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By Michael P. Sudbury

Non-ferrous slags are granulated and stockpiled as an alternative to pit cooling or transporting molten slag to a dump. The chemical composition of such slag is determined by the pyrometallurgical process in which it is produced, while the size distribution is set by safety concerns or a desire to reduce wear of pumps, pipelines and other equipment. Relatively few operations give consideration to the effect of granulation conditions on other properties of the granulate as the material is typically accumulated on the smelter site. It is becoming recognized that slag has many potential commercial uses and carries much of the energy applied to the smelting operation. This paper outlines the findings of extensive work to identify uses for granulated non-ferrous slag, the importance of preparation conditions on the properties, impediments to more extensive use of granulated slag, the real costs of slag stockpiling and the opportunities for further productive research.

Jan 1, 2006

Jan 1, 1967

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By E. N. Pugh, J. V. Craig

WhILE it has been established that well-defined microhardness impressions can be produced in germanium by room-temperature indentation,1-3 the role of dislocations in the process is the subject of continuing discussion.4-7 Recently, Carroll and ~anaka'

Jan 1, 1969

Jan 1, 1971

By Charles White Merrill

Money is one of the most .pervasive elements in human life. The compensation for a workman's daily efforts is expressed as a wage and is measured in money. What an individual may consume depends largely on his income which also is expressed in terms of money. If he would start an enterprise its size would be determined in large part by the amount of money available for capitalization and its success would be measured in net income expressed in money. In short, the most widely used common denominator for comparing merchandise, real property, jobs, enterprises, gross national product, or personal success is money. Despite this use of money by almost everyone past infancy to express his appraisal of the in- numerable values he sees around himself, the complexity of the device called money makes its nature and workings a mystery to most users. Some of the difficulty in understanding money results from the fact that it has three distinct but interrelated functions: (1) a medium of exchange, (2) a unit of account, and (3) a store of value. In many statements about money the discussion moves from one function of money to another without the speaker or the listener recognizing the changes. For example, the housewife says "We took the money we had saved up to make the down payment and after twelve monthly payments the television will be ours." When this housewife spoke of "saving up the down payment" she referred to money in its function as a store of value; when she spoke of "the down payment" she was using money as a medium of exchange; and when she referred to the "monthly payments" she spoke of money as a unit of account. Another cause of confusion in understanding money is its paradoxical nature in that it represents both the power to produce and the power to consume. For example, when the rich uncle dies one nephew may regard his inheritance as an opportunity to buy a farm and leave the ranks of the wage earners to become an independent producer, whereas the other nephew may regard his portion as the means of living in complete leisure as a pure consumer.

Jan 1, 1959

By M. Hochenhofer

Due to economic aspects and environmental regulations recycling of slag and waste from ferroalloy production became a very important issue for the companies during the last years. The treatment of slag depends prior on the composition, especially on their content of valuable metals and impurities. The final aim should be a total re-use of these materials in the industry e.g. cement industry, pig-iron production etc.. Therefore, to reach the required physical and chemical properties for a further use, possibilities of a metallurgical treatment have been investigated. The conditioning of slag with a high V-, Mo- and P-content via reducing metal bath showed to be one alternative. To determine the optimal process parameters, practical investigations with different slag compositions and thermodynamic calculations were carried out.

Jan 1, 2006

By Taylor G. R

Fluid inclusions within quartz accompanying several stages of mineralization at Hillgrove are de cri bed. Pyrite-arsenopyrite-gold mineralization shows uncorrected filling temperatures of between 195°C and 250°C. Later stibnite-antimonide-siderite and stibnite-calcite mineralization has filling temperatures between 100°C and 195°C and a bimodal distribution of temperature peaking at 175°C and 145°C, possibly correlated with the two stages of mineral deposition. Secondary included fluids within an earlier generation of deformed quartz veins are derived from hydrothermal fluids contemporary with the main-stage mineralizing fluids described above. Primary inclusions within latestage, cross-cutting quartz-chlorite-calcite veins show these veins to be unrelated to the mineralization.A correlation between filling temperatures and salinities indicates that mineralization accompanied the mixing of a hot, partly saline, fluid (at 5 per cent equivalent NaCI) with cooler, less-saline meteoric or connate water. Over a vertical distance of 200 m, equivalent mineral assemblages were deposited over the same temperature range. Studies on single crystals suggest rapid deposition with fluid temperature dropping 45°C during their growth. Ore mineragraphy and the fluid inclusion data suggest that the metals were transported by sulphur-poor, relatively low-temperature, low-salinity solutions, possibly as carbonate complexe , and that a vertical zonation of the W-Sb-Au mineralization is compatible with the mixing of this hydrothermal fluid with cooler groundwater. Regional metallogenic and geological considerations suggest that ore metals are derived from the remobilization of deep-seated stratabound deposits or from metamorphic fluids expelled from deepseated volcanoclastic sediments.

