Search Documents

By Robert S. MacPhail, Chilombo Henry, Arnold Kabamba, David Mukelebai, Suresh Thirunagari, Bukali Victor, Yoram Kapai, Chomba Leonard, Kanna Amarasingham

"FLEX 31 is a chemically enhanced sodium isopropyl xanthate. Developed by Charles Tennant & Co (Canada) Ltd and has shown improved collection properties over SIPX for sulphide minerals flotation. Improvement of recoveries, grades, faster kinetics, lower dosages, high pyrite and pyrrhotite rejection capabilities have all been exhibited by FLEX 31. Recent plant trial carried out in the copper circuit at one of the largest copper mine in Zambia shown over US $ 2.00 Million annual improvement on the bottom line over SIPX at current copper prices. Data produced also showed superior grade and recoveries from rougher concentrates that previously had not been attainable with other reagents effectively. Flex 31 has also shown positive outcomes with zinc, Copper/Zinc, arsenopyrite and copper/molybdenum ores.IntroductionSodium Isopropyl Xanthate (SIPX) is one of the most popular flotation chemicals on the market today. Somewhat more specific than amyl xanthate, SIPX is used in a variety of ores like copper/zinc, lead/zinc, arsenopyrite/pyrite, and many others (Melis et al., 1991). An investigation carried out by the research division of Charles Tennant & Company (Canada) Limited has produced a chemically enhanced SIPX. This product has shown all the advantages of normal SIPX along with improved recoveries of copper and copper activated minerals. The product was named “FLEX 31”."

Jan 1, 2016

By Louis D. Huntoon

CANADIAN gold production is forging ahead annually and the prospects are that it will continue to do so for many years. Table 1 shows recent annual increases. Production for 1933 will probably reach $70,000,000, and further increases are likely in 1934 and 1935. (Data for November and December, 1932, are estimated throughout this article.) The depression sent many prospectors to the woods so during the last two years many new gold areas have been discovered and are attracting real capital for exploration and development. Several mills came into production in 1932 and mills now under construction will start production in 1933. The offices of mining lawyers are busy. Capital for this new work is obtained from well financed mining companies, syndicates, and individuals who were fortunate enough to invest in the dividend-paying gold mines of the north country in the early days. Prospectors and capital are cooperating. An interest is always retained by the prospector or vender and usually a small amount of real money is given the prospector.

Jan 1, 1933

By G. A. Grandy, P. F. Thomas, C. D. Danecki

When considering the mill drive system for a grinding application, a large number of questions must be answered. Depending on the mill size and type, the mill can be driven by several configurations of drive systems: a single low-speed motor connected to a pinion driving a ring gear, two low-speed motors connected to two pinions and driving a ring gear, or a gearless motor mounted directly. In addition, a gear drive system can have a reducer placed between a high-speed motor(s) and pinion(s) or a power path splitting pinion stand. In some designs the reducer is integral with the pinion stand driven by a high-speed motor. The technical and commercial implications of several mill drive options are presented. Initial cost, cost of installation, cost of commissioning, and cost of operation and maintenance are presented for each drive option considered. The impact of each drive system on the design, cost and operation of the overall plant electrical system is discussed. Also, consideration is given to mill drive availability, and the potential cost resulting from delays in plant production.

