tutor in chemistry and at the same time continued his work for the Ph. D. degree, which he received in 1898. He was at one time awarded a fellowship in chemistry, and for 1900, 1901 and 1902 re- ceived the award of the Ear- nard Fellowship for the En- couragement of Scientific Re- search, spending one year at the Royal School of Mines, in London, studying alloys un- der Sir William Roberts- Austen, another at Columbia under Henry M. Howe, and the third at Sanderson Bros. works, Syracuse. While in England, he was one of the first three, recipients of an Andrew Carnegie Scholarship of the Iron and Steel Institute of Great Britain, which later awarded him the first Car- negie Gold Medal for Re-search. He entered the employ of the Crucible Steel Company of America, at its Sanderson works, in 1902, as metal- lurgist and soon became as- sistant manager. In 1908 he ent to the Halcomb Steel JOHN A. Co., Syracuse, N. Y., as superintendent, later becoming general manager and president in 1915. In 1920 he returned to Crucible Steel Co. of America, first as vice-president and later became president from 1921 to 1924. He retired from the presidency in 1924, made a metal-lurgical trip to Europe, and returned as vice-president to resume his "favorite pastime" of directing research and development work in the production of special tool and alloy steels. He has taken a particular interest in the development of austenitic steels which, in addition to an extraordinary resistance to corrosive attack, show under fatigue, torsion, and tension tests superior qualities as compared with the ordinary engineering steels, and at elevated temperatures show remarkable resistance to oxidation and scaling and several times the strength of many of the complex alloys that are not of the natural austenitic variety.

Jan 2, 1928

By Douglas J. Uhren, Gary W. Gilbert

This paper describes the risk elements associated with difficult glacial geology, including boulders, heavy groundwater inflow, and potential running soils all coupled with a potentially corrosive service environment. The matrix workshop for the 168-inchfinished diameter sanitary sewer interceptor tunnel in Columbus, Ohio is assembled with the Design Team and the Owner’s design, operations, and fiscal staff. Corrosion protection alternatives are compared against cost and non-cost parameters with relative risk and weighting factors assigned. The Owner working in cooperation with the Design Team uses the matrix workshop to se

Jan 1, 2001

By B. Pitchumani, D. Venkateswarlu

INTRODUCTION The characteristics of feed and product of any size reduction operation are normally expressed as mean size, the size corresponding to 80 percent undersize or the percentage below a specified size or specific surface area. But the feed has a distribution of sizes and quite often it becomes essential to obtain a product of desired distribution. In such cases, size distribution of feed is related to product by matrix methods. The technique of matrix representation of crushing operation was proposed by Broadbent and Calcott (1 to 4). They divided the complete crushing mechanism of coal into breakage, selection and classifying functions for a closed-circuit system to establish relations between the feed and product distribution. Ellis, Ray and Venables (6) suggested an empirical method of determining the breakage matrix by combining the characteristic functions and proposed the following hypotheses: 1. The breakage of individual size fractions passing through the mill at a given rate is the same whether passed separately or as part of a mixed feed. 2. The breakage of a mixed feed may be estimated from the products of individual size fractions passed through the mill separately at a rate at which they would be crushed as part of the mixed feed. This method is stated to be applicable when there is no interaction between the individual sizes.

Jan 1, 1980

By Cindy Robles, Jose León Avalos

Poderosa es una empresa de mediana minería, socialmente responsable, con operaciones subterráneas, que explora, explota, procesa y comercializa recursos minerales con contenidos de oro, y comprometidos a: Mejorar continuamente el desempeño de nuestro sistema, Promover el comportamiento ético de nuestros colaboradores, Identi?car, comunicar y capacitar a nuestros colaboradores, Desarrollar el trabajo en equipo a través de los círculos de mejoramiento continuo (CMC) entre otras.

