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By H. Bouzahzah

The field of quantitative mineralogy has evolved significantly through the development of image analysis techniques and information technology. Quantitative mineralogical characterization can now be routinely conducted for determining ore compositions and understanding the behaviour of minerals within mineral separation processes. The characterization of mine tailings is another important application of quantitative mineralogy. The estimation of acid and neutralization potential as well as the interpretation of kinetic leaching test results are often based on quantitative mineralogical knowledge (mineral abundance, texture, metal distribution amongst minerals, etc.). The objective of this paper is to determine and compare the accuracy of four mineralogical characterization techniques that are often used for environmental sample analysis: (1) X-ray diffraction, (2) normal analysis from chemistry analyses, (3) normal analysis from specific gravity measurements and (4) SEM-EDS image analysis. For this purpose, three artificial samples were assembled by mixing pure minerals in proportions often observed in mineral processing plant tailings. BILMAT, a statistical data reconciliation software, was applied to reconcile the chemical analyses with the results of other mineralogical analysis techniques and to estimate the acid and neutralization potential of actual mine tailings samples. The acid mine drainage was qualified from the acid potential and neutralization potential equilibrium as determined through quantitative mineralogical analysis. The statistically reconciled data made it possible to predict the metal deportment as a function of their bearing minerals and therefore, in the case of neutral contaminated drainage, to assess metal leaching potential.

Jan 1, 2016

By A. J. Richins, M. G. Nelson, R. Dunne

From the inception of flotation in the late 1800s, coarse particle recovery has been a challenge to practitioners. By the early 1900s, flotation processes included oil flotation, skin flotation, agglomeration flotation, and froth flotation, and for each there was a proliferation of flotation equipment. Ensuring good coarse particle recovery included desliming of the feed and proper conditioning were required. Froth flotation was at first used mainly to treat finer materials from grinding circuits. The maximum size for coarse particles was from 3.18 to 4.78 mm. In froth flotation, large particles with high specific gravity tend not to be recovered. Coal and minerals of low specific gravity and flaky minerals such as graphite, mica, and talc can be floated in larger sizes. In the early 1960s, the phosphate industry began using column cells to recover coarse particle by froth flotation, but early columns suffered from poor bubble generation and sanding at the flat base of the column. Recently, improved coarse particle recovery has been the object of new cell designs—the Eriez HydroFloat™, the Jord NovaCell™, the FLS coarseAir™ cell, and the Cidra P29 integrated system. The paper will follow the development of coarse particle flotation with a focus on the development, laboratory assessment, and operation of the new flotation equipment and technology designed to recover coarse particles.

Feb 22, 2026

By Silvia França, Hudson Couto

"In this paper, an alternative beneficiation process was developed to recover nickel minerals from low-grade weathered ores. The studied sample, 0.3% Ni grade, is essentially composed of nickel sulfides (pyrrhotite and pentlandite); magnetite and silicates (mostly talc and amphibolites) are the primary gangue minerals. The particle size distribution was controlled using a grinding operation to avoid producing an excess of fine particles by overgrinding. The sample underwent a grinding step for the fine degree of liberation. The slimes (-20 ?m) were removed via two desliming stages in hydrocyclones (diameters of 1.5" and 2"); the ground material, which was classified in a range of (-150+20) ?m, was processed by column flotation in three different stages: rougher flotation for magnesium silicates, rougher flotation for sulfides, and cleaner flotation for sulfides, using pilot flotation columns (2" and 6" in diameter and 20 ft high). The goal of using the preliminary magnesium silicate flotation step was to remove hydrophobic minerals (mostly talc) that would float naturally with the sulfides, which would decrease the Ni grade in the concentrate, as well as to reduce the MgO content because this compound is considered harmful in metallurgical processes when a grade greater than 9% is used. The final concentrate obtained in the cleaner flotation step reached up to 2% Ni and 7.0% MgO. The global and flotation recoveries in the process were approximately 30% and 60%, respectively, due to the losses of Ni during the desliming process. Despite this low global recovery, the adopted beneficiation process can be considered an interesting alternative to produce nickel concentrate from tailings or waste materials."