Jan 1, 2001

By William B. Hughes

The rubber-sleeve core barrel was developed to improve core recovery from unconsolidated sands, where it is most difficult to obtain cores with conventional barrels. The use of a rubber-sleeve core retainer, together with other departures from clsual design, has required a considerable amount of testing to prove its op-erability. Tests run in shallow experimental holes and in drilling wells in the U. S. and Vemzuela have, to a large extent, proved the operation of the barrel. Internal mechanism troubles, such as sandbinding of the sleeve, have been largely overcome. Cores have been recovered from completely unconsolidated sands where conventional coring has almost been abandoned because of poor recovery. In addition to retaining the core until brought to the surface, the barrel gives a "packaged-ar-cut" core, which is coilverzient for handling and transportatiorz. In the initial work, drag blade cutters, roller cutters, and tungsten carbide insert cutters were usrd for cutting unconsolidated sands. Further bit head development is presently being conducted using diamond heads in unconsolidated sands where shaler, hard sands, and limestones are encountered in adjacent formations. Thir work should render the barrel capable of cratting and recovering most types of formations, possibly including broken and frac- tured fornlations. This development is being carried on in cooperation with a diamond bit manufacturer. INTRODUCTIO N For many years the oil industry has needed greater recovery of cores from unconsolidated formations. Conventional equipment has been used to core unconsolidated sands with little success. Specifically, a core barrel was needed which would recover unconsolidated sands in a condition that would give useful reservoir information. DEVELOPMENT OF 'THE RUBBER-SLEEVE CORE BARREL Basic Requirements of Unconsolidated Sand Corino The basic need was defined as a core barrel that would obtain a continuous unconsolidated core with sand grains in place as deposited in the formation. A preliminary survey of coring equipment and search of the literature pointed out the weaknesses of conventional core barrels. Laboratory tests using unconsolidated sand in a metal tube simulated actual sand movement into the core barrel during conventional coring. In conventional barrels the core sometimes crumbles and bridges, or fails under compressive column action, becomes oversize, and wedges against the walls of the inner barrel. The core barrel requirements established by the surveys and preliminary tests are as follows. 1. The core should be held to- gether as it is cut so it cannot crumble and bridge against the walls of the coring tool, care being taken not to permit damage from fluid circulation. 2. The core should be continuously supported as it is cut so it will not have to support itself in compression. 3. The core should be packaged in the barrel to retain an undisturbed condition during the trip out of the well. The packaging should be such that the core can be removed from the barrel and shipped to the core analysis laboratory without physical disturbance or alteration of fluid content by exposure to the atmosphere. Operation of the Rubber-Sleeve Core Barrel The rubber-sleeve core barrel (Fig. 1) meets the basic requirements for the recovery of unconsolidated sands.

By Otto Ruhl

The zinc-lead ore reserves of the Tri-State district of Kansas, Missouri, and Oklahoma, as of December 31, 1947, are estimated at a total of 66,100,000 tons of crude ore containing 2.18 percent metallic zinc and 0.38 percent metallic lead. The Bureau of Mines began estimating the reserves in October 1945 and completed the' work December 31, 1947. A total of 38,900 acres of land representing approximately 5 percent of the area of the district is covered in this report. The work was confined for the most part to properties developed or partly developed by drilling and underground workings, and to acreage sufficiently drilled out to indicate ore of enough tonnage to make a commercial undertaking. The acreage in which ore reserves exist is widely distributed in all three States. A map of the Tri-State area is shown in figure 1. The remaining 95 percent of the area is not necessarily nonproductive but represents, possibilities for future exploration and development of additional mineral resources when and if economic conditions or national necessity encourage such work. Of the total reserves, 41 percent are in Missouri, 38 percent in Kansas, and 21 percent in Oklahoma.

Jan 1, 1949

By W. C. Holliman

Commercial production of synthetic rubber in the United States became a reality in 1931 when E. I. duPont de Nemours, Inc., announced the manufacture of Duprene, a synthetic rubber made by polymerizing r chloroprene. Duprene was later improved and reintroduced as neoprene. Since 1931 other synthetic rubbers and rubberlike materials have been announced and are now produced commercially or are in the pilot-plant stage in the United States. These include Thiokol, Buna S, Perbunan, Koroseal, Vistanex, Flamenol, Ameripol or Hycar, Chemigum, Butyl rubber, and Flexon. None of these is synthetic rubber in the strict chemical meaning of the word synthetic, as none is identical in chemical structure with natural rubber. However, all possess some of the physical properties of natural rubber, and in addition usually have some outstanding property not found in natural rubber that makes them superior for certain uses. Because of these superior qualitites, a considerable demand had arisen for synthetic rubbers before the present emer¬gency, although the price was several times that of natural rubber.

