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By Robert F. Mehl, Gerhard Derge

The gamma-alpha transformation in iron and iron-rich alloys is of such practical and theoretical importance that many papers have been published upon the subject relating to critical temperatures, transformation rates and accompanying property changes. Although crystallo-graphic studies are of less immediate practical usefulness, the opportunities which these offer to furnish data on the basic atomic movements which characterize the transformation are not to be neglected1. The early work on the crystallography of this transformation has been reviewed in the fourth paper of this series2; since then several important papers have appeared. Our present knowledge may be briefly summarized as follows. Kurdjumow and Sachs, working with a 1.4 per cent carbon steel3, established the orientation relationships subsisting between the face-centered gamma and the metastable tetragonal lattices in freshly quenched martensite, and between the face-centered gamma and the body-centered alpha lattices in tempered martensite. The orientation relationship observed in the latter case may be stated in terms of planes and directions observed to lie parallel in the two lattices: {111} ?//{110}a [110] ?// [111]a (This notation is used throughout as the most descriptive means of expressing the fact that any (111) plane of the gamma phase may be parallel to any (110) plane of the alpha phase, and that a [110] direction in a particular (111)? plane is parallel to a [Ill] direction in the corresponding (110)a plane.) From these relationships the atomic movements that transform the gamma lattice into the alpha may be inferred. In the present experiment these may be considered as consisting primarily in a shear of the atoms parallel to the {111} planes in [110]? Directions

Jan 1, 1937

By Warren H. Westphal

For mining and exploration, and indeed the entire mineral industry, the first century of AIME has ended with far more problems than it began. Paradoxically, most of these problems have arisen not because, the industry has been unsuccessful, but rather because it has succeeded too well. Whatever the public demand for minerals over the past 100 years, it has somehow been met-and met at a price well within the public's ability to pay for the products. But as AIME moves into its second century, the past successes of mining and exploration are beginning to levy a tax on the future. Prospectors have already found most of the rich and ready ores, and miners have dug them out. New mineral assets grow progressively harder to come by, and as they do, the need for them grows inversely more pressing. How and where and at what cost can adequate supplies be found? How and at what cost can they be mined from heretofore inaccessible recesses deep underground and under the seas-or from vast surface tonnages containing only minor values? And once they are found or won, how can these assets be husbanded for generations to come? How also can they be extracted without injury to the land, air and water on which we and our successors must depend? And what constructive use can be made of the incidental materials now treated merely as wastes-sometimes at great expense?

Jan 1, 1971

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By E. W. Davis

I . OPERATING TESTS 1. CHARACTER OF ORE UNDER INVESTIGATION On the eastern end of the Mesabi Range, in Northern Minnesota, is a large formation of siliceous rock which contains bands and fine grains of magnetite . The magnetite comprises about 35 per cent. of the rock. Fig.. 1 show&apos;s graphically that the tonnage of minus 200-mesh material produced varies directly with the tonnage fed to the mill. There is undoubtedly some limit to this relation, but there seems to be no indication of it at 18 T. per hr. Some of the conclusions drawn from this test are that: (a) The ball-mill is naturally a machine of very large capacity; (b) if it is not possible to deliver a large tonnage of original feed to the mill, a closed circuit should be provided so that the mill may crush its own oversize.

Jan 2, 1919

By Myrick N. Bolles

The concentration of gold and silver in mattes low in copper, and the subsequent separation and recovery of either or both of these metals, is a question the satisfactory solution of which has long vexed metallurgists. It covers a broad and important department of metallurgical science and brings in its train a series of attendant problems continuing from the initial operations of concentration to the final recovery of " values."

Jan 1, 1905

By Wayne Loel

THE application of aerial photographs to all phases of geologic mapping is set forth, indicating the advantages to be gained in different types of country and under varying climatic conditions, Methods of field and office procedure are given from a geological point of view, as well as suggestions regarding the best methods of aerial mapping for different uses and under varying field conditions, including the study of submarine geology. Aerial photographs with accompanying geologic maps are shown to illus-trate the appearance from the air of different geologic features under varying climatic and topographic conditions.