Jan 1, 2014

By J. D. Wright

This paper describes current milling practice at Endako Mines Ltd., a molybdenum producer in central British Columbia. The various steps in the crushing, grinding and flotation of the ore are outlined, with emphasis on the metallurgy of the latter operation. Tailings disposal and concentrate assaying methods are also described.

Jan 1, 1969

By A. McQuillan, N. Bar

Geotechnical models developed during the planning stages of open pit mines are three-dimensional so as to capture the spatial variation in lithological, structural, hydrogeological, and geomechanical conditions. Geological models that describe the lithological and structural (faulting and folding) characteristics of a deposit are always 3D. Likewise, boreholes and piezometers used to develop geomechanical properties and groundwater models are drilled at spatial offsets across the deposit to understand the lateral and vertical characteristics. Yet when geotechnical analysis is completed, often the three-dimensional geological, hydrogeological, and structural models as well as geometrically complex 3D mine designs for optimizing economic mineral recovery and overburden removal are simplified to two-dimensional sections. In this paper we demonstrate that this simplification can lead to the wrong failure mechanism being identified, analysed, and/or a conservative factor of safety being calculated and hence an over-estimation of slope stability. Through case studies we show how three-dimensional analysis methods are more suited to rock slopes, particularly those with anisotropic material strength, when singularities such as geological faults are present, and nonlinear slope geometry. When the same slopes are analysed in two dimensions, the failure mechanism calculated is often fundamentally incorrect. The case studies further reveal that the factor of safety calculated in three dimensions is not always higher than the two-dimensional factor of safety.

Feb 6, 2023

By J Palarski

Over the last 100 years in the Polish mining industry considerable work has been done to assess optimum slurry, develop flexible delivery systems and adjust the fill technology to a wide variety of mining and geological conditions. Sand or industrial mineral waste materials for the backfilling of underground voids are used to control ground movement and surface deformation. This paper discusses various criteria to he considered in the preparation of a fill, including slurry properties, mine infrastructure, mining geometry, placement methods and the purpose of the backfill. This paper presents laboratory and in situ test data on the influence of materials parameters on the slurry flow in a pipeline system, stiffness, permeability, binding time and strength of a backfill, on the distribution of mixture in underground voids or the penetration between roof fall Materials.

Jan 1, 1998

By G Tsatouhas, R Newell, K Y. Wong

A sulfide ion selective electrode was used to control sulfidiser addition in the flotation testing of a synthetic and a naturally occurring ore containing malachite in order to compare the behaviour of sodium sulfide and calcium polysulfide. Both slug and controlled potential sulfidisation methods of addition were used. Under defined optimum CPS conditions, calcium polysulfide was a more effective sulfidising agent than sodium sulfide on the basis of both capital and operating costs. Surface and solution studies were used to compare the mechanism of each sulfidiser. For calcium polysulfide, XPS showed that polysulfide ions are adsorbed, whereas for sodium sulfide it is the hydrosulfide ions that are adsorbed on the mineral surface. For calcium polysulfide, the CuSx layer was believed to form on the malachite surface, which promoted the flotation of the malachite, by xanthate. Studies of surface morphology of the sulfidised malachite showed that a fairly uniform sulfidised layer is formed with both reagents. The use of sodium sulfide resulted in a thinner initial sulfidised layer compared to polysulfide at equivalent initial sulfur concentration.

Jan 1, 2005

By R. Altman

A Brookfield viscometer fitted with a stainless steel bob was used to measure the viscosity of industrial lead blast furnace slags between 1126 and 1298°c. Slag oxidation state was characterized by first annealing the? slag samples at 750°c in sealed copper tubes in order to precipitate magnetite crystals. The magnetite concentration was then measured on an Outokumpu Saturated Magnetic Analyzer. Using an Arrhenius-type equation, a viscosity model was developed by regression. The equation below accounted for 75% of the variability in the data used to generate the regression coefficients and, on average, could predict viscosity within ± 12% of the measured value. The greatest difficulty encountered in measuring viscosity was due to the occasional presence of solids in the slag which caused, at times, erroneously high viscosity measurements. Precautions to minimize this problem are outlined in the text.

