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By M. R. Hatfield, F. J. Vosburgh

In a recent article, it was shown that in the blast furnaces in Germany that are lined with carbon blocks no cooling plates are used, and that shower cooling is employed on the hearth and bosh sections. While one of the authors was in Germany he was told that one furnace was being operated without even the shower cooling on the bosh section, though the hearth section was shower-cooled. In discussion of this interesting situation with a number of blast-furnace operators in this country, it was made clearly and promptly evident that shower cooling was very unpopular, probably because of its messiness and its ineffectiveness. Both of the causes for the dislike of shower coolings are reasonable ones. Shower cooling can be and frequently is messy, but the present cooling of blast furnaces leaves much to be desired on that score. Shower cooling is ineffective as compared with plate cooling, so far as its usefulness in keeping the bricks cool enough not to melt or fall to pieces is concerned. However, the introduction of carbon linings changes the situation. No one is concerned with keeping a carbon lining cool, for no temperature in the blast furnace has any effect on carbon, which is just as stable at 3000°F. as it is at 70°F. The only concern is for the shell—to keep it cool enough for safety and comfort— and for that shower cooling is sufficient. Of course, with only the shell to cool, instead of the shell plus all the refractory material, much less water would be required, and the necessity for constant attention to the flow would be lessened, as the hundreds of inlets and outlets would be eliminated. Probably half of the water used in cooling a blast furnace is used for cooling the shaft and tuyeres and the remainder for the bosh and hearth sections. However, in view of the dislike of shower cooling in the United States, and particularly because at least one German blast furnace is operated with no cooling of the bosh section, thought was given to the possibility that a carbon-lined blast furnace might be operated without any cooling of the entire carbon-lined portion. For that reason a series of experiments was performed to determine what might be the temperature of the shell of a blast furnace protected by a carbon lining and operated under varying conditions up to a maximum inside temperature of 3000°F. Experimental Procedure A schematic diagram of the experimental setup is shown in Fig. I and a photograph of the entire assembly in Fig. 2. The heating element was a a tubc nominally 25/8 in. 0.d. by 2 in. i.d. by 30 in., used as a resistor. Power was furnished by a I5-kva. transformer operating

Jan 1, 1942

By M. R. Hatfield, F. J. Vosburgh

IN a recent article,† it was shown that in the blast furnaces in Germany that are lined with carbon blocks no cooling plates are used, and that shower cooling is employed on the hearth and bosh sections. While one of the authors was in Germany he was told that one furnace was being operated without even the shower cooling on the bosh section, though the hearth section was shower-cooled. In discussion of this interesting situation with a number of blast-furnace operators in this country, it was made clearly and promptly evident that shower cooling was very unpopular, probably because of its messiness and its ineffectiveness. Both of the causes for the dislike of shower coolings are reasonable ones. Shower cooling can be and frequently is messy, but the present cooling of blast furnaces leaves much to be desired on that score. Shower cooling is ineffective as compared with plate cooling, so far as its usefulness in keeping the bricks cool enough not to melt or fall to pieces is concerned. However, the introduction of carbon linings changes the situation. No one is concerned with keeping a carbon lining cool, for no temperature in the blast furnace has any effect on carbon, which is just as stable at 3000°F. as it is at 70°F. The only concern is for the shell-to keep it cool enough for safety and comfort and for that shower cooling is sufficient. Of course, with only the shell to cool, instead of the shell plus all the refractory material, much less water would be required, and the necessity for constant attention to the flow would be lessened, as the hundreds of inlets and outlets would be eliminated. Probably half of the water used in cooling a blast furnace is used for cooling the shaft and tuyeres and the remainder for the bosh and hearth sections. However, in view of the dislike of shower cooling in the United States, and particularly because at least one German blast furnace is operated with no cooling of the bosh section, thought was given to the possibility that a carbon-lined blast furnace might be operated without any cooling of the entire carbon-lined portion. For that reason a series of experiments was performed to determine what might be the temperature of the shell of a blast furnace protected by a carbon lining and operated under varying conditions up to a maximum inside temperature of 3000°F. EXPERIMENTAL PROCEDURE A schematic diagram of the experimental setup is shown in Fig. I and a photograph of the entire assembly in Fig. 2. The heating element was a carbon tube nominally 2 5/8 in. o.d. by 2 in. i.d. by 30 in., used as a resistor. Power was furnished by a 15-kva. transformer operating

