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By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.'TheRittinger In its first form, as stated by P. R. Ritted.'tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin' as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By C. Cánepa

In the treatment of many problems related with the optimization of a given ore dressing process, microscopic studies can provide invaluable assistance. Such studies are generally carried out through mineralogical determinations both qualitatively and quantitatively. Frequently the solution of a specific problem requires the combination of these in adequate proportions. Often the nature? of the problem poses some conditions regarding the way the microscopic determinations are made in order to yield useful information. Most publications applied to mineral beneficiation show results of ore microscopy without mentioning the methodological details involved in the determinative work and therefore it is not possible to judge their reliability and/or their relevance. As methodology must necessarily change from case to case, it is very important for the microscopist to identify first the direct and indirect mineralogical information required to solve the problem. Without such guidelines selection of methods for the qualitative and/or quantitative determinations cannot be made.

Jan 1, 1981

By A. Balint

The Photometric Optical Separation process is introduced and examples of sorting machines are given. Applications of the process are outlined in general terms with reference to specific types of industrial installations. Brief description is given of the capabilities and limitations of available equipment, including cost estimates.

Jan 1, 1967

By R. W. Smith

Living and killed organisms, particularly microorganisms, and extracellular products derived from the organisms are increasingly finding use in minerals engineering. Goals include both enhancement of mineral processing/11.ydrometallurgica,l operations and remediation of mineral industry wastes. Some of the applications, such as biologically assisted leaching of ?sulfide ores and bioxidation of refractory gold ores, are well established commercial ?processes used around the world. Others, such as the use. of organisms for the removal of heavy metal ions from dilute aqueous streams, are nearing commercial application. Many other uses of microorganisms and. their derivatives are potentially possible. These include use of microorganisms in flocculation or flotation of minerals., remediation of organics potentially discharged from mineral engineering operations, degradation of cyanide, the recovery of bitumen from heavy oil reservoirs and tar sands and the solubilisation of lignites and low rank coals. In order to fully exploit these many possible uses of organisms and their derivatives, extensive fundamental .and .applied research work exploring the fundamentals, potential and practicality of the various possible uses of microorganisms in mineral engineering should be vigorously pursued. ?

Jan 1, 1991

By William E. Hughes, Roderick K. Davey

The objective of this chapter is to review and discuss interpolation techniques commonly in use in the mining Industry today, including simple examples. This chapter will not attempt to compare the relative accuracy of each technique as this subject has adequately been covered by several authors (Knudsen and Kim, 1967; David, 1974; and Barnes, 1979) When appropriate, methods will be compared relative to the results of simple examples and computational ease. The examples presented are based on metallic deposits. The techniques, however, are not restricted to metallic deposits and can generally be applied to nonmetallic ones. The purpose of interpolation, as applied to a mineralized deposit, 1s to extend the knowledge of the grade and geology of localized samples to an estimate of the grade and mineralogy of a larger block of ground or even an entire deposit. The word interpolation means to compute values between given values and is limited to that region between the known values. The distinction between interpolation and extrapolation is important and must be adhered to in the application of these techniques in general, the interpolation must be limited to the area enclosed by verified samples. The methods being discussed can be broadly broken into three categories. ( 1 ) geometrical methods, (2) distance weighting methods, and (3) geostatistical techniques.

Jan 1, 1979

1. Domestic Production and Use: In 1978, 12 companies operated 31 primary aluminum reduction plants, with 3 firms accounting for 65% of production capacity. Washington, Oregon, and Montana accounted for 31% of the total capacity; Gulf Coast States 23%; Northern States 26%; and other Southern States 20%. Based on published producer prices, output of primary metal in 1978 was valued at $5 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Of aluminum consuming industries in 1978, building accounted for about 25%; packaging 22%; transportation 23%; electrical 11%; consumer durables 8%; and other uses 11%.

