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By Andrea Brickey, JUDITH BUABA, RICHARD AMOAKO

The global mining industry has recorded significant declines in accident and injury rates attributed to the advancement in technology, increased enforcement, and safety consciousness. A goal of the mining industry is to achieve zero injury and occupational illness on all mine sites, prompting increased research into ways to further reduce mine accidents. A machine learning technique known as multiclass logistic regression is applied on a 10-year injury dataset from the Mine Safety and Health Administration (MSHA) to determine a miner’s susceptibility to a class of injury and to help identify significant risk factors associated with different classes of injury. The data is aggregated based on injury classification to provide statistically relevant results. The analysis identifies specific risk factors that influence a mine worker’s susceptibility to a given class of injury, i.e., non-fatal with no days lost or restricted activity, non-fatal with days lost and/or days of restricted work activity, and fatal and total permanent or partial permanent disability. These factors include miner’s age, mine type (coal vs. non-coal), experience on the current job (years), shift start time, employment type (operator vs. contractor), mining district, and type of accident. The results of the analysis indicate that a miner’s experience on the job, i.e., the number of years worked in a current job, is a significant risk to injury occurrence, even for those with decades of total mining experience. We further show the differences and similarities between the surface and underground mine incidents.

Nov 3, 2020

By Connor Langford, Murray Gant, Ken Massé

For public organizations, preparing accurate project cost estimates is a critical component in capital project planning. Project delivery methods provide a structured approach to moving projects through the design and construction lifecycle, and typically use cost estimates as key inputs at each stage to determine if the project will advance. As design stages can occur years or even decades before construction contracts are awarded, estimates need to make reasonable assumptions about how the work may be executed (means and methods) as well as potential future market trends so that appropriate values for material pricing, labour costs, escalation, and owner’s costs can be included. This process is challenging enough during stable markets, as historic trends can often be misleading and require a suitable understanding of economic factors to use appropriately. When you mix in the market volatility that has been observed since 2020, developing accurate project cost estimates becomes even more challenging. In cases such as this, having a structured approach to cost estimating that includes an adequate risk-based reserves cannot be overstated as it provides the basis for ongoing project decisions. This paper explores some of the historic and more recent market trends that have impacted key aspects of project cost estimates for capital project planning. It also provides recommendations on how to develop cost estimates for infrastructure projects, with examples from Metro Vancouver, which plans for and delivers regional-scale services to 2.6 million residents. A brief commentary on the use of escalation clauses in contracts is also presented.

Jun 13, 2023

By C. Sunderman, G. Feagan, C. Stazick

Galvanic corrosion between dissimilar materials, such as steel and graphite, leads to safety concerns for many industries, including mining. In this study, researchers from the National Institute for Occupational Safety and Health (NIOSH) analyzed rock samples from two mines in the United States that exhibit electrochemical properties similar to graphite through laboratory measurements to investigate their observed in-situ influence on underground metal support. Uniform corrosion rates of mild steel coupons, inflatable bolt coupons, and friction bolt coupons galvanically coupled to rock samples were obtained using both potentiodynamic polarization and zero resistance ammetry. Increased uniform corrosion rates were witnessed between the coupled rock and steel system, over those of just the steel alone. Surface analysis of the metal samples showed the presence of pitting corrosion, reflective of bolt samples removed from partner mines. Corrosion pitting of ground support structures in contact with graphitic rock in underground mines poses safety concerns for mine workers by increasing the rate of corrosion and decreasing bolt strength over time and will be further investigated for intervention strategies.

