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By R. Raring, W. J. Harris, J. A. Rinebolt

The effects of additions of alloying elements on the true-stress, true-strain characteristics of 0.30 pct C, 1.00 pct Mn, 0.30 pct Si pearlitic steel were studied. The alloying elements investigated were C, Mn, Si, P, The alloys are compared on the basis of fracture stress, fracture strain, energy to fracture, rate of strain hardening, strain hardening exponent, height of the flow curve, and lower yield point. IN the past, nearly all studies of the effects of alloying elements on the tensile properties of metals have compared the conventional engineering parameters, namely, tensile strength, yield strength, elongation, and reduction of area. Recently, however, the true-stress, true-strain method of recording results from the tension test has been used; Lacy and Gensamer,' Hollomon," and French and Hibbard- are used this method to study the effects of composition on strength and ductility of metals. In this paper, the effects of certain alloying elements on true-stress, true-strain curves of steels with nearly constant grain size and pearlite spacing are presented. The notation employed in this paper is given in Table I. Since the definitions of stress and strain and the analytical geometry of the stress-strain curve have been explained previously, for example by Gensamer,' they will not be reviewed here. However, the method used for the determination of energy to fracture, E,, requires mention. These energy values were calculated on the assumption that the flow curve followed the idealized equation:' corresponds to the specific energy absorption to that strain value. There is justification for preferring the use of eq 1 for the determination of the energy to a particular strain rather than the area under the experimental stress-strain curve, since Gensamer showed that the use of the Bridgman correctione for stress at the neck of a tensile specimen brought the corrected experimental curve nearer to the idealized power-law curve than to the uncorrected experimental curve. However, it should be noted that the difference between the areas under the idealized curve and the experimental curve is not great for strain of less than 1.0, as can be seen from Fig. 1. In this figure, the true-stress, true-strain curve for a 0.01 pct C, 1.00 pct Mn steel is plotted through the experimental data points. From the value of a,, from this curve and the value of n as determined by the Inm-

Jan 1, 1952

By A. G. Weber, K. H. Coats, M. H. Terhune, R. L. Nielsen

Two computer-oriented techniques for simulating the three-dimensional flow behavior of two fluid phases in petroleum reservoirs were developed. Under the first technique the flow equations are solved to model three-dimensional flow in a reservoir. The second technique was developed for modeling flow in three-dimensional media that have sufficiently high permeability in the vertical direction so that vertical flow is not seriously restricted. Since this latter technique is a modified two-dimensional meal analysis, suitably structured three-dimensional reservoirs can be simulated at considerably lower computational expenses than is required using the three-dimensional analysis. A quantitative criterion is provided for determining when vertical communication is good enough to permit use of the modified two-dimensional areal analysis. The equations solved by both techniques treat both fluids as compressible, and, for gas-oil applications, provide for the evolution of dissolved gas. Accounted for are the effects of relative permeability, capillary pressure and gravity in addition to reservoir geomety and rock heterogeneity. Calculations are compared with laboratory waterflood data to indicate the validity of the analyses. Other results were calculated with both techniques which show the equivalence of the two solutions for reservoirs satisfying the vertical communication criterion. INTRODUCTION Obtaining the maximum profits from oil and gas reservoirs during all stages of depletion is the fundamental charge to the reservoir engineering profession. In recent years much quantitative assistance in evaluating field development programs has been provided by computerized techniques for predicting reservoir flow behavior. Because of the spatially distributed and dynamic nature of producing operations, automatic optimization procedures, such as those now in use for planning refining operations, are not now available for planning reservoir development. However, present mathematical simulation techniques do furnish powerful means for making case studies to help in planning primary recovery operations and in selecting and timing supplemental recovery operations. A number of methods have been reported which simulate the flow of one, two or three fluid phases within porous media of one or two effective spatial dimensions>-4 However, applying computer analyses to actual reservoirs have been limited mostly to two-dimensional areal or cross-sectional flow studies for two immiscible reservoir fluids. To obtain a three-dimensional picture of reservoir performance using such two-dimensional techniques, it has been necessary to interpret the calculations by combining somehow the results from essentially independent areal and cross-sectional studies. To the authors' knowledge, the only other three-dimensional computational procedure, in addition to those presented here, was developed by Peaceman and Rachford8 to simulate the behavior of a laboratory waterflood. Two computational techniques which may be used to simulate three-dimensional flow of two fluid phases are described in this paper. The first method, called the "three-dimensional analysis", employs a fully three-dimensional mathematical model that treats simultaneously both the areal and cross-sectional aspects of reservoir flow. The second method, called the vertical equilibrium (VE) analysis", is applicable

By Robert Adams

Secondary or scrap materials appear at all stages in the industrial process and in a bewildering variety of forms, grades, and values. It is useful to begin analyzing them by dividing the broad concept of "Secondary Supply" into three parts First, the concept must encompass the stock, or pool, of secondary materials. In the process of satisfying his wants, man produces desired products from the materials and natural resources found around him. As long as the rate of production is greater than the rate of obsolescence of a given product, the total stock or pool of materials embodied in that product will increase in size This stock concept relating to secondary materials is directly analogous to the "resource" concept used for primary raw materials in the preceding chapter, and includes all materials embodied in existing products (Obviously, this excludes those materials which are destroyed in the consumption process, viz , fuel oil burned to provide heat.) Consumption of a primary material in a productive process tends to reduce the resource base of that primary material In direct contrast, however, the production or use of products increases the resource base of the secondary material. Thus, we find that a country which has no resource of a primary material can, by importing products that contain the material, build up a large enough stock to provide a basis for secondary recovery. The estimated growth of the pool of copper in use in the United States through 1967 is shown in Table 5.B.1.a The estimate of 39 3 million tons at the end of 1967 includes only technologically recoverable copper and is, therefore, somewhat less than the stock concept described previously, which does not distinguish between recoverable and unrecoverable material. Nevertheless, Table 5 B.1 does give an idea of how a nation's secondary resource of a material can grow over the years. A second aspect of the concept of secondary supply is the generation of secondary materials. This includes materials generated as scrap in production as well as the movement of a material out of the stock of existing products via wear, damage, or obsolescence The quantity of materials generated is usually either nearly or completely independent of the technologic capabilities and economic forces which prevail in the secondary recovery market.b The justifications for and the qualifications to this statement are considered later. The final aspect of the concept of secondary supply consists in the secondary recovery process It is at this point that the technologic and economic forces of the secondary recovery market become the controlling fac-