Jan 1, 1984

By C. C. Hamilton, G. R. Lane

Traditionally, mineral sands are evaluated by preparing several mineral products using a combination of heavy liquid-, magnetic-, and electrostatic methods. Whole-rock assays (WRA) are then conducted on ilmenite, rutile and zircon products in order to determine trace element contents, which may affect project feasibility. Combined methods can be time consuming, expensive and even outdated due to the use of banned and toxic chemicals such as clerici solution. Coupled with large field-sample quantities, these procedures can potentially introduce unacceptable sampling and related errors. Modern mineralogical analysis techniques can provide complete mineralogical inventories on a single THM product, reducing the amount of processing involved in satisfactory characterization of early exploration samples. A small exploration sample can be processed to produce a small THM concentrate using readily available gravity/density methods. In turn, the THM product is submitted for Whole Rock Analysis (WRA) and mineralogical inspection by X-ray diffraction (XRD), and microscopic evaluation. Modal mineralogy and textural data can be determined using optical methods, automated image analysis, and scanning electron microscope (SEM) based systems. Benefits of automation are reproducibility and the capability of rapidly analysing thousands of particles as opposed to manual optical methods. Automated systems include the use of Automated Digital Image Analysis (ADIS), and SEM-based systems such as the Mineral Liberation Analyser (MLA) and QemSCAN. For detailed mineral chemistry, microanalysis techniques ranging from electron microprobe (EMPA) to Secondary Ion Mass Spectrometry and Laser Ablation Mass-Induced Coupled Plasma-Mass Spectrometry (LAM-ICP-MS) are used. Examples of these automated and analytical methods are presented. ADIS at SGS-Lakefield Research uses optical characteristics to identify and measure mineral species in THM samples; rutile, pseudorutile, ilmenite and leucoxene can be distinguished. Analysis of a single THM product provides bulk modal mineralogy and grain size distribution of particles and the individual mineral grains. Textural information is also obtained detailing mineral associations as well as degree of alteration. Where textural and chemical resolution renders mineral identification ambiguous, SEM-based methods offer better resolution. Examples of this ambiguity are shown in this paper, which leads to QemSCAN as the preferred method where within-grain variability is concerned. Sampling and measurement strategies are followed to meet study objectives, providing a value-added framework for a sequential, cost-effective strategy, which will meet due diligence and bankable accreditation criteria. Studying a THM product by electron microprobe and LAMICP-MS may reveal potential fatal flaws related to mineral chemistry. Low detection limits in the range of 200 to 500ppm are possible using electron microprobe analysis for suitable matrixes (U, Th in zircon). For the detection of ultra low level elemental contaminants, LAM ICPMS is the most accurate method of evaluation. Elements including U, Th, La, Ce, Nb, and V in Ti-minerals can be determined down to 50 ppm.

Jan 1, 2005

By D. J. Bowen

"The Great Dyke extends for 540 krn along strike, to unknown depth, and varies in width from 3 krn to 11 krn. Rb/Sr age determinations gives values of approximately 2470 Ma.The Dyke consists of a variety of mafic and ultramafic rocks, many altered to serpentinites. These include, from top to bottom, successions of gabbro/norites, pyroxenites, peridotiteslharzburgites, and dunites/picrites.The layers dip in from either margin, steepest at the edges (20°) and flattening toward the central sections. Four separate complexes are present. From north to south these are termed the Musengezi, Hartley, Selukwe and Wedza Complexes, and are described as 'boat-shaped' or 'pig-troughed'. All are similar in petrological sequences. Physiographically, the Dyke is spectacular in the north, where as a mountain range it meets the Zarnbezi Escarpment. Elsewhere in the central parts there is little surface expression and wide open treeless vleis. Dyke rocks cut through granite and schist belt terrain and are termed 'The Magnesia Belt'.Vast mineral resources exist. These include chrome, asbestos, platinoids, nickel, copper and gold. Up to eleven chrome seams numbered from top to bottom occur in the lower ultramafic sequences. Seams are narrow at 10 em to 30 em but of high grade. The platinum occurs 10 m to 40 m below the norite/pyroxenite contact.A 60 m wide zone of Light Sulfide Mineralization (LSM) of less than 1070 sulfides extends from the lower gabbronorites into the upper pyroxenites. In this LSM, four enriched zones carry up to 5% sulfides. The most widespread is termed the Main Sulfide Zone (MSZ), below which is No. 2, No.3 and No.4 Sulfide Zones. The MSZ carrying pyrite, pyrrhotite and chalcopyrite is a multielement ore with components of PGE (pt-Pd-Rh), nickel, copper and cobalt, and gold and silver.Extensive exploration programs have been carried out and the intention is to begin large-scale mining. However, with Russia supplying metals to the western markets, South Africa's cutback on production, and an end to the Cold War, delays have arisen."

