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By A. M. Rowe, I. H. Silberberg

A computer program was written to predict the phase behavior generated by the enriched-gas-drive process. This program is based, in part, on a new concept of convergence pressme, which is then used to select vapor - liquid equilibrium ratios (K-factors) for performing a series of flash calculations. The results of these calculations are the equilibrium vapor and liquid phase compositions which define the phase envelopes. The program was used to predict phase envelopes for 11 different hydrocarbon systems on which published experimental data were available. The predicted and experimental results compare favorably. INTRODUCTION The reservoir engineer is frequently faced with the problem of predicting what will happen if gas is injected into a reservoir. One aspect of this, general problem is predicting the phase changes that will occur when a non-equilibrium gas displaces a reservoir fluid. In particular, a "dry" gas, upon displacing a volatile oil, will pick up intermediate components from the oil. On the other hand, a "wet" gas, containing a high concentration of intermediates, will lose some of these components to a relatively low-gravity, non-eouilibrium1- crude. It is this latter Drocess. occurring in the enriched-gas displacement, which is treated in this paper. In the past, these phase changes have been determined experimentally and the results incorporated into various modifications of the Buckley-Leverett analysis.112 Such experimental work is time consuming, and the results are sensitive to numerous experimental errors. With the wide availability of high-speed digital computing equipment and numerous correlations pertaining to the vapor-liquid equilibria of hydrocarbon systems, it is now practical to calculate such phase behavior. This paper describes a computer program for performing these calculations. THE ENRICHED GAS DISPLACEMENT PROCESS Experimental results have shown that oil recovery can be significantly increased by enriching the displacing gas with intermediate hydrocarbon c0m~onents.3 The essential features of the phase behavior generated by this enriched-gas-drive process are commonly illustrated with ternary diagrams such as Fig. 1.4 In this figure, Gas D, which contains a high concentration of intermediate hydrocarbons with respect to the undersaturated Crude A, is injected into the reservoir. When D contacts A, gas goes into solution until the oil becomes saturated (Point. B). Further contacting of Gas D and saturated Oil B results in a Mixture C which separates into Vapor Y(c) and Liquid X(c). Liquid X(c) is contacted by additional Gas O, resulting in Mixture E which separates into Vapor Y(e) and Liquid X(e). Repeated contacts of the liquid by the injected gas will eventually result in Liquid X(4 of maximum enrichment existing in equilibrium with Gas Y(d). The equilibrium tie-line X(4 Y(4, when extended, passes through the Point D representing the enriched injection gas. For systems of more than three components, the predicted equilibrium states are dependent upon not only reservoir temperature and pressure, but also the compositions of the crude oil and injected gas. If the gas is sufficiently enriched, a miscible displacement is generated. Line If is tangent to the phas,e envelope at the critical point (Point Z) and represents the limiting slope of the tie-lines as the critical state is approached. Point 1 therefore represents the minimum enrichment of injection gas required to generate a miscible displacement. Point G represents the minimum enrichment required for initial miscibility of the injection gas with Crude A. Accra has presented a method to be used for prediction of oil recovery by the enriched gas displacement process.l To develop the phase behavior data needed, he designed the experimental procedure described in the following quotation from his paper: The original liquid was contacted by a volume of displacing gas and allowed to come to equi-

Jan 1, 1966

By F. D. Rosi, C. H. Mathews

THE plastic properties of face-centered cubic metals below room temperature present a field of investigation which has not been extensively ex-plored. The work by Schmid and Boas1 has demonstrated the importance of temperature upon such properties as strain hardening and critical resolved shear stress. The work by Yamaguchi2 upon the shear stress as related to the number of slip bands accentuates the necessity for further experiments of a similar nature. The approach to a mechanical equation of state from the standpoint of thermal fluctuations and activation energies by Becker3 and more recently by Kauzmann4 further emphasizes the need for a quantitative and more comprehensive analysis of the dependence of fundamental plastic properties on temperature. The purpose of the present work was to investigate specifically: (1) The gross shape of the stress-strain curves at several temperatures, (2) the change in the critical shear stress as a function of temperature, and (3) the number and appearance of slip bands as a function of strain and temperature. Preparation of Specimens Single-crystal specimens of 99.996+ pct alumi-num, 1/2 in. in diam and 5 to 6 in. in length, were made by the Bridgman method of gradual solidification from the liquid state. The crystallographic orientation of the single crystals was determined from back-reflection, Laue X-ray photograms ac-cording to the method described by Greninger.6 In most specimens the Laue photograms showed double diffraction spots indicative of the lineage structure type of imperfection, discussed in great detail by Buerger.7 The angular spread of these spots was never observed to exceed 2". Most of the crystals were radiographed to insure against microporosity. In preparing the metal surface for optical microscopy, the following sequence of operations gave good results: The as-cast crystals were turned down in a lathe, 0.001 in. per cut, to obtain a 2.5 in. gauge length. The cold-worked layer resulting from this operation was removed chemically by etching with Tucker's reagent. Then the specimen was polished mechanically through 2/0 metallographic emery paper, after which it was etched again to remove the cold-worked layer resulting from the mechanical treatment. A 48-hr anneal at 580°C ±10°C followed so as to insure an essentially stress-free single crystal. After the annealing treatment, the specimen was electrolytically polished in a 2:l solution of methyl alcohol and concentrated nitric acid. With a current density of 10 amp per sq dm (decimeter) the time required to obtain a satisfactory surface varied from 10 to 12 min. The polish-ing was carried out for short periods of 2 min to avoid rapid deterioration of the solution as well as to enable the rotation of the specimen 180" for uniformity of polish. It was necessary to place the solution in a bath of dry ice in view of its explosive nature at room temperature. Etching of the electrolytically polished surface was accomplished by using the fuming etch-pit method recommended by Lacombe and Beaujard8 for high-purity aluminum. Method for Tensile Testing A modification of the loading equipment devised by Miller9 was used. In this apparatus, the specimen was suspended from a chain and gimbal arrangement (for axial loading) in a heavy steel framework connected at the bottom to a balanced 6:1 lever and bucket system. Loading of the specimen was accomplished by allowing sand to flow from a reservoir into the bucket suspended from the longer end of the lever-arm at a rate of approximately 3 lb per min. Strain measurements were made using the Baldwin SR-4, bonded, resistance-wire, strain gauge and an SR-4 portable strain indicator (type K), which permits a reading accuracy of 2 microinches per inch. For low-temperature study, the gauge was calibrated by measuring the elastic modulus of an annealed stainless steel rod, which is known to be independent of temperature."