Jan 1, 1979

The U.S. economy continued to expand during 1986, although at the slowest pace since 1982 when the current business expansion began. Real gross national product (GNP) grew about 2.6%, slightly below 1985 growth but significantly below that of 1984. The continuing expansion was fueled predominantly by rising personal consumption expenditures as well as growing government purchases of goods and services. Fixed investment, although positive, failed to grow at the rate of the overall economy. The trade deficit, which increased more than 30% over the record 1985 level, continued to depress economic growth despite significant declines in the price of petroleum and the value of the dollar. On a more positive note, domestic employment continued to grow--increasing over 2 million from the 1985 level--and inflation and interest rates declined. The unemployment rate dropped slightly to 7.0%. Of direct importance to the minerals-producing industries, expenditures for consumer and producer durables as well as investment in residential construction each grew faster than the overall economy, but investment in nonresidential structures fell more than 10% from the 1985 level. The low level of real capital spending declined about 3% in 1986, following strong gains in 1985 and in 1984. Capital expenditures for new plant and equipment bottomed out in the second quarter and expanded in the third and fourth quarters. The decline in the first half of the year was partially attributed to uncertainty arising from the then-proposed tax bill. Also, there was little impetus for corporations to invest in new capacity since factories were operating at less than 80% of capacity during most of the year, in part because of continued competition from imports.

Jan 1, 1987

By Stewart Murray, Philip Klapwijk

INTRODUCTION Forecasting commodity markets is like predicting winners in a horse race: to get the answers right, one needs both luck and judgement. Commodity analysts bear some resemblance to racing tipsters as they try to convince interested parties that they have an inside track on which metal is going to win the great minerals race of the 1990s. Commodity analysts share some features with the gentlemen of the turf: • They influence other people in how to spend risk capital, • They don't put their own money at risk, and • If their tips consistently fail to deliver, then they end up looking elsewhere for employment. In order to find winners we need to know about the kind of race we are in and the strengths and weaknesses of all the runners. Miners are not interested in a five furlong sprint: their race is a long distance affair -- after all, the lead-times between discovery and start-up generally approach a decade for mines that will provide the staying power which leaders require in this industry. We need to look at the environment in which our commodities will be competing: in racing parlance, the going. Our equivalent is the economic background: just as some horses are at a relative advantage when the going is soft, so some commodities will do better than others if economic growth is sluggish. If we are going to pick the winners for the late 1990s, and as an industry, make the right investment decisions, nothing is more important than being able to forecast (with at least a semblance of accuracy) how and where the world's economy is going to develop in the next decade. In addressing the question of whether minerals are going to be leaders in the 1990s, this paper considers the idea that it will increasingly be the world outside the industrialised OECD that will provide the incremental growth in demand for mineral products. Economic growth in the Developing World is fundamentally different from that in the OECD, and the pattern of demand for materials in relation to economic output is much more favourable than in the OECD. If we are to forecast the future, we need to be able to understand the past, both in the boom times of the so called Golden Sixties and in the lean years that followed them. This should help us to decide whether the future is going to be like one or other of these extremes or, on the other hand, a return to normality. Having forecast the going, we can look at individual competitors. • Which are best placed to take advantage of the economic, social and industrial trends that we can now dimly foresee? • Which can resist the continued onslaught of the new materials and technologies? • Which of them will best weather the economic storms (assuming that recessions have not yet been abolished)? If we can provide answers to these questions, we will be well on our way to picking winners, i.e., the metals and minerals that will reward their owners with growing demand, steady (and high) prices leading to profits beyond the dreams of avarice.

Jan 1, 1990

1. Domestic Production and Use: In 1977, 12 companies operated 31 primary aluminum reduction plants, with 3 firms accounting for 65% of production capacity. Washington, Oregon, and Montana accounted for 31% of the total capacity; Gulf Coast States 23%, Northern States 26%, and other Southern States 20%. Based on estimated producer prices output of primary metal in 1977 Has valued at $4.6 billion. Aluminum consumption by 25,000 firms was centered 'in the East Central United States. Of aluminum consuming industries in 1977, building accounted for about 25%; packaging 22%; transportation 21%; electrical 11%; consumer durables 9%; and other uses, 12%.

