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By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6' dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

By A. J. Ardell, O. D. Sherby

The elevated-temperature steady-state creep behavior of polycrystalline a Zr was studied in vacuo under constant tensile stress. The experiments were conducted from 660° to 845°C over the stress range 870 to 5400 psi. The steady-state creep rate, is, of a Zr was found to be related to the applied stress, a, and temperature, T, by the equation where C is a constant. Two interpretations of the data are considered, each requiring different values of the parameters ß, Q, and . It is shown that this formula can be derived using Gilman's phenomeno logical equation relating dislocation velocity to the shear stress for the case where dislocation mobility is limited by the nucleation of kink motion. From the fundamental dependence of strain rate on dislocation velocity and the density of mobile dislocations, the factor exp(ßo) can be related to the stress dependence of the dislocation density, and Q to the energy of kink formation. The two interpretations considered are as follows: Case I—the parameters are adjusted so that the equation above describes the data over the entire range of stress and temperature, implying that creep is controlled exclusively by dislocation glide; Case IIthe parameters are adjusted to allow for the possibility that creep is diffusion-controlled at high stresses but glide-controlled at low stresses. For both cases the values of the parameters are within the spread permitted by the data. Factors favorable to the observation of the unusual stress -dependence of i, for a Zr are discussed and it is shown that the anomalously rapid rates of self-diffusion and the low modulus on the principal glide system are primarily responsible for the anomalous creep behavior. Metal-lograflhic observations are presented and discussed with reference to the overall creep behavior. PREVIOUS investigations of the creep behavior of a Zr have been conducted from room temperature to about 500C The results of these investigations are primarily of engineering significance because of the variety of conditions under which they were carried out, and the low testing temperatures employed. Little information is available concerning the fundamental nature of the elevated-temperature creep behavior of a Zr. This investigation of the creep behavior of a Zr above half the melting temperature (the melting temperature, T,, of a Zr is estimated to be about 1860"K was initiated because there are two significant anomalies of the physical properties of a Zr: a) the rate of self-diffusion in polycrystalline a Zr is anomalously rapid: b) both Young's modulus for polycrystalline a Zr and the shear modylus as-sociated with the prismatic slip system { 1010)( 1120) (the principal slip system in a Zr 7) have anomalously large temperature variations The importance of these quantities to the understanding of creep behavior has been demonstrated, and it was hoped that this investigation would provide a critical test of the predictions based upon the analysis of creep data for other pure metals. However, as the investigation progressed it became increasingly clear that the unusual creep behavior of a Zr could not be analyzed in a conventional manner. 1) EXPERIMENTAL EQUIPMENT AND PROCEDURES Two grades of zirconium, designated A and B, were used in this investigation. The analyses, as supplied by the vendors, are presented in Table I. Material A, with a nominal purity of 99.84 pct, was supplied by the Wah Chang Corp. in the form of cold-rolled sheet from which specimens were machined without further fabrication. Material B, with a nominal purity of 99.95 pct, was purchased from the Nuclear Materials and Equipment Corp. in the form of iodide crystal bar.

Jan 1, 1968

By Homer Turner

THE nature and comparative features of anthracite and bituminous coals have been discussed by the writer in two previous papers.1 Although this paper is offered as a further contribution to the subject, it seems desirable at the outset to repeat some of the descriptive matter of the early works in order to show the actual connection between various constituents of both coals and the new photomicrographs and other physical and chemical properties.

Jan 1, 1929

By Clarence Seyler

THE technical difficulties of cutting thin sections of coal for examination by transmitted light have hitherto restricted the investigation of the important subject of the microstructure of coal to the few possessed of the requisite skill and time. Apart from this, the method fails with anthracites and other coals rich in carbon, owing to the opacity of the material. Occasional use of the method of polishing a surface, with or without etching, has been made, but it was not until Winter1 published an account of his results that attention was seriously directed to the method. In May, 1923, a specimen of dull anthracite came into my hands; I tried Winter's method on it and the presence of megaspores and other vegetable structures became clearly visible. A preliminary notice was published by me;2 but I soon abandoned the use of Schulze's solution having found that a mixture of chromic and sulfuric acids gave far better results. In the meantime Turner and Randall, in America, had independently developed the method of flame etching, as applied to anthracite, with great success. I have spent a year studying the method of chromic etching, which gives excellent results with bituminous coals and cannels, as well as with anthracite. For anthracites, I have used the chromic method and Turner's method of flame etching, whichever was the more convenient or as a check one on the other. The polishing is done, according to metallurgical practice, by the use of a polishing machine and successively finer emery paper, followed by polishing on cloth moistened with a suspension of levigated green oxide of chromium, and a final rubbing on "selvyt" (a cotton velvet polishing cloth) moistened' with alcohol. The polished sample is examined by reflected light with a 2/3 and 1/6 in. objective. Bituminous coals usually show considerable structure, and even anthracites show it faintly in places. The sample is then etched by immersion in a boiling solution made by adding 10 c.c. of concentrated sulfuric acid to 30 c.c of a saturated solution of chromic acid; enough water is then added to dissolve

