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By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By H. N. Hall

Reservoir and producing characteristics can govern the decision to use either a one-, two- or three-dimensional model for making predictions for gravity-drainage reservoirs. Examples of conditions requiring one-, two- and three-dimensional calculations are given. In 1961 the author presented a method for predicting one-dimensional gravity-drainage performance. This work has been exrendcd to obtain a three-dimensional model, which is described and for which a sample problem is presented. Introduction Many papers on gravity drainage or gas-cap drive'-3 have been presented for conditions where the reservoir is treated as a single areal segment so that, in effect, only one-dimen-sional flow is considered. Other authors'-Q ave given evidence showing that the one-dimensional concept would be unsatisfactory to predict reservoir performance for certain types of reservoirs. Experience has indicated that specific reservoir and producing conditions govern whether one-, two- or three-dimensional concepts must be used as a basis for reliable reservoir performance predictioils. Previously the author presented a paper outlining a method for predicting the performance of gravity-drainage reservoirs.' That paper treated the reservoir as a single areal segment so that it was applicable for only one-dimensional flow. The work has been extended to obtain a three-dimensional model that can be used to predict performance of gravity-drainage reservoirs. Although capable of being three-dimensional, it can be used equally well for one- and two-dimensional predictions. This paper discusses those reservoir and producing conditions governing the choice of model, and also describes a three-dimensional model suitable for predicting reservoir performance in the more complex situations. Discussion The Choice of Model To predict reservoir performance, it is necessary to represent the reservoir by a physical model. A mathematical model, based on the assumed physical model, then is used to predict the movement of oil and gas within the reservoir. The word "model" is used here to connote the combination of both a physical model and a mathematical model based on the physical model. Certain types of reservoir situations may be predicted suitably with a one-dimensional model, whereas two- and three-dimensional models may be required for other situations. This section illustrates reservoir conditions associated with the use of a specific type of model. Many types of reservoir structures are such that gravity drainage possibly could be an important factor in oil production. Production practices, as well as the nature of the structure. can influence the type of model that should be used. obviously, it is impossible to discuss all combinations of reservoir structure and production practices that might be encountered in gravity-drainage reservoirs. The following are typical examples of conditions where a choice must be made among a one-, two- or three-dimensional model to predict reservoir performance satisfactorily. Conditions Requiring a One-Dimensional Model Fig. la shows contours for an asymmetrical anticline in which gravity drainage might be expected to be important. Fig. Ib depicts a cross-section along Line A-A in Fig. la. Existence of a gas cap is a good clue that gravity drainage will be an important factor in producing oil from this type of reservoir. However, it is not essential since a gas cap will form as oil is produced from the reservoir. If the proper combination of reservoir permeability and withdrawal rates is present, the reservoir will behave like a

Jan 1, 1969

By Carl F. Lutz, Robert F. Mehl

A layer of brass was formed on 0 brass using a vapor-solid reaction technique. The variation in composition with distance within the phase layer and across the a -ß interface was determined by an electron probe. The diffusivities were calculated as a function of concentration; the diffusion coefficient in brass was found to change by a factor of twenty-five over a compositional range of 8 at. pct. An explanation is proposed to account for the large change in the diffusivity, based on possible stresses in the diffusion zone; it is suggested that the concentration dependence of the thermodynamic factor might decrease the activation energy with increasing zinc content. ALTHOUGH the body of data on diffusion coefficients (D- values) in terminal solid solutions and in isomorphous systems is quite large, there is but little quantitative information for intermediate alloy phases. This paper recounts measurements of D-values for the ? phase in the Cu-Zn system. The experimental method employed consists in the forming of alloy layers and determining and analyzing the concentration-distance (c-x) curve. The experimental method employed could have been applied to several systems; the Cu-Zn system was chosen because the D-values in the a and ß phases are well known, and can thus be used for purposes of comparison. The rates of growth, of intermediate alloy layers are known for a number of systems. In nearly all cases the thickness varies parabolically with time, as to be expected if the rate of growth is controlled by the D-values. In a few cases, nonparabolic behavior has been noted.1 Nonparabolic growth may be the result of a) a variation of the composition at the phase interface with time, b) interface-controlled kinetics, c) short diffusion times coupled with long vacancy lifetimes (in vacancy diffusion),2 and d) crystal reorientation during diffusion in anisotropic systems.3 In the Al-Ni system4 and in the Al-u5 system parabolic growth kinetics are slowly approached after an initial transient period. In general those phases stable at a given temperature in a system A-B appear as separate phase layers when A and B are put in contact and given a diffusion he at-treatment. In most cases the compositions at the interface of adjacent phase layers are those read from the phase diagrams for the termini of the respective phases. This discontinuity in concentration is taken as independent of time, and the growth of one phase at the expense of another is assumed to be independent of interface kinetics, i.e., the rate of interface movement is controlled by volume diffusion in the phases concerned. wagner6 has given many solutions for multi-phase diffusion processes, assuming that the chemical diffusion coefficient, D, is independent of concentration, as have others. Jost7 has pointed out that the familiar Boltzmann-Matano solution is as valid for a (c-x) curve exhibiting concentration discontinuities at phase boundaries as for the usual single-phase case. Heumann and associates8,9 have applied this solution to the multi-phase case, but lacking concentration data within the several layers were forced to assume linear concentration gradients, thus calculating only average D-values. The purposes of the present study were: 1) to determine the dependence of D on concentration, 2) to calculate the intrinsic diffusion coefficients D?Cu and D?Zn, 3) to establish the time-law for the movement of the interface, 4) to determine the concentration limits at the ß-? interface, and, 5) to attempt to clarify the mechanism of diffusion. EXPERIMENTAL PROCEDURE The ? phase is exceedingly brittle; conventional solid couples and conventional sectioning methods were thus inapplicable. Vapor-solid couples were accordingly employed. Unfortunately the equilibrium vapor pressures of Zn for the ? phase are unknown; to escape this awkwardness, samples were enclosed in a capsule containing powder of an alloy of known composition, sufficiently large in quantity as to be effectively an infinite source, maintaining the concentration of Zn at the sample surface constant with time. The sources of Zn-vapor which can be employed in reaction with Cu, or a brass, or ß brass, to form a layer of ? brass satisfactorily wide in concentration range, are alloys of the phases ?, or ? + E or ? + d (depending on the temperature).

