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The increasing transportation of solids by pipeline, in South Africa and internationally, replacing the conventional transportation methods of rail, road, and conveyors, has resulted in much research into this area of solids transportation. Pipeline wear continues to be an area of specific concern, since it constitutes a major cost during the life of a pipeline installation. Wear data from an accelerated wear test and actual pipeline tests are presented. Trends in the performance of the pipeline materials tested are discussed, and possible solutions to the problem of pipeline wear are presented.

Jan 1, 1992

By P. R. Jochens, D. D. Howat, A. A. Hejja

The effect of the reactivity of lime on desulphurization efficiency in the basic oxygen furnace A. A. HEJJA, Dipl. Ing. (Budapest) (Visitor) D. D. HOWAT, B.Sc. (Glas.), Ph. D., F.I.M. (Fellow) P. R. JOCHENS, Pr.Eng., M.Sc. (Eng.) Rand, Ph.D., A.I.M. (Member) The iron charged to the basic oxygen furnace at the steel plant of Highveld Steel and Vanadium Corporation has a relatively high sulphur content. Considerable emphasis is therefore placed on the reactivity of the lime. An investigation of the lime used at the steel plant showed that its reactivity had deteriorated considerably both during transport from the supplier (Northern Lime Company) and during storage and handling at the steel plant. The deterioration on the steel plant is the more severe, and is due to hydration and carbonation. Rapid deterioration is a characteristic of highly reactive lime when exposed to the atmosphere. Plant tests showed that the desulphurization efficiency decreases with a decrease in the reactivity of the lime. The addition of slag rich in manganous oxide to the furnace considerably improved the efficiency of desulphurization that can be achieved with limes of lower reactivity and with lime that has deteriorated. A decrease in particle size of lime of lower reactivity greatly increased the desulphurization efficiency. Less lime of higher reactivity is required for the same degree of desulphurization to be achieved. Lime of higher reactivity gives rise to slags with lower ferrous oxide contents and hence the steel yield is increased.

By F. L. D. Cloete, M. C. Coetzee

This study was aimed at a comparison of the efectiveness of a new axial-flow type of mixer impeller (the Prochem design) with the traditional inclined-blade turbine. The intended application of the mixers was in carbon-in-pulp plants for the extraction of gold from cyanide-leached pulps. The first part of the project involved water and ion-exchange resin, and measurement of the power drawn by the various sizes of impeller to fully suspend the resin. The rate of reaction between the resin and the solution was measured as a function of the power input to the mixer. In the second part of the project, use was made of activated carbon, silver cyanide solutions, and ore pulps. The rate of absorption of silver from the solutions and pulps was determined, as well as the rate of attrition of the activated carbon caused by the various impellers in clear water. The Prochem design of axial-flow impeller was shown to fully suspend solids at only one-quarter of the power requireabyan inclined-blade turbine of similar size. The axial-flow pattern produced was responsible for the more uniform vertical concentration profile of suspended beads produced by the Prochem design. These measurements verified the observations of other researchers that the rate of reaction is not affected by the ;design of impeller provided that al the solids are fully suspended. The Prochem design of impeller therefore achieved the same reaction rate as the conventional turbine at a quarter of the power input. The atrition rates of activated carbon could be correlated, in terms of the energy absorbed, by the same equation for al the impellers. Higher concentrations of activated carbon increased the amount of carbon fines produced. These results emphasize the importance of designing mixers for minimum power consumption.

Jan 1, 1989

By B. Maybee, J. Venter, J. Wesseloo

The selection of open-pit slope angles involves high-value decisions with small changes in slope angle, often representing significant changes in net present value. The existing methods used to define design acceptance criteria have evolved from factor of safety to probability of failure (P[F]) to risk consequence to risk frontiers, which represents current state of the art. Current design acceptance measures are based on references to published tables representing the experience and judgement of their authors, who did not specify the purpose of the measures contained therein. As the purpose of the published design acceptance criteria is not specified (i.e., definite stability, marginal stability, optimization, etc.), such tables cannot be used to achieve optimum slope angles that maximize profitability. This paper develops a design acceptance criterion that maximizes profitability by defining a formulation for optimum risk that balances expected risk and reward. The model developed is titled the Mining Risk Model (MRM), and is applied to open-pit slope angle selection through an equation for optimum probability of downside (P[D]O) that balances the upside or opportunity, the P[F], and the downside impact. This formulation for optimum risk is unique, as many authors have presented objective functions for their risk models that can be optimized, but none of the sources reviewed contained a formulation for optimum risk. The MRM is sufficiently flexible to allow the design performance measure that drives P[F], and hence P[D]O, to be selected based on the intended goal. Furthermore, the essential information that must be known to quantify optimum risk is defined. This allows users to determine what information to collect for optimum risk decisions. A further benefit of the MRM is that slope angle decisions and pit shells can be ranked to select the best option, and a threshold is provided that separates acceptable from unacceptable decisions. Finally, the workflow and information required to determine optimum risk are presented.