Jan 1, 1938

By C. Altstetter, Y. Huang, E. de Lamotte

Nitrogen was introduced into pure niobium (colutn-bium) and dilute Nb- Zr alloy wires by equilibration with pure nitrogen gas at high temperatures. Room-temperature hardness was correlated with the alloy composition, heat treatment, and microstructure. Hardness was found to be most sensitive to the amount of nitrogen in solution; however, a significant hardening up to 500 Dph look place upon aging of quenched alloys. A coarse dispersion of nitride did not significantly increase the hardness of the material though the nitride was found to have a hardness of 1400 Khn. BY now the marked effect of nitrogen on the properties of bcc refractorv metals is we ll-documented. There are few studies, however, in which the state of the solute has been carefully controlled. Indeed, the composition-temperature-pressure relationships in nitrogen-refractory metal systems have been determined precisely for only niobium and tantalum.&apos;-4 Most investigations on niobium have dealt with alloys High-nitrogen alloys cleaved on (100) planes and had negligible ductility. Precipitation was found to occur in either a discontinuous or a continuous fashion, depending on the composition and cooling rates. Upon cooling, the precipitation first proceeded discontinu-ously by the nucleation of nilride needles at subbound-aries and subsequent growth of a two-phase microcon-stituent. At lower temperatures continuous precipitation occurred in the subgrain interior ahead of the discontinuous precipitation interface. containing nitrogen, carbon, and oxygen in significant but uncontrolled and, in several instances, undetermined amounts. Thus, there has been some uncertainty regarding the presence and the distribution of precipitates. This paper presents results which relate the hardness and microstructure to the heat treatment and nitrogen content of niobium and Nb-Zr alloys. Niobium rod* produced by the Wah Chang Corp.

Jan 1, 1968

By Edward Keller

About a dozen years ago the art of bessemerizing copper- * matte, brought to these shores from France, was first established at the smelter, in Butte, Montana, of the Parrot Silver and Copper Company, which had bought the process from Mr. Manhks, the inventor. Through the efforts of Mr. J. E. Gaylord, general manager, and Mr. A. J. Schumacher, snperintendent,, assisted by an able staff, the new method rapidly underwent, at the Parrot establishment, an evolution towards higher perfedion, and within a few years its success and its advantages were so marked that all the great works in the west followed in the footsteps of this pioneer. The converter-process has now practically superseded the reverberatory-process in this country. The latter will undoubtedly, in a not very distant future, be relegated to metallurgical history. The writer has availed himself of what was perhaps the last chance to make comparisons of the two methods, working practically on the same material on an extensive scale, the reverberatory process being that of the Baltimore Copper Smelting and Rolling Company,* while the converter-process is that of the Anaconda Copper Company—both using the matte from the latter company&apos;s works in Anaconda, Montana. For the greater portion of the material considered in this paper, the writer is indebted to the two companies. In order to understand the difference of behavior of the several elements, and the difference of the copper produced in the two processes, it is best to study and follow those elements

