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By George T. Hansen

WHY try to find oil in Utah? Why try to find oil anywhere? Isn't there too much oil already? Answers to these questions involve general oil conditions but are pertinent to my subject. In the first place oil produced in Utah up to the total amount of local consumption would not be subject to nor concerned with the national oil situation. An oil field in this State capable of producing up to 15,000 bbl. per day would have a large value and prompt realization. In the sec¬ond place, there is not too much oil nationally although the markets have been upset temporarily from time to time. Petroleum is so necessary and is in such general demand that an oil field anywhere, anytime, is a valuable and live asset. The oil business in general shows the best condition of any major industry. It has never been hit as hard as most industries and 1932 was a large improvement over its low spot of 1931. It can be and probably will be the one to lead the country back into business stability. Consumption of its products has been reduced less than that of any other important commodity. There are good and valid reasons why it should have been making a normal profit continuously. It has the oil and the processes and the facilities and the policies and the consumption of its products. There is only one reason why it has not been profitable recently and that is the lack of intelligence of from five to ten per cent of the producers. An op¬erator lacks intelligence when he cannot see that it is better for him to sell one barrel of oil at $1 than two or three barrels at 25 or 35c. per bbl.

Jan 1, 1933

By Ezequiel Ordonez

MOST spectacular of Nature's contributions to the making of the postwar world is the Paricutin volcano, in Mexico, which I described in the July issue of this magazine last year, a few months after it was born. Now, after more than a year of continuous eruption, it is still and perhaps will remain a comparatively small though no less interesting volcano. The cone on April 1 had an altitude of nearly 1200 ft. above the level of the small flat field from which it began to grow on Feb. 20, 1943. This cone is now almost entirely surrounded by the lava flows that poured out at different dates, from its base or from outlets on the slopes near its base. To the north and northwest these lavas were

Jan 1, 1944

By Subhas G. Malghan

Feldspathic deposits occur widely throughout the United States, but North Carolina, California, Connecticut, and South Carolina accounted for over 80% of the total domestic feldspar output for the year 1973.1 Pegmatites and granites constitute the major feldspar reserves of the United States, 2 and in addition, feldspar is produced as a byproduct by firms whose major products are spodumene and mica. 3 Feldspar flotation is practiced in the United States, Mexico, Finland, Norway, West Germany, Japan, and the USSR. According to the US Bureau of Mines estimates, the production of feldspar in the United States and rest of the world were 704,000 and 2,514,000 t, respectively. Feldspar is principally used as a flux in making glass, pottery, porcelain, enamel, tile, and other ceramic products. In recent years, the domestic feldspar industry is faced with a number of problems. As a result of increased cost of energy and the introduction in 1972 of new legislative programs relating to air, water, and noise pollution, land-use restrictions, and mined-land rehabilitation, the production costs have increased. Apart from the increased cost of operation, an operational problem exists with the feldspar producers in North Carolina, especially those in the Spruce Pine area. This problem is concerned with the use of hydrofluoric acid in the feldspar flotation. Feldspar producers in Spruce Pine, NC, have been discharging process waste water into the North Toe River. The mill waste water contains active fluoride ions. Fluoride in excessive concentrations is undesirable in waters used for drinking. It is stated that water containing 0.9-1.0 ppm fluoride will seldom cause mottled enamel on children's teeth; and for adults, concentrations less than 3-4 are not likely to cause endemic cumulative fluorosis and skeletal effect. Although the literature on this subject is rather confusing and inconclusive, the inference that concentrations over 4 ppm may affect bone structure is clear. According to the recent Federal Register,4 maximum fluoride level of 1.4 ppm at 79°-98°F is considered to be adequate and safe for the protection of health of the consumers. The EPA and state environmental agencies have accelerated their drive to reduce water pollution on a faster schedule. By 1977, the EPA specifications for maximum contaminant level of fluoride ions in the discharge waters of feldspar milling operatins is expected to be reduced to 2.0 ppm. The other problems of using hydrofluoric acid are the following: toxicity, hazards of handling and storage, and high cost as compared to other inorganic acids (almost 16 times the cost of sulfuric acid). In order to reduce fluoride levels in mill discharge waters, mining companies have taken the following steps: I) Recirculating a part of their mill water. Even though recirculation of mill water seems to be a novel method of reducing fluoride contamination of the discharge water, there are certain operational and handling problems. 2) Conducting research on the treatment of fluorides in mill waste water. The technology of treatment of fluoride ions has received considerable interest in the recent years. A recent research report5 estimates that the cost of fluoride ion removal to meet the present specifications in the feldspar industry is approximately $0.25/t of ore processed, and about $0.50/t of feldspar produced. At the request of the feldspar producing industries in North Carolina, the North Carolina State University (NCSU) Minerals Research Laboratory has taken up a research program directed towards overcoming the fluoride ion pollution problem. After a close study of the operational, technical, and economic aspects of feldspar flotation, it was decided to attempt to replace the conventional hydrofluoric acid process. Conventional Feldspar Flotatin Using Hydrofluoric Acid Since the inception of the feldspar flotation process using hydrofluoric acid by O'Meara2,6 the process has achieved a great commercial success. In the conventional flotation separation of feldspar-quartz, hydrofluoric acid is used to suppress quartz and activate feldspar, and a long chain amine salt (acetate or chloride) is used as a collector. The bulk of amine collectors used in current feldspar operations are applied as the water-soluble acetates of the free-base amines. These products are pastes or waxy solids which are available in a range of acetic acid neutralization levels generally 50 to 100% neutralized. In spite of the problems mentioned in connection with the use of hydrofluoric acid, this process is extremely stable with respect to changes in the process variables. With the exception of a few operations, alaskite and pegmatite are the major sources of feldspar.7 In the flotation treatment of a pegmatite that contains iron-bearing minerals (heavy minerals), mica, feldspar, and silica, a logical order of removal presents itself considering the following:8 1) Mica is readily floated by an amine collector in a pulp pH 3.5. Some iron-bearing minerals will usually respond to amine collector in acid circuit with the mica concentrate. 2) Since iron minerals tend to occur invariably in the feldspar concentrate, it is desirable to remove most of these prior to feldspar flotation. A fatty acid or a petroleum sulfonate collector used in this flotation step in acid circuit will float iron-bearing minerals. 3) Using hydrofluoric acid to maintain pH of 2.5, an amine collector employed in a final step will float feldspar away from silica, usually leaving the latter in the tailing as a high-grade silica concentrate. The problems connected with the flotation separation of feldspar-quartz arise due to the similarities in their chemical structure. Therefore, any reagent system that is likely to succeed in feldspar-quartz separation should have adsorption affinity towards one of the minerals and depression effect towards the other mineral.