Sep 9, 2024

By M. Mpofu, G. Stenzel, F. Magweregwede, B. Maphalala, T. Kgarume

Surface coal operations in which mining activities are conducted above old underground workings experience hot holes after drilling. In a coal mine, hot holes are defined as shot holes, which after being drilled have an in-hole ambient temperature of 40°C or above or show a temperature increase of 3°C or more during monitoring. Hot holes and other cavities, such as cracks, pose health and safety risks to workers, such as exposure to hot air and high concentrations of noxious gases released from these holes. In addition, workers may be exposed to premature detonation of explosives caused by in-hole temperature increases and chemical reactions. To this end, Coaltech Research Association commissioned a project to develop a Best Practice Guideline for the management of hot holes. This paper is a compilation of the activities conducted in the development of the Best Practice Guideline between 2021 and 2022. The activities included a review of standard operating procedures and hot-hole temperature-measuring and -monitoring devices, and the assessment of current hot-hole procedures at selected mines. The results indicated that management of hot holes requires a focus on pre-emptive risk assessment of mining blocks, identification of hot holes using the correct temperature-measuring devices, and continuous monitoring of hot holes from the time of drilling until just before blasting. Hot-hole management accessories, such as polyvinyl chloride sleeves, were found to be effective in insulating the hot-hole emulsion from the rock mass temperature, thus preventing the potential for premature detonation.

Sep 9, 2024

"Chairman: Professor B. W. MacKenzieRapporteur: Professor D. A. PretoriusPapers:Optimum spacing for soil sample traverses by W. A. HodgsonEvaluation of geochemical data by C. J. LenzResearch in oil exploration decision-making by J. W. Harbaugh and A. Prelat A drill hole data bank by M. R. AndertonOre reserve estimation and depletion planning for a beach diamond deposit by M. M. OosterveldIn opening the session, the Chairman indicated that the papers and discussions would revolve about quantitative methods of analysis and optimization of various aspects of exploration planning. The five papers would cover a wide range of topics within a general theme of exploration analysis, and it would be appropriate, therefore, to present the. papers as representing a sequential information-gathering process, namely, (i)geochemical and geophysical types of surveying for the location and identification of anomalous zones, (ii) tren¬ching and drilling of the anomalous zones found, and (iii) further refinement of the data for ore reserve calculations and production planning.The first paper, which was presented by Dr W. A. Hodgson, dealt with the optimum spacing between soil sample traverses conducted during geochemical prospecting. The theme of the paper was that the critical sampling interval should be based on the concept of element continuity, and that this interval could be determined by means of a correlogram. Ensuing discussion concerned the probability of the method, designed for areas where dispersion was high, working in localities where dispersion was either low or virtually non-existent. In the latter eases, specific orientation surveys for varying topographic, climatic and geological conditions would possibly be more useful than the preparation of correlograms. A further suggestion was made that cost versus risk should be taken into consideration when deciding upon the spacing between traverses. A balance could be struck by mathematical optimization. If the exploration budget was fixed, then the variance of risk could be minimized.The second paper was a short contribution by Mr C. J. Lenz. Computer-based plotting and evaluation of geochemical prospecting results were carried out because the low cost of analysis in Rhodesia permitted very large volumes of data to be accumulated in mass-coverage operations. Anomalous areas were demarcated within different environments by selecting probability or population boundary values from frequency distributions. In the short discussion which took place it was debated whether the method should be used only in the early high-risk stages of geochemical exploration and whether the introduction of geological bias could influence the actual results of an exploration program."

