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By X. T. Feng, Y. H. Hatzor, Y. Tal, G. Yagoda-Biran

"When studying jointed rock mass deformation around underground openings it is of great importance to model correctly the excavation sequence during the numerical simulation. This is because for effective arching mechanism to develop in the roof minute block displacements must take place and some of the available discontinuities shear strength must be mobilized. If from the beginning of the simulation the underground opening already exists in the numerical model, block displacements into the excavation space will initiate and develop from time zero, before the initial stresses in the model have attained their actual initial level in the field. These initial block displacements are therefore artificial and exist only in the numerical model, not in the physical reality, and may lead to erroneous assessment of the stability of the designed structure, typically on the conservative side. We have introduced sequence excavation capabilities both in the numerical manifold (NMM) and the discontinuous deformation analysis (DDA) methods and show here the advantages of this modification using three different case studies, each illuminating a different aspect of this enhancement.We begin with the 25 meter deep 2000 year old underground Zedekiah limestone quarry below the old city of Jerusalem, Israel, which is still standing today unsupported with a free span of 40 m. We show that when the opening exists from the beginning of the numerical simulation the required friction angle for roof stability is 25 degrees, whereas when the opening is removed after all stresses and displacements in the model have been stabilized the required friction angle for stability is only 15 degrees.We then model the excavation sequence of a tunnel model representing a 2500 meter deep research tunnel in the Jinping hydroelectric project, China, in order to determine the in situ stress field at this depth by a grid search inversion of displacement data obtained using the sliding micrometer technology in the course of tunnel excavation. Thus we are able to constrain the in situ stress field at these depths where standard in situ stress measurement procedures are extremely difficult to execute properly.Finally, we use sequence excavation modeling capability to find the total height of the expected loosening zone around tunnels excavated through columnar jointed basalts which pose a great engineering challenge because of the characteristic dense network of slender prismatic blocks that transect the opening at a steep inclination. We use MPBX data obtained during excavation of a deep tunnel through such a rock mass to validate our numerical results and show that application of standard empirical guidelines for dimensioning rock bolt reinforcement in such rock masses may in fact result in very un-conservative design because existing empirical approaches typically ignore the anisotropic nature of the structure of such rock masses which, as we show, plays a very significant role in determination of the extent, shape, and geometry of the loosening zone around the opening."

Jan 1, 2015

By Y. Tanaka, M. Maeda, S. Suzuki, C. Tokoro, T. Kato, K. Muto

Boron (B) co-precipitation was investigated with ettringite to establish a cost efficient method of removing B from acid mine drainage. For 25 mg/L of B solution, most appropriate pH for B removal was pH 11.5. The most appropriate amount of reagent for B removal within Japanese effluent standard (10 mg/L) was B:Al:Ca:SO4 = 1:3:9:4.5, which corresponds to the composition of Ettringite (Al:Ca:SO4 = 2:6:3). The effect of silicate, carbonate and temperature on efficiency of B removal is important as groundwater and hot spring water are often contaminated. When silicate and carbonate are present, more Al and Ca salts are needed for B removal since some aluminum and calcium precipitate with silicate and carbonate as kaolinite and calcium carbonate. These precipitates do not contribute much to B removal. As the temperature raised, the most appropriate pH for B removal decreased. B removal became less efficient as monosulfate precipitated more rapidly as ettringite.

Jan 1, 2015

By Mory Ghomshei

As fossil fuels become depleted over the next century, it is imperative that Canada and other countries examine ways to transition to other sources of energy, particularly renewable resources. A critical obstacle to developing Canada?s renewable energy resources is the scarcity of infrastructure to wheel the generated electricity to a viable market. For each megawatt of renewable electrical power, a maximum of 1 km of connecting power line is typically feasible. This means that hydropower, geothermal, and wind power projects with capacities up to 100 MW must be located within a maximum of 100 km of a main power line in order to be economically viable. With a total length of about 1200 km, the proposed Northern Gateway oil pipeline project creates an excellent opportunity to become a corridor that can seed renewable energy projects in Northern British Columbia and Alberta. Utility companies must build new infrastructure to provide the electricity for constructing and operating the proposed pipeline. The pipeline and linked power line infrastructure therefore, should be designed and built with consideration to create an energy highway to the significant renewable energy resources, such as hydro, wind, and geothermal, in the vicinity of the proposed pipeline. Some of the important renewable energy resources in northern British Columbia can be developed in connection with the proposed pipeline. It is estimated that close to 2,500 MW of commercially viable wind, geothermal and run-of-river power resources are present in the proximity of the proposed pipeline corridor. While oil flows westward from the Alberta bitumen fields, the generated green power can flow eastward to help the Canadian oil sand industry to offset as much as 10 Megatons of carbon emissions per year. The generated carbon credits are equivalent to 75% of the emissions associated with extraction of the 525,000 barrels per day of oil from oil sands, intended to be carried by the pipeline.

