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By F. W. Glaser, W. Ivanick

A pressure-sintering method was used to produce binder-free and very dense TiC specimens. Some physical properties of these TIC bodies were determined and found to compare favorably with those of certain cemented Tic grades. It was also observed that the hot transverse rupture strength of TiC bodies remained substantially the same regardless of the amount or type of binder material used. STUDIES of the structure and physical properties of refractory materials have been intensified recently because of the urgent need for nonstrategic materials that retain their strength at high temperatures. Research aimed at determining and improving the physical properties of cemented carbides and borides has been accelerated with a view toward possible use of such materials in connection with turbine blades, rocket nozzles, and other high temperature applications. On the hypothesis that the strength requirements in connection with some of the above applications could be met only by proper choice of cementing agents for such refractory materials, the literature describing the physical properties of borides or carbides was reviewed. However, with a few exceptions,'-" references were found only to compositions containing at least one or more auxiliary binder metals. Cobalt and nickel are among the most frequently employed cementing agents. The melting point of Tic (approximately 3250°C) and therefore the sintering temperature, at which notable densification of a cold pressed Tic powder compact could be expected in the absence of a liquid binder phase, is relatively high. The present study makes use of a high temperature, pressure-sintering procedure, recently described by one of the authors in connection with the sintering of binder-free ZrB,," to produce dense bodies of sintered Tic—free of any cementing agent. During the course of this sintering study, some physical properties of dense Tic bodies produced by this method will be discussed. Materials, Preparation of Samples, Testing Methods The procedure for the forming of Tic powder consisted of mixing graphite and TiH, powders in stoi-chiometric proportions, and heating this mixture in a H, atmosphere and carbon crucible by high frequency, to temperatures ranging between 1900° and 2100°C (3452" and 3812°F). The powdered carbide was then comminuted and screened to the desired particle size. Table I shows the chemical analysis of the two grades that were employed for the production of samples during this work. Bodies of Tic, approximately 2.5xlx0.5 cm were produced in graphite molds that were heated by direct conduction. Sintering was carried out at temperatures for time intervals ranging from approximately 0 to 30 sec under a constant pressure of about 1.3 tons per sq in. An alternate method for the production of samples consisted in cold pressing the individual Tic grades at pressures ranging from 4 to 10 tons per sq in. and sintering in a hydrogen atmosphere in graphite crucibles heated by high frequency induction. Sintering temperatures ranged from 2600° to 2900°C (4715° to 5255°F). Electrical testing was done by measuring potentiometrically the voltage drop over a length of 1.5 cm for a current of 10 amp at room temperature. Cross-sectional areas as well as densi-

Jan 1, 1953

By R. H. Winn

In this paper a heterogeneous carbonate reservoir is considered as a succession of layers of formations of radically different porosities, permeabilities, water saturations, and rock matrix types; i.e., the heterogeneity is vertical rather than radial to the wellbore. Presumably each layer is more or less homogeneous. To determine the "net oil in place" in this reservoir it is desirable to know the porosity and water saturation of each layer. In addition, the section must be subdivided into that which will produce oil, that which will produce water, and that which will produce little or nothing. In numerous wells drilled in these reservoirs radioactivity surveys, guard electrode surveys, and caliper surveys have been made. These logs have been compared with core analysis data, when available, and the analysis of the surveys compared with production data. This study, still in progress, is intended to provide improved analytical techniques if such are possible. This paper is a progress report on the work. DETERMINATION OF POROSITY The neutron-gamma log has long been recognized as a measure of hydrogen concentration.1,2,3 In reservoirs that are free of clay, shale, or other hydrogen containing matrices, it has been accepted as a measure of porosity.4,5 Empirical methods to relate relative neu-tron-gamma intensity to porosity are often employed." To provide a more precise determination of porosity from the neutron-gamma log each instrument is calibrated immediately prior to each survey by a method which refers all tools to a hydrogenous cylinder. To insure stability a calibration check is made after each survey. These calibration records are printed as an integral part of the log that is recorded in standard counts per second. A detailed description of the calibration procedure is available in the literature.' The procedure employed insures that each Survey is numerically reproducible within the limits of statistical variation. To relate the standard neutron counts per second to porosity and hole size, records were made in test wells constructed of blocks of limestone. The porosities of the blocks were accurately measured and the blocks completely saturated with fresh water. Fig. 1 presents some of the results obtained in these test wells.' The lines shown in Fig. 1 were obtained by deriving an empirical equation relating the 11 points shown so that the relationship may be projected to larger and smaller hole sizes. A detailed description of the tool is available in the literature.' Field tests indicate that the tool is adjacent to the wall of the hole most of the time when the surveys are made in uncased holes drilled with saline muds. In this circumstance porosity may be calculated from Fig. 1 if the hole size is known. When fresh muds that form thick mud cakes are employed, the centralizing effect of the mud cake must be considered and the porosity determination is less reliable. In cased holes the combined effect of variations in hole diameter and the unknown eccentricity of the casing in the hole may make porosity determinations extremely unreliable. In any event, an accurate knowledge of hole size is essen-

Jan 1, 1958

By J. R. Kyte, L. A. Rapoport, R. J. Stanclift, S. C. Stephan

Experimental studies covering a wide range of core materials and fluid properties have been conducted to determine the mechanism of oil displacement by water in a partially gas-saturated porous medium. In all instances, the presence of a gas phase was found to have a beneficial effect in reducing residual oil saturations. The practical significance of this benefit is discussed, and a simplified procedure is outlined for evaluating the effects of free gas on water flooding by means of short core tests. INTRODUCTION In addition to oil and water, reservoirs subjected to water flooding frequently contain, also, a gas phase. Common engineering procedures account for the presence of this "free gas" only from the viewpoint of volumetric balance, implying that the only role of the gas consists of providing "fill up" space. It is usually visualized that during the initial stages of the water invasion, the oil, moving ahead of the water, displaces part of the gas and that subsequently the remaining portion of the gas phase is totally compressed and dissolved in the advancing oil bank. Thus, consideration of a two-phase, water-oil flooding mechanism supplies an adequate basis for predictions of oil recovery if the pressure build-up caused by the flood is sufficiently great, so as to reduce the free gas saturation to a negligible value in any portion of the reservoir by the time that portion is reached by the advancing flood water. In many in- stances, however, waterflooding operations are carried out when the reservoir pressure is still relatively high SO that the pressure build-up associated with the water flood may not result in complete dissipation of the gas phase. Under such circumstances it is necessary to ascertain whether or not the presence of free gas has an effect on waterflood behavior and, if so, to account for any such effect in the evaluation of field operations. The difficulties encountered in attempting to arrive at a comprehensive picture of the displacement mechanism of oil by water in the presence of free gas stem from the fact that most of the published data on this subject were obtained under conditions that were either not clearly representative of those existing in a reservoir or not sufficiently controlled to permit evaluation of the effects specifically caused by the gas phase. Some of the most precise data found in the literature were obtained in tests using a "static" gas phase created prior to each water flood by circulating oil through partly gas-saturated cores until a "trapped," residual gas saturation was established throughout the system.' Other investigations were conducted under more representative conditions where the gas phase was free to move during the water flood: but in most cases the results of these tests were obscured by auxiliary phenomena which arise from the compressibility and solubility of the gas and preclude quantitative conclusions.2,3,4 Prior to water flooding, a reservoir usually contains oil and gas, distributed in a manner in which both are free to move. Thus, the principal objective of the present studies was to determine the type of displacement mechanism occurring when water invades a porous medium containing oil and a "mobile" gas phase. Further-

