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By D. M. Maijer, S. L. Cockcroft, A. B. Phillion, P. Fan, C. Reilly, H. Khadivinassab

A combined experimental / numerical approach is proposed to investigate the bulk transfer of solute due to liquid metal feeding during shape casting of aluminum alloy A356 (Al-7Si-0.3Mg). A dumbbell-shaped experimental casting geometry has been developed, which promotes solute redistribution due to liquid metal feeding. The redistribution of solute in trial castings is evaluated based on the area fraction of eutectic phases. In the numerical model, silicon species segregation during solidification are calculated assuming the Scheil approximation, and are coupled with macro-scale solute transport due to Darcy flow in the mushy zone and feeding flow. The model has been implemented within the commercial CFD software, FLUENT, which simultaneously solves the thermal, fluid flow fields and species segregation on the macro-scale. The experimental and numerical results are compared and contrasted to examine the effects of liquid metal feeding in this casting.

Jan 1, 2014

By Franz Simon

Conventional fine gold electrolytes for barrel applications working electrolytically actually permit significant precious metal savings by corresponding optimizations but the most gold is still deposited on areas of the components where it is not absolutely essential for the desired bonding and soldering applications, i.e. in high current density areas. Therefore an electrolyte working electrolessly has been developed which inevitably leads to a much more uniform thickness distribution since in an electroless process there are no areas favoured by metal deposition and current distribution. The new electrolyte will be presented and its performance will be compared with conventional electrolytes as regards thickness distribution. The potential gold savings will be discussed.

Oct 1, 2003

By K. Soldenhoff, M. Fainerman-Melnikova

The use of strong base resins for uranium recovery is severely affected by the presence of chloride ions in solution. In areas where high-quality process water is not readily available, the use of saline water would extend the potential application for ion exchange in uranium processing. This study presents measurements of uranium uptake, using a wide range of commercially available weak base anionic exchangers, from solutions with chloride concentrations ranging from 2.5 to 22 g/L Cl. Out of 14 weak base anionic resins tested, 3 were identified that were not severely impacted by the presence of chloride and significantly outperformed a gel strong base resin typically used for uranium recovery in high-chloride environments. The uranium loading was sufficiently high for the consideration of development of the application of uranium recovery from uranium ores leached with seawater.

Jan 1, 2012

Bahuerachi Project Characteristics Why it?s nicer at Bahuerachi Mexico is a mining country Low political, regulatory and trade risk Low social/permitting risk Proximity to infrastructure Road Power grid (8 km) Rail line (25 km) High grade zones (skarns), CRD and near surface oxide component are sweet spots to the overall system. Size of low grade system points to potential long mine life?and numerous new targets developing. Timelines-2006? 90 to 100 combined RC and core holes to go! MAIN ZONE Drilling ? Goat ?Finish Mid April ? Main Zone, going North, depth of testing dependent, estimated for May ? North Lobe-May ? Commission independent resource estimate by May 06 for results of first pass drilling to date ?tonnesand grades ?Main Zone Milestone. ? Continue infill or expanded drilling to July (minimum) ? 1stpass RC scheduled until September OTHER Targets ? Begin drill testing North Skarn target Mid-April, minimum 5 drill holes, 1,000 meters. Ongoing expansion of target with surface work (mapping) ? Road to Colome(Skarnin north of Main Zone) as part of porphyry program ? Tule(southern) porphyry and skarn system-soils and mapping OUTSTANDING events Metallurgical report on floating and leaching tests (Sulphide/oxides).

