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By Charles C. Rodd

Prior to 1938, proration procedure in Kansas required the physical testing of wells in order to set up a basis for allocating production. Subsequently the use of liquid-level data and bottom-hole pressure data was authorized on certain types of wells as a basis for calculating well capacities, thereby permitting wells to be tested at low rates and with small volumes of production. This paper gives some attention to the equipment used for obtaining liquid-level data but in general it is devoted to the theoretical and physical factors involved in well testing by drawdown methods. These tests are divided into two classifications: (I) liquid-level data used directly to calculate capacities, and (2) liquid-level data and liquid-level measuring equipment used in connection with other data to determine bottom-hole pressure. Equations and calculations for both types are shown. Well capacities calculated from fill-up data have not been used generally but offer a simple means of testing some wells. Theoretical factors and calculations for such tests are shown. In the state of Kansas, proration laws required that the "ability of a well to produce" be given consideration in state allocation orders and for many years this was the only factor used in prorating the allowed oil. The "ability of a well to produce", was the quantity of oil that could be obtained from a well in a prescribed period, usually 24 hr. Early in the history of State-regulated proration, Kansas operators realized that, unless some restriction were placed upon equip- ment, the competition between producers to obtain large well "potentials" might result in a race to install the largest pumping equipment. Consequently, restrictions were placed upon the size of tubing and length of pump stroke that could be used in pumping wells during potential tests. Later, restrictions were placed also upon the size of tubing and chokes that could be used in flowing walls. Despite the restriction setup, better pumping equipment was designed and installed, pumps were improved, and various devices were invoked to obtain high rates of production for short periods of time. By 1937 pumping cycles of forty to forty-five 54-in. strokes per minute were not uncommon, and numerous wells had produced at the rate of 3500 bbl. per day for short periods. Such production was far beyond any rate that could be long sustained. Equipment necessary to take "potentials" was several times larger than that needed for normal producing purposes, and repairs and replacements required by the high pumping speeds were excessive. Also, many operators suspected that the high rates of production main tained during '"potential" tests were conducivc to early water encroachment. By 1938 large-scale physical testing of wells in Kansas ended, the use of the bottom-hole pressure gauge had become common, engineers and operators were becoming familiar with the term ''productivity index," and bottom-hole pressure was being used as a factor in allocation in many areas. There were many drawbacks, however, to large-scale use of

Jan 1, 1943

Discussion of the paper of HOWARD N. EAVENSON, presented at the Pittsburgh meeting, October, 1914, and printed in Bulletin No. 94, October,' 1914, pp. 2637 to 2660. GEORGE S. RICE, Pittsburgh, Pa.-I think it is very wise to point out the greater liability to explosions in certain parts of the year, if there be such difference, with the caution, however, that vigilance be not relaxed at other times. In comparing the figures for the United States with those of Europe, I think we should separate them as far as possible according to cause of origin and means of propagation. That is to say, it would appear to me that the majority of our explosions are due more directly to the ignition of coal dust directly from the flame of explosives, whereas, judging from my inquiries and observations in some of the mines of Europe, the majority of their explosions have been caused by the ignition of fire damp. Now, in the case of fire damp, I do not think that anybody has yet attempted or has been able to find any connection between the seasons and the issuance of methane into mines. One thing must be borne in mind, that if you get a strong explosion of fire damp, dust of a character that might not ignite readily by itself might assist in the extension of an explosion of fire damp through a considerable area in the mine, if not throughout the mine. While it is true we have many lesser explosions in this country attributable to fire damp, it would appear that the majority of all the mine explosions of the country, in considering the means of propagation beyond the locality of the origin, are due to coal dust; and it is the liability to coal-dust explosions that appears to be affected by seasonal changes. Hence the desirability of separating statistically (if it could be done by the inspectors) fire-damp explosions from coal-dust explosions, in order to obtain the true value of the seasonal effect. Nevertheless, in spite of the inclusion of fire-damp explosions with coal-dust explosions, the preponderance of the evidence, as indicated in Mr. Eavenson's figures for American mines, has shown that' in this country there were more explosions in the winter and spring months, when the mines are drier; that is, when the mines are apt to be drier. Whereas, according to the European figures that he has gathered, it seems to be very clearly demonstrated that in France, England, and Belgium, the time when explosions occur has no connection with any particular season. That, I think, is partly due to the point just mentioned, that a majority of their explosions have originated from fire damp. The European mining men have been more careful, generally speaking, with the use of explosives than we have, so that the cause of ignition from that source has been less. Only comparatively few of the mines in foreign

