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By H. A. Schwartz, W. Kenneth Bock

In this paper it is shown that when the tensile strength of a given steel in various states of heat-treatment is plotted against its elongation, a straight line results. The equation of this straight line can be computed with considerable accuracy from its chemical composition. The appropriate equations are given. The logarithm of the slope of the tensile-strength locus is shown to be proportional to the cumulative effect of the total alloy addition and the vosition of the line to be directly proportional to the cumulative effect of the alloy content. It is further pointed out that heat-treatment is more effective than composition in determining yield ratio. The latter enters mainly by its effect on hardenability, which is briefly discussed. Reduction of area and Brinell number are given some incidental attention. The data are applicable only to steels that have been normalized and/or quenched. The steels, if normalized, may or may not have been tempered. If quenched they must have been tempered at or above 4oo°C. (75o°F.). Introduction Cast steels vary in composition and frequently are used in various states of heat-treatment. It is obviously important to be able to predict the compositions that might accompany specific engineering properties by suitable selection of heat-treatments. For cast steels, which are of necessity produced heat by heat in accordance with the particular requirements of the castings to be poured, there has been, happily, much less tendency to standardization than for rolled products, whose destination is not necessarily known when particular ingots are made or rolled. It is of distinct advantage to the steel foundry-men to be able to make steel of given properties, using alloys that can be recovered from scrap, or most conveniently or cheaply bought, rather than a particular formula adopted in the interest of standardization. The heat-treatment appropriate to securing a given result in a given steel is well known to be closely related to composition. For example, molybdenum steels are not much softened by tempering except at rather high temperatures. Highly alloyed steels are "air-hardening," and on cooling in air behave like carbon steels that have been quenched. With these matters, we do not concern ourselves in this paper, although we recognize their importance. The entire picture evidently will be very complex and can be brought within accurate understanding only if our knowledge of test results can be coordinated in terms of general principles.

Jan 1, 1944

By H. A. Schwartz, W. Kenneth Bock

In this paper it is shown that when the tensile strength of a given steel in various states of heat-treatment is plotted against its elongation, a straight line results. The equation of this straight line can be computed with considerable accuracy from its chemical composition. The appropriate equations are given. The logarithm of the slope of the tensile-strength locus is shown to be proportional to the cumulative effect of the total alloy addition and the vosition of the line to be directly proportional to the cumulative effect of the alloy content. It is further pointed out that heat-treatment is more effective than composition in determining yield ratio. The latter enters mainly by its effect on hardenability, which is briefly discussed. Reduction of area and Brinell number are given some incidental attention. The data are applicable only to steels that have been normalized and/or quenched. The steels, if normalized, may or may not have been tempered. If quenched they must have been tempered at or above 4oo°C. (75o°F.). Introduction Cast steels vary in composition and frequently are used in various states of heat-treatment. It is obviously important to be able to predict the compositions that might accompany specific engineering properties by suitable selection of heat-treatments. For cast steels, which are of necessity produced heat by heat in accordance with the particular requirements of the castings to be poured, there has been, happily, much less tendency to standardization than for rolled products, whose destination is not necessarily known when particular ingots are made or rolled. It is of distinct advantage to the steel foundry-men to be able to make steel of given properties, using alloys that can be recovered from scrap, or most conveniently or cheaply bought, rather than a particular formula adopted in the interest of standardization. The heat-treatment appropriate to securing a given result in a given steel is well known to be closely related to composition. For example, molybdenum steels are not much softened by tempering except at rather high temperatures. Highly alloyed steels are "air-hardening," and on cooling in air behave like carbon steels that have been quenched. With these matters, we do not concern ourselves in this paper, although we recognize their importance. The entire picture evidently will be very complex and can be brought within accurate understanding only if our knowledge of test results can be coordinated in terms of general principles.

Jan 1, 1944

By C. G. Palagi, S. S. Stillar

The C. E. Weed concentrator treats 51,000 tons per day of 0.5% to 0.7% copper ore received from the Berkeley Pit, the Continental East Pit and the Butte underground mines. Improved operating techniques and conversion from semi-autogenous secondary grinding to ball milling have increased tonnage from an original design of 42,000 tpd. Separate treatment of sands and slimes, with recovery of soluble copper from the slimes, has increased total copper recovery. Concentrator tailings are pumped 600 vertical feet and 20,000 horizontal feet for disposal.