Jan 3, 1925

By W. E. Ruder

IT has been pointed out by Stead 1 that grains of considerable coarseness may be developed in steels containing from 3 to 5 per cent. of silicon, and in a previous paper 2 the present author has shown that under the proper conditions of annealing single grains having an area of 50 sq. cm. may be obtained. It is the purpose of this paper to discuss in more detail the conditions, promoting the growth of these grains, in the hope that the experiments described may throw some additional light upon the general problem of grain growth in metals. These silicon steels lend themselves particularly well to such experiments because of the ease with which the change in structure may be followed and because of the fact that the effect of the carbon present is largely obliterated by the high percentage of silicon. This forms a solid solution with the iron, which acts very much like a pure metal. This alloy has been found to have but one critical point, viz., Are. This point, determined by Roberts-Austen for Hadfield's 4 per cent. Si alloy, was found to lie at 703° C. Vigouroux3, in working with pure Fe-Si alloys, finds this point to rise from 750° C. for 0.5 per cent. Si to 860° for 6 per cent alloy, with a flat region in the curve from 3 to 4 per cent. Si. No accurate determination of this point has been undertaken by the present author, but it has been roughly determined to lie between 730° and 750°.

Jan 12, 1913

Jan 1, 1924

By W. P. Sykes

ThiS investigation was undertaken primarily to establish the relations existing between temperature and mechanical properties in molybdenum, nickel, and an aluminum-copper alloy. Mlolybdenutn (m.p. 2500" C.) was chosen because it is partly similar to tungsten and partly similar to the common ductile metals. Also it is known to furnish, by proper treatment, a desirable material to use in studying relation of grain size and physical properties. The molybdenum used was of the quality that is drawn into wire 0.003 in. in diameter for use as filament supports in incandescent lamps; Chemical analysis shows less than 0.1 per cent. of impurities. Nickel belongs to the same class as iron. Its melting point is 1450" C. and an allotropic change at about 370" C. results in a loss of magnetism above that temperature. This feature made nickel doubly valuable for the purposes of these tests. The nickel used was obtained from the Driver-Harris Co. as 0.090 in. (2.3-mm.) wire, annealed; analysis showed 99.8 per cent. nickel and 0.150 per ccnt. iron. Aluminum is one of the low melting-point metals. Some tensile tests at clevated temperatures have been reported by Bengough but the possibility of learning more with the low temperature and sensitive apparatus available rccommendcd this metal. The samples marked A1 arc an aluminum-copper alloy that contains 3 per cent. copper, 0.42 per cent. iron, and 0.21 per cent. silicon. The presence of the copper somewhat coniplicates the analysis of the results; but the action of copper in aluminum has been studied so that its influence might have been foretold, in part at least. The material and analyses were furnished by the Aluminum Castings Co. The nickel wire, which was deformed at 400" C., was drawn under a bath of molten lead and through a die, which also was immersed in the bath. A thermocouple was suspended in the molten metal to indicate the temperature. Hot oil was uscd as the heating bath for drawing the

Jan 1, 1921

By Henry Lloyd Smyth

In 1891-92 1 was entrusted with the geological survey of part of the large area lying between the Marquette and Menominee iron-ranges in the Upper Peninsula of Michigan, and extending from the Republic trough on the north, through portions of the valleys of the Michigamme and Fence rivers, to and including the intermediate Felch mountain range on the south. Until a few years back the larger part of this area has been very difficult of access, and much of it is difficult still. The rock-surface is for the most part covered with swamp, forest and glacial deposits of various kinds, and therefore has not invited geological study. For these reasons the district, as a whole, with the exception of the Felch mountain range, remained almost unknown from a geological standpoint until our work in 1892. Our main object was to map the pre-Cambrian rocks, particularly the iron-bearing formations of Algonkian or Huronian age, and to obtain as much information as possible with reference to their sequence and structure, In carrying out this purpose, the use of simple magnetic instruments was found to be of the greatest assistance, and indeed indispensable. In this paper the results of our experience in tracing magnetic rocks by means of the disturbances produced in these instruments, have been brought together in systematic form, with such references to the particular area as are necessary in order to illustrate general principles, with the hope that they will prove useful to other workers in the same region, or in other regions where similar conditions may be encountered. The writer was efficiently aided in the field-work by Messrs. Samuel Sanford and Charlea N. Fairchild for nearly the whole period, and E. B. Mathews and H. F. Phillips for part of it,