Jan 4, 1915

By F. W. Rols-Hausen, F. W. Jessen

It is the purpose of this paper to present data on brines occurring in the Frio formation of the Texas Gulf Coast, and to show how their composition varies, (1) with depth below the surface, (2) with depth below the top of the formation, and (3) along the approximate strike. The brines vary in chloride content from 3,180 to 73,000 p.p.m., though the average salinity of the salt waters is shown to vary with total depth; the concentration being 35,000 to 40,000 p.p.m. at 3500 to 5500 ft., slightly less than 50,000 p.p.m. chloride at 5500 to 6500 ft. and average 38,000 to 40,000 below 6500 feet. From the analyses available, it appears that the highest concentration of salts occurs in the upper 300 ft. of the formation, while lower salinity is found with increasing depth below this point. The salt waters from wells in Starr County show less concentration of dissolved salts than in any other group of wells farther north along the strike. In all, 116 analyses from 63 fields and 14 wildcats, from depths ranging from 1300 to 11,400 ft. below the surface and from z to 3240 ft. below the top of the Frio, are recorded. Introduction Brines have been studied for many Years in an attempt to solve some of the geologic and production problems associated with the production of oil and gas. One practical application of study of . water analyses is the correlation of waters occurring above, in, or below the producing sand in the same field or throughout the same formation. The Frio formation, the series of sands and shales occurring below the Marginulina zone and above the Vicksburg, is one of the major oil and gas-producing formations in the Texas Gulf Coast. Fossils are rare or absent in the upper Frio throughout most of the area. When available, cuttings and cores, and electric logs were used to determine the top of the Frio. A change in lithology was used to determine this point in most of the wells, and fossils were used in some of the deep wells. It is realized that a change in lithology is not perfect for correlation purposes over long distances and some of the trends may be influenced by the inability to differentiate between the nonfossiliferous Marginulina zone and the Frio. It underlies virtually all the area shown on the accompanying map (Fig. I). Although it is not productive in the updip facies, it has been explored to a limited degree below I2,000 ft. Further more, toward the coast line future drilling to deeper depths should encounter this formation. Although thousands of wells have penetrated or drilled entirely through the formation, very few water samples have been secured from the many sands occurring in this formation and analyzed. Previous Investigation No previous published study has been made of the chemical composition and concentration of waters from the Frio formation. However, one water analysis

Jan 1, 1944

By H. W. Schadler

Single crystals of tungsten, which were grown by electron bombardment floating zone refining, were strained 2 pet in tension and bending at 298°, 77°, and 20°K to determine the modes and crystallography of the plastic deformation of these temperatures. At 77° and 20°K plastic deformation occurs by slip on systems of the type (011) [111] and by twinning on (112)-type planes. For crystals strained at 298°K, deformation occurs by slip in [111] directions on either (Oil)- or (112)-type planes. CURRENT models for the initiation of brittle fracture in crystalline materials are based on a knowledge of the details of their plastic deformation.1 Body-centered cubic tungsten exhibits brittle failure at temperatures below about 500 °K yet the modes and crystallography of its plastic deformation have not been studied below 1000°K. In 1924, Goucher2 reported that tungsten single crystals with a total impurity content of less than 0.01 wt pet deformed by slip on the (112) [111] system in the temperature range 1000° to 3000°K. He also observed (001) [010] slip in one crystal which was constrained by the presence of a large fissure. According to Barrett3 tungsten also deforms by twinning on the (112) plane in the [111] direction, but he gives no details on the tendency for twin formation or the temperature range in which twinning occurs. Therefore, as a necessary part of a study of the factors influencing the brittle fracture of tungsten, the modes and crystallography of the plastic deformation were determined at 298°, 77°, and 20°K. Tungsten single crystals, grown using the electron-bombardment zone-refining technique first described by Calverly,4 were deformed to between 1 and 2 pet plastic strain in tension and bending. The surface offset resulting from slip or twinning was observed with an optical microscope to determine the crystallography of the deformation. The existence of twins was proven by the standard polishing and etching technique; and the crystallography of dislocation motion was followed using the dislocation etchant described by Wolff.5 Some observations on the fracture characteristics of tungsten single crystals are included. EXPERIMENTAL TECHNIQUES Growth, Purity, and Perfection of the Crystals-Several years ago Calverly, Davis, and Lever4 dem-onstrated the feasibility of growing tungsten single crystals by the electron-bombardment floating zone-refining technique, and Carlson6 showed that crystals produced in this way had a high degree of purity and were ductile at room temperature. Tungsten single crystals produced by this technique in equipment similar to that described by Carlson were used in this study. The starting material, a powder metallurgy product, was obtained in the form of a swaged 1/8-in. rod from the General Electric Wire Plant in Cleveland, Ohio. The crystals were grown from this material in a vacuum of 10"4 mm of Hg by passing a molten zone 1/8 in. long down the rod twice at a speed of 3 mm per min. At this zone speed

Jan 1, 1961

Secretary Membership Committee Increase of Membership Papers and Publications Committee Library Committee Treasurer Report of the Secretary TO THE BOARDOF DIRECTORASN D THE MEMBEROS F THE AMERICANIN STITUTE OF MINING AND METALLURGICAENL GINEERS GENTLEME:N As will be shown by the special reports of the Finance, Membership, Library, Papers and Publications, Increase of Membership, and other standing Committees, together with that of the Treasurer, the year 1927 was one in which the Institute made very satisfactory progress in a number of directions. In total numbers the membership is no larger but in revenue from dues there has been a marked increase. This has been due to the promotion to full membership of Junior Associates of earlier years, to the larger proportion that come in originally as members rather than juniors, and to the keener interest in the work of the Institute reflected in prompter payment of dues. The latter is important, since experience shows that of those who fall behind a large number must ultimately be dropped for non-payment. Conditions in the mining industries have been healthy though not booming. It has been much easier for members to find employment and meet their financial obligations but there has not been that flow of young men into mining, and hence in part into the Institute, that characterized certain earlier years. Rather the tendency toward centralization and larger industrial units has restricted the number, though not the scope, of opportunities for technical men in the mineral industries. The Institute is constantly receiving resignations from members crowded out of mining into other lines of activity. On the other hand, those who remain in mining and metallurgy have a greatly increased necessity for i,dormation and contacts with technology. A few years ago many superintendents and most foremen were non-technical men. Today the reverse rule obtains and shift bosses and men who occupy even lower positions in industrial units are called upon to know and to apply such an amount of technical knowledge that graduate engineers are the rule rather than the exception. The curious situation has obtained that with a much smaller enrolment of students in the schools of mining and metallurgy there has been at times an actual shortage of young engineers for beginners' jobs. The young men retort that the conditions of employment and pay offered in mining are not equal to those in other lines and, while it is undoubtedly true that the young engineer beginning in mining is able to start under conditions markedly better as to pay, living, and responsibility than did the men who are now leaders, they are required to know much more and have usually spent more in time and money to qualify for their jobs. The whole matter is one which warrants much more attention than has been given to it. For the Institute it is important since the young men