Feb 1, 2023

By T. Grammatikopoulos, C. Gibson, M. Aghamirian

"Lithium is a silver-white alkali metal that has recently become a target commodity for many junior mining companies. Lithium has a wide range of applications including ceramics and glass, lubricating greases, air treatment, continuous cast mold flux powders, polymer production, and primary aluminium production, but the current popularity of lithium can be attributed to an anticipated increase in demand for lithium ion batteries. The most common lithium-bearing minerals occur globally in pegmatites and granites. Spodumene [LiAl(Si2O6)] is the most desirable economic lithium-bearing mineral due to its high lithium content (theoretical Li2O content of about 8 wt%). However, lithium can also be hosted in petalite, micas, tourmaline, and phosphate minerals. In Canada there are a number of spodumene deposits in Ontario and Quebec at development stage that have the potential to help narrow the forecast lithium supply gap stemming from the widespread acceptance and use of electric vehicles. This paper discusses the beneficiation of hard rock lithium deposits, including an in depth review of the use of flotation to upgrade spodumene. A review of the use of dense media separation (DMS), magnetic separation, and roasting as means to process spodumene bearing ores is also discussed. INTRODUCTION Lithium is a soft, silver-white alkali metal with atomic number 3. As of 2015, the end use of lithium was estimated to be as follows: lithium-ion batteries (35%), ceramics and glass (32%), lubricating greases (9%), air treatment (5%), continuous casting mould flux powders (5%), polymer production (4%), primary aluminium production (1%) and other uses (9%) (Jaskula, 2014). Lithium is found in brine lake deposits containing lithium chloride and in hard rock pegmatite deposits. It can be sold in a range of product types; as mineral concentrate, brine, compound (lithium carbonate or lithium hydroxide) and metal depending on its intended end use (Goonan, 2012; Jaskula 2014). In the 1990s the United States and Chile were the largest producers of lithium globally, primarily from brine operations (Ober, 1994). Most of the lithium compounds produced over this period were consumed in the glass, ceramics and aluminium industries. In the 1980s and 1990s there were two major lithium operations in the United States: brine operations at Silver Peak, Nevada, and a spodumene mine and lithium carbonate/lithium hydroxide plant in Kings Mountain, North Carolina. The Kings Mountain operations ceased production in 1991 and were eventually dismantled in 1994. Brine operations were also active in Argentina and Chile, while the largest lithium ore deposit in the world was operated at Greenbushes, Western Australia. During this period it was predicted that major shifts in demand for lithium would come from the success and widespread use of electric vehicles (Ober, 1994)."

Jan 1, 2017

By Jonathan K. Hrica, CASSANDRA L. HOEBBEL, Jennica L. Bellanca

Accidents involving powered haulage and mobile equipment such as haul trucks often account for the greatest number of fatalities in the mining industry each year. Despite previous analyses that have identified root causes and other contributing factors, there is still a need to better understand the events leading up to these types of accidents, what lessons may be learned, and what strategies can be employed to prevent fatal accidents from occurring. This study examines Naturalistic Decision Making (NDM) using the critical decision method (CDM). The CDM is a retrospective interview approach used to explore timelimited, high-stakes, decision-making. In this study the CDM is used to obtain more information about what happens prior to, during, and after a potentially fatal situation such as a near-miss event, loss of control, or minor accident involving equipment damage. Researchers captured firsthand accounts from 21 haul truck operators involved in near-miss events from mine sites of various sizes and commodities throughout the United States. These accounts provide rich and detailed narratives from the perspective of haul truck operators themselves and reveal insights into what decisions haul truck operators make, what sensory cues they perceive, and what strategies they employ during challenging and non-routine situations. Decision-related themes that emerged from the data are presented and discussed. These results, along with potential solutions offered by study participants, can help to inform future research, raise awareness about hidden hazards, and build more creative interventions and realistic training scenarios for use by the industry to address haul truck safety issues.

Feb 1, 2024

By Saghar Farajzadeh, Fatemeh Kazemi, Ataallah Bahrami

Spirals, the most common equipment for the separation of heavy minerals such as chromite, are greatly affected by size distribution and the liberation degree (hence the specific gravity and size) of the feed particles. In this study, the efficiency of spirals in separation of low-grade chromite particles has been investigated by studying the distribution of grade, size distribution and liberation degree of feed, concentrate, and tailings of spiral. For this purpose, mass balance constraints were applied to the spiral-containing chromite processing circuit. Afterwards, the grade variations and size distributions have been investigated. According to the results, when the feed to the spiral has a larger size distribution, the enrichment ratio of the feed is 1.32 and, with the smaller feed size, this value has increased to 1.99. When the spiral feed has a larger size distribution and higher specific gravity, the recovery of chromite increases with increasing particle size up to 250 microns, and then with increasing particle size, recovery decreases with a relatively steep slope. Evaluation of spiral efficiency with respect to particle liberation degree has also shown that despite the high degree of liberation of spiral feed in size fractions smaller than 75 microns (88.9%), the liberation degree of spiral concentrate and tail in this faction is equal to and less than that of feed, which can indicate poor spiral performance in these size fractions.