Jan 1, 1979

By W. E. D. Stokes

The faster that aircraft fly the sooner some new and stronger material must be found to take the place of the present aluminum alloy used in all-metal planes. Experts of the National Advisory Committee for Aeronautics. in studying hi-speed aircraft, are convinced that the present all-metal plane, of semi-monocoque, aluminum alloy construction, is not the ultimate in aircraft design. Magnesium alloys and steel are under consideration.

Jan 1, 1942

The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-

By L. E. PORTNER

INCREASING military demands on the petroleum industry have brought into bold relief the crude-oil reserves now available to meet combined military and civilian demands, emphasizing the necessity for a greater efficiency in recovery from what has been discovered than ever before, particularly in light of the absence of new discoveries. This situation-and the fact that the industry, as well as members of the Government charged with governing oil production, desire to meet all crude-oil demands made of the industry with the least loss in tangible reserves through production practices-paves the way for increasing application of sound principles of production engineering and conservation.

Jan 1, 1944

By T. A. Wright

THE-Institute of Metals Division opened on Tuesday afternoon with Wheeler P. Davey as chairman and G. E. Edmunds as vice-chairman. Four papers were on the program, two being of a fundamental character. A paper on "Internal Surface in Minerals and Metals," by R. S. Dean and J. Roster, was presented by the latter; C. H. Gottschalk discussed coercive forces in powders. In answer to a question by the chairman. The author stated that he had not investigated [he temperature coefficient of resistance. A paper on "Recrystallization and Grain Growth in Cold Worked Polycrystalline Metals," by L. W. Eastwood, Arthur E. Bousu, 'and C. T. Eddy, was presented by Mr. Eastwood. A. great many quantitative data were given, with little reference to the theory. Theoretical considerations were discussed by Dr. Gottschalk, and C. A. Edwards of the University College of Wales, contributed very interesting comment on the relationship of size and critical strain. Dr. Edwards discussed the necessity of considering strain with time and temperature.

