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By Vladimir Panjkovic, Ostrovski. Oieg, Campbell Cripps Clark, John Truelove

"Effects of properties of raw materials and blast on the performance of an iron bath reactor have been examined by a mathematical model. The model consists of three modules: 1) chemical reactions in the gas phase and heat transfer from gas to droplets ejected from the bath; 2) heat losses from the vessel and radiative heat transfer from the freeboard to the bath; and 3) heat and mass balances for the bath. The following parameters of the process are calculated: coal, ore, flux and oxygen consumption, post-combustion ratio and heat-transfer efficiency, temperature and composition of the off-gas, and slag and metal chemistry.IntroductionOne of the anticipated advantages of smelting reduction over conventional ironmaking is the use of lower-grade raw materials. In this work, the effect of-properties of raw materials on the performance of an iron-bath reactor is examined with a numerical model. The model is also used to assess the effect of properties of the blast (flowrate, temperature and oxygen enrichment) and ejected droplets (generation rate, size and ratio of total weights of slag and iron droplets) on the key parameters of the process. In the process coal, oxygen, ore (which may be partly prereduced) and fluxes for specified slag composition are charged to the bath. Slag and iron droplets are ejected from the bath into the gas phase, where they are heated before returning to the bath. Iron droplets undergo decarburisation and reoxidation with CO2 and H2O. Dust is also generated from the bath, and oxygen or preheated air for post combustion is injected from the top of the vessel.The model consists of three modules: 1) reactions in the gas phase and heat transfer from gas to droplets ejected from the bath; 2) heat losses from the vessel and radiative heat transfer from the freeboard to the bath; and 3) heat and mass balances for the bath. The structure of the model and the data exchange between the modules are shown in Fig. 1. The following parameters of the process are calculated: coal, ore, flux and oxygen consumption, postcombustion ratio (PCR), heat transfer efficiency (HTE), off-gas temperature and composition, slag and metal chemistry, and rates of decarburisation and reoxidation of the iron droplets."

Jan 1, 1996

By Isobe K, Muchi I, Hsieh YS

Theoretical and experimental studies have been made-to clarify the physical and chemical behavior of the tuyere combustion zone of blast furnace. Gas streamlines around this zone were visualized by the use of the two-dimensional equip- ment. Close agreement between the observed stream- lines and the calculated ones is found. The three- dimensional experimental studies have revealed that there exists a so-called dry zone in the neighbor- hood of the raceway and the trickling liquid be- haves approximately like a continuum. A kinetic model is develdped to describe the behavior of coke combustion in the tuyere zone. The model is based on the reaction kinetics, the differential balances of heat and mass, and the mechanics of gas flows. Regarding-the-axial distribution of gas composition in the tuyere zone, good agreement is obtained be- tween the model prediction and the data observed in a working furnace by the other investigators. Cal- culated results-show that the maximum consumption of coke occurs at the intermediate region of the raceway. For the blowing of oxygen-enriched or high -humidity blast, the position at which the maximum consumption of coke occurs is shifted toward the tuyere nose. Similar effect is found when the par- ticle diameter of coke in the tuyere zone is de- creased. The solid flow pattern around the tuyere combustion zone was visualized by the use of the two-dimensional equipment in which the sublimation of dry ice particles in front of the tuyere was

Jan 1, 1981

By Bruno Alves Resende, Antonio Adel dos Santos

Temperature, microstructure and dimensions are the main material parameters to be controlled during hot rolling of steel. Although thermal mathematical models have long been developed and applied for hot strip rolling, each Hot Strip Mill (HSM) must have its own model adapted to its facilities. Thus, a mathematical model for temperature evolution during rough rolling has been developed for the Usiminas HSM at Ipatinga Plant. The model achieved a high level of accuracy, which was assessed by comparing measured values of temperature at the hot strip mill entry with the calculated ones, the difference ranging from 9°C to 17°C. Application examples have shown that the slab can be occasionally stopped before start of rolling for as long as a couple of minutes without compromising its further processing. On the other hand, if the transfer bar stops after rough rolling even for short time, further processing in the HSM can be hindered, due to excessive temperature drop. In case of such abnormal line stop, the model can be used as a tool for decision-making to either continuing the planned rolling schedule or to changing the route, thus improving the overall rolling process.

Oct 1, 2019

By Samyguin VD, Filippov LO

The aim of this paper is to emphasise the importance of knowing of the rate of the elementary flotation acts (EFA) - attachment and detachment. By studying the simplest linear model notion of the column flotation, the results of the nonlinear simulaton of flotation separation in the column with lengthwise upward mixing show two principal different types of separative mass-transfer in the column. The first is, the case of a small EFA intensity, almost without the detachment. The second is, the case of a big EFA rate, when the process is close to a local attachment-detachment equilibrium. There is also an attempt to estimate the EFA rate for three different kinds of quartz particles, floated by cation collector in the laboratory column apparatus.