Jan 1, 1899

By W. H. Herrnstein, J. B. Clark, E. C. Utley, A. J. McEvily

The ratio of the endurance limit (10&apos; cycles) to tensile strength of age-hardened aluminum alloys is approximately 0.3, whereas the ratio for annealed alloys is about 0.5. The lower value for the age-hardened alloys has been associated with the instability of coherent precipitate during cyclic loading, but it has not been definitely established whether this instability is due to overaging or reversion during cyclic loading. The results of the present investigatzon support the reversion viewpoint. In this work specimem of 2024-T4 aluminum alloy were aged for 16 hr at 150°C after cycling for 10 pct of the life at 25.000 psi. These specimens were then tested to failure and exhibzted a marked increase in fatigue life. It is proposed that during the early stages of fatigue in this alloy dislocations cut through the coherent precipitate and bring about the reversion of the precipitate. Subsequent aging at 150ºC induces reprecipitation in the precipitate-free zones so that the weakened regions are strengthened and the fatigue life is extended. It Is recognized that the fatigue strengths of precipitation hardened aluminum alloys are unusually low relative to their tensile strength.&apos;-= This feature is illustrated in Fig. 1 where it can be seen that age-hardened alloys have lower fatigue ratios (the ratio of the fatigue strength to the tensile strength) than those in the annealed or cold worked state. Further, as shown in Fig. 2, the more an alloy is dependent upon precipitation hardening for its total strength, the lower is the ratio of the fatigue strength to the tensile strength. This state of affairs has been associated with an instability of the metastable metallurgical structure of precipitation hardened aluminum alloys during cyclic loading. Evidence2 in support of this view is that the fatigue ratio increases in these alloys as the test temperature is lowered, thereby indicating that thermo-mechanical instability, rather than some other factor such as a non-uniform distribution of precipitate, is the factor responsible for the low fatigue ratio at room temperature. Two mutually exclusive proposals have been ad- vanced to account for this instability. Hanstock has proposed that overaging takes place during cyclic loading, and in support of this view, Broom et a1.2 have indicated that an overaging process might be promoted by the large numbers of vacancies which are created during cyclic loading. The creation of vacancies by radiation4 has been shown to lead to rapid overaging. Hanstockl obtained visual evidence of overaging in an aluminum alloy after cyclic loading, but in this instance it has been pointed ou? that because of the high frequency used (60,000 cpm) the observed effect may have been due to normal high temperature precipitation around energy dissipating cracks. Efforts to discern visual evidence of overaging in this alloy at lower test frequencies were not successful.3 The alternative postulate3 is that reversion takes place during cyclic loading and leads to localized soft spots at which fatigue cracks are readily initiated. Evidence for this process has recently been provided by Polmear and Bainbridge5 who demonstrated metallographically that regions depleted of precipitate were created during cyclic loading of an aluminum alloy. Inasmuch as precipitate particles bordering the depleted region had not grown in size, it was concluded that the solute atoms which had constituted the missing particles had gone back into solution. No mechanism for the reversion process was presented. The present study was undertaken to investigate further the conditions leading to instability during cyclic loading, and to determine whether reversion or overaging had taken place as a result of cyclic loading. BACKGROUND AND TEST PROCEDURE In order to differentiate between the processes of reversion and overaging, rest periods at an elevated temperature, which ordinarily would insure additional precipitation, were used in this investigation. It was expected that after a period of cyclic loading an elevated temperature rest period would result in a decrease in the remaining life of the specimen if overaging were occurring during cyclic loading, whereas in the case of reversion, reprecipitation would occur and the fatigue life would be extended. Such an expectation is based on the assumption that the crack-nucleation phase is a significant portion of the total fatigue life, and that such a treatment is of influence in the crack-nucleation stage and is relatively unimportant thereafter.

Jan 1, 1963

By C. K. Donoho

SILICON is used in almost all commercial steels; up to about 0.20 pct in killed wrought steels and 0.50 pct in steel castings. Above about 0.50 pct in wrought steels and 0.70 pct in cast steels, silicon is considered an alloy. As an alloy, silicon is useful for several purposes: (I) for its effect on magnetic properties of parts for electrical apparatus; (2) for increasing the yield strength of carbon and low-alloy steels without too much sacrifice of ductility and weldability; (3) for adding hardness and toughness to spring and chisel steels; (4) for adding resistance to scaling and carburization to heat-resistant steels; and (5) for its graphitizing effect in graphitic steels. In acid electric steels for casting we are principally interested in the effect listed second; i.e., increase of strength with minimum sacrifice of ductility.