Jan 1, 1976

By George W. Sears

In preparing this symposium, our ambition was to elicit authoritative expression of opinion concerning important selected phases of the industry from men active in it. Responses to requests for contributions were gratifying, especially so in view of the short time available. The generous and cooperative spirit of the industry as a whole is amply evident. Responses were received from the following, who are therefore the true authors of the paper: W. G. Adamson, General Manager of the pershin; Quicksilver Co., Lovelock, Nev.; Dudley Baird, Vice President, Pacific Foundry Co., San Francisco; Walter W. Bradley, State Mineralogist of California; W. D. Burcham, General Manager of the Brewster Quicksilver Consolidated, Terlingua, Tex.; William Forstner, San Francisco; H. W. Gould, of H. W. Gould & Co., San Francisco; Marcus Hulings, General Manager of the Chisos Mining Co., Terlingua, Tex.; Frank J. Katz, Chief Engineer, Division Mineral Statistics, United States Bureau of Mines, Washington, D. C.; Lloyd J. Lathrap, Superintendent, Nevada Quicksilver Mines, Inc., Lovelock, Nev.; W. R. Moorehead, General Manager, New Idria Quicksilver Mings, Inc., Idria, Calif.; F. W. Oakes, Jr., Terlingua, Tex.; C. N. Schuette, San Francisco. Brief Economic History of Quicksilver in the United States Quicksilver ore was first discovered in the United States at what was later the New Almaden mine in California, in the year 1824. Production also began here, but not until 1850, when it was stimulated by the active demand caused by gold-mining operations. Prospecting for quicksilver was active, high-grade ores were found and ample production lowered the price from $100 per flask in 1850 to about half that figure for the greater part of the next 10 years. During the succeeding decade, many new quicksilver mines were found; production increased at a time when the local demand diminished, so that most of the product was exported. The third decade of quicksilver mining in the United States witnessed the development of the pan amalgamation process, particularly in Com-stock silver-mining operations. A suddenly increased demand sent prices soaring, the all-time peak of quicksilver production followed, and the highest price was soon replaced by the lowest one on record. Huge quantities of quicksilver were exported between 1870 and 1880 and exports continued in decreasing measure for three decades to 1910. In

Jan 1, 1930

By A. S. Richardson

THE conditions that make necessary the mechanical ventilation of the Butte mines of the Anaconda Copper Mining Co. are due to a number of causes, all of which are incidental to the depth at which mining operations are now carried on. The main object to be accomplished, of course, is the reduction of the temperature and humidity of the air in the working places. Ventilation fans, both surface and underground, have been used for many years, but increasing depth has made the problem much more difficult. Further improvement in both ventilation equipment and methods, therefore, became necessary; and it is the purpose of this paper to describe the work planned and done under the improvement program. The mines of the district have been frequently described in various technical publications, so a description is unnecessary here. From a mine-ventilation viewpoint, compared with coal-mine ventilation systems, the problem is complicated by the fact that the workings to be ventilated are situated on a large number of steeply dipping veins which frequently intersect and are faulted, and also by the fact that the extent, or existence, of orebodies is not definitely known in advance of actual development work. For these reasons ventilation work cannot be planned in advance of actual operations, nor can such regular systems of ventilation as are used in working the more uniform and continuous bodies of coal be developed. When operations are conducted at a normal rate, about 10,000 miners are employed on two shifts, so that about 5000 men will be underground at one time. But as ventilation is necessary to reduce high temperature and humidity due, mainly, to natural causes, the quantity of air per man per minute is not a governing consideration in determining ventilation requirements. Most important among the numerous sources of heat and humidity in the mines are : heat generated during decay of mine timber; heat and humidity given off by mine rock and water; heat generated by oxidation of sulfide minerals; heat given off by electrical equipment; heat generated by mine fires (in certain localities).