Jan 1, 1951

By O. K. Miniato, L. Massé, K. Nobe, J. S. Aronofsky, W. F. 213-000-000-016 Seyer

MUCH work has been done dealing with the effect of mechanical stress on electrode potential in an electrochemical system. The contradictory nature of the experimental results indicates the complexity of the problem although thermodynamic considerations show that a simple relationshir, should exist. In those systems where a gas was the electromotive active substance satisfactory agreement between theory and practice has been found. Des Coudres' found this to be so even when the active substance of the electrode, in this case mercury, was in the liquid state. In contrast, attempts to correlate theory and experiment for the solid state have met with a very limited success. The early workers in this field, Andrews,2 Walker and Dill3 used iron, certainly one of the most reactive of metals. Others have made use of less active metals such as copper and nickel. Recently Fryxell and Nachtrieb4 investigated the electrochemical behavior of gold and silver under both tensile and compressive stresses and concluded that it was doubtful whether true stress potentials could ever be measured. Much of the lack of success to measure the thermodynamic stress potential can be ascribed to the presence or formation of a complex film on the metal surface in contact with the electrolyte. Further, the theoretical stress potential is very small and therefore difficult to measure directly. Thus the calculated emf between a 24 B & S gage cold-drawn copper wire stressed with a weight of 1 kg and an unstressed portion of the same wire is only 2.60 X 10"7 volts. This is very small compared to that which can be produced by chemical reactions at the metal electrolyte interface which in turn can be so large as to mask completely the stress potential. Hence in this type of measurement all chemical side effects must be eliminated or reduced as much as possible. It was for this reason that the system copper-sodium chloride solution was selected for study. INSTRUMENTATION In the many preliminary experiments conducted, two major difficulties were encountered. The first was to measure the small electro-potentials to be expected and the second to obtain a suitable electrode surface. The conventional potentiometric method was found to be unsatisfactory for measuring the small emf expected. However, by using an L & N No. 2290 galvanometer having a resistance of 915 ohms consistent measurements were possible. The reference electrode was always the unstressed one made from the same sample of wire. The steady current flow was approximately 10-8 amp. Lewis and Randell5 have stated that for currents of the order of 10-8, if there is no sensible polarization, the measured emf may be taken as a reversible one. To check the galvanomenter readings an alternative method was devised to measure the potential difference between the wires. This involved a Liston-Falb d-c breaker amplifier model 10, an L & N k-2 potentiometer and a moving-coil galvanometer having a sensitivity greater than 0.1 µv (microvolt) per mm. To increase further the output voltage of the amplifier a d-c amplifier, model B. L.-932 was introduced into the circuit. This amplifier was in turn connected to a Brush recorder which had been calibrated previously by the test signals from the Liston-Falb instrument. These test voltages employed took into account the impedance of the input current. Unfortunately, this method had too low a sensitivity for measurement below 10 µv. Above this value the voltage agreed reasonably well with those obtained directly by the simple galvanometer method. The main advantage of the amplifier setup was that one did not have to wait until no deflection occurred on the galvanometer in the circuit when first exposing the wires to the solu-

Jan 1, 1959

By H. M. Otte, A. G. Crocker

SLIP, twinning, stacking faults, and precipitates on well-defined planes in a crystal produce traces that are visible on either a polished or an etched surface. The purpose of this note is to establish the usefulness and limitations of the information obtained from such traces when determining the orientation of single crystals or grains in a polycrystal. Attention will be confined specifically to traces produced by octahedral planes in cubic crystals, though most of the remarks can be taken as more generally valid. The problem of determining the crystal orientation is completely solved in principle' and in particular for the special case under consideration.1'2 Tables are available3 in which the orientations can simply be looked up when given the two or three angles between the traces. Thus a quick and simple method is available for obtaining the orientation of a crystal from surface traces. In this note two examples will be given from recently published papers and will show the use of the method with the aid of the Tables, as well as some of the precautions that should be taken in the procedure. As part of an analysis of X-ray Kossel lines, Peters and Ogilvie 4 determined from them the crystallographic orientation of the specimen. They chose a Cu-5.10 wt pct Si alloy that had been partly transformed from the a (fee) phase to the k (hcp) phase. The latter formed as very straight platelets along the octahedral planes of the a phase, and a photograph (Fig. 7 of Ref. 4) was reproduced in the paper4 of the region for which the orientation had been determined from the Kossel lines. Apart from a very small area (about 0.15 mm diam) near the top center of the photograph, the region shown was clearly all of one orientation. Traces in four different directions were readily identified. Starting with the smallest angle and proceeding counterclockwise, the angles between the traces were measured to be 27° 43', 55° 16', 64 3 43 1, and32"26'. These add up to 1802 08 1, indicating a cumulative error of 8'. The correct values should, of course, be taken from the original glass plates, or at least from prints on distortion-free paper, so the precision of the quoted values is actually greater than their accuracy. The solutions can be looked up in the Tables3 in four ways, depending on how the angles are paired, tion for the minutes of arc is required and the solution obtained will be identical for all the four pairs if the values of the angles are not in error. In a practical situation, such as this one, there are several sources of error, so that the four solutions obtained will all be slightly different. An arithmetic average of the four solutions is mathematically incorrect, but may, in special cases, give an answer close to the correct one. A rigorous procedure for refining the orientation has been described by Mackenzie;5 he gives a least-squares method that can be applied, if necessary, to this type of problem. The orientation thus determined can be compared with the one from the Kosel lines and discrepancies larger than the experimental error assigned to nonor thogonality of the X-ray or electron beam to the specimen. Here the example will only be used to illustrate the general procedure for making a very rapid rough check. From measurements on the stereographic projection, Fig. 9 of the paper,4 we can determine that the surface normal is approximately (0.434, 0.704, 0.562). From the Tables3 we find, using 28°, 55" as a good approximation to the first pair (27°43', 55°16'), that the surface normal is (0.453, 0.678, 0.579).* These two values are within 2 deg of each