Jan 1, 1947

By R. A. L. Black, J. E. Jennings

The problems of slope stability in open cast mines are examined. A criterion, the instantaneous stripping ratio, is suggested for use in the design of pit slopes and as an index of control at all stages of the exploitation of the orebody. This criterion may also be related to safety and to the maximizing of profits. Two approaches to safe design of slopes, one from the point of view of soil mechanics and the other from the point of view of rock mechanics, are described and critically compared. The effect on slope stability of the regional tectonic stress field is discussed. Explanation is given of the application of the Terzaghi effective stress concept to problems in both soil and rock environments, including possible effects when borehole deformation techniques are used to measure stresses in rock in situ. A company embarking on open cast mining is faced with two basic questions: 1) will the venture be profitable and 2) can it be carried out with safety? The two questions are obviously interrelated because both depend upon the slope angles adopted for the pit. The cost of open cast mining depends largely upon the stripping ratio, defined as the volume of overburden that must be removed to the volume of ore recovered. The steeper the slope angles, the more favorable the stripping ratio, but the stability of the slopes, and therefore the safety of men and materials in the pit, require that the angles be made relatively flat. Consequently, the design depends upon a compromise: the slopes must be steep enough to result in economical mining and flat enough to ensure safety. Today there is a world trend towards deeper mining by open cast methods. This is mainly due to the higher cost of underground mining and the lower cost of open excavation resulting from the introduction of large modern earth and rock-moving machinery. Deeper open cast mining has led to a very great increase in the volumes of wasted overburden, and much thought is being given to the considerable economic benefits which would result if pit slopes could be made steeper by even one or two degrees. The result has been an increasing interest in research into slope stability problems in the expectation that the application of scientific principles will provide solutions leading both to economies and to more predictable operation of the mines. In at least four places, the U.S., Australia, Western Germany and Southern Africa, comprehensive investigations are at present in progress, and it is the object of this paper to review some of the more important aspects of these programs. RELATION BETWEEN ECONOMY OF OPERATION AND SLOPE ANGLES The main object of any industrial enterprise in a free economy is to make a profit. In mining, where profits must be made from a wasting capital asset, a further definition of the profit motive is imposed, namely that the economic aim should be to maximize the total possible profit. But since profits deferred for a number of years are not as valuable as profits that are immediately available, it is usual to discount deferred profits at some rate of interest which reflects their current or present value in the hands of the investor. Thus, in mining the logical aim can be defined more closely still: to maximize the present value of the total future profits. In commercial terms the present value represents the market value of the operation as a going concern. Many factors enter into the forecast of current and future profits. They include the volume of production, the price of the salable product and the cost of production. Current profits can be estimated with reasonable accuracy by the operating engineers; but it is the task of economists and management to assess future trends in the mineral markets and in the economy as a whole, and together with the engineers, they can then estimate the future cost and profitability of the mining operations. In open cast mining, the rate of ore production once decided on remains a virtually constant factor unless a major change in the capital structure of the mine is made. But one factor over which the operator has a considerable measure of control is the ratio of the volume of ore mined to the volume of waste over-

Jan 1, 1963

||Abad, Leopoldo F, College of Min, Univ of California Berkeley, Cal &apos;23 ||Abarquez, Ramon F, Met, Bureau of Science Manila, P I &apos;24 ||Abbey, Robert Graham, Student, Case School of Applied Science Cleveland, Ohio &apos;21 Abbott, A N , Mines Supt , Mazapel Copper Co , Ltd Concepcion del Oro, Zacatecas, Mexico &apos;23 Abbott, Clarence E, Gen&apos;l Supt, Iron Mines Div, Tenn Coal, Iron & R R Co, 1405 Minnesota Ave, Bessemer, Ala &apos;04 Abbott, Louis Benjamin, Chief Engr, Consolidation Coal Co, Elkhorn Div &apos;Jenkins, Ky &apos;15 Abbott, Robert R , Met Engr, Peerless Motor Car Co Cleveland, Ohio &apos;12 ||Abbott, Wells Osborn, Ray Consolidated Copper Co Hayden, Ariz &apos;23 Abeel, George H, Jr, Cons Min Engr 4612 W 17th St, Los Angeles, Cal &apos;18 Abel, Albert E, Asst to Pres, Valley Mould & Iron Corpn Sharpsville, Pa &apos;19 ?Abeloff, Miran S Address Wanted &apos;21 Abernathy, G E, Kansas State Teachers College Pittsburgh, Kans &apos;20 Abey, Hiroshi, Min & Met Engr, Takata & Co, 2 Yeirakucho, Nechome, Kojimachi-ku,