Jan 1, 1985

By Timothy O’Rourke, Karrie Buxton, Chris Lynagh, Daniel Dobbels, Frederick Vincent

The Doan Valley Storage Tunnel Project in Cleveland Ohio was constructed to control Combined Sewer Overflows (CSOs). It is a complex system of three tunnels ranging from 8.5 to 18 feet in diameter with a total length of about 2.3 miles that was put into operation in mid-2021. The project lies within and below the cultural, educational, and medical hub of Cleveland, which presented unique design and construction challenges. This paper provides a case history of the design and construction, with particular attention given to lessons learned in devising a large tunnel system that can carry both dry and wet weather flows constructed in rock with limited cover, within a flood plain area and vibrant urban center

Dec 1, 2022

By R. V. Lundquist

Aeration in water slurries and controlled drying of manganous hydroxide produced from dithionate leaching of Artillery Peak manganese ores from Arizona were investigated by the Bureau of Mines at its Electrometallurgical Experiment Station, Boulder City, Nev., to determine whether a simple process could be developed for converting this product into a battery-grade manganese dioxide. The properties of manganese dioxide prepared by the thermal decomposition of manganous nitrate were investigated also. Manganese dioxide suitable for use in batteries was not obtained from the dithionate leach product, but some of the factors controlling its oxidation were isolated. Aging of manganous hydroxide was of major importance in retarding its oxidation by aeration. Sodium hydroxide and sodium silicate promoted oxidation by drying. Optimum quantities were about 0.85 mol of sodium hydroxide and 0.2 mol of sodium silicate per mol of manganese, and drying temperatures of 200° C. produced yields of manganese dioxide up to 90 percent of the manganese present. Higher temperatures and concentrations of reagents carried oxidation of manganese beyond its tetravalent state.

Jan 1, 1957

By R. J. Seibel

A statistical comparison of the dust exposures of coal miners with identical occupations in Pittsburgh, Pocahontas, Freeport, and Kittanning seams was conducted. Results indicated that, in some cases, identical occupations have different dust exposures in different seams. For example, the continuous miner operator in the Pittsburgh and Pocahontas seams is exposed to more dust than the same man in the Kittanning seam, but the Kittanning seam has more dust along the haulage roads than the other seams. Also, average dust exposures for similar occupations in continuous and conventional mining operations are similar.

Jan 1, 1974

By Roland Arnold, Richard Gradnik, Martin Zeindl

This paper presents the details of the Kramer tunnel project in the Federal State of Bavaria, Germany. This road tunnel, which has been under construction since December 2019, is the key component of the western bypass of the town of GarmischPartenkirchen. Once completed, it will relieve the town’s central district from enormous volumes of traffic. The contractor is the joint venture named ARGE Kramertunnel consisting of BeMo Tunnelling and Subterra. The whole project will be completed and handed over to the project owner, Staatliches Bauamt Weilheim, in 2023. The opening of the entire bypass section including the tunnel to traffic is planned for 2024. The tunnel, with a total length of 3,609 m (2.24 miles) and an estimated cost of EUR 178 million (incl. VAT), is designed as a single-tube, double-lane structure with one traffic lane for each direction of travel. The safety issue that exists for single-tube tunnels is solved by a parallel escape tunnel passable for vehicles. All tunnels and ducts are excavated according to the principles of the New Austrian Tunnelling Method (NATM). In order to reduce the geological risk for the owner, the escape tunnel was supposed to be completed before the design process for the main tunnel ever began. The exploratory tunnel was awarded to a competitor with an separate contract.