Jan 1, 1928

By D. H. Turner, F. A. Crossley

The titanium-rich corner of the system Ti-Al-Si has been studied to determine the phase relationships in the temperature interval 600° to 1200°C. Metallographic examination of long time isothermally annealed specimens was the means of investigation. PART of a program on phase relations and transformation processes of titanium alloy systems included the study of the titanium-rich corner of the Ti-Al-Si system. The investigation covered ternary compositions in the range 2 to 8 pet A1 and 0.1 to 2 pet Si and binary compositions in the range 0.2 to 2 pet Si. Temperatures were in the range of 600" to 1200°C. Alloys containing 6 pet A1-0.1 to 0.5 pet Si were investigated down to 400°C. Partial vertical sections are presented for 2, 4, 6, and 8 pet Al. The Ti-Si system has been reported by Hansen et al.' It is characterized by a eutectoid decomposition, ß = ± a + Ti3Si3, at 860°C. The maximum solubility of silicon in a is reported to be about 0.5 pet at the eutectoid temperature. The solubility of silicon in 0 increases from 0.9 pet at the eutectoid temperature to approximately 3 pet at the eutectic temperature, 1330°C. Several investigations in the composition range of interest have been reported for the Ti-A1 system."' These investigations are in agreement on the phase fields, but differ to small extents on boundary positions. However, very recent, and as yet unpublished, findings" " indicate that there are perhaps two phases which occur at lower aluminum contents than the ? (TiA1) phase, and that the solubility of aluminum in a titanium is less than 6 pet. In the present investigation phase relations found are in agreement with the published literature exemplified by the work of Bumps et al.3 Therefore, it is probable that the partial system reported herein is metastable and does not represent true equilibrium. Experimental Procedure High purity Bureau of Mines titanium sponge of 103 Bhn hardness, granulated aluminum shot of 99.7 pet purity, and silicon powder of 99.8 pet purity were used in making the alloys. For the work in the range from 600" to 1200°C, 100 g ingots were prepared by arc melting. Melting losses were negligible and spot checks by chemical analysis showed good agreement between nominal and analyzed results. Nominal compositions are used throughout this paper. Ingots were forged to 3/8 in. rounds and cut into specimens for heat treatment. Isothermal anneals in the range from 600" to 900°C were preceded by solution treatment at 1000°C for 1 hr, followed by furnace cooling to the annealing temperature. Samples were sealed in evacuated Vycor bulbs for heat treatments up to 1000°C. Higher temperature anneals were done with the samples sealed in quartz bulbs under a partial pressure of argon.

Jan 1, 1959

By F. W. Jessen, F. W. Rols-Hausen

It is the purpose of this paper to present data on brines occurring in the Frio formation of the Texas Gulf Coast, and to show how their composition varies, (1) with depth below the surface, (2) with depth below the top of the formation, and (3) along the approximate strike. The brines vary in chloride content from 3,180 to 73,000 p.p.m., though the average salinity of the salt waters is shown to vary with total depth; the concentration being 35,000 to 40,000 p.p.m. at 3500 to 5500 ft., slightly less than 50,000 p.p.m. chloride at 5500 to 6500 ft. and average 38,000 to 40,000 below 6500 feet. From the analyses available, it appears that the highest concentration of salts occurs in the upper 300 ft. of the formation, while lower salinity is found with increasing depth below this point. The salt waters from wells in Starr County show less concentration of dissolved salts than in any other group of wells farther north along the strike. In all, 116 analyses from 63 fields and 14 wildcats, from depths ranging from 1300 to 11,400 ft. below the surface and from z to 3240 ft. below the top of the Frio, are recorded. Introduction Brines have been studied for many Years in an attempt to solve some of the geologic and production problems associated with the production of oil and gas. One practical application of study of . water analyses is the correlation of waters occurring above, in, or below the producing sand in the same field or throughout the same formation. The Frio formation, the series of sands and shales occurring below the Marginulina zone and above the Vicksburg, is one of the major oil and gas-producing formations in the Texas Gulf Coast. Fossils are rare or absent in the upper Frio throughout most of the area. When available, cuttings and cores, and electric logs were used to determine the top of the Frio. A change in lithology was used to determine this point in most of the wells, and fossils were used in some of the deep wells. It is realized that a change in lithology is not perfect for correlation purposes over long distances and some of the trends may be influenced by the inability to differentiate between the nonfossiliferous Marginulina zone and the Frio. It underlies virtually all the area shown on the accompanying map (Fig. I). Although it is not productive in the updip facies, it has been explored to a limited degree below I2,000 ft. Further more, toward the coast line future drilling to deeper depths should encounter this formation. Although thousands of wells have penetrated or drilled entirely through the formation, very few water samples have been secured from the many sands occurring in this formation and analyzed. Previous Investigation No previous published study has been made of the chemical composition and concentration of waters from the Frio formation. However, one water analysis