Jan 1, 1962

By A. Chakravarti, C. C. Harris

First-order kinetics adequately describe the recovery of a single floatable species. The conditions under which cell behazior can be simulated by a single-phase model are discussed; deviations from the multiphase model are accountable. The rate coefficient depends upon operating conditions besides particle size and mineralogy and the physicochemical properties of the pulp constituents. The model for a real flotation system combines the first -order, single-phase model with a distribution of noninteracting species. Methods for determining the distributions are discussed. Applications of the procedure to flotation studies are outlined. The mathematical description of flotation as a rate process can be traced to Garcia1 who reported cases in which the fraction of solid remaining in a cell in semi-batch operation, F (for Notation used throughout, see Table l), decays exponentially with experimental time T. F = e-k>r. (1 The differential equation leading to Eq. 1 is dF ----= -k,F (2) dT which is recognized as the algebraic analog of the chemical kinetics first-order reaction equation.' This has led to suggested mechanisms for flotation and mathematical relationships other than first order: with very little foundation other than analogy. The flotation rate coefficient kl can be accounted for as the product of several probabilities concerning bub-ble-particle attachment and detachment, aggregate entry from pulp into froth and return from froth to pulp, and removal from froth as concentrate. These factors clearly contribute to the magnitude of the overall flotation rate, and there are others also, but describing flotation merely as the overall probability of consecutive gross events hardly appears a significant advance in understanding. More recently, it has been described in terms of a stochastic process, which promises to provide a more satisfactory approach? The present paper will be more concerned with a phenomeno-logical description of the flotation process than with an account of the internal mechanics of the process. This is not a statement of priorities, or a judgement of the relative importance of these options but rather an assessment of what is presently possible. Previous investigators'" have developed methods for interpreting semi-batch flotation data in terms of species distribution. These methods have been used in an attempt to explain flotation behavior in response to changes in operating conditions." Inspection of examples given in the literature" reveals discrepancies between theory and experiment, and data obtained in the Colum-

Jan 1, 1971

By R. G. Wayland

SINCE the installation at Kropfmuehl, Bavaria, of a modern flotation concentrator in 1938, the flake and fine graphite from the Passau area can now be delivered in about any normal specified carbon content of any size range up to a flake averaging about 0.7 mm. The graphite finds a wide German and export market for crucible manufacture, pencil leads, dry cells and other uses. A controversy over the origin of the graphite deposits is being resolved in favor of syngenesis rather than epigenesis. The syngenetic theory is newly supported by the yet unpublished work of Hartmann of the Bavarian Geological Survey. Development work and exploration for graphite in the area may be changed in direction as the syngenetic theory is accepted. Crystalline graphite is produced in the area east of Passau near the junction of Germany, Austria and Czechoslovakia, as shown in Fig. 1. This is the only graphite area of importance in Germany, and Gra-phitwerk Kropfmuehl AG is the only operating firm in the area. The plant and mine are located at Kropfmuehl near Hauzenberg, Kreis Wegscheid, about 10 miles east of Passau. A narrow gage railway from the mine connects with the German Railway at Schaibing Bahnhof. The Pfaffenreuth mines date from about 1730. Until the early 20th century mining operations were carried out in a haphazard fashion. During World War I graphite mining and milling was increased, since it had to cover almost all of the crucible needs of the Central Powers. Between the wars some 11 mines were operated by two large and several small companies, but under the Nazis these were consolidated by 1938 into the Kropfmuehl enterprise. Kropfmuehl built a modern flotation mill to treat its own ores and small amounts of custom ores and tailings from the area. Since Graphitwerk Kropfmuehl AG was an I.G. Farbenindustry subsidiary, it has been under Military Government Property Control and probably will be sold to private German capital. Geology The country rock of the graphite area is part of the "kristallines Grundgebirge," the series of old gneissic and schistose rocks that constitutes the bed rock of most of the Bohemian basin and rims the Sudeten-land. The gneissic rocks of the graphite area are considered to have been metamorphosed during the Carboniferous period. They are bordered on the north by granite stocks and penetrated by numerous smaller granite and pegmatitic intrusive rocks, as shown in Fig. 1. The gneiss is classed as a micaceous, coarse-grained cordierite gneiss by most investigators. It is much metamorphosed by the granite, particularly in the north near the larger granite bodies. Interbedded in the gneiss are the graphite seams and lenses, and also beds and lenses of crystalline limestone containing disseminated graphite in noncommercial quantities. The gneiss, together with the included graphite and limestone seams and lenses, is cut and displaced by a number of granite sills of medium to fine grain and by a large number of diorite lamprophyre dikes and a few syenite-pegmatite dikes. The lamprophyre dikes are of various mineral compositions and textures, but many are banded and richly impregnated with pyrite; while the syenite-pegmatite dikes are coarse-grained with good crystals of titanite, pyroxene, uralite and other green amphiboles. Most investigators and the miners speak only of diorite and granite dikes cutting the graphite seams. The diorite dikes are later than the granite and some of the faulting, as is evident from Figs. 1 and 2. Individual graphite seams and lenses may be mined for thicknesses of several feet up to several scores of feet, and for distances of several hundred feet. The aggregate thickness of a series of some 20 seams of graphite, limestone and interbedded gneiss at Kropfmuehl is stratigraphically about 450 ft. Laterally, the graphite in a seam may pinch out or grade into crystalline limestone. Graphite crystals also are found disseminated in the gneiss itself, although in unmineable concentrations. The faults that cut the graphite seams carry graphite for some feet or tens of feet away from the seams, apparently mechanically. Similarily, the graphite lenses themselves often contain mechanically introduced inclusions of wall rock, probably from flowage during folding. Graphite crystals make up 10 to 30 pct of the fresh, mineable graphite lenses at Kropfmuehl, averaging about 20 to 25 pct after hand-sorting by the miners. In weathered lenses, the graphite concentration is said to be as high as 50 pct. The associated primary and hydrothermal minerals are dom-inantly feldspar and calcite, plus quartz, pyrrhotite, pyrite, biotite and occasional garnet, hornblende, sphalerite and galena. Associated secondary minerals include kaolin, nontronite, mangano-oxide-silicates (mog), adularia and chlorite. The superimposed suite of siliceous cementation minerals present consist largely of opal, chloropal, chalcedony, jasper, and hyalite. The kaolin is of special interest since it too was mined as early as 1730 and was used in the well-known Nymphenburg porcelain from 1756 on. The kaolin is derived from the gneiss and the syenite pegmatites. The crystals of graphite vary in size within a given seam, but in seams more than a mile away from the granite on the north the average crystal-linity is less coarse, lowering the commercial value. The lenses in the Kropfmuehl-Pfaffenreuth area are the most developed, and are the only ones with deep workings now accessible. Other similar crystalline graphite lenses are known from older workings at Habersdorf, Oberoetzdorf, Ficht, Diendorf, and

