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By Morris Muskat

Analytical calculations have been carried out on the effect of casing perforations on the productivity of wells, and formulas have been derived for general types of perforation patterns. The numerical calculations, however, show that the resultant well productivity is essentially independent of the perforation pattern, but is determined mainly by the total perforation density. Thus, for example, for a density of three perforations per foot of casing, the well productivity will be cut to one third of that of the uncased well for a perforation radius of 1/8 in., and to approximately one half for a perforation radius of 1/4 in., regardless of the detailed manner in which the perforations are distributed over the casing surface. The analytical theory is also extended to include wells completed with slotted liners. It is shown that the reduction in productivity due to such liners will be relatively small as compared with that due to perforated casings. The increasingly important role being played by productivity factors of wells in determining well potentials and in the general evaluation of producing formations lends interest to the analysis of all the various factors that may infuence the productivity of a well. In recent papers1 the results have been given of theoretical studies made to determine the effect on the productivity factor of a well of the gas-oil ratio of the production and the connate water within the sand. These have served to show that both of these factors may, under suitable conditions, materially reduce the effective productivity factors below those that would be anticipated on the assumption that the wells produce homogeneous fluids. In this paper will be presented the results of the analysis of an entirely different factor influencing the productivity of a well. This refers to that resulting from the increased use of the method of completing wells by setting casing opposite all of the productive strata and then gun-perforating the particular zones of immediate interest. The practical success of this method of completion would appear to be an answer to the question as to whether it seriously reduces the well productivity or materially cuts down the ultimate oil recovery that may be derived from the producing section. Nevertheless, it is of interest to examine just how great the effect of the restricted flow channels, represented by the gun perforations, may be in increasing the over-all effective sand resistance. Of course, to the extent that the well potentials are severely restricted by proration regulations, minor reductions in well productivities are even less serious than if the wells were to be allowed to produce wide open. On the other hand, even under these circumstances there may be at least the academic interest in such calculations in being able to correct and evaluate the effect of the perforations in order to carry

Jan 1, 1943

By R. G. Paterson

THE usual procedure in determining the magnetic susceptibilities of rocks and formations has been to take samples in the field and measure their volume susceptibilities in the laboratory, using one of numerous methods available. In none of these methods is the measuring instrument suited for field use. Usually the sample is pulverized; sometimes it is machined to a desired size and shape, and in one method' a cast of the sample is made and the susceptibility of the rock compared with that of a material of known susceptibility of the same size and shape, made from the cast of the original sample. Some writers assert that the difference in susceptibility of a rock sample in powdered and solid forms is negligible, and while doubtless this is true in many cases there are others in which the difference becomes appreciable. Further, the susceptibility of a small specimen may differ from that of the rock from which it is taken, owing to the stresses produced by the hammering or other forces used to obtain the sample and shape it for testing. Wilson2 found that an individual specimen of granite had about the same susceptibility in the solid as in the powdered form, but that pieces from different parts of the rock varied as much as 750 per cent because of unequal distribution of magnetite. The most accurate value of susceptibility would, obviously, be obtained from averaging a number of tests on the undisturbed rock instead of from one or two samples. No such procedures have been published, to the writer's knowledge. It is the purpose of this paper to describe a method by which susceptibilities of rocks may be determined in place by means of a portable instrument. METHOD The principle involved in this new method is that there is a change in inductance of a coil due to the presence in its magnetic field of a paramagnetic or diamagnetic medium. In this case, however, the windings of the coil do not enclose any part of the rock under test. Instead, the coil is circular, being small in cross section as compared to its radius, and consists of several hundred turns of fine wire. It is placed flat on the rock of which the susceptibility is to be measured. Thus only part of the magnetic field from the coil penetrates the rock under test. The relation between the change in field strength or inductance of the coil and the susceptibility of the medium will be developed later. To measure the change in the inductance of the coil due to the presence of a magnetic material an alternating-current inductance bridge was chosen. DESCRIPTION OF APPARATUS Of many alternating-current bridge methods applicable,3 the one shown in Fig. I (Owen's bridge') was adopted for its simplicity and sensitivity. In Fig. I, the test coil is indicated by P1L1. It is connected to the bridge by about

Jan 1, 1941

By A. G. H. Anderson, A. W. Kingsbury

Silicon bronzes containing ken are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith1 and of A. G. H. Andersen.2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 etermined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at iioo°C. Hanson and Ford,5 using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West? have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,l,2,7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. Preparation of Samples Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates 1/8 in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1943

