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By Robert W. Fullerton, Barry G. McMillan, Donald T. King, Henning E. Soderberg

INTRODUCTION Dust control in coal preparation and related transport is a multi- faceted problem which must be anticipated whenever dry, fine coal is subject to rough handling which can disperse it in the air. This problem can be minimized by careful planning and proper design, by eliminating procedures which maximize dust production, and by utilizing the most appropriate dust-collection "hardware" for a given situation. Proper maintenance after dust-collection systems are installed is also very important, and will not only enable the selected equipment to perform properly, but will also reduce component wear, recover valuable product with the highest efficiency, provide cleaner and safer working conditions, and allow local clean-air standards to be met. This chapter is designed to provide basic information about dust control in relation to material processing and handling during coal preparation. Areas discussed should provide the reader with insight into basic dust-collection theory, particle behavior, equipment types, ductwork and hood considerations, general maintenance and design planning, and the economics of dust collection. Because of the wide range of areas covered and the various specialized problems inherent in each, the text is organized to be a practical reference, and not a complete, unabridged treatise of ventilation and dust-control design. Nevertheless, the information presented should be of value in both understanding and reducing problems of dust control in coal preparation.

Jan 1, 1979

By Charles H. Jacoby, Stanley J. LeFond

Salt, or halite, has had a long and most varied history. While we know the Chinese were producing salt as early as 3000 B.C., the first written reference to salt appears in the book of Job recorded about 2250 B.C., which reads: "Can nothing which is unsavory be eaten without salt?" We do not know when man first used or realized that he needed salt. Perhaps one of our early Eolithic ancestors noted a piece of salt shining along the shore of a salt lake or a bay. He may have been attracted by its shining luster and tasted it. He found that it had a tart, zesty, distinctive flavor and perhaps chewing a large piece, became ill. However, by experimentation he soon learned that taken in the proper proportions salt was a very pleasant additive to his food. He may have noticed, too, that it increased his feeling of well-being. Thus, when the curtain of recorded history rises, we find man using salt for his health's sake, seasoning his food with it, feeding it to his animals, and using it in many superstitious and religious ceremonies. These uses, however, are a far cry from the uses for salt today. The first attempts of white man to make salt in continental United States were reported in the year 1614, while the first commercial production was in 1790. Practically all of this salt was for human consumption, preserving food, and curing hides. Prior to the coming of the "white man" Indians are known to have made salt from such salt springs as those that existed at Avery Island, La., Charleston, W.Va., Saltville, Va., and Onondaga, N.Y. In 1862 the first rock salt was mined in the U.S. from the Avery Island salt dome. Almost immediately thereafter, rock salt was mined at Saltville, Va., and then at Retsof, N.Y., in 1885. Of the more than 40 million tons produced annually in the United States, about 68% or 27 million tons are consumed by the chemical industry in the production of chlorine, caustic soda, hydrochloric acid, sodium metal, and some 30 other basic chemicals. These basic chemicals, in turn, are used in the preparation of approximately 14,000 chemicals which range from soap and detergents, to such chlorinated hydrocarbons as DDT, BHC, carbon tetrachloride, etc.

Jan 1, 1975

By H. D. Hoskold

This paper is presented in fulfillment of the promise made in my paper, " Remarks upon Surveying-Instruments,"" etc., and much of the material which would constitute an appropriate introductioil here is omitted, because it has been already published by the Institute, in connection with my own contributions- or those of Mr. Scott and others, in vols. xxviii. to xxxi. of the Transactions, and in the special Institute volume on Mine-Surveying Instruments. In these preceding publications will be found, for instance, descriptions of the writer's " miner's transit-theodolite" of 1863,† and his later " angleometer,"‡ both of which were steps of the progress in engineering instruments and methods which originated in the work of Bourns, before 1842, on the " BoxTunnel " of the Great Western railway in England, in which he had to make connections by direct telescopic sights down the shafts. About 1870 the writer devised a practical and much superior plan, and made detailed drawings for an instrument to meet all the conditions he had proposed prior to that year. The detailed plans were communicated to a celebrated optical firm in London; but, owing to their loss (in Paris or Germany, it is believed) and to other reasons, the matter was, for the time, allowed to lapse. Following upon Bourns's idea, my friend, the late Mr. Beansland, introduced, in 1856, a new system and a portable astronomical instrument.§ Such instruments, however, were neither common nor convenient, and did not come into general use among engineers.