Jan 1, 1952

By Ashok K. Sinha

During the course of an in~*estigation into the occurrence of ordered AB3 structures, the following new phases have been found —CrRh3 (AuCu3 type), CrCo3 (MgCd3 type), HfCo4 (Ths Mn23 type), and WPt, MoPh type). The composition of the TiPt3-x phase (TiNi, type) is close to Ti23Pl77. The alloy chenzistry of transition rnetal AB3 structures is rezliewed in the light of electron concentration correlations of hex-agonality recently obtained for quasi-binary alloys. The relatizte colurne contraction in the AB3 structures increases with increasing difference in volume of the conzponents. A family of ordered close-packed layered structures is formed by stacking identical layers of composition AB, in various sequences, such that the coordination is twelvefold throughout and there are no A-A contacts. Previous work' on quasi-binary AB3 alloys has led to the conclusion that the stacking sequence of the AB, structures changes with increasing radius ratio RA/RB from a purely cubic, through different mixtures of hexagonal and cubic stacking to a purely hexagonal stacking. However. for binary AB3 alloys, a correlation between the type of the crystal structure and the position of the components in the various volumns of the periodic table has been noted.2-5 It has been noted6 that this correlation appears to hold even though the radius ratio RA/RB may vary over a considerable range with the location of the components in the three long periods. Another study7" of several quasi-binary systems led to the conclusion that an increase in hexagonality of the stacking is associated with increase in the electron concentration e/a. as defined by the average per atom of the total number of electrons outside the inert gas shells. In apparent conflict with this conclusion, it is known that seven binary alloy structures isotypic with TiNi3 which is 50 pct hexagonal occur at a higher electron concentration (e/n = 8.5) than that (e/a = 8.25) for the 100 pct hexagonal MgCd3 type structure present in seven binary AB3 alloys. Table 111. In the present work, an investigation into the occurrence of binary AB3 structures in transition metal alloys was made, and a survey of binary AB3 structures is presented. EXPERIMENTAL The starting materials were pure metals of 99.9 wt pct purity. The alloys were arc-melted under partial pressure of argon and annealed in sealed silica capsules lined with molybdenum foil under argon at- mosphere. The total weight loss upon melting and subsequent annealing was always less than 1 pct and hence the alloys will be referred to by their intended (unanalyzed) compositions. Wherever the constitution permitted. the alloys were given a homogenizing treatment at 1200°C (3 days) prior to annealing. Unless otherwise stated all alloys were annealed at 900°C for 1 week and water-quenched. Sometimes the final annealing treatment was carried out on powders to accelerate the attainment of equilibrium. X-ray powder patterns were taken using a Guinier-de Wolff focusing camera (CuK, radiation) or an asymmetrical focusing camera (Co or CrK, radiation). For lattice parameter determination. internal silicon standards were employed. The intensity calculations were made using a Fortran IV program written by Jeitschko and parthe.9 RESULTS Twenty AB3 and three AB4 alloys were investigated. Table I lists the crystallographic data on some of the intermediate phases encountered in the present work. Table II contains the X-ray data for HfCo, (Th,,Mn,, type). The positional parameter, x. was assumed to be 0.378. the value for Th6Mnn2310 The X-ray pattern of ZrCo, was very similar to that of HfCo, and the previous structure determination of ZrCo, by Kuzma el al." was confirmed. Ordering in the alloy CrCo could be ascertained by the presence of only one weak super lattice line (101). the others being too weak presumably owing to the small difference in the scattering powers of chromium and cobalt. This line was observed in the X-ray pattern of powder from the massive sample annealed at 830°C (7 days) after the powder had been reannealed at 600°C (24 hr). The diffraction pattern of the powder similarly reannealed at 830°C (24 hr) contained only the lines due to a mixture of hcp and fcc Co(Crj solid solutions. Therefore, it appears reasonable to assume that O2 and/or N2 contamination which would be less likely to occur during the 600°C anneal was not responsible for the observed weak reflection. Also. this reflection cannot be identified with any of the strong lines of the neighboring s phase which is present in the Co-Cr system at higher chromium contents. The composition corresponding to the TiNi3 structure observed by Raman et al.12 in the two-phase alloy Ti,zt,, has been established in the present work as being between There was satisfactory agreement for the low-angle lines (up to d = 1.997A) between the observed diffraction pattern of TiCua and that calculated assuming the ZrAu, structure. as recently proposed by Pfeifer-et a1.I3 However. some of the superlattice lines. e.g., at d = 1.937 and 1.919A. predicted by the ZrAu, structure were not actually observed eve? though neighboring lines. at d = 1.947 and 1.986A. of comparable calculated intensity were present. The ZrAu

Jan 1, 1970

By R. P. Alger, M. P. Tixier, D. R. Tanguy

In the combination induction-electrical log used at present in the field, the induction logging tool is appropriate for the investigation of moderately invaded formations. A new induction sonde with a radius and investigation about twice as large has been developed recently for the case of deep invasion. It has very nearly the same vertical resolution as the present sonde so that thin beds are defined as accurately as before. The characteristics of the new tool are described, the corresponding interpretation charts are given and field examples are discussed. The design of the sonic logging tool has been modified to improve the calibration and the reliability. The fact that porosity can be accurately recorded by means of the sonic log has prompted new interpretation procedures for saturation estimation, wherein the data concerning the various permeable beds in a given well are correlated. One approach consists of plotting transit time vs true resistivity, with an appropriate scale. With this approach, saturations can be estimated conveniently even in cases where formation water resistivity is not well known. In another approach, a comparison is made of the values of the formation waters computed from the re- sistivity and sonic logs. Using the concept of continuity, this procedure makes possible a quick determination of zones of saturation in shaly sands and/or in case of appreciable variations of formation salinities with depth. It has been found that the comparison of porosity from the sonic log with the apparent porosity computed from a short-investigation resistivity log may reveal, in many cases, the presence of residual oil and thus detect potentially productive formations; this procedure is valuable when the true formation resistivity and the resistivity of the formation water are in doubt. INTRODUCTION During the past year, the efficiency of log interpretation has been vastly improved. The improvements have largely resulted from the introduction of a deep-investigation induction device and from the application of new interpretation techniques that utilize sonic vs resistivity readings. Since the new interpretation techniques depend, in part, upon good values of true formation resistivity, the new induction log will be discussed under Part I. The sonic interpretation techniques will be studied under Part 11. Early in 1959, the 6FF40 induction equipment was introduced in the field. This device was designed for a better approach to true formation resistivities in deeply invaded zones. The greatly improved radial investigation of the 6FF40 equipment has been achieved without sacrificing vertical resolution. The first combination induction-electrical log, the 5FF40, was introduced as a standard tool in 1956 for the logging of wells drilled with fresh muds. The tool has received wide industry acceptance in the United States. 'The 5FF40 induction log has a radial investigation sufficient to overcome average depths of mud filtrate invasion. At 5d invasion, for example, the 5FF40 induction log will read about 1.4 R. in a water sand where R., = 10R,. At 10d invasion, such induction log would read 2.45 R. in the same water sand. In either case, the effects of invasion would not be sufficiently great to cause a water sand to be mistaken for a shale-free oil- or gas-producing zone. Some formations, however, invade deeply — in excess of 10d. Such water zones could be mistaken for oil-or gas-saturated sands unless the porosity balance' can clearly make the distinction. It is for these deeply invaded formations that the 6FF40 was developed. CHARACTERISTICS OF THE 6FF40 Radial Investigation Characteristics To describe the comparative responses of the 5FF40