By A. G. H. Anderson, A. W. Kingsbury

Silicon bronzes containing ken are used to a considerable extent in industry, under the trade name of P.M.G. alloys. Various classes of wrought alloys fall in the composition range 1.5 to 3.5 per cent silicon, and 0.5 to 2.5 per cent iron. Castings may contain as much as 6 per cent silicon and 3 per cent iron at present. The constitutional diagrams of these alloys are thus of considerable practical importance. Copper-silicon-binary alloys have been thoroughly investigated by a number of workers, the latest reports being those of C. S. Smith1 and of A. G. H. Andersen.2 Although much work has been done on iron-copper alloys,3 recorded investigations on the copper-rich copper-iron binary constitutional diagram are not numerous. Tammann and Oelsen4 etermined the solubility limits of iron in copper by means of magnetic measurements, and found that the solubility of iron in copper amounts to a fraction of one per cent at 400°C., increasing slowly to one per cent at 800°C. From 800°C., the solubility increases rapidly and attains 4 per cent at iioo°C. Hanson and Ford,5 using electrical resistivity measurements and the microscope, determined a somewhat different solubility limit. of earlier X-ray works on the copper-iron system, very little has been published. The work by Bradley and Goldschmidt6 on copper-iron-aluminum alloys includes some information on the copper-iron binary. These investigators conclude that substitution of iron in the copper lattice decreases the spacings, which is contrary to the evidence of the present work. Hanson and West? have investigated the ternary alloys of copper with iron and silicon. Although their diagrams are valuable contributions to the understanding of these alloys, they did not recognize the kappa phase,l,2,7,8 and their diagrams do not everywhere conform to the phase rule. The present work contains a check by means of X-rays of the solid solubility limit of iron in copper, and an X-ray investigation of the ternary-phase diagram, which, owing to present conditions, it became necessary to curtail considerably. Preparation of Samples Castings weighing about 75 grams were melted under vacuum. The charges were made up of ingot iron, copper cathodes from Laurel Hill, and refined silicon supplied by the Electrometallurgical Co. Alundum crucibles were generally used. The exceptions were alloys 77 and 78, which were melted in graphite crucibles. The ingots were annealed at 800°C. for one week, then samples were cut for chemical analysis. Longitudinal sections of the binary alloy ingots were hammered into plates 1/8 in. thick. Wherever possible, these plates were homogenized at temperatures ensuring

Jan 1, 1943

By J. J. Tietjen, D. Richman

Single-crystal Gap lms been epitaxially grow from the vapor phase at a rate oJ 3 p per nzin without encountering a7Zy low-ang-le grain boundaries or debwading- the electrical properties of the material. This growth rate exceeds any value previol~sly reported for the vapor phase growth of Gap. In pure material, mObilities ns high as 175 sq cm per U-sec at room tenzperature and 1450 sq cm per v-sec at 77°K have been obtained. These values are anLong the highest that have been attai)led for this material. For the first time, Gap possesses a number of important properties which make it well-suited for use in electro-optic modulators. First, the transverse electro-optic effect is operable in this material, which makes it possible to increase the path length of the modulated iron doping of Gap has been achieved; this results i?z resistivities of approximately 10" ohm-cm. The problelrls of residual strain and isolated shorting paths in these crystals have been partially solved. Electro-optic modulation of visible radiation has been demonstrated with this material. It is anticipated that further improvement with regard to the probleins of strain and shorting paths will result in a practical Gap electro-optic modulator. radiation without increasing the applied voltage. In addition, this permits the use of thin crystals so that relatively small voltages are needed to provide the requisite high electric fields. Second, GaP is a cubic crystal and therefore does not introduce critical optical-alignment problems associated with birefrin-gent crystals, such as ammonium dihydrogen phosphate (ADP), and potassium dihydrogen phosphate

Jan 1, 1968

By Harry Gard Knox, F. R. Harris

This paper covers some of the problems presented to the oil industry in the drilling of oil wells in the open waters of the Gulf of Mexico. The hazards, delays and relative costs of offshore drilling are reviewed and various forms of drilling platforms discussed. The requirements of the offshore drilling rig are summarized together with the principal items affecting the cost of construction. Sea waves and their size and characteristics as affecting offshore platforms are reviewed. Drilling platforms are classified as fixed, or fixed and floating. Fixed platforms of the conventional cofferdam and pile-supported type are discussed together with their good points and their limitations. The desirability is pointed out of eliminating as much offshore work as possible where operations are subjected to constant and expensive delay and substituting therefor the prefabrication of structures ashore or in sheltered waters. Marked economy will come with the standardization of offshore rigs aid special means of transporting them to the site. Several types of structure which are partly pile-supported and partly buoyancy-supported are discussed and their possibilities of future usefulness commented upon. General Considerations The predominant attribute of offshore drilling equipment is that it must be equal to the job in hand. We therefore give first thought to the matter of adequacy. In view of the probable depth of drilling, the investment involved and the per diem labor costs, it is assumed heavy modern drilling equipment will be employed. In order to usc such equipment efficiently, the working deck must be ample in size and strength and supported so as to be relatively free from motion and from green seas even in heavy storms. These requirements necessitate a high and rigid land-based support for the drilling rig and machinery with plenty of space for supplies, such as pipe, mud, water and fuel, with reserves for days when transportation from shore is impracticable. In offshore rigs the crew will be housed onboard in comfortable quarters, probably air conditioned and equipped with a galley and refrigerated food storage. An important consideration will be the ability to transfer stores and crew to and from the rig in all but the heaviest weather and the platforms must be protected from the impact of supply vessels when alongside. It will be essential to maintain continuous communication with shore by radio or cable, not forgetting the possibility of a helicopter landing space for the transfer of crew and light stores as well as a means of general communication. Whatever structure is constructed must be secure from storms of hurricane force and a safe place for the operating crew to work. If the well comes in, the drilling rig will presumably be removed and a small but rugged pile-supported platform will remain to carry the Christmas tree with safe working space around it. It will be protected from damage on all sides by buffer piles or dolphins. It is assumed that the flowing oil will be piped to storage tanks in the vicinity of the well. An individual tank for each well or a