May 1, 2006

By Golaleh Riahi

An original method is used to obtain stable nanoparticles of gold-based mono- and bimetallic systems supported on an acidic zeolite. This approach has been applied to PtHY (1wt% Pt) and to bimetallic Pt-AuHY containing 1% of platinum to which is added the amount of gold required to give Au/Pt molar ratios of 20,40,60 and 80%. Metal clusters of Au or Pt-AuHY are formed inside the supercages of the zeolite framework by the thermal reduction of cations by the ligands (en = H2N-CH2-CH2-NH2) under inert gas flow at a temperature depending on the metal. The use of acidic zeolites favours the dispersion of the metal and the thermal stability of the particles. This stability is explained by chemical anchoring of metal clusters by the Brønsted sites of the support. Several techniques have proved that for a molar ratio of 20% metal particles of Pt-AuHY are bimetallic. The segregation of Pt and Au starts for molar ratio =?40%. The catalysts tested on the methylcyclopentane hydroconversion reaction reveal that the addition of gold to platinum leads to an increase in the activity and an improvement in the selectivity for isomerization of the skeleton (cyclohexane and benzene) to the detriment of hydrogenolysis. Similar results were obtained for the dodecane isomerisation to isododecane. These catalysts were also tested in CO, propene and propane oxidation. The activity of fresh catalysts is rather low. It increases after their pretreatment in oxygen or hydrogen atmosphere. In propene oxidation in the reaction mixture O2 ? H2, beside total oxidation of propene to CO2, also propene hydrogenation was observed, particularly at low temperatures. The presence of Au enhances the hydrogenation properties: high selectivities (> 90%) to propane and high propane yields on PtAu HY are observed up to ~150oC, whereas for Pt HY catalyst the selectivity and yield to C3H8 decreases rapidly with the temperature beginning from ~100oC.

Oct 1, 2003

By Larry G. Twidwell, Corby G. Anderson, Camille M. Fleuriault

"The selective precipitation of iron as ammonium jarosite is a well-established industrial technology in base metals hydrometallurgy. It is a key technology in minimizing iron tenors which would be disruptive to downstream processing. It also provides a more readily filterable iron solid to better facilitate materials handling. This paper elucidates the fundamentals behind industrial iron precipitation. Then, the details of the successful optimization of an industrial ammonium jarosite circuit are presented.HYDROMETALLURGICAL IRON REMOVAL FUNDAMENTALS Iron is the fourth most abundant element in the Earth’s crust (5% by weight) and is often found in complex ores such as sulphide-bearing formations. Iron represents an issue though during leaching, a technology which is widely used for the treatment of this type of ore: •,Iron has the particularity of forming hydroxides when leached under certain conditions. Iron hydroxides form a viscous gel, which is difficult to filter and traps valuable elements such as silver. •,Iron is solubilized along with other metals and interferes with the subsequent extraction steps. As a result, purification of the pregnant leach solutions is required to achieve economical extraction of base metals. In the 1960s, metallurgists developed iron precipitation processes for solution purification (Habashi, 1999). Nowadays, precipitation of iron bearing species, such as goethite, hematite or jarosite, has become one of the most common methods used in the industry to purify leach liquors. To be suitable, the precipitate has to be readily filterable and thus must not be too fine of particle size. Precipitation can take place in autoclaves at medium to high temperatures, under an oxygen or air overpressure (Tourre, 1984, Fleuriault 2016, Fleuriault Anderson Shuey, 2016))."

Jan 1, 2016

By Vincent Doyon

For several years, the GDD SSW EM Probe is being used in nickel?s mines in Canada and Brazil to define ore limits, reduce dilution and predict nickel grades. It is used with success to test most if not all percussion blast holes at all Falconbridge Mines in Sudbury and Raglan and all Inco?s Thompson mines. However, after testing the SSW Probe in other metal mines, we realized that EM conductivity does not define ore limits by testing blast holes for copper, zinc or gold. For non-conductive ores, no instrumentation is yet available on the market to reduce dilution, by outlining quickly and inexpensively the real shape of an orebody. To that effect, Instrumentation GDD Inc has developed a new revolutionary photonic probe that will make the reduction of dilution possible by probing blast holes. Once surveyed with the probe, a computer draws graphs of the ore grade as a function of depth for each blast hole. A contribution by Canada Economic Development made possible the development of this new technology. Canmet and Soredem also cautioned this technology developed by Instrumentation GDD Inc. This new photonic probe will allow: 1) to better understand the shape of the orebody 2) to raise the grade of the ore fed to the mill 3) a more complete extraction of the ore 4) to raise the competitiveness of mines