By J. O. Brittain, E. P. Lautenschlager, D. A. Kiewit

Compression tests were run in the temperature range of 700° to 900°C ox 0' phase NiAl intermetal-lic alloys of several grain sizes. At these temperatures the minimum strengths were observed at the stoichiometric composition. While significant increases in strength occurved in both the low-nickel (vacancy) and high-nickel (substitutional) regions, the highest strengths were found in the high-nickel region. During deformation serrated flow was sometimes observed in the low-nickel alloys. After deformation transgranular cvacking and deformation striations were observed in all compositions tested. AS part of a general investigation of the properties of NiAl inter metallic compounds, a preliminary study of the role of point defects upon plasticity was made by high-temperature compression tests on ß' NiAl specimens of several grain sizes and compositions. ß' NiAl is an intermetallic compound having a CsCl structure and a rather wide range of composition from A1-45 at. pct to 60 at. pct Ni.1 According to Bradley and Taylor2 and to cooper,' it possesses a defect lattice in which departures from stoichiometry in the direction of decreased nickel content lead to the presence of vacant nickel sites (although Cooper's work indicates that a small amount of substitution also occurs) whereas departures on the high-nickel side lead to substitution of nickel on aluminum sites. NiAl forms congru-ently from the melt at approximately 1650°C,1 and thus has a higher melting point than either of its component elements. Up to this time, although this and other high-melting intermetallic compounds have been suggested for elevated-temperature usage,4 only the hardness4 and a few tensile-strength measurements5 have been reported for NiAl at high temperatures. In the present investigation the effects of composition upon the compressive-strength properties in a range of 700° to 900°C have been measured for NiAl of several grain sizes. EXPERIMENTAL PROCEDURES The alloys were made as described elsewhere6 from an A1-46.8 at. pct Ni master alloy furnished by the International Nickel Co. with additions of high-purity nickel and aluminum. The charges were vacuum-induction-melted in A12O3 crucibles with small amounts of helium added to the atmosphere to suppress vaporization. They were cooled slowly from the melting temperature to achieve uniform grain size. In order to refine the as-grown grain size a special rolling technique was developed. Alloys were packed into 0.10-in. wall-type 302 stainless-steel tubes which were partially filled with magnesium oxide to prevent bonding between the alloy and the steel jacket. The ends of the tubes were closed by hot forging, and the packets were then hot-rolled. The alloys with greater than 50 at. pct Ni were rolled at 1100°C, but it was found necessary to increase the temperature to 1350° C before alloys with less than 50 at. pct Ni would roll without cracking. With these temperatures, reductions as high as 48 pct were achieved in a single pass. The rolled alloys will hereafter be referred to as "fine grained" whereas the as-grown material will be designated "coarse-grained''. The compression specimens were made by cutting square cross-sectional pieces, approximately 3/16 by 3/16 by 1/2 in., with a water-cooled diamond cut-off wheel from the as-grown or the rolled alloys. Specimens were ground to their final dimensions by polishing through 3/0 grit silicon carbide papers. The final shape was a rectangular parallelepiped of square cross section having a height-to-width ratio of 3:1. Compression testing was carried out in a compression rig of our own design mounted on an In-stron Floor Model. The specimen chamber could be heated to 1000°C and was controlled within ±2°C. The compression rig was enclosed within a bell jar and was maintained at a 50 µ of mercury vacuum throughout the duration of the test. The test cham -ber was heated from room to test temperature within 15 min. Specimens were then held at the test temperature 30 min prior to testing. Previous experiments indicated that no grain growth would occur within this time. An Instron Variable Crosshead speed unit was used to adjust for small variations in specimen lengths in order to have a constant initial strain rate, €, for all specimens of a group. For the fine-grained specimens the strain rate was changed rapidly at constant temperature by a factor of 10 with the speed lever on the Instron. For a given € the compression data was analyzed in terms of true plastic strain (E) and true compressive stress (0).