Jan 1, 1957

By J. Wade Watkins, E. S. Mardock

The accurate evaluation of reservoir-performance characteristics in the secondary recovery of petroleum by water flooding requires use of a water tracer that may be injected into water-input wells and detected at oil-production wells to supplement data obtained from core analyses, wellhead tests, and subsurface measurements. Radioactive iodine has been used successfully as a water tracer in field tests to determine: (I) relative rates and patterns of flow of injected water between water-input and oil-production wells and (2) zones of excessive water entry into oil-production wells. Laboratory evaluations of potential water tracers, previous tracer studies, the value of using a radioactive tracer, general field procedures, and the use of surface and subsurface instruments for the detection of the emitted gamma radiation, are summarized. Data from the field tests are presented graphically and discussed in detail. It is concluded that the radioactive-tracer method, using radioactive iodine, may be used successfully to measure either the relative rates and patterns of flow or zones of excessive water entry into wells under conditions of comparatively rapid transit time between wells. INTRODUCTION Extensive use is made of data obtained from core analyses, wellhead tests, fluid characteristics, and subsurface measurements in evaluating the sweep efficiency of water injected into oil sands for the recovery of oil. Theoretical flow rates and patterns may be calculated from those data using radial-flow formulas, if it is assumed that the physical conditions in the productive formation are homogeneous. Unfortunately, homogeneous conditions rarely, if ever, exist in oil-productive formations. The use of a tracer that may be injected into an oil sand and detected quantitatively, or even qualitatively, at offsetting oil-production wells provides basic data that may be used in determining more accurately the subsurface rates and patterns of flow of injected water between wells than is possible by theoretical calculations based on assumed conditions. Consideration of the data obtained by using a water tracer assists in the application of remedial measures to water-input wells, such as plugging of channels, or selective plugging of highly permeable zones, thereby effecting a more uniform flood and a greater ultimate oil recovery. A water tracer should have the following characteristics: (1) low adsorption on solid reservoir material; (2) high solubility in water; (3) low or negligible solubility in crude petroleum; (4) a wide range of solubility of compounds that may be formed by chemical reactions with ions present in reservoir rocks or waters; (5) high detectability in low concentrations by portable apparatus; and (6) general availability at low cost. Additional desirable characteristics are that the tracer should be nonhazardous in nature under normal working conditions and quantitatively detectable in the well bore, as well as at the surface. Review of Previous Tracer Studies The need for a water tracer has been recognized for many years. As far back as 1906, Dole1 described the use of fluorescein in flow-rate studies made in France in 1901. In 1921, Ambrose" discussed in detail the use of organic and inorganic dyes, chlorides, nitrates, and other anions, lithium salts, and the Slichter electrical

Jan 1, 1955

By D. J. Carney, E. C. Rudolphy

Large macroscopic nonmetallic inclusions were related to altered fireclay refractories by chemical and microscopic means. Pouring refractories are discussed as a source of these large inclusions. Nozzles and wells are major contributors. Use of alkali and titania contents as tracers is described. Recommendations are offered to minimize the sources of inclusions from pouring refractories. IN any attempt to improve the cleanliness of plain carbon and alloy steels, consideration must be given not only to the proper deoxidation practice to minimize inclusions, but also to sources of inclusions from pouring refractories. In some cases, the inclusions resulting from deoxidation may be minor in amount, yet a relatively dirty steel may be produced as a result of improper care in the pouring practices for the steel. The number of studies of inclusions resulting from pouring refractories has increased recently and some excellent reports on this subject have already been published.'4 Some of these reports were reviewed briefly in a companion paper by M. P. Fedock.5 Mr. Fedock's contribution is a fine addition to the studies necessary to improve steel cleanliness for the ultimate benefit of all steel producers and consumers. In the interest of constantly improving cleanliness, the authors have been actively engaged for the past two years in experimentation to determine more closely the sources of inclusions in steel. One phase of this work was associated with efforts to define more closely the sources of macroscopic inclusions which have been experienced on occasional heats. The term "macroscopic inclusions" is defined in general as those inclusions which are visible to the naked eye or at low magnifications of the order of less than X25. These inclusions sometimes can be seen in the macro-etch tests of billets and slabs. This report summarizes a few of the field experiments and laboratory studies conducted at the South Works of the United States Steel Corp., which were made regarding nozzles, wells, and ingot scums, as well as inclusions occurring in steel products. The data in the present study, together with the data of Mr. Fedock concerning ladle erosion, should be of value in regard to future studies of inclusions arising from pouring refractories. The knowledge gained as a result of data collected thus far at South Works has been helpful in improving the cleanliness of the products and in pointing the way toward further improvements. Similarity of Large Inclusions to Refractories and Altered Refractories In the routine inspection of billet etch tests, occasional inclusions visible to the naked eye have been observed. These large inclusions most frequently occur near the top of the ingot and near the billet surface. When such material was encountered, careful examinations were made in an attempt to determine the origin of these inclusions. In a relatively few cases, examination revealed that the material was unaltered fireclay refractory of a type similar to that used for hot-top material, with only the surface of the inclusions having an altered appearance under the microscope. However, the great majority of these inclusions were completely altered-refractory material. The term "altered refractory" is defined

