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By Karel SPIRKO

The one-dimensional mathematical model of unsteady-state heat conduction through semi-infinite homogeneous and isotropic airway walls with convective heat and moisture transfer between their wet or dry naked surfaces and mine air with time variable temperature and humidity has been developed on the basis of introduction of acceptable simplifications of description of heat and moisture transfer between rock mass and mine air. The analytical solutions for computation of the temperature distribution and surface temperature of the airway walls and floor and for calculation of water vapour pressure near the wet surfaces at given time are obtained by means of the model presented. The presented solutions are derived for general conditions and they could be easily adapted to the actual ones. Results of the model represent basis for balancing heat and moisture transfer between mine air and its surrounding in deep mines under time variable temperature and humidity of the air and enable us to solve complicated dynamic changes of mine air temperature and humidity in an airway system by relatively simple mathematical tools. INTRODUCTION The importance of unfavourable influences and the costs of condition arrangements increases with mine depth. Precision demands on the methods which predict the environmental condition changes and by which it is possible to optimize condition arragements are still increasing. Environmental conditions in deep mines are determined especially by flow velocity, barometric pressure, temperature, and humidity of mine air. Therefore new and more exact mathematical models of mine air flow through airway system and those of heat and moisture transfer between mine air and individual important sources of heat and moisture are developed. The paper presented deals with description and solution of problems of heat and moisture transfer between mine air and airway walls as the rock mass is one of the important heat and moisture sources in deep mines. There are several different approaches to the problem. In some models the moisture transfer between mine air and airway walls is not considered at all. In other models the moisture transfer is described only by certain empirical coefficients. Simultaneous heat and moisture transfer is described seldom. This paper tries to describe in a simple way simultaneous convective heat- and mass-transfer processes taking place on wet naked surface of airway walls by means of corresponding

Jan 1, 1993

By Kevin D. Lofftus

This paper presents a dynamic model for column flotation. The model equations are normalized and the dimensionless groups that are directly responsible in determining the column flotation behavior are identified. The resulting model equations are incorporated for computer simulation. Numerical results from computer simulations are analyzed to gather information about design and operation of column flotation devices.

Jan 1, 1988

By W. E. Horst

In Part I of this paper we describe two techniques that were employed in the development of mathematical descriptions of the size reduction process which takes place in a ball mill. In Part II we show how the comminution model was imbedded in a process model to effect steady-state and dynamic simulation of a closed-circuit grinding operation. Increasing emphasis is being placed on development of approaches whereby the essential characteristics of a process can be succinctly represented in terms of a mathematical description of the relationships that exist among important process variables. This activity, commonly known as mathematical modeling, predates modern electronic computers: however, these computers with their tremendous computational capability have given new impetus to the whole field. Although the computer is quite helpful in the development of mathematical models, the real value to the engineer lies in the fact that computers represent such a powerful tool for simulating systems described by mathematical models. As a consequence, engineers may simulate and thereby study the behavior of complex. interacting, systems over a broad range of process variables and configurations once appropriate process models have been developed for the sequence of steps comprising the process.

Jan 1, 1970

By E. J. Freech

In this part of the two-part paper we discuss briefly the adaptation of the comminution model to describe the observed behavior of an industrial grinding circuit. Although reported verification of comminution models for continuous systems is limited, some interesting work has been reported 1,2 recently. The data acquisition and modeling efforts are described first, followed by discussion of some of the simulation results. Observations pertinent to steady-state operation are presented followed by a description of the application of a dynamic model of the grinding circuit for synthesis and evaluation of grinding-circuit control. The pilot-scale work indicated the comminution model should be capable of describing an industrial size-reduction process. Recognizing the broad utility of a process model based on first- principles, the Industrial Nucleonics Corporation of Columbus, Ohio, embarked on a joint program with the Duval Corporation of Tucson, Arizona, to evaluate the industrial applicability of the models described in Part I. This program was conducted in a grinding circuit, which included a rod mill 12.5 feet in diameter and 16 feet long and a ball mill 12.5 feet in diameter and 14 feet long, at Duval Corporation's Esperanza property3. The rod mill was operated in open circuit and the ball mill in closed circuit with cyclone classifiers.

Jan 1, 1970

By K. Oraee

Excessive emissions of methane from the coal seams can have a serious adverse effect on both safety and productivity of longwall coal faces. Mechanization of coal faces has increased production possibilities to the extent that normal ventilation systems may not be able to ventilate coal face areas in order to lower methane content in the air to within legal limits. Production increases may therefore be prohibited for this reason, especially in gassy seams. Methane drainage from the coal seam by means of long holes and before production starts can act as a useful remedial action. In this paper a two dimensional mathematical model has been produced. The model that is based on finite elements, simulates a methane drainage system where the resultant risk is linked to the coefficient of diffusion, coal permeability, holes pattern and the duration for which the seam is subject to drainage. It is concluded that methane drainage of this type can assist in achieving production increases in many coals seems, especially where high gas content is a virtue of the seam.

