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By A. Roberts

This paper reviews progress in equipment design and in the techniques applied to mine lighting in Great Britain. The incidence of the disease miner's nystagmus, which was a major source of concern only a few years ago, has now diminished, largely owing to improvements in standards of lighting in mines. The reorganisation of the coal mining industry, involving increasing mech-anisation, together with new safety legislation, has brought about the widespread use of mains electric lighting underground. An account is given of some of the results of research to determine the lighting conditions needed for compliance with the compulsory legal requirement of "sufficient and suitable" general lighting at specific localities in British mines. Some details are given of the techniques applied and the results of recent research in the problem of glare from miners' cap lamps. Of the various factors in the working environment of the miner, it is true to say that lighting is seldom given attention comparable with that devoted to other factors, such as dust, heat and humidity, or atmospheric gas content. No doubt one reason for this lies in the ability of the human eye to adapt itself to low brightness levels. Be that as it may, the fact is that at the turn of the 20th century the miner's working light improved little throughout the centuries during which mining technology has developed. Indeed, in coal mines which encounter a methane explosion hazard, flame safety lamps, with a luminous intensity less than one candle power, were virtually the sole means of lighting during almost the whole of the 19th century. The 20th century has witnessed a substantial improvement in lighting techniques underground in coal and metalliferous mining. In Great Britain the general pattern has been one of standards periodically raised by the implementation of Statutory Regulations imposed under successive hlines Acts, but it is fair to add that the more progressive mining companies usually anticipated the Statutory Regulations, which when they have been put into effect have served to turn into general practice what was already being done at the better mines. In earlier years, official requirements were limited to the specification of approved lamp designs, with stipulated minimum values of luminous intensity and light output, but more recently the necessity of satisfactory maintenance of standards during service has been recognized, and the current regulations not only require that a maintenance organisation should exist, but also specify a maximum permissible depreciation below initial approval standards.'

Jan 1, 1961

By Edward Capillon

THE problem of scrap is probably of greater importance inn the production of gold, silver and other precious metal alloys than is the case for base metals and alloys. Remelting of gold and silver scrap in the shop is always a costly process because it involves losses by oxidation of the base metals in the alloy with a consequent increase in the percentage of precious metal. This is most marked in the case of alloys containing the low-boiling and easily oxidized metals zinc and cadmium. Since it is. not generally feasible to assay every shop remelt it follows that the possibilities of lost values are large. So-called rolled gold and silver plate is made by soldering or welding the precious metal alloys onto base, metal. Such plate when defective must be sent to the refinery to recover the gold and silver values, thereby involving additional expense in the form of refining charges. It is obvious therefore that gold and silver alloy scrap is an important item in manufacturing cost and must be reduced to a minimum. The amount of scrap resulting from poor metal will depend on a number of factors in the manufacturing operations, not least among which is the melting and casting practice. The notes which follow are a summary of experiments performed at various times to determine what variables in melting and casting are influential in the production of sound alloys.

Jan 1, 1930

By H.A. Bedworth

AlloTs of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry l proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche 3 and Corson. 4 The constitution of the system has also been recently investigated by Matuyama, 5 and in the laboratories of the American Brass Co. by Smith. 6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of the constitution of copper-silicon alloys, the solubility reaches its maximium value, 6.7 per cent. silicon, between 721" and '782" C. At 852" (1. the solubility is 5.25 per cent., while at 400" C. it is only 4.1 per cent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent, silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By H. A. Bedworth

AlloTs of copper and silicon have been known for one hundred years or more but the commercial development of this type of alloy has taken place during the past few years. In 1905, Sperry l proposed the use of copper-silicon alloys for springs and other purposes for which copper-tin bronzes were used. Some attention was given to this proposal at the time but no one succeeded in producing a practical alloy containing more than a fraction of a per cent. of silicon. The equilibrium relations of the copper-silicon system were studied first by Rudolfi2 and later by Sanfourche 3 and Corson. 4 The constitution of the system has also been recently investigated by Matuyama, 5 and in the laboratories of the American Brass Co. by Smith. 6 Some of the physical properties of the copper-silicon alloys have been investigated by Norbury7 and by Geiss and Van Liempt.8 Summarizing the results of various investigators of the constitution of copper-silicon alloys, the solubility reaches its maximium value, 6.7 per cent. silicon, between 721" and '782" C. At 852" (1. the solubility is 5.25 per cent., while at 400" C. it is only 4.1 per cent. silicon. The copper-silicon alloy begins to get so hard at about 3 per cent, silicon that it is difficult to manage. It was found by Jacobs that the addition of manganese to this alloy considerably improved the working