Oct 27, 2020

By D. Blackwell, W. R. Reed, G. Ross, S. Peters, M. Shahan

Dust collectors for roof bolting machines generally use a dry box to collect the roof bolting material. Recently, an underground mining operation converted a dry box dust collector to a wet box dust collector with a unique exception from MSHA for testing purposes.Water is routed to the roof bolter fromthe main water line of the continuous miner. The wet box utilizes a water spray to wet the incoming material. Testing was conducted comparing the two different collector types. Respirable dust concentrations surrounding the roof bolter with the different collection boxes were similar. The main difference in respirable dust concentrations occurred when cleaning the dust boxes. The average respirable dust concentration during cleaning of the wet box was 0.475 mg/ m3, and during the cleaning of the dry box, the average respirable dust concentration was 1.188 mg/m3, a 60% reduction in respirable dust concentration. The quartz content of the roofmaterialwas high, ranging from 28.9 to 52.7%during this study. The results from this study indicate that using the wet box as a collector reduced exposure to respirable dust up to 60% when cleaning the collector boxes.

Aug 26, 2020

By Ali Jaberi Zamharir, Abolfazl Shoghian‐Alanaghi, Hossein Aghajani, Arvin Taghizadeh Tabrizi

In this study, the leaching rate of molybdenite concentrate was evaluated in sulfuric medium, and the influence of the diverse oxidants including hydrogen peroxide, manganese oxide, copper sulfate on the leaching rate was studied. Also, the effect of the addition of the ethylene glycol to the hydrogen peroxide was studied and results showed that with the addition of ethylene glycol, the leaching rate is increased 55% from 41% up to 80.3%. The optimum condition is achieved as 0.7 M of H2SO4, 4.4 M of H2O2, and 3.5 M of EG at 30 °C within 4 h of leaching time and 500 rpm. Also, inserting the oxygen with the pressure of 6 bar to the leaching autoclave, the leaching rate is increased more up to 86.4%. Finally, the leaching process was studied kinetically and the determined mode of controlling factor was specified based on the activation energy which equals 46.252 kJ/mole indicating the chemical reaction mode.

Jun 5, 2022

By Yasutaka Izumi, Tuneyoshi Funasaki, Keizou Miki, Makoto Kanai

INTRODUCTION The Tokyo metropolitan region, inclusive of the three neighboring prefectures (Kanagawa, Chiba and Saitama), has the highest concentration of population and industry in Japan; with an area of 13,500 km2 or only 3.6 percent of the national land, but a population of 31.8 million or 26 percent of the national total, and a Gross Regional Product (GRP) of146 trillion yen (US$1.33 trillion) or 36 percent of the overall GDP of Japan as of 1990. Tokyo Bay, embraced by the metropolitan region as shown in Figure 1 (a), (b), is open to the Pacific Ocean as a marine gateway and is ringed by large cities and coastal industrial zones together with port facilities, all constituting a concentration of prime importance for socio-economic activities. The Trans-Tokyo Bay Highway (TTB highway), which crosses Tokyo Bay and provides a direct transportation link between the west and east sides of the bay, has long been a sort of “dream-come-true” project in Japan. As shown in Figure 2, linked to the Tokyo Bay Shore Highway, Metropolitan Inter-city Expressway, Tokyo Outer Ring Road, Tateyama Express-way, and others, it will play an important role as an integral part of the regional highway network to help promote spatial redistribution and multi polarization of urban functions, thus strengthening cooperation between cities and restructuring the metropolitan region. The TTB Highway is a project of 15.1 km in length designed as a toll highway to cross the bay by tunnel and bridge, and will require ten years to complete at a total cost of more than 1,438 billion yen (US$13.077 billion). Following more than 20 years of feasibility and environmental assessment studies, construction of this giant offshore highway project commenced in May 1989 as the first large-scale highway project with private-sector participation under the prevailing Road Law in Japan, and is now steadily proceeding toward the goal of completion in fiscal1997. This report outlines the entire TTB Highway project, including the waterproofing measures against high water pressure and the rapid construction method applied in the construction of shield tunnel sections.