Jan 2, 1922

By Kyle Wightman

INTRODUCTION CRA Limited is the largest mining group in Australia by value of sales and the second largest company in Australia in terms of share market capitalisation. In the past 25 years, CRA, its predecessors and affiliates have been involved in a number of mining and further processing developments in Australia and elsewhere. Many of these have been financed using project financing techniques. These include Comalco's development of the Weipa bauxite deposits in Northern Queensland in the late 1950's, the Hamersley iron ore developments in the Pilbara region of Western Australia in the mid 1960's, the Queensland Alumina Limited alumina refinery in Gladstone, Queensland, at about the same time, and the Bougainville copper project in 1969/70. In the past three years CRA has again utilised project financing techniques to fund its Tarong steaming coal project in Queensland, the Blair Athol steaming coal project also in that State and CRA's interest in the Argyle diamond project in the Kimberley region of Western Austrlia. PROJECT FINANCE DEFINED Nevitt Definition Nevitt's is the most frequently quoted definition - "A financing of a particular economic unit in which a lender is satisfied to look initially to the cash flows and earnings of the economic unit as the source of funds from which a loan will be repaid and to the assets of the economic unit as collateral for the loan." Risk and Balance Sheet Treatment It is important to focus in more detail on two aspects of project financing, risk and balance sheet treatment. The assessment of the various elements of risk in a project and the sharing of that risk between sponsors and lenders is the most critical feature. At one end of the spectrum is full absorption of risk by the sponsor(s). This can be described as "on risk" or "on credit" or "full recourse" to the sponsor(s) and is effectively a corporate financing. At the other end of the spectrum the lenders absorb the whole risk in a non-recourse financing which is "off risk" or "off credit" for the sponsor. The other aspect is the sponsor's balance sheet treatment. If the balance sheet of the economic unit undertaking the project and the financing need not be consolidated into the balance sheet of the sponsor (because ownership does not exceed 50%) then the financing may be described as off-¬balance sheet. If consolidation is required then the financing is described as on-balance sheet. Most project financings involve some recourse to the sponsor, i.e. they are limited recourse. Very few are non-recourse or off credit to the sponsor. Limited recourse financings may be on-balance sheet although many may also be off-balance sheet insofar as consolidation is concerned. However, sponsor support may very well be a contingent liability to the sponsor and require disclosure by way of note to the balance sheet should consolidation not be required. CORPORATE FINANCE CONTRASTED A financing which is on credit or full recourse to the sponsor, whether it is directly borrowed or guaranteed by that sponsor, is a corporate financing. Lenders will tend to base their credit assessment on a historical assessment of the sponsor's activities and its financial results rather than an assessment of the project or a detailed assessment of the future activities and prospects of the sponsor. PROJECT FINANCE - A BORROWER'S PERCEPTION Although CRA could choose to arrange all finance on a corporate basis (except perhaps for the very largest projects or acquisitions), project financing techniques provide a number of specific advantages which CRA has noted and which should be carefully considered by a project sponsor. Advantages

Jan 1, 1985

By M. J. Mullikin, J. B. Conway

Several different equation forms were studied to determine the extent to which each particular equation type yielded an accurate representation of a given set of first-stage creep data. Specially developed least-squares computer programs were employed to obtain unique solutions for the creep-equation constants. In studies of creep data for lead at 14.5"C, nickel at 70OCC, and arc-cast tungsten at 2400°C consistently good representations were afforded by a third-degvee polynomial in t113. Other effective correlations were obtained with the Andrade, Cottrell-Aytekin, and de Lacombe equations along with a third-degree polynomial in t112. A newly proposed creep equation involving a hyperbolic-sine term in t1'3 was also found to yield very satisfactory results. This appears to be the first use of such a functional relationship in the analysis of transient creep behavior. In general, the deformation behavior of a material subjected to a tensile load is described in a strain-time plot. Experiments have shown that, following the instantaneous elongation which results on loading, the instantaneous slope (i.e., creep rate) of the strain-time curve decreases gradually with time and approaches what appears to be a constant value. Equations, therefore, which are proposed to provide an analytical representation of such first-stage or transient creep behavior must be consistent with these observations. In other words, at time zero, these equations must yield a finite deformation value corresponding to the elongation on loading. Furthermore, the first derivative of these equations must exhibit a fairly high although finite value at time zero, and then values which decrease with time. It is also preferable, in general, that the derivative eventually assume a constant value at high time values. Although many studies of first-stage creep behavior have been made and numerous equation forms have been proposed for expressing this type of deformation behavior, it is still not possible to state with any assurance which functional relationship will be adequate for a given set of measurements. Parabolic relationships have been employed most extensively although logarithmic expressions have been shown to be applicable in some instances. Combined forms1 have been studied in considerable detail and have on occasion been found to be very effective. One such expression is that of iXndradea and involves a modified parabolic expression: where 1 is the instantaneous length, lo is the length immediately following load application, t is the time, and p and k are constants. Another combined form has been proposed by weaver3 as follows: where E is the instantaneous strain, is is the linear creep rate, t is the time, and a and b are constants.

