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By C. B. Manula, H. Gezik

In planning modem-day mining operations, management needs to pass from the area of subjective decision-making to an area of objective decision-makirlg. Planning procedures currently being practiced by many mine managers depend primarily on common sense and trial-and-error methods which oftentimes never reach optimum solutions. For this reason, an attempt is made to provide an understanding of linear programming to solve production planning problems. More specifically, a linear programming model is proposed to solve the production scheduling problem as it was found to exist in the crushed stone industry. Optimal production scheduling is of prime concern here, since the industry has to cope with seasonal demands for its products. The solution, as determined through the application of the model, provides management not only with an optimal production schedule but also with the following information regarding the improvement of existing facilities: (I) the location of bottlenecks which limit production and profit; (2) the directions in which the company i fixed equipment should be expanded or modified; and (3) the evaluation of unused resources. Future trends in stone production will quite likely parallel those in the construction industry. Continued record expenditures for structures such as dams, highways, and buildings are the reasons for this accelerated growth. Production forecasts for the next decade are predicted to be around one billion tons with an approximate 7% annual increase. The problem of increasing production from 570 million tons in 1966 to 1 billion tons by 1976 offers no small challenge. This situation is further compounded by other problems and economic factors. Population expansion, government regulation, labor agreement, and changes in technology wd cause managers and operators to be confronted by many more complexities than characterize present-day operations. Some of these. problems and economic factors are: (1) In some metropolitan and other urban areas, easily accessible sources of stone are almost depleted. Transportation costs will be a prime concern of the industry. (2) Population growth has forced residential expansion to a point where many quarry operators must conform to urban and suburban regulations. (3) Government regulation in regard to air and water pollution, noise, and reclamation as well as zoning developments necessitate that crushed stone producers keep abreast of changing conditions and requirements. (4) The crushed stone industry operates under pressure of a highly competitive situation. Every company's objective is to retain a favorable marketing position by exercising great attention to production and marketing costs. This is rather difficult, since the crushed stone industry is one segment of modern mining which has to cope with a seasonal demand for its products. Among the problems posed here, the one of exercising great attention to production and marketing costs is of current interest to management. Under seasonal demand conditions, this problem creates further difficulties for managers who need to plan and forecast. STATEMENT OF THE PROBLEM Various methods of Operations Research have been developed to handle a problem whose genesis is explained above. It is very seldom, however, that these quantitative means are used in practice by the mining industry. This paper describes the use of Operations Research methods to solve a production planning problem when demand is seasonal. The seasonal production planning problem is an important one because of the substantial costs associated with changing production, employment, and inventory levels to adjust to seasonal sales patterns. Most companies try to operate within reasonable levels of employment changes and hold inventories within storage capacities. In general, little or no attempts were made to develop minimum cosl schedules or to provide objective means to compare various production policies. When demand varies within a fixed time period, 11:-oduction requirements may be met by following one

Jan 1, 1970

By H. F. Porter

MUCH has been written relative to the errors involved in the use of a galvanometer for measuring thermocouple electromotive forces. In general, it may be said that accuracy with a galvanometer is secured only at the sacrifice of durability, unless manual adjustment is made in the operation of the instrument to overcome the errors of resistance. and resistance changes. The pyrovolter and the potentiometer both require manual adjustment for every reading, readings being taken on a "null" method. To the end that some of these balances may be eliminated and only an occasional balance be made as a check reading, the "continuously deflecting pyrovolter" was developed. Essentially, the operation of the continuously deflecting pyrovolter is to determine the resistance of the thermocouple circuit, though its value is not noted or indicated, then throwing in series with the thermocouple sufficient resistance to bring the sum up to some standard value for which the indications of the galvanometer will be correct. This result may, however, be accomplished in a somewhat simpler manner, for which general method patents are now in the course of application. If we devise a galvanometer circuit so that by means of a simple adjustment the resistance of the entire circuit will be rendered equal to some constant predetermined value, we may rely on the galvanometer to give correct e.m.f. indications (assuming that the errors of temperature resistance coefficient and cold junction have been properly allowed for), and will indicate temperature continuously where the e.m.f. measured is developed by a thermocouple.

