Search Documents

By Colin P. Pigott

The paper describes a variety of existing techniques and equipment which when combined together permit faster and cheaper drilling of shafts in soft to medium strength formations. Drilling fluid circulation, methods of hole stabilisation and bit design, including the advantages of flat bottomed and conical bits, shrouds and skirts, tungsten carbide, long tooth and disc cutters are considered. The principles of rock chip transportation and bottom hole cleaning are described together with a new and very efficient fluid circulation system which was invented by the author.

Jan 1, 1985

By I. Iwasaki

Differential flotation of bulk sulfide concentrates from Duluth gabbro into copper and nickel concentrates could be implemented by first destroying the hydrophobic coating with ozone and then by recovering the copper concentrate with a copper-selective collector. A number of parameters involved in the use of ozone; such as the sequence and the conditioning time of ozone treatment, the pulp pH, and the level of xanthate addition, were investigated.

Jan 1, 1985

By Ned Baker

This report describes the development, construction and testing of a hydrogen-fueled underground mining vehicle. A hydrogen burning engine and a hydride fuel system, both previously developed, were installed on a modified utility vehicle, together with the necessary controls. In tests and in actual use, the vehicle performance in terms of speed, acceleration, and gradeability exceeded that of the standard, unmodified vehicle.

Jan 1, 1985

By Brenda Myers-Bohlke, Tor L. Brekke

INTRODUCTION In recent years several cities in the Eastern United States have constructed subway systems in deeply weathered igneous and metamorphic rocks. Portions of these transit tunnels and shafts have penetrated zones of saprolite. The purpose of this paper is to define saprolite and discuss saprolite behavior in terms of construction and design of tunnels and shafts. Saprolites are products of in situ weathering of rock, with properties intermediate between those of soil and rock. A well-developed weathering profile can be divided into zones of residual soil, saprolite, transition zone materials, weathered rock, and fresh rock. Saprolites are distinguished by a high degree of weathering and by retention of parent rock textures and discontinuities. These structures persist as relict features because of iso-volumetric weathering (Cleaves, 1974) and formation of intergranular bonds that give cohesion to the saprolitic material. As saprolite continues to weather, the bonds are broken, causing the saprolite to decompose and disintegrate into a true residual soil mass without relict structure. Saprolites may form from igneous, metamorphic or sedimentary rocks, but are most easily recognized when derived from igneous and metamorphic rocks because of their inherent structures. The physical characteristics and properties of residual material vary as a function of mineralogic composition, structure, and discontinuities of its parent rock.

Jan 1, 1985

By S. A. Lang

Mine management in general, and mine maintenance in particular, has lagged in using computers as an effective management tool. SF Coal Corporation, in conjunction with the development of the new Lee Ranch Mine, is developing a computer-based maintenance system as an integral part of a total mine management information system. The system includes the ability to schedule and plan preventative maintenance on all rolling stock and mine facilities, project and track component life, and evaluate and schedule manpower requirements. The system hardware, shared by accounting, warehousing, engineering, production and management, consists of a multi-user, multi-processor micro-computer.

Jan 1, 1985

By L. H. E. Weyher

Minerals beneficiation commonly requires initial crushing and grinding so that the mineral phase we seek to concentrate is adequately liberated to obtain a product of specified grade at optimum recovery. To some degree this also is true for coal preparation. In the comminution process we liberate not only the product but also the tailings phase. The true objective is, therefor, to eliminate from the comminution circuit whatever particulate matter has reached specified liberation, regardless of whether the particle is product or tailings material. Overgrinding either of the two phases ties up mill capacity and usually also burdens the downstream processing steps by increasing costs or decreasing recovery, or both. In view of this situation, one would expect concentration steps to be commonly incorporated into the cominution circuit. The reasons this is not done may vary, but probably include the desire to utilize large scale unit operations, e.g., large mills, in conjunction with very simple processes. Hydrocyclones have satisfied this desire but may not always be employed for the right reasons. Hydrocyclones are indeed simple. They also are rugged and forgiving. Unfortunately, these virtues are frequently misused. The direct results are inefficient classification and overgrinding. The indirect results are added costs through recovery losses, unnecessary recirculation, and so on,