Jan 1, 1976

By A. G. Weber, R. L. Ledbetter, A. L. Hicks

A procedure which makes use of both analog and digital computers has been developed for predicting the pressure-production behavior. of water-drive reservoirs. The electric analyzer is used for matching the past pressure and production history of the reservoir and inferring the physical characteristies of the aquifer. When the history has been matched, a .set of base curves called influence functionce" are derived and the future behavior of the reservoir is calculated from these curves. INTRODUCTION Electric analog methods are particularly well-suited for complex water-drive problems. Like all other methods of analyzing water-drive reservoirs, however, analog methods are subject to certain limitations. One of the more obvious and serious of these results from inaccurate or insufficient knowledge about physical characteristics of the reservoir and aquifer. However, it is not insurmountable because the unknown characteristics can usually be inferred from the reservoir's previous behavior. Simons and Spain have shown that even with scant reservoir data and limited production history, electric analyzer studies can provide useful and reliable results. Aside from this limitation on analyzer predictions, the main disadvantage has been lack of a technique for keeping predictions abreast of latest production forecasts. Pressure behavior of a reservoir depends on the rate at which fluid is withdrawn; it is therefore necessary to specify the future withdrawal schedule before the future pressure behavior can be calculated. Conventionally, the electric analyzer predicts pressure behavior for a specific production schedule. If this schedule is abandoned in favor of some new one, as is frequently the case, either the study must be rerun or results adjusted in some manner. The usual procedure is to predict pressures for several different forecasts covering a wide range of production rates. Pressures for specific rates other than those studied can then be approximated by interpolating between the analyzer predicted curves. However, reliability of this type of prediction is doubtful. This paper describes a technique for predicting future behavior of water-drive reservoirs that retains all advantages of electric analyzer analysis and eliminates the main disadvantage. That is, the analyzer is used conventionally to infer unknown reservoir parameters from the pressure history, but not to predict the future behavior directly. Instead, a derived set of base curves, called influence l'unctions, can be used to calculate future behavior for any production schedule.

By H. K. Work, G. H. Enzian

In the manufacture of steel for commercial purposes, the deoxidation practice used, i.e., the method and degree of deoxidation, is an important factor affecting the structure and mechanical properties of the finished steel. Deoxidation practice exerts a pronounced influence not only on the soundness of the ingots but also on the reaction of the steel to a number of mechanical and thermal treatments. The first mentioned effect of deoxidation is more or less obvious and was first demonstrated, though perhaps not fully appreciated, by Robert Mushet when, in 1856, he added speigeleisen to low-carbon bessemer blown metal. In 1861. Bessemer patented the addition of one pound per ton of silicon to his blown metal to "cause the metal to lie quietly in the mold." The second effect of deoxidation-—that is, the effect on the properties and behavior of the steel—is, one might say, more subtle, and certainly not as well understood as the first, although in many cases it is the more important consideration. This paper is limited to a discussion of only the second effect of deoxidation and: in particular, to the effect on the strain-sensitivity of low-carbon steels. General Discussion Originally it was thought that the function of a deoxidizer was to combine with the oxygen present in the steel as iron oxide and prevent its subsequent evolution as a gas. -More recently it has been realized that a deoxidizer does more than this. Frequent reference has been made to the effect of deoxidizers on the nitrogen in the steel, and some attention has also been paid to hydrogen. As a consequence of the above situation any study of deoxidation must be concerned with the gas content of the steel and the effect of the deoxidizer on the gases involved. The term "gas content" as used here refers to gases extracted from steel during melting in vacuum rather than to elements present in steel in the gaseous state. The extracted gases, at least in the case of oxygen and nitrogen, are generally accepted to be products of decomposition of oxides, nitrides, or other more complex compounds. The manner in which deoxidation affects the gas content of steel and the significance of gases in steel have been and still are subjects of considerable speculation. No attempt will be made here to give a complete discussion of the literature on this subject but a few references will be cited for purposes of illustration. N. Hamilton1 found a correlation between the oxygen content of alloy steel and the behavior of the steel during tube piercing. Davenport, Bain, and others associated oxygen with aging properties of steel while Köster5 and a number of others6-lo made similar claims for nitrogen. Daniloff, Mehl, and Hertyll stated that "deoxidation decreases the susceptibility of steels to aging directly

Jan 1, 1945

By J. T. McGrath, G. B. Craig

Tensile tests on aluminum single crystals, grown from the melt, revealed that the yield stress of these crystals was raised as the amount of striation substructure was increased. The number of striation-type boundaries was varied by changing the rate of growth of the crystals. The results are interpreted in terns of a blockage of dislocation movement by striation boundaries. IMPERFECTIONS are known to have a large effect on the mechanical properties of metals. Teghtsoonian and Chalmers 1 studied a block or striation-type substructure in tin and found that the formation of the striations depended upon rate of crystal growth and orientation. They found that the angular misorienta-tion between neighboring striations varied between 15 min and 5 deg. Atwater and chalmers2 investigated striations in tin and lead, and found that purity was another factor which influenced their formation. There was a limiting purity above which the striations were straight and regular. There is little information in the literature concerning how substructures in melt-grown crystals affect strength. washburn3 introduced small-angle boundaries into zinc by a shear process and found a subsequent increase in yield stress which he attributed to the presence of these boundaries. Lauriente and pond4 found the critical resolved shear stress in aluminium crystals grown from the melt, to increase with etch pit density. The etch pits were used as an indication of growth imperfections. In Hibbard's5 work on lineage structure in copper crystals grown from the melt, he tested one crystal containing interlineage boundaries, and found a 50 pct increase in the critical resolved shear stress. Fleischer and Chalmers6, in a recent paper, mention briefly that, in the production of aluminium crystals from the melt when the growth rate was raised from 1.2 to 18 cm per hr, the yield stress increased 50 pct. They felt that the increase in yield stress with rate of growth might be attributed to a higher concentration of impurities in the gage length and also might be affected by the increased number of small-angle boundaries (striations). The present investigation was undertaken to determine the effect of the striation substructure on the strength of aluminum single crystals. EXPERIMENTAL PROCEDURE Aluminum single crystals of 99.9992 purity were grown from the melt using a technique described by Chalmers.7 The growth rate was varied from 0.6 to 20 mm per min, thus producing crystals with varying numbers of striation boundaries. To avoid prior deformation, the crystals were chemically cut to the desired length with a saturated solution of cupric chloride. They were then annealed at 580°C for 24 hr and allowed to cool slowly in the furnace. Finally, the specimens were electropolished using an electrolyte of 5 parts ethyl alcohol and 1 part perchloric acid. Each specimen was approximately 5 in. in length and 0.125 sq in. in cross section. The average orientations of the 5 series of crystals studied are shown on the stereographic projection of Fig. 1. The crystals were strained approximately 2 pct in a soft tensile machine. The strain sensitivity was 3.6 x 10-4 cm over a 5-cm gage length.