Jan 9, 1919

By I. Iwasaki

In the flotation of iron ores and nonmetallic ores desliming is the key to a successful operation; the technology of flotation of well-deslimed ores has become fairly well established. When finely disseminated ores are ground to liberation, however, conventional desliming of the fully dispersed pulp results in an excessive loss of valuable constituents. Selective flocculation of iron oxides followed by removal of dispersed siliceous slimes is a new development and is one of the most promising approaches to the treatment of finely disseminated, oxidized iron ores, available in vast quantities both here and abroad (1,2,3). To apply selective flocculation to the variety of refractory iron ores or to cope with the fluctuations in an individual ore and the make-up water, the factors governing this technique must be clearly formulated. For the removal of siliceous and clayey slimes from oxidized iron ores by selective flocculation, the optimum conditions are extremely sensitive to the mineralogical characteristics of the ore, the type and the amount of soluble salts in pulp solutions, and the mesh-of-grind. Certain starches appear to function better than others (4, 5). Selection of the proper reagents and their judicious use is important not only for their efficient utilization but also for minimizing the adverse effects they might exert on the flocculation and flotation steps, and the pollution the effluents might cause when discharged, either intentionally or accidentally, into lakes and streams. In the present article some of the major factors that influence the selective flocculation of iron ores are summarized.

Jan 1, 1979

By E. Hoek

The stability of a rock structure depends primarily upon the extent to which fracture develops within the structure, The prediction of the extent of potential fracture, the first step in the study of fracture development, involves a knowledge of both the stress distribution in the structure and the criterion which governs rock fracture under various stress conditions. While a great deal of research effort has been devoted to the development of techniques for analyzing the stresses in mining and civil engineering structures1-3 and to the investigation of the fracture mechanism of rock 4-6 relatively little attention has been paid to the application of available knowledge to the solution of practical engineering problems. This paper describes a photoelastic technique for the determination of potential fracture zones in certain types of rock structures. A practical example, based upon a problem which might be encountered in designing the layout of deep-level mine excavations, is given as an illustration of the application of this technique. STRESS ANALYSIS AND ROCK FRACTURE In deciding upon the technique to be used for the solution of a problem involving the prediction of rock fracture it is necessary to consider: 1) What type of stress information is required to satisfy the fracture criterion for rock; anti 2) How this information can most conveniently be obtained. It has been established, both theoretically 4,7 and experimentally 5,6,8that the fracture of hard rock depends primarily upon the relationship between the algebraically greatest and the algebraically smallest of the

Jan 1, 1967

By C. H. Mathewson

CONSIDERABLE progress has been made during the last few years in analyzing the action of plastic deformation in metallic crystals. This is due largely to the development of X-ray spectrographic methods for studying changes in the orientation of single crystals, or of conglomerates, as they occur during the process of plastic deformation, but partly to the widespread knowledge of suitable technique for preparing large (single or variously combined) crystals for direct crystallographic observation under stress or in various conditions of strain. These two methods of studying changes in the crystalline structure of metals may of course be used in conjunction with features of mutual support, but unfortunately the advantage of direct crystallographic observation is lost when we proceed to the study of severely cold-worked structures, owing to the occurrence of real or apparent crystalline discontinuities which become more and more complicated as the amount of plastic action increases. Furthermore, the X-ray methods do not appear to be adequate, at least in their present stage of development, to fix definitely the character of structural alteration in the parent crystal lattice by plastic deformation. The principal question at issue concerns the nature of the crystalline particles that remain after plastic deformation. These are generally known in our American metallurgical literature as crystalline fragments,1 and they seem, indeed, to diffract as individuals causing the Hull pattern of a, severely cold-worked metal to resemble the pattern of a fine powder,2 with certain features of preferred orientation among the particles determined by the manner and intensity of cold working.