Jan 1, 1944

By W. N. Lacey, B. H. Sage

THE results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of gravel screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. INTRODUCTION Gravel screens have been placed in water and oil wells for a number of years1,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. INFLUENCE OF GRAVEL SCREENS UPON PRODUCTIVITY The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the. average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized- spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1941

By J. D. Hanawalt, C. E. Nelson, J. A. Peloubet

THE subject of the salt-water corrosion resistance of magnesium alloys is somewhat like that of the pitting of stainless steels, in that it involves a relatively small percentage of the applications but receives a much greater proportion of the publicity. Actually magnesium alloys are in use in many exterior applications as well as interior, with no trouble from corrosion. Magnesium and its alloys have a striking stability against atmospheric attack, being far superior to iron. Specimens exposed unprotected to atmospheric weathering for 10 years show only a superficial surface-film formation. The basic nature of magnesium and of its important alloys is that they are also resistant to the attack of salt water even in an unprotected state, giving substantially no loss in weight after one year of alternate immersion in 3 per cent NaCl solution (Fig. I). This basic behavior is often masked because of the extreme sensitivity of these alloys to certain impurities and combinations of impurities. It is known, and the subject of increasing emphasis, that higher purity leads generally to greater stability for many materials, nonmetallic as well as metallic. However, a review of the literature on the corrosion factors in magnesium alloys shows that almost all researchers worked with base metal in which metallic impurities varied in uncontrolled amounts. The major factor, that of metallic impurities, probably greatly overshadowed the effects of minor ones such as flux inclusions, nonmetallic impurities, porosity, metallographic state, which these researchers presumed to study. In the present investigation the first observation of interest is that whereas magnesium of commercial purity (99.9 per cent pure) has a corrosion rate in alternate immersion in 3 per cent NaCl solution at room temperature of anywhere from 5 to 100 mg. per sq. cm. per day, the corrosion rate of high-purity magnesium is 0.15 ± 0.05 mg. per sq. cm. per day. The principle followed in the experiments was to add to such base magnesium other elements, singly and in combination, in controlled and known amounts and to observe the corrosion behavior of the resulting alloy. These experiments show the existence of what may be called "tolerance limits" of magnesium and some of its alloys for certain impurities. The extremely small percentages of impurities involved and the sharpness of the corrosion discontinuities appear to be quite unpredictable. In order to carry on this work, it was necessary to develop an analysis technique suitable to the problem. In some cases it was necessary quantitatively to analyze impurities to less than 0.001 per cent. The experimental data to be presented are based on observation of about 5000 alloy specimens and on more than 50,000 quantitative analyses. While the primary purpose of this paper is to present the experimentally obtained data on corrosion rates as a function of composition, and particularly to demon-

Jan 1, 1941

By Roshan B. Bhappu, Ronald J. Roman, Dexter H. Reynolds

The reaction between manganese dioxide and molybdenite in a water- sulfuric acid medium was studied at atmospheric pressure and from 25° to 103°C. Both solids are dissolved to give, as final products in solution, Mo(VI), S(VI), and Mn(II). Stoichiornetric relationshifis are most simply represented by the equation MoSz + YMnO2 + 15H+ - HMoO-4 + 2HSO-4 + 9Mn++ + 6H20 The rate of this reaction was found to be dependent on temperature, manganese sulfate concentration, acid concentration, and, in a complex way, the surface areas of both manganese dioxide and molybdenite. Both the total amount of manganese dioxide and tnolybdenite and the ratio of manganese dioxide to molybdenite played a part in determining the over-all rate of the reaction. The effect of acid concentration on the rate was also dependent on the ratio of manganese dioxide to molybdenite. SEVERAL reports in the literature describe reactions using manganese dioxide in water-sulfuric acid media as an oxidizing agent. Nearly all previous work describes interactions between an ion and manganese dioxide, such as the oxidation of ferrous to ferric iron,' or the interaction between a molecule in solution and manganese dioxide, such as the oxidation of toluene to benzaldehyde.2 Only a few references describe the use of solid manganese dioxide to oxidize another solid in sulfuric acid. One report3 states, "Manganese dioxide in dilute sulfuric acid solutions had no beneficial effect (in leaching copper from chalcopyrite), but in more concentrated acid solutions the rate of solution was about the same as that for permanganate." In 1902 a German patent4 described a process which used manganese dioxide in strong (50°Be') sulfuric acid for oxidizing chromite ores to soluble iron and chromium salts. The process consisted of mixing the sulfuric acid with the finely ground ore and manganese dioxide. The pulp was then heated to about 120°C and an electric current passed through it. The manganese dioxide apparently dissolved in the strong, hot acid solution, oxidized the iron and chromium and itself was reduced to manganese 11! then was oxidized at the anode back to manganese dioxide, and the cycle repeated. An extensive study5 of the kinetics of the oxidation of pyrite with manganese dioxide indicated that in dilute sulfuric acid solutions (about 0.1 N) and at elevated pressures the dissolution of the pyrite was brought about by air oxidation of the iron to ferrous sulfate, followed by manganese dioxide oxidation of the ferrous sulfate to ferric sulfate. The mechanism proposed by the authors involved the oxidation of the iron at the surface of the manganese dioxide. Also! the oxidation of sulfide sulfur to sulfate was credited to the oxygen in the air, not to the manganese dioxide. Since the metallurgical literature is lacking in information concerning the use of one solid to oxidize another solid. the current investigation was under-

