Search Documents

By John Devine

DURING the past few years the Bureau of Mines has been studying hydrogen-sulfide corrosion in the petroleum and natural-gas industries. Early work was confined to investigating the various practical, or operat-ing, factors that control the corrosion reaction when ordinary mild steel is being attacked. In that work it was shown that, if the optimum operating conditions1 are obtainable, . gas containing hydrogen sulfide can be handled at ordinary temperatures without serious corrosion resulting. However, frequently "sour" gas must be handled under other than optimum operating conditions, and combating corrosion then becomes a problem to be considered more during the construction of a system than during its subsequent operation. That is, where economi-cally practicable in such cases the designer will seek to substitute for mild steel other steels or ferrous metals more resistant to corrosion by hydro-gen sulfide. The comparative resistance of various commercial steels and alloy steels to corrosion by hydrogen sulfide at elevated temperatures has been reported systematically by previous investigators,2 but similar information for corrosion at ordinary temperatures is available only from scattered sources, representing different methods of testing. As the value of comparative corrosion tests depends largely upon the use of a

Jan 1, 1934

By J. Weng

The equations of heat conduction are numerically solved for two kinds of artificial freezing- mechanical freezing and liquid nitrogen freezing. A two dimensional finite difference model simulating the freezing field is developed. The procedure introduces a way to simulate the effect of latent heat released when water transforms from liquid to solid. The procedure also produces a way to calculate the harmonic mean of heat conductivity used when dealing with heterogeneous material. The theoretically derived temperature distributions in frozen soil are given and compared with measured data. An analysis made on the thermal design in shaft freezing. The average temperature of frozen soil is calculated by using numerical integration. The regularity of development of frozen soil radius is revealed and given in an appropriate mathematical model.

Jan 1, 1984

By F. Rosenblum, P. Spira, F. Kitzinger

The possibility of increasing the efficiency of mineral processing plants by means of computer control has prompted metallurgists to examine their flowsheets more critically in order to develop practical control strategies. Control schemes in use to date generally rely on the automation of traditional and previously manually regulated control loops, e.g., the addition of reagents to maintain a constant assay or a constant pH. This approach is predicated on the availability of well established primary sensors such as pH electrodes or on-stream analyzers. Noranda Research Center, in cooperation with Noranda Group concentrators, has developed a froth level monitor and a pulp density meter adaptable to this type of control. Although some of the basic principles on which they are based have been known for some time, their incorporation into the design of reliable, direct-reading instruments which can be interfaced with a computer is believed to be novel.

Jan 4, 1979

By Michael B. Gross

A numerical study of the vulnerability of unlined tunnels in jointed rock has been performed with the STEALTH computer program, using the CAVS model for jointed rock. CAVS, for Cracking And Void Strain, is a constitutive model that can simulate the initiation/propagation of fractures and the slip along fracture planes in a jointed rock mass. The CAVS model is unique because it represents a spatially oriented approach to rock failure, rather than the traditional invariant formulation, and because the CAVS submodels for slip friction and slip-induced dilatancy are used to represent the weakening influence of joints, rather than applying ad hoc modifications to the elastic moduli of the host rock. The CAVS model, as embedded in the STEALTH computer program, has performed numerical simulations of tunnel collapse at high overstress levels. These calculations show that the ultimate strength of the tunnel depends strongly on the joint properties, and that the results of the calculations are in qualitative agreement with the observed data for collapse of a tunnel in tuff.

Jan 1, 1984

By R. A. Marriot

The steam-generating plant at the Garfield smelter of The American Smelting and Refining Co. consists of two divisions in which the boilers are classed as direct-fired or waste-heat. The direct-fired boiler plant consists of eight 330-boiler hp. type K-19 and S-I 7 Stirling boilers located in the boiler room adjacent to the power house, and two 330-boiler hp. Stirling type K-19 boilers in the reverberatory building, which formerly were connected to a reverberatory furnace but now are arranged for direct firing. All direct-fired boilers are now fired with natural gas. The waste-heat boiler plant consists of all units connected to reverberatory furnaces, and receiving heat from the exit gases therefrom. In this classification there are two 490-boiler hp. Erie City vertical water-tube boilers, and six 330-boiler hp. type K-19 Stirling water-tube waste-heat boilers. Each furnace has boilers arranged in battery setting. The boilers are directly in front of the furnace and connection is made through a short uptake and flue (Fig. 1). The Stirling boiler settings rest on concrete foundations at ground level, with the furnace uptake and flue at a low elevation. The Erie boilers are carried on steelwork some 15 ft. above ground level, and stand against the face of the uptake with no connecting flue. The constructional requirements of a larger furnace dictated this type of setting.