Aug 1, 2013

By P. A. Riveros, J. Binvignat, V. M. McNamara, D. Koren

The recovery of cyanide from a gold mill solution containing high levels of copper (400 mg/L to 900 mg/L) using the AVR process was evaluated. It was determined that acidification to pH 2 to 3 provides a suitable balance between HCN generation, copper precipitation and acid consumption. A short pilot plant campaign showed that ~75% of the feed WAD cyanide was recovered while the remainder precipitated along with copper upon acidification. The acid consumption averaged 3.5 g H2SO4 per litre of solution. The copper precipitate, consisting mostly of CuCN and CuSCN, was readily separated from the solution by gravity. The volatilization of HCN in countercurrent packed columns averaged 98.7% efficiency. Reabsorption of HCN was practically 100% in NaOH solutions and slightly lower in a lime slurry. Basic volatilizer design parameters applicable to a large-scale operation were determined, including the Henry’s Law constant and the mass transfer coefficient of HCN gas.

Jan 1, 1998

By G. Guzman

In the framework of the optimization of Teniente Converter operation the new system of automatic flux feeding through gar-gun was implemented in the Potrerillos Smelter, Codelco Chile, Salvador Division. The control algoritm based on simple iron and silica balance adjusted by empirical coefficients was incorporated in the logical programmer. The programmer works in real time gathering information from the plant instrumentation events and introduced chemical assays of concentrate, slag and flux. Through the auto-tuning of the automatic operation the criterions of optimal flux dosage were determined. Four month of operation of the automatic flux feeding system demonstrated the stabilization of magnetite content in the slag in the narrow range from 18 to 20% and the decrease of flux consumption, corresponding to annual savings US$ 340,000. Additionally, the automatic system helps operators in the control room in fast determination of optimal fluxing and avoid the errors in flux dosage affecting the slag quality and its impact on refractory wear.

Jan 1, 2007

By Ray Walton, Ron Colquhoun, Ken Thomas, Dwayne Fentie, Barney Burke

"The new Roasting Facility at Barrick’s Goldstrike Mine in Nevada, U.S.A. was developed to process 12,000 tons per day of refractory gold ore. The process consists of crushing, dry grinding, roasting, extensive gas purification, calcine quenching and leaching in the presence of activated carbon. The new plant is integrated into the existing Goldstrike facility, treating ore from both open pit and underground sources.The process design, procurement, construction and commissioning of the Roaster facility was performed successfully over a 3% year period with peaks of 400 engineering personnel and 950 construction personnel supporting the project. The US$330,000,000 project was completed ahead of schedule and under budget. The commissioning was well planned and proceeded smoothly through a rapid start-up to achieve all primary goals within three months of the start of processing of ore.BACKGROUNDAs early as 1992, Barrick’s Goldstrike Mine, located north of Carlin, Nevada had indications of the ore becoming ever increasingly carbonaceous in nature. As the open pit and underground exploration programs proceeded to step out over the years that followed, the accumulative amount of carbonaceous refractory ore and tons had become significant. By 1997, 29 million tons of double refractory carbonaceous ore containing an estimated 11.6 million ounces of gold had been identified. By 2000 the resource had increased to 14.3 million ounces."

