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It is well known that the electrochemical precipitation of metals from aqueous solutions is conducted by the electrochemical standard potential scale. This scale indicates the order of nobility of different metals. Consequently, the standard potential scale shows the nocivity of metals when they are present as impurities in aqueous solutions containing metals. In the hydrometallurgy of cobalt, nickel and zinc are co-deposited during cobalt electrodeposition. Nickel has almost the same chemical, physical and electro-chemical properties as cobalt. Furthermore, the electrochemical potential of nickel is relatively higher than that of cobalt. For this reason nickel is preferentially reduced at the cathode in the presence of cobalt. The presence of small amounts of zinc in solution leads to contamination of cobalt electrowon. In spite of its lower electrochemical potential in comparison to cobalt, zinc is reduced on the cathode because of its higher hydrogen-overvoltage. But, in the hydrometallurgy of zinc, small amounts of cobalt present solution will contaminate the zinc reduced at the cathode. This is easily explained by the fact that cobalt is more electropositive than zinc. The co-deposition mechanism of sulphur at the cathode is not yet well understood. Great attention has to be paid to the mechanism of co-deposition of sulphur during cobalt electrolysis. This work aimed to investigate the influence of some parameters on the co-deposition of nickel, zinc and sulphur during cobalt electrowinning. The following parameters have been investigated: Co2+concentration in the electrolyte, current density and ammonium sulphate (NH4)2SO4additions. It has been established that important nickel, zinc and sulphur co-deposition takes place at relatively low Co2+ concentration in solution. The behaviour of these elements with regard to the cathodic phenomena has been established.

Jan 1, 2005

By B. Samanta

A quality characteristic analysed through construction of the Shewhart control chart is required to be normally distributed. In mining applications, this assumption is often violated as many quality characteristics follow skewed or lognormal distribution. In this paper, two methods were investigated using a heuristic approach for setting up the control limits for a skewed population. Based on these approaches a Mode chart, and a Weighted Variance (WV) control charts were constructed. The performance of the proposed methods was compared with the normal based Shewhart method through a case study conducted in a surface mine supplying iron ore to a steel plant. A simulation study was also conducted to evaluate the effectiveness of the proposed methods over the Shewhart method. The study revealed that the Shewhart control charts generated more out of control alarms compared with the Mode and Weighted Variance control charts for a skewed population of Fe%. The simulation results also revealed that for extremely high skewed population, the WV control chart and Mode control chart provided higher probability of coverage than the Shewhart method; although the detection rate (probability of detection) of out of control condition for these methods was slightly reduced compared with Shewhart method.

Jan 1, 2004

By R. M. Jara

This work evaluates and characterizes the impact of the support size and mining dilution of a block model in the operation and selection of equipment at an open pit mine. An exploratory analysis and geostatistical modelling of the grades assayed on a set of drill hole samples is performed, which allows constructing a grade model on a dense grid by means of a conditional simulation. The grades are then averaged to greater selective mining unit supports in order to proceed with the study and methodology. First, the metal-tonnage curves are used to analyse the loss of selectivity on the in situ resources caused by a change of support. Concerning the ore reserves and their mining sequence, defined in the pit optimization and analysis process, the same curves prove that the loss of selectivity is more accentuated. Second, the importance of the block boundary dilution produced during mining operations is assessed. Its value depends on the amount of ore in contact with waste, on the loading error of the equipment and on the ore loss/waste dilution criterion assumed by the planner. The dilution percentage and the differences between waste and ore grades become higher when the block size decreases. For these reasons, considering the dilution in the production plans makes mining a small support more constraining. An adequate delimitation of the orebody can improve the mining selectivity, leading to greater income. Finally, a study of the increase in mining cost that provides a zero difference in NPV between the different block size options is carried out, in order to determine the maximum increase in mining costs for which it remains profitable to mine at a smaller block size. Keywords: Mining selectivity, support effect, block boundary dilution, selective mining unit size, block model.