Jan 1, 1967

By J. Husson, R. Iffly, M. Gondouin

A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and non - Darcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results has been possible, and future predictions have been obtained. An application of this method to the Hassi Er R'Mel gas-condensate field in Algeria is tentatively shown. INTRODUCTION Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C (?p2)n used by Rawlins and Schellhardtl can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy's law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender2 which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains -close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (k h/ u) of the reservoir, and eventually on the 'drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt.3 At high flow rates, Darcy's law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the backpressure tests becomes smaller than 1, and a slight curvature of the log-log plot of ?p2 vs q can be predicted when going from very low to high rates of flow (Elenbaas and Katz).5 The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky.7 Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice.8 In the case of gas condensate wells, however, the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow.

By F. W. Jessen, N. Mungan

The plastic flow characteristics of clay water suspensions were first recognized by Binghaml in 1916 and further studied by Ambrose and Loomis' in 1931-1932. Many physical and chemical properties of clay suspensions are deeply influenced by particle size distribution as well as by the exchange cation. Separation of a number of fractions is particularly helpful in making a detailed study of a suspension. A limited amount of work has been conducted on the effects of particle size on specific properties of mud drilling fluids. A knowledge of particle size distribution is essential for a better understanding of fundamental properties of clay suspensions, particularly viscosity and gel strength. The purpose of this investigation was to study the effect of particle size on the viscosity and gel properties of clay suspensions and to determine any changes in mineral composition accompanying variation in size. EXPERIMENTAL PROCEDURE Numerous methods may be used to fractionate a poly-dispersed clay suspension into nearly mono-dispersed systems. Particles larger than 44 micron (325-mesh) may be obtained by wet screening. For sizes from 44 to 1 micron, the fractionation may be accomplished by sedimentation, elutriation plus microscopy,' or turbidimetry.6 When dealing with systems which contain a major portion of particles below l-mi-cron size, slit ultramicroscopy,7 centrifuge methods of Svedberg,5 eams,9 and McBain,l0 and X-ray methods" may be employed. The Sharples super centrifuge has been proved suitable for the economical separation of suspended particles of submicron range.12,13,14 Three-hundred and forty-five gal of 1 per cent by weight Aquagel suspension was mixed in a high-speed 5-gallon mud mixer and the suspension was allowed to stand in 5-gal glass bottles for 30 days to assure full hydration. All particles larger than 44 microns were removed by wet screening. Five fractions in the range of 44 to 1 micron were obtained by sedimentation. The Sharples super centrifuge method described by Hauser and Reed.13 Norton and Speil,14 Ha user and Lynn,15 and Hauser and Schachman,10 as employed to yield five fractions of submicron size. A super centrifuge operation chart prepared by Fancher, Oliphant, and Houssierre12 was used to determine operating conditions for the desired particle ranges. The clay suspension, after removal of all material above 1-micron size, was centrifuged. During rotation of the bowl, the particles were deposited on a thin plastic liner which fit closely inside the bowl. After passing 5 gal of suspension through the centrifuge, the liner was removed and the particles on the liner were scraped off, remixed and recentrifuged. This was repeated five times. Thus, Fractions H, I, K, and L were obtained. The finest fraction, M, remained in an approximately 0.4 per cent suspension. Water was evaporated under reduced pressure from this suspension to yield the finest particles. Results of the fractionation are included in Table 1. In order to achieve proper orientation and humidity conditions for X-ray diffraction analysis, the following procedure was employed. The dilute suspensions were placed on glass slides and allowed to dry at room temperature. This was repeated several times. Previous to measurement each sample first was placed in a water desiccator for half an hour and then allowed to stand for 15 minutes at room temperature. thus yielding an equilibrium condition of about 52 per cent relative humidity. The relative humidity of the room in which the X-ray diffraction was carried out was maintained at approximately 50 per cent so that there was no change in the spacings during the X-ray examination. Samples

By H. J. McQueen, G. C. Kuczynski

ThE useful properties of k6-Alfenol and the thermenol alloys (summarized by J. E. Nachman and W. J. Buehler') have encouraged research into those alloys which, having compositions near 25 at. pct Al, 75 at. pct Fe, undergo an ordering transformation between 500° and 550°C. The equilibrium diagram of the iron-rich iron-aluminum alloys was first determined by Bradley and Jay.2,3 They distinguished three structures: the disordered, which is bcc; FeAl, which is simple cubic with one Fe atom and one Al atom per lattice site; and Fe3Al, which is fcc with three Fe atoms and one Al atom per lattice site. This last structure may be conceived as eight body-centered cubes with Al atoms at the centers of alternate ones, so that Al atoms have only Fe as first and second nearest neighbors. Later, Osawa and Murata4 determined the boundaries of the different superlattice regions in the iron-rich Fe-Al solid solution by dilatometric and X-ray methods. Two of the six phases, which they found between 0 and 50 at. pct Al, were never identified by other workers. A. Taylor and R. M. ones,' concurrently with and independently of this research, redetermined this diagram by measuring lattice parameters at temperature. Further reference will be made to their results. EQUILIBRIUM DIAGRAM A) Experimental Procedure—The alloys were prepared from NRC gas-free iron (99.9 pct Fe) and 99.99 pct Al. They were melted in alumina' crucubles under vacuum in an induction furnace. If the ingots were unsound or showed more than a 3 pct weight loss, they were rejected. The ingots were homogenized at 1100°C for 24 hr before hot-rolling at 700" to 900°C from 1 in. to 0.25 in. thick. It is interesting to note that alloys containing more than 28 at. pct Al were able to take an 80 pct reduction of area in the ordered FeAl region. The dilatometer specimens and specimens for chemical analysis were cut from these plates. A Leitz dilatometer was used to measure the coefficient of linear expansion as a function of temperature. The specimens were slowly cooled from 900" to 300°C where they were annealed for 10 hr before slowly cooling to room temperature. The expansion was recorded photographically as the alloys were heated and cooled at 1.5oC per min between 100" and 1000°C. The magnetic measurements determining the Curie points were performed on the dilatometer specimens in the dilatometer, by using direct current in the furnace windings both to heat the specimen at 1.5°C per min and to serve as the primary coil. The regular specimen holder was replaced by a thin alundum tube on which was wound, as a secondary, a closely spaced coil of fine copper wire. A reversal of current in the furnace windings produced, in the secondary, an emf which was proportional to the induction in the specimen, and which could be detected on a galvanometer. In this way, it was possible to determine the Curie points of alloys to within * 5°C. B) Results and Discussion—The coefficients of linear expansion, as obtained from the dilatometer curves, are plotted as a function of temperature and composition in Fig. 1. Since in many cases the heating and cooling curves were superimposed, it was decided to measure slopes of heating curves only. Definite high peaks, due to the transformations, were observed on each curve between 400" and 520°C, and, for alloys containing more than 23 at. pct Al, a second set of smaller peaks at temperatures above 660°C. The sharpness of the peaks indicates that ordering to Fe3Al is a first-order reaction. The compositions and the temperatures of these peaks are listed in Table I. When these temperatures are plotted as a function of the composition, the result is the constitution diagram presented in