Jan 1, 1965

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By H. H. Hausner, H. S. Kalish

IN recent years zirconium and beryllium have become of great interest because of their special properties. Zirconium is known for its remarkable ability to absorb the gases oxygen, nitrogen and hydrogen, has extensive use as a getter in electron tubes and has indeed become the primary metal in the manufacture of photoflash bulbs. Beryllium is of interest because it is light metal and as such could supplement aluminum and magnesium in light metal applications. The late development of zirconium ductile at room temperature produced by both the iodide and calcium reduction methods has stimulated frequent articles on this metal in the recent literature. Beryllium is so closely akin to zirconium crystall-ographically that some investigators are of the opinion that beryllium should be ductile at room temperature if it were pure enough. The crystallographic relationship of beryllium and zirconium, the interest created in Be-Zr alloys where the zirconium is believed to function as a remover of solid solution gas in beryllium and thus increase the ductility of the beryllium rich alloy, and the amenability of these metals to powder metallurgy methods stimulated this approach to an investigation of the system Be-Zr. Preliminary work showed that a zirconium compact melted when pressed in contact with a beryllium compact and sintered at 1250°C, without any apparent final bond between the two. A search of the literature revealed nothing pertinent about the Zr-Be system or about any zirconium - beryllium alloys. In 1936 Misch³ vaguely identified the compound ZrBe2 and reported that it has a deformed cubic structure. Two patents," , were issued to Mach-lett Laboratories in 1943 and in 1946 regarding the addition of small amounts of zirconium to beryllium in order to improve the ductility of beryllium so that it may better be used for X ray windows. In considering the alloy formation of beryllium with other metals Raynor thought it unlikely that zirconium would have any solid solubility in beryllium. From this indefinite information nothing could be ascertained about the possible use of Zr-Be alloys or the use of these metals intimately. A brief preliminary study of the system Zr-Be by powder metallurgy methods was undertaken to provide regions for more intense studies of Zr-Be alloys and as a guide to a formal phase diagram determination. The investigation described in the following pages was completed in less than three weeks. The usefulness of this rapid method to facilitate phase diagram studies and new alloy investigations will be shown. Materials and Procedure Zirconium powder was produced from crystal bar stock of high purity supplied by Foote Mineral Co. The crystal bar was converted to hydride at 730°C, crushed, and the hydride decomposed in purified argon at 850°C. 60 pct of the powder passed through a 325 mesh screen, 40 pct of the powder was —140 mesh, +325 mesh and the average particle size of the total was 8 to 12 microns. The beryllium powder was used as re-

Jan 1, 1951

By E. M. Tory, P. T. Shannon

An analysis of batch and continuous thickening in terms of the movement of planes of constant concentration (i.e. continuity waves) is presented. Use of solids flux as a primary variable greatly facilitates the analysis and clarifies the relationship between batch and continuous thickening. An "ideal" slurry is defined as one whose settling rate is a function only of the local solids concentration. An analysis of continuous thickening of this ideal slurry in an ideal thickener explains many aspects of the steady — and unsteady — state behavior of real slurries, such as the main features of a thickener's "solids profile" (including the break attributed to rake action), the sudden appearance at abnormally high feed rates of a zone of constant concentration and the velocity with which it rises, and the effect of detention time at constant weight of sludge per unit area. Where deviations exist, they are explained in terms of the batch settling behavior of real slurries. The purpose of this paper is to interpret continuous thickening phenomena in terms of batch settling behavior. Both types of thickening may be considered as the process of propagating concentration changes, due to the downward movement of the solids, from the bottom of the settling vessel upward through the slurry.' These concentration changes may be either finite or infinitesimal as in the case of the propagation of a continuous concentration gradient. The slurry itself may be moving downward as in the case of continuous thickening. The downward velocity of the slurry may be such that the concentration changes being propagated up from below remain stationary relative to the thickener walls. This is the case for steady-state thickening. It seems appropriate to analyze continuous thickening in terms of the movement of planes of constant concentration. This has already been done for batch settling."3 Although our main interest is in real slurries, there are certain aspects of both types of settling which can be deduced from a theoretical analysis of highly idealized systems. To this end, an "ideal slurry" is defined as one for which the dimensionless settling rate at any point is a function only of the local solids concentration.1,2 An "ideal thickener" is one in which there is no radial variation in either the solids concentration or in the downward component of slurry velocity. The underflow outlet is a point sink. It is to be expected that the behavior of non-ideal systems will deviate in some measure from theoretical results. However, the same characteristics which cause deviations in continuous thickening should be evident in batch settling, permitting a rational explanation of the former in terms of the latter. PREDICTED RESULTS FOR AN IDEAL SLURRY IN AN IDEAL CONTINUOUS THICKENER General Theory: In continuous thickening, the downward solids flux (mass/area-time) relative to the thickener, G, results from two different