Jan 1, 2006

By A. Thoraval, K. B. Slimane, O. Ozanam

The REP experiment is part of the research programme conducted by Andra to investigate the possibility of reversible radwaste disposal in a Jurassic (Callovo-Oxfordian) argillite formation at the Meuse/Haute-Marne underground laboratory site in northeastern France. The experiment focuses on the hydromechanical response of the formation to sinking the laboratory access shaft. Modelling of boreholes and shaft sinking operations has helped to optimise measurement point locations based on initial stress tensor anisotropy, while minimising interaction between instrument boreholes. Analyses were made of model sensitivity to intrinsic rock characteristics, hydromechanical coupling properties and sensor installation procedures. L’expérimentation REP fait partie du programme de recherche pluridisciplinaire engagé par l’Andra pour étudier la possibilité d’un stockage réversible des déchets radioactifs dans la formation Callovo-Oxfordienne des argilites du site de Meuse/Haute-Marne (Commune de Bure - France). Cette expérimentation permettra d’étudier la REponse hydromécanique de la formation aux sollicitations engendrées par le fonçage du Puits d’accès du laboratoire souterrain de recherche. Afin d’optimiser le positionnement des points de mesures, compte tenu de l’anisotropie du tenseur des contraintes initiales, et de minimiser les interactions entre les forages d’instrumentation, des modélisations des forages et du creusement du puits ont été conduites. Des analyses de sensibilité aux caractéristiques intrinsèques de la roche, aux propriétés de couplage HM et aux protocoles d’installation des capteurs ont été faites. Die REP-Untersuchung ist Teil des multidisziplinären Forschungsprogramms, das die ANDRA im Callovo-Oxfordian-Tonstein in situ am Standort Meuse/Haute Marne (Gemeinde Bure – Frankreich) im Hinblick auf eine Eignung zur reversiblen Lagerung radioaktiver Abfälle durchführt. Dabei soll das hydro-mechanische Verhalten der Formation auf die Beanspruchungen, die durch das Abteufen des Zugangsschachts zum Untertage-Forschungslabor erzeugt werden, untersucht werden. Zur optimalen Positionierung der Messpunkte unter Berücksichtigung der Anisotropie des Tensors der Ausgangsspannungen und zur Minimierung der gegenseitigen Beeinflussung der Instrumentierbohrungen wurden ein Schachtabteuf- und Bohrmodelle entwickelt. Zur Untersuchung der inhärenten Eigenschaften des Gesteins, des gekoppelten HM-Verhaltens und der Installationsprotokolle der Messsonden wurden Sensibilitätsanalysen durchgeführt.

Jan 1, 2003

In recent years several mine researchers have studied the optimization of cutoff grade with the purpose of maximizing Net Present Value (NPV). The best and most popular one is the Lane algorithm. Based upon the Lane algorithm it is possible to calculate the optimum cutoff grade for mine, mill, and refinery capacities for single metal deposits with variable grades. The Lane algorithm cannot be used in multiple metal deposits. The reason is that, while in single metal deposits six points are possible candidates for the optimum cutoff grade, in multiple metal deposits an infinite number points are possible candidates for the optimum cutoff grades and objective function evaluation of these infinite points is impossible. In this study the Golden Section search method was used to calculate optimum cutoff grades of multiple metal deposits for the same conditions as Lane assumed in single metal deposits. Based on this method, grade-tonnage distribution uncertainty space of problem is guessed. In the next step, by selecting test points in uncertainty space and evaluating the objective function at these points, a part of uncertainty space will be eliminated. The procedure is then repeated until the uncertainty space has been sufficiently reduced to ensure that the optimum cutoff grades have been located to the required accuracy. Key words: Optimum cutoff grades, Optimization, Net Present Value (NPV), Golden Section search method