Jan 1, 1934

The following rules, upon approval by the Board of Directors, shall serve as guides in the practical applications of the Bylaws for the operation of the Institute and have the full power and effect of Bylaws, however, these rules may be changed, modified, re¬pealed or amended when deemed necessary by the Board of Directors Any change or alteration of these Rules shall be published in the Journals of the Institute within three months after such alteration is adopted ARTICLE I-ORGANIZATIONS OF THE INSTITUTE Section 1-Societies Rule 1-Governing Body Each Society shall form its own governing body composed of an Executive Committee, or similarly designated executive body, duly elected officers, and a Nominating Committee for the nomination of Institute officers as provided by the Bylaws of AIME and of each Society approved by the Board In all correspondence and printed matter the Society Boards of Directors shall be specifically identified For ex¬ample, the Mining Board of Directors or the Board of Directors of the Society of Mining Engineers Using simply the "Board of Directors" could cause confusion

Jan 1, 1960

Would you briefly describe how you chose the minerals industry and reflect upon some of your earliest experiences? I wish that I could say that I had a well-formulated career plan early in life and that mining engineering was always foremost in it, but I cannot, In fact, I was quite indecisive before I finally chose my life's vocation. But in another respect, I am glad my career unfolded in the manner it did because it gave me a better insight into advising others on career opportunities. Probably the greatest problem confronting our youth, and the one I find preys upon their minds the most, is their inability to select a career path early in life. This indecision frequently has a deep psychological effect upon them and they become down on themselves. Therefore, it fortifies them somewhat to learn that others who have become successful in their careers had difficulties choosing a career path early in life. However, while assuring young people that an early choice is not absolutely essential for success, I caution them to work toward as early a decision as possible.

Jan 3, 1979

By C. E. Sims, G. A. Lillieqvist

The following presentation is more a summation of observations made and conclusions drawn over a period of three to four years than a report of experiments made with a definite objective. Tests were made, of course, to verify hypotheses, but the large mass of data was collected incidental to other work. Lack of space forbids the presentation of more than a few of those data. On the other hand, it is unfortunate that some of the most illustrative examples are not available. The work is admittedly incomplete but is presented in the hope that it will stimulate further work along a similar line. The answers to many of the questions left unanswered by this paper will be found only after long and painstaking study, such as is scarcely possible in a commercial laboratory where problems of immediate importance consume most of the time. It is also hoped that this study will in some measure throw light on some of the dark spots of steelmaking, and help to clarify some of the annoyingly vague references to "good practice." Only cast steel was studied and the conclusions apply to cast steel, but it is the authors' opinion that the quality of rolled or forged steel is largely dependent on the quality of the ingot, which is a casting. Although this discussion deals almost entirely with inclusions, it is important that the reader understand that only those natural inclusions which owe their origin to the solubility of certain materials in steel and to the chemical reactions of steelmaking are considered. Accidental inclusions, such as entrapped particles of slag, nozzle, runner, or mold arc outside its province and are not considered. Such accidental inclusions are always dangerous and should be carefully avoided. Relation between Ductility and Nonmetallic Inclusions In September, 1928, an acid electric furnace was put into operation at the Indiana Harbor plant of the American Steel Foundries. Following the usual practice, aluminum additions were made in order to obtain sound castings. Immediately the problem of low ductility arose. Previous to that time, only open-hearth steel was produced, and, aluminum being used rarely in that steel, there had been practically no trouble with low ductility in the lower carbon range.