Jan 1, 1985

Ok Tedi Mining Limited commenced construction in mid-1981 of facilities and infrastructure to mine and process gold ore at Mt Fubilan in Papua ew Guinea. Production ofgold began more or less on schedule in mid-1984 although design capacity is yet to be achieved. Due to geotechnical problems, two important items of infrastructure, hydropower and permanent tailings disposal, are not yet in place. Current low metal prices make it likely that copper facilities will be postponed.The deposit compriscs a leached gold capping overlying copper sulphide porphyry mineralisation containing significant gold and molybdenum. Mining is by open pit methods. The soft leached capping gold ore is ripped and dozed, loaded by hydraulic shovel and trucked to a dump pocket. After passing a large semi-autogenous mill of nominal capacity of I, I00 tonnes per hour, the ore is treated by the carbon-inpulp process, with a gravity circuit to recover coarse gold. The final product is 12 kg dore bullion bars.At present, all tailings are detoxified with hydrogen peroxide; after cycloning, the coarse fraction is stored, and the slime fraction discharged into the river system; expected environmental impact is acceptable. Investigations for a suitable dam site for a permanent tailings system are still underway.Peak 'I. hour power demand for Stage I is 17 MW, presently supplied by a diesel alternator power station and a 2 MW mini hydropower plant.Initial access to the base camp at Tabubil was only by air. Eventually a road was pushed through 134 km from the river port at Kiunga (where port facilities have been constructed) and a further 23 km to Mt Fubilan.Roads are constructed of compacted gravel and crushed limestone generally underlain by geofabric. Eight major steel bridges were built.The town of Tabubil has been established, including housing, airport, shops, offices, schools and all facilities.Environmental studies have been extensive and a detailed monitoring program is maintained. Ok Tedi Mining Limited is making considerable efforts to train Papua New Guineans and to foster local business.

Jan 1, 1985

By E. G. Baglin

The Bureau of Mines devised a procedure for selectively extracting platinum-group metals (PGM) and gold from Stillwater Complex flotation concentrate. The Stillwater Complex is the only major U.S. PGM resource. Development of a suitable extraction technique will contribute to its exploitation. The concentrate was roasted at 1,050° C to convert host base-metal sulfides to oxides and the PGM from sulfide minerals to their elemental states. The roasted concentrate was preleached with dilute sulfuric acid to remove easily soluble gangue minerals. After pre-leaching, the concentrate was slurried with 6M HCI and leached at ambient temperature and pressure with a strong-oxidizing agent. Hydrogen peroxide, chlorine, sodium hypochlorite, nitric acid, and a persulfate salt were the oxidants investigated. The two-stage leaching scheme ex-tracted up to 97 pct of the platinum, 92 pct of the palladium, and 99 pct of the gold from the roasted concentrate. The base metals were not solubilized and reported to the residue. No attempt was made to devise a procedure to recover the copper and nickel because they comprise less than 5 pct of the value of the concentrate. Viable techniques for recovering the precious metals from the pregnant solution were sulfide precipitation, cementation with nickel, or adsorption on activated carbon.