Jan 1, 1978

1. Domestic Production and Use: In 1979, 12 companies operated 32 primary aluminum reduction plants, with 3 firms accounting for 64% of production. Washington, Oregon and Montana accounted for 32% of the total production; Gulf Coast States 20%; other Northern States 32%; and other Southern States 16%. Based on published producer prices output of primary metal in 1979 was valued at over $6 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Of aluminum consuming industries in 1979, building accounted for about 24%; packaging 23%; transportation 22%; electrical 11%; consumer durables 8%; and other uses, 12%.

Jan 1, 1980

1. Domestic Production and Use: In 1980, 13 companies operated 33 primary aluminum reduction plants, with 3 firms accounting for 62% of production. Washington, Oregon, and Montana accounted for 30% of the total production; Texas, Louisiana, and Arkansas 19%; Tennessee, Alabama, and North Carolina 15%; other central and eastern States 36%. Based on published producer prices output of primary metal in 1980 was valued at over $7 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Packaging accounted for an estimated 26% of domestic consumption in 1980, building 22%, transportation 21%, electrical 12%, consumer durables 7%, and other uses 12%.

Jan 1, 1981

I. Domestic Production and Use: In 1981, 13 companies operated 32 primary aluminum reduction plants, with 3 firms accounting for 58% of production, Washington, Oregon, and Montana accounted for 32% of the total production; Texas, Louisiana, and Arkansas 16%; Tennessee, Alabama, South Carolina, and North Carolina 17%; other central and eastern States 35%. Based on published producer prices output of primary metal in 1981 was valued at over $7.5 billion. Aluminum consumption by 25,300 firms was centered in the East Central United States. Packaging accounted for an estimated 30% of domestic consumption in 1981, building 21%, transportation 18%, electrical la%, consumer durables 8%, and other uses 13%

Jan 1, 1982

1. Domestic Production and Use: In 1982, 13 companies operated 30 primary aluminum reduction plants, with 3 firms accounting for 55% of production. Washington, Oregon, and Montana accounted for 34% of the production; Texas, Louisiana, Missouri, and Arkansas 18%; Tennessee, Alabama, South Carolina, and North Carolina 14%; other central and eastern States 34%. Based on published producer prices, output of primary metal in 1982 was valued at over $5.5 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Packaging accounted for an estimated 39% of domestic consumption in 1982, transportation 20%, building 14%, electrical 8%, consumer durables 8%, and other uses 11%.

Jan 1, 1983

1. Domestic Production and Use: In 1983, 12 companies operated 27 primary aluminum reduction plants, with 4 firms accounting for 65% of production. Washington, Oregon, and Montana accounted for 35% of the production; Indiana, Kentucky, Maryland, New York, Ohio, and West Virginia 35%; Tennessee, Alabama, South Carolina, and North Carolina 14%; other central States 16%. Based on published producer prices, output of primary metal in 1983 was valued at over $5.7 billion. Aluminum consumption by 25,000 firms was centered in the East Central United States. Packaging accounted for an estimated 37% of domestic consumption in 1983, transportation 19%, building 17%, electrical 9%, consumer durables 8%, and other uses 10%.

Jan 1, 1984

1. Domestic Production and Use: In 1984, 12 companies operated 27 primary aluminum reduction plants, with 3 firms accounting for 57% of production. Washington, Oregon, and Montana accounted for 35% of the production; Indiana, Kentucky, Missouri, and Tennessee 25%; Alabama, Arkansas, Texas, South Carolina, and North Carolina 20%; other States 20%. Based on published producer prices, output of primary metal in 1984 was valued at $7.2 billion. Aluminum consumption by 25,000 firms was centered in the east-central United States. Packaging accounted for an estimated 35% of domestic consumption in 1984, transportation, 20%; building, 18%; electrical, 9%; consumer durables, 8%; and other uses, 10%.