Jan 1, 1994

By Bart Bartholomew, Randall J. Essex

INTRODUCTION In June of 2004, at the North American Tunneling Conference in Atlanta, an all-day workshop was conducted to review the application of Geotechnical Baseline Reports (GBRs) for underground construction. The moderator for the program was Bart Bartholomew, former President of Fruin Colnon Construction Company. The program involved commentary by a panel of engineers, owners, contractors, and legal representatives within the North American tunneling industry, as well as an extended audience discussion. The panelists were: Peter Douglass, President, Peter Douglass, Inc. Randall Essex, Executive Vice President, Hatch Mott MacDonald Joseph Gildner, Deputy Director for Technical Services, Sound Transit Randall Hafer, Esq., Kilpatrick Stockton Robert Fitzgerald Esq., Watt, Tieder, Hoffer, & Fitzgerald Kirk Samuelson, Senior Vice President, Kiewit Construction Group DEVELOPMENT OF PROGRAM FORMAT The focus of the program was to assess the state of the practice in the preparation of GBRs, and to discuss improvements that could and should be made with regard to their preparation, interpretation, and application. The approach used to achieve this focus in the broadest possible way was unique, in that it involved the panelists’ preparation of the workshop format and materials months before the presentation of the workshop. First, each of the six panelists was selected by the moderator based on their reputation and involvement in their respective fields of expertise, taking care to maintain balance and contrast within the collective pool of talent assembled. Following selection and agreement to serve on the panel, each panelist was asked to independently submit to the moderator a list of the six most pressing issues involving GBRs that they each frequently encountered in their individual professional experience. Each was asked to rank their issues in descending order of perceived importance. This process resulting in a pool of thirty-six potential or “candidate” issues for use in the workshop program. Contrary to the moderator’s expectations, there was surprisingly little duplication among the thirty-six issues submitted.

Jan 1, 2005

By T. R. Ellis

Considerable movement is afoot internationally to rationalize standards and regulations relating to valuations and the qualifications for valuation professionals. In July 2000 the International Valuation Standards Committee released expanded standards, and additional important improvements are planned by 2003. Possible updates to the International Accounting Standards (IAS) and potential adoption of IAS by the U.S. could significantly impact minerals appraisers. Standards designed specifically for mineral asset valuation are under development in Canada and the U.S., with Australia’s internationally respected VALMIN Code providing the benchmark. In the U.S., the all-encompassing Uniform Standards of Professional Appraisal Practice (USPAP) is annually modified and continues to gain deeper acceptance, while the SEC holds fast to its antiquated rule prohibiting reporting of a quantitative estimate and value for non-reserve mineralization. Some important international trade agreements are driving actions to free the trade in professional services. In July 2000, an international workshop was held to initiate discussion on minimum qualifications for appraisers to work internationally. Pressure for uniform minimum qualifications and rules for professionals internationally will continue to build. The U.S. is historically among the slowest countries to implement such initiatives, with its state level licensure barriers having the potential to cause some of its professionals to be stranded in an international backwater. Structural change is needed in Australia’s VALMIN Code to remove conflict with the latest International Valuation Standards. The mineral valuation standards developers of Australia, Canada and the U.S. should work jointly on updating VALMIN for global use.