Jan 1, 1960

By E. S. Machlin, Morris Cohen

The isothermal formation of martensite in a 71 pct Fe, 29 pct Ni alloy is found to take place mainly by the nucleation of new plates rather than by the growth of existing ones, and is dependent on the temperature and time of the isothermal hold, the amount of atherrnal martensite present, the state of internal strain, and the application of tensile stress. The conclusion is reached that the isothermal nucleation is activated by thermal fluctuations superimposed on localized regions of very high strain. The reaction-path concept, involving martensite nucleation at strain embryos by athermal activation on cooling, or by thermal fluctuations on holding, reconciles the athermal and isothermal modes of transformation, and offers a unified picture of the kinetics of martensite formation. THE phenomenon of isothermal martensite formation has been the subject of considerable study lately,'-' and its reality has been thoroughly established. The existence of such isothermal transformation has been claimed to confirm the nucleation and growth hypothesis as applied to the martensitic reaction.1 " However, the isothermal formation of a martensitic phase is also compatible with the reaction-pathw escription of the transformation. The purpose of this investigation is to examine the isothermal mode of the martensitic reaction, both theoretically and experimentally, in order to test the likelihood of the above two mechanisms. Material and Methods The alloy used in this study contained about 71 pct Fe and 29 pct Ni. The complete analysis was 29.5 ± 0.2 pct Ni, 0.036 pct C, 0.02 pct N, 0.19 pct Mn, 0.09 pct Si, 0.008 pct P, and 0.006 pct S. The amount of isothermal transformation was determined by electrical resistance measurements using a Kelvin double bridge. The specimens were in the form of rods 1/16 in. diam x 4 in. long. Aus-tenitizing was performed at 1095°C for % hr either in a pre-purified nitrogen atmosphere or in an evacuated Vycor tube, followed by oil quenching to room temperature. After this treatment, the samples were completely austenitic, and the transformation studies were conducted at subatmospheric tempera- tures. Lineal analysis and X-ray determinations of retained austenite were used to calibrate the electrical resistance changes in terms of the percentage of martensite. The martensite range curve for this alloy is given in Fig. 9 of ref. 6. The M, temperature occurs at about -18°C (255°K). Reaction-Path Theory The nucleation and growth description of the martensitic transformation that occurs isothermally has already been given by Kurdjumow.','2 However, no comparable treatment exists using the reaction-path concept." Consequently this section presents the reaction-path description of the isothermal mode of the martensitic transformation. According to the latter theory, there is a reaction path (a strain) which describes the relative motion of the atoms during their transference from the austenitic to the martensitic state. The possibility exists, therefore, that the nucleation of a martensitic plate is accomplished by an embryo that comprises a state intermediate between that of austenite and martensite. This state may be attained within a finite volume by means of a homogeneous strain of the austenitic matrix. There is a free-energy barrier (F.) along the reaction path, corresponding to a critical strain in a critical volume. When activation is achieved, a spontaneous increase in strain and volume of the embryo takes place to generate the full-size martensitic plate. This mode of nucleation is to be distinguished from the more conventional mode involving embryos of the martensitic phase that merely grow in size by an interface motion. There are two ways whereby embryos in the austenitic phase can achieve the critical state of strain for isothermal nucleation: 1—through the formation of internal strains by plastic deformation or by stress; and 2—through thermal fluctuations, preferably superimposed upon existing internal strains. The activation free energy F,, must be supplied either mechanically by internal strains or thermally by energy fluctuations, or by a combination of both.

Jan 1, 1953

A. Cook K.A. Grace's article advocates usage of the terms describing resources as defined by the US Bureau of Mines (USBM) and the US Geological Survey (USGS). Originally recommended in 1943, the terms were revised in 1976 and again in 1980. Mr. Grace further recommends that the term reserves should be severely restricted and that it should encompass mining and processing factors. The list of references quoted in the article does not, however, mention the study concerning reserves that was made over a period of almost four years by a joint Committee on Definitions. This committee was sponsored by three societies - the American Institute of Mining, Metallurgical, and Petroleum Engineers (AIME), the Society of Economic Geologists (SEG), and the American Institute of Professional Geologists (AIPG). Most of the detailed work was done by a working party appointed by the Society of Mining Engineers (SME) of AIME. After studying previous definitions in the US as well as in the United Kingdom, Canada, Australia, France, and other European countries, the following definitions were proposed and accepted in 1974 by the SME board of directors. (Ore reserve definitions in Rhodesia, South Africa, or New Zealand were not mentioned as having been reviewed. Table 1 lists definitions from MINING ENGINEERING, July 1975. Notice in Table 1 it was mentioned, under Resources, that the definitions of reserves were recommended for the purposes of commercial evaluation. It was further stated that the terminology adopted by the USBM and the USGS, as released to the public, covering resources, was recognized as such. Mr. Grace also recommends that reserve calculations should allow for future losses in ore tonnage, ore grade, milling, and smelting. Unfortunately, it might take years to develop a prospect after it has been discovered. Mining methods have to be tested before being finalized in order to know what tonnage of ore is going to be lost, or how much dilution is likely to occur. The same problems are present in concentrating or in smelting. Operating mines usually know how mined grade compares with ore reserve grade. They can usually predict fairly closely what their final metal recoveries are probably going to be. It is, however, expecting too much to have to delay quoting reserves from say a recently drilled prospect. Any responsible mining geologist or mining engineer (or company for that matter) should state several things about an ore reserve calculation: that it is or is not a preliminary estimate only; that estimated grades have not been diluted to allow for a future, as yet unknown, mining method; that metal recoveries are or are not only tentative, based perhaps on drill hole samples only or on no metallurgical testing at all. [ ] Reserves of a partially explored prospect are always quoted when it becomes necessary to raise capital. If they are described as preliminary only (really just tonnage and grade estimates and not true "reserves") in addition to being accompanied by some of the items just mentioned, nobody is going to be misled. If, on the other hand, a report by a member of the SME or SEG is intentionally misleading, the individual must be reported and eventually disbarred from his or her society. To summarize, let us stay with the definitions of ore, ore reserves, and related terms as recommended and accepted by SME. I might add that on occasion I have used a fourth category in my ore reserve calculations, namely Geologically Possible Ore. This category is more or less the same as Inferred ore defined by the USBM and USGS. I have never given a grade to this category, which may be based only on geological mapping, geochemical sampling, or geophysical traversing. ?