Jan 1, 1932

By A. Aly Selim, Bruce D. Hanson

A computer model capable of simulating the basic production system in a variety of underground mining methods has been developed at the U.S. Bureau of Mines Twin Cities Mining Research Center. The simulation of the basic production system at the working face, which includes drilling, blasting, mucking, and roof bolting, is described in this paper. The model is event-oriented; that is, the status of the system is updated at the occurrence of an event. All event or activity times, including failure and repair of equipment, are treated as stochastic variables. A location dimension, in addition to the time dimension, is used, allowing the simulation of systems with a number of stopes or faces. To aid the user in determining the efficiency of his system, the model provides several reports. An event or activity report gives the frequency of occurrence, total active time, and cumulative delay statistics for each event. An equipment report delineates the availability and utilization of all equipment. A production report provides information on various performance measures such as tons produced and holes drilled. The cost report gives the cost of various elements in the system. Operating data from an actual mining situation were used in validating the model. In addition to the description of the model, examples of simulation experiments which were performed on a room-and-pillar mine system are given. Use of the model to determine methods for improving the efficiency of the system is discussed.

Jan 1, 1976

By W. S. Landis

IN brief, this is the story of an attempt to Americanize a process originally developed in Europe. The story will be recited in two sections, the first dealing with the process as developed by the European engineers; the second containing the improvements and modifications of American origin, together with some details of the operating results of the unit as finally assembled. Developments in other directions in this same field have not, up to the present, pointed out an economic future for the process, therefore our record here is largely a report of development progress. Whether some particularly favorable location will be found at some future time for a commercial installation cannot as yet be fore-told. The project is now at a standstill. The peculiar tools of the electrometallurgist should be of great interest to the zinc smelter. The low thermal efficiency of the zinc retort, its comparatively small-scale unit and its intermittent cycle as it stood in 1925, should make this art a particularly fertile field for the electric fur-nace. Yet in spite of years of work recorded in volumes of literature, and an expenditure of large sums of money, there is not a single electrothermic zinc smelter operating anywhere in the world. In this industry the electric furnace plays only a secondary part today.

Jan 1, 1936

"In the spring of 1927, six members of the American Institute of Mining and Metallurgical Engineers met for dinner at the Chemists' Club in New York to discuss the possibility of setting up a committee within the Institute to further the current interest in the science of steelmaking. Attention' to this subject had been crystallized by a symposium held by the Faraday Society in 1925. ' After a prolonged discussion, ranging from thermodynamics to slag conditioning, it was decided to approach the Institute with the request that a standing committee on "The Physical Chemistry of Steel Making" be set up. This committee proposed to promote scientific and practical papers on the subject, and was designed to cooperate with the Open Hearth Committee of the Institute in bringing scientific developments to the attention of open-hearth operators throughout the country... . "As the life of the [Physical Chemistry of Steelmaking] Committee lengthened and general interest in the technical phases of steelmaking grew, it became evident that there was a distinct need for a book that might serve the open-hearth interests to better advantage than standard texts whose scope is necessarily wide and whose detailed exposition of the open-hearth process is, therefore, somewhat limited. With this thought in mind, the Committee, after some years of consideration and debate, embarked on the venture of writing a manuscript on `Basic Open Hearth Steelmaking'." The foregoing paragraphs, taken from the introduction by C. H. Herty, Jr. to the first edition, well describe the circumstances which led to the publication of "Basic Open Hearth Steelmaking" in the spring of 1944. The book consisted of nineteen chapters contributed by twenty-three authors and edited by the staff of Alloys of Iron Research and T. S. Washburn, B. M. Larsen, and J. S. Marsh with Frank T. Sisco as consulting editor. The Engineering Foundation and the Open Hearth Steel Committee of the Iron and Steel Division, AIME, made financial grants; steel companies and other organizations supported the publication by contributing time and expenses of staff members in their capacity as authors or editors. The volume was sponsored by the Seeley W. Mudd Memorial Fund and appeared under the