Jan 1, 1997

By Hamid Mazouz, Mohammed Hakkar, Rim Jouraiphy, Fatima Ezzahra Arhouni, Ahmed Mahrou, Aziz Boukhair, Mohammed Fahad

The wet process is the most commonly used worldwide for phosphoric acid (PA) production, in which phosphate rock (PR) is reacted with strong acid mainly sulfuric acid. This work aims on studying the rare earth elements (REEs) distribution during the production of phosphoric acid using different qualities of phosphate through various industrial technologies. At the onset of this work, the process started with 12 samples of PR, PA, and phosphogypsum (PG) being taken simultaneously from two different Moroccan basins (Ouled Abdoun mine represented by K09 and Gantour mine depicted by G10, G20, BG) and various production lines at two processing platforms (Jorf Lasfar and Safi). Afterward, collected samples were prepared and analyzed for REE characterization using an inductively coupled plasma mass spectrometry (ICP-MS). Based on the analysis results, a transfer factor ( TFX) was introduced with the aim of gauging the REE distribution between PA and PG. The results showed that the total concentration of REEs in different phosphate qualities ranged from 411 to 631 ppm; the major part of this concentration was attributed to the four elements: Y, La, Ce, and Nd which constitute more than 77%. The REE distribution between PA and PG depends on neither the phosphate quality nor the industrial technology used since that the distribution results showed that 55 up to 66% of the initial REEs in phosphate rock ended up in the PG. The behavior of each REE was common except for the element scandium, which transferred mainly to the phosphoric acid.

Nov 3, 2021

By Kanhaiya Mishra, Phanil. K. Mandal, S. K. Behera, P. S. Paul, Prashant Singh, C. N. Ghosh

The techno-economic and social benefits of cemented paste backfill (CPB) resulted in its wide acceptance by the mining industry. The Ordinary Portland Cement (OPC) remains the key binder but to diminish its economical constraints, suitability of alternate binders has been examined worldwide. The present study aimed to investigate the effect of partial replacement of OPC with fly ash on the CPB’s strength and to determine the most optimal mix to achieve the required strength (1 MPa at 28 days of curing) at the most cost-effective way using the Bayesian network (BN). The CPB mixes were prepared at 72 wt.% solid concentration with mill tailings (87–91%), OPC (6–13%), and fly ash (0–4%), and instantly after mixing, fresh (slump, bleeding, density) CPB properties were measured. The strength was tested at 7, 14, 28, and 56 days of curing and initially analysed through traditional model. The traditional models follow the aleatory principle and are considered not appropriate for geotechnical engineering. Hence, the BN model was developed and tested. The reliability of two classifiers in learning model structure was compared which gives Naïve Bayes as the highest reliable tool. The CPB’s strength is most sensitive to the OPC content. The most consistent mix(s) is mill tailings: 87–88%, OPC: 9–11%, fly ash: 1–4%. Adding fly ash at 89–91wt% mill tailings possesses high failure probability of the CPB. The collinearity test indicates that the fines percentage and chemical composition of CPB’s ingredients are highly correlated with its slump, bleeding, and strength development.

Jul 14, 2022

By M. Sinirkaya

The dissolution process of phosphate rock from the Semikan area (Mardin-Mazidagi, Turkey) using dilute phosphoric acid has been investigated. The work involved studying the effect of important variables, such as reaction time, stirring speed, particle size fraction, phosphoric acid concentration and temperature. Van der Sluis et al.?s model was used to determine the rate of the partial dissolution of phosphate ore. Mass-transfer coefficients (kL) varied between 2.8 and 28.5.10-3 m.s-1. The activation energy of the process varied between 16 and 20 kJ.mol-1. It has been found that the dissolution process is controlled by calcium ion diffusion, rather than by chemical reaction.

Jan 1, 2010

By Richard L. Bullock

Believe it or not, mine evaluation and feasibility studies are as old as the industry itself. In the first recorded writing on mining by Agricola (1556), he gave several clues as what to look for in evaluating a mine, to determine if it was economically feasible. Below is the guidance from Agricola, with my interpretation of what he would include today. Now a miner, before he begins to mine the orebodies must consider seven things, namely: ? The situation (the geography/topography). ? The conditions (the geologic/mineralogic and mining conditions). ? The water (availability, hydrology and ownership). ? The roads (plus the railroads, power lines, all other infrastructure). ? The climate (the weather-rainfall/environment). ? The right of ownership (the land and legal entitlement). ? The neighbors (the social environmental concerns of the area). It is amazing how much of his guidance has not changed in 455 years. Yet Agricola gives no guidance on determining the correct cost, or determining the correct commodity pricing. But he does give a few words of caution on the related ethics involved on buying mineral properties: ?A prudent owner, before he buys shares, ought to go to the mine and carefully examine the nature of the vein, for it is very important that he should be on his guard lest fraudulent sellers of shares should deceive him.? Three hundred years later (1866), to further amplify this point, in the most famous thing that Mark Twain never said, as an introduction to a lecturer to an audience of gold-miners at Red Dog, CA, the famed author/humorist allegedly described a mine as ?a hole in the ground owned by a liar? (Farrar & Rinehart, 1935). So, one might conclude that between these two dates, the mining industry did little to improve its reputation. Unfortunately, since Mark Twain allegedly made those remarks, we have not done near enough to gain accountability for the mineral industry.