Jan 1, 2001

By W. A. Jones

THE estimation of the average value of gold ore involves many considerations, among them the correct sampling of the deposit, the dilution by waste, and the loss of high-grade fines. It is a common experience that, after all these factors have been evaluated, adjustment of the assays is necessary before satisfactory agreement between the calculated mine grade and the mill heads is obtained. In fact, at many mines the latter correction overshadows all others in the preparation of routine estimates. For this reason it is proposed to deal only with the mathematical treatment of mine assays and the problem of bringing estimates into conformity with the corrected mill heads. Mine assays differ from physical measurements because the range of values is very great and these are not symmetrically distributed above and below the average, there being fewer high than low results. There is no widely accepted mathematical procedure for determining the average of series of measurements which exhibit these characteristics. Customary practice consists in empirically reducing high assays until a satisfactory agreement with mill heads is reached. It was thought that more confidence could be placed in grade estimates if a logical basis for calculations could be devised .. In an attempt to find a fundamentally sound procedure, amenable to practical application, many series of assays comprising over 235,000 channel samples (1) were studied at Hollinger Consolidated Gold Mines, Limited. Such an investigation could only be made where records covering many years of operation are available and where tabulating and calculating machines are in use. The results are recorded in the hope that the relationships noted for the large groups of assays used are of fundamental character and that the data will be useful to others dealing with the problem of grade estimation.

Jan 1, 1943

By W. H. MacLean, S. Liaghat

Abstract- The Key Tuffite is a thick (0.3 m to 6 m) and laterally extensive (-10 km) cherty, sulfide-bearing tuff unit in Archean greenstones in the Matagami mining district in northwestern Quebec. It lies at the contact of the Watson Lake Group and overlying Wabassee Group volcanic rocks, and is host to major Zn-Cu volcanogenic massive sulfide deposits. The tuff component is highly altered and its volcanic precursors are not identifiable by petrographie means. The tuff is mixed with a volcanic exhalative component comprising chert, carbonate and sulfides (pyrite, pyrrhotite, and minor sphalerite and chalcopyrite). The normative mineral composition of the Key Tuffite is 33% quartz, 28% sulfides, 16% sericite, 8% carbonate, 60Jo chlorite and 9% other minerals. In the vicinity of the Bell Allard and Orchan mines, the precursor tuff components are identified using immobile major and trace elements, as Watson Lake tholeiitic rhyolite (Zr/Y = 1.5 to 3.5, LaN/Ybn. = 1.7 to 2.8, Si02 = 72.5 ± 1.2 wt %, and Wabassee calc-alkaline andesite (Zr/Y =9, LaN/Ybn. = 4 to 8, Si02 = 56% to 65%). Immobile element computation techniques were used to calculate mass additions and losses in the conversion of the tuff to the Key Tuffite. Average net amounts of Fep3 (27% total iron), Si02 (14%), CaO (8%), S and K20 ( + 2%), were added, Na2O was removed (-2.8%), and MgO was over-all unchanged. Total net mass change was +63%, which comprises mainly exhalative additions, but also includes changes owing to hydrothermal alteration of the tuff component.

Jan 1, 1992

By Marsh A. Cooper

THE THEME of my remarks provides a great deal of latitude. I shall therefore take advantage of the scope it offers to look at our industry across a broad spectrum. My observations reflect a Canadian mining man's varied career as a geologist, mine operator, geological consult ant and company executive in Canada and overseas ... under differing cultures, business environments and political jurisdictions. I was fortunate to come into this industry in the mid-1930's when it was characterized by great enthusiasm, drive and resourcefulness. It was the beginning of a burgeoning era of some 30 years' duration in which the individualist, the entrepreneur and the builder found ample room for expression. As I contemplate the environment in which we now have to operate and try to perceive what lies ahead, I find myself deeply disturbed. Something serious has happened to this industry along the way. It appears that our very success has been the source of our undoing. I believe it is useful to summarize our industry's basic strength at home as a take-off point f or assessing its position in world terms. I hope that I can focus on some of the things that, in my view, must be done for this industry and by this industry to restore Canada's historic role in the world mining community. The Canadian mineral industry provides 140,000 jobs. It pays the second -highest average weekly wages and salaries among the country's major industries. The output per employee in the mining industry is estimated at about three times that for the economy as a whole.