Jan 1, 1951

By Joseph C. Mead, James R. Cudworth

THE Birmingham district of Alabama has utilized the slag from its blast furnaces consistently since the earliest development of the slag industry. Today there are producers of slag cement who started business in 1900, and who have, under a progressive policy, expanded the number of their products to meet present demands. There are producers of slag aggregates and other crushed slag products who have been successful for periods of over thirty years. There are at the present two companies, Cheney Lime and Cement Co. and the Southern Cement Co., manufacturing puzzolan cement; two companies, Birmingham Slag Co. and Woodstock Slag Co., making slag aggregates and by-products; one company, Tennessee Coal, Iron and Railway Co., a subsidiary of the U. S. Steel Corporation, producing ground open-hearth basic slag for soil conditioning. Two companies, the Sloss Sheffield Steel and Iron Co. and the Woodstock Slag Co., make slag concrete in ready-mix plants and one company, the Superock Company, manufactures fine and coarse slag aggregates under a new granulation process. No Portland cement is made with slag as an ingredient, because dolomite is used so extensively as a blast-furnace flux that the magnesium content of the slag is excessive. Sources Of Slag In the Birmingham district there are 22 blast furnaces, of which the majority are in blast. The present production is 165,000 tons of pig iron monthly; the production in 1935 was 1,297,960 gross tons1. There are also two blast furnaces at Gadsden and one ferroalloy electric furnace at Anniston. From these two sources is obtained slag to approximately 1.1 tons per ton of pig iron.

Jan 1, 1937

Z. W. Bartlett, J. C. Carrington, H. C. Petersen and K. T. Price were elected vice-presidents of the Freeport Sulphur Co. Blandford C. Burgess was transferred on January 1 to the new Defense Materials Procurement Agency as strategic materials specialist. In May the Region III headquarters of this organization was moved to London. L. C. Campbell was elected president of National Coal Assn. Mr. Campbell, who has been a member of the National's Board of Directors and Executive Committee for many years, is vice-president of the Coal Div. of the Eastern Gas & Fuel Associates and in charge of their extensive mining operations in West Virginia, Pennsylvania and Kentucky. Vern H. Christoph has been transferred to Panama Canal Co., Marine Bureau, Navigation Division, Port Captains Office, as an admeasurer at Cristobal, Canal Zone. Eugene Cline, recently graduated from the University of Kentucky, has been employed by Pond Creek Pocahontas Coal Co., at Evanston, Ky. Sanford S. Cole, assistant manager of research at the Titanium div. of National Lead Co., received the Alumni Citation from his alma mater, Alfred University, Alfred, N. Y. This was in recognition of outstanding achievements and services in the field of ceramics which have brought honor to the institution. U. K. Custred, recently graduated from University of Kentucky, and may be reached now at Box 87, Monterey, Tenn. Robert E. Dwyer, executive vice-president of Anaconda since 1940, was recently elected president of this company and its subsidiaries, Chile Copper Co., Chile Exploration Co., and Andes Copper Mining Co. As president, Mr. Dwyer succeeds the late William H. Hoover who died in Butte, Mont.

Jan 1, 1952

By A. J. Lanea

INDUSTRIAL MEDICINE bids fair to become one of the most important and highly developed branches of medical science. Mining companies, even in remote districts, have developed large and efficient medical organizations that comprise the best types of physicians and surgeons. Not infrequently, however, company medical departments have been influenced too much by local conditions-including the compensation laws, which differ widely in the various states. The possibilities of industrial medicine are just beginning to be generally understood, and the variations in the organization and aims of medical departments of mining companies are no more pronounced than in industry as a whole. The industrial physician should be as much a part of the organization as any other official and he should know intimately the various types and phases of work in the plant and should look at his work from the viewpoint of the needs and requirements of his particular industry and company. He should not-be on the outside looking in, but on the inside, working hand in hand with the superintendent, manager, foremen, employment director, safety director, and anybody else with whom in his work he might associate. In any industry it is essential that the doctor be-familiar with working conditions. The mine doctor who never goes underground must remain ignorant of the factors causing many of the disorders he treats as well as miss the best opportunity of gaining the respect and cooperation of the men he. serves. If the mine doctor remains unfamiliar with underground working conditions he bars himself from valuable preventive medical work. It is estimated that the time lost by industrial workers, as a whole, because of illness is about four times as great as that lost because of accidents. While the effort to determine the responsibility of working conditions for illness is often futile, there is a wide field, both for study and practice, in the lessening of sickness among industrial workers. The first step in this direction must be a knowledge of the factors involved.