Jan 1, 2014

This paper describes experimental investigations into the reductive decomposition of arsenopyrite/pyrite (FeAsS/FeS2), a gold and silver bearing iron/arsenic sulphide using metallic iron powder. The main objective was to establish and experimentally confirm the thermodynamic and kinetic feasibility of reductively decomposing the sulphide matrix for precious metals recovery. In this context, cyanidation leach tests were conducted on the reductive leach residues. The arsenopyrite/pyrite flotation concentrate, mainly studied in the hydrochloric acid medium, decomposed through the non?oxidative chemical dissolution reaction and the reductive decomposition reaction for the arsenopyrite and pyrite components, respectively. Desulphurization levels below 65% were achieved at pH values below 0.15 and iron to concentrate ratios above 1, and the system was characterized by overall very slow kinetics. The reaction system had a direct linear relationship with iron to concentrate ratio and an inverse relationship with pH. An analysis of the pyrite/iron galvanic system showed that pyrite forms a partially inert cathodic surface on which the anodic dissolution of iron occurs, supported by the hydrogen evolution reaction. This phenomenon explained the low desulphurization levels and the mineral decomposition seemed to be restricted to the non?oxidative chemical dissolution reaction for the arsenopyrite component. The cyanide leach of the reductive leach residues showed very little improvement in gold recovery. The reductive leach process for arsenopyrite/pyrite has considerable limitations in terms of both desulphurization and precious metals liberation. Keywords: Pyrite, arsenopyrite reductive leaching, hydrogen sulphide, invisible gold

Jan 1, 2009

By S. M. Spottiswoode

Rock mechanics benefits of stope support in deep-level mining originate principally from the ability of the support to resist relative movements between the hangingwall and the footwall. While the role of stabilizing pillars and backfill on reducing the energy release rate (ERR) at the face is well understood on the basis of elastic behaviour of the rock mass, the effect of support on controlling movement of fractured ground around deep-level stopes has not yet been thoroughly studied. As part of a programme of studying the behaviour of this fractured ground, geophones were placed 10 m from the face on the roof and floor of a longwall stope in which packs were used as supports. It was found that differential movement between the roof and floor generally exceeds average stope movement during a seismic event. Conventional support therefore transmits very little seismic energy; this is expected to remain true until complete convergence occurs. In backfilled stopes, backfill can become at least as stiff as the fractured wall rock. This will have the effect of reducing the length of the hanging- wall beam. Amongst other rock mechanics considerations, a shorter hanging- wall beam should: (i) increase the resonance frequency of the hangingwall and thereby decrease the levels of vibration for seismic events with M > 1,0; (ii) reduce absolute vibration levels by increasing the mass of rock immediately adjacent to the stope which is shaken by seismic waves; and (iii) reduce differential movement between the roof and floor and thereby reduce cyclic strain on the backfill and on gully support.

Jan 1, 1988

By B. Kruger

After the milling and flotation of the platinum bearing ore, the flotation concentrate is electrically smelted in 6-in-line electric arc furnaces and the resulting furnace matte treated in Peirce Smith converters to remove the iron. The iron-free (less than 1% Fe) converter matte is granulated and sent to the base metals and precious metals refineries for further processing. During the smelting and converting processes two distinct gas-strength gas streams are produced: ?The Peirce Smith converter off-gas contains 4%?9% SO2which is treated in a conventional sulphuric acid plant to produce 94% H2SO4. ?The electric furnace off-gas contains 0.9% SO2which was (until September 2002) vented through a 91- metre high stack to atmosphere. In October 2002 Impala Platinum commissioned a SULFACID® plant at its smelter in Rustenburg, which recovers the SO2from the electric furnace off-gasses into a weak sulphuric acid solution. The SULFACID® technology utilizes wet activated carbon to oxidize the SO2toSO3. The SO3reacts with the water on the catalyst and is washed off the catalyst bed as a sulphuric acid solution with up to 13 wt. H2SO4. The plant operates at 60ºC and at atmospheric pressure. The SULFACID® technology is widely used in the pigment industry. This is, however, the first application of the technology on electric furnace off-gas. Keywords: SO2, sulphuric acid, electric furnace, off-gas, SULFACID®