Jan 1, 1967

By Albert A. Smith

The creep properties of metals have assumed increasing importance in recent years and many investigations have been made on various phases of the problem. In the past year the annual lectures of the Institute of Metals Division1 and the Iron and Steel Division2 were concerned with this subject, and are excellent reviews. For many years the creep properties of lead and lead alloys have been investigated at the Central Research Laboratories of the American Smelting and Refining Co., and it is hoped that the present paper will contribute knowledge of some of the factors that influence creep. Lead, being a metal that recrys-tallizes readily at room temperature, is an excellent material upon which to investigate creep phenomena because of the simplicity of the apparatus needed, and it might be expected that results would apply to some extent to elevated-temperature tests of other metals. Material The creep tests of this investigation were all made on high-purity lead (99.9998+ Pb) in which the only impurity that could be detected by spectrographic and chemical means was approximately 0.0001 per cent Fe. Flat strips, 0.750 in. wide by 0. 100 in. thick, were prepared by extruding 2-in. dia. cast billets at a temperature of 250°C. This gave a material of 2 to 3 mm. average grain size with a tensile strength of j.400 lb. per sq. in. when tested at a straining rate of 5 per cent per minute. With this extremely soft material, great care was necessary in handling the specimens, to avoid distortion and subsequent recrystallization. The creep tests at 30°C. were conducted in a constant-temperature room, specially built for the purpose in the basement of an office building in which there was no moving machinery, and no vibration was detectable under the most severe conditions of shock in the adjacent surroundings. The room was well insulated and heated electrically, control being by means of a de Khotinsky regulator operating a relay. Maximum temperature variation over a period of several years has been ± 1/2°C. Specimens of the extruded strip, 16 in. long, were used for test purposes with no reduced gauge section, thus eliminating any distortion due to machining. The method of clamping and supporting the specimens is shown diagrammatically in Fig. 1. The gauge marker for the measurement of extension consisted of an aluminum strip, 0.050 in. thick by 0.75 in. wide, one end of which was ground and sanded to a precise knife-edge and fastened to the specimen by suitable pins. After the strip was fastened in place a fine scratch was inscribed just below the knife-edge by means of a sharp teasing needle. Just below this gauge scratch a short vertical mark was made so that the same point could be located and read each time. Several hundred specimens have been prepared by this method, and it was found that with experi-

Jan 1, 1941

By Albert A. Smith

The creep properties of metals have assumed increasing importance in recent years and many investigations have been made on various phases of the problem. In the past year the annual lectures of the Institute of Metals Division1 and the Iron and Steel Division2 were concerned with this subject, and are excellent reviews. For many years the creep properties of lead and lead alloys have been investigated at the Central Research Laboratories of the American Smelting and Refining Co., and it is hoped that the present paper will contribute knowledge of some of the factors that influence creep. Lead, being a metal that recrys-tallizes readily at room temperature, is an excellent material upon which to investigate creep phenomena because of the simplicity of the apparatus needed, and it might be expected that results would apply to some extent to elevated-temperature tests of other metals. Material The creep tests of this investigation were all made on high-purity lead (99.9998+ Pb) in which the only impurity that could be detected by spectrographic and chemical means was approximately 0.0001 per cent Fe. Flat strips, 0.750 in. wide by 0. 100 in. thick, were prepared by extruding 2-in. dia. cast billets at a temperature of 250°C. This gave a material of 2 to 3 mm. average grain size with a tensile strength of j.400 lb. per sq. in. when tested at a straining rate of 5 per cent per minute. With this extremely soft material, great care was necessary in handling the specimens, to avoid distortion and subsequent recrystallization. The creep tests at 30°C. were conducted in a constant-temperature room, specially built for the purpose in the basement of an office building in which there was no moving machinery, and no vibration was detectable under the most severe conditions of shock in the adjacent surroundings. The room was well insulated and heated electrically, control being by means of a de Khotinsky regulator operating a relay. Maximum temperature variation over a period of several years has been ± 1/2°C. Specimens of the extruded strip, 16 in. long, were used for test purposes with no reduced gauge section, thus eliminating any distortion due to machining. The method of clamping and supporting the specimens is shown diagrammatically in Fig. 1. The gauge marker for the measurement of extension consisted of an aluminum strip, 0.050 in. thick by 0.75 in. wide, one end of which was ground and sanded to a precise knife-edge and fastened to the specimen by suitable pins. After the strip was fastened in place a fine scratch was inscribed just below the knife-edge by means of a sharp teasing needle. Just below this gauge scratch a short vertical mark was made so that the same point could be located and read each time. Several hundred specimens have been prepared by this method, and it was found that with experi-