Jan 1, 1965

By W. N. Poundstone, P. C. Thakur

Introduction Horizontal drilling in coal mines is a relatively new technology. The earliest recorded drilling in the United States was done in 1958 at the Humphrey mine of Consolidation Coal Co. for degasification of coal seams. Spindler and Poundstone experimented with vertical and horizontal holes for several years. They concluded in 1960 that horizontal drilling in advance of underground mining appeared to offer the most promising prospect (for degasification) but effective and extensive application would be dependent upon the ability to drill long holes, possibly 300 to 600 m, with reasonably precise directional control and within practical cost limits (Spindler and Poundstone, 1960). Mining Research Division of Conoco Inc., the parent company of Consolidation Coal Co., began a research program in the early 1970s to achieve the above objective. The technology needed to drill nearly 300 m in advance of working faces was developed by 1975 and experiments on advance degasification with such deep holes began in 1976. Preliminary results of this research have already been published (Thakur and Davis, 1977). To date nearly 4.5 km of horizontal holes have been drilled for advance degasification and earlier results were reconfirmed. In summary, these are: • The greatest impact of these boreholes was felt in the face area where methane concentrations were reduced to nearly 0.3% in course of two to three months from original values of nearly 0.95%. • The methane concentration in the section return reduced to 50% of its original value immediately after the boreholes were completed, indicating a capture ratio of 50%. • The total methane emission in the section (rib and face emission plus the borehole production) did not increase but rather gradually declined with time. • Initial production from 300 m deep boreholes in the Pittsburgh seam varied from 3 m3/min to 6 m3/min but then slowly declined as workings advanced inby of the drill site (well head) exposing a larger surface area parallel to the borehole. Encouraged by these results, it was decided to design a horizontal drilling system that would be mobile and compatible with other face equipment. A mobile horizontal drill can be divided into three subsystems: the drill rig, the drill bit guidance system, and borehole surveying instruments. The drill rig provides the thrust and torque necessary to drill 75- to 100-mm diam holes up to 600 m deep and contains the mud circulation and gas cuttings separation systems. The drill bit guidance system guides the bit up, down, left, or right as desired. Borehole surveying instruments measure the pitch, roll, and azimuth of the borehole assembly. Additionally, it also indicates the thickness of coal between the borehole and the roof or floor of the coal seam. Thus, it becomes a powerful tool for locating the presence of faults, clay veins, sand channels, and the thickness of coal seam in advance of mining. In recent years, many other potential uses of horizontal boreholes have come to light, such as in situ gasification, longwall blasting, improved auger mining, and oil and gas production from shallow deposits. The purpose of this paper is to describe the hardware and procedure for drilling deep horizontal holes. The Drilling Rig [Figures 1 and 2] show the two components of the mobile drilling rig: the drill unit and the auxiliary unit. The equipment (except for the chassis) was designed by Conoco Inc. and fabricated by J. H. Fletcher and Co. of Huntington, WV. The drill unit. It is mounted on a four-wheel drive chassis driven by two Staffa hydraulic motors with chains. The tires are 369 X 457 mm in size and provide a ground clearance of 305 mm. The prime mover is a 30-kw explosion-proof electric motor which is used only for tramming. Once the unit is Crammed to the drill site, electric power is disconnected and hydraulic power from the auxiliary unit is turned on. Four floor jacks are used to level the machine and raise the drill head to the desired level. Two 5-t telescopic hydraulic props, one on each side, anchor the drill unit to the roof. The drill unit houses the feed carriage, the drilling console, 300 m of 3-m-long NQ, drill rods, and the electric cable reel for instruments. The feed carriage is mounted more or less centrally, has a feed of 3.3 m, and can swing laterally by ± 17°. It can also sump forward by 1.2 m. The drill head has a "through" chuck such that drill pipes can be fed from the side or back end. General specifications of the feed carriage are: [ ] The auxiliary unit. The chassis for the auxiliary unit is identical to the drill unit but the prime movers are two 30-kW explosion proof electric motors. It is equipped with a methane detector- activated switch so that power will be cut off at a preset methane concentration in the air. No anchoring props are needed for this unit. The auxiliary unit houses the hydraulic power pack, the water (mud) circulating pump, control boxes for electric motors, a trailing cable spool, and a steel tank which serves for water storage and closed-loop separation of drill cuttings and gas.

Jan 1, 1981

By John H. G. Monypenny

The range of chromium content of stainless steel is, in most cases, included in the limits 11 to 14 per cent., or the middle part of the range, 9 to 16 per cent., specified by the discoverer. For some time after the steel was produced commercially, the carbon content was about 0.3 to 0.4 per cent. and occasionally higher; only rarely was material with 0.25 per cent. carbon or less produced. The reason for this is obvious from the nature of the alloys of chromium available for making such steels; as the lowest carbon content generally available was about 1 per cent., and this in conjunction with a chromium content of about 60 per cent., the production of a 12-per cent. chromium steel with less than 0.25 to 0.30 per cent. carbon was impossible. The advent, on a reasonable commercial scale, of carbonless ferrochromium has modified this condition, however, so that for the last three years stainless material containing 0.1 per cent. or less carbon and the normal amount of chromium has been on the market. As far as the author is aware, the material was first made on a commercial scale by the firm with which he is associated in June, 1920, when a 5- or 6-ton cast of material containing 0.07 per cent. carbon and 11.7 per cent. chromium was made and cast into 12-in. ingots. The necessity for using a totally different raw material, carbonless ferrochromium, instead of the ordinary low-carbon ferro (0.6 to 1.0 per cent. carbon) has led to the idea that stainless iron is a quite distinct product and quite different from stainless steel. While this may be true from a commercial aspect, it is wrong metallurgically. The name stainless iron is unfortunate as the material is a very mild stainless steel and forms the lowest carbon member of a series of steels of continuously varying content which are, in many respccts, the counterpart of the series of ordinary carbon steels ranging from "dead soft" to tool steels. In an article on stainless steel in the Journal of the Society of Chemical Industry, November, 1920, the author said "Just as in the far-off days 'steel' was regarded as a hard product of iron, and little or no attempt was made to grade it into harder or softer varieties, so at present stainless

Jan 1, 1924

Jan 1, 1953

By D. W. Reed, R. L. Reed, Tracht

Laboratory experiments on the reverse combustion of tar sands in a linear adiabatic system have shown that a highly upgraded oil can be produced from an exceedingly viscous, immobile oil. The dependence on the air-injection rate of peak temperature, combustion-zone velocity, oil recovery, air-oil ratio, residual coke and oil, fuel burned and distribution of product gases is shown graphically. Eflects of initial temperature, oxygen concentration, oil saturation and heat loss are discussed. Experiments bearing on the coking properties of heavy oils are mentioned and some results exhibited. Field application of the process hinges on the existence of adequate air permeability and the rate of reaction under reservoir conditions. INTRODUCTION It has been established that oil can be recovered from underground reservoirs by means of at least two fundamentally distinct methods involving in situ combustion of a certain fraction of the oil. Characteristic of both of these known methods is the production of oil from one or more wells by means of hot gases formed when a high-temperature reaction zone is advanced through the reservoir. In both cases, the reaction zone is created by heating certain of the wells to a sufficiently high temperature prior to the introduction of air, and the zone is maintained and advanced through the reservoir by appropriate control of the air-injection rate. In the first of these methods, which is called "forward combustion",' the combustion zone advances in a direction which is generally the same as that of the air flow; whereas in the second method, "reverse combustion",' the combustion zone moves in a direction generally opposite to that of the air flow. Forward combustion, on the one hand, is an ideal combustion process in the sense that a minimum of the most undesirable fraction of the oil is consumed as fuel in the form of coke, a clean sand is left behind and generated heat is used as efficiently as possible. However, the applicability of forward combustion is limited. Since the products of combustion, vaporized oil and connate water must flow into relatively cold regions of the reservoir, there is an upper limit on the viscosity of oil which can be moved by this process in a practical and economical fashion.' On the other hand, it is characteristic of reverse combustion that the vaporized oil and water together with the products of combustion are produced through sand which is already hot and has had its mobile liquid content eliminated. This means there is no upper limit on oil viscosity; indeed, the oil may be an entirely immobile semi-solid. However, fuel for the process is an intermediate fraction of the original oil, and the most undesirable fraction remains on the sand surface as a substantial deposit of coke. Since this coked material is not burned during reverse combustion, it represents energy which is available for the production of oil but is not used for this purpose. It follows that one can expect economics to be somewhat less attractive with reverse combustion than with forward combustion. Nevertheless, it is a process which is designed for reservoirs where forward combustion is impossible and, as such, has become a subject of experimental and theoretical investigation. In this paper, only experiments made with tar sands are discussed. DESCRIPTION OF THE PROCESS We proceed, then, to consider the process of reverse combustion in greater detail. Fig. 1 illustrates a temperature profile defining a combustion zone which moves from right to left when air flows from left to right. In Zone 1, the temperature is the initial reservoir temperature, and the tar sand is as yet unaltered. This statement must be modified to the extent that physical properties of the oil may be changed by low-temperature oxidation at reservoir temperature. As air passes into Zone 2, which has been warmed by conduction, it assists in vaporization of the very light ends (if there are any), and oxidation occurs at a significant rate. In this region, there is almost no production of carbon monoxide or carbon dioxide because predominantly addition-type reactions take place with the formation of oxygenated compounds such as aldehydes and acids together with water. The hydrocarbon-enriched and slightly oxygen-depleted gas stream enters Zone 3 where