Jun 13, 2021

By Q. Xiao, R. Naidu, W. Li, S. Song

Acid mine drainage (AMD) derives from the oxidation of sulfide minerals, primarily pyrite (FeS2), and is the most severe environmental issue facing the minerals industry. The most common short-term approach to AMD treatment is migration control, such as acid neutralization and metal/metalloid and sulfate removal, through the addition of alkaline materials, including lime (Ca (OH)2), limestone (Ca CO3), gangue minerals and industrial wastes. This requires the continuous input of materials and may result in the production of a vast amount of secondary sludge requiring further treatment and disposal. Addition of chemicals is usually more important in metal/metalloid removal than in sulfate removal unless the sulfate is present in very high concentrations. A more promising long-term strategy for AMD prevention is source control through the complete removal of pyritic minerals and encapsulation of potential risk minerals by coating with impermeable surface layers. This is regarded as the most cost-effective approach, although the mechanisms underpinning this and the implementation procedures are yet to be fully elucidated. It is likely that long- and short-term practices can be combined to optimize the remediation of contaminated mining sites. Some factors such as differing geological and mineralogical characteristics and transportation costs must also be considered for the successful implementation of AMD prevention and remediation strategies. This review also considers some implications for AMD remediation, but the promising bioremediation of AMD is not discussed as it has been extensively reviewed.

By L. H. Banning

In the fall of 1953 the Philippine Bureau of Mines, under a Foreign Operations Administration Technical Assistance (FOA-TA) program, began a systematic investigation of the nickel content of the well-known Surigao laterite areas, on the island of Nonoc northeast of Mindanao, to determine the occurrence, distribution, and grade of nickel contained in the laterite and in the subjacent serpentine. At the same time, a technical review of the possibility of producing commercial ferronickel from the nickeliferous materials in the Philippine Islands was made, and a smelting process was suggested. The proposed process would be similar to that developed by the Federal Bureau of Mines for the reduction of the nickeliferous serpentine occurring in the Nickel Mountain ?deposit at Riddle, Oreg. The potential avail-ability of electric power from the Maria Cristina facilities at 3 mils per kw.-hr. would enhance the economic possibility of this program. Development of an economically feasible process for recovering nickel from the nickeliferous serpentines and laterites should lead to the establishment of a new industry in the Philippines, to the development of a source of nickel in the Far East, of which at present there is none, and to partial solution of the problem of supplying the free world with nickel. Enough preliminary reconnaissance had been completed by early 1954 to permit sampling of the deposit for metallurgical investigations. The FOA then requested the Federal Bureau of Mines Northwest Electrodevelopment Laboratory, Albany, Oreg., to conduct preliminary electric smelting studies on nickeliferous serpentine and laterite samples.

Jan 1, 1955

By R. J. Nankee

Coal is our most abundant, low cost energy resource. Expansion of its use is being challenged due to "SO2 emission" regulation with even more restrictive legislation pending. High quality coal reserves are becoming more limited due to greater use in recent years. Aids to allow more use of coal in today's environment include beneficiation of coal before combustion and scrubbing the emissions from coal during combustion. Dow's efforts to help meet these challenges by beneficiating coal include true heavy media gravity separations with chlorinated solvents and liquid/liquid partitioning processes and "Dow Solvent Recovery Technology" to recover the solvent from product (or floats) and rejects (sinks), The objectives of the efforts to clean coal are to reduce sulfur and ash. In this paper, the solvents will be described; a general flow diagram presented; some of the results on upgrading various coals will be described, and projected costs of full-scale plants using chlorinated solvents will be compared to conventional cleaning plants.

Jan 1, 1985

By J. P. Bellot

During the non-ferrous metal processing, the melting step under vacuum or under rarefied gas leads to volatile metal losses. It is the case of the metallurgical processing of the nickel-based, titanium-based or zirconium-based alloys where the evaporation losses don't allow a sufficient control of the alloy chemical composition. A theoretical approach has been carried out involving both a continuum description in the liquid phase and a molecular approach in the rarefied gas phase. The finite volume method is used in order to solve the coupled transport equationsin the liquid, whereas the Boltzmann equation is modelled by using a Monte Carlo method. At the liquid metal and metallic vapor interface, the volatilization and recondensation fluxes link up the two calculations. Simulation results are given for the melting and refining of reactive metals such as titanium alloys where the control of the chemical composition remains a major difficulty. The validity of the kinetic Langmuir's law is discussed for different operating conditions.