Jan 1, 2001

Jan 1, 1963

By W. H. Young

PRODUCTION of bituminous coal and lignite increased substantially in 1964. There were upward trends also in consumption, average value, exports, mechanization, and productivity. However, a significant decline in employment continued. Production.-The output of bituminous coal and lignite in the United States in 1964-487 million tons-was 6 percent greater than the 459 million tons produced in 1963. The gain was attributed largely to expanded consumption by the electric utilities, greater use at coke ovens, and an increase in exports.

Jan 1, 1965

By T. T. Chen, J. E. Dutrizac, C. Canoo

The calcine consists principally of ZnO and ZnFe2O4, which occur as banded and porous grains, together with lesser amounts of Zn2SiO4, Zn-Fe-Pb silicate, sphalerite, quartz, PbSO4 and Fe2O3. Al is present in solid solution in most of the Fe-bearing phases and also as residual aluminosilicate minerals from the original concentrate. Si occurs mostly as Zn2SiO4, Zn-Fe-Pb silicate and as residual silicate minerals. As is commonly found in the ZnFe2O4, Fe2O3 and Zn-Fe-Pb silicate phases. The major As carrier may be calcium arsenate particles less than 1 micrometre in size which are dispersed throughout the calcine. The neutral leach residue consists mainly of ZnFe2O4 and precipitated masses of iron gel-silica gel. Lesser amounts of ZnO, Zn2SiO4, Zn-Fe-Pb silicate, PbSO4, sphalerite, Pb-K-jarosite and basic zinc sulphate are also present. Al occurs in minor concentrations in most of the Fe-bearing phases and in the Zn-Fe-Pb silicate. The residual aluminosilicates are also an important Al carrier. The major As carrier is the precipitated iron gel-silica gel phase, but some As is also present in the Zn-Fe-Pb silicate, ZnFe2O4 and Fe2O3 phases. Silicon is divided about equally between the iron gel-silica gel, Zn2SiO4, Zn-Fe-Pb silicate and residual silicate minerals. The weak acid leach residue is generally similar to the neutral leach residue except for its reduced content of ZnO and basic zinc sulphate.

Jan 4, 1993

By Herman L. Bauer

The Robinson Mining District near Ely, Nevada, is one of the major porphyry copper districts in the world. Within the district is an east-trending zone of altered porphyry, metamorphosed sedimentary rocks, and sulphide mineralization surrounded by Paleozoic limestone, dolomite, shale and sandstone, Tertiary volcanics, and Quaternary alluvium. Six major disseminated ore deposits have been exploited in this eight-mile zone. About 20% of the district production has come from disseminated ore in metamorphosed sedimentary rocks found adjacent to altered quartz-monzonite porphyry. The following brief statements summarize the inter-relationship of porphyry, alteration, metamorphism, and mineralization: 1. Disseminated copper ore does not occur in unaltered porphyry or in unmetamorphosed sedimentary rocks 2. Sedimentary rocks have been only weakly metamorphosed where intruded, by unaltered porphyry. 3. Intensely metamorphosed sedimentary rocks are found only adjacent to, altered porphyry. 4. Many hydrothermal minerals are common to both altered porphyry and adjacent metamorphosed sediments. 5. Disseminated ore is found in altered porphyry and adjacent meta¬morphosed sedimentary rocks. 6. In general, there is a direct correlation between grade of ore in porphyry and copper content in the adjacent rocks. 7. Chemical changes in the altered porphyry facies and metamorphosed rock facies appear to be related:

Jan 1, 1963

By T. Sun, J. Kou, C. Sun, China Railway Resources Group Limited

"The polymetallic sulfide ore in Jiama county of Tibet contains 0.78% Cu, 0.046% Mo, 0.31 g/t Au and 17.9 g/t Ag in average. However, heavy loss of valuable metals was observed using high-pH process and Butyl xanthate as the collector. In this paper, the flotation was optimized through the adoption of a novel collector C-7, which is a mixture of xanthate ester and thionocarbamate. This collector showed better flotation performance under weak base conditions. The recoveries of Cu, Mo, Au and Ag increased to 93.24%, 84.60%, 78.13% and 75.41%, respectively, under 15 g/t of C-7 at pH of 8.0. The adsorption mechanism of C-7 was investigated by micro-flotation tests, zeta potential measurements, FTIR analysis and adsorption quantity measurements. Chemisorption of C-7 on chalcopyrite surface is demonstrated with adsorption density 3.8 times higher than on pyrite.INTRODUCTIONXanthates are the most commonly used collectors of strong collecting ability for separating copper sulfide minerals from gangue in froth flotation. However, the selectivity of xanthates themselves is poor to realize separation of chalcopyrite and pyrite whose floatability are quite similar (Heyes & Trahar, 1977; Chandraprabha, Natarajan, & Modak, 2004). High pH process with xanthates as collectors is proved effective in copper-sulfur separation and is widely used in treatment of copper sulfide ore flotation (Smith, 1996; Valdivieso, Cervantes, Song, Cabrera, & Laskowski, 2004). This method could get ideal separation results, but large amount of lime must be added, and could bring about increased cost, device corrosion and environmental pollution. In addition, there could also be high depression and heavy loss of associated noble metal such as Mo, Au and Ag. Consequently, a large amount of research has been conducted on substitutions of xanthates for selective flotation of copper sulfide ores under low pH conditions (Gholivand, Khodadadian, & Ahmadi, 2010; Li, 2010)."

Jan 1, 2016

By Trevor L. L. Orr

"AbstractThe background to the harmonization of geotechnical standards that has taken place in recent years in Europe has been the move to more economic and political integration following World War II that has led to the formation of the European Union. Prior to 2010 the standards used in the European countries for geotechnical design, investigation and testing and for the carrying out geotechnical work, such as the installation of piles, were the different national standards, which were not harmonized. The harmonization of geotechnical standards in Europe started in 1981 with work on a model Eurocode 7 for geotechnical design that led eventually to publication by CEN, the European Committee for Standardization, of the European Standard version of Eurocode 7 in 2004. In parallel with the work on Eurocode 7, a large number of associated harmonized standards have been, and are being, prepared by CEN and by the International Standards Organization (ISO) for geotechnical investigation and testing and for the execution of geotechnical works. Standards published by CEN must be adopted by the CEN member countries and all conflicting standards withdrawn. Hence all the CEN countries have adopted the same the harmonized text of Eurocode 7, but with National Annexes that allow national choice with regard to Design Approach and partial factor values. The adoption of Eurocode 7 and its associated geotechnical standards has removed the barriers to geotechnical activity in Europe due to the presence of different national standards. It has also enhanced the ability of EU firms to compete in the global market.Background to harmonization of geotechnical standards in EuropeThe initial moves towards the harmonization of geotechnical standards in Europe can be related to the economic and political developments that took place in the period immediately following World War II to revive the economies of Western Europe. Europe at that time was divided by a political and, in many places, a physical barrier, known as the Iron Curtain, into two very different and separate zones: communist in the east and non-communist in the west. In 1952 the European Coal and Steel Community (ECSC) was formed, linking 6 countries: Belgium, West Germany, France, Italy, Luxembourg and the Netherlands, and establishing a common market in coal and steel. The ECSC was the first international organization to be established on the basis of supranational principles whereby negotiated power is delegated to an authority by the governments of the member states. In 1957 the ECSC became the European Economic Community (EEC), also known as the Common Market in the English-speaking world, with the aim to bring about economic integration. With the addition of Denmark, Ireland and the UK in 1973 and Greece in 1981, followed by Portugal and Spain in 1986, this led to the formation of the European Union (EU) in 1993. East and West Germany were reunified in 1990, following the fall of the Iron Curtain in 1989. In 1995, Austria, Finland and Sweden joined the EU, and since then the numbers of countries in the EU has increased to 28, many of which are countries that were formerly behind the Iron Curtain."

Jan 1, 2014

By Avery H. Reed

RECORD production of portland cement, crushed limestone, marble, lime, and clays highlighted the mineral industry of Alabama in 1959. Among the States, Alabama ranked second in production of bauxite, and third in output of iron ore, scrap mica, and native asphalt. Alabama's mineral industry was dominated by the mining and processing of coal and iron ore, which accounted for 51 percent of the total value of production in 1958 and 1959. Other important industries were cement manufacturing, petroleum, and stone quarrying. Leading companies were Tennessee Coal & Iron Division of United States Steel Corp. (coal;. iron ore, limestone, lime, and magnesium compounds), Southern Cement Co. Division of American-Marietta Co. (cement, lime, limestone, and miscellaneous clay) , Woodward Iron Co. (coal and iron ore), Alabama Power Co. (coal), and Ideal Cement Co. (cement lime, and miscellaneous clay) .

Jan 1, 1960

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951