Jan 1, 1960

By H. G. Sell, G. W. King

An investigation was made of the lensile proper-ties of recrystallized high-purity tungsten and a W-1 pel ThO2 dispersed-phase alloy over the temperature region of 800° to 2400°C. The thoria addition resulted in a modest strengthening effect over the entire temperature region. A decrease in ductility of both materials occurred above 0.5 Tm which was caused by void formation. Current theories of IT has long been recognized that a second phase of hard particles has a strengthening effect on a pure metal. At low or intermediate temperatures (<0.5 Tm), the strengthening effect is thought to arise mainly from the interaction of dislocations with dispersed particles. Above 0.5 Tm, dynamic recovery processes greatly alter the deformation mechanisms from those simply involving glide, and grain bound- strengthening by a dispersed second phase do not adequately explain the tensile results. Melallographic examination suggests that the improved strength of tire alloy results from the effect of thoria on the mierostructure. Stress-dependent thermally activated processes were found to occur high temperatures. aries may act as sources of weakness rather than strength because of grain boundary sliding. Grain boundary sliding at high temperatures has been postulated to be the primary factor giving rise to the formation of voids or cavities at grain boundaries1-3 which in turn cause premature failure and poor ductility.4 Voids, once formed, can grow by the condensation of vacancies from the equilibrium concentration&apos; or from the excess vacancies produced by the deformation.4,5 The high-temperature tensile properties of unalloyed tungsten have previously been investigated by Sikora and Ha116 and also by Taylor and Boone.7 The purpose of the present work was to investigate

Jan 1, 1965

By E. J. Ripling

TUBES may be produced by a large number of forming processes, the most common of which will be discussed analytically in this paper. In no case will the stress analysis for any given tube producing process be derived formally for where such analyses are available, they may be referred to readily. Rather, emphasis will be placed on the interpretation of the theory of the different processes, few of which are developed to a state that will allow rigorous mathematical analyses, in an attempt to give a rational description of the effects of the different variables involved in each method. Tube producing methods can be divided into two groups: Those used to form shells, and those used to further work these shells into a shape more suitable for their final use. Among the first group are included roll piercing, extrusion and cupping for seamless shells, and bending with welding for welded tubes. The re-forming processes include sinking, drawing with a plug, and drawing with a rod. Only the plastic forming operations will be discussed here; other forming processes such as casting shells will not be considered. PRODUCTION OF SHELLS Shells for Seamless Tubing Piercing: The extremely important process of forming an axial hole in a billet by oblique rolling never has been analyzed satisfactorily, although a certain amount of experimental work relating to this process has been conducted. There are a number of factors that make piercing difficult to analyze; one of these is the fact that piercing is not a problem in plasticity, but one in fracturing, and the laws of fracturing are even less well understood than those of plasticity. If, however, it is assumed that fracturing occurs on a surface as a result of tensile stresses acting normal to this surface, piercing can be analyzed qualitatively by examining the stresses established in the oblique rolling process. To determine the origin of the tensile stresses that are thought to effect piercing, it will be necessary to know the angular relationships between the maximum stresses that are established in piercing. These angles quite frequently can be determined in a plastic deformation process by an examination of the deformed product. For example, consider the stresses established when a tensile test is conducted on a rectangular cross-sectional specimen of pearlitic steel. When stretched, this material first flows plastically, exhibiting the well-known yield jog on a stress-strain curve. The formation of the slip areas that give rise to the yield jog can be detected during the straining, since these flowed areas cause depressions on the specimen surfaces which can be seen if the surfaces are polished highly. The plastically strained areas also can be found after the specimen has been stretched to a strain not exceeding the yield jog, by sectioning the test piece and. etching these sections with Fry&apos;s etch. With this etchant, it is possible to dis-