Jan 1, 1996

By R Redden

"The Didipio Gold-Copper project in the Philippines has been a well-defined reasonably high gold grade porphyry for almost two decades. OceanaGold are now bringing the project into production in late 2012 and have recently reoptimised the project with the goal of combining the inherent high grades with higher through-put than previously proposed that will see strong initial metal production. The project was discovered and well defined by 1995, but has seen some obstacles to development, namely sovereign risk, capital cost and project funding. The project strengths over this time that have kept the flames alive are: strong grades large orebody with low stripping ratios a simple beneficiation process and a clean high-grade concentrate strong support from the Philippines government.The initial study in 1998 used Gold and Copper price assumptions of $325/oz and $0.95 lb respectively. Today reserves are based on $950 and $2.85. So, being a porphyry with a large reducing grade halo, the deposit now lends itself to extraction on a much larger scale than before, without any significant capital expenditure as a larger open pit now dominates the project.Didipio is a game changer for OceanaGold, so it has been important to learn from history and to capitalise on a strong initial metal production profile. The project sits in a reasonably remote mountainous area of Luzon which sees annual typhoons and numerous short duration high intensity rainfall events and two rivers flowing through the project area, so it has not been without some innovative technical solutions.CITATION:Redden, R, 2012. Didipio - Learning the lessons, adapting and getting ready for production, in Proceedings Project Evaluation 2012, pp 67-76 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