Jan 1, 1897

By L. Seigle, R. Resnick

An inert-marker movement experiment indicates that the ratio of the intrinsic diffusion coefficients DC:DTa = 80:l in TaC at 2500°C. Measurements of the diffmion coefficient of carbon in nonstoichiometric TaC at temperatures from 1700° to 2700°C reveal that Dc increases with decreasing carbon content, but much less than expected from the probable change in vacancy concentration with carbon content. A diffusion process involving two simultaneously operating mechanisms is postulated, and shown to be theoretically feasible. The average value of the carbon diffusion coefficient is given by DC = 0.18 exp[(-85,000 ± 3000)/RT] sq cm per sec over the composition range 46 to 49.5 at. pct C. BECAUSE of their high melting points and hardness, the carbides of the IV, V, and VI group transition metals, along with those of uranium, have attracted considerable interest for applications at high temperatures. In these applications the reactivity of the materials is important, and, since rates of diffusion within the compounds influence reactivity, a knowledge of diffusion kinetics and mechanisms is desirable. While many investigations of the mechanical and electrical properties of these compounds have been made, only two fundamental investigations of diffusion in the carbides are known. Chubb, Getz, and Townleyl measured the diffusivity of carbon and uranium in UC, and Gel'd and Liubimov2 measured the diffusivity of carbon and niobium in NbC. This paper describes an investigation of the diffusion of carbon in tantalum monocarbide and, in particular, the influence of carbon deficiency on this process. Tantalum carbide melts at approximately 3800°C, which makes it one of the highest melting materials known. The compound exists over a rather wide range of carbon Content.3-7 At the peritectic temperature, 3240°C, the phase extends from about 36 to 50 at. pct C. Although the compound can exist with a substantial carbon deficiency, the high carbon phase boundary remains near the stoichiometric composition over the entire temperature range; i.e., no carbon excess is observed. The structure of TaC is the NaCl type wherein carbon atoms normally occupy the octahedral sites in a somewhat expanded fcc lattice of tantalum. Decrease of the lattice parameter with decreasing carbon suggests that the removal of carbon introduces octahedral vacancies into the lattice. I) EXPERIMENTAL DETAILS AND RESULTS Inert-Marker Experiments. In a compound such as TaC the interstitial element would be expected to diffuse more rapidly than the metal. This was confirmed by an inert-marker experiment, following Srnigelskas and irkeendall.8 Ideally, the markers should be placed at the interface between a slab of low-carbon TaC and graphite, and their movement during subsequent inter-diffusion measured. Unfortunately, no solid could be found which is unreactive in contact with carbon at the high temperatures employed in these experiments. In order to circumvent this problem, a specimen was designed in which the markers consisted of several small canals running just below the surface of a tantalum slab. This specimen was prepared by machining grooves on the surface of the tantalum slab and then diffusion-bonding a thin plate of tantalum to the slab over the grooves. The surface of the plate was then ground down until the distance between the canals and surface was as small as possible (about 0.01 cm). Thus, the canals would lie entirely within the TaC phase after a short period of diffusion. The diffusion anneal consisted of immersing the metal sample in high-purity graphite powder and heating for approximately 10 hr at 2500°C under vacuum. At this temperature, the vapor pressure is sufficiently high and the transfer of carbon from graphite sufficiently rapid to allow the surface of the diffusion sample to attain the stoichiometric carbon concentration very quickly. Conclusions regarding the relative diffusion rates of carbon and tantalum in the compound layers (TaC and Ta2C) can be drawn from the location of the canals after the diffusion anneals. If the growth of the layers is governed mainly by the diffusion of carbon, as expected, the canals should remain close to the sample surface. If the diffusion of tantalum contributes appreciably to formation of the compound layers, the distance from the markers (canals) to the surface should increase. Fig. 1 shows, diagrammatically, the appearance of the specimens after diffusion, and Table I presents the depth below the surface at which the