Jan 1, 1977

By C. Doyle, J. Brennan, C. Díaz, J. Hrepic, K. Cushnie

"In 1991/1992, INCO undertook a successful R&D program aimed at extending the lining lives of the top blown rotary converters (TBRCs)at its Copper Cliff Nickel Refinery (CCNR) and the electric furnace at INMETCO. At the laboratory scale, this effort was divided into three phases. In the first part, mineralogical work was performed on six refractories that were either currently being used to line these vessels or were considered suitable alternatives. In the second part, this mineralogical knowledge was used to help determine the compositions of slags that would not corrode the bricks at the operating temperature (1600°C) of the above furnaces. Finally, several important properties of the six refractories were measured to complete their evaluation as candidate linings. This paper reports the results of all three phases of the laboratory scale R&D work.The mineralogical work showed that rebonded fused grain magnesite-chrome (RFG-MC) bricks consist principally of periclase with minor amounts of free chromite and trace quantities of silicates monticellite and sometimes olivine. The bricks are principally held together by periclase-periclase direct bonding. Of note, the bulk of the chromite exists as exsolved precipitated blebs within the periclase grains. These likely redissolve at high temperature.Slags on the periclase liquidus coexist stably with these refractories. Examples are presented using CaO-MgO-Al2O3-SiO2 slags at~1600°C.Finally, the two refractories manufactured using close to 100% fused grain material generally outperformed the others in terms of physical properties and certainly were superior in their resistance to slag penetration damage."

Jan 1, 1997

By Bali. D. D., S. Chattopadhyay

"The planning and construction of prime coking coal beneficiation plants in the nationalized mines in India are reviewed. Flow schemes, construction practice, materials consumption, and costs are detailed.Medium-capacity beneficiation plants with multiple loops are recommended under Indian conditions.IntroductionThe reserve of high-grade and easily washed metallurgical coal in India are quite limited. Prime coking coal constitutes approximately 22% of the total resources and occurs exclusively in the Jharia coalfield in the state of Bihar. Bharat Coking Coal Limited (a subsidiary of Coal India Limited (CIL) the nationalized mining sector of India) owns 80% of the Jharia collieries. The development of Jharia coalfield in the pre-nationalized period before 1971 has been characterized by a large number of small mines with primitive mining methods and low productivity. The production of prime coking coal to meet the demand of the steel industry in India has to increase from the existing level of 11.1 million tonnes to 43.4 million tonnes per annum by 2000 AD, thereby producing 5.61 million tonnes and 22.7 million tonnes of clean coal respectively. An ambitious program has been undertaken for development of bigger mines with an average production of 1 to 3 million tonnes per annum. With the fast dwindling reserves of good quality coking coal, more inferior grade coal seams, having difficult washing characteristics, are now being mined. All the coal from the future mines will have to be beneficiated to make it suitable for consumption of steel plants; the following washeries are being planned for construction by 2000 AD:"

Jan 1, 1986

By Roy T. Bowles

This paper focusses on technological developments which occurred in the village of Deloro, Ontario between 1868 and 1919. These developments illustrate the manner in which improved metallurgical processes linked Ontario mineral resources to industrial expansion. Overview of Deloro The village of Deloro is in Hastings county, about 5 miles from the village of Marmora, the site of the old Marmora iron works and the more recent Marmoraton iron mine. In this area, the Canadian Shield meets the Great Lakes lowlands. The first settlement in the vicinity occurred in the 1820s and was associated with the Marmora iron works. Settlement grew around agriculture. Gold was discovered in Hastings county in 1868. Deloro - the name derives from gold - developed as a concentrated settlement in proximity to several gold mines and the related processing activities. By 1901, substantial smelting works were successfully producing gold and arsenic from local ores. The village was developing as a company town within the framework of benevolent paternalism. For reasons associated with markets and with local ore supplies, the Deloro mills were idle for a period beginning in 1902. Developments in later periods connected Deloro to world events. In 1903, silver was discovered at Cobalt, Ontario. By 1907, M.J. O'Brien, who owned mines at Cobalt, had purchased the Deloro works and was using them to process Cobalt-area ores*.

Jan 1, 1999

By M. Muinonen, R. Pandher

Royal Nickel Corporation is developing the Dumont Nickel Project, a large nickel sulphide deposit located near the town of Amos, Québec. The nickel occurs as pentlandite, heazlewoodite, and awaruite. The relatively low grade ore can be processed to a very high grade nickel concentrate, containing 29% Ni. The absence of copper and precious metals in the ore renders this concentrate amenable to processing by dead roasting in a fluid-bed roaster and smelting in an electric furnace to produce ferronickel for sale to stainless steel producers. Laboratory test work and conceptual engineering design was completed to demonstrate the amenability of Dumont concentrate to produce ferro-nickel.