Jan 1, 1967

By E. C. Harder

AT a Meeting of the New York Section, on May 23, 1918, the sole subject of discussion was the nature and occurrence of iron ores in certain parts of the world.? Owing to the importance of this subject, it has been deemed' advisable to publish the remarks made at that meeting in the form of a paper, for presentation at the Milwaukee Meeting, instead of in the usual place, under News of Local Sections. The remarks related to the following districts: Brazil, by E. C. Harder, of the U. S. Geological Survey; Scandinavia, by Waldemar Lindgren, of the U. S. Geological Survey; Cuba, by C. M. Weld, of the U. S. Bureau 'of Mines; Southern Europe, by A. C. Spencer, of the U. S. Geological Survey; China, by H. Foster Bain, of the U. S. Bureau of Mines; Alsace-Lorraine, by Sidney Paige, of the U. S. Geological Survey. BRAZIL By E. C. Harder During the years immediately preceding the war, the iron ores of Brazil were attracting the attention of iron operators both in Europe and in the United States. This was clue to the large quantities of practically undeveloped ore available, and to its great purity. It is reasonably safe to state that had capital not been diverted from the exploitation of these deposits to war purposes, Brazilian iron ores would probably now be offered in European and American markets. It is certain that after the war these ores will play a prominent part in the economic reconstruction of Europe and perhaps in the development of America.

Jan 9, 1918

By Philip B. Bucky

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Jan 1, 1942

By Ralph A. Sherman, J. M. Pilcher

BY surface treatment of coal is meant the application of a material, either solid or liquid, to the surface of pieces of coal. The purposes of surface treatment are varied. They may be to identify or "trade-mark" the coal, to modify the burning characteristics, the coking tendencies, or the behavior of the ash, to prevent the freezing of wet coal, or to control the dust. The control of dust is the usual purpose of surface treatment. TRADE-MARKING COAL The application of color to the surface of coal for the purpose of identification and registration of the trade-mark has been practiced to some extent. In 1928, the Glen Alden Coal Co. began to color its coal and adopted the trade-mark, "Blue Coal." The Old Ben Coal Co. later followed a similar practice with "Green Coal." A commoner means of identification of coal has been the stenciling of designs or pasting labels on large lumps or in the distribution of small cardboard tags through the smaller sizes. The details of the method used to color coal have not been revealed. Usually all of the coal is not treated, because of the expense. Only enough pieces are colored to show clearly when distributed through the coal.

Jan 1, 1943

GENERAL COMMITTEE GERALD F. G. SHERMAN, Chairman. ARTHUR NOTMAN, Secretary. NORMAN CARMICHAEL, JOHN C. GREENWAY, W. L. CLARK, W. G. McBRIDE, B. BRITTON GOTTSBERGER, FOREST RUTHERFORD. General Committee on Transportation WALTER DOUGLAS, Chairman. CLEVELAND E. DODGE, Secretary. ARTHUR S. DWIGHT, JOHN C. GREENWAY, JULIUS KRUTTSCHNITT, JR. Committee at El Paso W. D. GORDON, ROBERT McCART, JR., W. W. ROSE. Committee at Santa Rita JOHN M. SULLY, Chairman.