Jan 1, 1967

By G. Willard Quick, John R. Freeman

Jan 1, 1930

By R. J. Wagner, F. F. Craig, H. G. Riley, J. D. Griffith

Peripheral water injection has been underway in the Sholem Alechem Fault Block "A" Unit, Stephens County, Okla., since 1955. In the engineering planning of the flood, it was recognized that maintenance of pressure in the large, dry gas caps was vitally necessary to prevent the loss of an estimated 27 million bbl of oil through saturation of the gas caps by the oil banks moving updip on the peripheral flood pattern. The development of an abundant, low-cost water supply and the rising cost of makeup-gas purchases indicated that gas-cap control by water injection was desirable from an economic standpoint, provided an eflective water barrier could be placed without premature water breakthrough into downdip oil producers. A laboratory model scaled to the existing reservoir conditions was comtructed to evaluate the feasibility of gas-cap water injection. Model studies indicated that (I) water injected at the edge of the gar-oil contact would form a continuous barrier between the oil and gas zones, and (2) water would advance uniformly downdip without segregation due to gravity effects provided a specified, minimum water-injection rate was maintained. The model test results also indicated that it was not necessary to fill the gas cap completely with water. Water injection at the edge of one of the gas caps was initiated in March, 1958, to field test gas-cap water injection. Water breakthrough occurred at a downstruc-ture producing well in April, 1959, after approximately 2.5 million bbl of water had been injected into the gas cap. This was the volume calculated to be required to form the barrier between the oil zone and gas cap. This performance indicates that prevention of oil encroachment into dry gas caps in a peripheral water flood by water injection at the gas-oil contact appears practical and that the model studies provided a valid prediction of field performance. INTRODUCTION The Sholem Alechem Fault Block "A" Sims Sand Unit was one of the fist major waterflood projects in Oklahoma to utilize a peripheral injection pattern. Design of control measures to minimize oil encroachment into the large crestal gas caps was one of the greatest single problems during engineering planning of this flood. Engineering studies indicated that saturation of the gas caps with oil displaced by the peripheral water flood could result in a loss of about 27 million bbl of oil, or over one-half the estimated waterflood recovery. This estimate was based on a residual oil saturation after water flooding of 35 per cent pore volume, compared to the negligible oil saturation initially in the gas caps. The Sholem Alechem Springer field, located in Stephens County, Okla., is an elongated anticline with structural dips varying from 400 to 1,000 ft/mile. The structure contains numerous faults, some of which are sealing. The portion of the field considered in this paper is Fault Block "A", which is the largest of the five major fault segments in the field. A map of the unit is shown on Fig. 1. The unit is bounded on the east and west by major sealing faults, on the north by a water-oil contact and to the south by a deterioration of sand development. Two domes, each having gas caps, exist in the unit and are separated by a north-south fault as shown in Fig. 1. The sands being flooded are the Sims sand members of the Springer series of early Pennsylvanian age. The Sims sands average over 100 ft in thickness in Fault Block "A" and have a porosity of approximately 19 per cent. Core permeabilities average 160 md, with interstitial water saturation of about 23 per cent pore volume. Three different zones can be correlated over most of the area. However, they are commingled in most of the producing wells. The two upper zones, designated as First and Second Sims, are the most important. Both the First and Second Sims have gas caps in the east dome, while only the First Sims has a gas cap in the west dome. These gas caps, whose limits are also shown on Fig. 1, initially occupied nearly 11 per cent of the total reservoir volume. The major concern of this paper is the control of the two gas caps in the First Sims sand. Fig. 2 is a cross section, to scale, across the east dome of this formation. Notable features are the relatively shallow dip, the deterioration of the First Sims sand on the south side of the gas cap and the water-oil contact on the northern edge. The formation dip at the gas-oil contact in this cross section is approximately 5".

By R. A. Hadfield

It seems a specially fitting opportunity to present a paper on the alloys of iron and aluminum at the New York meeting of this Institute, owing to the fact that America has, more than any other country, originated and developed the manufacture of cheap aluminum. The Cowles, Castner, and Hall systems have all originated in the ever-busy brain of our cousin across the water. The problem of cheaply producing this valuable metal has been a difficult one, but to the writer it seems that the more arduous the task the greater the delight with which our American friend attempts to overcome the difficulties surrounding it, and the more vim he throws into the work. Another and equally striking proof of this is to be found in the recent appearance of the already wellknown remarkable work, The Mefallurgy of Steel, by Mr. H. M. Howe, of the Institute of Technology, Boston, Mass. It is to be hopel that this Institute will not be slow to recognize by some special mark its appreciation of this signally valuable and original work. The writer has been led to describe the following experiments, believing that so far no full and exact report has yet been presented to this Institute as to the effect of aluminum alloyed or combined with the metal iron. It has been a special object to make the material as far as possible a true alloy or combination of aluminum and iron, with as small quantities as possible of other disturbing ingredients, such as silicon, manganese, etc. In the material described in these experiments, the total amounts of other elements present (sulphur and phosphorus being disregarded as present in such small quantities) do not exceed about 0.5 per cent. Such material may therefore be probably taken as fairly illustrative of the effect of the metal aluminum upon iron. Since completing the experiments the writer

