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By R. V. Ramani, A. S. C. Owili-eger

Mathematical modeling is a scientific exercise with the objective of developing simplified mathematical statements that relate to one another the same way as the processes that are being modeled. The utility value of the model is dependent on the ability of the model to closely approximate prototype behavior. Development of a perfect model, therefore, is an unrealistic objective because of the simpli¬fying assumptions made in building it. However, for a model to be acceptable for application, its operating characteristics or data generated from it should, within reasonable accuracy, duplicate proto¬performance. The validity and accuracy of a model depends on the mathematical constraints presupposed in model formulation. The final model must be tested for mathematical validity and for closeness of representation of the prototype. Mathematical validity, does not, however, imply that the model is accurate and correct but is prerequisite. Model testing and verification for the steady state model are given in Owili-Eger et al (1973). The unsteady state model has been tested for mathematical validity and found to be correct but has not yet been applied to a field condition for lack of data. However, in the application discussed below, the unsteady state model results are compared with pressure curves reported in literature and also with results from the steady state model. Coal seam characteristics and gas reservoir pressure used in this application are extracted from Kissell (1972). These characteristics are for the Pittsburgh seam, Federal No. 2 Mine, Fairview, West Virginia.

Jan 1, 1974

By C. B. Manula, R. L. Sanford, R. A. Rivell

A central requirement for using simulation models is the need for retrospect testing to validate experimental conclusions. Acceptance of a model by managers and safety practitioners is more likely to depend on its tested performance in-the field rather than on the underlying logic or the validity aspects of the model itself. It is here that simulation bridges the gap between theory and useful design procedures. The original version of the rail haulage sub-assembly was success¬fully tested in the field (Sanford, 1969). However, the case studies that were described here involved single-stage haulage and restricted jobtypes from UGMHS. Since this report together with Volume VI (Production Subsystem) describes extensive changes and modifications to the rail haulage sub-assembly and UGMHS, field tests were necessary to verify both the rail model and the linking concepts to the Produc¬tion Sub-system. Mine Description The candidate mine selected for model verification works the 6 1/2 foot Pittsburgh seam. Shaft openings are used for manways and ventilation and a dual compartment slope for materials handling. In the bottom half of the slope, a hoist with track handles supplies and equipment. In the upper half, a 42 inch belt conveyor travelling at 450 fpm moves coal from a rotary dump to the surface. The immediate roof is shale with the first 12 inches taken during development mining. About 4500 raw tons are produced daily from seven face units and one spare working three shifts. At seven of the sections,

Jan 1, 1974

By R. V. Ramani, C. B. Manula, A. Owili-Eger

MINE PROTOTYPE The prototype chosen for application demonstration is from Kingery (1960). The mine and the ventilation plan is presented in Figure 11. A new coal mine is projected with entrance by slope 1,500 feet long. Nine train entries will be standard for development, five as intake and four as return. One return shaft is planned near the slope bottom. The slope will have an area of 150 square feet and a perimeter of 55 feet. The return shaft will be circular with a diameter of 18 feet and will be 500 feet deep. Two hundred feet of the shaft and 500 feet of the slope will be concrete lined. Will it be possible to operate five units per shift with amount of air at each unit not less than 25,000 cfm? Additionally, a shop at the slope bottom will require 10,000 cfm. The problem is completely worked out using standard ventilation formulas and simple manual calculations in the above reference and is reproduced here in Appendix II for ready reference. APPLICATION In this manual, four different applications of the PSU/MVS are outlined. An article by Stefanko et al (1972), outlines how one can move from a mine map to a network for the generation of computer input. Attention is drawn to Figure 12, which is the network line diagram of the mine ventilation system in Figure 11. Note that every roadway junction has been numbered. The dotted lines represent leakage paths and the letter 'R' on a branch denotes that the split is regulated for the quantity shown. For example, there is a leakage

Jan 1, 1975

By A. E. Reisenauer, R. W. Nelson, G. W. Gee

A model assessment was made to evaluate contaminant transport to ground water from clay-lined and unlined tailings pits. The input hydrologic soil characteristics were measured on materials typical of those found at the Morton Ranch uranium mill site in central Wyoming. The assessment involved combined saturated and partially saturated flow and contaminant transport models for two-dimensional cross-sections typical of the proposed Morton Ranch burial pits. Specifically obtained from the models were contaminant flow paths, the advancing contaminant flow fronts for sorbed and non-sorbed constituents, and travel times of contaminants along flow paths. Such results enable evaluation of the environmental consequences for the alternative control methods.