Jan 1, 1955

MEMBERS, JUNIOR MEMBERS, ASSOCIATES AND JUNIOR ASSOCIATES LIST OF MEMBERS ALPHABETICALLY ARRANGED EXPLANATION OF SYMBOLS ** Junior Member. t Associate. || Junior Associate. Members are not marked. Capital letters signify Honorary membership. Student Associate and Rocky Mountain members on pages 165-167. Abadilla. Quirico A Catanawan. Tayabas, P. I. Abbey. Robert Graham. District Mgr The W. W. Sly Mfn. Co., 60 Church St New York. N. Y. Abbott. A. N Mines Supt Mazapil Copper Co Ltd . .Conception del Oro. Zac., Mexico. Abbott. Ckrence E Mgr Mines & Quarries, Tenn. Coal. Iron & R. R. Co 1242 Brown Marx Bldg Birminrham. Ala. Abbott. Louie Benjamin. Chief Enar Consolidation Coal Co Elkhorn Div .Jenkins, KY. Abeel. Gsorge H Jr., Cons. Min. Enar .Box 427. Santa Monica. Cal. Abel. Albert E Asst. to Pres Valley Mould & Iron Corp Hubbard. Ohio. Abel. Raymond L. Asst. Prof., Dept. of Pet. Refin Univ. of Pittsburgh Pittsburgh. Pa. Abernathy. George Elmer. Prof. of Geol. & Min Kansas State Teachers College. Pittsburg. Kans. IlAbernethy. D. Carl, Jr. Min. Engr Hudson Coal Co .Scranton. Pa. Abey, Hiroshi. Min. & Met. Engr., Min. & Met. Dept., The Higher Technical School, Osaka. Japan. tAbarn, Robert H Instructor in Met Harvard University Cambridge, Mass tAbozeid,Mahmood. Pet. Production E r . . Marland Oil Co. Ponca City, Okla. Abraham. Arthur W Geol., Richfield Oil Co Box 788. Bakersfield, Cal. Abraham, W. E. V Member, Staff of Burmah Oil Co Ltd. Nyaunghla. Upper Burmz, India. Abrahams. Alexander I Gen'l Mgr., Racon Electrical Co Slough, Bucks England. tAbrahammn. C. W Min. Engr The Mond Nickel Co Ltd . Coniston, Ont Canada. IlAbmn. Guy W., Asst. Metallographist, Youngstown Sheet & Tube Co., Research Dept., Youngstown. Ohio. Abstein. Henry T., Engr. & Mgr Profile-Tamarack Mines Co . .Yellow Pine, Idaho. tAcker. E. O'C Met I28 East Washington Lane. Germantown, Philadelphia. Pa. Ackerman. D. E Met. Research Lab International Nickel Co Inc Bayonne. N. J. tAbckerman. Ernest R Pres., Lawrence Portland Cement Co . .Plainfield. Union Co N. J. ||Ackerman. George F Jr. Min. Engr El Potosi Min. Co. .Apt. 13. Chihuahua, Chih Mexico. Acres, T. H Geol. Dept Valuation & Pet. Engr., Richfield Oil Co. 655 S. Flower St Los Angeles. Cal. Adachi. Jinzoo Address Wanted. Adair. Arthur C Valuation Enar., Internal Revenue. Treasury Dept., Washington, D. C. Adam. John. Min. Ennr., The Zinc Corp. Ltd., Box 4 C. Broken Hill, N. S. W Australia. Adami. Arthur E V. P Montana State School of Mines.Butte, Mont. Adami. Charles J Min. Ensr St. Joseph Lead Co 4540 Lindel Blvd., St. Louis, Mo. Adams. C. W.729 South Normandie St LaGranada Apt Los Angeles, Cal. Adams. Cmyler Geerwwd. Minn. Adams. F. J Gen'l Anent. Gulf Production & Pipa Line Cos .Fort Worth. Tex. ADAMS. FRANK DAWSON. Logan Prof. of Geology and Dean, Faculty of Applied Science, McGill Univ Montreal. Que Canada. Adama, Gale L Research Enar., General Pet. Corp. of California, Higgins Bldg Los Angeles. Cal. Adams. George I, Prof. of Geol. & Mineralogy Univ. of Alabama, Tuscaloosa, Ala. Adams. H. H Cons. Geol Room 416, W. T. Waagoner Bldg Fort Worth. Tex. Adams, Henry. Cons. Min. Ennr 1050 Edgewood Ave., Plainfield, N. J. Adams, Henry H.285 Madison Ave., New York. N. Y. Adams, Henry Farnum. Engr., Charge. Experimental Work. Inspiration Concentrator, Inspiration Cons. Copper Co Box 354. Inspiration. Ariz. Adams. Huntington. Min. Enar I41 Broadway, New York. N. Y. Mama, Leland D., V. P., Leslie-California Salt Co 166 Montgomery St., San Francisco, Cal. Adams, Louis W., Illinois Steel Co .Gary. Ind.

Jan 1, 1929

By R. M. Hays

At the present time, oxidized taconite and semitaconite are not processed on the Mesabi Range except in vely limited tonnages. However, it is estimated that by 1990 shipments from the Range will approach 75 million tons of iron ore per year. To achieve this and future production, either additional magnetic taconite reserves must be proven or oxidized taconite and semitaconite must be processed. One beneficiation process which uses high-intensity magnetic separation and flotation for concentrating oxidized taconite and semitaconite is described. Detailed metallurgical results are given and an economic evaluation of the process is presented with comparison to other processes. The results of the present study indicate that the high-intensity magnetic separation and flotation process appears nearer commercialization for the processing of Mesabi Range semitaconite. The disadvantages of the process are nearer solution and are being solved by well-defined programs. During the twentieth century, the Mesabi Range in northeastern Minnesota has been the main source of iron ore for American steel mills. The Mesabi Range, which is about 120 miles long and up to 3 miles wide, is the pre-glacial outcrop of a group of sedimentary iron-bearing rocks known as the Biwabik formation. The formation, which is 200 to 650 ft thick and dips 50 to 10° to the southeast, is divided into four stratigraphic units. From top to bottom, these are the Upper Slaty, Upper Cherty, Lower Slaty, and Lower Cherty. Since its deposition in Precambrian time, most of the original Biwabik formation has been subject to alteration. Thus, although the iron content of the original formation was quite uniform, major variations in mineral composition now occur both laterally along the length of the formation and vertically within its units. Details of the mineralogical variations in the Biwabik formation have been described by Wolff,' Gruner, 2 and White.3 The unaltered portion of the Biwabik formation includes the magnetite taconites which are being commercially processed by Reserve Mining, Erie Mining, Eveleth Taconite, National Steel, Butler Taconite, and U.S. Steel. These six operations have a capacity of 32 million tons of iron ore pellets per year and have produced approximately 170milion tons of pellets since 1956. Capacity for another 30 million tons of pellets per year is being considered by the industry for the next ten years. This increase will be obtained by constructing new plants and by expanding present operations. Thus, by ! 978, it is estimated that approximately 60 million tons of iron ore vellets will be produced each vear from the magnetite taconites of the Biwabik formation. The portions of the Biwabik formation subjected to intense alteration resulted in direct shipping, wash, and heavy-media ores. Since 1892, 1.8 billion tons of direct shipping ore have been shipped from the Mesabi Range. This ore has been the major source of iron ore for American steel mills. In 1967, about 11 million tons of direct shipping ore and 13 million tons of wash, jig, heavy-media, and other gravity concentrates were shipped from the Mesabi Range.4 These products generally have poorer physical and chemical properties than the iron pellets produced from magnetic taconite. It is predicted that the shipment of these materials will decrease from 24 million tons in 1967 to 6 to 8 million tons in 1975.' This decrease will