Jan 1, 1941

By J. B. Bassett, E. S. Rowland

The experimental work reported herein firas inspired by the publication of a paper by Grange and stewart, in which it was suggested that at low chromium contents the effect of this element on the Ma point was greater than at higher chromium contents, It was argued that, if a small increase of chromium in solution in austenite caused a sharp lowering of the M, point, it might lead to an explanation of occasional unsolved stress cracking of SAE 52100 during heat treatment. Commercial hardening is carried out at temperatures of incomplete solution, leaving carbides available to enrich the austenite during any inadvertent increase in temperature, such enrichment of the austenite in chromium content would lower the M, point nearer room temperature where cracking is more likely to occur. According, it was decided to investigate the effect of chromium, in quantities between o and 2 pet, on the M, point of commercial steels. Fig I summarizes the data available on chromium steels. For purposes of comparison, the M, temperature values were corrected by means of the Grange and Stewart formulas to (I) Hypoeutectoid compositions: 0.50 pct carbon and 0.80 pct manganese (z) Hsereutectoid compos-sition': 1." pet carbon and O.35 pct manganese. Only the steels having compositions reasonably close to these corrected values were included, because large adjustments inevitably introduce increased error such as are experienced in using the formula. The straight lines of Fig I were drawn by the authors. These data obviously do not settle the question Of the effect Of chromium On the Md Oint, particularly at low chromium contents. While it is fairly well established that chromium causes the M, to be lowered when present in quantities of I pet Or more, Grange and Stewart1 have suggested that in small amounts (less than 1 pet) it is more effective in lowering the Ma point, while Klier and Troiano2 have suggested that in small amounts it is less effective in lowering the Ma point. Payson and Savage3 concur with Klier and Troiano and further suggest that the effect is not linear at these concentrations. Rose and Fischer4 report that small amounts of chromium actually raise the Ma point of a 0.20 carbon steel. Material Two series of 35 Ib induction heats were melted for this work, the analyses of which are given in Table I. One series was aimed at 0.50 pct carbon and 0.80 pct manganese with chromium additions in 0,25 pet increments from o to 1.5 pct with a single heat at 2.0 pct Cr. This series was considered necessary because the commercial heat treatment of SAE 52100 does not generally introduce more than about 0.60 pct carbon in solution in the austenite. The high

Jan 1, 1949

By A. W. Jenike

A theory of gravity flow of bulk solids like ores, concentrates, coal is outlined and an example of design for unobstructed flow is given. Mass-flow and plug-flow patterns are defined and related to the geometry of the bin. The effect of these patterns on segregation, first in-first out flow, and caking is described. This paper is a report on the results from the AIME sponsored project "Flow of Bulk Solids" which was carried out under the author's direction at the Utah Engineering Experiment Station, University of Utah, during the period 1956-1962. The theory has been applied to the design of numerous industrial storage plants. A QUANTITATIVE METHOD OF DESIGN FOR FLOW There is hardly an industry which does not store and handle solid materials in bulk form. When the volume of the solids is large, gravity is invariably relied upon to cause the solids to flow out of storage, through channels and chemical reactors. Such materials as ore, coal, cement, flour, plastics, clay, soil, to which a general term of bulk solids is applied, flow by gravity or are expected to flow by gravity in thousands of installations and by billions of tons annually. The chemical and process industry depends on gravity flow of solids in process and out of storage. Mining relies on gravity flow in block-caving, in ore passes, as well as in storage and loading bins. Agriculture uses gravity flow in elevators, in feed plants, and in farm silos. In practice, satisfactory gravity flow is seldom attained. Such problems as doming, piping (rat-holing), lack of live capacity, segregation, deterioration in storage, harass industry. In spite of the universality of these problems, until recently, there has been no theory of solids flow, no method of predicting how a solid would behave, and how the channel, bin, or hopper should be designed. In the late nineteen forties and early fifties, the theory of plasticity came of age and simultaneously the computer became widely available. These two factors permitted the development of a theory of flow of bulk solids. The work was conducted during the years 1953-1961. In conjunction with the development of the theory a method to measure the flowability of solids was also developed1-7 and the theory was ap-plied to the design of ore pockets, storage plants,16 chemical reactors and adsorption columns. A comprehensive report of this work is given in a previous work." THEORY OF FLOW The most important question which a theory of flow has to answer is: what conditions need to be satisfied for a given solid to flow uniformly and without obstructions through a channel? First of all, the following observations are made:

Jan 1, 1967

By M. W. Bartley, Hugh M. Roberts

Substantial deposits of Bessemer hematite have been found recently by drilling beneath Steep Rock Lake, Ontario, which is situated in the northern part of the Lake Superior Region. It will be practicable to divert the waters flowing into this lake and develop open pits on the upper pert of two large ore bodies by damming off and pumping out the water in the part of the lake in which they occur. Ultimately, the bulk of the ore will be mined by underground methods. Owing to the generally massive nature of the rocks in the area, no underground flows of major consequence are anticipated after diversion of the lake. The Steep Rock deposits are attributed in origin to hydrothermal replacement. They were formed, for the most part, along an unconform-able, brecciated contact between the Steep Rock limestone and an overlying younger volcanic series, The replacing solutions came in as igneous after-effects, following upon the intrusion of basic igneous rocks that invaded the hanging-wall volcanics. It is believed that this took place in a geological period roughly equivalent to late Middle Huronian, which was the period when the most extensive iron-bearing rocks of the Lake Superior Region were formed. Comparison is made with other deep-seated iron-ore bodies in the Lake Superior Region, the origins of which are ascribed in the discussion to hydrothermal replacement. Introduction Under the waters of Steep Rock Lake, Ontario, situated on the Canadian National Railway, 142 miles west of Port Arthur, the presence of three ore zones containing red and brown Bessemer hematite has been established. These were discovered and have been partly explored by means of diamond and churn drilling, The positions of the ore zones, designated as A, B and C, are shown on the accompanying maps and cross sections. This exploratory work, begun in 1938 by Joseph Errington* and Julian G. Cross, has been carried on by Steep Rock Iron Mines Ltd., and was continued during the winter of 1941-1942. For more than 60 years explorers have known that large quantities of hard hema. tite float of good grade existed along the south shore of Steep Rock Lake, and the presence of ore beneath the lake was inferred by many early geologists and explorers. Despite numerous previous attempts to find ore in place, actual discovery awaited the recent period of intensive exploratory effort in Canada. The results obtained in the drill holes put down since 1938 by steep Rock Iron Mines Ltd. are not only of interest, in themselves, to those concerned with the development of ore deposits, but, taken in connection with the surface exposures of adjoining formations, they form the assemblage of facts from which the geological reasoning in this paper proceeds; accordingly, they are set out here as briefly and exactly as may be.