Jan 1, 1949

Jan 1, 1928

By Gilbert L. Eggert

The effects of reactor irradiation on age hardening in a Cu-2 wt pct Be alloy have been investigated in two neutron-energy ranges. During some of the irradiations, specimens were exposed to high-energy fission neutrons which passed through a boron-10 shield; during other bombardments, the boron-10 was omitted and specimens were irradiated in a reactor thermal column, or the fuel configuration was modified to increase the thermal-neutron flux at a location in the core. Differences in length, X-ray diffraction angle, and hardness indicated that low-energy neutron irradiation made a small contribution to changes in the measured properties. The influence of defects generated by knock-om with less than the Brinkman critical energy or by prompt (n,y) recoil is suggested as the cause of this effect. EXPERIMENTS designed to test the effects of reactor irradiation on the properties of age-hardening alloys have to the present time employed fluxes un-differentiated according to neutron energy. Billing-ton and Siegell in 1950 were the first to perform such an experiment and to compare the results with those obtained by thermal aging. These authors concluded that precipitation in a Cu-2 wt pct Be alloy was not enhanced by the radiation. However, 4 years later, Murray and Taylor,2 working with specimens of the same Cu-2 wt pct Be alloy, reported that an increase in density, hardness, and resistivity which followed reactor irradiation resembled changes associated with thermal aging at about 100°C. (It should be noted that these authors reported that higher aging temperatures caused a decrease in resistivity.) cupp3 reported hardness results similar to those of Murray and Taylor. Koppenaal4 showed that irradiation-enhanced precipitation and irradiation defect hardening were not simply additive but that they acted separately in an irradiated alloy. Kernohan et a1.,5 working with Ni-Be, offered evidence that beryllium was removed from solid solution by reactor irradiation and suggested that the mechanism was one of increased diffusion through the use of vacancies in the structure. piercy6 also found that more precipitate particles were formed by fission-neutron irradiation of a Cu-Co alloy which contained a small amount of particles before irradiation. He proposed that the additional particles were caused by an appreciable amount of diffusion during the final cooling of displacement spikes. The retrogression of extant precipitate particles found by Murray and Taylor2 and Boltax7 as well as piercy6 indicated that nuclei were dissolved within a high-energy spike region and, upon resolidification of the perturbed volume, new nuclei precipitate and grow by enhanced diffusion. Bleiberg et al.' and Konobeevski et al.' explained phase changes obtained by irradiating fissionable alloys in terms of retrogression and re-precipitation in regions of high-energy spikes. Parsons and Balluffi10 used electron microscopy to verify that crystallization did indeed occur in displacement spikes which were formed in amorphous germanium by fast-neutron irradiation. The concept that low-energy neutron irradiation might cause structure-sensitive property changes in semiconductors by atomic recoil associated with the (n, y) reaction was first proposed by Schweinler" and walker." This thesis was tested by Cleland and crawford" and found to be valid. Coltman et al.14 exposed a variety of pure metals to thermal-neutron irradiation at cryogenic temperatures and attributed the resulting resistivity changes to the action of defects created by (n, y) recoil. The present work was undertaken to extend the concepts of Schweinler," walker," and Coltman et al.I4 to the case of an age-hardening alloy and to determine whether or not the action of defects produced by thermal-neutron irradiation would en-hance age hardening. EXPERIMENTAL PROCEDURE Omeea West Reactor Irradiations.* Thermal-

Jan 1, 1965

By D. F. Gibbons

THIS investigation was undertaken in order to gain further information on the mechanism of plastic deformation of iron at temperatures between room temperature and 77.2°K, and also to contribute to our understanding of the low temperature brittleness phenomenon that occurs in both the tensile and impact tests. It was decided to study as pure an iron as possible and to use the tensile test in order to simplify the problem as much as possible. Two series of iron were used throughout the investigation: iron A, obtained from the National Research Corp. and supplied as gas-free, high purity iron; and iron B, obtained from Fast' and produced by melting iron under purified hydrogen. Typical analyses of samples of both irons, after fabrication, are given in Table I. The main difference in composition of these irons is in their nickel and oxygen contents. Nickel has a very large solid solubility in iron. However, oxygen has an extremely small solid solubility. An attempt was made to reduce the oxygen content still further by remelting under purified hydrogen. This was successful in reducing the oxygen content to -0.0006 pct. However, no results on tests of this iron are included, since difficulty was encountered in fabricating the ingot. Wire specimens 1 mm in diameter were used for the investigation. The wires were produced from the ingots, as supplied, by cold rolling and swaging, with intermediate vacuum anneals at 700°C. Care was taken to reduce preferred orientation in the wires to a minimum by keeping the percentage of reduction in area between anneals of 30 to 40 pct. X-ray transmission photographs showed no indication of preferred orientation. The final grain size of iron A was 20 to 24 grains per linear mm and of iron B, 16 to 18 grains per linear mm. All specimens were tested in the decarburized and denitrided condition unless otherwise stated. The procedure was to pass hydrogen, saturated with water vapor at 26oC, over the specimens at 730°C for 2 hr. The specimens were quenched in iced water and then annealed in a vacuum of - 5x10-6 mm Hg for one day at 560°C to remove hydrogen. Higher temperatures were used for the vacuum anneal but this temperature was found to be quite satisfactory in removing hydrogen. The specimens were slow-cooled after the vacuum anneal. Where it is stated that the specimens were carburized, the specimens were given an identical decarburizing treatment and then carburized by passing hydrogen, saturated with pure n-heptane vapor at 0°C, over the specimens at 730°C. The specimens were then homogenized at 730°C for 2 hr in dry hydrogen. After the carburizing treatment the specimens were given the same vacuum anneal as for the decarburized specimens. The carbon content was determined from the maximum value of the internal friction carbon peak.2 Apparatus Fig. 1 shows a diagram of the tensile apparatus, with half the cooling coil removed. The cooling coil enabled temperatures from 200" to 77.2oK to be obtained. The apparatus was designed to fit a standard Tinius Olsen Universal tensile machine. The apparatus consisted of the rigid plate A which carried two carefully machined hooks H. These hooks attached the plate firmly to the moving crosshead of the tensile machine. The lower grip B was rigidly suspended from the plate A by three stainless steel rods. The upper grip C was joined to the upper grip of the tensile machine by the stainless steel rod E. The lower part of the apparatus was surrounded by a Dewar vessel, which was made a sliding fit inside the brass collar D. The specimen was held in a clamp which fitted into the grip, forming a ball and socket joint (see inset a). This was to attain as nearly pure