Jan 1, 1941

By M. R. Hatfield, F. J. Vosburgh

In a recent article, it was shown that in the blast furnaces in Germany that are lined with carbon blocks no cooling plates are used, and that shower cooling is employed on the hearth and bosh sections. While one of the authors was in Germany he was told that one furnace was being operated without even the shower cooling on the bosh section, though the hearth section was shower-cooled. In discussion of this interesting situation with a number of blast-furnace operators in this country, it was made clearly and promptly evident that shower cooling was very unpopular, probably because of its messiness and its ineffectiveness. Both of the causes for the dislike of shower coolings are reasonable ones. Shower cooling can be and frequently is messy, but the present cooling of blast furnaces leaves much to be desired on that score. Shower cooling is ineffective as compared with plate cooling, so far as its usefulness in keeping the bricks cool enough not to melt or fall to pieces is concerned. However, the introduction of carbon linings changes the situation. No one is concerned with keeping a carbon lining cool, for no temperature in the blast furnace has any effect on carbon, which is just as stable at 3000°F. as it is at 70°F. The only concern is for the shell—to keep it cool enough for safety and comfort— and for that shower cooling is sufficient. Of course, with only the shell to cool, instead of the shell plus all the refractory material, much less water would be required, and the necessity for constant attention to the flow would be lessened, as the hundreds of inlets and outlets would be eliminated. Probably half of the water used in cooling a blast furnace is used for cooling the shaft and tuyeres and the remainder for the bosh and hearth sections. However, in view of the dislike of shower cooling in the United States, and particularly because at least one German blast furnace is operated with no cooling of the bosh section, thought was given to the possibility that a carbon-lined blast furnace might be operated without any cooling of the entire carbon-lined portion. For that reason a series of experiments was performed to determine what might be the temperature of the shell of a blast furnace protected by a carbon lining and operated under varying conditions up to a maximum inside temperature of 3000°F. Experimental Procedure A schematic diagram of the experimental setup is shown in Fig. I and a photograph of the entire assembly in Fig. 2. The heating element was a a tubc nominally 25/8 in. 0.d. by 2 in. i.d. by 30 in., used as a resistor. Power was furnished by a I5-kva. transformer operating

Jan 1, 1942

By W. F. Mullen, C. W. Stickler

WITH few exceptions, unit operations in the Pennsylvania slate industry in 1950 did not differ appreciably from production methods described by Behrel and Bowles2-4 several decades ago. Many traditionally picturesque but relatively inefficient hand operations continued to contribute to high operating costs in an industry in which the margin of profit, for various reasons, was admittedly low. As part of a general program in which the Pennsylvania State College has been assisting the slate industry to solve some of its problems, time and method studies were used in an effort to determine the bottlenecks of production flow. The results are as applicable to other stone industries as they are to slate. A study of the basic elements in the production of roofing slate, structural slate, and slate blackboards among selected slate producers revealed comparatively few refinements. Any marked difference in operating method was characterized largely by the available equipment, a noticeable difference in the working properties of the rock quarried by a particular company, and by either the habit thinking or ingenuity of the individual operators. With the hope that significant economies in manufacture might result, all the unit operations were broken down into elements for study and analysis. The greater part of the study encompassed those operations from the quarry rim to the finished product; however, to obtain a reasonable synthesis of time allotments per operation, several analyses of quarrying from the finish of the wire saw cut are included for reference. The complete study of quarrying made by Bowles several years ago resulted in the introduction of the wire saw into the operation; there appears to be a need for as fundamental a change in the processing of finished slate as the wire saw was in the quarrying process. Fig. 1 illustrates the flowsheet of quarried rock from the parent bed to the quarry rim with the basic elements which contribute to the difficulty of removing slate from the ground. In Pennsylvania roofing slate is produced by one of three procedures, many operations of which are quite similar. In the traditional or classical method the quarried rock is reduced by sculping and auxiliary manual treatment to workable size and then is split and dressed (trimmed to size) in the conventional shanty. Archaic as this method might appear, there are several elements that result in substantial savings over more mechanized operations. In a modified version of this method, the block is reduced by sawing and gouging preparatory to splitting and dressing in indoor stations. This method is particularly adaptable to rock which fractures unevenly by conventional sculping methods. In the third and more modern method, reduced block received from the block maker is diamond-sawed to length and finished on a production line. Fig. 2 illustrates the flow pattern in each case. In the modified and more modern plans, dressing is done on mechanically-operated trimming machines, which appreciably reduce the fatigue factor of the operator. However, it should be noted that it is advantageous for the operator to be able to control the speed of the knife to prevent breakage of certain classes of stock. In the classical plan the splitter and dresser normally act as blockmakers also and carry their eighter slabs (equivalent in thickness to eight shingles) into the shanties themselves, all of which adds to fatigue and reduced efficiency. The extremely low investment and operating expense of the classical method has undoubtedly been of paramount importance in its continuation. Production of Mill Stock The production of mill stock is accomplished by less picturesque methods than enter into the production of roofing slate but it is, in the main, relatively more efficient because of the increased use of machinery for handling and for finishing. Mill stock can be classified into two categories as far as difference in production method is concerned: structural slate and blackboards. The significant difference in operation is caused largely by the nature of the rock used for each product with the best and easiest cleaved rock being reserved for blackboards to permit the splitting of large slabs to as little as 1/2 in. in thickness. Structural stock, on the other hand, is split into panels no thinner than 11/2 in. and