Jan 1, 2003

By Ike Madingoana, Stephan van Zyl, Antoine F. Mulaba-Bafubiandi

"The study presents a control strategy implemented at the Nkomati nickel mine flotation plant for process stabilization and improvement. The control strategy involves flotation concentrate volumetric flow rate stabilization and the flotation cell mass pull control. The flotation concentrate volumetric flow rate is operated at a fixed set point. The initial control strategy involved varying the flow rate to maintain the concentrate tank level thereby reducing pump cavitation. The flotation cells mass pull control comprises air rate manipulation into the cells with the exception of the recleaners. The air rate into cells is automated to adjust based on the concentrate tank level variation. The control strategy was implemented on the roughers, cleaners and the recleaner circuit. The recleaner cells air flow rate is adjusted based on the MgO content in the concentrate. The stabilization of the flotation concentrate volumetric flow rate and the mass pull by aerate automation will increase the scope of optimization for further process improvement. The immediate benefit of the control strategy implementation was plant stability. Disturbance to the flotation cells downstream was minimized due to stable flow rate, and the air addition manipulation ensured that the concentrate tank levels are maintained, minimizing pump cavitation. INTRODUCTION Froth flotation is a challenging process because it is influenced by a large number of factors, including the flotation feed characteristics. One of the ore types mined at Nkomati nickel mine is the main mineralized zone (MMZ). The MMZ ore is hosted in the Uikomst complex, a Ni-Cu-PGE-Cr- mineralized, layered basic to ultra-basic intrusion which hosts commercially viable magmatic base-metal sulphides (De Waal et al., 2001). The MMZ ore is a heterogeneous sulphide mineral resource with a varying sulphide mode of occurrence and texture. The beneficiation of the complex sulphide ore is challenging due to the presence of impurities in the ore. The impurities report to the flotation final concentrate and penalties are levied if the impurities are beyond the contractual limits."

Jan 1, 2015

By D. H. Diering

The paper deals with the technologies required for opening up anew idealized ultra-deep level mine. First the overall philosophy of accessing ore at ultra depths is discussed. Then the individual technologies which will be required are explored. Finally a detailed overview on one of the key technologies, namely tunnel support, is given. Because this project is still in its infancy, few definitive answers are provided; instead each of the envisaged technologies are briefly discussed, with emphasis on those which require the element of speed for rapidly accessing the ore body.

Jan 1, 1997

By N. Kornelius

In recent years there has been an increased focus on corporate governance matters worldwide. The duties and responsibilities of directors of companies have come under close scrutiny, with shareholders increasing their demands for greater responsibility and accountability. Media attention and pressure groups have also had their effect. Governmental actions have supported these demands and directors have witnessed sweeping legislative changes imposing more onerous duties and liabilities than formerly imposed upon them at common law and in terms of the Companies Act. At the same time, the power of regulatory bodies has been increased to enforce this legislation and make someone pay to remedy an alleged infringement. Breach of such duties may incur personal or criminal liability, or both. Environmental protection legislation has become a particularly prevalent feature in this regard, and the number and complexity of statutes concerning the environment have increased over the past few years. Directors of South African companies will be familiar with relevant acts such as the National Environmental Management Act 107 of 1998; Conservation of Agricultural Resources Act 43 of 1983;Hazardous Substances Act 15 of 1973, as well as the National Water Act 36 of 1998. Now the directors of mining companies are faced with the Mineral and Petroleum Resources Development Act 28 of 2002.

Jan 1, 2003

By A. J. Lynch

Mineral processing models have been discussed for many years but it was not until digital computers became available about 1960 that serious attempts at circuit simulation could be carried out. Even then the work was primarily academic until PCs could be used by engineers in plants and design offices in the mid-1980s. Since then simulation has moved quickly and it is now at the point that most processes can be simulated reasonably accurately for purposes of design and optimization. There are still some significant deficiencies, notably in dry grinding and separation, and in the chemical interactions in flotation. Future work will involve: ?improvements of existing models ?dynamic simulation for automatic control and, in particular ,for training which is a weak link ?using advanced simulation models to predict liberation and separation from data acquired from SEM-based liberation analysers. Eventually mineral processes models will be part of total simulation systems which will incorporate mining and downstream processes including all environmental impacts.

Jan 1, 1999

By R. G. B. Pickering

Over the last few years Lonmin Platinum and Sandvik have embarked on a unique partnership of collaboration through a systematic approach to developing equipment to mechanize and automate narrow reef platinum mining. After the initial design and manufacture of the equipment the key aspect is the integrating equipment, people and method into a mining system. Another key aspect of mechanization is the optimization of equipment utilization, and this philosophy has ensured continual evolvement of mining methods. This paper describes the trials and development that have resulted in the mining method described as Lonmin mechanized breast.

Jan 1, 2007

By David Norval

The increased tendency to use hydrometallurgy as an extraction step towards final refining following a pyrometallurgical smelting process requires melts which have to be cast and or comminuted which can then be taken up into solution or leached. To generate surface area for optimal leaching, a common process is to granulate and in many cases mill, which is a general practice with friable material with properties associated with higher sulphur, carbon and silicon levels. However, in the case of metallic melts milling can be unfeasible due to the ductility of the granulated particles. Water solidification is capable of producing either fine particles by means of granulation or atomisation. Atomisation however, can produce particles as fine as 40 microns without a milling circuit.