Jan 1, 1954

By A. Rosen, P. Wynblatt, J. E. Dorn

The temperature, strain rate, and structure dependence of the flow stress in a poly crystalline Fe-2 pct Mn alloy was investigated between 77" and 370°K. It was possible to identify the low-temperature data from 77° to 160°K with Dorn and Rajnak's theory of the Peierls mechanism of plastic deformation. Above 160°K one or more thermally activated mechanisms must he operative; however, these were not identified in this investigation. The mechanistic basis for the rapid decrease in the flow stress of bcc metals with an increase in temperature over the low-temperature range is yet being debated. Various dislocation mechanisms have been suggested in the past but the agreement between the various proposed theories and the experimental results have not been definitive. In the present paper, the authors will demonstrate that the plastic behavior of polycrystalline iron containing 2 wt pct Mn plus interstitials agrees excellently with predictions based on the Peierls mechanism from 77" to 160°K whereas from 160" to about 370°K other as yet unidentified thermally activated mechanisms take over. Undoubtedly, the overlap of these mechanisms with the Peierls mechanism contributed to the difficulties of rationalizing the low-temperature behavior of iron and its alloys. I) EXPERIMENTAL TECHNIQUES AND RESULTS Although extensive data are now available on the effect of temperature and strain rate on the flow stress of various bcc metals and alloys, it was, nevertheless, deemed necessary for the objectives of the present study to obtain highly accurate data of the type most pertinent for checking the theories on a series of well-documented work-hardened states. Iron containing 2 wt pct Mn was used in this investigation in order to obtain a lower ductile to brittle transition temperature than that for iron.' The additional elements present were 0.004 pct C, 0.05 pct 0, 0.004 pct S, 0.003 pct P, 0.006 pct N, and 0.001 pct Si. The as-received 3/8 by 3/4 in. bars were cold-rolled to 0.100-in. thickness, recrystallized under argon for 30 min at 1073"~, further cold-rolled to 0.063-in. thickness, and finally recrystallized under argon for 30 min at 1000°K. This treatment gave a stable reproducible equiaxed grain structure having an average grain diameter of about 90 p. Prior to the final recrystallization treatment, the sheet was machined into tensile specimens 1/4 in. wide having a 1.625-in.-long gage section. All specimens were tested in controlled-temperature baths on an Instron Testing Machine. For convenience in the theoretical analyses the data will be given in terms of the shear stress for flow, 7, the shear strain rate, f, and the shear strain, y. A series of three standard strain-hardened states were obtained by prestraining specimens at 300°K and at a shear strain rate of 7.68 x lo-' per sec to three stress levels of 6.89 X l08, 10.3 X lo8, and 14.5 x 10' dynes per sq cm, respectively. Immediately following this prestrain the temperature bath was changed and each specimen was pulled in tension at either f = 7.68 X lo-' or f = 3.06 X 10"3 per sec. In terms of the accuracy that was achieved, the values obtained did not deviate more than *0.1 X 10' dynes per sq cm and * 1°K from the reported values of stress and temperature and not more than *5 pct in the reported values of the strain rate. The tensile stresses were converted to shear stresses using a factor of 1/2. The shear stress for the initiation of flow at the test temperature was determined by taking a y = 6.16 x 10'3 offset. from the modulus line at which point good accuracy could be achieved in determining y and the associated flow stress 7, with only a negligible increase in the pre-

Jan 1, 1965

Executive HENRY A. BUEHLER, Chairman ERLE V. DAVELER EDGAR RICKARD JOHN M. LOVEJOY WILLIAM WRAITH J. V. W. REYNDERS, Consultant Finance HENRY KRUMB, Chairman E. E. ELLIS PAUL D. MERICA H. G. MOULTON, Consultant Admissions RALPH M. ROOSEVELT, Chairman GEORGE D. BARRON DONALD M. LIDDELL WILBER JUDSONW. D. B. MOTTER, JR.