Jan 1, 1902

Jan 1, 1970

By Sir Robert Hadfield

Introduction.-I esteem it a great honor to be asked by this Institute to give them an address chiefly devoted to metallurgy. While it is with great regret that I find myself unable to be present to deliver this in person, I take this opportunity of wishing your society every success in its continued career of usefulness to the metallurgists of the great Republic. To be elected, eight years ago, along with Dr. J. E. Stead, F. R. S., as one of your Honorary Members, was a privilege which I greatly esteemed, for I consider that no society in America has done so much as ours for the advancement of metallurgy. Those who have Served our Society.-Where many have served so well, it is difficult, without appearing to make unavoidable distinctions, to select names from those of your members who have done so much for the cause we have at heart-the advance and progress of metallurgy. As typical, however, and not in any way meant as a complete list, there are among others the following names which in the past and to-day stand out prominently in this science of ferrous metallurgy. With most of those now mentioned I have personally come in contact, or by correspondence in some few cases, and have exchanged views, since I first came over to America 30 years ago. Holley; Jones; Weeks; Andrew Carnegie; Thomas Carnegie; Fritz; Sterry Hunt;. Egleston; Maunsel White and Taylor, who did so much for high-speed tool steel, and helped to revolutionize machine-shop practice; W. J. Taylor; Robert Hunt; Alfred Hunt of Pittsburg, who did so much in the early history of aluminum, and, alas! did. not live to see the wonderful progress which has been made in that particular branch of metallurgical industry; James Douglas; C. B. Dudley; Birkinbine; Howe; Metcalf; Barus; Langley; Raymond; P. H. Dudley; H. H. Campbell; W. R. Webster; E. D. Campbell; Talbot; Spilsbury; Gayley; Dinkey, under whose supervision and responsibility modern armor has been so successfully produced in this country, which the writer can testify from personal knowledge of , test results possesses very high Figure of Merit; Schwab; Kennedy; Wellman; Garrison; Wood; Moldenke; Webster; Swank; Unger; Richards; Sauveur; Strat-

Jan 5, 1914

Jan 1, 1884

By J. W. Bolton

PRODUCTION of sound bronze castings is a matter of great practical interest to users and manufacturers of high-grade non-ferrous engineering specialties. Although there has been much excellent research in this field, there still remains some confusion regarding the fundamental principles underlying production of really sound bronze. The literature of the past 20 years on this subject indicates that the prevailing opinion of metallurgists and foundrymen has been that unsoundness in bronze is due generally to oxidation. The following references are typical.

Jan 1, 1929

By Richard A. Busch, Roy L. Soderberg

Large, high, open stopes resulting from vertical crater retreat (VCR) and similar methods are usually filled with sand tailings to support the stope walls and make it possible to mine the pillars. The hydrostatic head resulting from these high stope fills demands extremely heavy bulkheads in the crosscuts to withstand the pres- sure. Occasionally, these bulkheads fail because there are no drains or the installed drains are inadequate. Costly flooding of the mine and loss of life result from these failures. With proper design of blanket drains and filters, the fill can be made failure-proof, requiring only a minimum bulkhead, designed specifically for zero water retention. The effectiveness of the blanket drains can be increased by laying perforated pipes on the bottom of the crosscut within the blanket drain. These drains can have a safety factor of 10 with minimal expense. When the water is properly drained, the hydrostatic pressure on the bulkhead is reduced to zero, leaving only the lateral pressure of the sand. This lateral pressure is partially dissipated by arching and shear against the crosscut walls and consolidation of the tailings as the water is drained. The bulkhead should be placed at least one cross-cut diameter back from the collar of the drawpoint.