Jan 1, 2010

By Paul M. Bommer

Abstract. This cater presents the development of and results from a computer model of in-situ uranium leaching. This model uses a streamline-concentration balance approach and is useful with a vide range of reservoirs. It can be used with any type of veil system, in a reservoir with or without boundaries, and with any form of descriptive kinetics. The model also includes the effects of dispersion and consumption of oxidant by minerals other than uranium. The effects of areal sweep, variable uranium concentrations, variable permeability, and the presence of oxidant consumers on uranium production are shown and discussed.

Jan 1, 1979

By Edgar E. Vidal, Patrick R. Taylor

Standard textbook equations for heterogeneous kinetics typically utilize a constant driving force to solve for rates and times of reactions. In order to more closely model real systems, equations and solutions are presented for particle leaching kinetics in which the driving force is decreased as the reactions proceeds. In addition, models for continuous co-current and continuous counter current aqueous-solid reactions are presented.

Jan 1, 2005

By B. Moudgil, M. Bogan

A mathematical model, based on first-order kinetics, is derived to describe batch settling data. The model is used to predict the settling behavior of solid suspensions under different conditions. The potential benefits of this model to solid-liquid separation processes are discussed.

Jan 1, 1994

Sedimentation is used to clarify process effluents or to thicken process slurries. The sedimentation cycle of a suspension is presented as a settling curve. This curve is simply a plot of the height of the interface between the settled suspension and clear liquor versus time. Figure 1 shows a series of graduate cylinders which contain a suspension at various stages in its settling cycle. Cylinder 1 shows the suspension completely mixed at time zero. After a brief period of time (see cylinder 2), the suspension is observed to settle from its initial height Ho to height H1, leaving behind a volume of clear (or turbid) liquor, called the supernatant. The interface between the supernatant and suspension is termed the mud line. It is also possible to distinguish at the bottom of the cylinder a layer of sludge representing solids which have settled from the suspension. The interface between it and the suspension is called the sludge line. The sludge line moves upward in the cylinder.

Jan 1, 1992

By G. F. Friel, J. C. Edwards, C. C. Hwang

In the implementation of a mine fire alarm and location strategy, the Interpretation of the fire signature Is Important. Smoke and CO are the two dominant fire signatures, and many mine fire detection systems utilize sensors which respond to smoke or CO through a diffusion mode or a mechanical pump mode. The fire signature may be modified during its transport along airways and at crosscuts. The modification occurs through dilution of the contaminants. In this Investigation, computer codes were employed to compute the effects of contaminant dilution on the contaminant signature when a straight flow passage has one dead-end crosscut. The model predicted the airflow within always and the entrainment of contaminants into the crosscut from the airway. One application of the model is to determine the most suitable location for CO detectors for early mine fire detection.

Jan 1, 1995

By Robert C. Bates

Background is given on the various equations used to describe diffusion and convective flow of radon in porous media. Bureau-developed equations for modeling diffusion and Darcy flow through multilayered porous media are described briefly, and examples of their use are given. Analysis results discussed include: The transient effect of pressure changes in different length models, time dependent flux changes in multi-layered models, and radon flux through pinholes in sealants

Jan 1, 1980

By Edmond Donovan, O&apos

With the increase in complexity of conveyor systems and the inexorable demand for more capacity and availability, the ability of designers to accurately predict performance is becoming increasingly important. Dynamic analysis techniques for modelling wave mechanics in conveyors are finding increased applications. Unfortunately, the reliability of these modelling techniques is dependent on a thorough understanding of the performance characteristics of the components that make up the system. These characteristics include such things as response rate, hysteresis and efficiency. Some parameters such as idler rolling resistance can be easily quantified by measurement. More complicated drive parameters are difficult or impossible to measure, particularly in large horse-power equipment. One method of quantifying or at least bracketing the performance envelope of complicated pieces of equipment is to construct a mathematical model. This can be done quickly and economically, and the influence of various parameters can be determined. This paper sets out to demonstrate by example the usefulness of this technique in gaining an understanding of complicated systems. The model is developed and the influence of a number of variables are examined.

Jan 1, 1996

By Gemei Yang, Pierre Mousset-Jones, Felipe Calizaya, Malcolm J. McPherson

Laboratory tests on controlled airflow recirculation have shown the development of transient states in response to changes in system prevailing conditions such as those generated by a sudden start-up and stoppage of fans. Researchers in many European countries have developed various models to explain these phenomena. However, these models failed to consider some important factors such as diffusion and dispersion of gas in turbulent flows. For both in-line and cross-cut recirculation, tests have shown that after the start- up of a booster fan, the gas concentration in the system fluctuates, reaching high levels at the initial states and slowly dying out with time. These fluctuations cannot be represented adequately by simple step-wise functions but rather by smooth, albeit complex equations. In this paper, the phenomena are explained by the convection-dispersion theory, and represented by a mathematical model. Based on a few simplifications and applying Fourier's Transform Method to the differential equations of the flow recirculation model, an integral form of gas concentration function was derived. The Simpson Integration Method was used to compute numerical results for two laboratory tests. The paper also discusses the range of the dispersion coefficient to improve the accuracy of the model.

Jan 1, 1989

By Lynton Gormely

Oxygen transfer in a stirred tank bioreactor has been modelled mathematically to determine the trends in transfer efficiency (kg transferred per kWh) with transfer rate, tank depth, superficial velocity, and mixer power.

Jan 1, 1990

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 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 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 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