Jan 1, 1970

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By J. J. Gilvarry, B. H. Bergstorm

The first part of this paper describes a new approach to the problem of energy relationships in fracture and comminution. The basic theoretical method used (as contrasted to previous empirical or semi-empirical approaches) is an attempt to verify or disprove the hypothesis of von Rittinger, In the second part of the paper, theoretical conclusions for the three headings of single fracture, plural fracture, and comminution are tested. Agreement between theory and experimental results is demonstrated. The classical hypotheses on the energy relationship in brittle fracture are those of von Rittinger-that the energy required is proportional to the new surface formed— and the alternative one of Kick.' Over the years, repeated attempts have been made to discriminate experimentally between the two assumptions, or to replace both of them, as has been done by Bond? However, no semblance of agreement seems to exist among different investigators. This paper is the first in a series essaying a new approach to the entire problem of energy relationships in fracture and comminution. The purpose of this program of research is to verify (or disprove) the hypothesis of von Rittinger. In contrast to previous empirical or semi-empirical approaches to the problem, the basic method adopted is theoretical. The prime aim is to determine the distribution function for fragment size theoretically and to verify the predicted distribution experimentally. This approach should make possible determination of the total surface of the particles by integration over the corresponding distribution function; one may hope that this direct procedure will yield more definitive results than use of gas adsorption or other methods. The surface area so obtained can then be compared with experimental energies, as obtained by Bergstrom, Sollenberger, and Mitchell,4 for example. It is convenient to distinguish between single fratture, plural fracture, and comminution. Single fracture of a brittle solid is defined as fracture by an external stress system which is removed instantly and permanently when fracture is initiated. Plural fracture consists of single fracture of the original specimen, followed by a sequence of only a few secondary fractures; comminution differs in that the sequence of secondary fractures consists of a large number of repetitive steps. For single fracture, Gilvarrys has given a rigorous derivation of the proper distribution function for fragment size, based on a closely defined physical model and deduced strictly by the laws of probability. Gilvarry and Bergstrome have compared the predictions of the theory with experiment, and have found excellent agreement. The prior work of Gilvarry and of Gilvarry and Bergstrom considers only single and plural fracture. The purpose of the present paper is to extend the discussion to the case of comminution. For prefatory purposes, the theory of Gilvarry for single fracture will be outlined. The considerations will then be applied to the cases of plural fracture and comminution. SINGLE FRACTURE The derivation is based on the Poisson law.7 For Points distributed with mean density y over a domain, this law states that the probability p(t)dt of one point lying in the range t to t + dt with none in the interval 0 to Ms p(t)dt = ye-yt dt. For this distribution to be valid, it is necessary and sufficient that the points be distributed at random, individually and collectively in the sense of ~~~.7 The former qualification requires that the position of One Point be independent of another, and the latter implies that the probability of a region containing a

Jan 1, 1961

By B. S. Gottfried

A generalized mathematical model is presented, which describes the thermal recovery of oil in linear systems with convective external heat loss. Three-phase fluid flow, conduction-convection heat transfer, chemical reaction between oxygen and oil and aqueous phase change are included, making the model applicable to a variety of thermal recovery processes. The complexity of the model requires that numerical solutions be obtained with a digital computer. The numerical approximations of the partial differential equations are presented and the algorithm is discussed in detail. The analysis is applied to the detailed simulation of a forward-combustion laboratory tube experiment. The results of the simulation exhibit with reasonable accuracy all of the principal thermal and bydrodynamic characteristics observed in the laboratory (i.e., the propagation of a combustion zone, a steam plateau, and oil and water banks). Numerical variations in the parameters appearing in the external heat-loss term, the aqueous phase-change term, and the Arrhenius combustion term are examined, and their effects on the predicted temperature profiles, oil and water production histories, and the air-oil ratio are presented. In spite of an oversimplification in the chemical reaction mechanism and the considerable computer time required to obtain solutions, the model represents a major advance in the ability to simulate the phenomena observed in thermal recovery experiments. INTRODUCTION Thermal oil recovery refers to a class of recovery processes where heat is supplied to a reservoir to provide the necessary expulsive energy. This thermal energy can be supplied externally as steam or hot water, or it can be generated in situ by forward or reverse combustion. In either case, however, thermal recovery processes are charac- terized by the simultaneous flow of two or three fluid phases in a variable - temperature field, accompanied by possible chemical reaction or phase-change effects.2-5, 7- 10, 14,16-18,20-22 Although a physical understanding of the thermal recovery processes is far from complete, it is possible to construct mathematical models which describe approximately all of the principal physical and chemical phenomena. However, attempts to solve such models, even with high-speed computers, involve formidable mathematical difficulties. Consequently, theoretical solutions have been obtained only for idealized cases in which important physical phenomena are neglected. For example, consider the process of forward in situ combustion. All such theories which have been developed consider only certain aspects of the process, such as heat transfer, 2-4,8,9,l6,l8 heat transfer with phase change,10 heat transfer with chemical reaction,7 or the hydrodynamics of three-phase flow.21 A general theory including all of the above phenomena has not been developed to date. This paper presents a unified theory of thermal recovery processes in linear systems. A mathematical model is developed which explicitly includes conduction-convection heat transfer with convective external heat loss, chemical reaction between air and oil, aqueous phase change, and the hydrodynamics of three-phase flow. A system of equations is developed which can be solved numerically on a high-speed digital computer, resulting in predicted temperature, pressure, and saturation histories in space and time. The model allows a more detailed simulation of thermal recovery tube experiments than had previously been possible. THEORETICAL DEVELOPMENT Consider the linear flow of gas, water and oil in a homogeneous porous medium. Assume that the oil will react with gaseous oxygen, and that mass is transferred between the water and gas phase by evaporation or condensation. In the absence of hydrocarbon phase change, intraphase diffusion,

Jan 1, 1966

By R. Ehrlich, F. E. Crane

A consolidated porous medium is mathematically modeled by networks of irregularly shaped, interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached. 1. Relative permeability at a given saturation is everywhere independent of flow rate. 2. Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting-phase relative permeability. 3. Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity. 4. lrreducible wetting-phase saturation following unsteady-state drainage is lower than fir steady-state drainage. 5. Irreducible nonwetting-phase saturation 101lowing imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualithtiveIy verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. INTRODUCTION Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting liquid by a gas. 1-5 It has long been recognized that relative permeability depends not only on saturation but also on saturation history as we11.6,7 Naar and Henderson8 described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt9 proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and slobod,10 Rose and Witherspoon,11 and Rose and Cleary12 each considered flow in a pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. They limited