Jan 2, 1921

By R. L. Smith, J. L. Rutherford

ALTHOUGH considerable effort has been devoted toward the determination of the mechanical properties of pure metals, it is extremely difficult to compare the results of such work. This is because of differences in method and type of test, grain size, heat treatment, and purity of material. There is very little information on the properties of most of the high melting point reactive metals with purities greater than 99.9 pct. Previous evidence concerning the tensile properties of unalloyed metals show that: body-centered-cubic metals are brittle at low temperatures; face-centered-cubic metals remain ductile; some hexagonal metals remain ductile, others become brittle. It may be that traces of impurities decrease the low temperature ductility of the body-centered-cubic lattice. This would suppose that a body-centered-cubic lattice free from impurities would exhibit nearly the same ductility as a face-centered-cubic structure. The present investigation has been an evaluation of the tensile properties of zone refined iron in order to determine whether higher purity material than that previously evaluated behaves differently. Experimental Procedure In this investigation, high purity iron was zone purified using the floating zone method.' The starting stock was obtained from two sources. The first,

Jan 1, 1958

By G. J. Saulnier, K. E. Goddard

The US Geological Survey has developed mathematical modeling techniques to assess potential impacts on the hydrologic system resulting from mining of coal and oil shale in northwestern Colorado. Potential impacts of oil shale mining on groundwater hydrology have been simulated using a quasi-three-dimensional, finite-difference model. The model has been used to simulate hypothetical mine dewatering operations at two proposed oil shale mines. Dissolved-solids distribution and solute transport were simulated with a three-dimensional, finite-difference model that was used to evaluate the effects of flooding in hypothetical abandoned mines. The potential impacts of coal and oil shale mining on water-sheds were investigated using a digital watershed model. This deterministic physical-process model predicts responses of the hydrologic system to modifications resulting from mining in basins having snow as the major source of runoff and recharge. Potential impacts of coal development on surface water quality were investigated using a river quality assessment model. The models developed by the US Geological Survey have been useful in defining the potential effects of mining in northwestern Colorado. They are an important first step in analyzing the existing data base and in predicting impacts and new data needs. The models may not be totally applicable on the local scale but are very meaningful on the regional level.

Jan 1, 1983

By J. A. Snyder, W. L. Finlay

SEVERAL notable studies of the effects of sub- stitutional solutes have been reported. Outstanding among these for its elucidation of general principles, is the summarized work of Hume-Rothery and coworkers.1 For a systematic study of the effects of substitutional solutes on the mechanical properties of the solvent lattice, the work of Brick, Martin, and Angier² on copper; of Frye and coworkers³,4,5 on copper and silver; and of Lacy and Gensamer6 and of Austin7 on iron may be mentioned. Titanium is one of the few elements offering the possibility of a similar study of interstitial solutes since, unlike most metallic elements, it exhibits extended solid solubility for most of the interstitial solutes—hydrogen, boron, nitrogen, oxygen, and carbon. This paper reports a survey of the effects of dilute solutions of nitrogen, oxygen, and carbon on the mechanical properties of high-purity alpha titanium. Previous Work: Van Arkel and De Boer showed" that high purity titanium was quite ductile and De Boer, Burgers and Fast established".' that not only were oxygen and nitrogen very soluble in solid titanium but that, long before the limit of solid solubility of either had been reached, these interstitial solutes rendered the metal brittle. Their electrical resistance data as a function of