Jan 1, 1934

By C. C. Templeton, S. S. Rushing

Methods previously developed for the study of air-liquid displacements in microscopic capillaries (inner diameters of 3 to 40 microns) have been used to investigate oil-water displacements in capillaries initially filled with water. Displacement calculations assuming perfect displacement and no capillary pressure hysteresis yielded oil effective viscosities smaller than the macroscopic viscosities. For a given liquid pair, the oil effective viscosity decreased both with decreasing capillary size and with increasing oil-water viscosity ratio. This behavior can be explained by the existence of an annular water film (20 A to 260 A thick) on the capillary wall. When the capillary was first filled with oil, the ratio of the oil effective viscosity to the normal oil vircosity was highest for the first water displacement and decreased with subsequent displacements. Sometimes the oil effective viscosity ratio during the initial water displacement was greater than unity. INTRODUCTION In a previous paper1 a technique was described for studying air-liquid and liquid-liquid displacements in very small capillaries of uniform diameter, in the hope that such microscopic data would further the understanding of the nature of multiphase fluid flow through porous media. That paper contained comprehensive data for air-liquid displacements in Pyrex capillaries, with a few data for oil-water displacements in capillaries initially filled with water. The purpose of this paper is to present more complete results for oil-water displacements in capillaries initially filled with water, and to describe for the first time such observations in capillaries initially filled with oil. In this way the effect of the wetting history of the system upon the displacement process may be studied. METHODS The basic techniques employed were described in the previous paper.1 The measuring procedure and the working equations will be briefly summarized here and a few modilications will be pointed out. For the present study, temperature control within 0.l °C was obtained by placing the microscope and its immediate accessories in a thermostated air bath made of a steel frame covered with plexiglas. The water and oils used in this work were the same as in the previous paper,1 with the addition of "Medium Mineral Oil, U.S.P. supplied by the Harshaw Scientific Co. When the first liquid was introduced into the horizontal capillary, the air-liquid static capillary pressure Poc was measured along the observable length of the capillary. From the relation Poc = 4y cos 0/d, the capillary diameter d could be calculated from Poc if the "microscopic" air-liquid boundary tension, To = y cos On, was taken as equal to its known "macroscopic" value. This calculation involves assuming that cos 6 = 1 and that capillary size or the resulting high interfa-cial curvature has no effect on surface tension, or y cos 6, as was verified by our work, and also by that of Cohan and Meyers on air-liquid-solid systems. For several capillaries these calculated diameter values were compared with values measured visually with a filar micrometer eyepiece. For a given capillary the average values for the two methods agreed within 1 or 2 per cent, but the visual values were less reproducible than the calculated values. Further the calculated values were much less subject to personal bias and took into account any slight ellipticity that might be present. Hence diameters calculated from air-liquid Poc data were used throughout this paper. The second liquid was introduced in such a way that a single spherical interface separated the two liquids. Displacements were always made with a constant pressure, Pt, between the ends of the capillary. The times (t) at which the interface passed certain

Jan 1, 1957

By John R. Keith

Lead and zinc contents of elm, maple, and oak trees and of soils in which the trees grew were determined in samples from the Upper Mississippi Valley mining district, and from an area outside but contiguous to the district. The lead and zinc analyses of plant materials served to differentiate the mineralized and nonminer-alized areas. Stems contained about two times as much lead and about two to five times as much zinc as did leaves taken from the same stems. Lead and zinc analyses of all soil horizons could be used to differentiate between the two areas. Soils at most sample sites in the mineralized district seemed to be more reliable than plants for geochemical prospecting and are a more practical sampling medium. Soil samples from areas with thick loess cover, however, failed to indicate the presence of mineralized bodies whereas tree samples from the same sites contained anomalous amounts of lead and zinc. It is suggested that in areas of thick loess cover, plant samples could be used in prospecting for lead and zinc. The important part that plants play in the cycling of elements through the soil horizons is well-known. The concentration of elements in the upper soil horizons by the action of plants has been called the Goldschmidt enrichment principle.' The fact that plant species vary greatly in their ability to concentrate particular elements in their tissues is also well-known.' Agricultural literature has dealt extensively with relationships of the major nutritive elements in soils and plants3 The extent, however, to which plant actions cycle the minor nutritive and the nonmetabolic elements in the soil has not been adequately investigated. Lead is non-nutritive and toxic to plants, whereas zinc is a micronutrient in low, but toxic in high, concentrations.4 This report presents the results of a biogeochemical study concerned with the amounts of lead and zinc in some plants and soils that occurred both within and adjacent to the Upper Mississippi Valley lead-zinc district. Field work for this study was done in the summers of 1961 and 1962. SAMPLE TARGETS AND CHEMICAL ANALYSES Geologic and physiographic descriptions of' the district have been made by Heyl 5 and several other authors in a series of U.S. Geological Survey (USGS) reports and quadrangle maps.6-I Sedimentary rocks, mostly dolomite, limestone, shale, and sandstone, of Cambrian, Ordovician, and Silurian age predominate in the area. Mineral deposits are of the vein and cavity-fill type; the principal ore minerals are galena and sphalerite. Vegetation of the area was characterized by Curtis1 6 as southern hardwood forest interspersed with patches of oak savanna and prairie. Plant genera typical of the eastern United States Temperate Zone, including ash, cherry, dogwood, elm, hackberry, hickory, maple, oak, and other woody and herbaceous genera, are present. The natural vegetation has been greatly modified by agricultural, logging, and mining operations. The species of the original flora are present, but not in their former relative abundance. Soils of this district belong, for the most part, to the Brunizem and Gray-Brown Podzolic great soil groups. The Brunizems are the soils developed under prairie vegetation.'' The Gray-Brown Podzolics are the soils developed under deciduous forests,18 They are derived from both bedrock and from loess parent materials, and