Jan 1, 1983

By H. C. H. Darley

The influence of particle size and concentration on the development of chip hold-down pressure (CHDP) was studied in an apparatus designed to measure the change of filtration rate during the first second of the filtration process. CHDP is controlled by the "bridging" particles (i.e., particles in the 50 to 0.2 micron range), whereas filter loss is controlled by the colloid fraction. The results indicated that a fast drilling fluid with a low filter loss could be obtained if the concentration of bridging solids and the viscosity were kept very low. A novel group of drilling fluids, which we have named colloid emulsions, was developed to meet the above requirements. These colloid emulsions are made by dispersing art oleophilic colloid in oil and emulsifying about 5 per cent of this dispersion in water or a dense brine. Good results have been obtained in field trials with emulsions which use asphalt as the oleophilic colloid. INTRODUCTION In recent years it has been found that fast rates of penetration can be maintained in hard formations by using "clear" water as a drilling fluid. In some cases, however, water cannot be used because the very high down-hole filter loss creates various difficulties in drilling, in logging, or in producing the well. It then becomes necessary to "mud up", which results in a decrease in drilling rate. The reason that mud decreases drilling rates is a complex subject which has been well covered by such authors as Garnier and van Lingen, Cunningham and Eenink,' and van Lingen.3 One of the principal factors involved is the tendency of the drilling fluid to develop a filter cake on the bottom of the hole. The pressure differential which develops across this filter cake opposes the action of the bit in dislodging chips from the rock. This pressure differential is referred to by Garnier and van Lingen' as the chip hold-down pressure, which is denoted by the initials CHDP in this paper. The work described in this paper was undertaken to develop a drilling fluid which would minimize CHDP but which would still have a low filter loss—in other words, a fluid which would deposit a filter cake on the sides but would lay little or no filter cake on the bottom of the hole. EVALUATION OF CHDP EXPERIMENTAL Conditions governing the growth of filter cake on the sides of the hole are obviously different from those on the bottom of the hole. On the sides of the hole, cake will form continuously but at a decreasing rate, until eventually the rate of growth will equal the rate of cake erosion by the mud stream.' On the bottom of the hole, each time a bit tooth dislodges a chip the cake is removed, a fresh rock surface is exposed, and the filtration process must start over again. Thus the CHDP is determined by the amount of cake which can form in the interval between successive tooth strikes at a particular spot, normally a fraction of a second. Our first step therefore was to study filtration rates over the first second or so of the filtration process. These tests were conducted in the simple type of dynamic filter cell shown in Figs. 1 and 2. In this cell the mud was filtered through a train of rock cores while rotating blades kept the mud flowing over the surface of the core. The procedure was to evacuate the cores to 0.05 mm of mercury, saturate with brine, and assemble in the holder under brine. The permeability of the core train was then determined. A plastic seal was placed on the face of the core train, and a rip cord was attached from the seal to one of the blades. At the start of the test, 500 psi was applied to the mud, and the meniscus in the capillary measuring tube was adjusted to zero. When the blades were started, t,he seal was ripped from the face of the core, and filtration began. The filtration rate was at first measured by photographing the advance of the meniscus in the capillary tube. Using

Jan 1, 1966

By Sydney H. Ball

MINERALS used primarily for personal adornment and decorative purposes are called precious stones. To be so prized, the stones must possess beauty of color, must not be too common, and must be hard enough to withstand ordinary wear. If transparent, they must have brilliancy and fire. Almost one hundred minerals have been used as precious stones, the noble gems being the diamond, emerald, ruby, and sapphire; pearls are frequently included by courtesy. These gem stones, however, are sometimes equaled in beauty by fine opals, aquamarines, ourmalines, spinels, chrysoberyls (both cat's-eye and alexandrite), and spodumenes (hiddenite and kunzite). The Greeks, Romans, and medieval Europeans grouped together gem stones according to color and degree of transparency, and only as the niceties of mineralogy began to be known, about a century ago, was it realized how many different minerals have the beauty required of gem stones. Pliny, for example, did not distinguish between rubies and the red varieties of spinel and garnet, although he conjectured that the beryl and emerald were one mineral. GENERAL SURVEY Early man treasured bright colored berries, attractive shells, white teeth of wild animals and brightly colored pebbles, and used them as personal ornaments. In the eastern hemisphere, the earliest stones used were members of the quartz family (100,000 to 75,000 B.C.); then obsidian and amber (50,000 to 25,000 B.C.); the jade minerals, fluorspar and jet (22,000 to 7000 B.C.); turquoise (7000 to 3400 B.C.); lapis lazuli and garnet (prior to 3500 B.C.) ; emerald (2000 to 1800 B.C.) ; sapphire, ruby and diamond (800 to 500 B.C.). Indeed, gem mining is the oldest form of mining, and before any metals were known primitive man recognized about 18 gems and decorative stones. At first he sought them in stream gravels and residual deposits but by 3400 B.C. the turquoise mines of the Sinai Peninsula were operated. This was the world's first important hard-rock mining enterprise. The Afghanistan lapis lazuli mines may