Jan 1, 1951

By R. H. Hopkins, R. W. Kraft

X-ray and metallographic analysis reveal that the preferred cryslallograPhic relationships in direc-tionally solid~fied Pb-Sn eutectic specimens can be stated: interface growth direction, Experiments in which tin single-crystal seeds were used to nucleate the eutectic demonstrate that the normal lamellar structure observed at steady state can be forced to break down initially to a semide-generate structure when the crystallograPhic direction of the tin seed does not lie within the preferred eutectic interface plane. A normal structure eventually develops by preferred grain growth. X-ray topo-graphs and rocking curves substantiate that the perfection of eutectic samples increases as growth proceeds until steady-state conditions prevail. RECENT years have seen substantial progress made in the understanding of eutectic solidification through both intensive theoretical1'' and experimental investigations (see Ref. 7 for a review and extensive bibliography of both aspects). Several important observations concerning the nucleation and growth aspects of binary eutectic solidification have been brought to light. Briefly some of these include the nonrecipro-cal nucleation of one phase upon another,'j9 the tendency for a specific low-index direction of one or both phases of the eutectic to be aligned in the growth direction during unidirectional solidification,'0711 and the production of lamellar microstructures having a preferred interface plane between "11-13 phases. Questions quite naturally arise as to the mechanism by which preferred grain growth evolves during eutectic solidification and what relationships (if any) connect the initial nucleation of one phase upon another with the preferred growth directions and interface planes observed after a few centimeters of growth in many systems. This study was initiated in an attempt to answer these questions. An experiment was devised in which both the nucleation and growth steps in the crystallization of a binary eutectic, Pb-Sn, could be correlated with subsequently developed eutectic morphology and crystallography. This was accomplished by nucleating the eutectic upon a tin single crystal seed and then causing the eutectic to grow from the seed by directional freezing. The morphology of the structures produced in this manner was then monitored metallographically and the orientation relationships and substructural perfection determined by X-ray analysis. The information thus ob- tained was correlated to the growth history of the samples. EXPERIMENTAL DETAILS The eutectic of composition 38.1 wt pct Pb and 61.9 wt pct sn14 was prepared by accurately weighing lead and tin of 99.999+ (from ASARCO and Lytess Metals and Chemicals, respectively), melting in a clean Pyrex beaker under an argon blanket, and casting into the proper crucible for resolidification as described below. Tin seeds were grown by the method of ~halmers," saw-cut, oriented by the Laue method, and soldered to the pull rod of the Czochralski puller. All seeds were given a final electropolishing (to assure the removal of any deformed material from the cutting operation) and acetone degreasing immediately prior to the nucleation experiment in which they were to be used. Eutectic samples were unidirectionally solidified in a horizontal graphite boat1' or by pulling from the melt16 with tin (or graphite) seeds. A flowing argon atmosphere was employed in all experiments and growth rates and temperature gradients, constant for a given run, varied from 2 to 4 cm per hr and 8" to 15°C per cm over the course of all the experi-