Jan 12, 1916

By E. V. d’Invilliers

The position of these magnetic ore-mines, with reference to the county-seat, is shown in Fig. 1. They are situated on the south margin of the Great Valley, five miles south of Lebanon, and about midway between Reading on the Schuylkill River and Harrisburg on the Susquehanna River, in three prominent, contiguous hills, standing in front of the Mesozoic red shale arid sandstone hill country of northern Lancaster and southern Lebanon counties, and overlooking the great limestone plain to the north. The three hills, named respectively Big, Middle, and Grassy Hills, and separated from each other by two branches of Furnace Creek, range in a nearly east and west direction for a distance of about one mile. Their summits are respectively 870, 715, and 700 feet above tide. The railroad line opposite the base of Middle Hill is 575 feet above tide at Cornwall and 471 feet at Lebauon. These features are all distinctly illustrated in the contour-line map accompanying this paper, but are made still more clear in the relief. map, Fig. 2, comprising, as it does, about six square miles of territory contiguous to the ore-mines. This is a photographic plate of a model made by Mr. A. E. Lehman, from surveys of my own and Mr. W. F. Shunk. The model was built in layers of cardboard, each layer representing one 10-foot contour-carve line. The scale was the same as the original map, 400 feet= 1 inch, without any vertical exaggeration. The lowest contour-line is 530 feet above ocean level; the highest, 1075 feet. The center of the model was made the focusing-point of the view, which was taken—according to scale—51/2 miles north from and 24 miles above the focusing-point, looking southward. When first mined in the last century these hills exhibited smoothlyrounded surfaces, composed of soft weathered ore of great parity, beneath which lay the great mass of hard ore, constituting the whole

Jan 1, 1886

By W. D. Felix, R. D. Smith, J. A. Campbell

The mechanism most consistent with available information on atmospheric trace element emissions involves the volatilization of a significant fraction of many trace elements during coal combustion, with subsequent condensation on fly ash as the combustion gases cool. The larger surface-td-volume ratio of the smaller particles leads to an enrichment of the volatile trace elements. From an environmental viewpoint, the submicron size particles are of greatest concern. These particles show the highest concentrations of trace elements, are least efficiently collected by pollution control devices, have high atmospheric mobilities, and are deposited preferentially in the pulmonary and bronchial regions of the respiratory system. The mechanisms for trace element enrichment and formation of submicron particles will be described.

Jan 1, 1981

By Young C. Kim, Francis Martino, Ish Chopra

For the past two and one-half years, various emission control strategies were jointly developed by the University of Arizona and the Homer City Owners to com- ply with the clean air requirements at its Homer City Power Plant. Some of the available options for the SO2 emission control by the Homer City Owners were:l)cleaning of run-of-mine coal,2) scheduling of mining operations at its captive mines, 3) blending the captive mine coal with externally purchased low sulfur coa1,and 4) placing a partial FGD system. This paper describes two specific emission control strategies developed and implemented. These are: 1) production scheduling at the mining face to minimize sulfur variability, and 2) external purchasing of low sulfur coal for further blending. The main objective of this paper is to share our experiences on implementing the developed strategies. This paper emphasizesthe need for proper mine planning on a short-term basis, if the power plant is to meet the desired objective.

Jan 1, 1983

PRODUCTION of nonmetallic mineral raw materials used by the fertilizer, ceramic, chemical, and construction industries and many others, was greater during 1953 than in any previous year. Production of fertilizer minerals was the highest in history despite somewhat decreased consumption in the second half of the year. Marketable phosphate rock production increased 10 pct to an estimated total of 13.1 million LT, valued at $78.5 million, and potash production was estimated at 1.8 million tons of K2O equivalent, valued at over $60 million. Crude gypsum output exceeded the 1952 total and approached the record of 8.66 million tons mined in 1951, with indications that 1953 will show a new all-time high. Gains and losses among gypsum products were irregular, with major gains in plate- glass and terra-cotta plasters, sanded building plasters and miscellaneous building plasters, and principal declines in base-coat plasters, prepared finishes and tile. Lath and wallboard outputs were each about 20 pct higher than in 1952.