Jan 1, 1949

By M. W. Bartley, Hugh M. Roberts

Substantial deposits of Bessemer hematite have been found recently by drilling beneath Steep Rock Lake, Ontario, which is situated in the northern part of the Lake Superior Region. It will be practicable to divert the waters flowing into this lake and develop open pits on the upper pert of two large ore bodies by damming off and pumping out the water in the part of the lake in which they occur. Ultimately, the bulk of the ore will be mined by underground methods. Owing to the generally massive nature of the rocks in the area, no underground flows of major consequence are anticipated after diversion of the lake. The Steep Rock deposits are attributed in origin to hydrothermal replacement. They were formed, for the most part, along an unconform-able, brecciated contact between the Steep Rock limestone and an overlying younger volcanic series, The replacing solutions came in as igneous after-effects, following upon the intrusion of basic igneous rocks that invaded the hanging-wall volcanics. It is believed that this took place in a geological period roughly equivalent to late Middle Huronian, which was the period when the most extensive iron-bearing rocks of the Lake Superior Region were formed. Comparison is made with other deep-seated iron-ore bodies in the Lake Superior Region, the origins of which are ascribed in the discussion to hydrothermal replacement. Introduction Under the waters of Steep Rock Lake, Ontario, situated on the Canadian National Railway, 142 miles west of Port Arthur, the presence of three ore zones containing red and brown Bessemer hematite has been established. These were discovered and have been partly explored by means of diamond and churn drilling, The positions of the ore zones, designated as A, B and C, are shown on the accompanying maps and cross sections. This exploratory work, begun in 1938 by Joseph Errington* and Julian G. Cross, has been carried on by Steep Rock Iron Mines Ltd., and was continued during the winter of 1941-1942. For more than 60 years explorers have known that large quantities of hard hema. tite float of good grade existed along the south shore of Steep Rock Lake, and the presence of ore beneath the lake was inferred by many early geologists and explorers. Despite numerous previous attempts to find ore in place, actual discovery awaited the recent period of intensive exploratory effort in Canada. The results obtained in the drill holes put down since 1938 by steep Rock Iron Mines Ltd. are not only of interest, in themselves, to those concerned with the development of ore deposits, but, taken in connection with the surface exposures of adjoining formations, they form the assemblage of facts from which the geological reasoning in this paper proceeds; accordingly, they are set out here as briefly and exactly as may be.

Jan 1, 1949

By A. H. Geisler, F. Keller

Some of the important changes that take lace in the structure of aluminum alloys are largely submicroscopic in character. This is especially true of the changes that accompany age-hardening and recrys-tallization. Although improved metal-lographic practices have been helpful in indicating some of these changes indirectly, results are limited by the resolving power of optical microscope lenses. The electron microscope, however, provides a new and important means for investigating the fine structure of metals in a range not possible heretofore. It is anticipated that this microscope will yield new and useful information to metallurgists when suitable techniques are developed to utilize its very high resolving power. Several unique methods have been devised to permit the examination of the structure of opaque samples by the electron microscope. These are all based 011 the principle of producing a very thin film that represents the prepared surface of the opaque metal sample, which can be examined in the transmission microscope; however, the available methods fall into three categories, depending on the manner in which the film is obtained. With the oxide-film method developed by Mah13-l7 a very thin surface layer of the metallographic sample is converted into oxide by a thermal, chcmical or anodic treatment. .After removal from the metal sample by one of the special techniques described by Evans,l9 this oxide film is examined in the electron microscope, and is found to portray the structure of the original metal surface. Films formed on aluminum,8,l7 nicke1,7 iron3,8,9 and a nickel-beryllium alloyl1 by heating; films formed on iron8,9 by chemical action; and films formed on aluminum3-'" by anodic oxidation, have been examined. The other two are more recent methods developed principally in this country; they consist in making the thin film in the form of a mold or replica of the surface contour of an etched sample. With the negative replica method the thin film is made directly on the sample; with the positive replica method it is made on a negative reproduction of the sample. With both methods, variations in the contour of the metal sample, caused mainly by etching, produce variations in the thickness of the surface replica. Because of the direct dependence of the amount of scattering of the illuminating electrons upon the thickness of the film penetrated, only the variations in thickness of the replica are responsible for tones in the electron image. Negative replicas are made by forming a thin film of some suitable material directly on the polished and etched metal sample, and derive their name from the fact that after removal from the sample they have the high and low points in the sample reversed, as shown in Fig. I. Nega-

Jan 1, 1944