Jan 1, 1952

By T. L. Joseph

LARGE deposits of manganiferous iron ores, representing several million tons of metallic manganese, occur in the United States. The Minnesota deposits of such ore-are of outstanding importance because of their size, state of development, ease of mining and proximity to the Great Lakes, which permits water transportation to steel centers. In' view of the fact that our steel industry requires large quantities of manganese, for which no satisfactory substitute-has been found, and because our reserves of ferro-grade ore are comparatively small, the development of methods that will make our large deposits of manganiferous iron ores available as a source of ferromanganese is an important problem. Realizing the importance of this problem, some years ago the North Central Station of the U. S. Bureau of Mines and the Minnesota School of Mines Experiment Station undertook jointly the development of methods for recovering the manganese content of manganiferous iron ores in a: form suitable for the production of ferromanganese, the 80 per cent. alloy indispensable in producing steel. Two types of manganiferous iron ores have been described in previous reports. I The brown ores are higher in iron and lower in manganese than the black ores; the black ores are more siliceous but contain less phosphorus. The utilization of the iron content of the brown ores in the production of steel appears to furnish the best basis for their treat-ment. The method of attack has been to work out modifications in iron and steel practice so as to recover manganese in the form of slag comparable to ferro-grade ores. The greater part of the experimental work has been conducted with a 6-ton blast furnace and a Y2-ton basic open hearth. This paper is devoted mainly to open-hearth tests in which high-phosphorus spiegel

Jan 1, 1930

By Basil B. Zavoico

The symposium on production for the year 1942 contains no papers on the foreign situation except those on Argentina and Mexico. It has always been the policy of officers in charge of the symposium to refrain from publishing information that might possibly injure national or private interests. At the close of the war we hope again to publish full and accurate records of production abroad. Excerpts From Circular to Authors In order to facilitate interpretation of the data in this chapter, we print the following excerpts from the Circular to Authors. The field is the unit in this tabulation. In cases of fields extending across State boundaries, such as Rodessa, it is suggested that each State author treat the section of the field in his State as a unit, and by a footnote indicate that the field extends into an adjacent State. Each space in Table I may represent one of four possibilities; either it is not applicable to the particular field, or the proper entry is not determinable, or the proper entry may be determinable but is not determinable from data available to the author, or the proper entry is determinable. When spaces are not applicable, leave blank; in spaces where the proper entries are determinable but not determinable from data available to the author, please insert y; in spaces where the proper entries are determinable by the author, make such entries. y implies a Rope that in some future year a definite figure will be available. The entry of a zero is a positive declaration, and it is an important declaration where it is in order. Inability to determine precisely the correct entry for a particular space should not lead the author to insert merely y. Contributions of great value may be made by the author in many cases where entries are not subject to precise determination. In such cases the author should use his good judgment and make the best entry possible under the circumstances. For many spaces the correct entries represent the opinion of the author (for example, "Area Proved") and in such cases the entry need not be hedged to such extent as when the quantities are definite yet can be ascertained only approximately by the author. In cases under definite headings but where figures are only approximate, the author may use x. It is thought that the nearest whole numbers are sufficiently accurate for our purposes except as to percentage of sulphur in oil. If an author desires to report any other figures to tenths, he may do so. The quantity of gas produced should include, where possible, gas sold or otherwise marketed, and gas blown into the air, burned as flares or otherwise wasted. Segregation of these figures would be interesting if the authors can make such segregation. In any event, the figures should represent as nearly as possible the total quantity of gas removed from the reservoir. Under the columns on "Depth," the average depth to the top of the productive zones and to the bottom of the productive wells, when subtracted, should give the approximate thickness of the productive zone. For fields where this is not true because of unusually high dip or for some other reasons, it is suggested that the authors indicate in their text the approximate average thickness of the productive zone.

Jan 1, 1943

By Gregory Dybalski

The purpose of this paper is to illustrate the forecast capability of the econometric model of the cobalt industry1/ as utilized by the Federal Preparedness Agency. Forecasts from this model are illustrated from the premise that the leading producer continues production of cobalt. An alternate forecast is presented where the model structure is altered to reflect the condition where the leading producer leaves the market. All estimations and forecasts presented here are shown for illustrative purposes. The cobalt industry is highly concentrated; one company, owned by the Zaire government, accounts for approximately three-fifths of world production. The cobalt supply outside of Zaire is determined by the level of activity of copper or nickel markets, as cobalt is mined as a by-product of copper or nickel. The demand for cobalt reflects a diversified usage pattern; cobalt is used mainly in heat and corrosion-resistant materials, high- strength materials and permanent magnets. According to 1974 U.S. consumption data superalloys accounted for 22%, magnetic alloys 18%, cutting and wear-resistant materials 13%, and catalyst 7%. Foreign consumption is probably similar in terms of usage categories, but the relative order of the categories is in variance.2/ The Cobalt Model The cobalt model's object is to explain consumption, supply and price movements by utilizing statistically estimated equations. Central to the econometric model is the role of Zaire as the profit-maximizing "dominant firm". Zaire sets the price that is most profitable for itself. The price of cobalt depends on industrial demand, production of other firms, and net exogenous purchases, such as government