Sep 1, 2017

By A. E. Hilder

Introductory The following pages present the results of field investigations, laboratory and commercial tests, drilling, surveying, and preliminary development of the refractory clays which have been discovered recently in the township of Kipling, at the foot of Long rapids on the west side of the Mattagami river about 57 miles north of Kapuskasing and approximately 7 miles north of Smoky Falls, the terminus of the privately owned railway operated by the Spruce Falls Power and Paper Company, Kapuskasing (see Figure 1). Investigations on the clays of northern Ontario have been carried on over a period of seven years by officers of the Ontario Department of Mines, and I am indebted to the information published by that Department in reports by W. S. Dyer and A. R. Crozier, as well as?by Professor R. J. Montgomery, of the Ceramic Department, University of Toronto. It was, in large measure, the data given in the 37th, 38th, and 42nd Annual Reports of the Ontario Department of Mines that led me to make a personal investigation of the Mattagami River clays, with the result that we now have a commercial undertaking that will develop eventually into an industry of considerable importance in supplying the central manufacturing districts of Canada with refractories that heretofore have been largely imported from the United States. An extract from the 42nd Annual Report of the Department, Part III, 1933, page 75, reads as follows: "As for the refractory clay, the deposits are undoubtedly very large, but what is urgently needed is a deposit near the railway under sufficiently shallow overburden for recovery by stripping'. Having previously made an investigation of the clays adjacent to the Temiskaming and Northern Ontario railway, and these clays proving unsuitable, I turned my attention to the outcrops of refractory clays on the Mattagami river, first reported by Keele in 1919. This area offered possibilities within the economically permissible distance from rail transportation.

Jan 1, 1935

By R H. Hallam

The Mattagami mining district encompasses a favour-?able belt of folded Keewatin-type rocks, with intercalated sediments and intrusives of late Keewatin age. This environment has been subjected to periods of basic and acidic intrusion. The orebodies lie within the fold structure and are associated with faulting and shearing of considerable magnitude. The No. 1 orebody contains 60 to 70 per cent massive sulphides. The minerals, in their order of abundance, are generally: pyrite, sphalerite, pyrrhotite, magnetite and chalcopyrite. It is evident that the broad geological structure of the district is amenable to ore deposition. There are two ? prominent linear expressions which comprise this broad structure. Both strike directions lie at the edge of, or are related to, a complex gabbro-anorthosite-peridotite zone. The fact that eleven of the ore zones discovered to date coincide with the broad structure indicates its over-all importance. It is estimated that the production from Mattagami Lake Mines will be in the range of 600 to 700 tons of zinc concentrate and 70 tons of copper concentrate per day.

Jan 1, 1964

Recovery of tin and copper from concen trates containing cassiterite, stannite and chalcopyrite was studied in laboratory-scale tests designed to simulate continuous operation of the matte fuming process in which tin is recovered as SnS fume while copper accumulates in the matte. Charges made up of 300g of mixtures of the concentrate and siliceous flux were added at a uniform rate in pelletized form to crucibles containing 300g of matte and 50g of slag (both of which were recovered from previous tests), while blowing through the matte with air or oxygen-nitrogen mixtures at a rate of 3 to 5 1/min. Accurate material balances enabled the effects of process operating conditions on tin recovery and sulfur utilization to be deter- mined. When operated correctly, the matte fuming process gave tin recoveries exceeding 90 percent in spite of wide variations in the copper content of the matte and in the operat- ing conditions. Deterioration of tin recovery was associated with undersaturation of the slag with respect to silica, and with high partial pressure of sulfur dioxide (greater than approx- imately 0.2) brought about by oxygen enrichment of the blowing air. The utilization of sulfur varied widely in low grade mattes. Copper in excess of approx- imately 10% promoted formation of SO2 by the commonly accepted reaction: FeS + 1-120 2= FeO + S02 while in copper-free and lower grade mattes a substantial fraction of the oxygen was consumed in the alternative reaction FeS + i 02 = FeO + z S2.

Jan 1, 1980