Jan 1, 1935

By W. S. Row

This mine is operated at 4000 to 4500 tons daily through a single shaft, with one rock hoist and one service hoist. Latest shaft construction is concrete with wooden dividers. Economics of drifters and air-leg drills are compared, as well as costs of shrinkage and sub-level stoping. Economy of large haulage equipment and underground crushing is shown.

Jan 3, 1953

BUMPS in No. 2 Mine, Springhill, N. S., furnished the main feature for discussion at the morning meeting* on Ground Movement and Subsidence on Feb. 18. Walter Herd, the author of the paper by which the discussion was introduced, not being well, was unable to be present. The paper was presented by T. L. McCall, who laid stress on the presence of sand- stone as the cause of bumps, on the value of retreating longwall in eliminating such phenomena at the coal face and on the advantage of wide headings with packs on either side, leaving space behind them for any coal that bumps might dislodge. George S. Rice, who presided, referred to his visits to the Nova Scotia mines and said that bumps usually occurred only where the coal was thick and strong and the roof and floor both more than usually hard. If any of the three were weak, bumps were not likely to occur. In the Nova Scotia mine, to which Mr. Herd referred, there was no material for packwalls and for this reason as well as for safety he had been convinced that long- wall retreating with a small percentage of pack walling was the most feasible plan.

Jan 1, 1929

By D. J. McAdam, R. W. Mebs

THE technical cohesive strength of a metal means, not the interatomic forces, but the technically estimated resistance to fracture. An example of such resistance to fracture is the so-called "true" breaking stress of a tension-test specimen, the breaking load divided by the sectional area at fracture, According to the prevalent view,8 the technical cohesive strength of a metal, in any particular state as regards prior mechanical treatment and heat-treatment, is determined by a limiting value of the algebraically greatest principal stress.? In two previous papers by one of the authors,14,15 evidence was presented to indicate that the technical cohesive strength of a metal cannot be represented by a single stress value, but that it comprises an infinite number of values corresponding to the infinite number of possible combinations of the principal stresses. The technical cohesive strength thus comprises an infinite number of technical cohesion limits, each representing a specific stress combination at fracture. In the same papers, evidence was presented that plastic extension causes a continuous increase in the technical cohesive strength. Such a variation is not in accordance with the prevalent view that plastic extension first increases, then decreases, the technical cohesive strength.8 In this paper, as in the previous papers,14,15 the algebraically greatest principal stress will be designated S1, the least principal stress will be designated S3, and the intermediate principal stress will be designated S2. The technical cohesion limit under polarsymmetric tension (S1 = S2 = S3) will be termed the "disruptive stress," and the cohesion limit under unidirectional tension (S2 and S3 = o) will be termed the "severing stress." 14,15 The yield strength of a metal, according to the generally accepted theory, may be represented by a constant value of the shearing-strain energy, and hence by a constant value of the sum of the squares of the three principal stress differences. In the second of the previous papers,"' however, evidence was presented that the limiting yield stress decreases with increase in the volume stress, the algebraic average of the three principal stresses.* This influence of the volume stress becomes prominent only in the field of triaxial tension. In the two previous papers, 14,15 diagrams were presented to show the variation of the technical cohesion limit, yield stress, and ultimate stress with the combination of principal stresses and with plastic extension. Those diagrams and the resultant conclusions are derived from experimental data obtained by other investigators. They are based chiefly on results of tension tests