Oct 1, 2004

By Chenming Liu, Xiao Lin, Bo Wang, Hongbin Cao, Xingang Li

Over 2 million tons of NH3-N were discharged in China per year recently, rare earth industry contributed 7.03% of NH3-N pollutant from industrial wastewater in 2007. Wastewater containing NH3-N and heavy metals mainly produced in RE extraction saponificated with ammonia and precipitated by ammonia bicarbonate. Generally, 1 ton REO cost 0.6-1.2 ton ammonia for extraction and 1.6 ton ammonia bicarbonate for precipitation, and produce 35-100 ton wastewater. Processes, like Na-saponificated, Ca-saponificated and Non-saponificated technique, are widely studied to reduce the adverse environmental effect of RE industry, while traditional processes still have advantage in production cost, process stability and product quality. In this study, a novel process that combines distillation and air-stripping is developed. NH3-N is removed and recovered based on relative volatility difference of NH3 and H2O. Phase equilibrium, heat equilibrium are calculated to determine process parameters. Hydrodynamic performance like flow field distribution is also simulated. Then, design parameters for distillation trays or structured packing are determined based on calculations and simulations. Besides, the phase diagram of (NH4)2SO4-NH4Cl-H2O in 30°C - 100°C, the typical salts composition of nonferrous wastewater, is studied to ensure commercial plants’ continuous operation. Ammonia removal tower (ART) with different high efficient column internals is designed to fit RE wastewater treatment requirement. The novel process has been commercialized in RE industry in Jiangxi, China. The commercial project operation results show the novel process reached a nearly zero-emission with >99.5% NH3-N was removed and then recovered as ammonia. Combined the novel process, the traditional REO separation process using ammonia and ammonia bicarbonate could achieve NH3-N reuse and the effluent quality meets the discharge standards.

Jan 1, 2016

By Dillon. Patricia

Business Growth ?Coal ?Targeting 30 million tonnes by 2013 compared to 19 million tonnes produced in 2009 ?Expanding Energy Business unit (Oil Sands) ?Copper -Strong growth potential for existing operations and development projects ?New gold strategy recently launched ?New markets for zinc Need to retain existing and attract new employees to support growth Engaged Employee ?Has a positive attitude towards the organization and its values ?Is a person who is fully involved in, and enthusiastic about, his or her work Engaged employees are more likely to stay with the organization.

May 1, 2010

By L. Mohammadi

Outline ?Background on the accident at the Sullivan Mine No.1 Waste Dump ?Holistic approach to understand the reason for accidents (Atmospheric) ?Specific hazards at reclamation sites ?Regular atmospheric risk assessment at reclamation sites ?Fuzzy risk assessment ?Managing risk at legacy sites

May 1, 2010

By M. Mahfoud

The effect of grain refinement on the tensile and fatigue crack propagation behavior of sand cast magnesium alloy AM60B has been investigated in the present study, C2Cl6 in the amount of 0,3% was used to grain refine the melt, The fracture toughness tests were conducted in laboratory air at room temperature (25°C) using a sine-wave cyclic frequency of 20Hz and a load ratio of R = 0,1, The response in the Paris's regime and the critical stress range were determined, Preliminary findings have shown that C2Cl6 has a significant effect on both the tensile properties and fatigue crack propagation of the alloy tested, Grain refinement increased both the yield and ultimate tensile strength by more than 46%, and decreased the crack growth rate from 2,7 to 1,4 MPa Vm , However, the grain size seems to have a smaller effect on threshold stress intensity factor range. The fracture surfaces of specimens were examined optically and under the scanning electron microscope (SEM) to determine the relationship between grain size and fatigue properties.

Jan 1, 2005

By Nirmal Weerasekara, Lian X. Liu, The University of Queensland, Weiguo Xie, Benjamin Bonfils, Ping Yu

A mill model structure based on the population mass balance framework incorporating breakage characteristics, slurry and solids transport, product classification and discharge and energy consumption was reported in XXVII IMPC and named the Generic Tumbling Mill Model Structure Version I (GTMMS I). In this work, a new 4D (four dimensional) appearance function sub-model based on the experimental results of the JK Rotary Breakage Tester (JK RBT) was developed to describe the breakage characteristics and was applied to this new model structure. The newly developed 4D appearance function model has fewer fitting parameters and is more generic in nature. Most importantly, it is applicable to both high and low energy impact breakage. It is therefore much more versatile in comparison to the existing JKMRC t10- tn appearance function and the size-dependent JK M-p-q t10-tn appearance function. In addition, the Discrete Element Method (DEM) energy distribution model was integrated into the new model structure. With DEM results providing energy distribution information inside the mill directly, the selection function and the back-calculation method used in the existing JKSimMet modelling method are not needed in this model structure. With the above two revolutionary innovations, the previous model structure was upgraded to the Generic Tumbling Mill Model Structure Version II (GTMMS II). Furthermore, the new model structure is dynamic in nature with time-stepping technique for non-steady-state simulation. A case of the dynamic grinding of a SAG mill was studied to validate the GTMMS II. The model simulation results agreed well with the plant data. With the newly developed 4D appearance function model, the incorporation of DEM energy distribution and transport function, the GTMMS II is an important step forward towards mechanistic modelling of tumbling mills.