By John H. Schemel

Large Zircaloy-2 hammer or press forged bars did not exhibit the uniform excellent corrosion resistance to steam normally expected of the alloy in wrought form. Weight gains of coupons cut from forged bars were 40 to 60 mg per sq dm compared to the 28 mg per sq dm obtained on hot rolled sheet and strip. The mechanism of this corrosion and its relation to microstructure is discussed. After these observations, a solution heat treatment followed by rapid cooling was tried on coupons from eight heats of forged bars. The basket-weave structure resulting from the quench did not show agglomeration of intermetallic compounds. These coupons showed uniformly good corrosion resistance with weight gains very close to the 28 mg per sq dm expected of Zircaloy-2 after the 14-day steam test. A large forging was solution heat-treated and tested for structure, mechanical properties, and corrosion resistance. Corrosion resistance was excellent and uniform throughout the section. The normally anisotropic mechanical properties were changed to completely iso-tropic. Strength levels were raised while there was a small loss in ductility at the service temperature. Tempering of the quenched structure below the ß transus did not improve the ductility at the test temperature of 600°F. ZIRCALOY-2 end caps for nuclear fuel elements Zircaloy-2 is an alloy of 1.5 pct Sn, 0.1 pct Fe, 0.1 pct Cr, and 0.05 pct Ni, balance hafnium-free zirconium patented by Westing-house Electric Co. used in pressurized water reactors are machined from large hammer-finished forged bars. The bars forged for this application range from 3 1/2 in. to 7 1/2 in. squares. One of the tests used to evaluate Zircaloy-2 for this service is a 14-day exposure to very high-purity steam at 75oF and 1500 psi pressure. Normally wrought products will exhibit a black lustrous film of zirconium oxide after the test and show a weight gain of approximately 28 mg per sq dm. Coupons representing the forged bars exhibited a wide variety of corrosion results ranging from acceptable black coupons to some covered with white crystals of zirconium oxide that had weight gains of nearly 100 mg per sq dm. One of the most common effects was a white corrosion product that looked like a stain to some observers and the outline of massive metal grains to others. Very careful specimen preparation prior to the corrosion test did not affect the result and metallographic examination did not reveal a structural feature of a size and shape that would correlate with the corrosion product. In addition to the relatively poor corrosion resistance, the forged product was not as ductile as desired. The problem of obtaining uniform and more acceptable properties in these heavy-forged sections seemed to be a function of the microstructure of the metal and, in particular, the distribution of the intermetallic compounds. None of the four alloying elements however are appreciably soluble in a zirconium and are present as compounds which usually appear scattered randomly throughout the structure. Moudryl showed that the distribution of these intermetallic compounds in Zircaloy could be related to a ostringero corrosion failure. Grozier et al. discussed another structural defect that causes a similar corrosion effect. In this case, an elongated gas-void was determined to be the cause. M. L. Picklesimer held in his discussion of the Grozier paper that at least a part of the observed =stringersn were caused by the distribution of the intermetallic compounds. He proposed a

Jan 1, 1962

By F. E. Pawlek, J. K. Gerlach

The chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. In the first part of the investigations the reaction rate of the chlorides of sodium or calcium with gas mixtures of SO,-0, or SO ,-O2 ,-SO , was measured. The rate for reactions with gas mixtures SO2-O2 is ThE chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. At present the process is mainly applied to produce nonferrous metals which occur in pyrite cinders in small concentrations. Thereby the nonferrous metals are converted into water-soluble, acid-soluble, or volatile compounds whereas all the iron remains as insoluble oxide. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. The reactions occurring during the roasting process can be divided into two groups: solid-solid reaction and gas-solid reaction. The reactions between solids proceed by means of solid-state diffusion and are therefore of low velocity. The heterogeneous reactions between solids and gases of the roasting atmosphere5 are high-velocity processes and determine the velocity of the chloridizing roasting. These gas-solid reactions shall be the subject of the paper presented. In order to investigate the still little-known processes which occur during the chloridizing roasting 6-' the complex reaction is split into several partial steps. First the reactions of NaCl and CaCl, with gas mixtures of SO2 and 0, have been investigated at temperatures between 500" and 600°C by measuring the weight increase of the samples. The gas mixtures used in this series of experiments had first variable compositions, then the amount of SO 2 had been increased. Furthermore the influence of Fe 2 O3 admixtures upon these reactions, the behavior of pure Fe 2 O3 with the gaseous reactants, and the chlorination of the sulfides of lead, copper, nickel, and zinc have been investigated. FORMATION OF GASEOUS CHLORINE Pyrite cinders are never completely roasted and therefore contain still a small amount of sulfide sulfur. When heated again in air, this sulfur is converted into SO,. Accordingly the formation of chlorine can first be described by the reactions: dependent on the composition of the gas phase. If more than 1 pct SO 3 is added to the roasting gas, the reaction rate is determined only by the concentrations of the SO,. In the second part the reactions between chlorine and metal sulfides are discussed. The rate of formation of gaseous chlorine is higher by me order of magnitude than is the reaction rate between ZnS and chlorine. The reaction rate of NiS and PbS lies considerably below that of ZnS. The conversion rate of both pure Fe 2 O 3 and Fe 2 O 3 containing NaCl or CaCl2 when reacting with SO2-O2, mixtures with and without SO3 portions was measured at temperatures of 500", 550°, and 600°C. The weight increase of pressings was determined by means of a spiral balanceg and the reaction rate calculated therefrom according to Eqs. [ll to [31 and [5] to [7]. The prepared samples were suspended on a platinum filament in a vertically mounted tube of mullite (ID 4 cm, length 110 cm) which could be heated by a resistance tube furnace. The platinum filament was tied to the lower end of the spiral balance. A supremax glass tube (length 70 cm) was mounted gas-tight on top of the reaction tube. The unit was sealed up at its top by a ground-in stopper which was holding the spiral balance with the sample. The spiral balance therefore hung outside the high-temperature region of the furnace. Fig. 2 shows the experimental arrangement schematically. While lowering the sample into the reaction tube pure nitrogen was flowing through the reaction zone providing a protective atmosphere. After the sample had reached the reaction temperature within approximately 1 min, the protective gas was replaced by the sulfur dioxide-oxygen reaction mixture. It took about 30 sec until the mixture filled the tube homogeneously. A Ni/NiCr thermocouple placed in the center of the furnace where the sample hung during the measure-