Jan 1, 1943

By R. D. Satterley

The Sherwood mine is an iron-ore mine owned and operated by the Inland Steel CO. in the Iron River district of the Menominee Range in Michigan. The property consists of an 80-acre tract in the village of Mineral Hills, about a mile north of the city of Iron River. The Ore mined is a reddish brown, nonbessemer hematite and limonite. The ore bodies lie in a large syncline having an east-west strike and are associated with a rock structure that is folded in a complex manner. The two 40-acre tracts run north and south and the shaft is at about the center of the north forty. The shaft is 1286 ft. deep, with the principal operating level at a depth of 1000 ft. from surface. A new level at a depth of 1200 ft. is in process of development. The ore body at the 1000 ft. level is east and west at approximately the line between the north and south forties and at this elevation is from 50 to 250 ft. wide and extends above the level at varying heights of from 50 to 250 feet. The 1000-ft. haulage drift extends south from the shaft, through the east-west ore body to the slates on the south side of the body. The ore body was intercepted in the drifting at about goo ft. from the shaft and was about 200 ft. wide at that point. A crosscut was extended to the east and west property lines along the south boundary of the ore body. This east-west ore body is laid out in areas go ft. wide for stoping with pillars 40 ft. wide. With this plan a stope is approximately 80 by 200 ft. and has a pillar on both sides that is approximately 40 by 200 ft. The ore has a height of from 50 to 250 ft. above the elevation of the level, therefore the height of the stopes varies in accordance with the height of the ore body at each location. From the crosscut, two main raises, each 6 by 7 ft., are put up into each 80 ft. stope area (Fig. 1). One of the main raises serves as a manway and the other as an ore raise, through which the ore is transferred from the stope to the tramming equipment. The original layout as for scraping of the ore from under the stopes into the ore raises. The ore raise is put halfway (east and west) along the 80-ft. stope area and usually is in iron formation. The manway and ore raise are on approximately 15-ft. centers. These main raises are Put up to a height of from 22 to 30 ft. above the level floor, then from the toll of the ore raise a scraper drift (8 X 8 ft.) is driven across the width of the ore body, which is in the neighborhood of 200 ft. From the scraper drift, mill raises are put up at 12½-ft. centers, staggered on opposite sides of the drift, and these are extended 23 ft. above the elevation of the scraper-drift floor. The sublevel connecting the top of these mill raises is called a mill "sub." Other sublevels are developed parallel to the scraper and mill subs at 25-ft. vertical intervals above the mill sub. The mill sub and the other subs above the mill sub are known as sublevels or dog drifts, and are 4 ft. wide and 6 ft. high. These dog drifts

Jan 1, 1946

By E. T. Turkdogan

The activities of SiO2, FeO, and Fe2O3 are calculated from previous experimental data on the activity of oxygen in Fe-Si-O melts at 1550°C. Using the oxide-activity data, the free energy of formation of fayalite from its oxides is evaluated for 1550°C. A number of investigators1-4 contributed to the study of the state of oxidation of iron in SiO,-FeO-Fe,O3 melts and the phase equilibria in the system Fe-Si-O. In a more detailed study, Schuhmann and Ensio5 and Michal and Schuhmann% easured the state of equilibrium in the SiO,-FeO-Fe,O3 melts saturated with y-iron or silica or both under low-oxygen potentials and within the temperature range 1250" to 1350°C. Similar measurements were also made by Turkdogan and Bills7,' over wide ranges of composition and oxygen potentials at 1550"C. Using the experimental data on the oxygen activities in the ternary system, Schuhmann' calculated the activities of silica and ferrous oxide in Si0,-FeO-Fe2O3 melts for 1350°C. Adequate knowledge on the activities of the constituent oxides of melts is essential in the study of reaction-equilibria and reaction-kinetics in oxide-melts. With this in view, the activities of oxides in SiO2-FeO-Fe2O3 melts at 1550°C are computed using the experimental data of Turkdogan and Bills7'8 on the oxygen activities in these melts.

Jan 1, 1962

By JOHN D. SUMMER

THE Premium Price Plan for copper, lead, and represent, the approach of the Office of Price Administration to the urgent of wartime problem of securing increased output of nonferrous metals. Some of the problems encountered in too operation of the Plan and the considerations which led to it?s adopt it will here he reviewed. The Plan provides for extra payment by the Metals Reserve Co., to mine operators who exceed established quotas of production. Producers are thus directly, compensated for the higher costs of working ores that are not commercial at the ceiling price, although the metal obtained from these ores is directed into regular channels of distribution at the established prices for copper, lead, and zinc. Higher-cost metal is thus available to fabricators and to the government agencies at the regular ceiling price and the dual objective of increased production and table pries is achieved.

Jan 1, 1943

By George T. Bator

If confronted with the problem of pumping a mixture of slime-free sand, gravel and boulders up to six in. in diameter, at the rate of 175 tons per hr in one single-stage pump against a static head of 90 ft and a total head of 140 ft, of which 20 is on the suction side, an engineer might be forgiven for backing away from the job, especially if he were also told that the pump wearing parts must have a minimum hardness of 550 Brinell for the sake of abrasion resistance.