Jan 1, 2004

By D. Duncanson, R. J. Davidson

The elution of gold from activated carbon using deionized water by R. J. DAVIDSON, M.Sc., Ph.D. (Rhodes) (Visitor) and D. DUNCANSON, H.N.C., B.Sc. Hons. (Strathclyde) (Visitor) The pretreatment of gold-loaded activated carbon with a relatively strong sodium cyanide solution prior to elution with deionized water at 90 to 125°Chas been shown to have a most beneficial effect on the elution of gold. The findings emphasize the important role played by the calcium cation and the hydroxyl anion in effecting efficient elution of gold. The elution of the relatively unstable complexes of silver and base metals with cyanide was also significantly affected by the ratio of the sodium cyanide to sodium hydroxide in the reagents used in the pretreatment stage. It was demonstrated that the use of 0,5 bed volume of a pretreatment reagent comprising 10 per cent sodium cyanide stabilized with I per cent sodium hydroxide for safety reasons resulted in a virtually 100 per cent recovery of adsorbed gold, silver, and base metals on subsequent elution with deionized water. The elution procedure takes a relatively short time, about 14 hours at 90°C (7 bed volumes) or 3 hours if pressure elution at 125°C (4 to 5 bed volumes) is used. Because the mechanism of elution after pretreatment entails the shifting of a physical rather than a chemical equilibrium, the higher the gold loading on the activated carbon, the more efficient is the elution procedure. When compared with other elution procedures, the proposed method appears to have several economic advantages.

Jan 7, 1977

By F. S. Hoseinian, D. Deglon, L. leal Filho, M. Safari, T. C. Souza Pinto

This paper investigates the effect of chemical and physical operational parameters on the reverse flotation of Timbopeba itabirite iron ore in a pilot-scale pneumatic flotation cell. Operational parameters include collector and depressant dosages, feed rate, superficial gas velocity and solids concentration. Results show that increasing collector dosage results in an increase in quartz recovery, particularly for the coarser quartz where recovery increases by nearly 30%. Increasing depressant dosage results in a decrease in both quartz recovery and hematite loss, for the coarser hematite particles. Increasing the feed rate has no effect on quartz recovery or hematite loss, suggesting that the pneumatic flotation cell is not residence time constrained. Increasing the superficial gas velocity results in an increase in quartz recovery to an optimum at a Jg of around 0.6 cm/s after which it decreases significantly, particularly for the coarser particles where recovery decreases by as much as 50%. Decreasing the solids concentration does not affect quartz recovery but results in significant decreases in hematite loss. Here, fine and coarse hematite loss decreases from around 25% to 12% and 10% to 2% respectively. Superficial gas velocity and solids concentration are operating parameters which have the largest effect on the flotation performance of the pneumatic flotation cell. Results suggest that this flotation cell should be operated at relatively low superficial gas velocities and solids concentrations. However, these are pilot-scale findings and would need to be tested at an industrial-scale where different operating conditions may be optimal. Keywords: Operational parameters, reverse froth flotation; entrainment; iron ore

Jan 1, 2020

By A. Buncombe

In March 1984, two years' work by senior metallurgical personnel from the six major mining groups culminated in the formation of the Mine Metallurgical Managers' Association of South Africa. This Association has joined a group of specialist Associations operating within the South African mining industry whose aims are to uphold the standards and promote the interests of their various professions.

Jan 1, 1987

By O. K. H. Sheff

An editorial in the April 1990 edition of Mining Magazine is worth a wider audience in South Africa, particularly as the SAIMM enters its own centenary decade and the process of change in the minerals industry world-wide makes increasing demands on the professionalism of its leaders. The editorial considers the changing status of engineers, who up to the 1880s had been held in high regard by society. Alumina and bauxite Economists forecast a slower economic growth rate in 1990, but expect continued increase in demand for aluminum at a 3 per cent annual rate during the decade. Structural and numerical analysis Struceng & Femcad (structural analysis and finiteelement method) is a conference and exhibition that is to be held in Grenoble (France) on 17th and 18th October, 1990. It is sponsored by the Institute for Industrial Technology Transfer (ITT-International).

Jan 1, 1990

By L. W. Helle

In this investigation, which was conducted at the Metallurgical Research Plant, Lulea, Sweden, a series of experiments were carried out using a water-model to simulate the gas rinsing of a ladle containing liquid metal. The factors examined include the effect of gas flowrate, the position of a porous plug or lance, the immersion depth of the lance, and the geometry of the bath at the time of complete mixing. Mixing times were recorded by conductivity measurements. The results showed that there is a threshold level for mixing above which no advantage is to be gained from an increase in the gas flowrate. It is suggested that the results can be applied to rinsing ladles in working situations, the levels being approximately 270 dm3/min for 40 t ladles and 780 dm3/min for 150 t heats. The optimum siting of the lance or porous plug is a position that is three-quarters of the internal radius from the centre of the ladle with the lance penetrating as deeply as possible into the ladle. The best design of liquid bath is that having a diameter-to-height ratio of I. An equation was developed for the calculation, by dimensional analysis, of the time required for mixing during gas rinsing, and a comparison of the calculated mixing times with the results from production trials shows a satisfactory agreement (with a correlation factor of 0,91). Thus, an equation is available for the calculation of the stirring time needed to completely mix the bath in production situations.