May 24, 2012

Abadilla, Quirico A., Geol.. Lago Pet. Corp Box 172 Maracaiho, Venezuela. IIAbbw. Robert Graham. The W. W. Sly Mfg. Co.Train Ave.. Cleveland. Ohio. Abbotf A. N., Mines Supt., Maznpil Copper Co.. Ltd..Conception del Oro, Zac., Mexico. Abbotf Clarence E, Mgr.. Mines & Quarries, Tenn. Coal. Iron & R. R. Co., 1242 Brown Marx Bldg., Birmingham, Ala. Abbott. Louis Benjamin. Chief Engr.. Consolidation Coal Co. ... .Elkhorn Div., Jenkins, Ky. Abeel, George 8.. Jr., Cons. Min. Engr...4612 West 17th St., Los Angeles, Cal. Abel. Albert E.. Asst. to Pres.. Valley Mould & Iron Corp..Hubbard, Ohio. Abel. Raymond L Asst. Prof., Dept. of Pet. Refin.. Univ. of Pittsburgh. .. .Pittsburgh. Pa. Abernathy. George Elmer. Prof. of Geol. & Min.. Kansas State Teachers College. Pittahurg. Kans. Abernethy, D. Carl, Jr. Min. Engr., Hudson Coal Co. .Scranton, Pa. Abw, Hirouhi. Min. & Met. Engr., Min. & Met. Dept., The Higher Technical School, Osaka, Japan. Aborn. Robert H.. Research Assoc.. Mass. Inst. of Tech..Cambridge, Mass. Abouchar. Bylvain Sley. Min. Engr. & Geol., c/o S. H. Sekaly, 13 Rue El Nimr, Cairo, Egypt. tAbozeid. Mahmood. Pet. Min. Engr., Marland Oil Co. of California, Subway Terminal Bldg., Los Angeles, Cal. Abraham. Arthur W.A. pt. 40, Barcelona. Anzoatmui, Venezuela. Abrahams. Alexander I.. Gen'l Mgr., Racon Electrical Co.. ..... .Slough, London, England. tAbrahamuon, C. W., Min. Engr.. The Mond Nickel Co., Ltd.. ..... .Levack. Ont., Canada. Abstein, Henry T.. Engr. & Mgr.. Profile-Tamarack Mines Co.. ...... .Yellow Pine, Idaho. tAcker, E. WC.. Met.. ........ .I28 East Washington Lane. Germantuwn. Philadelphia, Pa. IlAckerman, D. E.. Research Engr.. Research Lab., International Nickel Co., Bayonne, N. J. tAckerman. Ernest R., Pres., Lawrence Portland Cement Co.. . .Plainfield, Union Co., N. J. Adachi. Jinzoo.A..d dress Wanted Adachi, Yuichi, Chief Engr.. Anzan Steel Works, South Manchuria RY. Co., Anzan, South Manchuria. China. (Via Dairen). Adair, Arthur C, Valuation Engr., Internal Revenue. Treasury Dept.. . .Washington, D. C. Adami. Arthur E., Prof. of Min. Engrg., Montana State School of Mines. Butte, Mont. Adami. Charles J.. Min. Engr., Gen'l Mnr., St. Jos~ph Lead Co.. ....... .Bonne Terre, Mo. Adama, C. W., Pres. Adams Pacific Corp .I66 Montgomery St., San Francisco. Cal. Adams. Cuyler .Dee rwood, Minn. Adams, David T, 514 Wrigley Bldg.. Chicago, Ill. ADAMS, FRANK DAWSON, Logan Prof. of Geology and Dean, Faculty of Applied Science. McGiU Univ., Montreal. Que.. Canada. Adams. Gale L, Research Engr.. General Pet. Corp...Los Angeles. Cal. Adams. George I.. Prof. of Geol. & Mineralogy. Univ. of Alabama. .Tuscalmsa, Ala. Adams. H. H.. Cons. Gml..Room 415, W. T. Waggoner Bldg., Fort Worth. Tex. Adams, Henry, Cons. Min. Engr. . 934 Park Ave., Plainfield, N. J. Adame, Henry H. 285 Madison Ave., New York. N. Y. Adams. Henry Farnum. Engr.. Charge Experimental Work, Inspiration Concentrator. Inspiration Cons. Copper Co.. Box 364, Inspiration. Ariz. Adams, Huntington, Min. Engr, 149 Broadway, New York, N. Y. Adams. Leland D, V.P.. Leslie-California Salt Co., 166 Montgomery St.. San Francisco. Cal. Adams. Louie W.. Illinois Steel Co Gary, Ind. Adama, XL L. Min. Engr.. Old Ben Coal Corp., Mine 12.. Christopher. IU. Adams, Robert M. Robert M. Adam Co. .I201 Fidelity Bldg., Duluth, Minn. Adams. Sidney F.. Geol., Empire Zinc Co .Gilman, Colo. tAdams, Waldo Peck..P ittsfield, Pike Co.. Ill. Addams. Charles 1. Min. Engr.. Bo x 663. Phoenix, Ariz. Addicka, Lawrence. Cons. Enar..... .61 Maiden Lane. New York. N. Y. Addison, Herbert, V.P.. Big Horn Collieries Co ,412 Colorado Bldg., Denver, Colo. Adkemn. J. Carson. Min. Engr.. HY Grade Manganese Co., Inc..Woodstock, Va. Ady. Joseph Wesley. Jr.. Min. Enar., 314 Mining Exchange Blda., Colorado Springs, Colo. Affelder. William Lewis. Asst. to Pres., Hillman Coal & Coke Co. & Allied Companies. 2006 First National Bank Bldg.. Pittshurgh, Pa. Ameck, B. F.. Pres.. Universal Portland Cement Co. .. .210 South La Salle St., Chicago. Ill. Agabeg, Edgar C.. Cons. Min. Engr.. ..... .Evelyn Lodae. Asansol, E. I. R. Bengal, India. tAsar. William M.. Aest. Prof. of Geol.. Kirtland Hall, Yale Univ.. ... .New Haven, Conn. Agaeniz. Rodolphe L, Pres.. Calumet & Hecla Consolidated Copper Co. ...... .Boston, Mass. tAgens, William Holmes. District Mgr.. Traylor Engrg. & Mfg. Co., 362 I. W. Hellman Blda.. Los Aneeles. Cal.