Jan 1, 1985

By Henry J. Sandri

ACQUISITION JUSTIFICATION There are many reasons why companies consider acquisitions as a means to expand their operations. Some wish to reduce the impact of business cycles on their businesses. Others seek firms within the same industry for expansion and increased market share. Still others diversify in order to avoid takeovers. Whatever the reasons or justification, an evaluation of an acquisition candidate should be systematic and thorough. To many financial managers the concept of a systematic acquisition evaluation indicates the need for a regular set of evaluation criteria. While these are available from numerous sources, one basic parameter frequently overlooked is the application of these criteria to an industry which is different from the acquirer. This becomes particularly important when evaluating firms within the mineral industry. The mineral industry is significantly different from other industries to require different valuing techniques. • This paper will present a number of reasons why an acquisition candidate in the mineral industry should be evaluated differently from other acquisitions, including by other mineral firms. Additionally, this paper will review the most appropriate means of valuing a mineral firm. • Firms considering the acquisition of a mineral firm should understand the nature of the industry before ever making a tender offer. Some of the general considerations include the following: • Level of Capital Intensity: In the mid-1980's the start up cost for a gold mine has been between 20-200 million dollars and 500-1,500 million dollars for a bauxite operation. • Global Nature of Competition: Except for certain industrial minerals, most minerals and metals are traded worldwide and many on national exchanges, such as COMEX. • Start-Up Time: Many mining operations in developed and developing countries have long lead times, 7 to 10 years in some cases, prior to the start-up of production. • Long Term Nature of Investment: For most mineral operations payback usually occurs at least 7 years after production has started. Additionally, many mining operations will continue producing for 80-100 years. • High Level of Risk: The number of factors that a mining firm cannot control such as grade, volume, world supply and demand, plus the long payback periods tend to classify mineral firms at a higher than average risk compared to other investments. • Cyclical Nature: The mineral industry is cyclical in nature, experiencing long troughs and explosive peaks, thus making timing a critical issue. • Labor Intensive: Even with the large capital requirements needed to operate a mine, most mines are labor intensive in proportion to their capital equipment. • Location: Obviously, the nature of this industry requires operators to work in difficult locations, frequently far from civilized localities, in poor weather conditions and without proper supply and distribution infrastructure. One of the most important considerations is an understanding of asset replacement and asset value. Unlike manufacturing concerns, firms in the mineral industry are working toward the elimination, through depletion, of their asset base. Product flexibility is not available to a mining operation. A mineral firm basically has two options as its resource base is depleted: 1) replace the asset with new production, or 2) deplete the asset and close down operation, as in the South African gold mining model referred to later in this paper. An understanding of the