Jan 1, 1927

By John Dasher

Extrapolation is a useful technique, but it can be overdone. Seldom is it justified to study over a range of 1 to 6 and extrapolate the results to 150,000. It is especially dangerous if the extrapolation is based on a false assumption. The authors assume settlers scale-up by residence time rather than by area, admit their result (a settler depth of 7 m) is "unreasonable" and suggest longer, wider, shallower settlers might be better. Various authors have noted for a copper-LIX system a total flow basis of 2 gpm per sq ft for sizing settlers. The results of this are compared with those in the paper in [Table 7]. The authors note that flooding of their settlers was never approached. Thus the smallest unit calculated is understandably twice too big. The largest however, is 5% of the required size. I note that the figures in [Table 6] for 1/min/cm2 are based on plan area rather than cross section as titled and are wrong by l0 4. A flow of 2050 1/min/cm2 is about Mach I. It is also 10 5/3 or 46.5 times that of the little one, although the abstract says the design was based on constant flow rate per unit cross section.

Jan 1, 1977

J. B. MCGRAW, New York, N. Y. (written discussion*).-In Mr. Burke Baker's description of the process of the American Briquet Co., he speaks only of the attractive features, but every process which uses a compound or emulsified binder has certain undesirable features which must be considered. In making an emulsion, the success of which depends upon the introduction of the various ingredients at certain fixed temperatures and the complete intermixing of a soluble solution with an oil which has absolutely no affinity for it, considerable difficulty is found in keeping the various factors in strict accordance with the formula. To serve its purpose properly or, in other words, to be right for easy mixing with the coal, it should be of a certain predetermined density. Among the controlling factors of this ate the proportion of moisture contained and the temperature of the oil when introduced. If the latter is higher than intended, a greater proportion of moisture will be evaporated than is proper, and if the oil is not sufficiently hot the process of emulsification is retarded. These various factors can be controlled with more or less certainty where working in a laboratory or in a small experimental way, but when it is attempted on a large commercial scale, certain obstacles not otherwise apparent are likely to be encountered.

Jan 5, 1918

By L. Adler

Some estimate of the geologic pressures existine at the site of a proposed underground opening is essential for its economic design and construction. Regardless of the size of such an opening, drill hole, or mine stope, these primitive stresses need evaluation; at present a number of techniques are available for this purpose. However, a new method of analysind stresses is proposed in this paper. Some estimate of the geologic pressures existing at the site of a proposed underground opening is essential for its economic design and construction. Regardless of the size of such an opening, drill hole or mine stope, these primitive stresses need evaluation. At present a number of techniques are available for this purpose, and another one is to be proposed. These may be grouped into three general methods: 1) precedent, 2) instrumentation, and 3) theoretical analysis. The first two are covered in the literature where their advantages, as well as limitations, are discussed.'9' Generally a theoretical approach combines structural geology with engineering mechanics. The former deals with the geodynamic causes of residual stresses (stresses not related to overburden weight) and presents interesting, but controversial, views.'" A general and useful conclusion, however, can be drawn - vertical residual stresses are much less prevalent than horizontal. However, if for some reason, the values and effects of horizontal pressures were better known to engineers the following analysis

Jan 1, 1962

RICHARD R. HICE, Beaver, Pa. (written discussion *).-The matter of selective. mining is probably of more importance in Pennsylvania than is washing, and perhaps washing would not be necessary at some plants where now practised if proper care were taken in the mining. I have in mind one plant where the sulfur content of the entire bed is more than 2 per cent., yet if the bottom 12 in. and the top 12 or 15 in. are separated, the main portion of the bed, some 6 ft., will not contain more than 1.25 per cent. sulfur; and yet in this mine the entire bed .is worked together, the resultant coke, as a matter of course, not being fit for use in iron smelting. Not sufficient notice is taken of the "Double-thick" Upper Freeport coal in Allegheny and Butler counties. This is a very valuable deposit. Other areas where there is a, top member of the Upper Freeport coal are also known, which add to the value of this bed as a coking coal. This double Freeport coal is especially suited for byproduct coking. I cannot be as optimistic as regards the "low-sulfur" Pittsburgh coal in Greene county as the authors. If the term low-sulfur is to he confined to coal with not exceeding 1.25 per cent. sulfur, there is probably little