Jan 1, 1891

By E. S. Bumps, W. F. Craig, M. Baeyertz

Metallurgists have looked at fractures macroscopically for many years and have evolved a vocabulary in which such words as "cleavage," "brittle," "shear," "ductile," "granular," "fibrous," and "silky" are used to describe the appearance of the fractured surface; but the meaning of these words in terms of metal structure is not well established. Observations of the structural meaning of "brittle" and "ductile" fractures in plate steels have been made, notably, by Kramer and coworkers1 and by Tipper.2 Grossman3 has studied the fracture of tempered martensite and combinations of ferrite and martensite. Notwithstanding these and other less concerted attacks on the problem, present understanding of fracture rests more on assumptions and logic than on experiment. It is the purpose of this paper to add a little to the growing fund of experimental observations of the nature of fractures in steel. The particular fractures to be described were obtained in conventional impact testing of an ordinary structural steel shape. In impact tests of the Charpy type, the specimens fail in a characteristic manner that depends on the steel and the temperature of testing. With ordinary structural and many other steel products, an appropriate range of testing temperature will cause a considerable change in the energy absorbed before fracture. This change is known as the energy transition and is accompanied, more or less closely, by alteration in the appearance of the fracture. At testing temperatures below the transition, the terms "brittle," "cleavage," or "granular" are used to describe the fracture; above it, "ductile" or "shear" are often used. Within the transition, the fracture changes from "brittle" to "ductile" by a progression in appearance, wherein the "brittle" portion of the fracture becomes restricted to a smaller and smaller central area of the fracture, as the testing temperature is raised and the "ductile" type of fracture is approached. All this is well known to metallurgists. The specimens under consideration are of the conventional V-notch Charpy type. They were taken from a structural steel shape of the following analysis: C Mn P S Si 0.17 0.46 0.009 0.029 0.03 Both longitudinal and transverse specimens were tested and examined. Fig 1 shows the energy values plotted against testing temperatures in the usual way. The curves for both longitudinal and transverse specimens show an energy transition, although the maximum energy absorbed at testing temperatures above the transition is greater in the case of the longitudinal specimens. Fig 2 illustrates the changes in the macroscopic appearance of the fractures that are associated with the energy transitions shown in Fig 1. Macrographs of the fractured surfaces of the specimens have been identified with the fracture ratings at intervals on each fracture curve. The numerical fracture rating on the ordinate of Fig 2 indicates the percentage of the area of each fracture that was considered to be "brittle" on macroscopic observation. Such rating of the fracture type in impact tests is now customary in many laboratories. Hereafter the specimens will be identified by reference to Fig 2 as 90 pct "brittle," 80 pct "brittle," and so on, in accordance with this macroscopic evaluation of the appearance of the fractured surface. The discussion of the fractures is divided into three parts. The first two are concerned with the mode of fracture and its relation to general structural features. As the same metal-lographic features occur in both longi-