Jan 1, 2005

By M. Gous

Namakwa Sands is a heavy minerals mining and beneficiation business in the Anglo Base Metals Division, and operates along the West Coast of South Africa. The business encompasses mining, mineral concentration, separation, and smelting operations. The smelting process comprises the carbonaceous reduction of ilmenite to produce titania slag with a TiO2 content of 86%, and iron with a carbon content of 2.5%. The Namakwa Sands smelter, situated near the Saldanha Bay harbour, commenced smelting operations in 1994, when a 25 MW DC-arc furnace was commissioned. The smelting operations were expanded in 1999, with the commissioning of a second 35 MW DC-arc furnace. Despite the fact that ilmenite smelting poses a technical challenge in terms of the high temperatures required, the physical characteristics of the slag, the constraints placed on the feedstock, and the tight product specifications, Namakwa Sands has continually increased slag production since 1995. High furnace feed-on utilization and furnace stability, complemented by continuous improvement drives, will be thevehicle to drive performance in the short-term, with longer-term performance enhancements due to strategic process development. Keywords: Pyrometallurgy, Namakwa Sands, ilmenite, DC-arc furnace, titania slag, pig iron

Jan 1, 2006

By M. Nyoka

Consideration of the economic, environmental, and social impacts associated with the life-cycle of a technology is of increasing importance for decision-making in industry. It has been suggested that economic assessment of technology deployment projects requires the translation of associated environmental effects into monetary values. This paper introduces an approach for identifying and evaluating environmental damage in monetary terms. The approach groups the environmental impacts associated with a technology life-cycle system into four main criteria: air, water, land, and mined abiotic resources. The valuation of the impacts on the resources consists of an economic cost benefit analysis (CBA) procedure that comprises four steps: the compiling of an impact inventory, a monetary valuation of the inventory, discounting, and a risk/uncertainty analysis. The monetary valuation step for impacts on air resources is primarily based on published externality costs for Europe and the United States, which are adopted and converted to reflect the South African context. Local opportunity costs are utilized for the other resource criteria. The damage costs are transformed into South African Rand at 2005 prices. The paper demonstrates how the approach may be applied in the assessment of projects in the metallurgical industry. Shortcomings in the approach are identified. For example, not all of the aspects that are considered necessary to assess environmental performances comprehensively can be valued in monetary terms. Also, certain values, specifically those pertaining to opportunity costs, need to be determined on a case-by-case basis. Furthermore, the uncertainties associated with the indicators obtained may strongly influence the usability of the results of an environmental performance assessment, e.g. future damage costs will change with fluctuations in the markets. It is concluded that although such an approach has merit in increasing the understanding of the potential financial implications of a technology?s environmental performance, further research is required to improve the approach described if it is to be used further in the South African metallurgical industry. Damage cost estimates that are specific to South Africa need to be developed to reduce uncertainty, and the combination of both quantitative and qualitative approaches is recommended for comprehensive sustain-ability decision-making.

Jan 1, 2007

By P. N. Vernon

Ausmelt top entry submerged lance technology offers a cost-effective means of carrying out a range of base metal smelting operations with minimum impact on the environment. The system is capable of using a range of fuels depending upon local costs. Due to the intense, localised reaction zone, high energy efficiency is obtained and the physical size of the plant is relatively small compared to that of most competing technologies. Capital cost can thereby be minimised. The furnace is well enclosed, such that fugitive emissions and ingress of diluting air to the gas stream are both minimised. The oxygen potential in the slag can be varied over a wide range such that the system can be applied in both oxidising and reducing duties. Following a general description of the technology, the paper discusses Ausmelt plants already in operation. The application of the technology for the provision of additional smelting capacity, for the improvement of converting operations and for slag cleaning is then described. A brief explanation of how these processes could be applied at southern African smelters is given and the paper closes with an assessment of novel Ausmelt applications for this geographical region, such as zinc recovery from sulphides.