Jan 1, 1951

By M. J. Duggin

Structural similarities between the E, X, and iron carbides are illustrated. Experimental evidence regarding phase transformations occurring during ternpering reactions in finely divided carbides, thin-film carbides, and carbides which occur in steels is considered and possible mechanisms for the E — x and x — 9 transformations proposed. HOFER1 has shown that within the appropriate temperature ranges carbon monoxide will react with finely divided a iron to form either iron carbide or x iron carbide. He has shown that at an elevated temperature the E iron carbide will transform to the x iron carbide (Hagg carbide) which, upon further elevation of temperature, will transform to 9 iron carbide (cementite). Jack,2,3 using X-ray diffraction methods, has observed that during the tempering reactions occurring in steel the E iron carbide formed in the first stage of tempering passes into two-dimensional platelets of 0 iron carbide during the second stage of tempering. The three-dimensional form of the 0 carbide is formed during the third stage of tempering. Jack suggested2 that the two-dimensional platelets of 0 carbide could be related to the faulted x iron carbide. Okada and Arata4 investigated a Swedish steel containing 1.05 wt pct C and approximately 1.0 wt pct Mn using permeability measurements at low field strength. A Curie point of 360°C was observed in the quenched steel, which indicated the presence of E iron carbide. On tempering at 400°C the specimen developed a Curie point at 230°C, indicating the presence of x iron carbide, and on tempering at 700°C the specimen developed a Curie point at 190°C which was assigned to 0 iron carbide. The carbides were extracted electro-lytically and the use of X-ray diffraction techniques4r5 indicated the carbide with a Curie point of 230°C to be x iron carbide. The Curie points of the carbides are 10 to 22°C lower than the accepted values which is probably due to the presence of manganese in the carbides, since it has often been observed (e.g., Ref, 6) that a partial substitution of manganese for iron in cementite will lower the Curie point of this carbide. Hofer&apos; summarizes additional evidence of the tempering reactions in steel in which E iron carbide, formed during the first stage of tempering, transforms to x iron carbide during the second stage of tempering. During the third stage of tempering, the x carbide disappears as the 0 carbide is formed. By carburizing thin iron films in a CO gas stream, ~a~akura&apos; has been able to produce the E, X, and 0 iron carbides. He found that below 250°C the E iron carbide was formed; between 250" and 350°C the x iron carbide was formed and above 350°C the 0 iron carbide was formed. He has shown that the E iron carbide transforms to form x iron carbide at 380" to 400°C and that the x ir°n carbide transforms to form the 0 iron carbide at approximately 550" C; both of these phase transformations are irreversible. Hofer&apos; presents a review of evidence to show that the sequence of reactions occurring during tempering processes subsequent to the formation of E iron carbide formed by the direct carburization of finely divided a iron is the same as the sequence of reactions which occur during the tempering processes subsequent to the formation of E iron carbide in steel during the first stage of tempering. It is evident from Nagakura&apos;s work that identical tempering reactions are found in thin films of iron which have been carburized to form iron carbide. The purpose of this paper is to discuss the structural similarities between the E, X, and 0 carbides and to suggest a possible mechanism by which regions of the E carbide, formed during the first stage of tempering, may transform to the x carbide during the second stage of tempering. For the finely divided or thin film carbides a mechanism will be proposed for the transformation of the x carbide to the 0 carbide during the third stage of tempering, although it will be suggested that there is evidence that such a transformation may not occur in steels. STRUCTURAL DATA OF THE E, X, AND 0 IRON CARBIDES € Iron Carbide. It is evident from X-ray diffractions and electron diffraction&apos;, investigations that the metal atoms in the E iron carbide form an hcp structure with lattice constants ah = 2.752A, ch = 4.3534, using electron diffraction, reports the lattice paramet$rs of the superlattice cell to be a = 4.767A, c = 4.354, c/a = 0.9134. He finds that the carbon atoms occupy the octahedral voids in the metal atom structure so as to form a hexagonal stacking sequence with its basal plane parallel to that of the metal atoms. Considerable long-range disorder occurs in the positioning of the carbon atoms, however, which is in agreement with the possible range of composition Fe2C-Fe3C discussed by Hofer.&apos; Barton and ale" have made X-ray diffraction measurements on a sample of E iron carbide extracted from a catalyst in an organic process. Although there were few reflections recorded on the obtained X-ray powder diffraction pattern, they have proposed that the structure could belong to one of the three possible space groups p3m1, P63/mmc, or Pbcn if one assumed the composition to be Fe2C. Nagakura, using electron diffraction data, suggests a space group of P 6322 for a specimen of c iron carbide of apparent composition Fez.&. x Iron Carbide. The x iron carbide has been studied by Duggin and Hofer" and by Jack and wild,&apos; who

Jan 1, 1969

By G. W. Tracy, R. D. Carter

Numerical calculations were made to determine the behavior of reservoirs with high-pressure drawdown and wide well spacing where the initial productivity is low and the wells are completed by hydraulic fracturing. The two-phase flow equations were solved for the flow into a single well. This well was assumed to be producing from a reservoir with hydraulically created horizontal fractures (four different systems with fractures were studied). For comparison purposes, additional two-phase flow calculations were made assuming a reservoir with uniform rock properties. The two-phase flow results were also compared with the conventional calculation methods, which do not include the effect of saturation gradients resulting from a simultaneous flow of oil and gas which are normal to this type reservoir. It was found that the conventional methods predict (1) a high and too optimistic value of ultimate recovery, (2) a high producing rate and a high reservoir pressure at a given oil recovery and (3) a low trend of gas-oil ratio with oil recovery. Included in the two-phase flow calculations were provisions to control the oil production rate by an allowable rate and, also, by a gas-oil ratio penalty rule. For the systems with hydraulic fractures, the producing rate was controlled by the gas-oil ratio penalty rule for most of the life. This is in contrast to the system with uniform rock properties which went "on decline" almost immediately. An unexpected characteristic of the systems which included fractures was the early rise in producing gas-oil ratio from 730 cu ft/bbl to approximately 1,200 cu ft/bbl, followed by a "leveling off" before the normally expected gas-oil ratio rise began. Additional features which are a result of hydraulic fracturing are (I) greater ultimate recovery, (2) higher average producing rates and (3) a lower average reservoir pressure at a given oil recovery. INTRODUCTION Some oil fields discovered during the past few years are producing from certain volumetric ally controlled reservoirs (often referred to as solution or internal gas- drive reservoirs) which are characterized by high-pressure drawdown at the wells. Since the available pressure drawdown at a well is limited by the static reservoir pressure and the producing rate is controlled by the available drawdown, wells completed in this type of reservoir usually produce at a rate less than the allowable from the time of completion. Because of this, this type of reservoir is referred to as a low productivity reservoir. Economic considerations require the use of wide well spacing and well stimulation by hydraulic fracturing to make commercial wells in this type of reservoir. Performance predictions for volumetrically controlled reservoirs have been made using a combination of two standard equations. 1. The "Schilthuis" or "Muskat" type material balance equation is used to relate the average reservoir pressure and the cumulative oil recovery. 2. The results from the material balance equation and the productivity factor as described by Pirson&apos; are used to relate the cumulative recovery with producing rate and time. The material balance equation assumed uniform pressure and liquid saturation conditions throughout a reservoir. The steady-state radial flow formula allows for a pressure gradient toward a well but assumes uniform liquid saturation. These calculation methods are adequate for application to reservoirs wherein the drawdown at the well to realize satisfactory producing rates is small compared to the total pressure. In low productivity, volumetrically controlled reservoirs, the pressure drawdown at the well is large cornpared to the total pressure. Although a precise number cannot be given for the magnitude of a large pressure drawdown, values in excess of 1,000 psi would definitely be included. For practical considerations, this usually occurs when the formation flow capacity is less than about 100 md-ft. However, this limit of formation flow capacity will vary with the well producing rate. The low pressure in the neighborhood of the well which results from a high drawdown causes evolution of large volumes of gas. This causes the gas saturation to be higher near the well than at a greater distance—-hence, a non-uniform gas saturation. Also, the relationship between the relative permeability to oil (K/K) and gas saturation is nonlinear but decreases approximately in an exponential way with increases in gas saturation. Because of this, the following chain reaction is established.