Jan 1, 1968

By N. S. Stoloff, R. C. Ku, R. G. Davies

The stress-strain behavior of Fe-Co and Fe- V alloys containing up to 25 pct solute have been studied in the temperature range 25° to - 196°C. The microyield stress is independent of temperature for all alloys studied, while the temperature dependence of the ordinary yield stress is large and comparable to that for unalloyed iron. An alloy-softening phenomenon is observed for many alloys relative to unalloyed iron, and appears to be a consequence of removal of inter-stitials from solution and their subsequent agglomeration. The ductile to brittle transition temperature is increased markedly by both cobalt and vanadium. Transmission electron microscopy observations reveal that cross slip and cell formation are restricted with increasing solute, which can account for many aspects of yielding and fracture behavior. IRON and other metals of bcc structure slip on many planes of the (111) zone at moderate and elevated temperatures, giving rise to wavy glide. At low temperatures, however, there is a tendency for slip to be restricted to planes of only one or two crystallographic types; in the case of Fe-Si alloys for example, (110) glide predominates, giving rise to planar slip bands."' Restriction of cross slip at low temperatures in iron has been linked by Brown and Ekvall3 to increased strain hardening in the preyield microstrain region, leading to an apparently large temperature dependence of the yield stress. Support for this view has been provided by Lawley and Gaigher4 from a transmission electron microscope study of molybdenum. They concluded that dislocations at lower temperatures, by virtue of their inability to change planes readily, are unable to interact and annihilate, leading to an increase in internal stress and work-hardening capacity. Restriction of cross slip at low temperatures has also been suggested to be an important factor in determining the ductile to brittle transition of single-phase solids, including metals of bcc structure.5 It is pertinent to note that most solute elements tend to raise the ductile to brittle transition temperature of poly crystalline ferrite,6,7 although in some cases, e.g., Fe-Cr7 and Fe-Al,8 the dilute alloys may actually yield at lower stresses than unalloyed iron. It appears, therefore, that solute elements may have an effect analogous to lowering the test temperature with regard to restricting cross glide. Such an effect has indeed been observed in the ionic alloy system KCl-KBr,9 in which bromine atoms, although causing little misfit and consequently little effect on the yield stress of KC1, have a pronounced effect in restricting wavy glide and inducing brittleness. The purpose of the present investigation was to determine the effects of selected solute atoms on the yield stress and fracture behavior of iron, and to elucidate in turn how the slip character was related to these properties. Since it is known that interstitial atoms exert a strong influence on the mechanical behavior of iron, the solute elements chosen for study were vanadium, which reacts strong with interstitials,10 and cobalt, which does not form highly stable interstitial compounds." EXPERIMENTAL PROCEDURE Four-pound ingots of each of the following alloys were vacuum-melted in zirconia crucibles: Fe-1, 5, 10, 25 at. pct Co, and Fe-1, 4, 10, 20 at. pct V. An ingot of unalloyed iron from the same original stock as that used for the alloy was remelted under similar conditions to eliminate variations in interstitial content arising from differing thermal histories. Chemical analyses of the iron, cobalt, and vanadium melt stock are listed in Table I. All ingots were rolled and swaged, commencing at 850°C, to 1/4-in.-diameter bar. The bars were then annealed at 850°C for 1 hr (except that the 10 and 20 pct V alloys were heated for 2 hr) to give a uniform equiaxed grain size of about 0.05 mm. Tensile samples of 0.125 in. diameter by 0.8 in. gage length were utilized for studies of the ductile to brittle transition. A second set of tensile samples were utilized for microstrain experiments in which strain sensitivity of 1 x 10"6 was achieved by a capacitance method.3 Cylindrical compression samples 0.250 in. diameter by 0.4 in. long also were prepared to study the influence of composition on the macroscopic yield stress, and for metallographic analyses of defor-

Jan 1, 1965

By M. H. Caron

BASIC U. S. Patent 1,487,145 on ammonia leaching of nickel ores was issued to the author on March 18, 1924. Equivalent patents in other countries were obtained later. The Dutch Syndicate Brikcarbo became interested in the process in 1935; and a couple of years later the late Dr. H. Foster Bain sent samples of Surigao laterite iron ore to Delft and witnessed tests made there on this material for the Philippines Commonwealth. As a result, the author was asked in April 1940 by Dr. Bain to go to the Philippines to erect and take charge of a pilot plant for the process. The World War prevented carrying out this proposal. The Dorr Co. also became interested in the process at about the same period. The investigations by the Freeport Sulphur Co. on the process as applied to the Cuban nickeliferous laterites, which resulted in the Nicaro enterprise, and the results of this operation have been well described elsewhere.1,²,³,4,5 This Nicaro plant was, in operation for almost two years, and during this period produced about 10 pct of the world nickel production from laterites containing 1.35 pct nickel. This plant and its operation were war measures and, in view of this, activities were suspended in April 1947. The results obtained fully demonstrated the technical feasibility of the process and its economical aspects on a commercial scale. In this respect, it should be understood that it is probable that improvements may be made by further development, and that there are possibilities for advantageous application of the process to garnierite and similar ores with higher values in nickel than the laterite iron ores at Nicaro. While the articles cited above have given a certain amount of information, no general article containing all the important process data has been pub- lished. Since the process is of more than local interest, a fuller knowledge of the fundamental and practical factors of the method may be welcome to those interested in this new field of metals technology. The author, accordingly, takes pleasure in submitting this article to the AIME as it represents in a condensed form the results of many years of research. The brief outlines of the fundamental and other factors and the explanation of observed phenomena are presented with as little discussion of details as possible, consistent with clarity. It is a special satisfaction to the author to make some contribution of his own in return for the benefits of the many valuable publications issued by the Institute during his thirty years of membership. Ores Adapted for Ammonia Leaching: All nickel and cobalt ores which originate from weathering of peridotites or similar basic rocks having sufficient values are suitable for treatment by the ammonia leaching process after a preliminary reduction under proper conditions. The formation of these deposits was probably as follows: In the course of time the basic rocks were attacked by atmospheric agencies; MgO and SiO2 were gradually leached out, and secondary nickel minerals formed, such as garnierite, a hydrated silicate of nickel and magnesia. These secondary products are, however, not stable. They decompose in a further stage of weathering and ultimately only a relatively small residue of insoluble oxides remains, known as laterite iron ore with a small nickel content and very little cobalt. Under these mantles of laterite, richer nickel values may be found, usually indicated by the occurrence of garnierite. The more the ore is disintegrated by nature, the higher the iron content and the better the nickel extractions that may be expected therefrom. Table I shows extractions that may be expected from different types of ores, assuming treatment of -200 mesh products and that all precautions have been taken for obtaining maximum extractions. As for the distribution of the various nickel minerals and compounds that may be present, great variations may occur from locality to locality as well as vertically in a deposit. From such "run of