Jan 1, 1997

By N N/A

To the members of The South African Institute of Mining and Metallurgy We have audited the annual financial statements set out on pages 239 to 245. These financial statements are the responsibility of the Institute?s Council. Our responsibility is to express an opinion on these financial statements based on our audit. Scope We have conducted our audit in accordance with statements of South African Auditing Standards. These standards require that we plan and perform the audit to obtain reasonable assurance that the financial statements are free of material misstatement. An audit includes: ?examining, on a test basis, evidence supporting the amounts and disclosures in the financial statements ?assessing the accounting principles used and significant estimates made by management ?evaluating the overall financial statement presentation. We believe that our audit provides a reasonable basis for our opinion. Audit opinion In our opinion, the financial statements fairly present, in all material respects, the financial position of the Institute at 30 June, 2000, and the results of its operations and cash flows for the year then ended in accordance with South African Statements of Generally Accepted Accounting Practice.

Jan 1, 2000

By K. S. Rao, R. P. Tiwari, V. K. Shrivastava

ABSRACT: In this paper numerical simulation of jointed block mass behaviour obtained in an experimental study has been presented. Singh et al. (2002) conducted extensive tests on the jointed model materials with several joint configurations. The results of this experimental study were used to validate the strength behaviour of numerical block mass model developed using professionally available software. This software basically contains different kinds of material models. From the results of numerical simulation the existence of strength anisotropy was observed. The strength anisotropy so obtained has been compared with the experimental values reported by Singh et al. (2002). The anisotropic curves in both cases are U-shaped with flat base. They show good agreement in sliding mode of failure zone in which inclination ß (= 90° - ?) of joint set-I lie between 20° to 40° for all cases of interlocking. ZUSAMMENFASSUNG: In dieser numerischen Papiersimulation des verbundenen Blockmasse Verhaltens, das in einer experimentellen Studie erhalten wird, ist dargestellt worden. Singh et al. (2002) leiteten umfangreiche Tests auf den verbundenen vorbildlichen Materialien mit einigen gemeinsamen Konfigurationen. Die Resultate dieser experimentellen Studie wurden verwendet, um das Stärke Verhalten des numerischen Blockmasse Modells zu validieren, das mit professionell vorhandener Software entwickelt wurde. Diese Software enthält im Allgemeinen unterschiedliche Arten der materiellen Modelle. Von den Resultaten der numerischen Simulation wurde das Bestehen von Stärke Anisotrophie beobachtet. Die Stärke Anisotrophie also erreicht ist mit den experimentellen Werten verglichen worden, die von Singh et al. (2002) berichtet werden. Die anisotropen Kurven in beiden Fällen sind mit flacher Unterseite u-förmig. Sie zeigen gute Vereinbarung in gleitender Erscheinungsform des Ausfalls Zone, in der Neigung ß (= 90° - ?) von der Verbindung stellenSie Lüge zwischen 20° auf 40° für alle Fälle vom Ineinandergreifen ein. RESUME: Dans cette simulation numérique de papier du comportement joint de la masse de bloc obtenu en étude expérimentale a été présenté. Singh et autres (2002) ont effectué les essais étendus sur les matériaux modèles joints avec plusieurs configurations communes. Les résultats de cette étude expérimentale ont été employés pour valider le comportement de résistance du modèle numérique de la masse de bloc développé en utilisant le logiciel professionnellement disponible. Ce logiciel contient fondamentalement différents genres de modèles matériels. Des résultats de la simulation numérique on a observé l'existence de l'anisotropie de force. L'anisotropie de force ainsi obtenu a été comparée aux valeurs expérimentales rapportées par Singh et autres (2002). Les courbes anisotropes dans les deux cas sont en U avec la base plate. Elles montrent la bonne concordance dans le mode coulissant de la zone d'échec en lequel la inclination ß (= 90° - ?) du joint placez-Je le mensonge entre 20° à 40° pour tous les cas d'enclencher.