Jan 1, 1970

By J. E. Owen

A model of a porous body is presented in which the pore space consists of a system of voids and interconnecting tubes. Relationships between porosity and resistivity formation factor are determined partly by calculation, partly by experiment. Con triction effects characteristic of the model are shown to be sufficient to account for high formation factors. It is shown that constriction may be combined with moderate amounts of tortuosity to give model pore systems exhibiting to a first approximation porosity and resistivity properties similiar to those of natural porous bodies. INTRODUCTION The relationship between the electric resistivity of a fluid-filled porous body and the geometry of its pore space is so complex that the calculation of the resistivity of a natural porous rock is a practical impossibility. Both the resistivity of a body and its porosity are measurable quantities, however, and previous successes at relating them have been reached by an empirical approach. Efforts at obtaining theoretically derived formulae relating them have generally been unsatisfactory. One of the reasons for this may lie in the pore geometry that has been assumed. THE TORTUOSITY CONCEPT A Parameter called the formation factor is useful in dis-cussing the resistivity of a fluid-filled porous body. This parameter is the ratio of the resistivity of a fluid saturated porous body to the resistivity of the saturating fluid. Formation factors are often available from measurements on cores or from electric logs, and many attempts have been made to correlate formation factors and porosities of geological formations. Whenever a successful correlation is found, the engineer working with electrical logs has a useful tool for the determination of porsities of pay section?. One of the more successful formulae applicable to these correlations is the familiar equation empirically obtained by Archie.' which F is the formation factor. $ is the porosity, and rn is an exponent called the cementation factor. When the for- mula applies, the cementation factor usually is found to be between 1.3 and 2.2. The values for formation factors experimentally obtained are often higher than simple pore geometry would lead one to expect. In an effort to account for such high values certain formulae have been derived based on a so-called "tortuosity concept." In deriving these formulae a synthetic porous body is usually assumed in which the solid material is an electrical non-conductor. and in which the pore system consists of three sets of fluid-filled tubes of uniform diameter connecting opposite faces of the body which, for convenience, is considered to be cubical in shape. The three sets of tubes account for the whole of the effective porosity of the body, and usually, it is specified that they do not interconnect. By considering that the pore tubes are not straight but tortuous, their resistance to the flow of electric currents can be made as high as needed to explain high formation factors. Such an explanation has some basis in fact, but it appears that the tortuosity concept is often incorrectly applied when other factors are largely responsible for observed high resistivities. Recently, Wyllie and Spangler have recognized that tortuosity as calculated by conventional formulae has little if any physical significance.' RESISTIVITY AND THE CONSTRICTION CONCEPT Any explanation of high formation factors which depends solely on tortuosity of uniform pore paths necessarily ignores the effect that variations in the cross-sectional area of the conducting paths have on the resistivity of a body. Although, as previously pointed out, the calculation of such paths for an actual body is impossible, it will he shown that a synthetic pore network can be devised which will yield to analysis, and lead to results in agreement with the experimental data represented by Equation (1). The porous body to be considered is assumed to be homogeneous and isotropic or, for present purposes, identical in its characteristics in the three directions parallel to its coordinate axes. It will he assumed to be built of identical unit cubes, each of which contains a single pore network connecting all faces of the unit cube. A unit of such a pore network is shown