Jan 1, 1943

By Fabiano Mendes

Processos industriais de carbonização são tecnologias maduras e operam há mais de 7 décadas. Contudo, o sistema integrado de produção de ferro primário e aços a base de biomassa como fonte de energia e termorredutor, mesmo sendo a alternativa ambiental de menor impacto existente, chega a seus limites tecnológicos, ambiental e econômico, ameaçando a sua sustentabilidade. O grupo Vallourec buscou o processo Lambiotte como base tecnológica para desenvolver seu ambicioso projeto de carbonização contínua, em substituição ao processo artesanal de fornos retangulares de batelada, utilizados atualmente. O esforço experimental de mais de meia década, com a adaptação e profunda reengenharia do processo Lambiotte, que é o que melhor representa esta classe de reatores, para que ele atendesse as condições brasileiras e o uso das espécies de madeira da família dos Eucaliptos culminou no desenvolvimento do processo de carbonização continua Carboval, que demonstrou sua plena capacidade, para atender aspectos econômicos, sustentáveis e de qualidade siderúrgica do carvão vegetal produzido.

Aug 17, 2017

By A. Pellegrino, F. Collin, C. Guiducci, R. Charlier

A numerical approach for modeling coupled Hydro-Mechanical fracture behavior in 2D is presented in this paper. This approach accounts for the strong dependence of the flow characteristics on fracture apertures and offers an anisotropic description of the flow propagation in the fracture. An interface finite element and a constitutive model are developed . In order to validate the applicability of the model to general geomechanic problems, 2D simulations were performed. Results show the good application of the mathematical model and the fundamental hydraulic role played by the fractures. In diesem Beitrag wird ein Stoffgesetz vorgeschlagen um hydromechanisches Kluftverhalten numerisch zu Modellieren. Dieser Vorgang nimmt die starke Abhängigkeit der Fliesseigenschaften von der Kluftöffnung mit in Anbetracht. Ein Interfaceelement und ein Stoffgesetz wurden entwickelt. Zum validieren der Anwendbarkeit dieses Modells wurden 2D Simulationen durchgeführt. Ergebnisse haben gezeigt dass das mathematische Model anwendbar ist und dass Klüfte eine fundamentale hydraulische Rolle spielen. Une approche numérique pour la modélisation du comportement couplé hydro-mécanique des fractures en 2D est présentée dans ce papier. Cette approche prend en compte la forte dépendance des caractéristiques du flux de fluide sur les ouvertures des fractures et présente une description anisotrope de la propagation du flux dans la fracture. Un élément fini d'interface et un modèle constitutif sont développés. Dans le but de valider l'applicabilité du modèle à des problèmes généraux de géomécanique, des simulations 2D ont été réalisées. Les résultats montrent la bonne application du modèle mathématique et le rôle hydraulique fondamental joué par les fractures.

Jan 1, 2003

By C. J. Allen, L. Battiston

"Introduction It has long been recognized by the hot-dip galvanizing industry that the characteristics of the galvanized coating can be influenced significantly by steel and pro cessing variables. Probably the variable of most concern to galvan izers today is steel chemistry. More specifically, the problem is the excessive reactivity of continuously-cast, silicon-bearing steels. In the past, structural steels processed by general galvanizers were in the low-to-medium ca rbon category and contained silicon at either low impurity levels (as with rimmed steels), or less than approximately 0.10% (as with semi-killed steels). The structures of the coatings produced on such steels are characterized by dense, compact layers of delta and zeta iron-zinc alloy phases and a distinct outer layer of eta zinc, which usually imparts a bright shiny appearance to the coating. The presence of silicon in steel, above the so-called semi-killed levels, is known to cause marked stru ctural changes in galvanized coatings. Such coatings are characterized by a relatively thin delta layer, a thick , coarse zeta layer and frequently an absence of the eta layer. The eta phase, comprising zinc which is carried out of the bath during withdrawal of the work, can be consumed by the continuation of the coating reactions until its temperature drops to the solidification point. This results in a dull grey and often mottled surface instead of the usually bright metallic appearance. These galvanized coatings are usually much thicker than coating specifications requ ire and they are usually more brittle and have poor adhesion to the steel. In service, these coatings tend to develop a rust-like discolouration. With the wider use of continuous casting by the steel producers and the associated additions of silicon in this process, the problem is becoming more important and receiving greater attention from the galvanizing industry ."