Jan 10, 1919

By A. M. Gaudin

TEN years ago Taggart, Taylor and Ince1 described a workable, convenient apparatus for the measurement of contact angles be-tween cleaved, ground or polished particles and captive bubbles. Wark and Cox2 and Wark and Sutherland3 have done an im-mense amount of experimental work with this apparatus. Their work has had as principal object the determination of "con-tact curves." Contact curves are Cartesian charts in which pH (or some other variable) is plot-ted against quantity of modifying agent. The rectangular area is broken into two or more curvilinear areas separated by the contact curve. The curve indicates that a sharp demarcation exists between condi-tions that bring about sticking of particles to bubbles and conditions that do not pro-duce sticking, The type curve appears in the TRANSACTIONS as Fig. 1, page 248, volume 112. Wark and Cox offer data to show that the contact angle has a value determined by and characteristic of the agent used. Wark and Cox also make the statement that they believe this value is independent of concen-tration (ref. 2a, p. 209), They say: It is suspected that, given sufficient time and provided that there are no disturbing factors. the full ethyl xanthate angle (corresponding to a complete xanthate film) would be obtained in every case where contact occurs.

Jan 1, 1940

By Arthur G. Metcalfe

Arthur G. Metcalfe (SOLAR)—Three explanations to account for mechanical nucleation effects are considered in the paper, viz., theories based on fragmentation, agglomeration, and pressure-wave mechanisms. The authors show that none of these mechanisms will explain the results observed with tin and Sn-Pb alloys. A fourth mechanism of nucleation enhancement was developed during work at Armour Research Foundation on casting of beryllium and, although presented briefly on various occasions, the theory has never been discussed adequately. It is believed that this theory will explain many of the observations. Classical homogeneous nucleation theories assume that embryo nuclei are formed in the melt as a result of compositional and/or thermal fluctuations. Stable nuclei are formed when a critical size is reached such that the decrease in free energy for conversion of this volume of melt to solid offsets the increase of surface, energy. The assumption is made that the average properties of liquid and solid metal can be used. In practice this assumption is invalid and indeed is contrary to the postulation of thermal and compositional fluctuations in the melt. Actually the conditions favoring embryo formation bring the seeds of its own destruction—the thermal and compositional fluctuations leave the embryo surrounded by atoms of higher thermal energies and/or by solute atoms that depress the melting point. Any mechanical method of dispersing this destructive

Jan 1, 1964

By George Anagnostache

AMONG the petroleum-producing countries of the world, Roumania occupies the fifth place; in Europe, it occupies second place, coming after Russia. The extraction and the use of petroleum in Roumania, may be trace( as far back as 1856, but the production on an industrial scale started in 1896, when the "Steaua Romana," was formed. From that time until the beginning of the war, the petroleum industry had a rapid growth the number of the producing companies increased to 37, and production FIG. 1.-ROUMANIAN OIL AND GAS FIELDS. increased from 81,571 tons, in 1896, to 1,898,545 tons, in 1912, when the greatest production was reached. In 1916, when the Germans invaded Roumania, the oilfields, at the order of the Allies and under British supervision, were destroyed, to pre vent their exploitation by the Central Powers; the wells were blown in the refineries and the storage tanks burnt, and pipelines put out of order This voluntary destruction, which weakened the resistance of the Central Powers, set back the petroleum industry at least one decade. Reconstruction after the war was slow, because of bad transportation conditions the scarcity of drilling and refining material, the insufficiency of. electric power, and the continuous depreciation of the Roumanian money, which made difficult the buying of the necessary materials for reconstruction.

Jan 3, 1925

By W. McDermott

It is well known that many so-called free-milling silver arcs are so classed more from their value necessitating a cheap process than from a real adaptability to raw amalgamation. Such low--grade ores, carrying more or less sulphurets, are more profitably treated by a cheap rapid process than by the more effective but costly process of roasting arid amalgamation. The tailings are sometimes crudely concentrated, or, after lying and becoming partially oxidized, are again worked in pans. Of late years, by the use of improved methods of concentration, many old low-grade tailings-piles have been reworked to a good profit; and in some improved mills arrangements are made to concentrate before or after amalgamation, thus making a single treatment in mill suffice. It is self-evident that on a low-grade ore a small increase in percentage saved is of no commercial advantage if accompanied by a material increase in cost, and therefore a cheap and continuous system of work is the real necessity, if a fair saving be effected. As an illustration of the possibilities of combined concentration and amalgamation on some ores, the following results of a working test at the New York Ore-Milling and Testing Works will be of some interest. The ore treated was a hard white quartz from Mexico, carrying a very small percentage of finely divided sulphurets, chiefly iron