Jan 1, 1950

By N. Brown, R. Kossowsky

Plain carbon steels with 0.48 and 0.95 pct C were quenched and tempered at 705°C to produce carbide dispersions with spacings on the order of 1 p. The morphology of the structure consisted of a carbide-dislocation network. The strengthening due to the dispersion was found to vary linearly with M-½ where M is the mean free-ferrite path determined by the entire network. No preyield microstrain preceded the upper yield point. After prestraining, the lowest stress at which dislocation movement could be detected was 104 psi; this frictional stress was independent of the dispersion and prestrains up to 6.5 pct. The Cottrell-Petch equation for grain-size strengthening was used to discuss the dispersion strengthening in this investigation. The results support an impurity mechanism for the upper yield point rather than one based on the Johns ton- Gilman theory. IT was pointed out by Gensamerl that the mean free path in the matrix is the important variable which controls the degree of dispersion strengthening. Gensamer's data on steels showed a linear relationship between the yield point and the logarithm of the mean free-ferrite path. The first theory was by Orowan,2 who suggested the mechanism of dislocations bowing between particles, with the resulting relationship that where a is the yield point, P is the distance between particles, and G is the shear modulus. The Orowan equation applies to that range of dispersion where P is large compared to the particle size and the particles are not coherent, so that the matrix is essentially free of internal stresses. As was pointed out by Orowan, there are different degrees of dispersion which, in turn, will influence the strength-controlling mechanism. However, in this investigation, we wish to confine ourselves to the region of coarse dispersion, where the Orowan mechanism should, intuitively, be applicable. It was soon evident that the data, which existed at about the time that the Orowan theory was proposed, did not agree with the Orowan equation in that the actual strengthening was always greater than the theoretical predictions. Thus, Fisher, Hart, and pry3 modified the Orowan theory by suggesting that the Orowan process took place in the microstrain region preceding macroscopic yielding and the subsequent, rapid work hardening in the form of residual dislocation loops around the particles largely determined the observed macroscopic yield point. The F-H-P theory stated that the increment of strengthening due to the work-hardening mechanism was proportional to f3/2 where f is the volume fraction of the precipitate. F-H-P used data by Shaw, Shepard, Starr, and Dorn4 on A1 3-5 pct Cu to support their theory. Roberts, Carruthers, and Averbach5 were the first to make a microstrain study of dispersion strengthening, and they found that for steel the Gensamer relationship was obeyed. Hayman and Nutting6 suggested that in the case of tempered steel 1) the ferrite grain boundary was the primary obstacle and 2) the carbide particles simply formed part of the grain boundary obstacles. They found that the strength varied as G"" where G is the ferrite grain size. Turkalo and LOW' determined the structure of quenched and tempered plain carbon steel using a replica technique; they concluded that the carbide particles did not necessarily lie in the ferrite grain boundaries. When they defined the mean free-ferrite path as being determined by both particles and the ferrite path boundaries, their data obeyed the Gensamer relationship. Meiklejohn and skoda8 showed that the strengthening from iron particles in mercury was a function of the particle size and the distance between particles. Dew-Hughes9 explained the Meiklejohn and Skoda results by the following theory: 1) grown-in dislocations which surrounded the particles were produced by the thermal stresses during the time the material was cooled to the testing temperature, and 2) the observed strengthening was associated with the cutting of the grown-in dislocations by the glide dislocations. Ansell and Lenel10 proposed a theory in which the glide dislocations pile-up or surround the particle until the number of dislocations in the pile-up is sufficient to yield or fracture the particle. The resulting theory says that the yield point varies as p-1/2, where P is the distance between particles. The Ansell-Lenel theory is almost identical to the

Jan 1, 1965

By Donald C. Barton

The theory of gravitation is based on Newton's law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e., A = KMRm2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth's gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations,in regard to gravity, that other body usually is taken as a unit of mass: in the C:. C:. S. system, a body of one gram in mass. Gravity and Level Surfaces Gravity is defined in geophysics as the force of attraction exerted by the earth, towards itself, on a body of unit mass. The intensity of gravity is usually expressed in dynes of force or in centimeters of acceleration In geophysical work in America, most commonly it is expressed in dynes (per gram) with the "per gram" understood and not directly expressed. In geophysical work in Europe, most commonly it is expressed in centimeters per second per second (cm. /sec.2) and less commonly lrierely as centimeter-gram-second units (c. g. s). At sea level, the intensity of gravity amounts very nearly to 980 dynes. The vertical is the direction along which the attraction of gravity is exerted at any point. In most cases, it is very nearly, but not quite, perpendicular to the earth's surface. The path that would be taken by a body falling freely through space toward the earth is vertical at each point and may be spoken of also as ('the vertical," or as the line of the vertical, or as a line of force of gravity. At the earth's surface it comrrlonly is very nearly, but not quite, a straight line.