Jan 1, 1970

By K. E. Gray, A. Podio

ABSTRACT Berea and Bandera sandstone samples were impacted with both 3/4-in. and 1/2-in. long wedges, each having a 60° included angle and a 0.05-in. flat, at various confining pressures, with borehole and pore pressures held fixed at atmospheric pressure. Samples were saturated with air, water, glycerine-water, solirol, mineral oil and soltrol-mineral oil mixtures to obtain a wide range of pore fluid viscosity. Penetration depth was held constant at 0.1 in. Dry and soltrol-mineral oil-saturated Berea samples were impacted at depths of penetration from 0.01 to 0.04 in. under 1,000 psi confining pressure to study crater initiation. Results indicate that viscosity of the pore fluid is influential primarily during the early stages of crater formation. Differences in bit force, crater volume and blow energy for tests parallel and perpendicular to bedding were significant, but decreased as the stress state was elevated. Crater volume, blow energy and bit force were nonlinearly related with depth of penetration. Crater volume was nonlinear with energy of blow. Fixed-penetration tests on saturated Berea yielded greater crater volume than did similar tests on dry samples. Differences in the nature of deformation for low values of bit penetration were noted between saturated and unsaturated samples. INTRODUCTION Rock failure during bit-tooth impact and scouring action constitutes a vital part of the drilling process and a difficult problem for researchers. Much study has been devoted to various aspects of the problem, and much has been learned about mechanics of rock failure. However, analytical treatment of drilling at depth remains difficult, partly because there are so many factors involved and because valid simulation of downhole conditions is extremely difficult. Forming individual craters by a bit tooth or chisel impacting, or indenting, a rock mass has been studied by many investigators.1-18 Similarity between single-tooth chisel impact and the corresponding action of a rotary bit has been discussed by Appl and Gatley, Garner, Podio, and Gatlin l8 compared the similarity in single-blow impact tests with microbit drilling data reported by Cunningham and Eenink.l9 Maurerll has used single-tooth impact data to develop a "perfect cleaning" theory of rotary drilling. Individual roller cutter-tooth impact data have been reported by Young. 20 Single-tooth tests in all of the cited literature were carried out on dry rocks. Inasmuch as any subsurface rock of oilfield interest is saturated with some fluid, it seemed desirable to study crater formation in permeable rocks saturated with a viscous pore fluid as a step, however short, toward more realistic simulation of subsurface conditions. This paper presents results of single-blow chisel impact studies on Berea and Bandera sandstones, both dry and saturated with pore fluids of various viscosities at confining pressures to 10,000 psi. EXPERIMENTAL APPARATUS AND PROCEDURE EXPERIMENTAL APPARATUS The same basic apparatus for single-blow chisel impact at elevated stress states, described in earlier papers was used in this study. l6. l8 Fig. 1 shows the complete experimental system; Fig. 2 shows a cross section of the pressure cell, with a sample ready to be impacted. EXPERIMENTAL PROCEDURE Two different rocks, Berea and Bandera sandstones, were used in this study. Both rocks have been used extensively in research, and rock descriptions can be found in a paper by Gnirk and Cheatham.15 Permeability to air of Berea is about 300 md normal to bedding and 540 md parallel to bedding. Bandera had vertical and horizontal air permeabilities of 18 and 57 md, respectively.

Jan 1, 1966

By W. Ivanick, Frank W. Glaser

ORDERING reactions of Fe-Si compositions in the a region have been mentioned in a number of review articles.7-8 However, little is known in regard to the critical temperature, T at which this transformation takes place. Greiner and Stoughton,' in a study of the constitution of iron-rich Fe-Si alloys below 800°C, placed the onset of order at a composition of about 4 to 5 wt pct (7.5 to 9.5 atomic pct) Si. They observed that at this composition the ductility and strength begin to decrease sharply and brittleness develops. During X-ray studies they observed only the appearance of superlattice lines for compositions containing 12.5 atomic pct Si. More recent X-ray diffraction studies- etected the appearance of superstructure lines (corresponding to the calculated positions of [Ill] and [ZOO] reflections) for alloys containing 9.5 atomic pct. This fact confirms Greiner and Stoughton's original hypothesis in regard to the onset of order at compositions containing about 7.5 to 9.5 atomic pct Si. The physical properties.of Fe-Si alloys containing more than 10 atomic pct Si have been studied only to a limited extent. Their extreme brittleness and difficulties of sample preparation render them of little industrial use in comparison with alloys in the 0 to 10 atomic pct Si range. The properties of Fe-Si alloys reported to date are mostly properties measured at room temperature on ordered compositions It appears that because of experimental difficulties fully disordered alloys could not be produced in the critical composition ranges and their properties could therefore not be reported. In Figs. la, lb, and lc, a summary of physical properties of Fe-Si alloys, measured during recent investigations of the influence of silicon additions to iron, is presented. No mention of determination of the critical temperature, T for disorder could be found in the literature. The following is an account of work done in an attempt to: 1) produce the disordered state of various Fe-Si alloys and establish the critical temperature, T for disordering, and 2) compare the electrical and thermal conductivity characteristics of the ordered and disordered phases as functions of composition. Materials, Preparation of Test Samples, and Testing Methods Fe-Si alloys with high silicon contents (about 10 atomic pct) are usually prepared using powder metallurgy techniques. This method insures accurate compositions and high purity through the use of protective atmospheres during solid state diffusion alloying of the mixed powders."" Iron and silicon powders were mixed in the desired proportions, cold or hot pressed, and then homogenized at 1150°C for periods ranging from 6 to 12 hr under a protective getter and in a hydrogen atmosphere. Fully homogenized samples were quenched in water from various and successively higher temperatures to establish the critical temperature for disorder. Temperatures were determined using Pt—Pt-Rh thermocouples in contact with the test samples. Test bars were approximately 0.6x1.25x7.5 cm. Electrical measurements were made at room temperature by determining the potential drop over a 1.5 cm span for a current of 10 amp. Densities of the samples were determined by immersion. High temperature electrical resistivities were measured using previously described techniques.'" Specific heat conductivity up to 200°C was measured by heating one end of the test bar and water-cooling the other; heat conductivity was then obtained by subtracting the rate at which heat entered the water from the

Jan 1, 1957

By J. E. 214-000-000-010 Warren, M. R. J. Wyllie, T. Meidav, L. Scharon, R. Uhley, A. J. deWitte