Jan 1, 1987

By B Xiao, J Yang, H Chen

"An EXTENDED ABSTRACT is available for download. A full-length paper was not prepared for this presentation. The Tuwu-Yandong Cu deposit, located in the East Tianshan mountains in the eastern section of the Central Asian Orogenic Belt, is the largest and economically most important porphyry Cu deposit in Xinjiang, China. It contains ~3 Mt of copper at an average grade of 0.46 per cent Cu and 0.2 g/t Au, with significant amounts of Mo and Ag. The deposit is mainly hosted in the Carboniferous Qi’eshan Group and plagiogranite porphyry, and is controlled by faults that are east–west-, north-west- and north-east-trending. Ore minerals in the Tuwu-Yandong deposit are dominated by pyrite, chalcopyrite and molybdenite, with minor bornite, chalcocite, magnetite, sphalerite and galena. Gangue minerals are mainly composed of quartz, sericite, chlorite, epidote, anhydrite, gypsum, muscovite, biotite, phosphorite, sphene, dolomite, actinolite, barite, albite and calcite. Based on the megascopic and microscopic textural relationships and mineral assemblages, five stages of hydrothermal alteration and hypogene mineralisation are recognized in the Tuwu-Yandong Cu deposit: the potassic stage, propylitic stage, phyllic stage, late veins stage and supergene stage. Most of the copper was deposited during the phyllic stage, along with less molybdenite.CITATION:Xiao, B, Chen, H, Wang, Y and Yang, J, 2015. Geology, mineralisation and alteration of the Tuwu-Yandong porphyry Cu deposit, north-west China, in Proceedings PACRIM 2015 Congress, pp 641–644 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Mar 18, 2015

By A. López-Valdivieso, M. A. Corona-Arroyo, M. Llamas-Bueno

Magnetite (Fe3O4) ore is concentrated by low-magnetic-field drums to recover a magnetite concentrate that is low in silica (SiO2). The presence of SiO2 in the magnetite concentrate for steel production increases the steel processing costs, so a major challenge in magnetic concentration is to lower the SiO2 grade in the Fe concentrate. This work presents studies that were carried out on the removal of SiO2 from the magnetite concentration at the plant scale. Studies were performed with a three 36 × 96″ drum unit processing 46 ton/h of rougher magnetite concentrate. These studies showed that silica appears in the magnetite concentrate by three mechanisms, namely SiO2 entrainment in Fe3O4 chains, heterocoagulation between Fe3O4 and SiO2 particles, and mineral locking of SiO2 to Fe3O4. The SiO2 entrainment mechanism had the highest contribution (75%) to the SiO2 recovered in the Fe concentrate. Electrokinetic studies on Fe3O4 and SiO2 showed that heterocoagulation occurs because of the low negative zeta potential of the minerals at the pH of the plant slurry. This study also showed that a high percentage of ultrafine size SiO2 particles trapped in Fe3O4 agglomerates was not removed by the dilution water for the slurry fed to the drum. To lower the SiO2 recovery in the drum magnetic concentration process, work should be directed towards the removal of trapped SiO2 in Fe3O4 agglomerates.