Jan 1, 1977

By A. A. Burr, D. Caplan

IN carrying out experiments in metal-gas systems, it is often difficult to estimate how long a reaction period must be allowed for equilibration. This is especially true in systems for which the diffusion coefficient is not known. In an investigation of the Cr-O system, the necessary information was obtained in the way described subsequently. Two pieces of chromium sheet of different thicknesses were packed in mixed powders of chromium and Cr2O3 and sealed into an evacuated metal capsule by welding. Austenitic stainless steel proved suitable as a capsule material up to 1350°C and molybdenum at higher temperatures. The capsule then was heated at a specific temperature for a time sufficient to saturate with oxygen the thinner but not the thicker specimen. The time is readily estimated from a preliminary experiment if a sufficient thickness differential is chosen. Under these experimental conditions, the metal sheet is exposed to a partial pressure of oxygen equal to that of the dissociation pressure of the oxide and hence can become saturated with oxygen without developing any second phase. After cooling, both samples were analyzed for oxygen by the vacuum fusion technique. Assuming that the surface of the specimens is kept saturated with oxygen throughout the experiment, the diffusivity can be calculated by application of the appropriate solution to Fick's second law. This is most conveniently accomplished by use of a plot of mean fractional saturation (Cm-Co) / (Cs-Co) vs (Dt) ½/L as given by Darken,' where t is time, L the half-thickness of the sheet, and D the diffusion coefficient. Cm, the mean concentration at time t, is given by the oxygen percentage in the thicker specimen; Cs, the constant surface concentration, is the oxygen percentage in the thinner specimen; Co is the oxygen content of the original chromium sheet. (Cm-Co) / (Cs-Co) is calculated and the corresponding (Dt) ½/L is read from the graph and D thereby calculated. By performing the experiment at two temperatures and plotting log D vs 1/T, the D for any temperature is established. (The activation energy for diffusion may be obtained from the slope of the line.) Once D is known as a function of temperature, it is a simple matter to estimate the correct reaction time for experiments with single specimens at other temperatures by equating (Dt) ½/L to its value for effective saturation. Darken' points out that this is approximately unity. The solubility of oxygen in chromium, as determined from the thin samples at each temperature, proved to be approximately 0.03 pct at 1350°C and less at lower temperatures. Due to low solubility and to the known difficulties of the vacuum fusion method in this low range, the values obtained for D (5x10-0 sq cm per sec at 1350°C) are estimated to be correct only within an order of magnitude. Nevertheless, the method has proved useful in estimating reaction times. Its usefulness will be greater in metal-gas systems where the solubility is appreciable. A second function of the method is to permit the determination of diffusion coefficients in systems for which the conventional techniques are experimentally difficult or impossible.

Jan 1, 1956

By T. Egleston

THE manufacture of charcoal in kilns was declared many years ago, after a series of experiments made in poorly constructed furnaces, to be unprofitable, and the subject is dismissed by most writers with the remark that in order to use the method economically the products of distillation, both liquid and gaseous, must be collected. It is asserted with truth that the number of kilns required for a large production of iron would be so great that it is doubtful whether any works would be justified in making the necessary outlay for their construction, but it can also be asserted with equal truth that for any such production in a given locality the use of charcoal as fuel would be equally unjustifiable. It appears to have been forgotten that there were other manufactures besides iron in which large amounts of charcoal were used, but these consumers seem to have been guided entirely by the results of the experiments of the iron men, who necessarily made the largest quantity of it. Some authors speak in a doubtful way of the quality of the charcoal produced, and a few concede that with great care good charcoal can be made in kilns, but that most of the workmen do not like kiln charcoal. This is the real secret of the opposition to this method of manufacture. Most of these objections were written when charcoal was the most important fuel used by the iron manufacturer, and when what was a large production of iron for several furnaces was less than that produced by a single modern one, in localities where other fuels can be had. Almost all that has been written on the subject related to the use of the fuel for the manufacture of iron in the blast furnace, where very peculiar properties are required, and where the quantity produced is limited by the height of the furnace, and this in turn by the crushing resistance of the charcoal. A large production was, therefore, only possible when the best and hardest woods were used. Of all these objections there is not a single one which is not equally applicable to any method of charcoal manufacture, whether it be meilers, pits, or furnaces. Until recently, therefore, the manufacturers of charcoal iron * Read at the Pittsburgh meeting, May, 1879.