Jan 1, 1981

By Mr P. W. J. van Rensburg

SOUTH AFRICAN NATIONAL COMMITTEE ON TUNNELLING In 1970, the South African Institution of Civil Engineers, the South African Institute of Mining and Metallurgy, the South African Institute of Mechanical Engineers, and the Geological Society of South Africa held an international conference on tunnelling, known as Tuncon 1970. SUID-AFRIKAANSE NASIONALE TONNELBOUKOMITEE In 1970 het die Suid-Afrikaanse Instituut van Siviele Ingenieurs, die Suid-Afrikaanse Instituut vir Mynbou en Metallurgie, die Suid-Afrikaanse Instituut van Meganiese Ingenieurs en Die Geologiese Vereniging van Suid-Afrika 'n internasionale konferensie in verband met tonnelbou gehou, wat bekend gestaan het as Tonkon 1970.

Jan 5, 1974

By A. W. S. Schumann

A. W. S. Schumann The first reason for todays success lies in the very high standard which was set by our speakers today and I think that we owe a very special vote of thanks to Messrs P. M. C. Wilson, A. A. Oakes, M. J. Deats, A. C. Coetzee, R. E. Burnton and J. G. Ferguson. This, however, cannot account for the fact that there was a tremendous response even before anyone knew who was going to speak or what they were going to speak about. I suggest that the response was enthusiastic because people expected a more informal gathering with a greater opportunity for feedback, for an exchange of views and for questions and answers. The very popularity of the idea has defeated its own ends to some extent. This gathering is too big and many people must have been left with questions unanswered. Possibly one should arrange for a number of meeting places-there are many in the Chamber and the surrounding mining houses-and then have separate meetings in the morning with joint reporting session in the afternoon. Alternatively, we could have a symposium after the colloquium, using Webster's definition of a symposium as as 'a drinking party of merry fellows'. We all know that it is easy to discuss mining into the small hours. Obviously one cannot summarise todays papers and discussions, but I would like to make a few comments on technical matters and after that I would like to speak for a moment about what I see as major trends or tendencies which arise from discussions of this nature. Regarding the question of placing a village on a mine or away from a mine, I would mention that there is quite a body of literature on the adverse sociological effects on the development of children in any community in which the great majority of parents share the same occupation. It is something to be avoided if possible. We discussed the concept of the moving stockpile. If this is proved to be successful, it could save a considerable amount of money for Escom who could then avoid the construction of very large and costly staithes which are now regarded as parts of power stations. One does not see why both a moving stockpile and a staith should be necessary. By the way, speaking of Escom, I see that Mr Bob Scott is here; he has stopped pulling my leg by saying that we sell stone to Escom; perhaps someone has told him that if this is true, it must be the cheapest stone you can buy in this country. My next point relates to the use of epidiascope. It struck me again that this instrument which provides a visual image to accompany your message, can be very effective if it is properly used. These papers speak of a great deal of hard work which went into their preparation, and one really feels that the authors should have taken a few minutes more to prepare their drawings specifically for the epidiascope. There should be nothing on the drawing which is not necessary to illustrate a particular point and there should be nothing on the drawing which is not visible from the back of the hall. In particular, if one cannot read the figures along the sides, then one

By C. A. Green, M. A. T. Cocquerel, R. T. Gates

"Engineering studies by Selection Trust, Limited, initially in connection with the development of a copper and nickel deposit for Bamangwato Concessions, Limited, and subsequently for several other clients, have required a large number of metallurgical design calculations. The flash smelting process, developed by Outokumpu Oy in Finland, has been selected as the most suitable method for these projects and the computer programs described in this paper have been developed to facilitate the computation.The data required by the programs arc the chemical and mineralogical analyses of the concentrate, gangue and flux materials and the specification of possible fuels. The required grade of furnace matte is set as the main design parameter and the programs calculate detailed heat and material balances for the smelting process."