Jan 1, 1950

By George S. Rice

INTERESTING developments going on in European coal mines look to: (1) increasing mechanization; 12) concentration of mining; (3) improvement in safety appliances; and (4) studies in bettering roof supports and. incident to this, studies of the way a roof behaves under different conditions of support and methods of mining and back-filling. Mechanization and concentration off mining is being adapted to a considerable extent in Great Britain coincident with the development of conveyors. Belt conveyors, shaker-pan conveyors, and a combination of the two are used. For pitching seams not steep enough for the coal to run in station-chutes, the. shaker-pan conveyor is more popular. For large outputs from a contiguous face, the double-unit system of face layout-that is, the conveyors meeting at a common point-is favored.

Jan 1, 1934

By A. D. Wilkinson

A CROSS-SECTION of the converter aisle through one of the converters and reverberatories is shown in Fig. 5. The aisle is 280 ft. long by 60, ft. wide by 681 ft. to the roof trusse, which have a 63-ft. span and are us )ported by steel columns spaced at 2b-ft. centers. Two 80-ton electric trails, supplied by the Welman Smith .Owen Engineering Co., with 20-ton auxiliary lifts, serve this building. Matte shells and converter-slag shells are dumped into heavily con¬structed flat-bottom bins located on the south side of the converter aisle and 1.0 ft. above the floor. The material is broken by ball and by hand, shoveled off into ladles for unloading on to the reverberatory charge floor, and charged into the furnace as previously mentioned.

Jan 1, 1934

By T. C. Sandford

Thermal conductivity measurements of intact rock specimens do not reflect the effects of natural rock discontinuities, and large scale insitu tests are location specific and costly. To allow extrapolation of laboratory measurements to rock masses with discontinuities, the effects of discontinuities on rock thermal conductivity were measured using divided-bar techniques. The introduced discontinuities lowered the thermal conductivity in all cases, and conductivity decreased systematically with increasing roughness of the discontinuity. Conductivity increased with increasing pressure on the discontinuity.

Jan 1, 1984

By A. P. Svenningsen

IN the early stages of design it was not considered necessary that separate crushing plants be built for the new sulphide concentrator and smelter until sometime in the future. The plan was to use the existing crushing facilities for both oxide and sulphide ore. A few additions were contemplated for the existing plants, such as increased bin capacity, and possibly two new secondary crushing units. The more the problem was studied and discussed with the plant operators, the more it became evident that it was complex. It involved the classification of different kinds of ore from the open pit mine -sulphide, oxide and mixed-and how best to separate them so that each kind of ore was given the proper processing and treatment. It also involved the problem of keeping the different ores from being contaminated in bins, hoppers and chutes. Added to these, transportation became complicated and would involve additional handling and loading of ore from crushing plants to conveyors, to bins, and finally to railroad cars which were to be hauled to the concentrator and dumped into the fine ore bin. General In the early part of 1951 it was decided that the concentrator be constructed with ten grinding units instead of seven as originally authorized. The smelter was to be increased proportionally and naturally also the overall tonnages of ore to be handled by the new sulphide plant. Due to this increase in plant capacity and the larger tonnages involved, the difficulties which would arise by using the existing crushing plants were increased to a point where it became evident that the building of new crushing plants for sulphide ore exclusively was technically, as well as economically, advantageous. Authorization was, therefore, given by the company to construct new crushing plants to handle 30,000 tons of ore per day, and capable of reducing the run-of-open-pit ore to the proper size feed for the 10x14-ft rod mills in the concentrator. The ore, mined in the open pit, sometimes comes in pieces as large as 6 to 7 ft diam. The rod mills may call for ore crushed to 3/4 in. The large .size of ore delivered from the open pit determined that a 60-in. gyratory crusher be used as primary breaker. Such a crusher will have a capacity considerably in excess of 30,000 tons per day. The crusher will be a single discharge unit driven by a 500-hp electric motor through a tear coupling and a floating shaft. This type of drive has proven successful at a number of other crusher installations which our company has operating in the United States, Mexico and South America. The tear coupling will protect both the crusher and motor against damage in case of overload. No new features are incorporated in the design of the crusher itself, except that the, discharge chute is made the full width of the crusher with parallel sides instead of the usual converging sides. This change in detail should eliminate, a feature which has been a bottleneck in some of the operating plants and has caused loss of production due to ore hanging up and blocking the chute. The secondary crushing plants will have three 7-ft standard Symons cone crushers and six 7-ft short head Symons crushers. Between the primary and secondary crushing plants a coarse ore bin will be constructed with a nominal draw-off capacity of 30,000 tons of ore. The standard Symons and the short head Symons will be in separate buildings. All the crushing plants and the coarse ore bin are interconnected with conveyor belts for transporting the ore to the crushers at the tonnage rate desired. The final product of the new crushing plants is produced by the short head crushers. It will be delivered onto a conveyor belt leading to the top of the fines ore bin in the concentrator. A separate conveyor belt running the full length of the fines ore bin and provided with a movable tripper of rugged design will discharge the sulphide ore into the bin. The concentrator bin is planned and designed so that the installation of this additional conveyor will not interfere with the operation of the two railroad tracks on which crushed ore is brought from the existing oxide plant. Thus when completed the bin can be filled simultaneously by ore from the new crushing plant and by ore from the existing leaching plant.