Jan 2, 1954

By R. R. Harvey

Recent evidence has indicated that the films forming at crude oil-water interfaces are the result of naturally occurring su,rface-active components in the crude oil rather than oxidation products resulting from exposure of the oil to air. Since the presence of such films may strongly affect the displacement of oil from porous media, a knowledge of their composition and formatiorz is of fundamental importance. In this study, without the assumption of a specific mechanism, film formation is considered to involve the transfer of a weakly surface-active species in solution in the oil to the oil-water interface. The film gas law and the Gibbs adsorption equation may thus he applied to the system. The rigid films which form upon decrease of the oil-water interfacial area are considered a result of the very slow rate of re-solution of the film material into the oil. When the shrinkage of the interface is very rapid, the amount of film material leaving the interface is negligible, and the system may then be treated in the same manner as an insoluble film. The combination of these treatments leads to a new concept of the film factor in which it may he quantitatively related to the concentration of film-forming material at the interface. Suitable experiments can then yield the following information. 1. Original concentration of surface-active species in the oil. 2. The change of concentration with time. 3. Concentration of surface active species at the interface. 4. The change of this concentration with time. 5. Interfacial tension of the system at any time and its variation with time. 6. Equilibriunz concentrations for a given set of conditions. 7. Concentration requirements for solid film formation. 8. Molecular diameter of the adrorbed species. These calculations may be made solely from data taken from measurements on the original oil. While using the pendant drop method of interfacial tension measurement of crude oil-water systems, Bartell and Niederhauser' remarked on the thin, transparent, pliable, solid films or membranes which were often formed at the interface between crude oil and water. As a result of their observations of these films, Bar-tell and Niederhauser concluded: 1. The films are formed by material from the oil adsorbed at the interface rather than by a reaction at the interface. 2. The adsorption of the film-forming material is a rather slow process. 3. There are good indications that the process is reversible; i.e., the film constituents may re-dissolve into the oil. 4. The film will spontaneously spread over any new surface formed. 5. The process of adsorption at the interface is accompanied by a decrease in the interfacial tension of the system. Although they had proved that film formation was not due to a reaction at the interface, Bartell and Niederhauser were unable to demonstrate conclusively whether these film-forming constituents were present in the original reservoir oil or whether they were formed as oxidation products after exposure of the oil to air. Recent evidence seems to point to their presence in the original oil. Although the true nature of the film-forming constituents is still uncertain, these conditions would be fulfilled by the assumption of the presence of a slightly soluble surface-active component in the original oil. This component would migrate to a freshly formed interface because it would thereby lower the free energy of the system. The component at the surface constitutes an expanded monolayer which would become compressed, upon retraction of drop, due to the slow rate of re-solution of the film components into the bulk of the oil. It is possible, by involved extraction processes, to separate or at least concentrate this film-forming fraction. However, using the assumptions made above, the technique of monolayer film study may be applied to reveal much of the nature of the adsorbing material without resorting to an actual separation of the film-forming constituents.

By W. B. Wise, H. D. Attra, W. M. Black

The purpose of this paper is to illustrate a comparatively new approach for solving a problem that has plagued oil producers for many years—how to make the most money with available field production capacity. In a very basic operation such as a top-allowable one-well field, a computer and staff of engineers are not required to determine that the best operation is to produce that well at its maximum for as long a time as it will produce. However, as the problem becomes more complex and the number of wells and number of reservoirs increase, it probably will be a wise choice to devote some engineering thought and calculation time to determine the best way to operate that field on both an ultimate and day-to-day basis. Continued developments in the field broadly referred to as "operations research" have led to a number of useful engineering analyses for optimizing field operational problems. One of these techniques, termed linear programing, is parlicularly interesting because of its potential applications to the study of complex oilfield operating problems. Linear programing is concerned with the problem of planning a complex set of interde~endenl activities in the best possible (optimal) fashion. A field application of linear programing is being used to maximize daily income from a multi-reservoir producing operation. The initial results of this study indicate that the linear programing technique (I) can be applied effectively to field problems, (2) can be used to detect unsuspected avenues for improving operations and (3) can effect a significantly improved means of controlling field operations through the use of the highspeed computer. INTRODUCTION The usual approach for studying complex field operational problems has been to look in detail at several basic plans suggested by judgement and experience and, then, to choose the best plan from those investigated. This approach is entirely satisfactory provided: (1) that judgment and experience alone will reliably pick the best or near the best program as one of the plans to be investigated; and (2), and most important, that the factors which control field production will not change. This paper deals with the large group of field operations which are at least one-step removed from a satisfactory solution using the conventional method of analysis. Problems such as pipeline- and gathering-system design, transportation studies, large field development projects and multi-reservoir producing operations fall in this latter category. To find the best program for handling these problems when the best program is not obvious, a complete optimization study is required, and high-speed computers are required to continually update the program once it is selected. Operations of this type have an extremely large number of possible solutions. However, only one will result in maximum economic return and, more important, this one program must be re-evaluated and adjusted constantly to accomodate such changing field factors as the number of producing days, the price of crude, the discovery of new reserves, declining reservoir pressure with subsequent decline in production and a host of other factors which characterize specific operations. One of the most widely used, direct methods of optimization is a numerical procedure termed "linear programing", which is designed to investigate systematically each of the possible solutions involved in a given problem, determining rapidly and uniquely the optimum answer. As implied by the name, linear programing requires that all field variables be either defined or expressed in a series of interdependent linear equalities or inequalities. These relationships are solved simultaneously, using a form of matrix solutions to determine the optimum values for each producing variable that will maximize net profits. The solution techniques used in a recent field case study is termed the "simplex method" and is discussed in full detail in Ref. 1.