Jan 1, 1880

By T. Cameron Kenney

INTRODUCTION Whereas the design of rock slopes in open-pit mines is done largely by mining engineers and geologists, the design of slopes in overburden at this point in time is a problem for which civil engineers or geotechnical engineers are best prepared to deal. The reasons for this situation are to be found in the educational curricula and the technical journals of the two groups, where soil mechanics has received little attention by mining engineers and geologists, and rock mechanics has similarly received little attention by civil engineers. In ten years' time this paper will hopefully be considered by young mining engineers to be a repeat of the material that they studied at university. However, even in ten years time I believe that the civil (or geotechnical) engineers will be extensively used as consultants on overburden- slope problems of open pit mines because mining companies will find this more expedient than maintaining their own geotechnical staff, special field equipment and special testing laboratories. For this reason, the purpose of this paper is not to condense several university soil mechanics courses into a twenty-page text for mining engineers and geologists. Rather, the purpose of the paper is to offer a general explanation of various factors affecting slope stability so that mining engineers and geologists will have a better understanding of the behaviour of overburden soils in slopes. A great deal has been written in soil mechanics literature on the subject of slope stability. No attempt will be made to reference all this material but rather only a selected number of references will be cited. Excellent general treatments of the subject of stability of overburden slopes are available (1,2,3,4). Further information of a more specialized nature is to be found in such publications as the Journal of the Soil Mechanics and Foundation Division of the American Society of Civil Engineers, Geotechnique (printed by the Institution of Civil Engineers, England), Canadian Geotechnical Journal, and the proceedings of the conferences of the International Society for Soil Mechanics and Foundation Engineering. FACTORS INFLUENCING SLOPE STABILITY There are two general scales of slope-stability problems, gross stability and local stability. Gross stability refers to large volumes of soil, and gross instability would involve large rotational-type shear failures. Local stability refers to something much smaller and examples

Jan 1, 1972

By S. J. Sindeband

Prior to discussing the metallurgy of sintered chromium borides, it is pertinent to outline some of the reasoning behind this investigation and the purposes underlying the work. This study was initiated as an aproach to the ubiquitous problem of a material for service at high temperatures under oxidizing atmospheres, and it was undertaken with a view to raising the 1500°F (816°C) ceiling to 2000°F (1093°C) or better. For the reason that no small, but rather a major, lifting of the high temperature working limit was being attempted, it was felt appropriate that a completely new approach be taken to this problem. A summary of the thinking behind this approach was published recently by Schwarzkopf.' In briefest terms, it was postulated that the following requirements could be set up for a material which would have high strength at high temperatures. 1. The individual crystals of the material must exhibit high strength interatomic bonds. This automatically leads to consideration of highly refractory materials, since their high energy requirements for melting are related to the strength of their atom-to-atom bonds. 2. On the polycrystalline basis, high boundary strength, superimposed on the above consideration, would also be a necessity. Since this implies control of boundary conditions, the powder metallurgy approach would hold considerable promise. Such materials actually had been fabricated for a number of years, and the cemented carbide is the best example of these. Here a highly refractory crystal was carefully bonded and resulted in a material of extremely high strength. That this strength was maintained at high temperature is exhibited by the ability of the cemented carbide tool to hold an edge for extended periods of heavy service. Nowick and Machlin2,3 have analytically approached the problem of creep and stress-rupture properties at high temperature and developed procedures whereby these properties can be approximately predicted from the room temperature physical constants of a material. The most important single constant in the provision of high temperature strength and creep resistance is shown to be the Modulus of Rigidity. On this basis, they proposed that a fertile field for investigation would be that of materials similar to cemented carbides, which have Moduli of Rigidity that are among the highest recorded. The cemented carbide, however, does not have good corrosion resistance in oxidizing atmospheres and without protection could not be used in gas turbines and similar pieces of equipment. It would be necessary then to attempt the fabrication of an allied material based upon a hard crystal which had good corrosion resistance as well. It was upon these premises that the subject study was undertaken and at an early stage it was sponsored by the U.S. Navy, Office of Naval Research. Since then, it has been carried on under contract with this agency. Chromium boride provided a logical starting point for such research, since it was relatively hard, exhibited good corrosion resistance, and, in addition, was commercially available, since it had found application in hard-surfacing alloys with iron and nickel. That chromium boride did not provide a material that met the ultimate aim of the study results from factors which are subsequently discussed. This, however, does not detract from the basis on which the study was conceived, nor from the value of reporting the results which follow. Chromium Boride While work on chromium boride proper dates back to Moissan,4 there has been a dearth of literature on borides since 1906. Subsequent to Moissan, principal investigators of chromium boride were Tucker and Moody,5 Wede-kind and Fetzer,6 du Jassoneix,7,8,9 and Andrieux." These investigators were generally limited to studies of methods of producing chromium boride and detennining its properties. Some study, however, was devoted to the chromium-boron system by du Jassoneix,7 who did this chemically and metal-lographically. This system is not amenable to normal methods of analysis by virtue of the refractory nature of the alloys involved, and the difficulties of measurement and control of temperature conditions in their range. Dilatometric apparatus is nonexistent for operation at these temperatures. Du Jassoneix made use of apparent chemical differences between two phases observed under the microscope and reported the existence of two definite compounds, namely: Cr3B2 and CrB. These two compounds, he reported, had quite similar chemical characteristics, but were sufficiently different to enable him to separate them. The easiest method for producing chromium boride is apparently the thermite process, first applied by Wede-

Jan 1, 1950

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By Morris Muskat, James M. McDowell