Jan 1, 2016

By Jochen Petersen, Alison Lewis, Cledwyn Mangunda

Run-off and waste water streams high in dissolved metal content are generated in all mining operations. The metals pose a threat to life due to their persistent bio-accumulative toxic (PBT) characteristics. Hence, there is a need to treat mine waste water effectively. Lime precipitation is the technology of choice through which Fe, as the major metal species, is removed as Fe (III) oxyhydroxides with other metals co-precipitated and/or adsorbed. Sulphates are removed as gypsum or incorporated into the Fe phases. The resulting sludge has poor dewatering characteristics and is deposited in landfills, with an inherent risk of returning the Fe back into the water cycle through leaching. This study seeks to understand the mechanisms behind the formation of this sludge in terms of product quality. The relationship between process conditions and product characteristics has been investigated through exploring the effect of Fe (III) concentration on the precipitate product characteristics (particle size distribution (PSD), size, morphology and structure) and quality (in terms of filterability, settling ability, etc.) in a simplified system. Neutralisation of acidic synthetic aqueous Fe (III) sulphate streams containing 50, 400 and 800 mg/L Fe(III), respectively, was effected by mixing it in a continuous stirred tank reactor (CSTR) with dissolved calcium hydroxide for pH control at a residence time of 15 minutes. Precipitate samples analysed for morphology and PSD, using nanoSEM and Zetasizer respectively, showed a general decrease in PSD and zeta potential with increases in feed Fe (III) concentration. These results were used to infer the particle size enlargement mechanisms of Fe (III) oxyhydroxide precipitates under a given set of operating conditions. Preliminary product quality results indicate that a high concentration (800 mg/L) leads to the rapid formation of metastable precursors with poor product quality, whilst a low concentration (50 mg/L) leads to formation of thermodynamically more stable precipitates with good product quality. The approach demonstrates a potential route forward in terms of linking operating conditions to the attainment of desirable characteristics rather than specific precipitate phases which are difficult to identify.

Jan 1, 2016

By Brendan Parker, Tyron Rees, Steven Hart, Abba Manesh, Ian Mcgaffin

"In September 2009, Newmont began the commissioning of a 3 stage crushing and milling circuit at its Boddington Gold Operation in Western Australia. The Boddington ore has been recognized as one of the hardest and most abrasive ores treated to date and this played a pivotal role in the selection of crushing and HPGR technology for this operation as opposed to the more conventional SABC circuit.This paper will examine the scale up from laboratory to pilot plant and full scale operation of the crushing circuit. There have been many challenges to overcome in the first 18 months of operation; however, the HPGRs have in general met design expectations and performance is expected to improve further with ongoing design changes"

Jan 1, 2012

By L. R. Bower

"This paper describes a highly versatile variable speed unit with a torque multiplication feature as a direct replacement for a fluid coupling .The unit is comprised of a modulating clutch with torque converter and lock-up options.The UCD does not start or stop the motor. This is carried out in the normal manner.The UCD continually monitors and rapidly regulates the output speed to the requirement of a set point demand from input signals or a pre-set program with full manual override.The pre-set program can include start and stop ramps, top speed and minimum speed regulation and also mid-speed set point with security for man-riding, etc. Speed variation is from zero to 100% on a constant duty basis.The input signals can be from any source, e.g. belt weigher. load profile bunker probes, mine monitoring system, etc.The UCD when fitted with a torque converter has a torque multiplication feature which automatically provides a starting torque up to two and a half times greater than the full load torque without exceeding the normal motor power levels.IntroductionIt is common practice in the mining industry to drive conveyors, whether they be belt or chain, through a transmission system incorporating a fluid coupling between the driving motor and gear-box .However, there are drawbacks and in an effort to attain a better degree of drive and control, two-speed motors - inverters cycle- converters - hydrostatic drives, etc ., have been introduced."