Aamot, Olav Crone, (M&apos;29) Chem. Engr., Elektro¬kemisk, Raadhusgt, 23; Oslo, Norway. Abadilla. Quirico A., (M&apos;33) Min. Engr., Dir., Bureau of Mines, Manila, P. I. Abbott, Agatin T., ( J&apos;40) Asst. Geol., Trench Mine, Patagonia, Ariz. Abbott, Clarence E., (M&apos;04) Civil Engr., V.P., Tennessee Coal Iron & R. R. Co.. 159&apos;3 Brown Marx Bldg.. Birmingham, Ala. Abel, Raymond L., (M&apos;28) Chem. Engr., Chief of Inspection Div., Pittsburgh Chem. Warfare Pro¬curement Dist., American Batik Bldg., Pitts¬burgh. Pa. Abel, Walter D., (M&apos;32) Min. Engr.. Div. of Cor¬porations, State of Calif.. 403 California State Bldg., Los Angeles, Calif. Abele. Louis T., (M&apos;31) 4800 Patterson Ave.. Richmond, Va. Abell, Leo M., (M&apos;311 Research Met., Mount Mor¬gan Ltd., Mount Morgan, Queensland, Australia. Abenius, Hakan V., (M&apos;37) c/o Falu Gruva, Falun, Sweden. Abernathy. G. E., (M &apos;33S) Geol., Kansas State Geol. Survey. Pittsburg, Kan. Abernathy, Jack. H.. (M&apos;40) Chief Engr., Sunray Oil Co.. Philtower B1dg., Tulsa. Okla. Ahorn, Robert H., (M&apos;19) Asst. Met., Research Lab., U. S. Steel Corp., Lincoln Highway, Kearny, N. J. Abraham, A. W., (M&apos;30) Petr. Engr., Richfield Oil Corp., 555 S. Flower St., Los Angeles. Calif. Abramowitz, William L., (J&apos;40) Chem., National Oil Products Co., Harrison, N. J. Abrams, Charles Jackson, (M&apos;36) Gen&apos;l Supt., Climax Molybdenum Co.; Climax, Colo. Abstein, Henry T., (M&apos;27) Yellow Pine, Idaho. Ackerman, D. E., (M&apos;35) McKinsey & Co., 2 Wall St., New York, N. Y. Ackerman. E. Dumont, (A&apos;3S) Petr. Geol.. Dist. Geol., Quiriquire&apos; Dist., Standard Oil Co. of Venezuela, Caripito, Venezuela.

Jan 1, 1941

"In the spring of 1927, six members of the American Institute of Mining and Metallurgical Engineers met for dinner at the Chemists&apos; Club in New York to discuss the possibility of setting up a committee within the Institute to further the current interest in the science of steelmaking. Attention&apos; to this subject had been crystallized by a symposium held by the Faraday Society in 1925. &apos; After a prolonged discussion, ranging from thermodynamics to slag conditioning, it was decided to approach the Institute with the request that a standing committee on "The Physical Chemistry of Steel Making" be set up. This committee proposed to promote scientific and practical papers on the subject, and was designed to cooperate with the Open Hearth Committee of the Institute in bringing scientific developments to the attention of open-hearth operators throughout the country... . "As the life of the [Physical Chemistry of Steelmaking] Committee lengthened and general interest in the technical phases of steelmaking grew, it became evident that there was a distinct need for a book that might serve the open-hearth interests to better advantage than standard texts whose scope is necessarily wide and whose detailed exposition of the open-hearth process is, therefore, somewhat limited. With this thought in mind, the Committee, after some years of consideration and debate, embarked on the venture of writing a manuscript on `Basic Open Hearth Steelmaking&apos;." The foregoing paragraphs, taken from the introduction by C. H. Herty, Jr. to the first edition, well describe the circumstances which led to the publication of "Basic Open Hearth Steelmaking" in the spring of 1944. The book consisted of nineteen chapters contributed by twenty-three authors and edited by the staff of Alloys of Iron Research and T. S. Washburn, B. M. Larsen, and J. S. Marsh with Frank T. Sisco as consulting editor. The Engineering Foundation and the Open Hearth Steel Committee of the Iron and Steel Division, AIME, made financial grants; steel companies and other organizations supported the publication by contributing time and expenses of staff members in their capacity as authors or editors. The volume was sponsored by the Seeley W. Mudd Memorial Fund and appeared under the

Jan 1, 1951

By B. M. Larsen, W. E. Shenk

This paper describes a method of reversal control of the open-hearth furnace that obtains in practice those effects considered below as essential to a completely automatic control, without appreciable interference with the natural rise and fall in temperature of the regenerative portions of the furnace system. Growing out of some studies of radiation pyrometry in open-hearth regenerators, it was developed during 1934-1938, and has been successfully applied to a number of commercial furnaces. The goal of open-hearth furnace operation is the highest rate of production of steel of proper quality consistent with good refractory life and fuel economy. This requires rapid heat transfer from furnace to charge, which in turn is dependent upon heating the furnace refractories to the highest safe operating temperature. The greater the heat input to the melting chamber, the sooner this limiting temperature will be reached, so that control methods in general that are designed to protect against overheating of refractories should help to maintain maximum fuel input and production rate. For the typical open-hearth system, with fixed regenerator capacity and with rate of fuel input usually restricted in its range of variation, our basic assumption is the idea that the only other important variable —that is, the time interval between successive reversals—should also be held constant or within a small range. The present reversal control was designed therefore so that, under normal operating conditions, no arbitrary limitation is imposed other than to keep the reversal interval within the optimum time range. However, since a near approach to completely automatic operation involves protection of refractories through the balancing of furnace end temperatures as well as emergency protection against temperature peaks above some upper limit, it was also felt essential to employ, as an integral part of the control unit, a temperature-measuring instrument to register the true temperature of the refractory surfaces at some critical region in the hot ends of the regenerative zones. As the basic elements of the control, we thus have one "maximum" and one lLminimum" time relay and a potentiometer recorder-controller, combined with switches and relays to operate as follows: I. Reversal normally occurs within an optimum range limited by the maximum and minimum settings to about 4 to 6 min. variation, but the actual interval usually is less variable and closer to the minimum setting. 2. The margin between minimum and maximum time is utilized, together with a "floating temperature limit" in the potenti-ometric control instrument, to correct any tendency toward temperature unbalance between ends of the furnace. 3. A second "maximum temperature