By considering the stoichiometry of the underground combustion process, an equrztion was derived relating the point velocity of the combustion front as a function of the air flux, fuel content, efficiency' of oxygen uitilization, hydrogen:carbon ratio, and ratio of carbon dioxide In carbon monoxide produced. In addition, an equation for cnlcrllating the amount of injected air necessary 10 produce the oil from I Cu. ft of reservoir space was derived. This equation has a direct bearing on evaluating compression costs for the process. Values calculated from these equations are in good agreement with experimentnlly obscrvcd values obtained from laborator) tube runs reported in the literature. The equations are also u\eful for atlcrlyzinf: experinlental data for inconsistencie.r.. I NTRODUCTION The injection of energy in the form of heat into an oil-bearing formation as a means of increasing the recovery of oil has been the subject of much discussion and experimentation as far back as 1920. The ideas have ranged from the injection of steam to the direct use of electricity as a means of getting thermal energy into a formation. However, most laboratory and field studies have been confined to the process whereby a portion of the crude in the reservoir is burned to generate the necessary heat to increase the mobility of the oil by reducing its viscosity. A recent paper by W. L. Martin, et al.', described the results of a number of laboratory experiments in which the combustion process was studied in a sandpack. Studies such as this indicate that with the temperatures involved, the oil is partially coked in this process and it is this coke which provides the fuel for combustion. The combustion of this residual coke can be analyzed theoretically by applying simple stoich-iometric principles to the combustion process. It is the purpose of this paper to compare the results reported in these experiments with those obtained from theoretical considerations. The variables studied by Martin, et al, among others, include combustion front velocity, air flux, oxygen utilization, fuel concentration, ratio of carbon dioxide and carbon monoxide in combustion gases, and the hydrogen:carbon ratio of the residual fuel. All these variables come into consideration when the stoichiometry of the combustion process is studied. The experimental conditions and results are tabulated in Tables 3 and 4 of Ref. 1. For purposes of comparison with calculated results, it was necessary to change the units of a number of the variables. UNDERGROUND COMBUSTION STOICHIOMETRY The combustion or oxidation of the carbonaceous residue or "coke" on the sand can be described in terms of the equation: where n is atomic ratio of hydrogen to carbon, m is ratio of moles of CO2 to CO produced, and CH. is taken as the unit molecular weight, realizing that actually the coke has a large range of high molecular weights. Assuming that all the fuel laid down in the sand is burned, the ratio of moles of oxygen consumed to moles of coke can be written as follows. Moles 0MolesMolescoke In terms of moles O2 per pound of coke, where 12 + n is the molecular weight in pounds per mole. If the 0, consumed is measured in standard cubic feet (60°F and 1 atm) and the coke in pounds per cubic foot of formation, 2, then:

By L. S. Darken

A quadratic formalism is developed lor the representation of the excess free energy, and of the activity coefficients of each component of a ternary system in the vicinity of a single component selected as solvent. This formalism, in contrast to the e formalism, is thermodynamically consistent at .finite concentrations. Numerous specific systems are used as illustrations, with cross checks where possible; these systems are Fe-C-X systems in the vicinity of 1600°C and include practically all those for which reliable data are available. It is shown that this formalism is usually quite adequate to rebresent available data up to a solute concentration of 20 to 30 at. pet. It is hoped that the formalism here presented may prove useful for the treatment and tabulation of data on ternary and multi-component solutions. SINCE, as discussed in a prior paper,' we do not as yet have an adequate basic understanding of the nature of binary metallic solutions, we cannot hope to be in better position for ternary and multicomponent systems. However, the accumulation of thermodynamic data on ternary and multicomponent metallic solutions has led to an urgent need for a rational formalism for the presentation and use of such data. Notable attempts to represent the isothermal isobaric thermodynamics of ternary solutions were made by Benedict et 01.' and by Wohl.3 These attempts were directed toward developing an analytic expression adequate to encompass the entire ternary triangle, primarily for organic systems; they generally involve the power-series approach, which has been shown' to be inappropriate, in general, even for binary metallic systems. On the other hand, interest in the thermodynamics of ternary and multicomponent metallic solutions has tended to focus either on general thermodynamic relations4-10 over wide compositional ranges, or on cases where one or more components have been at rather low concentration. This latter approach has been followed by Wagner,= by chipman,11 and by Alcock and Richardson,12 and more recently in many publications by the same and other authors. It has already been shown' that the thermodynamic behavior of binary metallic systems is, in general, relatively simple only in the terminal regions. Hence, it would appear that any approach, at this time, to a simple formalism for ternary and multicomponent systems must, a fortiori, be limited to the vicinity of the major component or solvent. The present treatment is aimed to be useful for a given solvent with moderate solute concentrations ranging up to 20 or 25 at. pet and in exceptional cases to considerably higher concentrations. In order to achieve even this modest objective, it is necessary that any appropriate formalism have built into it 1) a thermodynamic consistency (at least within the desired degree of approximation), and 2) an approach at infinite dilution to Raoult's law for the solvent and to Henry's law for each solute. Let us first formulate the condition of thermodynamic consistency for a ternary system. Under isothermal isobaric conditions, we may write for the molal value G of any extensive function dG - C1 dN1 + G2 dN2 + G3 dN3 [l] where the G's are the corresponding partial molal quantities and the N's are the atom fractions. Taking component 1 as the solvent, this relation may be rewritten in terms of the independent variables N2 and N3