Jan 1, 2015

By Eric Schraml

Wardrop Engineering and the Placer Dome?s Campbell Mine Design Team utilized leading edge directional raise boring techniques and an innovative, remote controlled application of steel fibre reinforced shotcrete ground support to achieve improved mine ventilation and a superior, safety focused secondary emergency egress. While more standardized methods may have provided a sufficient solution to either the requirement for a ventilation raise or for a traditional escape ladder way, innovative methodology ensured both objectives were met with a single, enhanced solution. Placer Dome committed to provide a solution that minimized energy consumption, optimized air delivery and facilitated an escape way focused on minimizing the negative physiological aspects associated with mine evacuation. The project was successful in providing a new airway, returning 47 m3/s (100,000 cfm) from the 39 Level to 30 Level, minimizing risk to the raise equipping crew and providing a fully equipped escape hoist. The resulting secure escape environment provided an efficient means of evacuating personnel working at depth without necessitating a potentially dangerous exhausting climb to surface. The project has substantiated, that optimized safety focused design can be achieved without jeopardizing project economics.

May 1, 2002

By W. J. Pearson

"""POTASH"" is a term applied to the compounds of the element potassium (K) and when used in agriculture and industry is ex-pressed in terms of potassium oxide (K2O), regardless of the actual com-position of the compound. When a chemical analysis is made of a fertilizer, the amount of K is deter-mined and then calculated to the equivalent amount of K2O. However, the compound K2O does not exist in nature. Most of the world's potash supply is derived from mineral deposits similar to those in Saskatchewan and New Mexico. However, there is some production from concentrated surface brines such as occur in Searles Lake, California; Salduro Marsh, Utah; the Dead Sea; and from well brines in Micl1igan."

Jan 1, 1960

By M. F. Gallerneault, V. Fallah, A. Howells, W. M. T. Gallerneault

"The occurrence of recrystallization in cold-worked aluminum sheet during the brazing process leads to loss of strength, an inhomogeneous grain structure and reduced corrosion resistance. AlMgScZr alloys are known for their extraordinary recrystallization resistance due to the influence of Sc and Zr addition on their microstructure. Here, we investigate the effect of alloy composition (i.e. Mn, Mg, Sc, Zr content), cold-roll reduction and pre-aging treatment on the recrystallization behavior of cold-rolled sheets at brazing temperatures typically used during the manufacture of heat exchanger units. The analysis of recrystallization behavior is carried out through microstructural characterization and the results are compared with the behavior of a commercial, AA3xxx-based heat exchanger alloy.INTRODUCTION Control of recrystallization is of critical importance during brazing, which is a widely-used joining technique for aluminum alloys in aircraft structures (Heinz, 2000) and automotive heat exchangers (Miller, 2000; Marshall, 1993). Due to excessive local heat at brazing temperatures, the cold work texture of aluminum alloys in the cold-rolled sheets may undergo a local recrystallization process (Marshall, 1993). This leads to the formation of an inhomogeneous microstructure and thus anisotropic mechanical properties (Miller, 2000) and low corrosion resistance (Marshall, 1993) across the sheet. X800, a commonly-used Al-Mn alloy series for automotive heat exchangers applications, has been developed specifically for a higher strength as well as an enhanced corrosion resistance as opposed to the traditionally-used AA3003 alloy (Marshall, 1993). X800 alloys, however, exhibit a low recrystallization resistance at normal brazing temperatures, i.e. 590°C. In contrast, Al-Sc-Zr alloys have been shown to exhibit an extraordinary recrystallization resistance at such temperatures (Riddle, 2004) while also being corrosion resistant and possessing a high room-temperature strength (Fuller, 2002). This has been shown to be due to the formation of coherent, nanoscale Al3(ScZr) precipitates that effectively impede grain boundaries while also exhibiting very slow coarsening kinetics at high temperatures (Riddle, 2004; Jones, 2003; Ocenasek, 2001). In this study, we analyze the recrystallization behavior of X800 alloys under brazing conditions through introducing Sc and Zr into the system as well as varying the Mn and Mg content. The effect of processing route is also studied by introducing a pre-aging stabilization treatment as well as varying the cold-roll reduction prior to the final brazing anneal."