Jan 1, 1986

By D. J. DeLazaro, W. Rostoker, R. E. Riley, M. Hansen

At very low concentrations, carbon dissolves interstitially in molybdenum resulting in a linear expansion of lattice parameter with increase of carbon in solid solution. Geometrical consideration of the relative size of carbon atom to size of interstice approximately predicts the observed volume expansion. THE element carbon, occurring in molybdenum, either as an unavoidable impurity, or purposely added, markedly affects the mechanical properties of molybdenum. Several investigators1-" have noted the occurrence of molybdenum carbide at the grain boundaries of cast molybdenum, and Fischer and Rengstorff' have shown that this intergranular constituent can induce intergranular brittleness. The appreciable change, with temperature, of the solid solubility of carbon in molybdenum, found by Few and Manning," suggests other important effects upon mechanical properties. Finally the relative atom diameters of carbon and molybdenum (the ratio of atom diameters is 0.59) are indicative, by analogy with iron (ratio of carbon atom diameter to iron atom diameter is 0.65), of a possible interstitial solid solution. If carbon dissolves intersti-tially in molybdenum, anelastic effects and age-hardening effects, similar to those observed in other body-centered cubic metals, could be expected. However, from the work of Sykes, Van Horn, and Tucker," it might be inferred that carbon forms only a substitutional solid solution with molybdenum. These considerations made it desirable to study the effect of carbon on the lattice parameter of molybdenum in greater detail than heretofore. All heat treating was done in a high temperature furnace7 built specifically for heat treatment of molybdenum. The temperatures and times of heat treatment were determined from the a solubility limit for the Mo-C system." These heat treatments were carried out in argon which was purified with respect to N, and H.!0." Purification of the argon was accomplished by passing the argon over hot (750°C) titanium and then through a magnesium perchlorate drying tower. As many as six samples were run concurrently and quenched at different times without interrupting the furnace cycle. Both the purity of the furnace atmosphere and ability to quench samples from any temperature up to 4000 °F were of prime importance in the successful heat treatment of samples for the lattice parameter investigation. Carbon Analysis The Leco Combustion apparatus was used for carbon analysis. This apparatus is capable of an accuracy of & 0.003 pct for a 1 g sample in the range below 0.10 pct. However, it is felt the degree of accuracy is somewhat better than this limit in view of the consistency evident by cross checking a number of determinations. The Battelle Analytical Laboratory consistently reported check results to within k 0.001 pct C. X-ray Measurements The molybdenum wire specimens (20 mils) were carefully filed down to about 12 mils and then etched with nitric acid to 8 mils. Carbon analyses were made on specimens before reduction in size; however, since there was no evidence of surface carburization, it is probable that the carbon was uniformly distributed throughout the sample. The resultant specimens were strain free and small enough to minimize the error in the lattice parameter determinations due to X-ray absorption. Diffraction patterns were obtained with a Debye-Scherrer powder camera 114.59 mm in diam utilizing the Straumanis type asymmetrical film mounting. Nickel-filtered copper. Ka radiation and zirconium-filtered molybdenum Ka radiation were used. Line positions on the film were measured with a traveling microscope equipped with a vernier scale permitting measurement to 0.001 cm. The average of five readings was used to determine the position of each line. The lattice parameter for each specimen was determined from the data by the extrapolation method of Bradley and Jay, Y.e., the intercept at 90" of the straight line obtained by plotting the apparent lat-