Jan 1, 1980

By DeVerle P. Harris

The structure of an exploration model reflects a number of design considerations, one of which is the question or issue-to be investigated by the model. Thus, a model designed to evaluate the magnitude of risk and its economic implication to optimal decision making at each decision juncture of a multistage exploration architecture differs considerably from one designed to evaluate, say, the long run average cost of discovery, in which the architecture of exploration is suppressed and risk is simply an element of average cost. The perspective of the model examined in this paper is that exploration is investment in (purchase of) information and that the next stage of an exploration program is undertaken only when the expected value of information to be acquired in that stage exceeds its cost. The degree to which this perspective is honored influences considerably model design. Consider two design objectives:

Jan 1, 1989

By R. V. Ramani, A. S. C. Owili-eger

The quantity of methane emitted into the mine atmosphere and the movement of gas through solid coal and the adjoining country rock are dependent on the physical properties of the medium, boundary con¬ditions, the initial gas pressure distribution, and the combination of natural and mining factors. Functional relationships between these factors are not yet known. Consequently, the development of rigorous mathematical models to predict methane flow into the mine air is difficult and to date no model has been reported which is capable of such a function. Thus far, empirical formulas available for the calculation of gas quantity released from underground sources require too much his¬torical data, not currently available. Again, these estimations are at best only crudely approximate. The numerical methods available have not been made practical enough for industry wide application. Therefore, the development of a relationship amenable to numerical analysis and practical enough for use in the industry would provide the flexibility lacking in analytical approaches. The mathematical models given in equations (7) and (8) are further attempts in presenting practical models for predicting the quantity of methane emission into the mine environment. Equation (7) is the steady state model and equation (8) is the unsteady state model.

Jan 1, 1974

By R. K. Mehta

An electrochemical coal oxidation model involving heterogeneous kinetics is presented. This model was tested by collecting current transient data on three coals assaying different ash content under varying operating conditions such as particle size, temperature, and % solids. In all cases, the model fitted the data very satisfactorily. Three intrinsic rate constants, namely mass transfer coefficient of Fe(II) Ions diffusing from solution to the anode (kma), mass transfer coefficient of Fe(II) Ions diffusing from solution to the coal surface (kmc), and chemical rate constant for coal oxidation with respect to Fe(III) at coal surface (k), were calculated. It was interesting to note that in this system, the mass transfer at anode was as important as the chemical reaction at the coal surface. The validity of this model was further demonstrated through a comparison of the activation energy of coal oxidation: firstly, by utilizing calculated chemical rate constant and assuming Arrhenius' type of relationship: secondly, by utilizing conventional approach using limiting current values. The comparison revealed that agreement was quite close. This kinetic analysis is useful because such a model can be used in predicting the intrinsic rate constants so that the relative importance of mass transport can be rationally analyzed.

Jan 1, 1991

By Daniel Augusto Godinho de Carvalho

Since the beginning of BOF process, slag formation has been subjected to extensive development. During the initial stages of the blow, fast slag formation is primordial for the process performance. This is mainly to allow oxidizing reactions, and also to protect the refractory. A modeling of BOF process for the purpose of process optimization requires precise knowledge concerning the dissolution of CaO and MgO based materials. Using this knowledge, the optimal process conditions can be ensured by a controlling of the slag formation during the converter steelmaking process. Taking into account an application of large amount of different raw materials, as well as location-specific process conditions, the characterization of the dissolution behavior of different additives is an important key to improve the technological process. Thereby, in the frames of this project, an appropriate model for slag formation is established and compared to operational results for a 330t BOF, operating at ThyssenKrupp CSA, Santa Cruz, Brazil.

Aug 16, 2017

By Frank F. Aplan, Edward C. Jr. Dowling, Richard R. Klimpel

Thirteen kinetic models that mathematically describe the flotation process have been statistically evaluated for the flotation of copper, lead and zinc ores. Comparisons have been made for a variety of circuits involving roughing, cleaning, scavenging and regrind followed by cleaning. Variations in collectors, frothers, depressants and activators have been considered. Based on the statistical criteria used for the evaluation, and the reagent, circuit and ore variations studied, the most reliable flotation models have been identified and subsequently used to characterize the metallurgical results.