Jan 1, 1985

The value of domestic raw nonfuel mineral output in 1985 was estimated at $23.7 billion, 2% above the 1984 value of $23.1 billion. This crude mineral output was the basis for approximately $244 billion worth of processed materials of mineral origin. [ ] A U.S. company permanently closed its alumina plant in St. Croix, U.S. Virgin Islands, reducing domestic alumina capacity by 10%. Another U.S. company sold its 26% interest in an alumina plant in Jamaica to its two U.S. partners. On completion of the purchase agreement, the two remaining partners promptly closed the plant for an indefinite period, citing a world oversupply of alumina and unacceptably low prices.

Jan 1, 1986

Real economic growth for 1988 may fall short of the 3.3% projected by the Department of Commerce in August 1988 because the summer drought and intense heat in many areas curtailed output more severely than expected. The economy grew at an average annual rate of 3.0% for the first three quarters of the year, slowing in the second and third quarters. Export growth, which occurred even as the dollar edged up compared with other industrial country currencies, was an important factor in the expansion. Notable gains were posted in sales of machinery, computers, aircraft, chemicals, and telecommunications equipment. Imports increased, but not as much as exports, and the U.S. trade position was still much improved from that of 1987. Personal consumption expenditures grew slightly faster than the economy as a whole. Purchases of consumer durables showed notable strength in the first half of 1988, but slowed down in the third quarter. Despite the moderate rise in interest rates, business spending for new plant and equipment also rose and contributed to 1988 gross national product (GNP) growth. Both new business investment and export demand spurred orders for U.S.-made machine tools. Orders for machine tools for the first 8 months of 1988 were almost triple those in the corresponding period in 1987.

Jan 1, 1989

U.S. demand for building and construction materials, such as construction aggregate, gypsum, and cement, remained strong in 1989. Cement imports declined slightly, representing about 17% of apparent consumption compared with 19% in 1988. Mexico, supplying 29% of the total, was the primary source of imports, followed by Canada with 21 %, Japan with 14%, and Spain and Greece with 10% each. Mexico was also the target of an antidumping petition, filed by producers in Arizona, Florida, New Mexico, and Texas, alleging that Mexican cement was being sold in these areas at less than fair value. This was the second petition filed against Mexico in the last 3 years. The International Trade Commission made a preliminary determination that the cement industry in these regions was materially injured by Mexican imports. U.S. demand improved for construction aggregate for the fourth consecutive year and was at a near-record level. The U.S. gypsum industry performed well, even though new housing starts decreased for the third consecutive year. Increased U.S. exports of gypsum wallboard and strength in the remodeling markets offset the impact of declining housing starts.

Jan 1, 1990

The value of processed materials of mineral origin was estimated to have exceeded $310 billion in 1990. U.S. raw nonfuel minerals mine production in 1990 was estimated at $33 billion, a 3.1 % increase over that of 1989. The value of minerals production increased in all but 3 of the last 30 years. The metals component of production value has fluctuated much more than the industrial minerals component. This reflects the greater volatility of metal prices. In 1990, total employment in metal mining continued the increase that began in 1987. This growth was partially offset by a slight decline in employment in industrial mineral mining, resulting in an overall in-crease of 1.1 % to 179,100 in 1990. Continuing high (by historical standards) metal prices led to expansions at some mines, as well as opening or reopening of additional mines, resulting in increased employment.

Jan 1, 1991

The value of processed materials of mineral origin was estimated to have exceeded $297 billion in 1991. U.S. raw non fuel minerals production in 1991 was estimated at $30.8 billion, a 5.8% decline from that in 1990. This estimate was based on data for the first quarter of 1991 (in some cases two quarters) for most of the 21 minerals that for many years have accounted for more than 95% of the industry's production value. The value of minerals production has increased in all but 4 of the last 30 years. The metals component of production value has fluctuated much more than the industrial minerals component, reflecting the greater volatility of metal prices. Employment in metal mining rose slightly in 1991, but this gain was more than offset by a decline in employment in industrial mineral mining, resulting in an overall decline of 3.0% to 164,600 workers in 1991. Prices of several major metals declined during 1991, reflecting weakness in the economy, causing some metal mines to shut down or reduce operations.

Jan 1, 1992