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By Henry D. Hibbard

A NOTED ordnance engineer once said to a friend, in speaking of the production of great steel guns, "How is it? We design our guns with a factor of safety of eight, and the guns burst." The vague way in which internal stresses and strains in iron and steel are often considered and spoken of makes it worth-while to examine them, as to their nature, their causes and results, how they may, for useful purposes, be advantageously dealt with, and how, when detrimental or dangerous, they may be reduced or kept within harmless proportions. Rankine defines ?strain " as a change of form or dimensions of a solid or liquid mass produced by a stress. This definition seems not intended to cover strains due to internal stresses, and it will help us in the present inquiry to consider strain as a tendency to change as well as an actual change of form. Internal strains in iron and steel are the result of stresses within the mass of the piece, some parts pulling and others pushing in resistance to them; or, in other words, some parts are in tension and some in compression, each part striving to relieve itself from strain and make the piece assume a form in which all parts are at rest. Subdivision, so that each part could relieve its strain by motion relative to the other parts, would, if carried out far enough, practically obliterate strain. The internal strains we are now to consider are not those due to the stresses of the service which the piece is rendering, either alone or as, a part of a structure, which may be termed service-strains, but those which originate or at least are contained in the piece itself. Internal stresses in a piece of metal are, like action and reaction, always equal and in opposite directions. The stresses

Sep 1, 1906

By Charles A. Chase

This paper, descriptive of a single mine, is presented in the belief that it may furnish useful suggestions to mine-managers encountering similar problems; and it includes the details which will enable them to estimate the value of the methods employed—especially where these depart from common practice. Tt should be added, however, that this mine is not typical of the San Juan district, but differs markedly from neighboring mines in physical conditions and metallurgical requirements. The Liberty Bell mine is situated in San Miguel county, Colo., on the west front of the San Juan mountains, 2 miles north of Telluride. The vein was discovered in 1876 by Wm. L. Cornett, who, with subsequeilt locators, took up claims along the apex. A few hundred feet of development-work was accomplished, and a few? tons of ore were smelted or milled; but profitable working proved impossible under existing

Jan 1, 1912

By Walter S. Lutz, J. T. Griffith

The rainfall during the last six months of 1942 in Scranton and vicinity was 24.06 in.—only 4.35 in more than the average for this district in any equivalent period—yet that rain forced The Hudson Coal Co. to handle 38.8 tons of water for every ton of coal mined. It filled to overflowing, or to a higher level, 14 flooded mine areas holding, in total volume, 8.3 billion gallons of water in storage; brought about a pumpage of 11.4 billion gallons in the months of December 1942 and January, February and March 1943 Half of the total energy generated or purchased (44,322,980 kw-hr.) was required to keep the mines sufficiently free of water to permit the mining of coal during a period of much needed output. Fig. I shows the extent to which this flooding of exhausted and idle properties has proceeded, and is known to be proceeding further, at the upper end of the Northern field. This rainfall (24.06 in.) means 80,559,444 tons of water on approximately 46.2 sq. miles of area tributary to the pumping plants. During the high rainfall period, 72,687,661 tons went underground, being pumped at the stations in this territory. This means an inflow of 88per cent, a runoff of 12 per cent compared with 64 per cent during normal conditions in a normal region. During this period no floods, either surface or underground, had to be dealt with, although the streams and rivers were high on several occasions. In general, the rainfall for the first three months of 1943 can be described as heavy but not abnormal.9 These figures not only indicate the large volumes of water to be handled but, by their very size, they also emphasize that the mine-water problem is not to be conquered, at least from an economical standpoint, by merely buying and installing more and more pumps. Into the solving of this water problem must go much planning, adhering to the principle of keeping the highest percentage of water at the highest possible level for the longest period of time; the storage of huge volumes in sumps capable of being reduced after the flood inflow and at rates less than the inflow; plans for prevention of surface inflow; provision of the minimum of pumping capacity arranged to as nearly 100 per cent pumping load factor as is possible; intercompany joint pumping plants; the conducting of water from one plant to another and from one property to another over distances measured in miles; priorities in power to the threatening situations; and. balance of the necessities and dangers existent in one colliery over another, day by day, when quantities of water are running high. Despite these astronomical figures of water volumes, their disposal to the surface is accomplished reasonably cheaply because, although the annual cost of $575,020 is a large sum, the cost per ton is about 0.1168 cents. Credit for this goes