Jan 1, 1929

By R. J. Colony

DEPOSITS of iron are widely scattered in the folded Cretaceous rocks and the associated igneous intrusives of Puerto Rico. Most of them are too small for commercial development, but a few have aroused some scientific and economic interest, among them the large body of residua] limonite at the west end of the island near Mayaguez1-6 (Fig. 1) and the mixed hematite and magnetite deposit on the southern slopes of the Sierra de Cayey, about four miles north of Arroyo.7-9 Neither of these orebodies has been developed, nor have investigations of the widely distributed deposits of magnetite, which include all the remaining occurrences of iron deserving of economic consideration, proceeded beyond the exploratory stage. With the possible exception of the mixed deposit near Arroyo, the magnetite is directly associated with andesitic and dioritic intrusives, which invade the Cretaceous rock section, and the bulk of it, occurring in calcareous sediments, is clearly of contact-replacement origin. The small deposit on Rio Portugues, north of Ponce, is found in a limestone band near its contact with an andesite dike.10,11 Two deposits of unde-

Jan 1, 1935

By R. C. Earlougher

Jan 1, 1970

By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967

By L. Russell Van Wert

DURING an investigation in which the solubility relations of the phases in Muntz metal (60 per cent. copper, 40 per cent. zinc) were under study, certain phenomena that had no immediate connection with the main problem were observed, which were thought sufficiently interesting to study further. Because of lack of time, only a preliminary survey was made of two of these; namely, the cleavage structure developed under certain conditions in a 60:40 brass and abnormal grain growth in this alloy. CLEAVAGE STRUCTURE IN HEAT-TREATED MUNTZ METAL Carpenter noted many years ago that cold-working a brass of the Muntz metal type, which had been quenched previously from within the beta field, results in a partial breakdown of the supersaturated beta solution and the precipitation of the solute (the alpha solution) in the cleavage planes of the beta grains. This manner of rejection of a solute from a metastable solid solution is not peculiar to this particular alloy, for among others, it occurs in the cold-working of certain austenitic steels; for example, the austenitic nickel steels. In these ferrous alloys, cold deformation produces a partial decomposition of the austenite, with the formation of martensitic "needles" and zigzags in the austenitic poly-hedra. It is interesting to note that while the two solid solutions-austenite and quenched Muntz metal- are metastable and in their mode of decomposition behave quite alike when deformed in the cold, the metastability of each results from a different cause; viz., that of the austenite from the fact that it is a supercooled solution (its solvent, gamma iron, at ordinary temperatures is below its normal stable range) whereas the metastability of the quenched Muntz metal is the result of supersaturation.