Jan 1, 1923

Some 15 years ago, Dr. Adolf Schmidt, director of the Magnetic Observatory in Potsdam, Germany, developed an instrument, which was a modification of Lloyds balance, for the measurement of the vertical component of the earth&apos;s magnetism in the field. There was a keen demand for this because (1) it was desirable to have a field instrument that would measure the component of the earth&apos;s magnetism which stands in the closest and simplest relation to the configuration of the subterranean magnetic formations-the vertical component; (2) it was desirable to have an instrument that was not only more sensitive but also more reliable than the existing vertical magnetometers (the dip needle, for instance). The application of the magnetometer in oil geology demanded such an instrument, because the magnetic disturbances produced by most types of magnetic formations associated with the occurrence of oil (salt domes, faults, anticlines with crystalline core, etc.) are too small to be detected with the ordinary dip needle. The writer can prove, by some investigations recently made for the U. S. Bureau of Mines, that these instruments may be used also to very great advantage in mining, because they are capable of measuring anomalies which are as great as twice the normal strength of the earth&apos;s magnetic field. Even for such anomalies, the field balance is more advantageous than the dip needle. First, the instrument rests on a firm support and can be adjusted in the proper azimuth, which insures measurement of the vertical intensity only, without a part of the horizontal intensity, which is very important for the interpretation. The readings give the vertical intensity in linear terms and not as a function of an angle; and the field balance is insensitive to temperature when used with scale values that are adequate for the determination of large anomalies. In another phase of mining, the gold placer work, the field balance has also shown excellent results for which the dip needle is not adequate. What has been said about the dip needle holds also, though to a lesser extent, for two other types of vertical variometers recently used, the Tiberg balance and the Thomson-Thalen magnetometer.

Jan 1, 1929

By Reginald Williams

THE amount or value of the precious metals consumed in dentistry is probably amazing to most people. It falls very little short of that which is consumed in jewelry. Inasmuch as the ultimate destination is in the human mouth, dental alloys enjoy some importance because life and health depend upon restorations made with them. Prosthetic dentistry has made wonderful progress in the last few years. The manufacturers who supply the metals also deserve commendation. This industry which deals with metals to go-into people&apos;s mouths is comparatively new. There is no literature on the subject, and little or no precedent by which to be guided. It was only by close cooperation with the dentist or prosthetic technician that desirable physical properties were produced, as-nearly as possible, in the metals which were available and permissible. It is true that there were and still are conflicting opinions among the dentists as to the physical properties they require. Sometimes they request the impossible, such as alloys which are exceedingly stiff and springy, yet will bend or adjust easily. Even in this latter instance, progress has been made by supplying methods of heat-treatment whereby metals may be softened or hardened at will. (Figs. 1 and 2.) The demands made upon manufacturers are extremely varied. They must supply metals of tensile strengths ranging from approximately 30,000 to 100,000 lb. per sq. in. and over. The latter metals must be workable and in many instances capable of extreme deformation. They must not be affected by mouth conditions, nor should they oxidize greatly when molten, at red heat, or during a soldering operation. In addition to physical, specifications, color demands must also be met. The firm of which I have the most, knowledge manufacturers 11,553 standard stock articles of precious metals, taking into consideration formulas, finenesses, grades, colors, gages, lengths, sizes and weights. If special demands are taken into consideration, the number would be in excess of 25,000. Wrought metals are manufactured in a great many alloys of different sizes and shapes, such as plate, bar, rod, wire, sheet, strip, mesh and foil. There are also other products of importance.