Jan 1, 1945

By J. W. Halley, G. L. Plimpton

BECAUSE of the two distinct stages in the solidification of rimmed steel, segregation in the rimmed ingot is more complex than that in the killed or semikilled ingot. In the earlier stage, chemical reactions, resulting in evolution of gas and vigorous stirring of the metal, effect a degree of negative segregation unique to rimmed steel. The composition of this zone constitutes the principal quality advantage of this type of steel. In the later stage of solidification, after the evolution of gas has ceased, the segregation follows the general pattern of a more completely deoxidized steel. However, the composition of the liquid remaining after the first solidification stage varies markedly from that of the original melt, some constituents having been partially removed as reaction products while the concentration of others has been intensified by rejection from the metal solidifying in the first zone. The aim, from the standpoint of segregation, in rimmed steel of high quality is to effect a maximum negative segregation in the rim zone without excessive concentration of undesirable elements at the center of the ingot. To achieve this aim, the composition of the melt may be varied and the furnace and pouring practice may be adjusted within certain limits. It is the purpose of this study to discuss segregation in rimmed steel from the standpoint of the mechanisms that produce it and to survey the phases of open-hearth practice that influence those mechanisms. MECHANISMS PRODUCING SEGREGATION The mechanisms that determine the degree of segregation in the rimmed ingot are closely interrelated, making it difficult to select the primary factors and to determine a satisfactory order for presenting them. For instance, the question of sulphur segregation is relatively simple, since sulphur is not directly involved in chemical reactions in the ingot; but its concentration in the rim zone is dependent not only on its original analysis in the melt, its segregation coefficient, and the freezing rate, but also on the rate of its removal from the impure film on the solidifying surface. This washing action involves all the factors (such as freezing rate, the carbon-oxygen product, pressure, etc.) that determine the rate of gas evolution and hence the efficiency of film removal. Sulphur distribution between the rim and core is affected by the volumetric ratio between the two zones, and its segregation in the core is a function not only of the freezing rate of the core but also of all the foregoing factors that determine its concentration in the metal when solidification of the core starts. To simplify the presentation, it is proposed to treat the mechanisms affecting segregation independently in this section, reserving a discussion of their over-all effects for the section in which actual segregation data are given. The factors affecting segregation will be treated in the following order: (I) differential solidification, (2) removal of constituents as

Jan 1, 1944

By G. W. Brock

Experiments in the form of aging of overstrained tension specimens and elevated temperature tension testing, have been carried out on recrystallized arc-cast molybdenum. The aging behavior of molybdenum was found to be strongly dependent on the degree of plastic strain present in the lattice: the reason for this being the low solid solubility for the common interstitial elements in molybdenum. GEORGE W. BROCK, formerly Research Associate, Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, III., is Research Associate, Department of Engineering Sciences, IBM Research Center, Yorktown Heights, N. Y. Manuscript submitted January 19, 1961. IMD THE term strain aging is familiar in connection with the recovery of the yield point in mild steel after tensile overstraining, and there are other instances where it is known to exert an appreciable effect on mechanical properties. For example, steel exhibits a greater tensile strength at mildly elevated temperatures than at room temperature and serrated stress-strain flow curves occur under certain conditions. It has been known for a number of years that the phenomenon of strain aging is directly connected with the presence of carbon and nitrogen in the lattice; and extremely small amounts of either element are sufficient to produce the effect. In this study, the aging behavior of overstrained tensile specimens of recrystallized molybdenum has

Jan 1, 1962

By W. P. Saunders, W. R. Hibbard, G. H. Eichelman

Interest in the various products of the austenite eutectoid transformation in iron-carbon alloys, particularly as produced by the isothermal sub-critical techniques introduced by Davenport and Bain,&apos; has resulted in the application of similar heat treatments to other eutectoid transformations. Studies o f the beta copper-aluminum alloy eutectoid transformation revealed microstructures very similar to those found in iron-carbon alloys. Investigations5t6 of the kappa phase in the copper-silicon alloy system have established the eutectoid type transformation of this phase into terminal alpha and intermediate gamma phases. This transformation has been reported5 as forming a eutectoid type structure in a very sluggish manner by a long time isothermal treatment. The purpose of the present investigation is to study the products of the kappa eutectoid transformation as affected by transformation temperatures by means of microscopic and hardness methods. Preparation of Alloys The copper-silicon alloy equilibrium diagram is shown in Fig 1. The kappa field converges to a minimum silicon solubility at the eutectoid composition and all other completely kappa alloys are hypereutec-toid. Thus, kappa decomposition involves first the proeutectoid precipitation of gamma, followed by the eutectoid transformation of a lower silicon content kappa (5.2 pct) Smith6 has indicated that alloys containing between 5.4 and 5.7 pct silicon could be hot rolled, but that the latter composition was desirable in order to permit a wider kappa temperature range. The alloy was prepared by adding Baker&apos;s commercially pure silicon to an ingot of copper-silicon alloy containing 2.34 pct silicon remaining from the investigation of Brick, Martin and Angier.&apos; Following the casting techniques of Krynitsky, Saunders and Stern,s the ingot was melted under a heavy layer of dried charcoal in a clay-graphite crucible in a gas-fired pot furnace. Small lumps of silicon were held under thc melt surface with a graphite rod. After the silicon had dissolved, the alloy was chill-cast and then remelted without a cover, stirred thoroughly, skimmed and poured into a preheated cast iron mold. The cast microstructure is shown in Fig 2. The casting, 10 X 4 X K in., was annealed at 750°C for 21 hr and furnace cooled, About }{& in. was milled from all surfaces. The plate was cut in half longitudinally and the bottom half analyzed by A.S.T.M. and The composition by weight was as follows: copper 94.24 pct, silicon 5.56 pct, iron 0.11 pct.