By Fred P. Gerbracht

Jul 20, 1955

By Rambabu Pothina, Rajive Ganguli

The economics of a mineral processing circuit is dependent on the numerous sensors that are critical to optimization and control systems. The sheer volume of sensors results in mines not being able to keep the sensors calibrated. When a sensor goes off calibration, it results in errors which can severely impact plant economics. Normally, these errors are not detected until the error grows and becomes a large (“gross”) error. Undetected errors are not remedied until the next calibration, which on average are a year apart Beamex (2019) [1] across all industries. Classical statistical methods that depend on linear relationships between input and response variables are typically used to find gross errors, but are not effective for highly non-linear and non-stationary operations in mining and mineral processing industries. Calibration of sensors is time-consuming and generally requires physical intervention that results in equipment downtimes causing production losses. Therefore, in situ detection methods are warranted that do not require physical removal of sensors to compare with standard measurements or well-calibrated sensors. Data-mining based techniques and algorithms have high success rate in tackling such problems. This paper presents results from a groundbreaking multi-year big data research project whose goal was to develop data-mining-based original techniques in a multi-sensor environment to identify when sensors start to stray, rather than wait for errors to grow. The carbon stripping (gold) circuit in the Pogo Mine of Alaska was selected for this project. Maintaining strip vessel temperatures at optimum levels is crucial for maximizing gold recoveries at Pogo, and hence the focus was on the temperature sensors of the two strip vessels. An automated algorithm to detect errors in strip vessel temperature sensors was developed that exploited data from multiple sensors in the strip circuit. This algorithm was able to detect with a high success rate when bias errors of magnitude as low as ± 2% were artificially induced into strip vessel temperature data streams. The detection times of about 1 month were much less than the industry average calibration frequency of 1 year. Thus, the algorithm helps detect errors early, without stopping the circuit. The algorithm alarms can serve as triggers when calibrations are done. Experimental methodology along with results, limitations of algorithms, and future research are also presented in this paper.

By Rambabu Pothina, Rajive Ganguli

The economics of a mineral processing circuit is dependent on the numerous sensors that are critical to optimization and control systems. The sheer volume of sensors results in mines not being able to keep the sensors calibrated. When a sensor goes off calibration, it results in errors which can severely impact plant economics. Normally, these errors are not detected until the error grows and becomes a large (“gross”) error. Undetected errors are not remedied until the next calibration, which on average are a year apart Beamex (2019) [1] across all industries. Classical statistical methods that depend on linear relationships between input and response variables are typically used to find gross errors, but are not effective for highly non-linear and non-stationary operations in mining and mineral processing industries. Calibration of sensors is time-consuming and generally requires physical intervention that results in equipment downtimes causing production losses. Therefore, in situ detection methods are warranted that do not require physical removal of sensors to compare with standard measurements or well-calibrated sensors. Data-mining based techniques and algorithms have high success rate in tackling such problems. This paper presents results from a groundbreaking multi-year big data research project whose goal was to develop data-mining-based original techniques in a multi-sensor environment to identify when sensors start to stray, rather than wait for errors to grow. The carbon stripping (gold) circuit in the Pogo Mine of Alaska was selected for this project. Maintaining strip vessel temperatures at optimum levels is crucial for maximizing gold recoveries at Pogo, and hence the focus was on the temperature sensors of the two strip vessels. An automated algorithm to detect errors in strip vessel temperature sensors was developed that exploited data from multiple sensors in the strip circuit. This algorithm was able to detect with a high success rate when bias errors of magnitude as low as ± 2% were artificially induced into strip vessel temperature data streams. The detection times of about 1 month were much less than the industry average calibration frequency of 1 year. Thus, the algorithm helps detect errors early, without stopping the circuit. The algorithm alarms can serve as triggers when calibrations are done. Experimental methodology along with results, limitations of algorithms, and future research are also presented in this paper.