Jan 1, 1929

By L. Adler

Longwall caving, one of the most economical and attractive mining methods, is yet one of the most difficult and hazardous.1 This dualism is inherent in a method which manipulates the mine supports themselves to aid in excavation. The difficulty is further compounded by the lack of an analytical method to predict and control results. This paper is intended to meet this need by providing a first approximation to the mechanics involved. The analysis will be limited to materials which are linear-elastic, homogeneous and isotropic. The rock structure is assumed to consist of beds of uniform thickness with no interbed bonding.2 Consequently, the mine roof can be likened to a beam, in which the action characteristic of longwall caving is the controlled deflection of the barrier supports. This deflection causes load to be intentionally transferred from these barrier props to the working face.3 Two of the requirements of this method, shared in common with other mining methods, are the provision of (1) adequate and (2) safe working space. The third requirement is the one characteristic of longwall caving and is somewhat in conflict with the second; (3) the development of near-failure static loads at the face. Requirement (1) is handled by spacing the barrier props sufficiently far from the working face for efficient operation. Requirement (2) limits the static stresses in the structure to predetermined allowable values. This means that it is not desirable to induce a maximum load on the working face as requirement (3) may imply. Such a condition could produce collapse in the whole structure. It is the purpose of the undercut to limit the depth, and thereby control the failure of the face. Therefore, requirement (3) really means the development of an optimum, not maximum, load which, in conjunction with undercutting, produces failure at the working face, with minimum powder consumption. Stress analysis requires an exact delineation of the structure and loads. The structure will be defined as the immediate roof and its supports. Since the roof is severed at the caving line, the supports reduce to the barrier props and the working face, as shown in Fig. 1. The mechanics of failure within the working face itself are complex and beyond the scope of this study, since the face represents a typical mine invert structure.4 However, this lack can be made good by the judicious collection of field data. The primary load on the structure is its own weight or body load which can be considered uniformly distributed over its upper surface. Additional loading occurs due to interference of overbeds with the structure. Wherever this occurs, the effect can be approximated by a load uniformly distributed on the upper surface of the structure.5 When this interference is intermittent, as with a much thicker overbed, the elastic curve for the overbed is superimposed on that for the structure and the extent of interference noted, as Fig. 2 shows. However, for simplicity, this study will ignore such intermittent loads without impairing the generality of approach. Consequently, the free-body diagram is that of a uniformly loaded cantilever beam with an inter-mediate support, as shown in Fig. 3. For convenience of analysis, the diagram will be divided just to the

Jan 1, 1961

By G. Beghi, G. Piatti

THE authors examined the problem of the gradual transformation of Al2O3 from the transition phases normally encountered in SAP (r -x-n)1-3 to the stable a phase. This phenomenon is well-known at temperatures above the melting point of aluminum,3"6 whereas in this paper the transformation was studied at temperatures lower than the melting point of the aluminum matrix.

Jan 1, 1967

This is a most interesting paper and some data in it are corroborated by work I did at Watertown Arsenal some time ago with iron powder. I would like to ask Dr. Wulff to say just a little more about the compressive and tensile stresses on the surface of compacts. JOHN WULFF (author's reply).-Our work has not yet been completed; although enough data have been obtained with cylindrical compacts of iron to permit some conclusions. Briefly, in a compact 3/4 in. high and 1/2 in. in diameter pressed at 48 tons per sq. in., the residual stresses on the surface measured by X-ray diffraction techniques are as follows: The radial stresses on top center and bottom of compacts are practically zero; the longitudinal residual stresses on the side walls are near the top quarter of the compact about seven tenths that of the yield point of mild steel in tension; at the center surface of the compact they are in compression and in magnitude about 0.3 that of mild steel in tension; near the bottom, they are practically zero. F. V. LENEL.?- I was particularly interested in the work that Messrs. Wulff and Seelig reported on the influence of lubrication on the density of parts. In connection with the work of the American Society for Testing Materials on determining the green density of a compact, we ran into considerable difficulty in getting reproducible results of green density determinations. It was much easier to get a reproducible green density when the lubricant was mixed with the powder than when the lubricant was applied to the die walls; particularly when the die was not perfect-i.e., if it was somewhat rough or out of round. In this case, it was almost impossible to get reproducible green densities when the die walls were lubricated, while it was not too difficult to get reproducible