Jan 1, 1949

By W. G. Pfann

Under certain conditions, a molten zone can be made to move through a solid by impressing a stationary temperature gradient across the solid. This phenomenon can be utilized in fabricating semiconductive devices, growing single crystals, joining, boring fine holes in solids, measuring diffusivities in liquids, small scale alloying, and purification. Fundamentals and exemplary applications are outlined. ANEW aspect of the travel of a molten zone through a solid is considered in this paper. Whereas, in previously described zone melting techniques,&apos;-&apos; zones were usually caused to move by changing the position or temperature of a heat source, in the present technique a zone is made to move by impressing a temperature gradient across it. For example, a thin layer of molten A1-Si alloy, sandwiched between two silicon slabs having a temperature gradient normal to the layer, will travel through the hotter slab. One feature of temperature gradient zone melting, as this technique will be called here, is that zones of unusually small dimensions can be maintained. This leads to such diverse uses as have been listed in the abstract. In this paper fundamentals of the movement of a molten zone in a temperature gradient, and some practical applications thereof, are outlined. Assumptions The movement of a molten zone through a solid body of solvent substance in which a temperature gradient exists will be discussed. The length of the zone will be its dimension in the direction of motion. The direction of the temperature gradient will be toward the region of higher temperature. To be considered is a binary or higher order solute-solvent system in which the concentration of solute in the molten zone is sufficient to produce a lowering of the freezing temperature of the solvent which is at least of the order of the temperature range impressed on the charge. While we discuss primarily molten zones in a solid matrix, the principles are applicable to solid or vaporous zones in a solid matrix, a requirement being that the diffusivity in the zone be substantially greater than in the matrix. Diffusion of solute into the surrounding solid will be assumed negligible. In general, its presence will not basically alter the conclusions to be drawn. For illustration, a system represented by the partial constitutional diagram of Fig. la will be discussed, in which k, the distribution coefficient defined in the figure, is constant and less than unity. However, the technique is applicable to any solute- solvent system in which one component lowers the melting point of another component. Movement of a Molten Zone in a Temperature Gradient Consider, in the system AB of Fig. 1, where B is designated the solute and A the solvent, the effect of sandwiching a thin layer of solid B between blocks of solid A and placing the whole in a temperature gradient such that the temperature of the layer is above the lowest melting temperature of the system. Surrounded by an excess of A, the layer will dissolve A, becoming molten, and expand in length." As so- lution of A continues, at both interfaces, the mean solute concentration in the zone will move to the right in Fig. la, until at temperature T, the liquid at the cooler interface reaches the liquidus concentration C,. Solution of A thereupon ceases because the liquid T1 is saturated with A. The liquid at the hotter end of the zone, being at temperature T2, is not saturated with A at concentration C1. Hence solution of A continues there and concentration C2 is approached. A concentration gradient therefore is set up in the zone, causing A to diffuse toward the cool end and B toward the hot end. As a result, the liquid at the cool interface becomes supersaturated and a layer of crystalline A containing concentration kc, of B in solid solution freezes. Since a source of A

Jan 1, 1956

By M. J. Spendlove, H. W. St. Clair

An automatic surface-follower mechanism was used to measure the surface temperature and the rate of evaporation of molten zinc while undergoing distillation at low pressure. At pressures of 50 to 100 microns Hg, the rate of evaporation may be 60 to 80 pct of the theoretical maximum corresponding to the measured temperature. The rate decreases rapidly at pressures above 100 microns Hg, to only 7 pct of the theoretical maximum at 2000 microns Hg. Measured temperature gradients at the surface are in agreement with theoretical gradients calculated from the heat of vaporization, rate of evaporation, and thermal conductivity of molten zinc. THIS paper covers a series of careful measurements of the rate of evaporation of molten zinc at low pressures, undertaken as a part of a general investigation on the separation of metals by distillation.&apos; Preliminary results on the rate of evaporation of zinc were described in a previous publication.&apos; The results of the preliminary study are as follows: 1—The observed rates of evaporation of zinc were as high as 0.60 g per sq cm per min, corresponding to 75 pct of the maximum rate as determined by the temperature of the metal. 2—The evaporation rate was decreased from 0.30 g per sq cm per min at a pressure of 25 microns to only 0.09 g per sq cm per min when the pressure was increased to 5 mm. 3—The temperature of the surface during rapid evaporation may be 35" to 100°C less than the main mass of metal. Observed temperature gradients at the surface are consistent with those calculated from the heat of vaporization and the thermal conductivity of liquid zinc. In the preliminary experiments, the rate of evaporation was determined from the loss in weight of the metal in the crucible during the test. This was compared with the weight of the condensate. Obviously, this method was subject to error because of some uncertainty as to the period of evaporation that should correspond to the loss in weight. Furthermore, this method did not permit taking into account probable variations in the rate of evaporation during the test. A more serious shortcoming was that the temperature at the evaporating surface was not known, so the maximum theoretical rate of evaporation could not be calculated accurately. To improve the precision of rate measurements and to allow accurate measurements of the surface temperature, a refined experimental technique was developed whereby the temperature and position of the surface could be measured accurately. This was done by an automatic surface-follower mechanism that gave a continuous record of the surface temperature and the amount of zinc evaporated. These data permitted an instantaneous determination of the actual rate of evaporation and the surface temperature throughout the test. Pure zinc (99.99 pct Zn) was used in all experiments. Description of Distillation Furnace The details of construction of the distillation furnace are shown in Fig. l. The furnace is enclosed in a large quartz tube open at one end. The open end of the quartz tube is sealed by means of a water-cooled head. The entire enclosure is vacuum tight. The connection between the water-cooled head and the quartz tube is sealed by means of a rubber gasket which fits tightly against the smooth end of the tube. The metal is heated by induced current set up in the molten zinc and the walls of the graphite crucible by means of a water-cooled induction coil outside the quartz tube. High frequency current is passed through the induction coil from a 6 kw mer-