A report is given of electrical analog experiments on the effect of casing perforation completions on well productivity for ideal uniform reservoirs under steady state homogeneous fluid flow conditions. Graphical results are presented for the effect of perforations of different densities and various degrees of penetration into the formation surrounding the casing or cement sheath. The latter range from perforations which terminate flush with the casing to those which extend into the formation a distance equal to the casing diameter. For the special case where the perforations terminate immediately beyond the casing with semi-spherical protrusions the electrical analog results correct and supersede previously reported theoretical calculations. It is found that the penetration of the perforations into the surrounding productive section may so increase the resultant productivity as to approach or even exceed that for open hole completions. INTRODUCTION A theoretical analysis of the effect of casing perforation on well completion, without additional penetration of the formation, was reported several years ago.' In this treatment the perforations were represented by mathematical sinks and no explicit account was taken of the imperviousness to flow of the casing in which the perforations were made. This procedure was justified by consideration of the mutual interference between the sinks, which seemed to indicate that the analytical method automatically eliminated flow across the casing radius between the perforations. However, both further theoretical investigation and the electrical analog measurements described below showed that this assumption in the previously developed theory was not valid and that the calculated well capacities would considerably exceed the correct values. § Even if this simplifying assumption were retained the generalization of the theory to situations where the perforations extend into the producing formation would be extremely difficult. On the other hand, the electrolytic model analog of this type of steady-state homogenous fluid system is, in principle, so simple that it has not been worthwhile to attempt to develop the exact analysis even for the more limited case of strict casing perforation. The whole problem has therefore been studied anew by electrical models to cover the range from holes in the casing which terminate flush with the casing surface to such as extend into the surrounding rock to a depth equal to the casing diameter. It is to be expected that the productivity of a well completed with casing radius* rw, perforated with holes of radius Tp, and extending to depths d into the surrounding rock, would depend primarily on the dimensionless geometrical parameters Te Tw TP d of the system, such as —, —, — , and —, where re is the Tw, a a rw external boundary radius and a is the mean vertical separation between the perforations. It will also depend, of course, on the number of perforation lines or total perforation density. While such parameters automatically control analytical treatments, it would require a very extensive series of model experiments to fully disclose their functional effect on the well productivity. For practical purposes, however, a rather limited range of the variables suffices to give the effects of interest. Accordingly, in the experimental study reported here the casing diameter has been kept fixed? at six in., the perforation diameter has been taken as either one-fourth in. or one-half in., their density has been varied from one to eight per ft, and their penetration into the formation has ranged from zero to six in., with a primary scaling factor of one to six. EXPERIMENTAL METHOD AND RESEARCH Although electrolytic model experiments have been made for years, there still seems to be some question as to what set of conditions will give the best results. For this reason a number of electrode materials and electrolytes were tried. Those chosen for the final experiments were copper electrodes and a weak copper sulphate solution as the electrolyte. This 'Assuming that the casing has been cemented with a uniform and impermeable cement sheath, the effective casing radius is to be interpreted as the external radius of the cement annulus. It is also assumed here that the casing is set through the complete producing section that it is perforated throughout with a uniform density and that tie formation has a a and isotropic permeability. As noted later, however, a uniform scale change permits reinterpreting the primary measurements to correspond to a casing diameter of 12 in.

Jan 1, 1950

By R. J. Borg, C. E. Birchenall

The self-diffusion coefficients for a iron have been deternzined between 980° and 1167° K using Fe55 as the tracer. With decreasing temperature the diffusivity was found to decrease more rapidly than predicted by the Arrhenius equation in the region of the Curie temperature. The diffusion coefficients obtained well above the temperature of the magnetic transformation are more precise ard differ substantially from all the previously reported values. In the temperature region beginning at least 50" above T,, the diffusion coefficient is given by D = 118 (±2) exp 1 HE self-diffusion coefficients for a iron have been reported previously as the result of four independent investigations The general lack of agreement and the poor precision of most of the previous work prompted the redetermination by the present authors. The possible effect of the onset of ferromagnetism upon the diffusivity5 provided an additional impetus for this investigation. The earlier measurements of Birchenall and Mehl1 gave low values for the diffusion coefficient at temperatures below the Curie temperature, Tc. However, the precision of these measurements is not sufficient to establish an indisputable correlation between the low values and the magnetic transformation. The results of this investigation along with all the previous ones are shown in Fig. 1. EXPERIMENTAL Small rectangular samples, approximately 1 by 0.5 by 0.3 cm, of high-purity iron (Vacuum Metals Corp., "Ferrovac") are first heated in hydrogen at 900°C for24hr in order to remove possible trace amounts of dissolved carbon and oxygen. The small

Jan 1, 1961

By Cyril Stanley Smith

METALLURGISTS - or at least metals - have been of central importance in most of the inventions that have shaped the course of man's history. From the first Bronze Age tools to the iron armor of the Roman soldier, the cannon, cast type for printing, the steam engine, the electric motor and modern electronic devices, technological progress has revolved around some particular property or comb nation of properties selected from the metallurgist's repertory. The recent utilization of the energy of the atomic nucleus (currently for military purposes alone but with great constructive implications for the future) is no exception to this, although the use of uranium and plutonium in metallic form is of secondary importance, since the significant properties are those of the nucleus and not of the electrons responsible for metallic behavior. THE METALLURGIST AND ATOMIC ENERGY The metallurgist has a role of central importance to play in the future development of atomic energy. Not only must he make and shape the fissionable materials themselves, but he must also develop auxiliary materials to withstand the extreme conditions imposed on nuclear reactor components by the high heat-transfer rates needed for efficient utilization of the fuel and by the perplexing but interesting effects of radiation on the structure and properties of materials. It is doubtful if there is currently any other field potentially more rewarding to a young metallurgist. Quite apart from the all important but relatively short-range considerations of national security is the vision of the effect on civiliza-