Jan 1, 1952

By R. T. Hukki

This paper presents a series of equations for mechanical ball wear, relating parameters of ball size, mill speed, and mill diameter. The fundamental equation, Eq. 12, presented here is introduced to correlate these basic parameters and thus define and clarify the concept of ball wear. This equation is offered as a general rule, which may be modified to apply to individual problems of grinding. BALL wear as observed in grinding installations is the combined result of mechanical wear and corrosion. Corrosion should be a linear function of the ball surface available. Ball corrosion, however, has been studied so little that its effect, although of great importance, cannot be included in the analyses given here. In a separate paper' it is shown that 1 n = 0.7663 np----=— rpm [1] vD P = c, np D kw [2] T=c²(np)n De tph [3] In these equations n — actual mill speed, rpm np = calculated percentage critical speed D = ID of mill in feet P = power required to operate a mill, kw T = capacity of a mill, tph C¹ and c² - appropriate constants in = exponent of numerical value of 1 5 m 1.5 Exponent m is the slope of a straight line on logarithmic paper relating mill speed (on the abscissa) and mill capacity (on the ordinate). It is generally accepted, although not sharply defined, that ball wear in mills running at low (cascading) speeds is a function of the ball surface available. Accordingly, the wear of a single ball may be considered to be a homogeneous, linear function of its surface and of the distance traveled. Thus dw = f¹(d2) . f2(ds) [4] where dw is the wear of a single ball in time dt, d the diameter of the average ball in ball charge, and ds the distance traveled by the ball in time dt. Indicating that ds - a D n dt, the wear of the average ball in time dt becomes dw = f¹(d2) . f2(Dn dt) 1 --- f¹ (d1) f² (D c3 np-----— dt) \/D = c,d² n, D dt The rate of wear of the average ball is given by dw/dt. dw/dt = c, d² np D lb per hr [5] The weight of the ball charge per unit of mill length is a function of D The number of balls of size d in the ball charge is = f³(D2)/f4(d³). The rate of wear of the total ball charge equals the number of balls times rate of wear of the average ball. Thus rate of total ball wear = — . (dw/dt) w. c, . (l/d) . n,, D lb per hr [6] which is the equation of ball wear in low speed mills. In a mill running at a low speed, grinding is the result of rubbing action within the ball mass and between the ball mass and mill liners. When the speed of the mill is gradually increased toward the critical, the impacting effect of freely falling balls becomes increasingly prominent in comparison with the rubbing action. Reduction of ore takes place partly by rubbing, partly by impact. The share of the freely falling balls in the reduction of ore reaches its practical maximum at a speed somewhat less than the critical; at that speed grinding by rubbing has decreased to a low value. It may be reasonable to think that size reduction by freely falling balls should reach its theoretical maximum at the critical speed, if the fall of the balls were not hindered by the shell of the mill beyond the top point; grinding by rubbing would cease at the critical speed. As a first approximation, wear of freely falling balls may be considered to be a homogeneous, linear function of the force at which they strike pieces of rock and other balls at the toe of the ball charge. The force equals mass times acceleration. The mass of a ball is a function of d3 and its acceleration is a function of the peripheral speed of the mill. The wear of a single ball of size d representing the average ball in a ball charge will therefore be w¹ = f3(F) = f (d3) f7 (v). [7] Indicating that v = D n, and n = c³ np 1/vD, Eq. 7 becomes W1 = cn d3 np Do.5 lb per hr. [8] Total wear of the ball charge equals number of balls times the wear of the average ball. Number of