Jan 1, 1952

By Adrian C. Dorenfeld, Theodore Balberyszski, Strathmore R. B. Cooke

This paper reports results of studies of sulfidiza-tion of base-metal oxides and silicates with gaseous sulfur, hydrogen sulfide gas and pyrite and of their subsequent flotation with xanthate collectors. It has been established that a 100% conversion of the oxides of lead, zinc, copper and manganese into their respective sulfides is possible and is a function of reaction time and temperature. Sulfidization of chrysocolla (with malachite and azurite inclusions) resulted in a product containing covellite, chalcocite and digenite in proportions depending on conditions of sulfidization. Reacting cassiterite with gaseous sulfur, H2S or pyrite at various reaction temperatures resulted in its partial conversion to a tin sulfide. Flotation of the products of sulfidization indicated that their behavior is similar to that of natural sulfide minerals, the recovery being a function of the con-version of the oxides to their respective sulfides. The gradual depletion of high-grade sulfide mineral deposits has turned the attention of the mineral industry to the recovery of metals from the oxides and silicates. Anionic (fatty acid) and cationic collectors have in some cases made flotation of nonsulfides possible, although, in general, flotation of oxide ores is not as yet an economic process. Consequently, many attempts have been made to sulfidize the surface of the relevant oxide mineral and thus make it amenable to to In recent years, Bautista and sollenberger4 have investigated the conversion of a number of oxides to sulfides by reacting them with molten sulfur. This paper presents the results of .investigations carried out at the School of Mineral and Metallurgical Engineering at the University of Minnesota to study the flotation characteristics of some sulfidized minerals. It is divided into two parts: The first describes the sulfidization of a number of oxides and a silicate, and the second presents the flotation behavior of the products of sulfidization. SULFIDIZATION OF METAL OXIDES AND SILICATES Experimental Procedure: SULFIDIZATION WITH HYDROGEN SULFIDE GAS — Sulfidization with H2S gas was carried out in a horizontal tube furnace (Fig. 1). The temperature of the furnace was regulated by means of a Variac and determined with a chromel-alumel thermocouple. The constant temperature zone in the furnace was about 6 in. in length, and it was within this zone that the experiments were carried out. The gases employed were supplied from standard compressed gas cylinders, and passed through a glass-wool filtering tower before entering the Pyrex reaction tube. Gaseous products were bubbled through a water tower (used as a flow indicator) and excess H2S was burned off at the end of the outlet tube. Samples of reagents or minerals were placed in a 3-in. Alundum boat and inserted within the constant temperature zone of the furnace. Nitrogen gas (6 ppm O2 content) was passed through the tubes at room temperature to remove air in the tube, and continued to pass while the furnace was heating up. When the required temperature was reached, H2S was allowed to enter the tube and the supply of nitrogen was shut off. At the end of the reaction period, the reverse procedure was carried out, the samples being cooled to room temperature in a nitrogen atmosphere. The flow rate of H2S gas was maintained fairly constant in all experiments, although the rate was not determined. SULFIDIZATION WITH SULFUR POWDER - To study the sulfidization of minerals with sulfur (liquid or gaseous), samples of the mineral, together with a measured quantity of sulfur powder, were placed in a stainless steel (SS316) reaction vessel (Fig. 2). The reaction vessel was heated in a vertical resistance coil furnace, the temperature being regulated through a Variac. At the end of the experiment the vessel was cooled to room temperature before the sample was removed. Cooled products were leached with CS2 to remove any free sulfur. SULFIDIZATION OF TIN CONCENTRATES - Fifty gram samples of sulfidized tin ore were prepared by mixing -48 mesh Bolivian tin concentrate with -48 mesh Ottawa sand in various proportions and sulfi-dizing these samples with H2S in the horizontal tube

Jan 1, 1969

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines' Monograph 7.' An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines' Monograph 7.' An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951

By Joseph W. Leonard, T. S. Spicer

INTRODUCTION Reasons for Thermal Drying The continuing increase in the percentage of minus %-inch coal produced as a result of the increased use of mechanical mining methods has, over the years, tended to shift considerable portions of the work of producing saleable coal to the fine coal cleaning section of the preparation plant. Because a given weight of fine coal will contain substantially greater surface area than an equivalent weight of coarse coal, it follows that, when subjected to wet cleaning processes, the fines will absorb and retain consider- ably more moisture than coarser fractions. Increased moisture pickup in the finer sizes complicates fine coal cleaning since beneficiation may not be limited to the removal of ash and sulfur but often must be expanded to include the additional step of thermal drying to remove excessive moisture. Thus, water which provides the medium for cleaning fine coal is in itself detrimental and, like ash and sulfur, reduces coal quality. Removal of surface moisture by drying is done for one or more of the following 1 reasons: (1) To avoid freezing difficulties and to facilitate handling during shipment, storage and transfer to the points of use; (2) to maintain high pulverizer capacity; (3) to reduce heat loss due to evaporation of surface moisture from the coal in the burning process, thus increasing heating efficiency; (4) to improve the quality of coal used for special purposes, such as in the production of coke, briquettes, and chemicals; (5) to decrease transportation costs; and (6) to facilitate dry coal-cleaning processes. Because benefits to coal transportation and utilization are the most common reasons for thermal drying, the following sections will examine these areas in greater detail. Benefits to Transportation Initial benefits from drying are the reduction of shipping costs from the mine to the point of utilization since more coal can be concentrated into a given weight of product when worthless moisture is removed. Non- combustible~ such as water and mineral matter in railroad shipments of coal are billed the same as coal at $3.32 per ton, according to the recent average costs. Savings of 10 to 20 dollars from drying on the shipment cost of each 50 to 60 tons of coal contained in a typical railroad car is common. Savings on coal shipments from individual mines which result from coal drying can be expressed in terms of hundreds of thousands of dollars and more each year. For example, a reduction of shipping charges of only 5 percent on one million tons per year would mean a savings of 166,000