Jan 1, 2018

By A. Villanueva

The effect of High Pressure Grinding Rolls (HPGR), as a preceding stage to a conventional ball mill circuit at PT Freeport Indonesia?s C1/C2 concentrators, has been studied in terms of downstream grinding efficiency and circuit performance. When milling the product from the HPGR, mill capacity increased by 21% for the same product grind size, when compared to processing similar ore from a conventional crushing circuit. This achievement is a result of several reasons, among them: reduction in feed size (F80), fines generation beyond the proportional reduction in F80, reduction in ore hardness induced by HPGR comminution mechanism, optimization of the recycle system of the HPGR and ball string optimization in the ball mill circuit given the new feed to the mill.

Jan 1, 2012

By Michel Massé

Eleonore Project- Agenda ? Purpose and Technical Overview ? SmartEXEC Control Capabilities ? SmartEXEC System Archetecture ? SmartEXEC System Advantage Eleonore Project- Purpose and Technical Overview ? Control air quality while maintaining target production levels at minimum energy operating cost ? Improve safety, work place conditions and operation flexibility ? Reduce energy consumption and green house gases footprint

Aug 1, 2013

In Canada and other countries, legislation dealing with accurate factual disclosure for mining projects is being expanded to include more metallurgical design information. Grinding characteristics, metallurgical recovery of contained metal and environmental hazards associated with tailings disposal will be part of the Canadian package. This paper will examine only that portion of the plant design standard practice that relates to grinding ? in SAG mills and ball mills that grind ore from as received crushed material to final ground product that is fed to downstream plant recovery processes. Since grinding plants represent a significant portion of the overall concentrator cost, accountability in grinding design should no longer be left to chance, opinion, or hidden proprietary information. This is the 21st century. It is reasonable to expect that a factual basis will be needed so that a Qualified Person (QP) reviewing the grinding mill design can understand it. That will also involve how many and what quality of samples are taken to define the characteristics of the deposit, the accuracy of the tests used to measure ore hardness and the method by which the dimensions and power of the mills are determined. If these criteria are not met, the QP may have no choice but to call attention to the lack of convincing information regarding the grinding mill design for the project. At the same time clients are expected to demand getting the correct design information at a cheaper price, results in a more timely way, and accurate design to the point where the risk of tonnage shortfalls are reduced or eliminated. Tables will be presented to show how this can be done to current standards using existing technologies. At the same time it is acknowledged that current standards are ill-defined and that to achieve consensus among those involved in SAG mill design work, it may require that a consortium funded project be set up to establish what tests and methods for grinding design are suitable to meet the new standards for metallurgical disclosure. By running parallel design methods on several major projects over a period of 5 years, the process of how to design grinding circuits will be better understood because the projects will start at the design stage, include procurement of the mills and will end with a benchmark test on the plant. Selecting the samples and the best schedule for doing test work on core samples submitted and mill design, will be discussed in this paper. The issue of completing the grinding design in time for early procurement decisions is on the critical path for most major projects. Discussions between mining engineers, geologists and process engineers are needed early in the development cycle, at the scoping study level (SS), preliminary engineering assessment (PEA), prefeasibility study (PFS), and at the feasibility study stage (FS), to ensure that proper planning for design sample selection is done. Using adequate sampling and testing methods in a timely way allows early procurement of the grinding mills and minimizes project risk.

Jan 1, 2012

By B. Friedrich, N. Anastasijevic, S. Stopic

The extraction of nickel from Serbian and Western Australian lateritic ore by sulphuric pressure acid leaching (PAL) has been studied. The following parameters were tested: stirring rate, acid to ore ratio, reaction time, pressure and temperature. These studies were performed with ore samples from the Rudjinci, Serbia and Silcrete, Australia, both belonging to the laterite-silicate group of deposits. An increase of the reaction temperature and the stirring speed at a fixed acid/ore ratio showed a positive influence on nickel extraction. The decrease of the oxidation potential with time correlated with the increase in Fe(II) in solution and nickel extraction as the reaction went to completion for both ores. The target values of 95 % Ni extraction and 60 % Co extraction were attained in 5 min at 250°C for the Serbian silicate ore, at an agitation rate of 1500 rpm, 10 % solids, and acid/ore ratio of 0.40. Under similar conditions only 60 % Ni, but 69 % Co could be extracted from the Australian Silcrcte ore due to different mineralogy. The nickel extraction was shown follow a diffusion-controlled reaction model.

Jan 1, 2004