Jan 1, 1946

By E. A. Gulbransen, J. W. Hickman

DURING the past two decades considerable progress has been made in the art of manufacturing heater alloys. The conventional iron-chromium-nickel alloys have been improved by the addition of small quantities of other elements. Up to the present time, to our knowledge, there has not appeared a systematic study of these alloys where the newer tools of investigation have been brought to bear on the problem. It is not yet clear what roles the additional elements play in increasing life time in usage. As a first approximation one might guess that elements such as manganese, silicon, zirconium, calcium and aluminum would aid in the formation of a protective film on the alloy surface, thus retarding the oxidation rate and increasing lifetime. If these additional elements do form protective oxides in the outer surface of the oxide film, it may be possible to identify them by means of reflection electron diffraction. It is also possible that the additional elements may not diffuse to the surface but may remain at the interface between the oxide and the metal. Then, too, the major elements in the alloys undoubtedly form oxides which are stratified on the surface. If the minor elements concentrate in a layer in contact with the substrate where they undergo oxidation and if this oxide film offers resistance to the diffusion of iron, chromium and nickel ions, then the lifetime of the heater element might be expected to increase. It is also possible that preferential reduction in the diffusion rates of the several ions may Occur to such a degree that oxides may form in the body Of the film and On the outer surface which are different from those that would normally form if the additional elements were not present. The use Of transmisson electron diffraction may aid us in jnterpreting these phenomena. UP to the Present time all Of the factors which influence the lifetime of a given heater element are not definitely known. Among these are: (I) The rate of oxidation of the alloy. This may be dependent upon the composition and the physica1 state of the "alloy. (2) The stability of the structure of the coating which forms. Transitions from one structure to another or solid phase reactions resulting in a change of composition may occur. The tendency of the film to adhere to the substrate when heated and cooled successively will be important. (3) The evaporation of various constituents from the alloy such as the remova1 of carbon by Oxygen in a decar-burization reaction. With these possibilities in view, an electron diffraction study of the oxides occurring on six different nickel-chromium alloys was undertaken with the hope that the results of this study could be correlated with oxidation rate studies as determined by means of the vacuum microbalance method1 and with lifetime tests carried

Jan 1, 1949

By L. M. Kaas

Production planning techniques, particularly a production scheduling model are proposed for use in taconite mining in Minnesota. Applications of the scheduling model, on a two-year mine plan, which evaluates the equipment involved, are detailed. Data and tables are included. INTRODUCTION Fifty years ago Walter Swart, a mining engineer investigating the Minnesota taconites for the Jackling interests, made this report: "There is no doubt in my mind that this taconite mining is a game worth playing and that it can be played to a successful finish. It seems now only a question of men, money, methods and details."' The prosperous industry envisioned by Swart and other taconite pioneers is today a reality. Its growth has been spurred by technological advances in mining and beneficiation, depletion of natural ore reserves, and improvement of the economic climate. However, the massive problems that were solved to make this development possible are only a foreshadowing of the questions of "men, money, methods and details" that will be encountered in the future. The increasing demands for higher quality taconite pellets have already forced producers to examine better methods of quality control for their operations. THE NEED FOR PRODUCTION SCHEDULING The maintenance of fairly constant crude ore characteristics is of major importance to mill quality control. Through careful mixing of ore from storage bins, the concentrator staff can partially reduce the deviations of the feed analysis from the analysis desired. However, the limited effectiveness of bin mixing systems has caused some mining companies to utilize large capacity blending piles to reduce grade variations. Although the analysis of material being reclaimed from such a pile is relatively uniform, raw materials still must be scheduled from the mine into the pile in such a manner that the average analysis of all material is close to the feed analysis prescribed by the mill. PRODUCTION SCHEDULING MODEL Minnesota taconite mining companies have used three analyses to estimate how a certain ore will react to concentration. These factors are the crude magnetic iron content of the ore, the iron content of the plant concentrate produced from the ore at a standard grind, and the grindability index of the ore. The actual laboratory tests used to determine these factors have been described by Apuli.2 These data are obtained from analysis of diamond drill cores, and are the established criteria used by mine planning engineers to formulate taconite production schedules. Variations in the grade of mine output should be controlled by any production scheduling system. However, to be truly practical, production scheduling methods must also consider many of the less tangible variables that affect mine operation. These include pit layout, available equipment, and ownership of ore leases. The number and scope of the variables inherent in this type of mine planning suggested that a computer simulation could be used to solve the problem. The preparation of information for use with a computer simulation program was the initial phase of this project. Meaningful data was developed from logs of diamond drill cores. Analyses were related to their respective areas of influence by means of mine maps, Fig. 1. The three assay variables and tonnages for each area were punched on cards. In addition to these values, a location code number was punched in the first eight columns of the cards. This code is explained as follows: Column 1 Bench number Column 2 Quadrant location as determined by mine reference lines Columns 3-5 East-west coordinate Columns 6-8 North-south coordinate The heart of any simulation techniques is a well engineered mathematical model. To develop a model for taconite production scheduling, the relationship between the three assay variables had to be established. Because changes in each analysis factor affect the mill circuits in different manners, a weighting system was used to determine the relative im-