Jan 1, 1986

By F. F. Aplan, E. C. Dowling, R. R. Klimpel

Numerous flotation models have been proposed in the literature. Thirteen of these have been applied to batch flotation data and evaluated with respect to one another using statistical techniques. Flotation tests were carried out on samples of a US porphyry copper ore (Pinto Valley, AZ). The ore was tested using various collector and frother systems to produce different time-recovery profiles. These were used to calculate flotation rate and ultimate recovery parameters for each model. The models were then evaluated statistically to determine the overall fit of the calculated to the observed data and to test the range of significance of the parameters in each model.

Jan 1, 1986

By Edward C. Dowling

Froth flotation has been used industrially for many years to separate valuable minerals from their associated gangue constituents. Notwithstanding the significance of this process to the mineral industry, many of the engineering tools needed for the evaluation of the flotation process are still in a developmental stage. Traditionally, the evaluation of a flotation test on both the laboratory and industrial scale has been based largely on a rougher recovery value achieved at a sufficiently long time to give a "final" or "equilibrium" recovery value. The assumption of a time equivalency for a given recovery value between various flotation tests or between laboratory tests and industrial operation underlies this method of evaluation. Such an assumption implies that flotation is an "equilibrium engineering process" and that the time-rate recovery of material from the flotation cell is not affected by changes in the flotation system. It has been shown by Bushell (1) and by Klimpel (2) that the assumption of time equivalency between various flotation tests is unjustified. Consequently, better tools are needed for evaluating flotation test results, Because mathematical flotation models which incorporate both a recovery and a rate function can completely describe flotation time-recovery profiles, they can provide an excellent tool to evaluate flotation tests.

Jan 1, 1984

By H. Y. Sohn, M. K. McCarter, Bradley C. Paul

"A computer model was constructed for bacterial leaching of the major sulfides found in porphyry deposits, including bornite, chalcocite, chalcopyrite, covellite, cubanite, enargite, native copper, pyrite, and pyrrhotite. The model incorporates equations for the sulfide minerals dispersed in the rock matrix. Leaching occurs by reactions with ferric ion diffusing into the rock fragment: Ferrous ion is resenerated to ferric with oxygen by bacteria at a temperature dependent rate. The model keeps track of the net acid generated, oxygen consumed by the bacterial oxidation of ferrous ion, heat generated, jarosite and hematite precipitated, and copper leached. The model was used to predict the rate of copper recovery, heat generation and oxygen demand for a variety of run-of-mine sized porphyry ores. These results were used in the design of a ventilation system and the economic analysis of a modified in situ extraction method that may be cost competitive with conventional copper production involving open pit mining.IntroductionA study was undertaken at the University of Utah to evaluate the technological and economic feasibility of mining copper by a method referred to as Flood Drain Leach Cell (FDLC) mining. Cells 60 by 75 meters in plan and 70 meters in height are created throughout the ore body by a modified Vertical Retreat Mining technique that includes the removal of 25% swell material. The swell material is leached in finger dumps on the surface while the cells underground are bulkheaded, flooded, drained, and artificially aerated to promote bacterial ferric sulfate leaching. Solutions are cycled through several cells to reach pregnant grade of 1 gram copper per liter of solution. These solutions are then fed to an underground solvent extraction plant and then a surface electrowinning tankhouse."

Jan 1, 1988

By C. Isaac Garcia, Sihai Jiao, Anthony J. DeArdo

"A practical model based on the Hill analysis has been developed to calculate the Lankford value of interstitial free (IF) steels and its distribution in different rolling directions, by considering only a few selected texture components. The Texture Intensity Ratio (TIR), i.e. (111 ) /(100), was used in the model to describe texture. By using the new TIR parameter, the texture-based prediction models can be used more easily to predict the Lankford value in a rather straightforward way.IntroductionThe deep drawing capacity of sheet steels is generally indicated by the Lankford value, which is mainly determined by the texture in steels1. Traditionally, various models derived from the Taylor model are employed to calculate the Lankford value from the texture2-4. In such models, the plastic deformation of steel is assumed to be the result of the slip of dislocations in certain slip systems, i.e., by either pencil glide or restraint glide. The slip direction is the <111> direction. In the case of pencil glide, the slip is thought to be possible in all crystal planes with the <111> crystal direction. Assuming the material is elongated in the X1-direction by d n and compressed in the X2 and x3-direction by qd n and (l-q)d n, respectively, corresponding to a deformation tensor"

