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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 Pramod C. Thakur

Tunnels are defined as underground passages made without removing the overlying materials. From time immemorial men have driven tunnels for mining purposes. Even today tunnels are the building blocks for underground mines. The total length of such a network of tunnels in a mine may add up to 10-100 miles! In addition to this, rapid development of vehicular traffic, needs for air raid protection and metropolitan traffic problems have given a great impetus to underground tunnel construction. But for the successful drivage of any tunnel an adequate air environment has always been and remains an essential prerequisite. This is particularly true for tunnels in mines which are driven in gas bearing strata often at a substantial depth from the surface. An adequate air environment is designed to promote the health, safety and comfort of workers which results in greater productivity and efficiency. Its legal definition varies from country to country but, in general, it means the provision of sufficient circulating air, often at specified velocities, to maintain: (i) at least 19% oxygen in the working areas (ii) Concentration of pollutants, e.g., methane, carbon monoxide, respirable dust, etc. below specified limits. Table 1 shows the maximum allowable concentrations for some of these pollutants.1 (iii) Temperature and relative humidity below specified limits. Ventilation of tunnels in mines assumes ever. greater importance today because of increased mechanization and concentration of output which leads to higher rate of production of inflammable gases and respirable dust. Efficient management of the tunnel air environment, however, depends heavily on a thorough knowledge of how

Jan 1, 1974

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 Shuyu Qin, Shujiang Sun, Jingfu Zhao

The three key parameters of mine fires are local airflow velocity, temperature and oxygen concentration. According to the theories of seepage in porous media, heat transfer and heat dispersion, mathematical models were constructed based on the three parameters. The models can be used for early prediction of mine fires and for estimation of the level of spontaneous combustion. Proper use of the models can assist in preventing and controlling mine fires. KEY WORDS: airflow velocity, temperature, oxygen concentration, numerical modelling, mine fire prediction.

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 Dan G. Cojocariu, E. Ene-Danalache, I. Huber-Panu

A general model which represents not only batch but also continuous flotation in multi-cell machines is presented. This model considers both the size distribution and the distribution of flotabilities in a size class for valuable mineral particles in the pulp. The general expression is shown to reduce to several previously reported models. In addition, a number of new models are found to arise for different specific assumptions concerning the flotability distribution and/or the size distribution of the particles undergoing flotation. Several of these new models are tested experimentally using laboratory-scale batch and pilot-scale continuous data. Model parameters are estimated from this data and a comparison of calculated recoveries and those experimentally determined are presented. Finally, the influence of the feed rate, aeration rate and valuable mineral content of the feed on the recovery is examined.

Jan 1, 1976

By J. Herbst, I. Heber-Panu, Dan G. Cojocariu, E. Ene-Danalache, G. Poling

A general model which represents not only batch but also continuous flotation in multi-cell machines is presented. This model considers both the size distribution and the distribution of flotabilities in a size class for valuable mineral particles in the pulp. The general expression is shown to reduce to several previously reported models. In addition, a number of new models are found to arise for different specific assumptions concerning the flotability distribution and/or the size distribution of the particles undergoing flotation. Several of these new models are tested experimentally using laboratory-scale batch and pilot-scale continuous data. Model parameters are estimated from this data and a comparison of calculated recoveries and those experimentally determined are presented. Finally, the influence of the feed rate, aeration rate and valuable mineral content of the feed on the recovery is examined.

Jan 1, 1976

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 C. B. Manula, R. Venkataramani, T. V. Falkie

A linear programming model has been developed to solve a production planning problem for a multi-plant stone operation serving several customers. The factors considered are production capacities, inventory restrictions, demand requirements, and available stone reserves. The objective function to be optimized is the total annual net returns from the quarry operations. For the purposes of model testing, annual stone sales from each plant were divided monthwise, productwise, and assigned to a market. The concept of assigning demands to market sectors and not to any particular plant creates the self-correcting interplay between the plants and the markets. Along with the inventory restrictions, and ending inventory requirements, this interaction enables the model to minimize the external diseconomics. The model was tested against an operating prototype and a number of alternative problems were also considered. Finally, the basic linear programming model has been enlarged by the addition of another dimension and the problem has been derived in a decomposition format.

Jan 1, 1972

The mathematical models of semivariograms can be classified according to whether or not they correspond to situations where the second order stationarity conditions are satisfied (§ 3.3.4). If second order stationarity exists, the a priori variance s2 of x (z) also exists and is finite. For large distances h such that x (z) and x (z + h) are not correlated, the semi- variogram ? (h) will reach a value equal to s2 [this is a consequence of (3.27) above]. This limiting value is called the sill C of the semivariogram, and the distance at which ? (h) reaches the sill is called the range. The range of the semi- variogram obtained from a given type of sample corresponds to the distance of influence of these samples. If only the intrinsic hypothesis is satisfied, the sample variance is an increasing function of the size of the area or volume in which the samples are located, and the semivariogram ? (h) will be a continuously increasing function of h. Remark: It will be shown in Chapter 7 that the variance s2 of x (z) in the ore body O is equal to the average value of ? (h) in O. If ? (h) is a non-decreasing function with sill C, the average value of ? (h) in O will be less than C. s2 and C will be equal only if for some values of h in O, ? (h) exceeds C. In practice, if the range of the semivariogram is small with respect to the dimensions of the ore body, the difference between C and s2 will be negligible.

Jan 1, 1978

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 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, 1975

By I. Koliabina

In this paper, the results of mathematical modeling of casing pipes decontamination from radio-active new mineral forms directly in boreholes using hydrochloric and hydro-silicic-fluoric acids are presented. Modeling for highly and low radioactive coatings on the walls of casing pipes of Anastasievka oil-and-gas deposit was performed using GEMS software, based on the method of Gibbs energy minimization. Calculations have shown that thorianite and goethite, that are present in low-active crusts, detected in casing pipes uplifted from comparatively low depths, are well dissolved in hydrochloric acid, but radiobarite is almost insoluble. For the same acid concentrations, almost all radiobarite of high-active coatings detected in pipes uplifted from considerable depth is dissolved. To evaluate the possibility of decontamination of pipes from radiobarite of low-active coatings, modeling of crust dissolution under the action of H2SiF6 has been performed. The results have shown that for acid concentrations of more than 13 % almost all Ra and Ba are dissolved while all iron and thorium remains in goethite-thorianite solid solution. For the same acid concentration, almost all radiobarite from high-active coatings is dissolved. Therefore, no reagent allows decontamination of pipes from coatings of both types. It seems that successive or simultaneous use of both reagents (HCl and H2SiF6) in certain ratio is required. To clarify this issue, further experimental and model investigations are necessary. The issue of decontamination of casing pipes from galena that is present in high-active crusts also needs to be clarified.

Jan 1, 2005

By J. A. Herbst, D. W. Fuerstenau

An analysis of the kinetics of dolomite grinding in a dry ball mill reveals that the following approximations apply for the parameters of the batch grinding model: (1) the size discretized selection functions are proportional to the specific power input to the mill, and (2) the breakage functions can be taken as invariant. These approximations are shown to provide the basis for accurate predictions of product size distributions obtained for several mill speed, ball load, and particle load combinations within the normal ball mill operating range. The engineering implications of these findings are discussed.

Jan 1, 1974

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