By Strathmore R. B. Cooke, William F. Stowasser

RESULTS presented in a previous paper1 have shown that the strength of fired pellets made from eastern Mesabi magnetite concentrates containing 8 to 9 pct Si02 as quartz and silicates is due to several processes which occur during firing. These are: l-recrystallization and cementation of the fragmented magnetite grains; 2-formation of slag from reaction between the quartz, silicates, and available ferrous iron, followed by slag-bonding of the magnetite grains; and 3-oxidation of the magnetite to hematite and subsequent recrystallization and grain growth of this constituent. Microscopic examination of all magnetite pellets fired in one operation in small and large-scale pilot plant furnaces and possessing normal strengths shows that the processes 1,2, and 3 have taken place; where strengths are low and the pellets are otherwise sub- normal, one or more of the processes has not occurred. For example, soft and friable red pellets may contain a central core of slag-bonded recrystallized magnetite which is strong enough in itself, but the shell contains only slightly recrystallized hematite, indicating that the maximum temperature reached was too low. Processes 1 and 2 can occur only under reducing conditions, as for example, when coal is intention- ally added to the original pellets; under neutral conditions, when pellets are fired in an inert atmosphere; or when pellets are brought so rapidly to temperature in an oxidizing atmosphere that oxygen diffusion to the core lags behind the recrystallization and slagging effects. This last-mentioned process has occurred in all pilot-plant shaft fur-

Jan 1, 1952

Note Any member who desires to be designated as being "Available for Consulting Work" can arrange it simply by sending a written request to the office of the Secretary of the Institute The following list of members is primarily arranged geographically, with secondary consideration to political subdivisions arranged alphabetically First, the states of the United States , then other North America, in order Alaska, Canada, Mexico, the West Indies, and Central America Then cones South America, Europe, Africa, and Asia, each including the near by islands associated with those continents Australia, the islands to the north, and the Pacific islands except Japan are grouped together under Oceania The various countries are indexed on the preceding page NORTH AMERICA UNITED STATES ALABAMA America -Dyar, G C Anniston -DePriest, S H Klugh, B G Lefforge, J W Auburn Poor, R S Bankhead -Armstrong, W D Bessemer -Beck, A IV, Jr Carnes, D Chabot, L S , Jr Creveling, J C

Jan 1, 1952

THE problem of reaction rates in the open-hearth process is essentially that of trying to form a fairly clear picture of the "chemical mechanisms" in the bath. Quantitative data on reaction rates would perhaps not be of much practical importance even if they were available; however, what few approximate data there are can be used in combination with data given in Chapters 16 and 17 to sketch a picture of the "chemical mechanics" of the open-hearth process that is consistent with essentially all the present available evidence. The result may later be found incorrect in many details but even so it will illustrate certain useful methods for obtaining a clearer understanding of the process. Consistent with the treatment in Chapter 15, but in simpler terms, we may say that chemical reactions in general involve the following elements or steps : 1. The reacting molecules are mixed together in space in such fashion as to favor collisions among them. 2. Units of what is usually an intermediate molecular arrangement called an activated complex are formed at a certain rate, depending on temperature and concentrations. 3. .These activated complex units decompose into the reaction products (this step usually assumed to be so rapid as never to limit the over-all process). 4. In any of these steps, heat energy may have to flow into, or away from, the reaction zone to permit the reaction to proceed. 5. The products of reaction will usually have to move out of the way to permit further reaction. The temperature factor enters mainly through step 2, and its effect is very marked. (What is called temperature is really the mean energy content of all the molecules of the substance involved; at any one temperature a certain proportion of the molecules will have much higher energy content than the mean value.) Various reaction rates measured at around room tem-

Jan 1, 1964