Jan 1, 1953

Shoveling ore cost so much at Tyrone during the year 1917 that it was deemed advisable to conduct tests to see where the fault lay. These tests were in the nature of time studies and extended over a period of very nearly a year. No data were available on this work to supply a starting point, so it was necessary to begin in a very elementary way, to find out the capacity of the average Mexican laborer. To' obtain a basis for comparison, it was necessary to determine the capacity of various types and sizes of shovels, so as to know whether the 21-1b. (9.5-kg.) load was the best load underground as well as on surface. A list of essential factors influencing shoveling was also made out during the course of a short series of preliminary time studies, and the motions involved in shoveling were analyzed and subdivided for convenience in studying. The necessary forms and record sheets were also decided upon at this time. A second short series of tests was then conducted on the surface, so as to be able to estimate the negative effects of underground work on the shovelers, and to minimize, as far as possible, the need for studying obviously poor types and sizes of shovels under the difficult conditions to be encountered in the mine. The test work underground consumed by far the greater proportion of the time and was divided into three series: Shoveling directly into a chute; shoveling into a wheelbarrow and tramming to a chute; and shoveling into a car and tramming to a chute. In each series the following points were determined for various lengths of time worked: Number of shovelfuls handled per minute, effect of distance thrown on shoveling speed, amount of rest required, amount of time consumed in tramming and dumping, proportion of working day occupied in shoveling, total tonnage handled during various working periods, effect of distance on tonnage handled during the day.

Jan 2, 1919

By W. A. Wood, H. L. Wain, R. I. Garrod

The mechanical behavior of recrystallized chromil~m of high purity has been studied, principally in torsion and to a lesser extent in tension, at temperatures between —196oand 350oC. Depending upon the conditions of test, the material may show brittle or ductile behavior or an intermediate or subduc-tile state having some of the characteristics of each. This latter state existed at temperatures between approximately ±50°C and was characterized by a) extensive creep at stresses well below the normal fracture stress, b) nonelastic loading/unloading effects during creep, c) strain softening under cyclic loading, and d) final failure of a brittle type. Suggestions are made on the dislocation processes and interactions which give rise to subductile behavior The ductile-brittle transition in bee metals has been studied mainly by tension and bend tests. These methods, however, favor crack propagation which may follow too closely on initiation for detailed study of the transition itself. For work of this nature, therefore, other modes of deformation less favorable to crack propagation may be preferable. This paper describes a study of the ductile-brittle transition in chromium which is based mainly on torsional testing although a few subsidiary experiments were made in tension. It appears to reveal at the transition an intermediate state that cannot properly be described as either brittle or ductile. Torsional tests on chromium have been made by other workers1 but not, as here, primarily for study of this intermediate state. EXPERIMENTAL The chromium, in the form of swaged rod, was prepared by techniques already described.' The particular material used was one in which the main impurities were 0.03 wt pet 0 and 0.006 wt pet N and one in which transition from ductile to brittle states in torsion conveniently fell at about room temperature. For torsion, test specimens were from 5/16-in.-diam rod to provide test portions 1-1/4 in. long by 7/32 in. diam, a twist of 1 deg thereby corresponding throughout this paper to 0.0015 surface shear. The specimens before test were annealed for 2 hr at 1200°C in vacuo, which left them with a re-crystallized grain size of about 0.01 mm, and then electropolished. They were tested under dead-weight loading in an apparatus in which they could be surrounded by a furnace or cooling chamber, tests in practice being made at various temperatures between -196" and +350°C. For tension tests, cylindrical specimens were prepared in a similar manner and tested at room temperature under dead-weight loading. RESULTS (TORSION) Subductile State. The state described above as intermediate between brittle and ductile may be perhaps best defined by reference to torque/twist curves at various temperatures. These are grouped in Fig. 1. Below about -50°C the material was brittle, in the sense that it exhibited little plastic deformation under stress and fractured by cleavage along planes of maximum resolved tension, which in torsion produces the well-known helical type of fracture. The deformation is typified by the curves for -196" and -150°C in Fig. 1; it shows a slight but progressive deviation from linearity above a certain torque, here about 50 lb-in., until fracture occurs at about 95 lb-in. A feature to which it is desired specially to call attention is that under none of the loads did the specimens show significant creep.