Jan 1, 1968

By Mark J. Klein, A. H. Clauer

The Snoek peak induced by solute nitrogen in chromium was studied. A rapid quenching rate is required to maintain nitvogen in solution in sufficient concentrations to be detectable by internal-friction techniques. An expression for the tertninal solubility, c, of nitrogen in weight pevcent is log,,c = -4130/T + 1.05. The diffusion of nitrogen in zhromium determined by internal friction is SNOEK&apos;S theory1 of the stress-induced ordering of interstitial solute elements in the bcc lattice has been used to deduce information on the behavior of interstitials in a number of bcc metals. Under the proper conditions, internal-friction studies of "Snoek peaks" permit a determination of diffu-sivities, solubilities, and precipitation kinetics of interstitial elements. Internal-friction studies of this type have been reviewed by Nowick,&apos; Wert,= Powers and Doyle,4 and others. The behavior of interstitial atoms in Group V-A metals and iron has been rather extensively studied in this way, and results are reasonably self-consistent. However, the study of interstitial elements using internal friction in the Group VI-A metals—tungsten, molybdenum, and chromium—is much less clear. Thus far, internal-friction studies have revealed a peak in tungsten tentatively attributed to carbon5 and a peak in chromium associated with nitrogen. In chromium, Bungardt and Preisendanz6 observed a peak at 180°C for a frequency of -1 cps which they associated with nitrogen. More recently, de Morton7 determined the diffusivity of nitrogen in chromium from studies of a nitrogen peak at 160°c for a frequency of -1 cps and from elastic aftereffect measurements. The objective of this investigation was to study the nitrogen peak in greater detail, to obtain information on the behavior of nitrogen in chromium. This information is of interest because nitrogen is known to have an embrittling effect on chromium. However, efforts to deduce the role played by nitrogen in influencing the mechanical behavior of chromium are handicapped by lack of information on its behavior and distribution in chromium. EXPERIMENTAL PROCEDURES The chromium wires used in these studies were drawn from arc-melted iodide-chromium stock that had been extruded, swaged, and centerless-ground to 0.25 in.-diameter rods. Internal-friction measurements were made in an evacuated torsional pendulum similar to the one described by Kê,8 utilizing wires 0.048 to 0.030 in. in diameter. A series of analyses of the fabricated wires showed that the major impurities were approximately 100 ppm Fe and a combined interstitial content of 50 to 100 ppm C, O, N, and H. A typical interstitial analysis of the wires after processing is 15 ppm C, 2 ppm H, 50 ppm O, and < 5 ppm N. Interstitial concentrations were determined by vacuum-fusion, combustion-conductimetric, and micro-Kjeldahl analyses. In general, vacuum-fusion analysis yielded a lower nitrogen concentration than did micro-Kjeldahl analysis. For consistency, the nitrogen concentrations reported in this investigation were determined by the former method. Heat treatments were carried out by encapsulating the specimens in quartz tubes containing argon. The fabricated wires were annealed at 1150°C for 1 hr to produce uniform recrystallized grain size of about 0.015 mm. Nitrogen and carbon were added to the fabricated wires by encapsulating them in a quartz tube containing ammonia or methane, and annealing them at 1150°C for 48 hr. In some instances, carbon was also introduced by coating the wires with carbon black prior to annealing.

Jan 1, 1965

By S. Weinig, J. Winter

The grain boundary adsorption of solutes as a function of bulk concentration and solution temperature was studied using internal-frictimz techniques. From the variation of the cor-responding energy of activation for the Phenomenon, the inter-actior2 energy between a solute atom and a high-angle boundary was calculated. Interaction energies in the range of 0.3 ev were obtained, and were used to obtain the actual concentration of solute at the grain boundary. In corroboralory creel, studies the direct grain boundary contribution to the total creep strain was measured. It was found that the interface creep varied with the type and magnitude of the solute adsorbed. Subscribing to the theory of their being energetically favorable sites at the grain boundary for solutes of both Positive and negative size deviations, ternaries were investigated in Which solutes of both types were present. A marked increase in the resistance to grain boundary creep was manifested. THE major difficulty which has been encountered in investigations of the grain boundary segregation of solutes has been the lack of a sufficiently sensitive method of measuring the amount of adsorbed solute at the boundary. For the general case of a high-angle boundary, no direct method of measuring the adsorption at the boundary has been found to date. Internal friction has been used in several studies of grain boundary adsorption1-3 and although it is somewhat indirect, it was demonstrated to have the necessary sensitivity. In this investigation the authors have used internal-friction techniques in conjunction with a study of the grain boundary contribution to the total creep strain. As both parts of the investigation were performed on the same specimens it was possible to combine a highly sensitive technique with a somewhat more direct method in order to obtain information about the adsorption phenomenon. From internal-friction studies the rate of increase of the activation energy was observed to be a function of the difference in size between the solute and solvent atoms. It was proposed that if Gibbs&apos; adsorption isotherm is considered, i.e., where r is the excess solute at the boundary, c is the bulk concentration, and ay/ac is the change in grain boundary energy with bulk concentration, then AH b/ac must vary in the same way as ay/ac and therefore In this way a relative measure of the grain boundary adsorption of solutes is directly obtainable from in-ternal-friction studies. If the previous work in the field of grain boundary adsorption of solutes is examined, certain apparent information is desirable if the phenomenon is to be understood. The most important questions that must be asked are as follows: 1) Is the adsorption of solutes at the grain boundary an equilibrium process? 2) Can the Mott model of the grain boundary be used as a basis of setting up an elastic interaction between the grain boundary and solute atoms? 3) Is it possible to obtain an exact measure of the excess solute at the grain boundary as a function of temperature and bulk concentration rather than merely a relative measure of the adsorption 4) Are the conclusions obtained from an indirect method such as internal-friction studies meaningful in considering gross grain boundary effects such as creep? EXPERIMENTAL PROCEDURE The material used in this investigation was Bureau of Mines "superpurity" titanium (79 Bhn—1500 kg

Jan 1, 1960

By K. C. Strebig, C. W. Schultz, A. A. Selim

The effect of some organic additives in diamond drilling of quartzite was investigated in the laboratory. The drill was designed to measure the rate of penetration, the thrust, and the torque and to record each as a function of the distance drilled. A statistical plan was followed throughout the investigation and an equation representing the bit performance was derived from the mathematical theory of reliability. The drilling torque was found to increase with the use of additives while the sliding coefficient of friction and the wear coefficient decreased. The energy per unit volume consumed was found to increase with the use of additives. A hypothesis explaining the effects achieved with the additives is given. INTRODUCTION For some time researchers have attempted to increase drilling efficiency by adding certain agents to the flushing medium. Much of this interest is the result of the observations of Rehbinder, Shreiner and Zhigach1 They postulated that "...in processes for the mechanical destruction of solids, a region of increased crack formation is created in the deformed layers adjoining that surface of destruction, forming the predestmction zone. The surrounding medium (for example, a liquid) which wets a given solid will penetrate the embryo microcracks of the predestruc-tion zone. Increasing the molecular affinity of this liquid for the surface of the solid considerably facilitates the deformation and destruction by softening the solid in the zone of increased crack formation. In this manner, the hardness or strength of the deformed body is decreased by the influence of the penetration of the liquid into the predestraction zone." This is known as the "Rehbinder effect". Rehbinder&apos;s work has prompted many investigators to examine the effect of additives on the mechanical destruction of rocks. Engelmann, Terichow and Selim reported that the maximum penetration of the rock by a diamond point in a solution environment was at the isoelectric point of the solution.* Robinson reported that his results did not appear to support the theory of Rehbinder.3 Joris and .McLaren suggested that additives with surface tension lower than water will be more efficient in cooling the diamonds.4 Their effectiveness in removing the fine cuttings from the face of the bit will also improve the efficiency of the system. They reported an improvement in impregnated bit life and penetration rates with the use of soluble oil additives. In contrast, Long and Agnew, drilling with surface set bits, reported that lubricating agents increase bit temperature and wear.5 A significant change was reported6 in the mechanical properties of rock with polar additives. It was concluded that this change in the mechanical properties of the rock in the presence of the additive is due to the rock hydrophilic properties. Ethylene glycol, glycerine and anionic detergent were selected for this investigation because their surface tension is lower than that of water. The surface tension of these additives for the concentrations studied was 42 to 75 percent of the surface tension of water. A low surface tension additive would wet the surface of the diamonds more easily and hence would be more effective in cooling the diamonds. Another characteristic of these low surface tension additives is their effectiveness in removing the cuttings and preventing the flocculation of the formed particles in the drilling process. This article summarizes the results of an investigation performed at the laboratories of USBM, Twin Cities Mining Research Center. The objective of the investigation was to study the over-all effects of some organic additives on the performance of diamond impregnated bits in atmospheric drilling conditions only and not in downhole pressured conditions.