Jan 1, 1949

By John B. Dilwoth

This paper treats primarily of the valuation of developed coal properties by the method of capitalizing their estimated average future earnings. However, reference is also made to valuations of undeveloped coal lands and to various methods of appraisal other than by future earnings. Fundamental Valuation Principles Before discussing in detail coal property valuations, a few statements bearing on the general subject will be made to present certain of the writer's views on the question as a whole. 1. A certain property at a given time has but one true value. This is not universally admitted. The appraiser rather frequently finds that a coal owner has in mind three valuations for his holdings; one, the figure at which he feels they should be appraised for taxation purposes; another, the much higher one that should be used if a loan is to be negotiated on the property; and a third, intermediate between the other two, the price for which he would be willing to dispose of his holdings were they for sale. The last is usually nearest to the true value, and because this is so the statement is generally accepted that the fair value of such a property is the price arrived at by negotiation between a willing seller and a willing buyer who are otherwise disinterested. 2. Notwithstanding the foregoing, it is only very generally and approximately true that the proper measure of the value of a given developed' coal acreage is the unit or per-acre price for which one or more bodies of similar coal in the same district have been sold recently. To give a few reasons why such a measure of value can not be strictly applied, it may be noted: a. That sales are often forced by circumstances at times when the coal business is depressed and buyers can be found only for properties that are offered at figures far below their true value. b. That conversely, during periods of unusual prosperity, abnormally high prices are paid. Such conditions obtained several years ago when coal brokers, with very profitable contracts but no sure source of supply, were bidding against inexperienced or shortsighted operators for proper-

Jan 1, 1928

Jan 1, 1910

Jan 1, 1884

By T. O. King, Y. P. Gupta

The self-diffusion of sodium in two sodium silicate liquids was measured in the temperature range 850" to 1500°C by the capillary-reservoir technique. Radioactive Na 22 was used as the tracer. The total count and autoradiographic methods were used for determination of the total Na 22 depletion and diffusion profiles of the dqy-used specimens. The diffusion coefficients obtained by the autoradiographic technique are slightly smaller than those obtained by a total count method. Error analysis of the two methods suggests that more confidence be placed in the results of the total count method. The experimental results were analyzed in terms of the existing activated rate process theory. The activation energy for diffusion was shown to decrease markedly as the temperature increased. This was attributed to a variation in the heat of activation with temperature, probably related to a change in the distribution of anions associated wilh the cation. In terms of a model, suggested for diffusion in liquid silicates, differences in the aclivation energies for diffusion and electrical conduction may arise from the effect of the electric field applied in conduction measurements. It is generally accepted that liquid silicates consist of cations and an equilibrium distribution of complex anions determined by temperature and composition. Transport properties in molten silicates are of interest, not merely because of their relevance to the kinetics of pyrometallurgical reactions and glassmak-ing processes, but also because they are useful to development of the theory of such ionic liquids. Self-diffusion is one such transport process that may, if studied for liquid silicates of widely varying compositions, indicate structural changes through changes in the activation energy for diffusion. The self-diffusion of calcium, silicon,' sulfur: aluminum, 4 and oxygenS in lime-alumina-silica melts and of iron6 in molten iron silicates have been measured. Unfortunately, the errors in some of the reported activation energies for diffusion are too large to allow firm conclusions concerning structure and the mechanism of the diffusion process to be drawn. The research reported here was a study of the self-diffusion of sodium in liquid sodium silicates. The soda-silica system was chosen since: i) a reasonable composition range can be covered in the binary system at moderate temperatures; ii) suitable isotopes of sodium (radioactive Na 22 and NaZ4) can be obtained; iii) data on the electrical conductivity and viscosity of sodium silicate liquids are available. However, the range of composition actually used in diffusion experiments was limited, to 20 to 35 wt pct soda, by the relatively high viscosity of silica-rich compositions and by evaporation of soda from basic melts. EXPERIMENTAL PROCEDURE The capillary-reservoir technique was used, wherein a radioactive tracer, Na 22, incorporated in the capillary melt, was allowed to diffuse out of the platinum capillary tube into a large reservoir of silicate liquid containing a chemically identical melt, but without radioactive tracer. After a specific diffusion time, both the total depletion in the tracer concentration and concentration-distance profiles of the diffused samples were measured by procedures to be described later. The diffusion cell assembly was similar to that used by Koros and King.' The temperature of the diffusion cell was measured with a calibrated Pt, Pt-10 pct Rh thermocouple located at the center of the liquid reservoir. The same thermocouple was used to obtain the temperature profile in the reservoir. The temperature at the top of the reservoir was slightly higher (2°C) than that at the bottom, to minimize convection in the capillary tubes, which were placed, open end up, in the reservoir. Convection was not expected to be a problem since the length-to-diameter ratio of the tubes was about 12:1 and the maximum capillary diameter was 1 mm. The diffusion cell was heated in a molybdenum-wire resistance furnace, previously used by Koros and King, but somewhat modified. A Pt, Pt-10 pct Rh thermocouple enclosed in an alumina tube and located near the furnace winding was used in conjunction with a preamplifier and Micromax proportional controller for temperature control, within 4°C, at temperatures near 1500°C. Before starting a diffusion run, the furnace was heated to the desired temperature and an alumina guide assembly for the capillaries was slowly lowered to within 2 cm of the liquid reservoir. The capillaries were thus heated to about the temperature of the bath. The run was started by lowering the assembly till the open ends of the capillaries were about 1 cm below the surface of the liquid. The run was ended by raising the assembly to about 15 cm above the liquid bath. Later, the sample assembly was slowly withdrawn from the furnace. Six diffusion samples were usually run at the same time. Three runs made with the open ends of the capillaries down were discarded because in the majority of these samples air bubbles trapped at the open end were observed. Some glass adhered to the outside of the capillary on withdrawal. This was carefully removed and used to check that the Na 22 activity in the sink remained at a low level. Materials. Nonradioactive sodium silicates were prepared by melting, in a platinum crucible, weighed quantities of sodium carbonate and powdered silica. To prepare radioactive sodium silicates, Na2 obtained in HC1 solution, was first checked for radioactive impurities by obtaining a y-ray energy spectrum, then the chloride ions were removed by anion-ex-