Jan 1, 1985

By Immo H. Redeker, O. E. Pothier, E. W. Gieseke

Phosphate rock is the primary source of phosphorus, an element necessary to all forms of life--plant, animal, and human. While phosphorus finds many uses in everyday life, it is an irreplaceable ingredient in all complete plant foods. With the present need for intensive farming, the fertility of the soil can be maintained only by external additions supplied by mines or other sources. A major consideration in any mining operation is to establish the economic and ecological impact of the development on the local population as well as the national interest. The Commodity Data Summaries, as published by the U.S. Bureau of Mines (USBM), is a ready reference concerning the importance of phosphate to the national and local interest. The summary of domestic and world pro¬duction is given in Table 1. During 19722 the demand for marketable phosphate rock exceeded the supply in the United States and the rest of the world. Domestic and world reserves are more than adequate to meet furture demands. Phosphate rock prices firmed and export prices increased, reflecting the change from oversupply to a shortage of phosphatic fertilizers. Demand is expected to exceed supply through 1973. New fertilizer plant capacity planned for 1973-74 will increase the production of phosphate rock by more than 5 million tons in the United States. Morocco and Spanish Sahara are scheduled to increase their production to 18 and 3 million tpy, respectively, within 2 to 3 years. The domestic phosphate rock production for 1972 was 40.8 million tons and 1973 was 42.1 million tons.' Industry, with government-supported programs, will emphasize restoration of mined land and solution of the colloidal slime disposal problem in Florida. The foregoing information comes by courtesy of The Division of Nonmetallic Minerals of the U.S. Bureau of Mines, January 1973. The summary gives a great deal of information but does not give a complete picture. There are many supporting industries which contrib¬ute to the area in which the mines are located. The figures shown in Table 1 deal with concentrates. To produce such concentrates many more tons of waste overburden and ore must be moved. Because of the competitive nature of the phosphate rock industry, data on concentration ratios not only are difficult to obtain but also are not for publication by companies. The concentration ratios vary from one mine to the next in Florida as well as in Tennessee and the western United States. To produce 42.4 million tons of phos¬phate rock in the United States required moving about 350 to 400 million tons of material. Domestic Industry. In 1972 some 26 firms and the Tennessee Valley Authority produced phosphate rock, with several firms produc¬ing from more than one mine. The distribution of marketable phos¬phate rock production was: Florida and North Carolina 82%; Idaho, Montana, Utah, and Wyoming 13%; and Missouri and Tennessee 5%. The value of this production was $223 million. The principal consuming classifications were: agriculture 75%, soaps and detergents 5%, plating and polishing 3%, animal feed supplements 4%, and miscellaneous applications 13%. Over 5,000 firms processed end-prod¬ucts for agricultural purposes. Uses of Phosphate Rock. The tendency in the United States has been to produce more phosphoric acid by the wet process, while the production of electric furnace phosphorus, triple superphosphate, and ordinary superphosphate has been on the decline. Exports of phosphate rock have been on the increase for several years and in 1971 reached 33% of total production. However, export sales of phos¬phate rock are expected to decline in the years ahead, both in total tons of sales and in percentage of production as domestic sales increase (see Table 2). The description and chemistry involved in the production of phos¬phate fertilizers is too complicated to be presented here. The Waggaman13 book is a very thorough reference on the subject involv¬ing production, utilization, and chemistry. The various operations generally have chemical plants near the dry plants or ship to associated chemical plants for further processing. Wet rock, dry rock, and ground dry rock of various grades are sold. In addition various grades of calcined phosphate rock, including defluorinated phosphate rock for animal food supplements, are pro¬duced. Various grades of phosphoric acid, superphosphate, triple suerphosphate, as well as diammonium phosphate, are produced. These products are available from the various producing compa¬nies listed in the text. For prices and specifications the producing companies should be contacted.

Jan 1, 1985

By William L. Langdon

PRELIMINARY COMMENTS Recent years have been difficult for the mining industry, as reported in the most recently published Minerals Yearbook (Volume III), the estimated value of world crude mineral production has been generally declining since an historical peak in 1979 (16).* The costs of mineral extraction have, however, been rising rapidly. Individual project costs are, in general, exceeding the growth rate of mining companies, while operating and technical risks continue to increase (16). Risks resulting from currency flotation and political actions in the host country are also on the increase. Labor difficulties (such as those experienced by Phelps Dodge) and the Reagan Administration's recent rejection of a proposal by the International Trade Commission for higher tariffs and/or quotas on copper imports have also contributed to the mining industry's difficulties. The net result of these factors has been financial difficulties for mining companies with respect to paying for their current financial obligations as well as trouble finding new financing. It may be that one of the main factors in determining the future of the mining industry will be centered upon capital structure, i.e. how its assets are financed. Historical Perspective on Capital Structure In The Mining Industry As discussed by Isreal Borenstein in (4) and Thomas Navin in (7), mining firms typically have used a financial model based upon high financial leverage, i.e. large amounts of debt relative to equity. This has been especially true for American firms developing orebodies discovered overseas. Problems sometimes occurred for those who were forced to commit themselves to completion guarantees in order to obtain bank loans. Mines under these circumstances must be brought into operation regardless of market conditions. Politicians in overseas countries also may use the high profits required by these high risk ventures to argue for nationalization of mines. Coupled with the frequent use of high leverage, mining companies traditionally have paid out a higher percentage of earnings in the form of dividends than manufacturing firms. This is significant, in that such funds paid out in dividends are not available for other uses. Hence, a greater reliance upon debt and/or additional stock issues than would ordinarily be the case for manufacturing firms. Thomas Navin has stated in (7), that the theory behind the high dividend payout was that, "most mining investors thought of themselves as investing in a wasting asset, one that would gradually deplete over time until it ultimately became valueless." Investors, therefore, required a receipt, in the form of dividends, of a percentage of current earnings and a return on original capital. This view of reality, apparently, has not changed in some quarters, even though modern mine management ordinarily replaces depleted mines with new ones. It may be that this practice of high dividend payout coupled with relatively high financial leverage should be reexamined. Current capital structure theory could prove interesting and useful for those concerned with current conditions. Capital structure patterns and related practices in this industry are not, in many cases, congruent with those thought by some to be theoretically optimal. Prelude to Capital Structure Discussion With a few notable exceptions (such as the Guggenheims and Anaconda's chief operating,. officer in 1971) mining companies' chief executives and boards of directors have not been persons with financial backgrounds. This, one could conjecture, might have accounted for the relatively nonsophisticated nature of capital structures of mining companies. In order to appreciate the possibilities with respect to alternative influence on a firm's performance, one must be acquainted with the basics of financial theory. This paper is an attempt to familiarize the reader with (1) capital structure in general, (2) the usual components of this structure, (3) the general theory behind the use of financial leverage, and