Jan 1, 1885

By Albert D. Brokaw

The accompanying charts are presented to extend and improve a chart published under the title "A Chart to Provide Approximate Correction for Temperature and Deviation from Boyle's Law."' The applicability of this earlier chart was limited by the fact that it was based on the work of Burke and Keyes² and Kvalnes and Gaddy3 whose experiments were conducted with pure methane, the adjustments suggested for natural gases of higher specific gravity were unsatisfactory except within limited ranges of temperatures and pressures, and precise interpolation was difficult. The extensive work of G. G. Brown, D. L. Katz and their associates on the heavier natural gases has provided better bases for the needed corrections, and the present charts. which are based largely on their work, are intended to simplify the computations involved. The design of the charts has been changed by plotting temperatures as a function of pressure and correction factor, on a semilogarithmic or "ratio" grid, which gives fairly even spacing of the graphs and simplifies interpolation. Charts have been prepared for natural gas with specific gravities of .60, .65, .70, .75 and .80. The standard computation for use in estimating the quantity of gas in a reservoir may be expressed as follows: _ PA X 520 X VR ZT where: Q is the volume of gas at 60°F and one atmosphere pressure PA is the absolute formation pressure in atmospheres

Jan 1, 1949

By Albert D. Brokaw

The accompanying charts are presented to extend and improve a chart published under the title "A Chart to Provide Approximate Correction for Temperature and Deviation from Boyle's Law."' The applicability of this earlier chart was limited by the fact that it was based on the work of Burke and Keyes² and Kvalnes and Gaddy3 whose experiments were conducted with pure methane, the adjustments suggested for natural gases of higher specific gravity were unsatisfactory except within limited ranges of temperatures and pressures, and precise interpolation was difficult. The extensive work of G. G. Brown, D. L. Katz and their associates on the heavier natural gases has provided better bases for the needed corrections, and the present charts. which are based largely on their work, are intended to simplify the computations involved. The design of the charts has been changed by plotting temperatures as a function of pressure and correction factor, on a semilogarithmic or "ratio" grid, which gives fairly even spacing of the graphs and simplifies interpolation. Charts have been prepared for natural gas with specific gravities of .60, .65, .70, .75 and .80. The standard computation for use in estimating the quantity of gas in a reservoir may be expressed as follows: _ PA X 520 X VR ZT where: Q is the volume of gas at 60°F and one atmosphere pressure PA is the absolute formation pressure in atmospheres

Jan 1, 1949

By M. K. Barnett

[ ] ENGINEERING research consists, broadly speaking, in the investigation of the effect of the variations in a number of factors on some property of a product or characteristic of a process. The unambiguous description of the product or process requires that the property or characteristic be expressible in quantitative terms. For the purpose of practical control, it is likewise desirable that the independently variable factors governing the product or process be quantities, although this ideal goal is not always attained. Maximum efficiency-i.e., the attainment of the maximum amount of reliable, useful information relating to the influence of the factors on the property of the product or characteristic of the process, for the least expense-is an important requirement for the satisfactory operation of a research organization. Obviously, a necessary condition for the attainment of maximum efficiency is an adequate knowledge of the specialized field in which the experimental research lies. While necessary, this condition is not sufficient. Proper attention must also be given to the general principles of experimental design together with the modem methods for the analysis and evaluation of experimental data. The present discussion is confined to a single design, the so-called "factorial" design. This design is of special interest in that it attains its goal, maximum efficiency, by directly departing from the