Jan 1, 2011

By Ken Deter

I have some general comments on optimizing profitability based on working in heap leach operations in tropical environments. Many of my planned comments this morning have been stated earlier in the Conference. I get the opportunity to say only a few words, and follow up on some specific comments and concerns. In normal operations, stack the ore higher, where possible. The surface area of the stacked ore controls the total solution volume that can be sprayed on the pad at a specific time period. With higher lifts, solution will contact more ore particles as it percolate through the lift, and therefore the solution grade flowing through the base will be increased, whether it is freshly stacked or almost completely leached ore. This also allows more tonnage to be stacked per lift on the pad, decreasing conveyor movement and downtime. Increasing from 6 to 8 meter (20 to 26 feet) lifts have worked successfully, and some mines are using 10 meter (33 feet) lifts in 10,000-15,000 dmtpd plants. The same concept will work with smaller plants, but initial 6 meter lifts should be used until the start-up period has shown the leaching is working as planned. As the stacked ore lifts get higher, the solution flowing through the highest lift is diluted by solution retained in the lower ones. Eventually no real increase is noted from putting fresh ore in service, and gold production rate suffers. To address the dilution problem, an HDPE liner should be installed between each 2 to 4 lifts, depending on each site specific lift height, recovery, % slump in the lift, recovery rates, and grade treated, among others. The surface of the previous lift should be leveled and sloped to control the effluent draining from the planned lift, then the liner is placed, including berms and discharge pipes. The intermediate HDPE liner does not need to be completely sealed as would be the case with the base liner, and can accept some solution penetrating into the lower lifts. A one-mm (40-mil) thickness liner can be used. This intermediate liner allows the upper lift(s) higher-grade effluent to report to the pad discharge point. This will maintain higher gold solution grades going to the ponds. The slopes of the previous lifts should not be covered with HDPE in this concept, and precipitation falling on the lower lift slopes and benches can be directed to barren or surge ponds.

Jan 1, 1999

By Floyd C. Bossard

In underground mining operations, the over- riding issue has to be protection of worker health and safety. The employees underground, making a living in a dangerous occupation, know these are major issues. These men bargain their lives and health on the presumption that the operating management knows its business, and they, the underground employees, can pursue their occupation with the assurance that management has provided a safe and healthy ambient underground environment. When management assumes the mantle of protection of underground workers, it has to be positive that qualified engineers have designed the project, and that capable operating personnel are in charge and always available. Those persons with these responsibilities must be knowledgeable in the engineering and occupational health aspects of sine ventilation. The ultimate function of a mine ventilation system is to provide a comfortable, healthy and safe ambient environment for the underground workers. The attainment of these objectives has been complicated with the increased application of electrical equipment and diesel-powered mechanized mining equipment underground (discharging toxic diesel emissions); increased production rates with the attendant increased production of airborne dust; and mine development in increasingly hostile mineral formations containing combustible strata gases, radon gas emissions, along with high heat and humidity. In general, the modern mechanization of present mining operations has resulted in a sore complex set of problems for the engineer planning the underground ambient environment.

Jan 1, 1983

By MOHAMMED AMINE BELMI, ANAS DRIOUCH, ABDELAZIZ LAHMILI, LATIFA OUADIF

For many years, underground workings in the Bou Azzer mine have been challenged by geotechnical problems related to the serpentinite instability. The stage of evaluation of the compression potential is crucial to develop an appropriate drilling method and the choice of non-standard support. This research work presents a retro-analysis of serpentinite behavior in underground excavations at different depths, using a multi-approach method, based on several empirical and semi-empirical and theoretical-analytical methods, calibrated by the observational method. The analysis performed in this work reveals that underground excavations in Bouazzer East and Ait Hmane area would encounter compression problems that were recognized as the most serious from a depth of 300 m because of the effects of lithology and tectonics. Therefore, the Aghbar region has a slightly negligible compression potential. The compressive failure mechanism in this mine, depending on the mechanical strength, is started at induced stress of 9 MPa.