Jan 1, 1928

By A. U. Seybolt

Precipitation of FeO from Fe-O solid solutions has been studied by metallographic methods. Such precipitation, which is visible, is composed largely of barely resolvable spheroidal particles. No metallographic evidence has been found for grain boundary oxide films. Oxygen diffusion into a iron does not occur chiefly by inter-granular penetration. IN an earlier communication&apos; dealing with the solid solubility of oxygen in a iron, it was shown that under one set of conditions it was possible to show FeO precipitated from supersaturated solid solution. However, to assist in rationalizing the effect of an FeO second phase upon the mechanical properties of iron, it would be desirable to have more information on the possible modes of precipitation and on the thermal treatments required to produce precipitation.

Jan 1, 1955

By A. G. Spillette, R. L. Nielsen

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by desuribing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterfioding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil us continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few." Even if extensive data were available, two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements," laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments — injectivity/productivity tests and pilot floods—results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey" and Spillette&apos; recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery.&apos;."1° Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot-water injection are that (1) no gas phase is present and (2) the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. Darcy&apos;s law for multiphase fluid flow relates the velocities of the oil and water phases to the phase pressure gradients by the following relations:

Jan 1, 1969

By I. Havenaar

EXPERIMENTAL DATA In an article by C. K. Ferguson and J. A. Klotz,1 experiments on the filtration of drilling muds under borehole conditions are discussed. Experimental data on mud filtration through the wall and the bottom of the hole are presented. From the data on bottom-hole filtration it was concluded that the filtrate does not flow freely into the formation, but that the pores of the formation are plugged by the mud. A quantitative interpretation of the data can be civen, by using a formula for bottom-hole filtration, dehved below. This formula is based on the following assumptions, 1. Each time a blade of a drag bit, or a cone of a roller bit, moves along the bottom of the hole, the mud cake is completely removed. 3. A new mud cake is immediately formed on the freshly produced surface, and losses of "whole" mud into the formation are negligible (this is equivalent to an immediate plugging of the pores). 3. The filtration of the mud on the bottom of the hole follows the classic law: V = A +1—(Eq. I), where t is the time required to yield a volume of filtrate V, A is the surface area of filter cake, and C is a constant. The application of this equation means that any eroding effect of the mud stream on the mud cake is neglected. The formula for the calculation of the volume of filtrate, Q,, flowing in one second through the hole bottom (diam. d cm), when using a bit with n cones or blades rotating at a rate of rn revolutions per second, is derived as follows: The mud cake is formed on the bottom of the hole in the time t =1; the filtrate volume V which passes n through the bottom In this time 1s given by Eq. 1: After1/nmsec the mud cake is removed. In one m second this process takes place nm times. Therefore the volume of filtrate, obtained in one second is given by This equation has now been applied to the experiments of Ferguson and Klotz. The constants C were derived by means of Eq. 1 from the API filter losses of the muds used by the authors (t = 1,800 sec; A = 45.16cm2). A three-cone bit was used (n = 3) at 90 rpm (m = 1.5). The calculated figures are compared with the experimental data in the table below. The calculated values of Q, are usually lower than the experimental values. This may be due to the following causes. 1. The value of C used in the calculation is based on the API filter test (filtration pressure of 100 psi), whereas the experimental data were obtained with a filtration pressure of 200 psi. Although the effect of the pressure on C is not large, C decreases somewhat with increasing pressure, and this leads to a higher filtration rate. 2. Mud losses and the eroding action of the mud stream on the cake are not entirely negligible. 3. The values of Q, derived by Ferguson and Klotz from their experiments are too high, because of their assumption that all pore liquid within the formation drilled is picked up by the drilling mud. It is found, however, that the calculated values of Qf, except in the case of oil base muds, are of the right order of magnitude. ACKNOWLEDGMENT The author wishes to thank the management of the Koninklijke/Shell-Laboratorium, Amsterdam, for permission to publish this note.