Jan 1, 1947

By J. T. Griffith, Walter S. Lutz

The rainfall during the last six months of 1942 in Scranton and vicinity was 24.06 in.—only 4.35 in more than the average for this district in any equivalent period—yet that rain forced The Hudson Coal Co. to handle 38.8 tons of water for every ton of coal mined. It filled to overflowing, or to a higher level, 14 flooded mine areas holding, in total volume, 8.3 billion gallons of water in storage; brought about a pumpage of 11.4 billion gallons in the months of December 1942 and January, February and March 1943 Half of the total energy generated or purchased (44,322,980 kw-hr.) was required to keep the mines sufficiently free of water to permit the mining of coal during a period of much needed output. Fig. I shows the extent to which this flooding of exhausted and idle properties has proceeded, and is known to be proceeding further, at the upper end of the Northern field. This rainfall (24.06 in.) means 80,559,444 tons of water on approximately 46.2 sq. miles of area tributary to the pumping plants. During the high rainfall period, 72,687,661 tons went underground, being pumped at the stations in this territory. This means an inflow of 88per cent, a runoff of 12 per cent compared with 64 per cent during normal conditions in a normal region. During this period no floods, either surface or underground, had to be dealt with, although the streams and rivers were high on several occasions. In general, the rainfall for the first three months of 1943 can be described as heavy but not abnormal.9 These figures not only indicate the large volumes of water to be handled but, by their very size, they also emphasize that the mine-water problem is not to be conquered, at least from an economical standpoint, by merely buying and installing more and more pumps. Into the solving of this water problem must go much planning, adhering to the principle of keeping the highest percentage of water at the highest possible level for the longest period of time; the storage of huge volumes in sumps capable of being reduced after the flood inflow and at rates less than the inflow; plans for prevention of surface inflow; provision of the minimum of pumping capacity arranged to as nearly 100 per cent pumping load factor as is possible; intercompany joint pumping plants; the conducting of water from one plant to another and from one property to another over distances measured in miles; priorities in power to the threatening situations; and. balance of the necessities and dangers existent in one colliery over another, day by day, when quantities of water are running high. Despite these astronomical figures of water volumes, their disposal to the surface is accomplished reasonably cheaply because, although the annual cost of $575,020 is a large sum, the cost per ton is about 0.1168 cents. Credit for this goes

Jan 1, 1947

Jan 1, 1900

By R. K. Hopkins

For a great many years fusion welding has been used in and around petroleum refineries, but it is only within six or seven years that the more important pressure vessels have been constructed by this process, because before that time the properties of fusion welds would not withstand such rigorous service. Since the adoption of fusion welding for the construction of this equipment, the refiner has required pressure vessels suitable for operation over a very wide range of conditions. On the one hand, vessels must operate at extremely high temperatures, in the range of 950" to 1000° F., and on the other vessels must be suitable for operation at sub-zero temperatures down as low as —75" F. Also, vessels are required suitable for operation at pressures upwards of 1000 lb. per sq. in., and as low as a 29-in. vacuum. In addition, vessels are required to withstand the attack of very corrosive mediums. It has been a rather difficult task for the fabricator to meet all of these requirements, but as a result of the extensive research carried on by steel manufacturers and several fabricators of class I vessels, practically all of these demands have been met. In order to meet the refiners' requirements for this wide range of conditions, the fabricator has worked closely with the metallurgist. This has enabled him to choose the proper base metal for each service condition, but it has been the fabricator's problem to develop a welding rod and welding technique, as well as a heat-treatment, that would produce in the welded vessel characteristics in and around the weld comparable to those in the base metal. Where corrosion is not a serious problem, and where the operating temperatures are not too high, ordinary carbon steel has served very well. But, when corrosion is serious, and/or when the temperatures are either very high or very low, it is necessary to use some form of alloy steel to give satisfactory service. A great deal of credit is due to the members of the Boiler Code Committee and also to the members of the Joint A.P.I.-A.S.M.E. Committee, who have formulated codes that insure the safety of the