Jan 1, 1969

By G. J. Heuer, J. N. Dew, G. C. Clark

The effect on well behavior of partial permeability barriers, changes in producing rates and well spacings have been calculated through use of a radial, unsteady-state, two-phase-flow mathematical model. This model allows for variations in permeabilities and porosities with distance from the wellbore. The numerical methods necessary to solve the problem require use of a highspeed digital computer, in this case an IBM 704. In each instance, pressure and saturation gradients, gas-oil ratios and recoveries around a well producing by solution-gas drive have been calculated as a function of time and distance from the wellbore. Comparisons are made to show the effect of changes in producing rate and of varying permeability near the wellbore and out in the formation on the production and pressure history of the well. The effect of different well spacings on producing rate and ultimate recovery is considered. Although the mathematical description of the reservoir is simplified in comparison to an actual reservoir, the results do give some insight into the difficult problem of spacing and proration in a heterogeneous solution-gas-drive reservoir. Results show that for the cases considered spacing has little effect on ultimate recovery and that permeability barriers removed from the well decrease producing rate for a period of time but have only a small effect on ultimate production. INTRODUCTION The effect of spacing and producing rate on the production characteristics and ultimate recovery of a well producing by the solution-gas-drive mechanism have been topics of interest to the oil industry for many years and the subject of many hearings before state regulatory bodies. The problem is very complicated because of the difficulty of simulating in the laboratory a reservoir producing by the solution-gas-drive mechanism under anything like normal field conditions. This paper gives the initial results of a study aimed at determining the effect of these factors on production from reservoirs simulated by a mathematical model. Two-phase, unsteady-state equations are used to calculate pressures, saturations, and rates of oil and gas flow as a function of time and distance from the wellbore. The model is radial, and reservoir properties may be varied with distance from the wellbore. A decrease in permeability at a given distance results in a low-permeability ring concentric with the wellbore through which all the fluids from more distant portions of the reservoir must flow. The current mathematical model allows for variation of permeability, porosity and saturations as a function of distance from the well. Any desired drainage radius for the well may be selected. Drainage radii of 745 and 1,053 ft, which correspond to 40- and 80-acre spacing, were chosen for the calculations which follow. A large amount of the input data has been held constant. No investigation was made into the effect of changes in fluid properties and relative permeability characteristics on oil and gas production behavior. Fluid properties and relative permeabilities are essentially those of the White Mesa portion of the Greater Aneth area in southeastern Utah. A recently concluded hearing before the Utah Oil and Gas Conservation Commission to determine spacing for the field aroused interest in the possible effect of permeability constrictions located some distance from the well on production and recovery. This interest stimulated the present study. In this paper, no attempt has been made to simulate any field production characteristics exactly. Only the solution-gas-drive mechanism has been investigated, and production by liquid expansion has not been considered. This investigation is exploratory in nature but does give some insight into the problems of spacing and proration in a solution-gas-drive field having permeability variations. THE MATHEMATICAL MODEL The mathematical model is similar to that proposed by West, Garvin and Sheldon.' Approximately the same techniques have been used in arriving at a solution. The equations are nonlinear, partial differential equations which have been known for some time. The particular equations used for this study neglect the effects of capillary pressure and gravitational forces. The advent of modern digital computing equipment has made their solution practical. Basically, the method solves for pressure, saturations, and oil and gas flow rates as a function of distance and time. In our model, distance to the

By T&apos Kê, ing-sui

INTRODUCTION ACCORDING to the classical theory of elasticity, the elastic portion of the stress-strain curve is represented by a straight line. Such a representation implies that there is a linear relationship between strain and stress and also that strain is a single-valued function of stress and vice versa. Actually, such a one-to-one correspondence between strain and stress does not exist in real metals. A well-known example is the elastic after-effect on unloading. Another familiar example is damping or internal friction, that is, the dissipation of energy attending vibration. In an extensive review of such phenomena, Zener1,2 has proposed the term "anelasticity" to denote that property of a solid in virtue of which strain is not a unique function of stress in the non-plastic region. The phenomena arising from anelasticity are called anelastic effects. The measurements on inelastic effects are, important in many fields of metals technology. Thus, in precise instruments such as watch springs, difficulties often arise from the slight dimensional changes after fabrication. The internal friction or damping capacity of metals is often an important factor in deciding whether they are appropriate for instruments in which there are accompanying vibrations.' However, for metal scientists, the study of anelastic effects furnishes a powerful tool for understanding many properties of metals in terms of their microstructures or atomic interactions. In order to utilize the anelastic measurements to their fullest extent for acquiring such information, the experimental studies of anelasticity must be interpreted by appropriate mathematical analysis. For a great many problems, however, the necessary information often can be obtained by general qualitative arguments. From the definition of anelasticity, any physical changes occurring in a specimen as a result of the applied stress will cause anelastic effects if such physical changes are accompanied by a delayed change of elastic strain. Under these circumstances, we have the condition that strain lags behind the stress. We may mention the stress-induced transportation phenomena as examples. These include the stress-induced thermal diffusion," the stress-induced diffusion of particles,8-12. and the stress-induced viscous slip along the microelements in metals.12-15 The differential equations describing the microscopic mechanism in these phenomena lead to relations in which stress is linear with respect to strain (and/or their derivatives). Thus if we can - demonstrate that the superposition principle is valid under the circumstances in which the anelastic effects are observed, we would expect in. the macroscopic relation a linear relationship between stress and strain and their derivatives. This report is to describe a number of anelastic effects observed in alpha-iron, and an attempt is made to derive valuable information from a critical study of these

Jan 1, 1948