Jan 1, 1955

By A. L. Bailey, B. A. Landry

W. W. ANDERSON and G. E. KELLER*—We want to compliment the authors on this very thorough paper. It gives information which the coal industry has needed for some time. We hope that the additional information which the authors are collecting will he available shortly. The mixing and riffling procedure that was followed for experimental purposes is obviously not practical in routine float-and-sink testing because of the particle size degradation which would result in handling the sample so many times. It is important to obtain our tloat-and-sink fractions with a minimum amount of handling of material. A statement is made in the paper (p. 80) that "the variable most likely to affect the size of sample required to meet a given preassigned accuracy would be the state or degree of mixing of the coal." We agree that this is a large factor, but do not believe it is the most important factor. Our own opinion is that the most important single factor governing the total gross weight of sample that must be collected is the percentage of the weight of material in the smallest fraction that results from the screening and float-and-\ink operations. In other words, size of sample is governed by the total number of fractionations that must he made, and the distribution of material within the fractions. We can imagine a coal with perfect mixing, but with such a small amount of material in some float-and-sink fraction in one of the coarse sizes that a much larger sample would have to be taken than would be the case with very poorly mixed material, but with a large percentage of coarse material more evenly distributed in all float-and-sink fractions. Our own observation of many float-and-sink tests that we have run in our own organization on many types of coal is that the size of sample that must be used on fine size float and sink is governed more by the requirements for weight of material to be used for analysis in the laboratory than by weight of material necessary to obtain accurate float and sink percentage of weight values. In other words, it is our opinion that very small samples can be used for float-and-sink fractionation in the fine sizes, but that accurate analysis of the fractions will depend on a larger weight of sample being pulverized for the laboratory than is necessary to establish the float-and-sink distribution with respect to weight. A. L. BAILEY and B. A. LANDRY (authors' reply)—The authors thank Messrs. Anderson and Keller for their comments based on long experience. It is agreed that the involved mixing and riming technique used may be disadvantageous from the standpoint of degradation. Fortunately, the paper does point out that the extended riming was unrewarding in causing further mixing. Two large unknowns remain, however: (1) how much of the mixing from the presumed highly unmixed state in the bed was achieved toward the random state during blasting, loading, transportation, screening, and further transportation to the point where the gross sample was taken, and (2) how much of the mixing took place during the preparation described preceding riming. As has been pointed out by one of the authors.6 the degree of mixing has a very large effect on the size of sample required and there are still too few experimental data to show at what stage of coal handling most of the mixing occurs. The discussion states that the weight of material in a screened fraction, or in a float-and-sink fraction, is more important than the mixing factor. We do not believe that these factors are comparable in this instance inasmuch as our purpose was to give minimum sampling requirements to achieve a preassigned accuracy in the percentages of float, middlings, or sink, and nothing more. The gross sample had already been screened and no further division by screening was made or contemplated; also, it was not intended that the middlings and sink fractions would necessarily be adequate for percentage ash or other determination. In other words, the sample obtained by the method outlined is not intended for washability studies but only for preparation plant control. Further experimental work has been done, since the paper was prepared, to investigate the effect of increasingly larger top and bottom sizes on the variability of float, etc., of a double-screened coal from Western Pennsylvania. Results will be published and eventually attention is to be given to the preparation of sampling specifications. E. H. M. BADGER*—I should like the authors to explain more fully the fundamental assumptions on which their Eq 4 is based. The equation is of the form s2 = p(l - p) which is the usual expression for the (standard deviation)2 when the chance of finding a particular kind of particle in the sample is proportional to the number fraetion, p. But instead of the number fraction, the authors have used the weight fraction, WF/W. The chance of finding a particular kind of particle in the sample can only be proportional to the weight fraction, if the average ?eig?ts of all kinds of particles, that is, float, midlings, or sink, are the same. Surely a much more justifiable assumption would be that the average volumes of the particles are the same, and, if this is so, Eq 4 would not be true. This may be demonstrated as follows: Let be the weight fraction of float, middlings, or sink, dl the density of this fraction, and d2 the density of the rest of the coal. Then assuming that the average volumes of the pieces in the three classes are the same, the number fraction, p, is given by ? P = d1/l-?/d2 + ?/d1 = ?d2/d1 + ?(d2-d1) The weight fraction, w, in terms of p is given by ? = pd1/(l-p)d2 + pd1 = pd1/d2 + p(d1-d2) _____ [61

Jan 1, 1950