Jan 1, 1935

By R. K. Hopkins

For a great many years fusion welding has been used in and around petroleum refineries, but it is only within six or seven years that the more important pressure vessels have been constructed by this process, because before that time the properties of fusion welds would not withstand such rigorous service. Since the adoption of fusion welding for the construction of this equipment, the refiner has required pressure vessels suitable for operation over a very wide range of conditions. On the one hand, vessels must operate at extremely high temperatures, in the range of 950" to 1000° F., and on the other vessels must be suitable for operation at sub-zero temperatures down as low as —75" F. Also, vessels are required suitable for operation at pressures upwards of 1000 lb. per sq. in., and as low as a 29-in. vacuum. In addition, vessels are required to withstand the attack of very corrosive mediums. It has been a rather difficult task for the fabricator to meet all of these requirements, but as a result of the extensive research carried on by steel manufacturers and several fabricators of class I vessels, practically all of these demands have been met. In order to meet the refiners' requirements for this wide range of conditions, the fabricator has worked closely with the metallurgist. This has enabled him to choose the proper base metal for each service condition, but it has been the fabricator's problem to develop a welding rod and welding technique, as well as a heat-treatment, that would produce in the welded vessel characteristics in and around the weld comparable to those in the base metal. Where corrosion is not a serious problem, and where the operating temperatures are not too high, ordinary carbon steel has served very well. But, when corrosion is serious, and/or when the temperatures are either very high or very low, it is necessary to use some form of alloy steel to give satisfactory service. A great deal of credit is due to the members of the Boiler Code Committee and also to the members of the Joint A.P.I.-A.S.M.E. Committee, who have formulated codes that insure the safety of the

Jan 1, 1935

By Frederick K. Allgaier

As part of an ongoing research program, the Bureau of Mines, U.S. Department of the Interior, is monitoring surface subsidence over six longwall panels at three Utah coal mines. These sites are characterized by mining depths of 244 to 610 meters (800 to 2,000 ft .), thick and massive sandstone layers in the overburden strata, multiple seam mining, extraction heights of approximately 1.8 to 3 meters (6 to 10 ft.), and rugged surface topography. Maximum subsidence, angle of draw, timing relative to mining, horizontal strain, and rate of subsidence development are being determined and correlated with mining and geologic variables. Results to date indicate the maximum vertical subsidence over the monitored panels ranges from 0.6 to 0.9 meters (2 to 3 ft.). The major factors controlling the amount of subsidence are the panel dimensions and the status of adjacent panel mining. Only minor surface cracking at the panel ends was evident at any of the sites. In all cases, there was a time lag of several months between the start of mining and subsidence at the surface. As subsequent panels are monitored and additional data become available, better estimates of the effect of various site characteristics on the subsidence will be possible. Ultimately, improved prediction capabilities will allow mine operators in the West to evaluate the potential for subsidence-related damage which could affect the current or future land use above the mine.

Jan 1, 1982

By C. G. Durdaller, W. H. Robinson, G. M. Pound

The nucleation rate of the a (pay) to 0 (white) tin transformation was measured as a function of temperature and a tin particle size using an X-ray diffraction technique. The powder specimens of a tin were essentially monodisperse and the small dinzension of the particles of these specimens was varied from 13 to 75 p. Several types of nucleation sites of differing potency were fbund to be operative in the nucleation process, but it could not be determined whether these sites were on the free surface of the tin particles or within the volume. Assuming that they were on the free surface, the average density of the most potent sites was calculated to be 2.5 to 5.3 x 10' sites per sq cnz through the application of a Poisson distribztion finction to the isothermal data. Analysis of the temperature dependence' of the rate constmts at a given fraction transformed suggests that the active sites are regions of higher free energy and not catalytic interfaces. Appreciable induction periods were observed at the lower temperatures of transformation. Experimental studies1 of solid-solid phase transformations have led to the belief that the new phase nucleates at structural imperfections. The purpose of the present work was to learn more about the mechanism of nucleation in solids and the nature of the singularities at which nucleation occurs. In this investigation nucleation rates in the isothermal transformation of gray to white tin were measured by an X-ray diffraction technique using essentially monodisperse powders of gray tin. This particular phase transformation was chosen for study because it presented fewer experimental difficulties than most others. The experimental temperature-control problems were minimal because the two phases coexist in equilibrium at 13.3"C, and measurable transformation rates occur at temperatures only slightly above room temperature. The growth rate of the P phase into the a2 is sufficiently fast to make the measured transformation rate equivalent to the nucleation rate, provided that the particle size of the samples is small enough; for the experimental temperatures used in this study, the particle diameter must be less than 100 p. EXPERIMENTAL TECHNIQUE The P tin used in this study was obtained from Capper Pass and Son Ltd., North Ferriby, Yorkshire, England, and was of 99.999 pct purity. It was transformedS to the a phase and ground into a fine powder in an agate mortar. This powder was separated by a Roller air classifier into seven fractions whose dimensions, as determined by microscopic measurement of many thousands of particles, are given in Table I and whose distribution of size within each fraction is given in Figs. 1 and 2. The shape of the particles was roughly that of an oblate spheroid,

Jan 1, 1964

By AIME AIME

AMERICAN participation in the World Engineering Congress in Japan will be generous. Nearly seventy papers have been prepared and for- warded for printing and the A. I. M. E. is well represented in the list. At our San Francisco meeting four of these will be briefly reviewed by the authors for the benefit of those who are unable to go on to Tokyo. They constitute a group dealing with the present economic status as seen by engineers of the world's iron, coal, petroleum and non-ferrous metals. Messrs. Leith, Smith and Tryon, Requa, and Probert have written papers that constitute a notable series. Messrs. Jeffries, Sweetser and Kinney, and other Institute members have written papers dealing more closely with technologic progress. The latest list of delegates and members is printed below, names of A. I. M. E. members being set in italics.