Jan 1, 1964

By d&apos, D. L. Guernsey, J. C. Entremont, John Chipman

The reaction of aluminum with oxygen in liquid iron has been studied at 1740° and 1910°C. Interaction coefficients are very much smaller than those previously published. The equilibrium constant falls within the approximate range of earlier experiments and calculations. It is now well established that the "deoxidation constant" for aluminum in liquid steel at normal steelmaking temperatures is extremely srnall. Thus at 1600 the product [% Al] is of the order of 10- 14. At this temperature, therefore, great experimental difficulties are encountered in any attempt to obtain a direct measure of the constant. If the aluminum content of the metal is high enough to permit accurate analytical determination, that of the oxygen is too low. If the oxygen content is high, the aluminum is below the limits of detection. Our best values of the constant have come, therefore, from indirect calculations or by extrapolation downward from observations at higher temperatures.. For their studies in the range 1695° to 1866°C, Gokcen and chipman' restricted their aluminum concentrations to less than 0.06 pct. Oxygen analyses were made by the vacuum fusion method which appears to be dependable at these low aluminum concentrations. Experimental results, even at the highest temperature employed, are extremely sensitive to small errors in the analysis of either element. The slight change in the equilibrium constant with aluminum and oxygen concentration was utilized in the calculation of interaction coefficients expressing the effect of aluminum on the activity coefficient of oxygen and the reciprocal effect of oxygen on the activity coefficient of aluminum. The range of concentration, however, was so limited that only a rough value for the interaction coefficient could be obtained. This value was much more negative than that found for any other pair of reactants. In view of the very limited range of concentration employed, the reported values have always been regarded as very questionable. A redetermination was the object of the work reported here. EXPERIMENTAL METHOD At high aluminum concentrations, the vacuum fusion method is susceptible to grave error due to absorption of gas by aluminum distilled from the sample. Since it was desirable to extend the study to at least as much as 1 pct Al, another method for analysis was sought. In steels containing more than a few hundredths of a percent aluminum and no other deoxidizing element, it is safe to assume that

Jan 1, 1963

By Harry Tufft

FOR many years the treatment of mine timbers with preservatives was confined to a few pioneer plants in the United States, and it is only in the past few years that the practice has grown appreciably. In a field study of the mine timber situation in Illinois, Pennsylvania, and further study of the situation in the country as a whole, I found that most mine operators did not keep records on mine timber that would afford the necessary data for determining the possible savings from preservative treatment. Some primary questions the mining engineer should be able to answer before making his decision on preservative treatment. for a particular mine are: (1) Quantity and cost of timber going into permanent workings annually; (2) quantity and cost of annual replacements due to decay; (3) life of untreated timber in different places; (4) desired life of timber. With the necessary facts in hand, he can then con-fidently select a method of treatment and preservative that is best suited to his needs. In former years when timber was cheap and an abundant supply could be had close at hand, as was the case in the majority of mining regions, the mine op-erator did not concern himself much except to see that enough was supplied to keep the workings safe. The cost figure for timber and labor, distributed to cost per ton of ore, was all the bookkeeping necessary. With present costs of timber, labor, and increasing length of haul to the mine, many operators are paying closer attention to timbering costs and studying them in. more detail. Some of the larger and more progressive opera-tions now keep detailed' figures that give information on all phases of their timber problems. However, at the majority of mines the data available do not permit such analysis. Checks as to where the different con-signments are placed, the date of setting, and the period

Jan 6, 1927

By A. C. Lane

Relations de la profondeur de plissement avec la gravita-tion et la hauteur des montagnes dans les Alpes. Par A. Heim (Zurich) 50me Anniversaire, Livre Jubilaire Soc. Geol. De Belgique, Rome, Fascicule 1, 17 to 28. Measurements show a negative anomaly, less densities of .the material below sea level. The author expresses it in terms of the thickness of rocks of an arbitrary density, 2.4, which might be considered wanting. The accordant heights of the summits, the depths of the folds, the deficiency in .gravity, and denudation he finds to be connected. The Alps float on the lightness of the folds of "sal" of weight 2.6 to 2.75 plunged into the heavier "Sima" according to a for-mula: P = h (2.7/2.8-2.7) where - P is the depth of fold-ing below sea level; 2.7 is the weight of the material accu-mulated in folding; 2.8 is the weight of the material dis-placed by it; and h is the mean height of the mountainous regions. For instance, between the valley of Saar and the Val de Bagne in Valais the depth of the folds according to Ar-gand's profiles is between 30 and 40 kilometers. The loss of gravity has been estimated in this region as 1450 X 2.4 = 3480 in units of weight. Obviously errors in the densities would profoundly affect the estimates of the thickness of folding, but his depths of folds are obtained from sections, and from them he works back to the densities. Of course other densities might be placed in the formula. Zur Dichte bestimmung von Tonen. By J. Koenigsberger, Berg u. Hüttenmannisches Jahrbuch, 75, I. Discusses Dr. B. Wilser's investigations as to the best way of obtaining the weight of rocks per unit volume. The use of mercury for rocks affected by water as there recom-mended may easily give too large volumes unless 1 to 3 atm. pressure is used. Thick machine oil is recommended for large lumps of clay.

Jan 4, 1928