Jan 1, 1953

By H. E. Cline, T. H. Alden

A study zvas made of rate-sensitive plastic deformation and superplasticity in alloys of lead and tin. These alloys (lead, PO-19 pct Sn, Sn-38 pct Pb, Sn-2 pct Pb, tin) were extruded, aged at room temperature, or melted and resolidified to produce a variety of ~nicrostrnctures. Flow stress us strain rate data were obtained frorn tension tests for strain rates between 10-6 and 1 min-1. The curve log o .us log £ was S-shaped jor fine-grained materials and approxinzately linear for coarse-grained nzaterials. At constant grain size, the behavior was relatively insensitive to conposition. High rate sensitivity (d log o/d log k) and superplasticity occurred at intermediate strain rates in fine-grained materials and are believed to be associated with a transition with strain rate in the mode of plastic flow. This transition was shifted to higher strain rates with increasing temperataire or decrensing grain size. The high rate rneclzanisrn is presunzed to be slip, while rnetallographic evidence sug-gests that the low rate lnechanism is pain boundary sliding. PEARSON' discovered that extruded eutectic alloys of Pb-Sn and Bi-Sn could be elongated as much as 2000 pct in tension. The ability for stretching decreased with aging time or annealing to increase the grain size. At high strain rates, or if the material was in the cast condition, normal ductility was observed. Following deformation of the extruded Pb-Sn eutectic at low rates, Pearson observed an equiaxed granular structure on an initially flat surface, while rapid straining produced elongated grains. He attributed the large deformation in the extruded alloys to the persistence of extremely small grains to a temperature sufficiently high for inter granular flow. Avery and backofen2 measured the strain rate sensitivity of the flow stress, m = d In old In 6, in the Pb-Sn eutectic and established a correlation between m and the tensile elongation. In the extruded eutectic alloy the strain rate sensitivity was 0.1 to 0.2 at rapid rates and the elongation was small, while at low rates m increased to 0.4 to 0.6 and superplastic elongation was observed. They also noted a grain size effect. In the case of the cast Pb-Sn eutectic the strain rate sensitivity remained at 0.1 over the range of strain rates of their experiment (3 x 10"3 to 2 min-I). These authors suggested that diffusional (Nabarro-Herring) creep was the mechanism by which deformation occurred at low strain rates, while climb-controlled creep occurred at high rates. Two predictions of this model are that, at low strain rates, the strain rate sensitivity approaches 1, i.e., Newtonian viscosity, and that the strain rate at constant stress varies as D/L2, where D is the coefficient of self-diffusion and L the grain size. More recently, a mechanical and microstructural investigation of the dilute superplastic alloy, Sn-5 pct Bi, has been done.3 The results show that the high strain rate sensitivity is associated with a transition with strain rate of the mechanism of plastic flow. At low strain rates, grain boundary sliding and its associated accommodation processes were evident, while at high strain rates quasi-uniform slip was concluded to be the dominant deformation process. The following experiments were performed to extend our knowledge of the phenomena of superplasticity to a larger range of strain rates, compositions, temperatures, and microstructures in the Pb-Sn alloy system. The question of why a cast structure does not exhibit viscous behavior although it appears to have a fine microstructure2 was investigated.

Jan 1, 1968

By E. J. Koval

Practical miscible displacement processes will be characterized by lingering of the solvent into the oil. The lingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. INTRODUCTION Theoretical considerations,1 laboratory experiments,2 and pilot tests3 lead to the conclusion that miscible displacements in the field will be unstable In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced. For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding by the usually less dense solvent. Al- though gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids. Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs4 or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. l Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.6 During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks2 and how it is affected by viscosity ratio,7 geometry,7 and slug size.2,* Peaceman and Rachfordg suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected. The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible dis placements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were: (1) The system was linear; (2) The solvent was miscible in all proportions with the oil in place; (3) The solvent was continuously injected into the porous medium; (4) Gravitational effects were eliminated by matching densities and (5) All the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. The use of

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By G. R. Wilms

A study has been made of the structural changes in polycrystalline high purity aluminum during the tertiary stage of creep under conditions of constant tensile load. It appears that there is no basic modification in the particular mechanism of deformation that characterized the preceding secondary stage of creep, but that the changes in crystalline structure produced during the tertiary stage are only a consequence and not a cause of the accelerated strain. Intercrystalline fissures were observed on entry into the tertiary stage, and these might supplement the accelerated rate of strain owing to local stress concentrations. There is evidence that the formation of these fissures may be associated with the presence of surface imperfections, and it is suggested that a more generalized treatment of the results may explain certain creep characteristics of commercial alloys. IN previous work'-4 a study was made of the changes produced when specimens of annealed aluminum were deformed at various temperatures and rates of strain, especially under conditions leading to creep under constant tensile load. It was shown that, as the temperature was increased or as the rate of strain was decreased, elements of the substructure produced within the grains became coarser, and with the strain rate constant at a given temperature, their size tended to an equilibrium value. The preliminary process of the breaking down of the grains into a substructure was identified with primary creep.' The subsequent equilibrium, condition was associated with secondary creep. The question then arose whether the tertiary stage corresponded to any further significant change in the substructure. The question is also of interest in view of the opinion, expressed for instance by Andrade,5 that the tertiary stage is merely an accelerated rate of strain due to the reduced area of section of a specimen under continuous tensile load, and the other opinion, as suggested by the observation by Sully, Cale, and Willoughby6 of a tertiary stage in com-pressive loading, that this third stage is a real effect in its own right. The object of this paper is to record some observations on the tertiary stage of high purity aluminum. Experimental Procedure The material was aluminum of 99.98 pct purity as previously used. The specimens had a rectangular section of l/8 x l/2 in., and extensions were measured over a 1 in. gage length. After machining to shape, the specimens were annealed to give a standard grain size of 0.2 mm and then electropolished. The general procedure involved metallographic and X-ray diffraction examination at progressive stages of elongation (marked by arrows on the curves shown in Figs. 1 and 2), the specimen being extended to fracture under constant load at a given temperature. The X-ray tests were made by the back-reflection method from a stationary specimen, using CoK radiation. The longer edge of the micrographs in the paper corresponds to the direction of applied stress. Results The previous work showed that, in the secondary stage of creep in aluminum, three basic types of structure could be developed according to the temperature and rate of strain. These were: 1—slip, which predominated at the lower temperatures and higher rates of strain and produced the finest and least perfect substructure; 2—cell structure, which superseded slip as the temperature was raised and the rate of strain decreased and which was characterized by a coarser and more perfect structure and an absence of slip lines; and 3—a stage termed "boundary microflow," which predominated at still higher temperatures and lower rates of strain when the cell size had increased and become comparable