Jan 1, 1929

By F. G. Smith

A few years ago, the writer encountered a problem that, at first, seemed to be due to peculiar conditions affecting grain growth. Large cups made from heavy metal failed in the first drawing operation in the process of making seamless tubes. The metal, as cast, appeared to be sound and strong; it rolled successfully and withstood the first cupping operation, but on the first draw it failed, with a crystalline fracture. The failure appeared in the slightly worked part of the bottom of the cup, and microscopic examination revealed exceptionally large grains. Knowing the general conditions governing recrystallization of brass, which were later published by Mathewson and Phillipsll an investigation was outlined with the idea of including various conditions under which new grains might form, and which would include the effect that a previous anneal might have upon the anneal following. These conditions were produced by annealing specimens of brass at five different temperatures, indenting them with a 10-mm. ball under four different pressures, and then reannealing at each of the five temperatures five specimens each of which had been annealed at one of the five temperatures. Preparation of Specimens The material used was cartridge brass 0.400 in. thick, having the following composition: Copper 66.60 per. cent., zinc 33.35 per cent., lead 0.02 per cent., iron 0.03 per cent. This was rolled with 35 per cent. reduction after a 700" C. anneal. Fig. 1 shows the structure of this original bar on which all subsequent anneals were made. Pieces 1 in. (2.5 cm.) wide and 3 in. long were prepared and annealed for 1/2 hr. at 450°, 550°, 650°, '750°, and 850" C. Each of these pieces are indented under the Brinell test with a 10-mm. ball at 500, 1000, 2000, and 3000 kg. pressure. Then, sets of five pieces from each of the original anneals were reannealed at 450°, 550°, 650°, 750°, and 850" C.

Jan 1, 1921

By W. O. Philbrook

An engineering analysis indicates that the coke rate in present blast-furnace practice is set not by chemical or thermal needs but to give adequate charge permeability for economical driving rates. An equation showing interrelations among pressure drop, gas flow, and charge characteristics has been derived. Flooding conditions and the location of the fusion zone are discussed. Maximum ore size is probably limited by chemical re-ducibility rather than by heat transfer. THE intention of this paper is to show that the ].imitations on the production rate and coke requirement of the iron blast furnace are not primarily chemical or thermal in nature but are related to characteristics of the burden and operation that govern gas flow, heat transfer, and stock movement. A semiquantitative analysis will be developed in terms of standard engineering principles to give a useful picture of the relative importance of physical and mechanical factors in contrast with the chemical features of the process that are more commonly emphasized. Most of the details of calculation have been omitted in the interest of brevity and to avoid submerging the rnain points in a sea of arithmetic. Numerical values have been arrived at by objective methods from reported operating data or by reasonable estimates of material properties where exact data are lacking and then tested to see how well they fit practice, rather than by working backward to find what assumptions are needed to give the desired answers. The analysis is oversimplified in many ways because exact engineering relations have not yet been studied for bed distributions as complex as are known to exist in the blast-furnace stock column. One objective of this paper is to show that the blast furnace, in spite of its complexity, can be at- tacked by engineering methods in the hope that this viewpoint will stimulate the kind of research needed for a more exact treatment. The basic ideas and many of the conclusions presented are qualitatively well known. A careful literature survey to credit the source of all observations not original to the author would indeed be voluminous, and such has not been attempted. T. L. Joseph's Howe Memorial Lecture' gives an excellent background of what is known about the internal workings of a blast furnace. Other important reference works or sources of specific information will be noted. It is hoped that the present paper will contribute something new, in method of attack and interpretation, that will aid in a clearer understanding of how to operate the blast furnace to best advantage. Factors Limiting Production and Coke Rates The rate of combustion of coke in a blast furnace, as in any fuel bed, is exactly proportional to the rate at which air is supplied. It is axiomatic, then, that the production rate of a furnace is limited by the rate at which it will take wind, i.e., burn coke, and the amount of coke that must be burned at the tuyeres to make a ton of iron of suitable composition. These two possible limiting factors will be considered briefly in the order mentioned. One common restriction on wind rate is flue-dust production. Since the volume of top gas is nearly proportional to the blast volume (by a factor of about 1.35 on a dry basis), an increased wind rate causes a correspondingly increased linear velocity of top gas in the throat of the furnace. The higher