Jan 1, 2001

By S. Simukanga, J. Masinja, P. A. Bepswa, A. N. Mwale

Screening is an important operation in dry and wet closed circuit mineral processing applications. Most of the operations have seen the benefits of using fine wet screens in primary grinding sections where the product is relatively coarse, and screens can handle the tonnage. Although many models are available, most of them are confined to dry and wet coarse screening applications. Most models do not give good predictions for wet fine screening. To facilitate model development, pilot plant tests were performed using a single deck Derrick Screen at aperture sizes of 45µm, 75µm, 106µm, and 150µm. Experimental data for a range of feed solids concentrations and flowrates was collected and used to calibrate the performance of the screen under the different operating conditions. The results showed that the performance of the screen deteriorated with an increase in feed solids concentration, and, similarly with an increasing feed flow rate. The percentage of fines carryover also increased with the reduction aperture size. The carryover was even more pronounced at higher feed rates and solids concentrations. A model was developed for predicting the performance of fine wet screening. Data from the test work was used to compare the actual and predicted results, and to calibrate the model. Additional independent data was used to validate the model and assess its limitations. This model will give an expected screen performance based on the initial feed conditions. It incorporates screen design parameters that allow for an estimation of a suitable screen size for a desired performance based on given feed conditions. This paper discusses; the results from the test work performed, the model development and its limitations.

Jan 1, 2016

By H. J. McQueen

Friction stir welding (FSW) generates complex microstructures in the nugget and thermomechamically affected zones (TMAZ) that have led to diverse explanations. However, consideration as an extension of microstructure development in piercing/extrusion can lead to a better understanding of flow patterns and microstructures during FSW. Furthermore, the intense strains in the nugget/TMAZ can be interpreted by comparison with ultra-high strains in torsion that exhibit dynamic recovery as extending into regions with high angle boundaries strongly serrated with spacing near the subgrain size defined by the high temperature. The subgrain diameter and extrusion pressure have been shown to be dependent on the Zener-Hollomon parameter Z (=t exp(Q/RT), Q activation energy, R gas constant) combining temperature T and strain rate E in the same mariner as for torsion and compression. Moreover, such tests exhibited steady state stress os above a certain strain Es (rising as Z increases) in which T, , subgrain diameter and dislocation spacing remain constant. Due to the subgrain boundaries (SGB, low angle <5°, i.e.,LAB), continually rearranging by migration, decomposition and reformation, the subgrains remain equiaxed in elongating grains, whose boundaries (GB) become serrated as they migrate to absorb SGB. As confirmed by straining in torsion at constant T and Z. , more subgrains bordering the greater GB area have several high-angle facets (HAB) ; these small cellular regions with a mixture of HAB and LAB facets are designated HAB-subgrains. As serrations in neighboring grain boundaries impinge, the grains pinch off becoming shorter; this occurs at higher strains as subgrain size decreases with rising Z. The pinching-off makes the neighbors thicker so the grains never become thinner than about two subgrain diameters. In conjunction with such geometric dynamic recrystallization (gDRX), GB&apos;s undergo a net migration into grains with denser substructure, enlarging those with larger subgrains. Consequently a better name has been proposed: grain dimensioning dynamic recovery (gDRV).

Jan 1, 2007

By Viswanathan N. Nurni

In metallurgical processes, more and more usage of hydrocarbons is encouragedto bring down the carbon emissions. In this regard, numerous investigations onreduction of oxides by C-O-H-N gas mixture have been reported. Attempts to simulatethese reduction processes using shrinking core model, one of the commonmodels used for such studies, have under predicted the reduction rates. This maybe owing to the fact that the homogeneous reaction in the gas phase is not being considered. If the reaction temperatures are above 1000K, generally so for manyreduction processes, the homogeneous gas reaction rates are expected to be sohigh that one can assume local equilibrium in the gas phase. In the present study,reduction of wustite in a C-O-H-N gas mixture has been modeled using shrinkingcore model considering the water gas shift equilibrium in the gas while it diffusesthrough the product layer.