Jan 1, 1929

By Wilbur T. Stuart

TO assist the mining industry in attacking problems of water control, the U. S. Geological Survey has begun a program of research in mining hydrology. In certain fundamental respects water control is similar to development of water supplies from wells or to the drainage of agricultural lands, as many of the tools developed in recent years for quantitative ground-water problems are applicable, with modification, to mine-water problems. In 1952 a 30-day pumping test conducted jointly by the Eureka Corp. Ltd. and the Defense Minerals Exploration Agency provided an opportunity to gain knowledge concerning water movements around a flooded mine shaft. The methods of analyzing the data may be used as a guide for the evaluation of similar problems elsewhere. The Fad shaft of the Eureka Corp. is on Ruby Hill, 1 1/2 miles west of Eureka, Nev. The shaft was completed at a depth of 2465 ft in November 1947 at a site adjacent to the downfaulted block in which the ore was found. As the drift on the 2250 level progressed toward the ore zone, a large flow of water was encountered after the Martin fault was intersected. This flow exceeded the installed pump capacity, and an unsuccessful attempt to recover the shaft and the 2250 level was made in 1948.1, 2 Geology and Hydrology: The complex structure of Ruby Hill is that of an anticline broken first by thrust faulting and later by normal faults. The present orebody comprises several mineralized zones within a block of the Eldorado limestone of middle Cambrian age which was downfaulted 1400 to 1600 ft, and it may be related to a similar body mined at a higher level south of the Ruby Hill fault. At the depth of the largest zone of ore the block is roughly rectangular in shape, about 1000 ft wide and 1500 ft long, and dips about 30" NE, see Fig. 1. It is apparently bounded on the south by the Ruby Hill fault, on the east by the Jackson fault, on the north by the Martin fault, and the west by the Bowman fault. Within the block, but between the Ruby Hill and the Martin faults, are the Office and Adams Hills faults; west of the block and the Bowman fault are the Albion and Spring Valley faults. There are many conflicting reports concerning the water-yielding characteristics of the Eldorado limestone and the condition of the fault zones, that is, whether they are open or tight. However, the diamond-drill records indicate that open spaces as much as 2 or 3 ft across were encountered, and considerable cementing and lining of holes was necessary to maintain circulation of drilling fluid. There is also evidence that the Eldorado limestone was cavernous where it was mined in the early days south of the Ruby Hill fault. At the site of the Fad shaft the formations encountered from the surface down included the Pogonip limestone, Dunderberg shale, Hamburg limestone, and Secret Canyon shale. These formations did not yield large quantities of water to the shaft. The Pogonip limestone, which appears to be permeable and might yield water elsewhere, is above the water table in the vicinity of the shaft. The Secret Canyon shale, immediately overlying the Eldorado in some places but in most places separated from it by the Geddes limestone,3 is apparently tight and does not transmit water. During the 30-day test period the shale briefly confined the water in the underlying formations so that artesian conditions were observed in drillholes E and F, which are cased into the Eldorado limestone, whereas unconfined conditions were observed in drillholes B, C, and D, which were open to the shale. The Geddes limestone, which normally lies between the Secret Canyon shale and the Eldorado limestone, was not encountered in the Fad shaft. The Geddes, a flaggy, fractured limestone, is reported capable of yielding large volumes of water. Water stored in the interstices of this thin-bedded limestone within the Ruby Hill fault zone on the 1200 level of the Locan shaft drowned the pumps in 1923 when the Richmond-Eureka Mining Co. attempted to explore the area along the fault. Eldorado limestone was not encountered in the Fad shaft. In the ore-block area the Eldorado limestone was not entirely offset from other water-yielding formations by movement along the Bowman fault; therefore it may be hydraulically connected with the other formations. Adjacent to the Ruby Hill, Jackson, and Martin faults, the Eldorado lies in contact with other possible water-yielding formations. One of these, the Prospect Mountain quartzite, is separated from the Eldorado by thin, sheared, and broken beds of the Geddes within the Ruby Hill fault zone. A limited examination by the author of the Prospect Mountain quartzite in the Richmond mine at a higher level and south of the Ruby Hill fault indicates that the quartzite is poorly permeable. The monzonite mass south of the quartzite would be a further barrier to the flow of water. The poor permeability of this area is substantiated by records of levels at which water was encountered south of the Ruby Hill fault. In view of the normally low rate of ground-water recharge, if this desert area had been permeable, water levels could not have been maintained at altitudes of many hundred feet above the present water table west and north of Ruby Hill. Thus the ore-bearing block of Eldorado limestone is in contact with possible water-yielding rocks on at least two sides, and if the fault zones are possible conduits for water circulation the geologic and hydrologic conditions are suitable for the infinite-aquifer type of analysis as used and modified here. History of Pumping: During sinking of the Fad shaft a maximum pumping rate of 1500 gpm kept the shaft dewatered sufficiently, but in March 1948, after the 2250 level drift passed through the Martin fault into the Eldorado limestone, the pumps and shaft were flooded. Subsequently additional pump-

Jan 1, 1956

By AIME AIME

LIFE will not be difficult for those who attend the fall meeting of the Petroleum Division at the Conoco Club, Ponca City, Okla., Sept. 30-Oct. 1. An attractive program to appeal to oil company executives and lawyers, as well as technologists, has been arranged and the Continental Oil Co. has contributed for the occasion the buildings, grounds and facilities of the club. E. 0. Bennett, Continental Oil Co., Ponca City, is chairman of the arrangements committee, and reservations for rooms and trips, requests for information, etc., should be sent to him.