Jan 1, 1968

By A. H. Tousley, C. L. Vickers

The author presents a history of the development of the Port of Long Beach from its beginning in 1905 to the present construction of a new bulk loading facility. In describing this new facility, emphasis is placed on such aspects as rail car and truck handling, gravity yard, rotary car dumping, bottom dumping, car dumping equipment, feeding and conveying, ship-loader-stockpiler, stockpiling and reclaim, dust control, and construction problems. Development of the Port of Long Beach, Calif. (see Fig. I), began in 1905. In that year private Long Beach interests acquired 800 acres of marshland in the Inner Harbor area and initiated a program of channel dredging and land reclamation. Efforts to establish a municipal port began a short time later and culminated in the opening of Pier 1 in 1911. An event of even greater significance to the port future also occurred in 1911. This was the tideland grant enactment by the state legislature that conveyed to the city of Long Beach all of the state's rights in the tidelands located within the city boundaries. The grant stipulated that all revenue produced from the tidelands be used for the development of navigation, commerce, and fisheries. During the next 15 years up to 1926, the port's commercial growth was steady, although relatively slow. During this period, several fundamental steps in the development of a major harbor were accomplished. These included the creation of the Board of Harbor Commissioners in 1917, the dredging of the Inner Harbor and entrance channel to accommodate deep draft vessels, and the correction of a serious silting problem through construction of the Los Angeles River Flood Control Channel. These efforts bore fruit during the ensuing 10 years in the establishment of more than $30,000,000 worth of industrial plants and private marine terminals in the Inner Harbor. Commerce over municipal wharves also increased more rapidly, and it became necessary to start the development of the harbor in a seaward direction. In 1936, oil was discovered in the harbor area, and the first Harbor Dept. well was brought in 2 years later. It soon became evident that the city of Long Beach would receive substantial revenue that, under the terms of the state grant of 1911, must be used in the development of the port. It was further realized that to properly guide and coordinate such development, a long range comprehensive plan was essential. The Board of Harbor Commissions contracted with G. F. Nicholson and J. F. Collins, consulting engineers, for the preparation of such a report that was completed in 1940. The Nicholson-Collins report proposed the development of an East Basin, between the entrance channel and the Los Angeles River, and a West Basin in the area now occupied by the Long Beach Naval Shipyard. Twenty full-size berths were to be provided in the East Basin and more than fifty berths in the West Basin. The report recommended extensive modern terminal facilities for handling waterborne cargo. Attention was given to improvement of the street and highway system to give better vehicular access and to avoid congestion within the port. To a large extent the recommendations of the Nicholson-Collins report were followed in the subsequent development of the East Basin. This development was greatly accelerated by World War 11, with its need for increased oil production and additional shipping facilities. The wartime and immediate postwar construction was largely concentrated on Pier A, with the development of Piers B, C and D following in more recent years. An important factor in the planning of these piers was their dual function as oil drilling sites and cargo piers. The Navy's acquisition of the West Basin area made it necessary to depart from the Nicholson-Collins plan and find other areas for future expansion. At the present time only one Inner Harbor Port-owned area having protected deep water frontage remains undeveloped. This is the property fronting on Channel 2 in the Inner Harbor acquired in December 1957, from Pacific Dock and Terminal Co. The growth of the port has been in a southerly direction since the construction of the Long Beach Naval Shipyard in the West Basin area. Recent extension of Piers F, G and J into the ocean follows typical port construction methods developed during the expansion of the Middle Harbor during the last 20 years.