Jan 1, 1986

By D. E. Salman, R. R. Maclachlan, R. J. Barclay

"There is a considerable resource of data for spherical charge cratering, both as single charges and in row-of-charge geometr(1). The data are. however, based on cratering performance to a single free planar surface.In practice. the more common circumstance involves an angular surf ace geometry. such as occurs at the toe of a bench or the wall of a stope. It is for the purpose of investigating this circumstance that the described test work was conducted.The test objectives were: (1) to observe the change in single-charge cratering performance between planesurface and angle geometry; (2) to identify the optimum performance of single charges cratering to a plane surface. cratering from a bench sub-grade position and cratering from a condition of zero sub-grade or stope wall geometry; and (3) to observe the performance of row-of-charges cratering to an angular surface at various row burials and spacing. The row charge burial and spacing dimensions were to be expressed in simple numerical multiples of single-charge depth-of-burial data."

Jan 1, 1981

"A 3-dimensional finite element model for stress/stability analysis of rock excavations in underground mines is presented. Developed for use on personal computer under OS/2 operating system, the model employs the 8-node isoparametric brick element and accounts for such loading conditions as in situ stresses and gravity loading of the rock mass. In addition, modelling of backfill in mine stopes as in situ stress-free material is incorporated. Material failure is assessed by Mohr-Coulomb or Hoek-Brown failure criterion. A mine design example is presented to illustrate the potential use of the model as a tool for stope design.IntroductionNumerical modelling of mine structures has become a vital tool for mine design in recent years. The need to maximize ore extraction ratio and to reach deeper mineral deposits underground has led the mining industry to employ numerical methods of analysis to undertake complex ground control studies in order to better understand the ground response to mining excavations and to evaluate the ground support requirements. Thanks to the rapid developments in computer technology, it is now possible to perform very comprehensive analyses including, but not limited to, 3-dimensional, elasto-plastic, or large deformation or time dependent nonlinear analyses on personal computer.During the past ten years or so, many researchers undertook 3-D finite element analyses of rock mechanics problems in mining engineering. The following is only a sample review. For example, Chan'!' used three-dimensional finite elements to study the mechanical response of jointed granite during shaft sinking at the Canadian Underground Research Laboratory. Wang et al.(2) performed 2-D and 3-D finite element analyses of room-and-pillar mining system with flat and rolling coal seams. Thatejatu used three-dimensional finite element method to examine the problem of branching tunnels. Dolezalovaw used three-dimensional finite elements for the analysis of tunnel-face advance with partial excavation as well as full-face excavation in combination with rein for cement of the face by long anchors. Peili (5) used three-dimensional finite elements for the simulation of rock-liner interaction near the tunnel face."

Jan 1, 1992

By M. Saghaeian, R. Hejazi, Sheikhzadeh. V., A. Abazarpoor

"The morphology of iron ore concentrate particles is known to influence several properties of iron ore pellets, including drop number, compression strength, and reduction properties. This study aimed to determine why grinding methods and particle morphology influence green pellet properties. Particle morphology can be directly related to the grinding method: ball mill (BM) or high pressure grinding roll (HPGR). In this research, two iron ore concentrates, namely Gol-e-gohar and Ardakan, were ground by a BM and HPGR to produce a suitable Blaine value for pelletizing (nearly 1,900 cm2/g). Morphological features of particles were subsequently investigated by sieving and cyclone sizing for particle size distribution, the Brunauer-Emmett-Teller (BET) and Blaine methods for specific surface area (SSA) and scanning electron microscopy (SEM) for the evaluation of shape descriptors. It was concluded that HPGR resulted in generating a greater proportion of fine particles compared to ball milling. The BET results showed that the SSA of HPGR pellet feed was higher than that from the BM due to a greater proportion of cracks, indents and bulges and the creation of new fracture surfaces. SEM images processed by ImageJ software indicated that particles ground by the BM tended to be more rounded and less elongated than HPGR particles because of the breakage model of each method. To show the effect of morphology on the green pellet quality, green pelletizing was performed in a pilot pelletizing disc. The HPGR pellet feed had a higher drop number in comparison to the BM pellet feed, due to the angular and rough shape of the particles.INTRODUCTIONThe demand for fine or ultra-fine particles as feed material for ceramics, composite materials, and mineral processing is on the rise (Kotake, Kuboki, Kiya, & Kanda, 2011). The final concentrate of iron ore processing plants (filter cake) has a size range roughly between 0 and 300 µm, depending on the liberation of Fe containing particles (Meyer, 1980). In general, to produce a suitable pellet feed of appropriate quality, Blaine numbers of 1800–2000 cm2/g should be achieved (Van der meer, 2015)."