Jan 1, 1957

By C. G. Fink

A PART of the material incorporated in this paper was derived from the studies of ancient metal objects examined by the authors from time to time for museums and art collectors, in order to verify the age of the metal. The data thus accumulated during several years was systemati-cally surveyed and supplemented by new material obtained in examina-tion of a set of specimens that had been generously donated by museums for this study. Altogether over 50 pieces were investigated, of which 39 are described in this paper. Every specimen is at least 1500 years old; the majority are considerably older. Exact conditions to which these bronze and copper objects were exposed in the ground are unknown, unfortunately. It is safe to say that exposure conditions did not remain constant during the long period of burial. Although the collection of specimens studied represents a wide variation in location and age of the objects, as well as in the nature and composition of the metals, it was found that fundamental changes in the metal structure were limited to a few typical cases which, therefore, may be considered as more or less general. The authors&apos; chief aim was to study the effect of extremely long periods of corrosion on the structure of bronze and copper.

Jan 1, 1936

By Herbert Kynor

BY THE term mechanical mining is meant that operation, or series of operations, that replace the hand methods of mining. The first undercutting machine to operate in anthracite was placed in the Butler mine of the Hillside Coal & Iron Co., Dec. 23, 1910, by the Sullivan Machinery Co. The first Jackhamer used in the anthracite field was installed at the Wadesville colliery of the Philadelphia & Reading Coal & Iron Co. in Oct., 1912, by the Ingersoll-Rand Co. The first longwall conveyor was installed at the Dodge mines of the Delaware, Lackawanna, & Western Coal Co. in March, 1912. The first mechanical scraper equipment was installed in the Seneca mines of the Lehigh Valley Coal Co. in January, 1914. The amount of anthracite mechanically mined since the first mining machine was installed in 1910a is as follows: PENNA. COAL Co. D. L. & W., SCRANTON TEMPLE HUDSON YEAR AND HILL- TONS COAL Co., COAL CO., COAL CO., TOTAL. SIDE COAL TONS TONS TONS TONS AND IRON, TONS 1920 372,737b 367,000d 322,892 74,127 371,878 1,508,634 1919 950,786 no record 306,616 81,575 319,356 1,658,333c 1918 917,778 744,966 24,880 44,756 288,781 2,021,161 1917 757,940 838,800 5,050 57,279 164,180 1,823,249 1916 286,780 860,663 13,960 114,173 101,475 1,377,051 1915 428,819 592,169 8,253 1,029,241 1914 219,188 153,896 373,084 1913 171,505 171,505 1912 124,267 124,267 1911 40,319 40,319 1910 1,184 1,184 a. A slightly greater production than shown was obtained as the tonnage from individual operations is not shown. b. Decrease due to strike conditions in 1920. c. Does not include tonnage of D., L., & W. d. D., L., & W. decrease in 1920 due to having less mining machines in operation. There are about 150 undercutters in use in the anthracite region, 80 mechanical loaders, and 10 longwall conveyors.

Jan 9, 1921

By L. R. Jackson

It is convenient to have a consistent system of notation that will allow the representation of the entire range of complex stresses from hydrostatic compression to hydrostatic tension on plastic flow in a single diagram. Such a system is provided by making use of the fact that any complex stress system can be resolved into a hydrostatic tension or compression and a pure shear. Consider a stress system having the principal stresses This system can be resolved into a new system consisting of the three components and three pure shears. If Sm is positive, the net stress effect is hydrostatic tension; if it is negative, the effect is hydrostatic compression. In order to produce a systematic notation, a quantity that will be referred to as the "triaxial ratio" will be defined by the equation _ Sm Tr = Sm - Sm is given by Eq. I and Sl is the absolute magnitude of the largest principal stress without regard to sign. Table I lists the triaxial ratios for various common systems. Table i.—Triaxid Ratios for Various CommonSyslems Triaxial Ratio Stress System Tr Hydrostatic compression — SI - —St - -S³............................... -1 Torsion or shear -SI - S². S² = O..... O Simple tension SI. SI = SI = 0......... +0.33 Biaxial tension SI = S² S³ - 0......... +0.66 Hydrostatic tension +SI - +S³ = +S³. +1.00 Representation of Strains Strains will be plotted as "true" strains according to the system proposed by Ludwik.1

Jan 1, 1945