Jan 1, 2014

"Chairman: Professor J. de V. Lambrechts Rapporteur: Mr R. HempPapers:Computer-aided design of a flash smelting installation by M. A. T. Cocquerel, R. T. Gates and L. A. GreenPlanning of mine ventilation by E. U. Reuther and A. DohrnenCoal mine ventilation systems in the U.S.A. by R. Stefanko and R. V. Ramani Heat flow models in ventilation planning by A. J. Dickson and A. M. StarfieldThe first of the papers in the session dealt with a flash smelter installation, while the remaining three papers dealt with mine ventilation. In view of this the Chairman proposed that the paper on flash smelting be introduced and discussed first, after which the remaining three papers would be introduced followed by discussion on all three.Dr Cocquerel, who presented the first paper, used some typical flow diagrams to illustrate the process and stated that the program considered only steady-state operations and did not take into account the dynamical changes. Subjective judgment was necessary for the preparation of input data and some degree of user appreciation was required.Dr Cocquerel said that no work bad yet been done on an optimization program, but that this was being considered. Such a program would require a large amount of physical and chemical data which were not yet available. The variables to be optimized were the energy and material consumptions and the loss of metal in the slag.The Chairman opened the discussion by asking Dr Cocquerel if he could give a brief description of the flash smelting process for the benefit of those not familiar with the subject. Dr Coquerel replied that in the Outokumpu process con¬centrates were injected directly into the furnace, and that the process was somewhat analogous to flash distillation or evaporation processes, but was perhaps closer to the burning of pulverized fuel.The process had two distinct advantages. First, the heat evolved in the smelting reaction was used to heat the furnace, which resulted in less fuel consumption, and, second, the effluent gases were cheaper to treat than the effluent gases from other pyrometallurgical processes. This was important particularly in view of the current interest in pollution problems.Mr P. Marais thought that the authors had done themselves an injustice by not including details of the very complex processes taking place in the furnace."

Jan 1, 2014

By T. Bhambhani, E. Arinaitwe

Solvay has developed several novel reagent innovations to improve separations in sulfide ore flotation and address major industry challenges. These innovations include: a) carbon management strategies to reduce the deleterious impact of organic carbon on flotation circuits; b) new collectors for heavily tarnished or oxidized Cu-Au ores; and c) a functionalized depressant for minimizing penalty elements in metal concentrates. Owing to their unique chemistries, these innovations exhibit a wide spectrum of rather unique properties that are quite in contrast to the traditionally used reagents. The chemistry, attributes, application, and advantages of these innovations are discussed in this paper based on laboratory, pilot, and plant results and observations for various ores

Jan 1, 2023

"Chairman: Professor J. C. Griffiths Rapporteur: Mr J. P. G. PRETORIUSPapers:Mine-mill production scheduling by dynamic programming by R. J. Roman Optimization of a large mining venture by J. C. Paynter, B. K. Loveday and C. G. Robinson Economic surface mining of multiple seams by T. V. Falkie and W. E. PorterIn introducing his paper, Mr Roman said that whereas in manufacturing plants the yearly production levels were usually chosen to produce the largest annual cash flow, in a mining operation, the raw materials (ore) were exhaustible so that the production had to be scheduled to maximize the total net present worth of the operation. This optimum production schedule could be determined by using dynamic programming. The required information was readily available to management at most mines. The 'possible operating range' of production rates lay between the rate with the highest profit per ton. and that with the highest profit per year. The optimum production rate started typically at the top of this range and decreased slowly as the deposit was depleted.Dynamic programming was used to determine several production schedules for a hypothetical mine-mill complex. The effects of changes in the ore grade estimates, size of deposit and acceptable rate of interest on the production schedule were taken into account. Apart from the fact that the net present worth of the overall profits was larger than that obtained by conventional methods, it appeared from the cases studied that the amount of metal recovered was also greater.Dr it P. King commented that this was a very interesting application of dynamic programming. He pointed out, however, that the market price of the metal was likely to vary significantly and randomly during the life of the mine, and he suggested that the problem should, therefore, be reformulated as a stochastic dynamic programming problem.If the price of the metal rose to abnormally high levels, a much higher than normal production rate could be expected. The results of analyses given in Table 5 showed that the production rate was a function of market price. In his view the stochastic problem could be solved just as easily as the deterministic problem.In reply to a question by Dr King as to whether the function relating recovery to production rate (Table I) was based on real data, the author replied that it was based on the results of an analysis conducted at the Union Carbide Corporation's Pine Creek tungsten mine in California.Dr D. M. Hawkins stated that costs were incurred when the production rate was altered, for example, in appointing or laying off staff, and that in practice it may be necessary to take these costs into account in finding the optimum production rate. Mr Roman replied that, while normal administrative costs were accounted for, the additional costs incurred in appointing and laying off staff were not taken into account."

Jan 1, 2014