Jan 1, 2016

By W. F. Harkness, D. Hodgkinson

"A non-destructive testing program was established at Crows Nest Resources (C.N.R.), Line Creek mining operation following an in-service fatigue failure of a front wheel spindle on a large haulage truck.This failure identified a definite need for improvements in the ultrasonic techniques used during the mandatory spindle integrity examinations. Initial investigations using common mining industry ultrasonic examination techniques showed that the smallest detectable cracks were 75 mm in length for the spindle types in service at the C.N.R. site. The Initial findings indicated that inadequate inspection technique design was the cause of the poor performance. To improve inspection reliability it was identified that improved ultrasonic techniques were required. Results using designed ultrasonic techniques were encouraging, with the detection of simulated and natural cracks 12 mm long achieved. The cost benefits associated with the extended spindle life, following the removal of these small fatigue cracks, far exceeded those of the expertise and effort necessary to implement and conduct the N.D.T. program.Introduction During 50 years of evolution, non-destructive testing (N.D. T.) has progressed from a laboratory curiosity to a well accepted and invaluable tool used in the assessment of material integrity. Unlike destructive testing, N.D.T. does not deform or render the material useless. Non-destructive tests may involve many applications, from the determination of a corrosion prevention coating thickness to the examination of a raw material for internal and external deformities.Within the mining sector, highly-stressed components will normally have been subjected to some form of non-destructive test during their manufacturing cycle. These tests are used to ensure the component does not contain material flaws whichmay be detrimental to its service performance.While the component may have assured quality when produced, deterioration by fatigue may occur during an aggressive service life. Large dynamically-loaded components such as haulage truck front wheel spindles are , in particular, prone to this service related problem."

Jan 1, 1987

By Ahmad Ghahreman, Denver Cowan, Yeonuk Choi

"Testwork was conducted in order to compare the effectiveness of carbon based catalysts while oxidizing a gold-bearing pyrite concentrate under atmospheric conditions. Without the use of a catalyst the oxidation of pyrite was incomplete after 96 hours, resulting in roughly 60% pyrite oxidation. Furthermore the resulting sulphate yield from unassisted pyrite oxidation ranged between 72 and 84%. It is evident that atmospheric oxidation of pyrite is not viable due to slow oxidation kinetics and high sulphuric acid production when using a ferric sulphate media without a catalyst. The effect of two different carbon based catalysts, one Lewatit® AF 5 a new microporous carbonaceous bead, and the second a granular coconut shell based activated carbon, were tested under the same oxidation conditions as the unassisted pyrite tests. After 96 hours, Lewatit® AF 5 assisted oxidation showed approximately 96% pyrite oxidation with a sulphate yield ranging between 26 and 35%, while the activated carbon assisted oxidation reached approximately 100% pyrite oxidation with a sulphate yield between 36 and 37%. Testwork indicated that not only does the addition of a carbon based catalyst greatly improve the oxidation kinetics and lead to almost complete oxidation, the sulphate yield is also drastically reduced, resulting in very high elemental sulphur yields.INTRODUCTION Pyrite is an important sulphide mineral due to its ability to contain invisible gold concentrations up to 132 g/t (Chryssoulis & Cabri, 1990). As a result, ores composed of only a small amount of pyrite still have the ability to contain high gold grades. This refractory gold cannot be accessed via conventional gold leaching processes, such as cyanidation, and additional oxidative pre-treatment is required to liberate the gold, making it more amenable to extraction (Marsden & House, 2006). Current oxidative pre-treatments do exist consisting of both pyrometallurgical and hydrometallurgical processes including high temperature and high pressure leaching within autoclaves, biological atmospheric leaching and roasting. Autoclaves are a proven process reaching desirable recoveries within approximately a 1–2 hour retention time, due to the increased temperatures and pressures, allowing for an increase in dissolved oxygen (Marsden & House, 2006). The typical reaction for pyrite oxidation within autoclaves is presented in Equations 1, 2 and 3."

Jan 1, 2017