Sep 1, 2012

By D. J. Varnes

Rocks in mines, quarries, and many outcrops commonly show evidence of being under high stress. Saw cuts and drillholes close in, partly mined coal bursts violently, and pillars crush and rock spalls in mines even at moderate depths. Similarly, strong and massive rocks such as granite and sandstone naturally divide themselves into sheets that lie more or less parallel to their outward topographic form. The sheets may be either convex or concave. Thin plates of bare rock surfaces bow up and buckle. Such effects often cannot be explained by the obvious loads now acting on the rock, that is, by loads resulting from overburden, topographic irregularities, or stress concentration around openings. The stresses exceed those that would result from such loads. Two interpretations of such excess stresses have been made. In one, the stresses are assigned in origin to now active tectonic forces. In the other, they are regarded as leftover and locked in from some previous state at which higher pressures prevailed. These two sources may both operate and they generally cannot be distinguished easily in the field. There are other complicating sources of stress such as temperature gradients and chemical alteration. Nevertheless, some bodies of rock, by exfoliating, show evidence of high internal stress even though they are practically unweathered and so isolated topographically that the presence in them of significant stress due to exterior loads or active tectonic forces seems unlikely (Fig. 1). Moreover, completely isolated rocks are known to change density, shape, or size 1,2 to expand under constant compressive stress;3 and even to disintegrate 4,5 without the intervention of weathering processes. The stresses involved here must be truly residual in the sense long used by metallurgists; that is, residual stresses in a body are those that remain.

Jan 1, 1970

By Young-Sool Jin, Heung Nam Han, Hong Joon Kim, Jae Kon Lee

A mathematical model was developed considering non-symmetric cooling' and stress distribution in both thickness and width direction of strip on a run-out table of hot strip mill. In order to solve a transient heat transfer equation including the heat evolved from phase transformation, a finite element method coupled with thermodynamic and kinetic analyses was applied. The heat capacity of each phase and heat evolution due to phase transformation were obtained from the thermodynamic analysis of the Fe-C-Mn-Si system based on a sub lattice model. The phase transformation kinetics of the steels was derived by using an inverse additivity technique with continuous cooling experiments. Heat transfer coefficients of strips on the run-out table were, by applying an inverse method, determined from the actual mill data under various cooling conditions. As for the stress analysis, the density change of strip due to cooling and phase transformation, and the transformation superplasticity were considered. A 90nstitutive equation for the transformation superplasticity, which is related to the phase transformation kinetics and the internal stress due to the density change of strip, was applied. A finite element method was adopted to calculate the deformation behaviour of strip on a run-out table of hot strip mill. Using the models, the temperature-phase-deformation history and distribution of a strip on the run-outtable was calculated.

Jan 1, 2001

By D. R. Zhu, H. S. Chiang, Y. M. Jiang, S. S. Peng

Two types of underground tests on three types of shield supports, 2-leg, 4-leg, and chock shield, were con- ducted to measure the horizontal movement of the canopy against the immediate roof. In no friction tests, steel rollers were placed between roof and canopy top, while in friction tests normal direct contact was used. Results indicate that the canopy for 2-leg shields always moves forward during setting, whereas there was no forward movement for 4-leg or chock shields. Based on the test results, a model for active horizontal force was proposed.

Jan 1, 1990

By R. P. King

"A model of the flotation process can be used effectively for design and control. For design purposes it can be used to predict the performance of a large plant from laboratory and pilot plant data. It can be used for control purposes to assess the utility of any proposed operating modification to an existing plant, and it can also be used to determine optimal control settings for best operating performance.A model has been developed that will allow for variations in feed properties and for variations in fineness of grind. The model can be used to assess the effects of reagent addition rate, aeration rate and pulp level on plant performance and these are the control variables that are used individually or together in all operating flotation plants. The model provides for a distribution in the values for flotation rate constants, particle size and mineral fraction, and, because of its complexity, requires a large computer when it is to be applied to a typical plant configuration. The computational method that is used to apply this model to such configurations is described in this paper, and particular attention is paid to the problem of allowing for feedback of tailings from cleaners and recleaners."

Jan 1, 2014