Jan 1, 1985

By John W. Critchfield

This paper presents an overview of some of the basic issues related to tunnel construction in the presence of flammable and toxic strata gases. Gas properties and possible sources are outlined for the various gases that are commonly encountered underground. Assessment of potential gas hazards prior to construction is discussed. Measures for mitigating the problem during construction are summarized. This RETC Session on Gassy Ground has been organized by the Underground Technology Research Council (UTRC), Technical Committee on Gassy Tunnels.

Jan 1, 1985

By W. P. Diamond

The Bureau of Mines has been investigating several techniques, including the use of horizontal and vertical boreholes, to remove gas from coal in advance of mining. Horizontal boreholes drilled from underground workings as part of the mining cycle have been shown (Finfinger, 1980; Hagwood, 1983; Perry, 1978; Prosser, 1981; Thakur, 1980; VonSchonfeldt, 1982) to be very effective in providing short-term, immediate relief from high methane emissions. This technique has been widely accepted in the coal mining industry, but it does require close coordination to integrate the drilling and subsequent gas drainage and disposal into the projected mine development plan. Vertical boreholes can be placed several years in advance of mining to predrain gas from coalbeds over relatively large areas (Dunn, 1984; Elder, 1975; Lambert, 1980; Steidl, 1978; Stubbs, 1979). The vertical borehole technique has the additional advantage over horizontal boreholes of allowing work to be performed on the surface instead of in the more restrictive underground environment. However, except for the relatively large scale vertical borehole programs for both mine safety and commercial production in the Black Warrior Basin of Alabama (Dunn, 1984; Lambert, 1980; Stubbs, 1979), the technique has been underutilized. The primary reason for this seems to be a combination of the current economic climate in the coal industry, legal questions as to the ownership of coalbed gas, and potential roof damage from the stimulation treatments required to increase the characteristically low permeability of coalbeds to enhance gas production. The question of potential roof damage is the subject of this paper.

Jan 1, 1985

By James E. Monsees, Richard J. Proctor

INTRODUCTION Los Angeles is one of the world's largest cities in area with a span of 70 km between its north and south limits. The population in the Los Angeles Basin exceeds 11 million people. Los Angeles is second only to New York City in density of U.S. urban population and it operates one of the largest city bus fleets in the world, 2,500 buses. After many years of planning and many consultants' reports, it is planned to initiate a 30 km (18.5 miles) starter line subway -- the "Wilshire Corridor" (Figure 1). Construction is to start in 1985. In several locations, subway routes ultimately will skirt or cross old oil fields, which may cause gassy tunneling. Of particular note are the La Brea Tar Pits, which overlie a part of the old Salt Lake oil field. Tunneling through tar sands for about 3 km will be unique for subway construction and will occur on the starter line. Experience with previous gassy tunnels in the greater Los Angeles area shows that tunnels can be completed safely if precautions are taken. Abundant ventilation is the main solution, although other precautions are discussed herein.