Jan 1, 1955

H. H. Kellogg (Columbia University)—The accurate measurements of the equilibrium gas ratios for the reaction: Pb(1) + H2S = PbS(c) + H2 [I] reported in this paper are a distinct contribution to the literature, and the authors are to be congratulated. I wish to comment, however, on the correlation of the data which is presented. The authors show a straight line correlation of log H2S/H2 vs 1/T, Fig. 1, and are satisfied with this for calculation of ?Fo even when extrapolated to low temperature (427 °C). Heat capacity data for the constituents of this reaction are available (at least to 900°K), however, and ACP for reaction [I] is finite and positive in the temperature range studied. Simplification of the heat capacity equations yields: ?CP= 2.71 + 1.65 x 10-3T (298°-900°K) This positive value of ?CP should result in a small but noticeable curvature of a plot of log K vs 1/T. That the experimental data fail to show such a curvature may be traced to another oversimplification of the author's treatment of their data. They assume that the activity of liquid lead is unity for all temperatures, so that

Jan 1, 1961

By S. V. Krusiewski, J. W. Gabelman

Regional metallogenic zones and areas of equal paragenetic range have been interpreted from a compiled metallogenic map. of Mexico. Mineralization gradients of the pattern subsequently identified extend inland from coastal zones of high-temperature mineralization, and join in a central longitudinal zone of relatively low-temperature mineralization, apparently leaving no zonal room for lowest temperature deposits. The striking regional zoning pattern can be correlated with regional deformation gradients of similar position and orientation. The gradients represent at least three major orogenic cycles in two structural belts. Paleozoic structural belts existed along each coast with deformation gradients diminishing inland toward a narrow, central peninsular craton. The Mesozoic-Tertiary Mexican (Cordilleran) belt covered the entire country with a gradient oriented toward the Gulf of Mexico. Most ore deposits in this belt are of Tertiary age, although Tertiary mineralization gradients seem to have "inherited" the pattern left by Paleozoic tectonic gradients. Mineralization gradients can be used to identify the regions most favorable for the occurrence of selected metals. A metallogenic province is characterized by particular proportions of various metals, and the relative proportions can vary from province to province; but within any province the same intensity of mineralization would produce similar deposits in different places. Declining intensity of minetalization produces different kinds and sizes of deposits in zones that are concentrically arranged around sites of strongest rock alteration. On a regional basis, districts of similar average intensity of mineralization occur in zones that generally parallel some tectonic grain with the result that tectonic deformation has been designated a principal cause of mineralization. Variations in the type and intensity of deformation would determine the type as well as size of metal deposits. Mexico is especially favorable for such a study be- cause of its great abundance and variety of epi-genetic mineral deposits in various lithologic, structural and tectonic environments. The concept is also useful in recognizing portions of Mexico favorable for the occurrence of specific metals. METALLOTECTONIC ZONING IN MEXICO Theory: In studies of individual districts and groups of districts throughout North and South America, areal zoning of metal deposits generally seemed to respond to the paragenetic sequence of iron, gold, copper, zinc, lead, silver, antimony and arsenic, gold and fluorite. However, the definition of district zones is greatly obscured by contemporaneous or rhythmic deposition of metals, especially in the middle of the paragenetic range, and by the common superimposi-tions of different generations of metals. Zones could usually be distinguished only for groups of metals, such as early precious metals, base-metal sulfides, sulfosalts and late precious metals. The best defined zoning in a district is normally the spatial separation of the greatest volumes of altered and metallized rocks.' Exceptions are districts representing the high- and low-temperature extremes of the mineralization range where the former creates a matrix for the latter. In most districts the total quantity of alteration products is greatly in excess of, and appears to be roughly proportional to, the total quantity of metallization products. Subsequent to the bicomponent nature of each district, the most important mineralogical feature is the great excess of one to several metals or minerals which results in a district identifiable as one of predominantly gold, copper, lead-zinc, fluorite, etc., although a great variety of other elements may be present. The para-genetic range for the abundant elements in any district is only a portion of the entire possible range for all the elements representing the complete process throughout the region. Early during investigations of this type, it became apparent that the consistent bicomponent character of districts allows two methods for studying epi-genetic mineralization patterns. One is to identify and plot altered rock "pipes,"* which are easily recognizable in the landscape by their anomalous