Jan 1, 1932

By E. H. Dix

All commercial aluminum contains small percentages of copper, iron, and silicon as unavoidable impurities. The purest metal obtainable commercially, special grade high purity ingot, contains a maximum of 0.50 per cent. impurities of which the usual minimum amount of copper is 0.01 per cent.; silicon, 0.12 per cent.; and iron, 0.20 per cent. This grade is too costly for most purposes. The two standard grades, Nos. 1 and 2, containing a minimum of 99.0 and 98.0 per cent. aluminum, respectively, are more generally used. Other grades of secondary aluminum often contain as high as 3 or 4 per cent. of impurities, which include 1 per cent., or more, of zinc. Specifications for high-grade aluminum-casting alloys generally allow a maximum of 1.7 per cent. for total impurities. The S. A. E. Specification No. 33, which is intended to cover alloys made from secondary aluminum ingot, gives the iron maximum as 1.5 per cent. and the maximum for silicon (including manganese and tin) as 0.75 per cent. The effect of even relatively small amounts of impurities on the physical properties of ingot aluminum is shown by the following cornparison of two lots of aluminum, which may be taken as representative of special grade and grade No. 2 ingot, respectively. AnalysEs Special Grade, Gbade No. 2, Per Cent. PeR CBnt. Copper................................. 0.01 0.32 Silicon................................. 0.12 0.32 Iron................................... 0.42 0.82 Aluminum.............................. 99.45 98.54

Jan 1, 1923

By David Sinclair, Philip B. Bucky

The dimensions and shapes of mine structures may at present be determined by (1) field experience, (2) structural calculations, and (3) barodynamic tests. § None of these, however, provide information as to the stresses, their direction and distribution in a mine structure. For the design of pillars, the placing of openings relative to working places such as gangways, haulage levels, etc., this information is desirable. Photoelastic methods provide this and, while relatively new, their application in all engineering fields is assuming increasing importance. This paper, therefore, will present the method with a few applications to mining, and with sufficient reference for further study by the reader. PART I The Photoelastic Method The photoelastic method of stress measurement determines the stress distribution in a two-dimensional model by optical means. It makes use of the fact that when a piece of isotropic transparent material, such as glass, celluloid, or Bakelite, is stressed and viewed in polarized** light a picture is seen which indicates by its color bands of light, or fringes, the magnitude of the stresses, their direction and their distribution. General Explanation The stress at any point 0 in a structure (Fig. I), may be resolved into two components, P and Q, each a pure tension or compression, at right angles to each other, called principal stresses.' To fully identify the stress, the values of P and Q and their directions or angle F must be known.

Jan 1, 1940

By J. R. Long, R. S. Dean, F. S. Wartman, E. T. Hayes

The production of titanium in I5-lb. lots and with a purity sufficient to be consolidated into ductile metal, as described in a previous paper,' has provided adequate material for a study of the physical properties of titanium and a more thorough examination of its working qualities. Data on the physical properties reported in that paper were obtained on metal fabricated by a fixed procedure, standardized for the purpose of control of the reduction, and are representative only of material fabricated under those conditions. There are many possible variables in the working schedule, which will have significant effects on the properties of the finished material; and since the previous working methods were not necessarily the best, an investigation of the fabrication of titanium by other methods was undertaken. In this work the consolidation of the powder by pressing and sintering was conducted essentially as outlined in the report cited' and all efforts were centered on fabrication methods for those powders and the proper- ties produced by them. Hardness, density, microstructure, and tensile properties were determined at various stages in the working and annealing; and resistivity measurements were made on a few bars and drawn wire. Consolidation of the PowdeR The screen analysis of the available titanium powder is given in Table I. No attempt was made to alter the size distribution from that noted because this powder, although coarse by normal powder-metallurgy standards, produced acceptable compacts suitable for the present work. Because of their large specific surface, finer powders are more contaminated by oxygen and produce harder compacts, which are difficult to work. The powder as produced is soft, compresses in a normal fashion, and exhibits very little tendency to adhere to the die surfaces. Unlike aluminum and magnesium powders, it can be readily pressed without the use of die lubricants. When compacted at 50 tons per

Jan 1, 1946