Jan 1, 1967

By R. E. Radabaugh, J. M. Brown, J. S. Merchant

The Gilman district is on the northeast flank of the Sawatch Range in central Colorado. It has yielded a total of 10,000,000 tons of ore having a value of over $250,000,000. Paleozoic sediments intruded by a Tertiary quartz latite sill and unconformably overlying Precambrian intrusives and metasediments comprise the country rock of the area. The sediments strike northwesterly and dip 8° to 12° northeasterly. Structures in the Precambrian are related to the Homestake shear zone of the Colorado mineral belt. Only minor folding and faulting occur in the sediments. The principal ore bodies are massive sulfide replacement deposits in carbonate rocks. They consist of long, pipe-like mantos in the completely dolomitized Mississippian Leadville Limestone and funnel-shaped chimneys of copper- silver ore cutting across the Mississippian and Devonian strata. Mineralization is continuous from the chimneys into the mantos. The principal ore bodies are roughly in the shape of a four-tined fork which points up dip. Smaller manto deposits occur in the Cambrian Sawatch Quartzite, and fissure veins are present in the Precambrian rocks. The principal minerals in the mantos are marmatite and galena in a gangue of pyrite and manganosiderite. The chimneys consist of a central core of pyrite with erratically distributed chalcopyrite, tetrahedrite, freibergite, and occasional galena with a shell of zinc ore on the outer margin. Both the chimneys and the mantos are surrounded by imperfect shells of manganosiderite and sanded dolomite. The mineralization is of Laramide age. Hydrothermal alteration affects all rock units to varying degrees. Clay mineral alteration halos occur around the ore bodies. Hydrothermal solutions have developed sanded rock, rubble filled channels, and banded zebra textures, principally in the Leadville Limestone. Structural control of the ore bodies is not well defined. Both the location of the district and the chimneys are probably related to basement structures. The mantos are largely controlled by stratigraphic factors and a pre-Pennsylvanian karst topography in the Leadville Limestone, which were modified by hydrothermal activity, and by weak zones of northeasterly trending faults.

Jan 1, 1968

By R. W. Parsons

The over-all apparent single-phase permeability of fracture-rock systems was studied using two different two-dimensional models. In a strict sense the results are applicable only to these models, yet may give some insight into real reseruoir behavior. The regular fracture-matrix model can have any number of regular fracture sets. All fractures within each set have the same orientation, width and spacing. The gross behavior is amlytically equivalent to that of an anisotropic permeable medium. In the heterogeneous fracture systems, individual fracture conductivities vary within a two-dinensioml network pattern. A computer program calculates the overall permeability after the conductivities are randomly placed in the network. The calculated permeability depends upon the distribution of these conductivities and the particular fracture pattern into which they are placed. Although detailed information on actual reseruoir fracture systems is not available, this study shows how some of the possible variables may affect obserued gross reservoir characteristics. INTRODUCTION Characteristics of reservoir rocks are determined by direct (core analysis) or indirect (logging and production tests) examination. Both methods, singly and together, are widely used in reservoir evaluations. For fractured reservoirs a problem exists in relating characteristics of cores to the in situ reservoir properties. Knowing fracture characteristics can be of value in determining production mechanisms. Because of the limitations of observation, the intimate details of a fractured rock system will never be known. One approach in analyzing fractures is to study the behavior of some conceptually simple models. The two models analyzed contain features which may be realistic, yet are mathematically tractable. Flow is considered in two dimensions only, with the plane of interest at right angles with the fractures. This concept represents the horizontal flow in a reservoir system with the fractures oriented vertically. Only single-phase, laminar flow is considered. The regular fracture-rock system permeability is calculable from a simple analytical expression. The heterogeneous system requires a computer program for calculating overall permeability.