Jan 1, 1969

By James E. York

AT a meeting of the American Society for Testing Materials at Atlantic City, June, 1908, Dr.. C. B. Dudley, in his presidential address,' showed the vital necessity of not only making a steel rail as good as in the past, but of making it considerably better in order to meet the present and prospective require¬ments of railroads. Doctor Dudley requested the co-operation of all who from personal experience could give information that would result in bringing about the production of a steel rail that could be relied upon to meet the present requirements. I have had considerable experience in the practical manufacture of steel of almost every grade, during the past 40 years, and I shall suggest changes that will bring about the results desired. Doctor Dudley has had a long experience as chemical and metallurgical expert for the Pennsylvania railroad, but he frankly admits that up to the present time both he and other metallurgical experts lack the practical knowledge of steel-making that is necessary to state correctly the reasons for the unreliability of the steel rails now produced. The necessity is self-evident for more positive practical knowledge on the part of these experts of what is possible and what is impossible regarding the practical manufacturing of steel rails from the ingot to the, finished product. Chemical knowledge in steel-making is far in advance of what it was years ago, and might be said to cover every requirement (in that department) for producing reliable steel. The study of the metallography of steel has been of great value, also the physical testing of steel, but this knowledge will only de-

May 1, 1909

By J. R. Stone, G. D. Storm

Design features and operating methods of ASARCO's new unit for the continuous melting and casting of tough pitch copper at Perth Amboy are described. Preliminary studies made for determinitzg economic feasibility and design details are also presented. Cathodes are preheated with oil and melted in an electric furnace at 40-ton per hr rate, from whence the molten copper is fed simultaneously to the wire bar casting wheel and the continuous casting of cakes and billets. In the early 1950's the copper refining furnaces at ASARCO's Perth Amboy plant reached a point where major expenditures would have to be made for replacement of the furnaces and the auxiliary equipment. The problem was whether to continue with the standard reverberatory furnaces or to consider continuous melting in electric furnaces. Reverberatory furnaces have been used for years in the copper industry and for some 50 years at the Perth Amboy plant. Reverberatory melting practice, however, imposes certain restrictions. First, labor costs are high, usually requiring three shifts per day. Secondly, they operate on a batch basis, the conventional operation being a 24-hr cycle including

Jan 1, 1961

By R. Al-Hussainy, P. B. Crawford, H. J. Ramey

The effect of variations of pressure-dependent viscosity and gas law deviation factor on the flow of real gases through porous media has been considered. A rigorous gas flow equation was developed which is a second order, non-linear partial differential equation with variable coeficients. This equation was reduced by a change of variable to a form similar to the diffusivity equation, but with potential-dependent diffusivity. The change of variable can be used as a new pseudo-pressure for gas flow which replaces pressure or pressure-squared as currently applied to gas flow. Substitution of the real gas pseudo-pressure has a nrtmber of important consequences. First, second degree pressure gradient terms which have commonly been neglected under the assumption that the pressure gradient is small everywhere in the flow system, are rigorously handled. Omission of second degree terms leads to verious errors in estimated pressure distributions for tight formations. Second, flow equations in terms of the real gas pseudo-pressure do not contain viscosity or gas law deviation factors, and thus avoid the need for selection of an average pressure to evaluate physical properties. Third, the real gas pseudo-pressure can be determined numerically in term of pseudo-reduced pressures and temperatures from existing physical property correlations to provide generally useful information. The real gas pseudo-pressure was determined by numerical integration and is presented in both tabular and graphical form in this paper. Finally, production of real gas can be correlated in terms of the real gas pseudo-pressure and shown to be similar to liquid flow as described by diffusivity equation solutions. Applications of the real gas pseudo-pressnre to radial flow systems under transient, steady-state or approximate pseudo-steady-state injection or production have been considered. Superposition of the linearized real gas flow solutions to generate variable rate performance was investigated and found satisfactory. This provides justification for pressure build-up testing. It is believed that the concept of the real gas pseudo-pressure will lead to improved interpretation of results of current gas well testing procedures, both steady and unsteady-state in nature, and improved forecasting of gas production. INTRODUCTION In recent years a considerable effort has been directed to the theory of isothermal flow of gases through porous media. The present state of knowledge is far from being fully developed. The difficulty lies in the non-linearity of partial differential equations which describe both real and ideal gas flow. Solutions which are available are approximate analytical solutions, graphical solutions, analogue solutions and numerical solutions. The earliest attempt to solve this problem involved the method of successions of steady states proposed by Muskat.' Approximate analytical solutions' were obtained by linearizing the flow equation for ideal gas to yield a diffusivity-type equation. Such solutions, though widely used and easy to apply to engineering problems, are of limited value bemuse of idealized assumptions and restrictions imposed upon the flow equation. The validity of linearized equations and the conditions under which their solutions apply have not been fully discussed in the literature. Approximate solutions are those of Heatherington et al.. MacRobertsl and Janicek and Katz.' A graphical solution of the linearized equation was given by Cornell and Katz. Also, by using the mean value of the time derivative in the flow equation, Rowan and Clegg' gave several simple approximate solutions. All the solutions were obtained assuming small pressure gradients and constant gas properties. Variation of gas properties with pressure has been neglected because of analytic difficulties. even in approximate analytic solutions. Green and Wilts8 used an electrical network for simulating one-dimensional flow of an ideal gas. Numerical methods using finite difference equations and digital computing techniques have been used extensively for solving both ideal and real gas equations. Aronofsky and Jenkins"I " and Bruce et al.11 gave numerical solutions for linear and radial gas flow. Douglas et al." gave a solution for a square drainage area. Aronofsky 13 included the effect of slippage on ideal gas flow. The most important contribution to the theory of flow of ideal gases through porous media was the conclusion reached by Aronofsky and Jenkins" that solutions for the liquid flow case'" could be used to generate approximate solutions for constant rate production of ideal gases. An equation describing the flow of real gases has been solved for special cases by a number of investigators using numerical methods. Aronofsky and Ferris 10 onsidered linear flow, while Aronofsky and Porter 17 considered radial gas flow. Gas properties were permitted to vary as linear functions of pressure. Recently, CarteP 18 proposed an empirical correlation by which gas well behavior can be estimated from solutions of the diffusivity equation using instantaneour values of pressure-dependent gas