Jan 1, 2003

By G. Hangone

Paper written on project work carried out in partial fulfilment of MSc thesis This paper investigates the effects of thiol collectors: xanthates, dithiophosphates, dithiocarbamates and mixtures of these on the froth flotation performance obtained with a bornite-rich copper sulphide ore from Okiep Copper Mine with a feed grade of 1.8%copper. Batch flotation tests were used to assess the performance in terms of mass-water recovery, sulphur grade-recovery and copper grade-recovery relationships and the Klimpel rate constant for copper recovery. The results showed that the di-ethyl-dithiocar-bamate (di C2-DTC) was the weakest collector of copper sulphide minerals. Highest copper recoveries were obtained with the di-ethyl-dithiophosphate (di C2-DTP), which were accompanied with more watery froths and lower copper grades demonstrating frothing properties in addition to collector action. Superior copper recoveries were obtained with the 90% ethyl xanthate (C2-X):10% di-ethyl-dithiophosphate (di C2-DTP) and 90% ethyl xanthate (C2-X):10%di-ethyl-dithiocarbamate (di C2-DTC) collector mixtures compared to that obtained with ethyl xanthate at an equivalent collector dosage of 0.139 mol/ton ore (a dosage equivalent to 20 g sodium ethyl xanthate per ton ore). A superior copper grade was obtained with the 90% ethyl xanthate: 10% di-ethyl-dithiocarbamate collector mixture at a dosage of 0.0695 mol/ton ore compared to that obtained with ethyl xanthate at the same equivalent dosage. Keywords: flotation, collector mixtures, copper sulphide ore

Jan 1, 2005

By B. Samanta

This paper investigates the performance of the neural network technique in a placer deposit situated at the Nome district in Alaska. Initially a single neural network model was constructed to estimate the gold grade. However, at a later stage, an ensemble model consisting of multiple networks was also constructed via the Adaboost algorithm. The reason behind the use of the ensemble model of the Adaboost algorithm was to examine if the ensemble model provided superior performance to the single neural network. As indicated by other studies, Adaboost did not have a better performance than a single neural network in this specific application. This may be due to the high noise inherent in the gold data used in this project. Consequently R2 values of gold prediction are also poor for both the single and multiple networks.

Jan 1, 2005

By J. van Deventer

Testwork was done with two different adsorbents, Dowex-Minix gold-selective resin and activated carbon, to detemine their relative performances with regard to gold recovery from clarified low-grade solution employing a fixed-bed operation. The mill discharge from the milling-in-cyanide operation at a Witwatersrand gold mine was used as feed to the adsorption columns. A small amount of gold was leached during the milling process, so that this solution simulates, to a certain extent, a low-grade solution representative of a heap-leach operation. A speciation of the feed solution was done to establish which metal complexes were present in the milling-in-cyanide solution. This information was necessary to interpret metal loadings on the resin, as base metal cyanide species and their respective charges have an effect on the final gold loading capacity of the resin. Equilibrium isotherms were established for both adsorbents to estimate the rate of adsorbent flow anticipated for this specific feed solution. Breakthrough profiles were obtained at two different superficial linear velocities for each adsorbent. Mass transfer zone heights determined from the test work and the elution/regeneration time requirements were used to size a 150 m3/h full-scale plant for both adsorbents. A counter current configuration of adsorption columns, using three columns, should be suitable to recover gold effectively and to produce an effluent with a gold concentration below 0.01 mg/l. Based on the results obtained from the breakthrough tests, a preliminary techno-economic comparison was done between the resin-in-solution and carbon-in-solution options for the recovery of gold from low-grade solutions. This study indicated that the capital expenditure for a carbon-in-solution plant would be about 33 percent higher than that of a resin-in-solution plant. The operating expenditure for a resin-in-solution plant is expected to be only 60per cent of that for a carbon-in-solution plant. Keywords: resin-in-solution, carbon-in-solution, heap leach.

Jan 1, 2000

By M. Kumral

Raw material fed into a processing or refining plant is required to be uniform in composition for several reasons. When the mined ore is highly variable in quality the only way to ensure consistency is to homogenize the ore prior to the process. The problem is more complicated in the case of multiple ore sources. The idea behind the research is that theoretical blending ratios can serve not only to meet predefined specific criteria but also to reduce grade fluctuations of variables under consideration. In this paper, the problem is formulated as a quadratic programming problem, whose objective function is in quadratic form and constraints are linear. A case study was conducted on a data set from an iron orebody to demonstrate the technique. The objective was to minimize the blend variability in terms of each variable (in this study, iron, silica, alumina and lime) grade of ores extracted in three different production faces. The stockpile capacity, lower and upper limits of each variable satisfying operational requirements and non-negativity were constrained to the model. A modified simplex method developed by Wolfe was used for solving the blending and homogenization problem. The promising results can be used as apart of the stacking and reclaiming design. Keywords: blending and homogenization problem, quadratic programming, Wolfe method.

Jan 1, 2005