Jan 1, 1955

By E. C. W. Perryman

IN spite of the large amount of work which has been carried out on the recrystallization of aluminum and its alloys, there has been no complete investigation of the recrystallization characteristics of A1-Mg alloys. The most complete investigation is that reported by Bungardt and Osswald' who, working with commercial-purity materials, found that the temperature both of beginning and of complete recrystallization increased with magnesium content up to about 2 pct Mg, then decreased with a further increase in magnesium up to 5.0 pct, and thereafter increased again. Michaud and Segolz working with 99.93 pct A1 also found the temperature of beginning of recrystallization to decrease as the magnesium content increased from 2.13 pct to about 4.5 pct. Chossat3 using aluminum of 99.99 pct purity found that 0.12 pct Mg had no effect but that 0.4 pct Mg increased the recrystallization temperature by about 30°C. That no effect was found for 0.12 pct Mg does not agree with the later results reported by Demer and Beck4 who found that 0.025 pct Mg in 99.99 pct A1 increased the time for complete recrystallization and furthermore increased the activation energy for the recrystallization process. Kratz" using 99.997 pct A1 found that 0.5 pct Mg increased both the temperature of beginning and of complete recrystallization by 100°C. Chadwick and Hooper" working with commercial-purity material found that 1 pct Mg increased the temperature of complete recrystallization by about 40 °C for cold reductions in the range 17 to 72 pct. With smaller amounts of cold work produced by stretching (10 pct strain), they found no significant effect of magnesium. The latter result agrees with that obtained by Williams and Eborall' who found no effect of 2 pct Mg on the recrystallization temperature of commercial-purity aluminum strained 10 pct or less by stretching. Experimental Procedure Material Used: The chemical analyses of the materials used throughout this investigation are given in Table I. Fabrication: The alloys were cast in iron molds which had been washed thoroughly with alumina. After scalping, the ingots were annealed for 16 hr at 450°C, pressed, annealed at 450°C for 16 hr and hot rolled to 0.25 in. After hot rolling, the slabs were alternately annealed and cold rolled to 0.036 in. Cold-rolling reductions between intermediate anneals were kept at about 30 pct and a high intermediate annealing temperature of 450°C was used so as to obtain, as nearly as possible, similar starting grain sizes for the different materials. All intermediate anneals were done in a salt bath and were followed by cold-water quenching so as to retain all the magnesium in solid solution. The final cold reductions investigated were 20, 30, 40, 50, 60, and 80 pct. The initial grain sizes, that is, the grain size before the final cold reduction, were all very similar. Annealing Procedure: Specimens, 1 in. sq, were cut from the 0.036 in. sheet and annealed in a salt bath, the temperature of which was controlled to k2"C. Separate specimens were annealed for different times at 350°, 375", 400°, and in one or two cases at 415°C and after annealing were quenched in cold water. The time taken for a specimen to reach temperature was approximately 5 sec. Metal-lographic examination after annealing showed that no precipitation of Mg+413 occurred during cooling. Procedures Used for Determining Recrystallization Characteristics: All specimens were electrolyti-cally polished and etched by the method described previously1° and polishing was continued until about 0.002 in. had been removed from each side of the specimen. Using this technique, the smallest recrys-tallized grain which could be observed with cer-

Jan 1, 1956

By H. H. Kellogg, T. R. Ingraham

Three anhydrous zinc sulfates have been identified. They are: ZnSO,(a), stable below 1007°K; ZnS04(/3), stable above 1007OK; and ZnO.ZZnSO,. The decomposition pressure of each sulfate has been measured and the following relations calculated from the results: The measured data have been combined with the known themzodynamic properties of ZnS, ZnO, Zn, SO,, and SO, to yield univariant and bivariant phase diagrams for the system Zn-S-0. The application of these diagrams to problems of roasting zinc concentrates is discussed. PRESENT knowledge of the equilibrium chemistry of the system Zn-S:O, so essential to scientific control of zinc-blende roasting, is deficient in several respects. A basic sulfate of zinc has been reported by many investigators, but its composition is in doubt and its thermodynamic properties have not been measured. Our scanty knowledge of the properties of the normal sulfate at roasting temperatures is based on old and inexact studies. A crystal transformation in the normal sulfate, involving a sizable heat effect, has been noted by several investigators but has never been quantified. The studies reported herein were designed to fill these gaps in knowledge and to make possible a reasonably complete thermodynamic description of the system Zn-S-0 at roasting temperatures. The results make possible a far more exact understanding of zinc roasting chemistry than was hitherto possible. EXPERIMENTAL The principal experimental technique employed was the measurement of the total gas pressure developed from decomposition of either ZnSO, or ZnO2ZnS0, in a closed system. The apparatus employed was essentially the same as that described by Warner and lngrahaml and Flengas and tngraham.' The unusual feature is a flexible Pyrex bellows used to separate the reaction gas mixture (S03, SOz, and 02) from the mercury in the manometer and thus prevent corrosion of the mercury by SO3. The bellows operates without evidence of hysteresis and, barring accidents, may be used for several months. The response of the bellows varies from manometer to manometer, but is generally of the order of 0.6-cm displacement for a l-cm change in pressure. The response for all manometers has been linear over the range 0 to 1 atm. To prevent condensation and polymerization of sulfur trioxide, the bellows-manometer was maintained at 100.0" * 0.5" by a circulating bath of silicone oil. The connecting tubing between the manometer and the furnace was maintained at 100.0" * 0.2"* also, with a stirred air bath. The open end of the manometer was connected with a chamber which was maintained at a known pressure. The pressure could be varied so that readings of the height of the mercury column, measured with a cathetometer, could be made with both rising and falling mercury column. By using the average of the readings, any error due to sticking of the mercury column was minimized. The sample was placed in a 2-in.-long platinum boat formed into the shape of a half-cylinder. The sample was prepared as a fine powder and pressed against the inner wall of the platinum boat. A silica thermocouple well, covered with a platinum sleeve, was placed lengthwise along the center of the boat. The temperature of the sample was read on a calibrated Pt-10 pct Rh theirnocouple. The temperature profile of the furnace was constant within ± 0.2 C over the length of furnace occupied by the sample. The horizontal furnace used to contain the sample and the quartz reaction tube was electrically heated, with the control thermocouple placed 1/4 in. from the windings. A Brown Pyro-O-Vane temperature controller with a 3-sec response time was used to maintain the furnace temperature. Before beginning a run, the apparatus, including the bellows manometer, was thoroughly washed in sib with acid and distilled water to remove any