Jan 1, 1967

By I. Tamura, J. O. Brittain, T. Mura

Plain carbon steel in the cold worked or marten-sitic conditions has an internal friction peak at about 250 oC at a frequency of I cps. The influence of substitutional alloying elements on this peak was examined experimentally. The alloys were vacuum melted Co-, Cr-, Mo-, Ni-, and Si-iron (about 3 pct alloying elements), and carburized Si-iron. The internal friction of the alloys in the temperature range 30o to 500 OC was determined by means of a torsion pendulum. The 250 oC peak of the cold-worked alloys was lower in height than that observed in plain C-iron and steel. Carburized Si-iron in the quenched condition had a peak which occurred at a slightly lower temperature than in quenched plain C-steel, but the height of the peak was substantially greater than that found for the same alloy in the cold-worked condition. The activation energy of this peak for martensitic Si-steel was about 35 kcal per mol. ANNEALED a iron has two internal friction peaks due to nitrogen and carbon at 20o and 40o C respectively, at a frequency of 1 cps. If a iron is cold worked, these diffusion peaks become smaller and a new peak appears at about 250o C. The activation energy for the 250o C peak is in the range of 32 to 44 kcal per mol and has an average value of 38 kcal per mo1. It has been experimentally verified that both interstitial solute atoms and dislocations are necessary for the 250o C peak. 3 Wert has also shown that an incubation period precedes the appearance of the 250 C peak.4 With regard to quenched martensitic steel, Ke et al.596 observed two peaks at around 130o and 250o C. They conjectured that the 250o C peak in martensite was due to the same mechanism as the 250°C peak in cold worked a iron, and the 130°C peak was due to the nature of tempered martensite. They did not report the activation energy for these peaks. Chernikova7 found only one peak at about 200° C in tempered martensite. In a previous paperS we reported an activation energy of approximately 40 kcal per mol for the 250° C peak in plain carbon martensitic steels. Ichiyama8 found the activation energy to be about 36 kcal per mol for the 250° C internal friction peak in steels in the martensitic condition. The present authors proposed a theory for the 250°C peak for cold worked and quenched iron and steel.= The theory for the peak is based upon the addition of a strain-energy term to the free energy for the formation of a carbide precipitate due to the presence of a disclocation. The model employed for the relaxation process consists of the growth and solution of a carbide precipitate of critical size as a consequence of an oscillating dislocation. In this report, the influence of substitutional alloy ing elements on the 250° C peak is examined and the experimental results are discussed in terms of our theory for the peak. Most of the experimental work on the alloy steels was confined to the Fe-Si-C alloys.