Jan 1, 1963

By Mark C. Malamphy

The occurrence of outcrops of bituminous schists and sandstones impregnated with heavy asphaltie petroleum first directed attention to the São Pedro area as a possible source of commercial production of petroleum. Since 1920, more than 20 wells have been drilled in this area. The discovery of oil shows and small quantities of natural gas in some of the early wells led to the continuation of drilling in the hope that more important findings would result. During the early part of 1934, detailed magnetometer observations were made in this area, and a considerable number of torsion balance stations were occupied. The results of these geophysical observations help considerably to clarify the structure of the area and the very considerable amount of geologic information available makes possible a much more exact interpretation of geophysical anomalies. In presenting the results of these observations, and interpretation of the geophysical data, certain actual case problems are included; i.e., geophysical anomalies due to anomalous masses of which the forms and positions are more or less known. Although anomalies due to igneous intrusions are probably more important to geophysicists in Brazil than in other countries, these data have a certain interest for all geophysicists, particularly because they were obtained in the south magnetic hemisphere, where the lines of magnetic force are directed upward, and in a region of moderately low inclination. This is considered as a geological-geophysical problem, and only passing mention will be given to the petroleum possibilities of the area. General Geology The location and general geology of the São Pedro area are shown in the sketch map of Fig. 1, which is adapted from the geologic map of South Brazil compiled by Oppenheim1,†- who gives the geologic column of South Brazil (So Pedro and vicinity) as follows:

Jan 1, 1940

By Mark C. Malamphy

The occurrence of outcrops of bituminous schists and sandstones impregnated with heavy asphaltie petroleum first directed attention to the São Pedro area as a possible source of commercial production of petroleum. Since 1920, more than 20 wells have been drilled in this area. The discovery of oil shows and small quantities of natural gas in some of the early wells led to the continuation of drilling in the hope that more important findings would result. During the early part of 1934, detailed magnetometer observations were made in this area, and a considerable number of torsion balance stations were occupied. The results of these geophysical observations help considerably to clarify the structure of the area and the very considerable amount of geologic information available makes possible a much more exact interpretation of geophysical anomalies. In presenting the results of these observations, and interpretation of the geophysical data, certain actual case problems are included; i.e., geophysical anomalies due to anomalous masses of which the forms and positions are more or less known. Although anomalies due to igneous intrusions are probably more important to geophysicists in Brazil than in other countries, these data have a certain interest for all geophysicists, particularly because they were obtained in the south magnetic hemisphere, where the lines of magnetic force are directed upward, and in a region of moderately low inclination. This is considered as a geological-geophysical problem, and only passing mention will be given to the petroleum possibilities of the area. General Geology The location and general geology of the São Pedro area are shown in the sketch map of Fig. 1, which is adapted from the geologic map of South Brazil compiled by Oppenheim1,†- who gives the geologic column of South Brazil (So Pedro and vicinity) as follows:

Jan 1, 1940

By D. J. Carney, R. R. Burt, E. J. Whittenberger

Hardenability (multiplying) factors for carbon, mongonese, silicon, chromium, nickel, and molybdenum have been developed for hypereutectoid low-alloy steels in which bainite is the first subcritical transformation product. These factors permit the calculation of 95, 80, and 50 pct martensite hardenability from chemical composition when steels with spheroidized structures are quenched from 1475°, 1525°, and 1575°F. The strong contributions to hardenability of the less expensive elements, silicon and manganese, suggest their use to obtain additional hardenability in hypereutectoid low-alloy steels. DURING the past decade a number of investigators'"11 have carefully developed information which permits calculation of the hardenability of medium -carbon low-alloy steels from chemical composition and grain size. These data have been especially valuable in developing less costly low-alloy steel compositions with equivalent or Improved

Jan 1, 1957

By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

Jan 5, 1950