Nov 27, 2021

By M. P. Roy, P. K. Singh, A. K. Mishra, Ashish K. Vishwakarma, Vivek K. Himanshu

Ground vibration is one of the major hazards produced by rock-blasting operation. The accurate prediction of vibration is necessary for designing controlled blasting parameters. The existing vibration predictors consider maximum explosive charge weight per delay and distance as the parameters responsible for ground vibration. These predictors are based on the assumption that the geometrical parameters of the blast will be constant for a site. However, the mining sites with bigger production targets have varying geometrical parameters to suit the excavator utility. Accordingly, the other blast design parameters will also have an impact on ground vibration intensity. A principal component analysis is a dimension reduction technique. This technique along with multivariate logarithmic regression has been used in this paper to predict the ground vibration. The technique has classified the blast design parameters into four principal components. The regression with the scores from these principal components has been carried out. The evaluation of the model performance of predictors along with the existing empirical predictors has been carried out using R2 and RMSE values. The evaluation suggests that the predictor with logarithmic regression followed by principal component analysis gives better performance with respect to the existing empirical predictors.

Jul 30, 2022

By A. B. Cecala

The Bureau of Mines performed a study to determine optimal locations for longwall face methane monitoring equipment. Longwall face ignitions continue to be a concern to the U.S. coal mining industry. Gains in ignition control technology have been somewhat negated by advances in longwall productivity. More reliable, heavy-duty longwall face systems generate higher production rates and increase methane liberation rates. These rates will likely continue to rise in the future as further coal production increases occur. Efforts will continue in the areas of methane drainage, methane containment, and methane dilution. In addition, more effective face methane monitoring is needed. As technology continues toward automated longwall panels, the importance of monitoring for methane at the shearer becomes even more significant. Since the primary face ignition source is the shearer mining machine, the Bureau ran tests to determine the best location to take methane readings on the shearer. This information, in conjunction with data obtained from field studies, provides a knowledge base for selecting optimum face methane monitoring locations.

Jan 1, 1993

By C. Villa Diniz

It is proposed that battery grade Mn02 can be produced directly from a manganese ore from Azul Mine in Brazil, by leaching with HCI to remove heavy metals selectively. We are working to find a way of selectively separating Cu, Ni, Co, Pb and Fe from the resulting acidic manganese chloride solution, to detoxify it and produce marketable chloride solution. Chelating ion exchange resins are proving more promising for this separation than solvent extraction with commercially available reagents. Results from batch and column ion exchange tests that characterize the behavior of copper, nickel, cobalt, lead and iron are reported.

Jan 1, 1999

By R. Y. Wan

Acid ferric sulfate solution has been used for heap and dump leaching of low-grade chalcopyrite ores and is being considered as a possible lixiviant for the hydrometallurgical processing of copper sulfide concentrates. For many years, researchers have attempted to explain the leaching behavior of chalcopyrite, since the reaction rate kinetics are extremely slow and seem to be significantly influenced by the nature of the reaction product. A summary of conclusions drawn from reported literature on chalcopyrite leaching is found in the paper by Munoz, Miller, and Wadsworth(1) and more recently by Dutrizac.(2) Lowe(3) and Jones and Peters (4) attributed rate control to a surface reaction. Linge,(5) Dutrizac,(6) Bauer,(7) and researchers at the University of Utah(1,8) reported that the reaction rate is limited by transport in the chalcopyrite lattice or through the elemental sulfur reaction product layer. Munoz et al.(1) presented a model, derived from the Wagner theory of oxidation, which is based on the formation of a protective sulfur layer with rate control by electron transport through the insulating sulfur layer. By utilizing Wagner's parabolic oxidation relationships, (9) the following equation was obtained: [ ] where a is the fraction of CuFeS2 reacted at time t, pB is the molar density of CuFeS2, do is the initial diameter of the particle, e is the electronic charge, s is the total electrical conductivity of the sulfur layer, and ?G is the Gibbs free energy for the reaction:

Jan 1, 1984