By Guy Deschênes

Thiourea solutions can be used as leach liquors to treat gold ores or slimes. It is also efficient to elute resins or strip solvents that were loaded in cyanides solutions. The hydrogen pressure reduction is a practical step to recover gold and silver from leach solutions, and strips and eluates without any destruction of thiourea. It is a critical point because these processes have to consider the recycling of the liquors to be irore economical. The effect of temperature, pressure, acidity, compotation of the solution and the nature of catalysts on pressure reduction by hydrogen were investigated. An electranetallurgical study was? carried out to investigate the mechanism. The composition of the products was studied by different analytical methods. The process shows a good selectivity to precipitate gold and silver in a thiourea solution containing iron and copper. Gold and silver concentrations can be decreased to 0.2 ppm and 0.1 ppm at respectively 70 KPa H2 and 28°C. No decomposition of thiourea was evident during the tests. Metals such as nickel powder or platinum activate the reaction and improve the reduction.

Jan 1, 1989

By King R. L

Low-enthalpy geothermal groundwater resources occur at relatively shallow depths in the Upper Cretaceous/1'ertiary sedimentary sequence in the on-shore Gippsland Basin. The main stratigraphic unit containing hot groundwater is the Latrobe Group. Groundwater temperatures in the range 30 to 70¦C have been recorded from depths between 500 and 1000 m. The hottest groundwater is in the Latrobe Valley and Lake Wellington depressions. Geothermal gradients in these areas range from less than 2¦C/100 m to over 10¦C/100 m (compared to a world average of about 3¦C/100 m). A number of theories have been advanced to explain the geothermal anomalies including exothermic reaction such as oxidation of coal, mixing with deeper, hotter groundwater and high geothermal fluxes along fault zones. Variations in geothermal gradients can also result from type and thickness (and hence thermal conductivities) of the sedimentary pile, depth to consolidated basement rocks, and influence of groundwater flow patterns including proximity to recharge zones. The hot groundwater in the Gippsland Basin has substantial potential as a source of energy for direct heat applications such as process heating, space and water heating for buildings, and agricultural and aquaculture. Geothermal energy has a number of environmental advantages over traditional sources of energy. It is clean, safe, causes minimal land disturbances and in most cases is naturally renewable.

Jan 1, 1992

By R K. W Merkle, S Madoom Hussain, T Yellappa

Cr-Ni-Cu¦PGE deposits are known to occur in early Archaean mafic-ultramafic rocks. Early Archaean mafic-ultramafic (MUMF) rocks occur in the western Dharwar craton and range in size from small pods to schist belts. These MUMF pods consist mainly of meta-peridotites, tremolite-actinolite schists, serpentinites, amphibolites and metabasalts. Spinifex, nodular and ocelli textures are also present. The rocks have been subjected to greenschist and amphibolite facies metamorphism. Geochemical studies were undertaken to evaluate the possible occurrence of economically important elements in the mafic-ultramafic enclaves around the major Arsikere-Tavarkere lineament and surrounding gneissic terrain adjoining local shear zones that occur as discontinuous pods between Arsikere and Chennagiri. Talc-serpentine and tremolite- actinolite schists contain chromite which is rimmed by ferrit-chromite. A notable feature of these MUMF rocks is that they exhibit high MgO (22 - 40 per cent), total iron (8.34 - 10.01 per cent), Ni and Cr (~3000, 2800 ppm) contents, with some samples showing komatiitic affinity. The rare earth elements (REE) data show slightly fractionated patterns with enriched LREE (LREE/HREE ~5.0) and negative europium anomalies. The Pt and Pd values reach 6500 and 191 ppb. The MUMF rocks, especially those exhibiting high chromium contents and occurring near shear zones, are potential hosts for economic platinum group element (PGE) deposits.