Jan 1, 1952

By R. S. Kinasevich, D. D. Crabtree, D. W. Fuerstenau, T. P. Meloy, A. L. Mular

This paper presents details of the concept that size reduction in comminution machines takes place by three mechanisms; namely impact, abrasion, and chipping grinding. Experimental evidence is presented to show that each of these comminution mechanisms produces particles of a characteristic size distribution. The actual product from a comminution device has been postulated to be the result of a composite of these three types of mechanisms. Composite curves are demonstrated for a material following the Gaudin-Schuhmann, Gaudin-Meloy, and Rosin-Rammler size distributions. About forty years ago, Gaudin1 showed that grinding may be considered a combination of impact and attrition. Since that time, major efforts have been devoted to studies, both experimental and theoretical, of impact and compression fracture, while attrition has been almost wholly neglected, at least quantitatively. A significant attempt to distinguish between attrition and impact grinding is the work of Tanaka2 in Japan. By means of an instrumented abrasion grinder and a drop weight device, he determined coefficients relating the increase in surface area of various materials to the energy expended by the two methods of comminution. He showed that physical properties of a material determine its response to attrition and impact grinding. By extending his ideas to ball milling, he concluded that to a large extent the basic comminution process in a ball mill is due to the impact of falling media. Because Tanaka used a mass of particles in his drop weight device, however, he did not obtain pure impact size reduction. The purpose of this paper is to define basic mechanisms of size reduction, to verify that each has a characteristic and meaningful distribution curve, and to show how a combination of these mechanisms results in a size distribution very like that produced by grinding mills. DEFINITION OF COMMINUTION MECHANISMS The product from a grinding device will be considered to be the sum of the contributions resulting from the action of three basic mechanisms of size reduction which operate in a ball and rod mill. These are impact grinding and two forms of attrition, namely abrasion grinding and chipping grinding. Each is defined below. Impact Grinding: If a straight line is obtained when the cumulative weight fraction finer than a given size is plotted on log-log paper as a function of that size, the slope of the line is defined as the distribution modulus. A number of investigators 3,4,5 have shown that impact fracture of single specimens of different composition and shape results in a distribution of daughter particles that exhibit a distribution modulus of unity. This has also been true for materials broken in slow compression. Moreover, under slow compression or impact fracture conditions, theoretical distribution equations6*&apos; which approximate the Gaudin-Schuhmann distribution when the distribution modulus is close to unity agree reasonably well with the experimentally obtained products. If one now considers a comminution process where many impact or compression fracture events are taking place, then any rational summation of the individual events yields, in the finer size range, a Gaudin-Schuhmann distribution whose distribution modulus is also unity. If the size distribution of the product from a mill has a distribution modulus of unity, it is implied that particles are fractured in a manner which results in a comminution event having a distribution like that obtained for the breakage of single specimens. These impact events would occur when a particle is smashed between balls or between a ball and the mill liner. Attrition, on the other hand, is that form of grinding which cannot be called impact grinding, and comprises both abrasion and chipping grinding. Abrasion Grinding: Abrasion is a form of surface wear resulting when particles rub against each other or against balls or the mill liner of a tumbling mill, somewhat like a piece of wood being rubbed over a piece of sandpaper. The surface wears at a more or

Jan 1, 1964

By A. L. Jr. Pozzi, A. O. Garder, D. W. Peaceman

A new numerical method is proposed for the solution of multidimensional miscible displacement problems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentrations are computed each time step. Based on the method of characteristics for treating combined transport and dispersion, the method applies equally well to any number of dimensions and, in contrast with other numerical procedures, properly takes into account the physical dispersion, no matter how small. Extensive tests show that accurate solutions of one-dimensional problems can be obtained over a wide range of values of the dispersion coefficient, including zero. They also show that the moving points do not need to be uniformly spaced, and that increasing the number of moving points beyond 2/grid interval does not significantly improve the accuracy of the solution. Two-dimmsional calculations using the new method were carried out to simulate laboratory model displacements in which gravity caused overriding of solvent. Good agreement between observed and computed profiles and measured and computed concentrations of produced fluid was obtained for a viscosity ratio of 1.89; at higher viscosity ratios, fair agreement was obtained Computed results were found to be significantly affected by vertical dispersion, and negligibly affected by dispersion in the direction of flow, in agreement with conclusions based on experimental observations. INTRODUCTION Although miscible displacement processes are potentially of great economic significance, limited progress has been made in developing mathematical methods for predicting the outcome of a solvent flood. Because of the complexity of the partial differential equations which describe multidimensional miscible displacement, numerical methods are a natural approach to their solution. The task of finding suitable numerical approximations to one of the partial differential equations, which involves both dispersion and convective transport, has been particularly difficult. Dispersion in the absence of transport is described by the heat flow equation, a second-order equation of parabolic type. This equation has been very successfully treated by numerical methods. Transport in the absence of dispersion is described by a first-order equation of hyperbolic type. This equation has been treated numerically with some success in one dimension, both by Lagrangian and Eulerian techniques, 1.2 but extension to two or more dimensions has not been satisfactorily accomplished. Usually one of two things happens: either the numerical solution develops oscillations or it becomes smeared by artificial dispersion resulting from the numerical process. When transport and dispersion are considered simultaneously, this numerical dispersion may dominate the low physical dispersivicy that generally characterizes miscible displacement. Stone and Brian2 have developed a new difference equation for treating combined transport and dispersion in one dimension. By suitable choice of certain parameters, they succeeded in markedly reducing both oscillation and numerical dispersion. However, a satisfactory extension to higher dimensions has not yet been found. Peaceman and Rachford3 presented a centered-in-time and centered-in-distance difference equation combined with a 1,transfer of overshoot" procedure which was demonstrated to work well in one dimension. The technique was applied to the two-dimensional miscible displacement problem, but subsequent calculations with zero dispersivity showed little change in results compared with the calculations they presented. This indicates that their method involved a numerical dispersion of the same order as the physical dispersion. The present paper describes an alternate method for solving the combined transport-dispersion

Jan 1, 1965