Jan 1, 1970

By A. Steiner, E. Miller, K. L. Komarek

Equations have been derived to calculate the chemical potentials of the components of liquid binary alloys from liquidus and enthalpy data. The equations are applicable to systems with intermetal-lic compounds of limited solid solubility. The liquidus curve of the Mg-Sn system was accurately redetermined, and the melting point of the compound Mg2Sn was found to be 770.5° * 0.3°C. The thermo-dynamic properties of the liquid alloys were calcu -lated from the liquidus data. The activity of tin shows both positive and negative deviations from Raoult&apos;s law and the relative integral entropy is positive. THE phase boundaries in an equilibrium phase diagram are functions of the thermodynamic properties of the coexisting phases. Specifically, the shape of the liquidus curve near an intermediate compound is determined by the properties of the compound and the liquid phase. Hauffe and wagnerl have derived an equation for the chemical potential differences (ui) of the liquid alloys near the congruent melting point when the heat of fusion of the compound and the liquidus curve are known. In their derivation the temperature dependence of the ui value was neglected, and liquid of stoichio-metric composition was chosen as the reference state. To obtain chemical potentials over the ntire composition range of the phase diagram with the pure components as the reference state, equations have been derived which incorporate the temperature dependence of the chemical potentials. Such a thermodynamic analysis can be carried out when the liquidus curve and the enthalpy values are known. The equations have been applied to the redetermined liquidus curve of the Mg-Sn system to obtain the thermodynamic properties of liquid Mg-Sn alloys. The Mg-Sn phase diagram has been studied by various investigators and the results have been compiled and critically assessed by Hansen.2 Preliminary thermal analyses showed that the basic features of the diagram were correct. The system has one congruent melting compound, Mg2Sn, two eutectics, and some solid solubility of tin in magnesium. However, the published liquidus temperatures show considerable scatter. In order to perform an accurate thermodynamic analysis, the liquidus curve between the magnesium-rich and tin-rich eutectic compositions was therefore redetermined by careful thermal analysis using highest-purity starting materials. EXPERIMENTAL PROCEDURE The magnesium metal (Dominion Magnesium Ltd, Toronto, Canada) had a purity of 99.99+ pct with the following impurities (in ppm): 20 Al, 30 Zn, 10 Si, <1 Ni, <1 Cu, <10 Fe; tin (Cominco Products, Spokane, Wash.) contained 99.999+ pct Sn. The graphite crucibles were machined from graphite rods (United Carbon Products Corp., Bay City, Mich.) which had an average total ash content of less than 30 ppm. All the graphite parts were baked out in vacuum at 950" to 1000°C for a minimum of 24 hr to remove volatile organic materials. The graphite crucibles (3 in. long, 1-5/8 in. OD, 1-3/8 in. ID) were tightly closed with a threaded cover (1/2 in. thick) which had a central thermocouple well (2-1/4 in. long, 5/16 in. OD, 3/16 in. ID). Cover and thermocouple well were machined from one piece of graphite. A thin sheath of quartz was inserted in the well to protect the thermocouple

Jan 1, 1964

By R. W. Fountain, W. D. Forgeng

A new constitutional diagram is presented for the cobalt-rich end of the cobalt-titaniurn system. The modifications result from the presence of a new, intermediate, fcc phase, ?, the existence and homogeneity limits of which were established by metallo-graphic and X-ray studies of alloys containing from about 3 to 30 pct Ti. The precipitation of the ? phase from supersaturated solid solution was studied by hardness and electrical resistivity measzsrements, and two distinct stages in the process were observed. COBALT forms the base for a number of precipitation -hardenable alloy systems which may be divided into two distinct categories of practical interest, a) those hardened by intermetallic compounds and b) those hardened by carbide formation. The precipitation of intermetallic compounds from solid solution in cobalt-rich alloys has, however, received very little attention. Although the phase diagrams for some binary systems capable of precipitation have been determined,&apos; there is an almost complete lack of data on the property changes associated with the precipitation, and even less information on the kinetics of the reactions or morphology of the products. More information is available on the precipitation of carbides because of the practical significance in superalloys. A survey of cobalt binary phase diagrams suggested that the cobalt-titanium alloys might provide interesting and useful precipitation-hardenable alloys. The equilibrium diagram as proposed by Wallbaum2 is shown in Fig. 1. Köster and wagner3 have indicated that the maximum solubility of titanium in cobalt is about 10 pct at the eutectic temperature (1135oC), and this decreases to about 7.2 pct at room temperature. The temperature of the allotropic transformation in cobalt is lowered by the addition of titanium, about 5 pct being sufficient to retain the high-temperature fcc modification to room temperature. Wallbaum and Witte 4,5 have indicated that the precipitating phase in alloys containing up to about 29 pct Ti is Co2Ti, a hexagonal Laves phase of the MgNi, type. With slightly higher titanium contents, they also report a cubic modification of Co2Ti of the MgCu2-type Laves phase. Duwez and Taylor6 confirmed the existence of the hexagonal (MgNi2) modification but not the cubic (MgCuz) modification of Co2Ti and suggested that existence of the cubic form may have resulted from impurities in Wallbaum&apos;s alloys. In their work on Laves-type phases, Elliott and Rostoker 7 reported the cubic modification of Co,Ti, but did not confirm the existence of the hexagonal modification. However, Dwight8 in a discussion of the work of Eliott and Rostoker again showed the existence of both modifications of Co2Ti, a result which was confirmed at that time by Elliott and Rostoker. As a result of a study on the iron-cobalt-titanium system, Köster and Gellers suggested the existence of a Co3Ti phase isomorphous with Fe3Ti. Witte and Wallbaum,&apos; however, established the fact that no compound, Fe3Ti, exists in the iron-titanium system, and in a later publication, wallbaum2 stated that Kitster and Geller&apos;s reasoning was not valid, and no compound, Co3Ti, exists. This conclusion was later acknowledged by Köster.10 Preliminary experiments by the present authors to determine the precipitation-hardening characteristics of the cobalt-rich, cobalt-titanium alloys re-

Jan 1, 1960