Jan 1, 2008

By John E. Rourke, O&apos

This report documents the process of site selection, instrument installation, data acquisition, and preliminary data analysis followed to characterize the physical response of overlying strata to longwall mining. A system of surface, subsurface and mine level instrumentation was installed at the Allen Mine in Weston, Colorado where the overburden varied in thickness from 600 to 900 feet. Survey monuments, automatic-recording strain-meters, multi-point rod extensometers, inclinometer-extensometers, stressmeters and tape extensometer convergence stations were installed to monitor displacements and stress changes. A preliminary analysis of the data acquired up until project termination has shown the system to be operative and strata response to be similar to that reported for other subsidence monitoring case histories. Recommendations for continued monitoring of the instrumentation systems are presented.

Jan 1, 1982

By J. G. George

A brief review of the silver industry is presented to set the stage for the analysis of the distribution of silver production by source from various types of mines in Canada and of the changing relationship between the total output of silver and the total output of base metals. The decline in the average grade of the Canadian mines is also discussed and a trend for the future is proposed. The report then examines in broader aspects the world primary silver production and concludes, in the section on outlook, that the effective supply in primary silver will grow at a rate significantly lower than the growth rate expected for base metals. A cumulative deficit of some 900 million ounces is projected for the period 1975-1980 and a further deficit of some 1,100 million ounces if projected for the 1980-to-1985 period.

Jan 1, 1977

By R. J. Charles

F. C. Bond: This is an outstanding paper on comminution theory and represents a considerable advance in mathematical formulation. It clears the way for a discussion that should ultimately decide whether the work index should be considered as a parameter according to the Third Theory or as a constant. In the empirical differential equation dE = —Cdx/x [1] either Corn must be treated as a variable to satisfy known crushing and grinding conditions. The author has chosen the exponent n as the variable, with C as a constant. According to the Third Theory, in the general case n is a constant equal to 3/2, and C is a variable related to the work index Wi. If x is placed equal to P (the size in microns which 80 pct of the product passes) and F is the size 80 pct of the feed passes, then C equals 5 W1, and dE = 5 -5 Widx/x = 10 Wi 10 Wi w = vP vF which is the basic equation of the Third Theory. It is apparent that this integration involves the error of treating the parameter Wi as a constant, just as the author's treatment involves the error of integrating his variable n as a constant. These errors are probably relatively unimportant, considering the small range of the variables. When more is known about the factors contained in the work index, Eq. 1 can be revised as a partial differential equation. The Third Theory exponent of 1/2, or n = 3/2 in the Charles' differential equation (Eq. l), was not chosen primarily because it is the average between the Kick and Rittinger exponents; this may be merely fortuitous, since it is illogical to define truth as the average between two errors. It was first discovered from the study of a large mass of crushing and grinding data and confirmed by laboratory testing. The general correspondence of the Third Theory equation to actual crushing and grinding results over the entire size reduction range argues strongly that a fundamental phenomenon is involved. The a posteriori theoretical explanation of the constant Third Theory exponent is that the work done in breaking rock is proportional to the length of the crack tips formed. Compressive force applied to the rock results in deformation and strain energy. When this locally exceeds the breaking strength a crack tip forms, the surrounding strain energy flows to the crack tip and extends it to split the rock, with release of the energy as heat. Under rapid impact the crack tip may form before the strain has reached equilibrium, resulting in less energy expenditure and probably a coarser product. In any case, the elastic limit of a brittle material is practically the same as its breaking strength, and the work necessary to form the crack tip is the work required to break. The crack length of a ton of broken rock cannot be measured directly. However, the particle shapes of feed and product are similar, and the crack length is considered equal to the square root of one half of the new surface area formed. It is, therefore, proportional to 1/vD, where D is the equivalent product particle diameter. This is the basis of the Third Theory equation. Many secondary factors can be imposed upon the crack length breakage. These may cause the Third Theory work index to increase or decrease somewhat as the product size becomes finer. The work index is properly a parameter rather than a constant, making it an increasingly valuable practical criterion of the work input required in crushing and grinding.

Jan 1, 1959