Jan 1, 1985

By Steven W. Schmauch

The Ruby Mountains study area encompasses 75,615 acres managed by the U.S. Bureau of Land Management in Madison County, MT. A mineral survey was conducted by the U.S. Bureau of Mines and U.S. Geological Survey in 1984. Bureau of Mines personnel reviewed literature and county mining records, and examined prospects or mineralized areas to determine mineral resources. Geological Survey personnel evaluated the area by geochemical sampling and geophysical surveys. There are no organized mining districts and no current claims in the study area. Significantly mineralized quartz veins, shear zones, or talc bodies apparently do not exist within the study area. A small part of the Kelly Iron Deposit is inside, but dips away from the study area; the main occurrence is estimated to have 32 million tons of subeconomic resources that average 21 percent iron.

Jan 1, 1985

By Michael K. O’Leary, William D. Coplin

Risks from political instability and government policies restricting equity ownership, local operations and transfers of payments affect the profitability of foreign mining ventures. More than seat-of-the-pants judgments and old-boy networks are required to anticipate these risks and to take actions appropriate to offsetting them. A system for making political forecasts, called the Prince System, and a series of charts relaying risks to a production of key minerals has been developed.

Jan 1, 1985

By Larry H. Heflin

The Washington Metropolitan Area Transit Authority's Wheaton Station and tunnel design was completed and offered for bid in the Spring of 1983. The format was unique to the Authority: a four part, four fiscal year contract developed in response to funding limitations with construction divided into four stages allowing the maximum amount of work to be done each year for the funds available. The bid was based on the entire contract, but was orginally awarded for only the first year's work. Each year's work had a maximum funding limitation thus safe guarding the Authority from a grossly unbalanced bid. The Authority's estimate for this work was $83,871,524. The low bid came in at 61% of this for a total low bid of $51,512,058. The low bidder was ILBAU America Corporation whose home offices are in Austria. Following receipt of the bids (and resolution of objections cited by other bidders who felt that the job could not be done for the $51 Million dollar figure), a Notice-To-Proceed was given on October 5, 1983. The construction contract allows a Value Engineering Change Proposal, called a VECP which is initiated and developed by the contractor to change the drawings, specifications or other requirements of the contract. Among other things the VECP should decrease the contract price while maintaining the service life, reliability, ease of maintenance, and standardized features and appearance and not require an unacceptable extension of the contract time. A VECP must estimate the amount of the net savings