Jan 1, 1993

By A. L. Mular

Some specific cases of the collection of data from industrial grinding and classifying operations, and the development of models from the data so obtained, will be described. The problems encountered, the effort involved, and the value of the derived models in improving the plant efficiencies will be discussed and documented where possible.

Jan 1, 1971

By A. G. Royle

The reasons for constructing a model of an orebody for which both the parent population and the sampling distribution are known are discussed and details of the model are given. A brief summary of Matheron's theory of regionalized variables is included, with particular reference to his kriging estimators and their variances. Using the model, a comparison is then made between these kriging estimators and other commonly-used estimators. These are compared to find the one with the minimum variance, and an analysis is included to investigate whether any of the estimators is biased. Also included is a comparison between theoretical and experimental variances for some of the estimators.

Jan 1, 2014

By D. N. Madge

A survey is given of production scheduling systems currently in use or contemplated for future use in Cominco operations. Emphasis in this presentation is made on the chain of decisions that are made with the help of mathematical programming models. Some attention is devoted to the structural properties of the models.

Jan 1, 1966

By R. Venkataramani

Crushed stone operations have become more difficult due to rising costs of labor and equipment, with the consequent reduction in profit margins. Competition from other operators and the encroachment of vertically integrated companies place severe restrictions on available markets. The seasonal demand for stone precludes any definite production level, and changes in productivity have to be accommodated. These influence profitability, and therefore production plans must be continuously adjusted to keep pace with rapidly changing conditions. The basic problem of stone companies seeking to maximize profits is one of balancing stone production costs, costs of inventory holding and stock-piling, marketing costs and any other charges accruing over time against the selling price of stone. Because of high peak demands, slack period production must be stored and then distributed to supplement peak period production. For a multi-plant operation, there is a need to evaluate at the same time the interaction between the plants and the various marketing sectors. In a multi-plant operation with different production capacities and production costs, stone producers are interested in the answers to the following questions: 1. How much stone should be produced at each plant in each time period? 2. What should be the optimum stone shipment from each plant to each market? 3. What are the effects on net returns and shipping plans, if production capacities are altered at the plants? These questions have many different answers that, will satisfy demands. From the point of production scheduling, the minimum production cost may be the objective. From the inventory standpoint, the best solution will be to synchronize production with sales. However, when the transportation of stone is also considered, the desired end is to achieve that delivered cost which maximizes the company f s net return. Besides, only an extremely naive analysis ,wouId attempt to

Jan 1, 1971

By Salim Akhtar

The operation of a mineral processing plant with a complex flowsheet is represented by a mathematical operator. Such a representation permits a quantitative evaluation and monitoring of the separation processes in different sections of a processing plant, and gives an overall separation efficiency of the plant.

Jan 1, 1973

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 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 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 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

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

By S. Paul Lindau

THREE years ago it was decided by the management to granulate the matte that is produced in the smelter of the St: Joseph Lead Co. at Herculaneum, Mo., thereby doing away with a large amount of labor in handling the matte and in subsequent crushing. On Mar. 1, 1915, the granulator was put in operation and up to Jan. 1, 1916, 18,735 tons had been, granulated. The four blast furnaces have a daily output of about 280 tons of pig lead and 100 tons of matte assaying about 11.0 per cent. Pb. It is expected that projected improvements in roasting methods will eliminate more sulphur from the charge, and cut down the matte-fall, to about one-half of the present figure. The blast furnaces are tapped into movable forehearths or settlers, 6 ft. by 4 ft. by 22 in., the slag overflowing into 27-cu. ft. slag cars which are hauled to the clump by electric locomotives. Previous to the adoption of granulation, the matte was tapped from the forehearths into small slag pots which were dumped after cooling. The matte cakes were broken with sledges, and transported to the crushing plant for fine crushing and screening. Here the matte was reduced to ¼ -in. size before being fed to the roaster bins.. A Wedge and a Holthoff mechanical furnace are used for preroasting before sintering on the Dwight and Lloyd machines. The matte is returned to the furnaces as an iron flux until the .gradually accumulating copper content reaches about 7 per cent., after which it is put aside to be concentrated in a small copper blast furnace, the resultant high-grade matte-being sold. When the matte does not settle readily from the slag, two settling devices are often used, the second one being a large catch-pot, which gathers any matte that may overflow from the forehearth, the slag then overflowing from the catch-pot into the slag cars. When full of matte, the catch-pot is removed, allowed to cool, and the contents broken and crushed.

Jan 10, 1916