Jan 1, 1947

By R. W. Smith

It is well known that certain silicates such as the feldspars and beryl can be readily floated from quartz at a low pH value using a long chain cationic collector in the presence of a fluoride.1-3 However, the mechanism whereby the fluoride activates feldspars and beryl is not known. Indeed, only a few authors have even speculated about possible mechanisms.1,3,4 As a first approach to the problem, it is perhaps best to look closely at the interesting character of hydrofluoric acid and how it dissolves silica and silicic acid. Hydrofluoric acid, unlike hydrochloric acid, is a weak acid with a dissociation constant of about 3.53 x 10-4 at 25°C.5 The reason for the weak acidic character of HF lies in the very small size of the fluoride ion.6 The pKa value is 3.45 which means that at pH 3.45 half the HF is present in molecular form and half in ionic form. The anion present is probably HF2.-6 At pH values below the pKa value, molecular concentration increases rapidly at the expense of the HF2- anion. It is known that HF readily attacks glass, silicates, quartz and silicic acid. The equation usually cited pertaining to the first step in HF attack of silica is6-'

Jan 1, 1965

By M. K. Barnett

Engineering research consists, broadly speaking, in the investigation of the effect of the variations in a number of factors on some property of a product or characteristic of a process. The unambiguous description of the product or process requires that the property or characteristic be expressible in quantitative terms. For the purpose of practical control, it is likewise desirable that the independently variable factors governing the product or process be quantities, although this ideal goal is not always attained. Maximum efficiency—i.e., the attain- ment of the maximum amount of reliable, useful information relating to the influence of, the factors on the property of the product or characteristic of the process, for the least expense—is an important requirement for the satisfactory operation of a research organization. Obviously, a necessary condition for the attainment of maximum efficiency is an adequate knowledge of the specialized field in which the experimental research lies. While necessary, this condition is not sufficient. Proper attention must also be given to the general principles of experimental design together with the modern methods for the analysis and evaluation of experimental data. The Present discussion is confined to a single design, the so-called "factorial" design. This design is of special interest in that it attains its goal, maximum efficiency, by directly departing from the

Jan 1, 1948

By M. K. Barnett

Engineering research consists, broadly speaking, in the investigation of the effect of the variations in a number of factors on some property of a product or characteristic of a process. The unambiguous description of the product or process requires that the property or characteristic be expressible in quantitative terms. For the purpose of practical control, it is likewise desirable that the independently variable factors governing the product or process be quantities, although this ideal goal is not always attained. Maximum efficiency—i.e., the attain- ment of the maximum amount of reliable, useful information relating to the influence of, the factors on the property of the product or characteristic of the process, for the least expense—is an important requirement for the satisfactory operation of a research organization. Obviously, a necessary condition for the attainment of maximum efficiency is an adequate knowledge of the specialized field in which the experimental research lies. While necessary, this condition is not sufficient. Proper attention must also be given to the general principles of experimental design together with the modern methods for the analysis and evaluation of experimental data. The Present discussion is confined to a single design, the so-called "factorial" design. This design is of special interest in that it attains its goal, maximum efficiency, by directly departing from the

Jan 1, 1948

By Henry Lloyd Smyth, J. Ralph Finlay

The most important area of the so-called Keewatin rocks of northern Minnesota is that which runs westerly from Lake Saganaga, near the national boundary, and finally disappears beneath the drift (or has not been farther traced), in the neighborhood of Vermilion Lake. With this belt we have a general acquaintance, extending back some four years. During the past year we have had the opportunity of studying in considerable detail a small part of it, embracing an area of about 12 square miles on the south and east shores of Vermilion Lake. In this paper we desire to record our observations and conclusions, which seem to us important. II.—Literature. Outside the Minnesota Geological Survey, the list of the investigators who have studied the geology of the Vermilion Lake area is not long. Whittlesey, in 1876,* mentioned the occurrence, in the area about Vermilion Lake, of rocks resembling the Canadian Laurentian. Chester,? in 1884, described the iron-ore at Vermilion Lake as occurring in connection with jasper and quartzite, intimately bedded with the country-rock, chiefly sericite schist, and standing in a nearly vertical attitude. The Vermilion iron-bearing rocks, and those of the Mesabi range, he says, are of the same age.

Jan 1, 1896