Jan 1, 1962

By R. F. Yap, N. Arbiter, C. C. Harris

A fully-instrumented driving mechanism has been constructed to study the power, aerating and solid suspension characteristics of several laboratory flotation machines. Machines operating over normal flotation speed ranges give substantially constant power numbers in liquid systems indicating that they operate close to fully baffled turbulent flow conditions. Owing to lack of geometrical scaling, power numbers for different sizes of cells of the same make are different. Even larger differences occur between cells of different manufacturers. For a given impeller, varying the tank size did not significantly affect the power consumption. Tank geometry and baffling has a slight effect on power consumption with shrouded impellers. For a given impeller speed, suspension height decreases while power increases with increasing mass of solids in suspension. While power consumption is hardly affected by particle size and clearance between the impeller and tank bottom, the suspension height significantly increases as clearance increases and as particle size decreases. Aeration was found to affect not only power but also the suspension characteristics of the machine. For closely sized particles, drastic sedimentation occurred when a critical value of the air flow number was exceeded. The critical air flow number decreased with increasing particle size. This effect was less marked with a wide particle size range. The self-aerating capacity of flotation machines increases with cell size at a given speed for the same impeller-shroud system, but decreases in the presence of frother and solids. Equations have been established for correlating all of the studied variables. Data taken from the literature were also correlated with these equations. The modern mechanical flotation machine has, over a period of 60 years, displaced other designs to become the dominant type. Once the correct chemical environmental conditions have been established, the major requirement, selective mineral-air adherence, is essentially a function of two operating variables — impeller speed and air rate. The special nature of this dependence is such that in the same apparatus, but under different operating conditions, adherence can be either prevented or destroyed. Another aspect of this observation is that flotation machines though differing in detail to a considerable extent can produce similar metallurgical results. It must be concluded that having determined the correct reagent levels, establishing the correct operating conditions are at least as important as machine design. Since about 1960, after 30 years of fairly stable circumstances, manufacturers have been developing new types of machines whose major feature is emphasis on pulp flow characteristics by virtue of new im-peller-stator designs. As far as can be ascertained, these new designs necessitate radical departures from accepted impeller speed-air rate values. Performance data are still awaited. Flotation machine development has been empirical, as is selection of operating conditions. The purpose of the work at Columbia University has been to elucidate the fundamentals of the subject so that the purely mechanical aspects of the flotation process can be understood in hydrodynamic terms.1-6 Hopefully, this might lead to intelligent selection of a particular machine and its operating conditions for a specific ore based on a minimum of testing, or even to new types of flotation machines. The present investigation is the most comprehensive to date.7,8 Earlier work, which was largely exploratory, has been repeated and extended and employes the most accurate measuring techniques available. Additionally, sufficient hydrodynamic data were obtained under flotation conditions to delineate the relevant operating ranges. Attention has been given to scaling in that several geometrically scaled tanks and impellers have been constructed and tested; it has been pointed out elsewhere that undistorted geometrical scaling rarely pertains in flotation machine design.5 This paper is divided into sections dealing with relevant combinations of the three phases: liquid, air and solid. Summaries of the literature have been given in previous publications2-4 and will not be repeated here. Recently, several reviews of mixing have appeared, which can be usefully referenced.9-11 It is of interest to note that flotation is not included

Jan 1, 1970

By F. G. Cottrell

(New York Meeting, February, 1912.) ABOUT a year and a half ago, at the San Francisco meeting of the American Chemical Society, in connection with the excursions to local smelting-works, I had occasion to show some lantern-slides illustrating the recent commercial development of electrical methods for precipitating the suspended matter from smelter-smoke, the underlying phenomena of which were clearly brought to the attention of the technical public by Sir Oliver Lodge as long ago as 1884. In the Journal of industrial and Engineering Chemistry, August, 1911, most of these views were reproduced, together with an account of the work from its beginning up to July, 1911. To-day I wish particularly to show you some of the further developments of the work since that time; but in order to make these clear they will be prefaced by a brief abstract of the article above referred to. The removal of suspended particles, front gases, by the aid of electric discharges is by no means a new idea. As early as 1824 we' find it suggested by Hohlfeld 1 as a means of suppressing ordinary smoke, and again a quarter of a, century later by Guitard.2 These suggestions, which do not seem to have stimulated any practical study of the question, were soon entirely forgotten, and only brought to light again by Sir Oliver Lodge,3 many years after he himself had independently rediscovered the same phenomena and brought them to public attention 4 in a lecture before the Liverpool Section of the So-

Jul 1, 1912