Jan 1, 1968

By C. E. Arnold

In attacking the problems of mining and treating large disseminated copper orebodies such as those occurring in the Miami or the Ray district of Arizona, one of the vital questions to be decided is, "What is the value of the orebody per ton in place?" The importance of this question lies in the fact that its answer helps to reach a decision concerning the method of mining to be employed. Let it be assumed for the moment that milling and smelting practice, especially the latter, is more or less standardized, and has a cost incapable of much variation, while the cost of mining has a considerable range owing to the large number of mining methods by which a mine may be exploited. For instance, a method may be adopted whereby all the available ore can be extracted perfectly clean (i.e., unmixed with barren material) at a relatively high cost; or a method may be used involving the necessary dilution of a portion of the ore with waste, in order to recover that portion, thus giving a relatively poorer extraction but nevertheless a lower working cost than the former method. Naturally, between these two extremes there lie intermediate methods. In order to arrive at a solution of a mining method problem that is of any value, it is necessary that accurate and complete estimates of mining, milling, and smelting performances and costs shall be established. By way of illustration is given a case of mining, by the system of undercutting and caving, a large orebody with an average content of 1.50 per cent. copper supposedly all in sulphide form, to which case has been applied those results in mining operations which one may fairly assume are to be expected when viewed in the light of G. R. Lehman's ore-drawing experiments, which form the subject of a paper to be presented at this meeting. It is assumed that the total costs will be as shown in the table on page 204. To attain these costs, a daily production and treatment of 14,400 tons has been assumed. Other assumptions are as follows: 15 per cent. of orebody is to be extracted clean by development work and undercutting; 63.8 per cent. (75 per cent. of 85 per cent.) is to be extracted clean by caving, leaving 21.2 per cent. part of which is to be extracted by diluting with waste, and the remainder lost. Dilution and extraction are to

Jan 1, 1917

ARTICLE I Name and Object Sec. 1. This Division shall be known as the Institute of Metals Division of the American Institute of Mining and Metallurgical Engineers. Sec. 2. The object of the Division shall be to furnish a medium of cooperation between those interested in the field of physical metallurgy; that is, the nature, structure, alloying, fabrication, heat treatment, properties and uses of metals; to represent the AIME insofar as physical metallurgy is concerned, within the rights given in AIME Bylaw, Article XI, Sec. 2, and not inconsistent with the Constitution and Bylaws of the AIME; to hold meetings for the discussion of physical metallurgy; to stimulate the writing, publication, presentation and discussion of papers of high quality on physical metallurgy; to accept or reject papers for presentation before meetings of the Division. ARTICLE II Members Sec. 1. Any member of the AIME of any class and in good standing may become a member of this Division upon registering in writing a desire to do so, but without additional dues. Sec. 2. Any member not in good standing in the AIME shall forfeit his privileges in the Division. ARTICLE III Funds Sec. 1. The expenditure of the funds received by the Division shall be authorized by the Executive Committee of the Division. ARTICLE IV Meetings Sec. 1. The Division shall meet at the same time and place as the annual meeting of the AIME, and at such other times and places as may be determined by the Executive Committee subject to the approval of the Board of Directors of the AIME. Sec. 2. The annual business meeting shall be held within a few days before or after the annual business meeting of the AIME. Sec. 3. At a meeting of the Division, for which notice has been sent to the members of the Division through the regular mail or by publication in the Journal of Metals at least one month in advance, a business meeting may be convened by order of the Executive Committee and any routine business transacted not inconsistent with these Bylaws or with the Constitution or Bylaws of the AIME. Sec. 4. For the transaction of business, the presence of a quorum of not less than 25 members of the Division shall be necessary. ARTICLE V Officers and Government Sec. 1. The officers of the Division shall consist of a Chairman, a Senior Vice-Chairman, a Vice-Chair -man, a Secretary and a Treasurer. The office of Secretary and Treasurer may be combined in one person, if desired by the Executive Committee. Sec. 2. The government of the affairs of the Division shall rest in an Executive Committee, insofar as is consistent with the Bylaws of the Division and the Constitution and Bylaws of the AIME. Sec. 3. The Executive Committee shall consist of the Chairman, Senior Vice-Chairman, Vice-Chairman, past Chairman, Secretary, and nine members, all of whom shall be nominated and elected as provided hereafter in Article VII. Sec. 4. The Chairman, Senior Vice-Chairman and Vice-Chairman shall serve for one year each, or until their successors are elected. Each member of the Executive Committee shall serve three years. The Chairman shall remain a voting member of the Executive Committee for one year after his term as Chairman. Sec. 5. The Treasurer of the Division shall be invited to meet with the Executive Committee, but without ex-officio right to vote. He shall be appointed annually by the Executive Committee, from the membership of the Executive Committee or otherwise. Sec. 6. The annual term of office for officers of the Division shall start at the close of the Annual Meeting of the Institute and shall terminate at the close of the next Annual Meeting. ARTICLE VI Committees Sec. 1. There shall be standing committees as follows: Programs Committee. Finance Committee, Membership Committee, Annual Lecture Committee, Technical Publications Committee, Mathewson Gold Medal Committee, Nominating Committee, Education Committee and such other Committees as the Executive Committee may authorize. Sec. 2. It shall be the duty of the Programs Committee to secure the presentation of papers of appropriate character at meetings of the Division. Sec. 3. It shall be the duty of the Finance Committee to inquire into and examine the financial condition of the Division and to consider proper means of increasing its revenue and limiting its expenses. The Finance Committee shall audit the accounts of the Division and report to the Executive Committee prior to the Annual Meeting of the Division. It shall render a budget to the Executive Committee estimating receipts and expenses for the ensuing year so that action can be taken on same at the first meeting following the Annual Meeting.

Jan 1, 1953