Jan 1, 1985

By William J. Potter, Roger N. Pyle

Introduction The primary ingredient for survival of mining companies during a recessionary period is to be innovative and resourceful in the structuring and financing of operations. Over the past decade, many mining companies have had to retrench and restructure their operations and to redeploy their assets just to survive. During the same period, traditional sources of financing for mining companies -- commercial banks, subsidized export credit loans and long term straight debt financing in the public markets -- became less available and more expensive. Meanwhile, new markets and new financing instruments provided new alternatives for mining companies. Those companies which exploited these alternatives greatly enhanced their capacity for survival and even for profitability. This article considers the strategies adopted by some companies to adapt to changes in this recessionary environment; the inadequacy of traditional sources of financing; certain of the new financing instruments, structures and markets which have become available; and how several mining companies have utilized these new instruments, structures and financial markets to improve their competitive positions. THE IMPACT OF RECESSION ON MINING COMPANIES AND TRADITIONAL FINANCING SOURCES In its 1983 year-end article "The New Economic Order" Mining Journal characterized many of the large private sector mining companies with operations in the industrialized countries as being "gripped between the jaws of high working costs and stagnating metal commodity prices." The article went on to characterize the Canadian mining industry in particular as being "in the difficult position of having to seek to sell the bulk of its output in a world market characterized by over-capacity, where production costs were determined by internal political and economic factors while prices were set by external competitive forces of supply and demand." Miners of a wide range of commodities in the industrialized countries have come to realize that their domestic mineral resources are in many cases no longer competitive with global sources of supply. To compete and survive they would have to rely on their technical and financial expertise in mineral exploration and development and in mining and processing. Strategies For Survival Global competition has compelled management in the extractive industries to improve their worldwide cost position. This is the only means whereby a mining company can differentiate its product and attain a substantial competitive advantage. During the past decade, for example, ASARCO Inc. and Inco Ltd. chopped their payrolls, postponed expansion plans and otherwise retrenched. ASARCO reduced its capital expenditures and cash requirements for operations in 1984 to a level almost equal to its internally generated cash. The company's finances were also strengthened by increasing total lines of credit from outside sources, by selling common stock, and by reducing annual pension funding through a change in actuarial assumptions. Other companies returned to their traditional organizational structure where they had a demonstrated competitive strength. Consolidated Gold Fields, for instance, resumed its operation as a mining finance house. Its capital investment programs are now devoted solely to resource development. In mid-1984, at a time of firming zinc prices, Union Miniere S.A. used the opportunity to integrate its smelting capacity and to direct investment to certain subsidiaries at the expense of less viable operations. Smaller corporations realized that it was not enough just to be the low-cost producer. For example, Drummond Coal Company in Alabama, which dominates its regional market due to its low-costs, has also developed a world-wide trading capability and has placed incremental tonnage from its own mines as well as brokered coal produced by others, thereby minimizing capital risk. In Canada, Campbell Resources has exploited difficult times by acquiring assets cheaply. In the process it improved its capacity to withstand cyclical economic swings by diversifying from solely a copper and gold producer to a company based upon asbestos, coal, copper, gold and natural gas.

Jan 1, 1985

By A. L. Stomberg

Federal and State surface coal mining regulations require special handling of prime soil materials which result in additional costs, and no actual benefit when prime and non-prime soils are similar. The Coteau Properties Company proposes to mix both prime and non-prime topsoil and subsoils at the Freedom Mine in Mercer County, North Dakota, based on an analysis of soil physical and chemical characteristics which show these materials to be comparable.

Jan 1, 1985

By F. C. Bond

Nature of Empirical Calculations The size reduction of large tonnages of ore and rock is an operation of great magnitude. It is a necessary and important part of industry. Its development has been motivated by practical need and has followed the path of an industrial art without much help from theoretical science. Knowledge has been accumulated from experience. Trial and error established the methods; then collected data were tabulated and served as the basis for empirical equations that have been continually modi¬fied and amplified as new data became available. These equations now constitute the bulk of our present knowledge of comminution. There is no accepted scientific theory that is basic to comminution. In electrical, mechanical, and civil engineering, as well as in many other industrial activities, such theories exist and are extremely help¬ful, but rock is essentially heterogeneous, and the zones of weakness that control its breakage are thoroughly diversified. No theory has yet been discovered which can account for the variability of rock, although many attempts have been made. Empirical equations tell nothing of the why of a phenomenon, but if they are properly derived they can tell much about the how. They always represent only an approximation of behavior but never a law. In a proper empirical equation a symbol is assigned for each of the variable quantities that obviously affect the relationship. In a grinding mill these include mill diameter, mill speed, and feed rate among them. In setting up and revising an empirical equation the cardinal princi¬ple in establishing and modifying it is this: any change must be strictly ascribed to the variable which caused it. A useful empirical equation is rendered useless when a change in any convenient coefficient or exponent is made to make it fit a particular set of data, without certainty that the altered coefficient or exponent is the responsible variable in the new data. Such indiscriminate revisions have brought the use of empirical equations into some disrepute. When existing equations are changed to accommodate new data it is a good rule to make a change which gives results intermediate between the new and the old. A halfway point is usually a good choice.

Jan 1, 1985