Jan 1, 1967

By K. W. John, L. Mueller

The rock mechanics approach to stability problems of steep rock slopes dealt with in this article has particular reference to the concept and methods of analysis developed by the Salzburg, Austria, school of rock mechanics. These theories are based on the principal postulate of the anistropy of the technological properties of in-situ rock masses. The present approach, which is more in line with geological engineering concepts, differs distinctively from the soil mechanics and engineering geological concepts commonly practiced in the United States. PRINCIPAL ENGINEERING APPROACH TO GEOTECHNICAL PROBLEMS AVAILABLE ENGINEERING CONCEPTS At the present time two different concepts are available for engineering analysis of underground structures and foundations in different earth material: soil mechanics and rock mechanics. Of these two branches, soil mechanics is, after 40 years of initially revolutionary and more recently evolutionary development, well established. Its principal concept of replacing in-situ soils or rock masses by perfectly homogeneous substitues has resulted in many practicable methods of analysis which, if applied with judgement, have resulted in successful applications throughout the world. Conversely, rock mechanics is still in the early stages of revolutionary development. Few, if any, standard concepts or methods of analysis have been established. Opinions vary widely. At present the professional background of an investigator very often determines the engineering concept to be applied to a particular problem, rather than its actual requirements if considered objectively. This paper stresses the rock mechanics or geological engineering point of view advocated by the Salzburg group. A review of the soil mechanics concepts is considered beyond the scope of this paper. THE "SALZBURG APPROACH" TO ROCK MECHANICS The rock mechanics concept as outlined here was initiated by Stini, based upon work by sander.1 Since

Jan 1, 1963

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers' knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

By Charles Hart

In this paper it is the author's intention to show the extent and character of foreign ores now known to be available; these deposits may be in active production or held in reserve until economic conditions may make them active. He hopes to show the relation existing between these ores and the American supply, and which of the former are now producing or will in turn come into production when our better ores have been exhausted. This phase of this discussion must of necessity include some data as to the present rate of consumption and a study of the changes we may expect here and abroad in the general steel trade and its sources of supply in raw materials. It is obvious that the occurrence of coal, ore and limestone in relation to one another and the proximity of a market are the elements in control of this feature of the problem. If the foregoing situation is favorable, all the other questions may be solved, for it is clear that with proper basic conditions finance, labor and operations will fall in line. We present a short outline of the present methods of carrying on the foreign iron ore trade, believing that it is of general interest in comparison with our own highly specialized methods, and that with the exhaustion of our better ores we will be compelled to seek a part of our supply abroad. A partial list of iron ores, with incomplete analyses (Table I), is added, to give a better understanding of the general situation and explain to some extent the reason for things being as they are in the iron and steel trade of the world and to help in bringing this paper to an informing conclusion. The question of the world supply of iron ores has been a subject for study on the part of geologists and engineers for many years, and found its best results in the Eleventh International Geological Congress, appropriately held at Stockholm, Sweden, in 1910. The proceedings are published in two volumes and are undoubtedly the best records available on this subject at the date of publication. It should be borne in mind, however, that much has happened in the 20 years since these figures were assembled. There is just as much known ore at present as at that time, minus the quantity consumed, plus newly discovered reserves. The World War had great effect upon this situation; during that time explorations were greatly reduced and the settlements after the

Jan 1, 1929

By G. W. Thomas

Jan 1, 1967

By J. E. Warren, J. H. Hartsock

An asymptotic solution to the equation that describes the flow of a slightly compressible fluid in an infinite porous medium has been used to estimate the interaction between two adjacent wells producing from a common reservoir. A direct method for approximating the interference time defined by Stevens and Thodosl has been suggested. An alternative definition for the time of interference, based on the minimum pressure change in the interference region, has been proposed; also, a direct method of determination has been prescribed. Examples have been employed to illustrate the use of both methods.