Jan 1, 1928

By J. P. Hager

The formation of the vapor complex AgFeC14 (g) baa been identified and its thermodynamic properties determined. The vapor pressure of silver chloride can be enhanced by a factor of 15-20 due to the formation of the vapor complex. The vapor pressure of both AgCl (g) and AgFeC14(g) were measured using a double-zone transpiration .technique. Gibbs free energies have been determined for the vapor transport reactions. Laboratory kiln tests were conducted to confirm the enhanced recovery of silver through the formation of the AgFeC14(g) vapor complex and to indicate the opportunities for process development using this new vaporization chemistry.

Jan 1, 1985

By C. C. Harris

The characteristics of some common size distribution equations are critically discussed. A generalized form of several well-known size distribution equations is obtained from a differential equation describing statistical distributions. The equation contains three parameters and can describe the major features of size distributions in the fine and the coarse size regions. A graphical method for its implementation is provided. The application of this and other equations to sets of data are compared both for the quality of fit and from a comminution kinetics viewpoint. If a narrow size range of a brittle material is broken sufficiently to obliterate the feed sizes, but not so severely that excessive secondary breakage occurs, a plot of cumulative fraction by weight undersize (Y) vs. sieve size (X) on a log log grid (sometimes called the Gates-Gaudin-Schuhmann plot)1-3 gives a straight line of slope ~ 1 over much of its range. On closer inspection, deviations in the extreme coarse range covering perhaps 10 to 30% of the total sample may be apparent (frequently, a change in slope from ~ 1 to a value different from unity) together with over-all slight irregular departures from a smooth line. One model of breakage postulates that the same fracture pattern persists throughout all size ranges.4 The fracture pattern is characterized by the slope of the line on a log log grid. Accordingly, a distribution of sizes broken in the manner specified earlier is expected to produce a size distribution having the same slope as that of a broken narrow size range. Additionally, the slight irregularities mentioned above should even out in the summation process, giving a smooth straight line of slope ~1 on a log log plot. This idealized state of affairs does not, however, describe the distribution of a multi-event process such as that for a tumbling mill product. On the average, these curves (plotted again log log) tend to have a slope in the fine region different from and usually less than unity,5 while the coarse size region curves with increasing slope for cases of mild reduction, and with decreasing slope when moderate or severe size reduction has occurred. In addition, there are usually slight irregular deviations from a smooth curve. Most curves display two distinct regions — fine and coarse — and a few curves show one or more intermediate regions. Feed size studies6,7 show an effect which theory is required to explain. For the same material, mill loading and other operating conditions, and the same time of grinding, plotting the dimensionless ratios Y vs. X/(feed size) does not reduce the size distribution data to the same curve. Y vs. X does not correlate the coarse region, but it can provide a crude correlation of the fine region which improves as size diminishes and as grinding time increases. The size distribution in the coarse region is somewhat more dependent on the feed size than is the distribution in the fine region wherein the degree of dependence diminishes as time proceeds; the distribution of sizes in the fine region are determined largely by the nature of the material and the comminution conditions. A comprehensive model of comminution must recognize that several different patterns or modes of breakage can occur in a mill; 5,8,9 that there can be some selection in that some size ranges are broken more than others; and that, while some particles may be the product of a single fracture event, or may even remain unbroken, others result from multiple rebreak-age. Thus, breakage in a tumbling mill is more complex than the Schuhmann4 model admits in that several different types of comminution micro-events* occur rather than just one type, and these events, though different in size scale, are of the same overall pattern as that which is visualized by the model. The concept of an average comminution micro-event has, therefore, a mathematical rather than a physical connotation, at least for tumbling milling. Equations with which to describe particle size distributions have been sought for over half a century.10-13 No equation presently in general use was first derived from an analysis of the statistical mechanics of breakage; whatever theoretical basis the existing

Jan 1, 1969