Jan 1, 1963

By P. G. Winchell, J. K. Jackson

The strtcture of body-centered Fe-Ni-C alloys (0 to 16.5 wt pct Ni) containing less than 0.015 wt pct C was investigated by measuring the carbon-diffusion peak at low frequencies with a torsion pendulurrr. By determining the Snoek damping in ferrite and in quenched alloys of identical composition, the effects of nickel content and heat treatment were separated, and the existence of a structure in which Snoek damping is greatly reduced was revealed in the quenched ternary alloys. The relative amount of this structure increases with increased nickel content and cooling rate. It is proposed that this structure may be highly imperfect or tetragonal. In Fe-Ni-C alloys containing only ferrite the addition of nickel (0 to 5.1 wt pet) decreases tke area of the carbon-diffusion peak and shifts its position to lower temperatures but broadens the peak only slightljl. The decrease in peak area with increasing nickel implies that short-range interactions with the nickel atoms prevent some of the carbon atoms from participating in the relaxation process. The shift in the peak position indicates a long-range effect of nickel on the movement of carbon atoms so that at 300°K the diffisivity of carbon in -ferrite is increased by about 35 pct by the addition of 5.1 tut pct Ni. The results are presented as distributions of relaxation strength 072 the activation energy under the assumption that the frequency factor is invariant. BODY-CENTERED iron-base solid solutions dissolve carbon interstitially in the octahedral sites. The occupation of an octahedral site produces a tetragonal distortion of the surrounding lattice. These sites fall into three sets according to the orientation of the tegragonal distortion associated with each and may be identified by their lattice coordinates as: type 1/2 0 0, type 0 1/2 0, type 0 0 1/2. At low carbon levels in cubic ferrite the carbon atoms are distributed at random1 among these sites. In high-carbon body-centered iron-base solid solutions, which are unstable with respect to several two-phase mixtures, a tetragonal structure occurs as the product of the diffusionless transformation of austenite. This transformation is commonly accompanied by appreciable microstrain and its product is called martensite. The tetragonality of martensite, a supersaturated solution of carbon in a iron, is maintained prior to decomposition even though local diffusion of carbon occurs as evidenced by carbide precipitation. The tetragonality is taken as evidence that one set of octahedral sites is preferentially occupied by carbon. (This preferential occupation is called ordering below.) Support for this view is presented by the absence of strain-induced carbon-atom diffusion in high-carbon solid solutions (martensite). Such diffusion occurs in ferrite and produces the 40°C internal-friction peak observed at 1 cps frequencies.' Thus, there appears to be qualitative evidence favoring the view that at sufficiently high carbon levels tetragonality arises spontaneously as a result of the ordering of the carbon atoms; however, no experimental evidence exists concerning an equilibrium between cubic and tetragonal body-centered solid solutions. Moreover, attempts to estimate the energy of ordering7-' predict a value too low to maintain the tetragonality observed at medium carbon levels, 0.3 to 0.6 wt pct C. In the present work an attempt using internal-friction measurements is made to establish the presence or absence of tetragonality in low-carbon body-centered solid solutions formed by quenching austenite. Fe-Ni alloys containing about 0.01 wt pct and 0 to 15 wt pct Ni were selected for the study. While the work was in progress Gilbert and Owen10 reported that the transformation which occurs in these alloys during quenching at rates up to 5000°C per sec is not martensitic but is more properly categorized as massive. Thus, the solid solution

Jan 1, 1964

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

By Walter Crafts, D. C. Hilty

The liquidus diagram for the iron field of the Fe-S-O system has been derived experimentally. The solubility of oxygen in molten Fe-S alloys has been measured at several temperatures and found first to decrease slightly and then increase rapidly with increasing sulphur content. IT is well-known that the types, distribution, and amount of inclusions in any given steel are closely allied with the oxygen and sulphur contents of the metal, so that the term "deoxidation" as conventionally applied in steelmaking refers not only to the control of oxygen and oxide inclusions but to collateral modification of sulphide inclusions as well. Inclusions commonly occur in steel as mixtures of oxides and sulphides, sometimes closely associated and sometimes apparently completely divorced. Their effects on the properties of the metal may vary widely depending on their types and distribution as well as on their quantity. The mechanism by which inclusions form, however, and the means for controlling it are exceedingly complex and not well understood. Nevertheless, as described by Benedicts and Lofquist' and by Wentrup' all oxide and sulphide inclusions, excluding mechanically entrained matter, must result from specific modifications of the basic equilibria of the Fe-S-O system. In an investigation of the mechanism of deoxidation and inclusion formation being carried out at the Union Carbide and Carbon Research Laboratories, it became evident that quantitative data for the fundamental Fe-S-O system were essential to a better understanding of the problem. Consequently, the liquidus surface of the portion of the Fe-S-O diagram of interest in steelmaking has been determined, and the solubility of oxygen in liquid iron containing sulphur has been measured. Fe-S-O Diagram The portion of the Fe-S-O diagram of specific interest in steelmaking is the Fe-FeS-FeO corner. Of the contiguous binary diagrams for this partial system, only those for Fe-FeO and Fe-FeS are known with reasonable certainty.3 Several attempts to derive the FeO-FeS diagram have been made, chief among them being the work of Giani as reported by Oberhoffer,4 and, more recently, that of Vogel and Fulling." Although both Giani and Vogel and Fulling published diagrams for the FeO-FeS system, their observations indicated that the oxide component approximated Fe3O4 rather than FeO, so that there is doubt whether the system is truly binary. Benedicts and Lofquist and also Wentrup published qualitative sketches of the ternary diagram based on the assumption that it was of the type described by Marsh for a ternary system in which two of the contiguous binary systems are simple eutectic systems and the third exhibits a solubility gap in the liquid. Apparently, however, the only previous effort to establish the diagram experimentally was that of Vogel and Fülling whose results are reproduced in Fig. 1. Although defining approximately the limits of the miscibility gap and the location of the ternary eutectic, point E in Fig. I, Vogel and Fülling's diagram must be considered only semiquantitative. It was derived from a limited number of observations mainly along two quasi-binary sections, and the directions of the tie-lines and the location of the critical point, K in Fig. 1, were estimated by computation. Experimental Procedure The experimental technique employed for the present investigation involved melting mixtures of ferrous sulphide and ferric oxide in contact with iron. Since it was considered that in this part of the system the vapor pressures of sulphur and SO, are so low that they would not affect the results significantly, the melting was carried out in a current of argon to sweep out products of any initial re-

Jan 1, 1953

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij'usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith's determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej'ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of' damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.'2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968