Jan 1, 1951

By Potts N. L., Eilerts C. K., Summer E. F.

The second-order, nonlinear, partial- dillerential equation representing the transient radial flow of gas - condensate fluids in reservoirs has been integmted by using finite -dillerence equations and electronic computers. Effect was given to pressure -dependent permeability, viscosity, and compressibility and to distance-dependent permeability. The influence of a second-degree velocity term in the Darcy equation was investigated. Implicit methods were used and practical, convergent solutions were obtained with material balance to less than 6 x 10-4 for recovery of one- hall the reserve at constant flow rate. Integration results provide the productive period of a reservoir for a given constant rate and the fraction of the fluid initially in place that can be recovered in that period. The properties of a lean and a rich fluid are represented in a set of integrations designed to demonstrate the effect of different constant-recovery rates and significant variables emphasized one at a time. INTRODUCTION A method is needed for computing the availability or reserve of a gas in a formation, making use of all technical and engineering information that is pertinent. As a step in this direction, a program for computing transient linear flow1 was developed that utilizes principles of earlier finite-difference computing for a similar purpose2-4 and gives effect to significant pressure- and distance-dependent properties of reservoirs and their contents. The present paper pertains to transient, radial flow of gas-condensate fluids. In the partial-differential equation of flow, effect is given to the variables viscosity and compressibility,5 and also to permeability. Included in the study is the quadratic form of the Darcy equation of flow that has been the subject of field tests6 and that has been applied to a gas with constant properties in transient flow computing. 7 Inclusion in the differential equation of variable coefficients to represent properties greatly complicates the higher derivatives of the equation. Because it was impractical to make a required improvement in certain of the finite-difference derivatives by Taylor-series expansion, five-term derivatives were used in the implicit computing. Related methods were developed that can improve general facility in manipulating finite-difference equations. BASIC EQUATIONS PARTIAL DIFFERENTIAL EQUATION The basic partial differential equation for transient radial flow in the direction of decreasing radius is l_ a(vpr) _? .......(1) r gr at where r = radius, L v = apparent velocity aIong radius, L/t p = density, M/L3 t = time, t Ø = porosity, dimensionless. In this equation, only the porosity is regarded constant. The density is where p = pressure, m/Lt2 M = molecular weight of fluid, m T = constant temperature of fluid, T z(p) = pressure-dependent compressibility factor, dimensionless R = gas Constant, mL2/t2t. The physical boundary of the reservoir is at re, and the producing boundary is defined to be at tq with rq = re /200. By definition,

Jan 1, 1966

By H. R. Ogden, E. S. Bartlett, A. G. Imgram

Unmodified disilicide coatirigs were applied to sheet-tensile specimens ofCb-Dg3 and Mo-TZM veJractovy- metal alloys. Coating thickness, degree of coating-substrate interdiffusion, and specimen geonzetry (notched and plain were included in the variables studied. Tensile tests were made to determine the ductile-lo-brittle transition temperature. The disilicide coating modestly increased the transition temperatlre of TZM, but had no effect on 043. Neither material condition (recrystallized or stress-velieved) nor specimen geometry (notched or unnotched) significantly altered the effects of coatings on the transilion temperatures of. the alloys. Cracks in the brittle coatings did not propagate into the substrate, and fracture modes appeared to be the same for both un-coated and coated specimens. MOST potential structural applications for refractory metals and alloys involve exposures to oxidizing environments at elevated temperatures. The general lack of oxidation resistance of these metals will require protective coatings to allow fulfillment of their potential. Currently preferred coatings for the oxidation protection of refractory metals are brittle intermetallic aluminides or silicides. These are typically formed on the surface of the refractory-metal substrate by a diffusion reaction between the substrate and a gaseous or liquid medium that is rich in aluminum or silicon. Because of the brittleness of these coatings, they will sustain no plastic deformation at low temperatures. They are frequently cracked by cooling from the coating temperature because of the thermal-expansion mismatch with the substrate alloy. Even if they survive cooling intact, they crack rather than sustain deformation under load at low temperatures. Thus, when a coated refractory metal is strained beyond the elastic limit of the coating at low temperatures, the mechanical environment of the substrate would include both static and dynamic cracks. These might be expected to influence the flow and fracture behavior of the substrate. This could be manifested in an altered fracture mode and/or an increase in the normal ductile-to-brittle transition temperature of the refractory-metal substrate. This paper presents the results of a research program that was conducted to determine the influence of the presence of a brittle surface coating on the low-strain-rate tensile behavior of typical refractory metals at low temperatures. EXPERIMENTAL PROCEDURES Material Preparation. Thirty-mil-thick sheets of molybdenum TZM alloy (Mo-0.5Ti-O.1Zr) and colum-bium D43 alloy (Cb-IOW-1Zr-O.1C) were obtained commercially. These alloys were selected as substrate materials representing two classes of materials important in current refractory-metal technology. The TZM was in the stress-relieved condition, and exhibited a heavily fibered grain structure. The D43 had been processed by the duPont "optimum" fabrication schedule,' and exhibited slightly elongated grains typical of this process. Tensile specimens of two geometries were prepared from these materials: 1) plain specimens with 0.2-in.-wide 1.0-in.-long gage sections; 2) specimens similar to above, but with a 0.06-in.-diam hole drilled in the center of the gage section, providing a stress concentration factor, Kt, of 2.5. The "notch" geometry was selected to represent a typical condition of a rivet hole or other geometric discontinuities as might be encountered in various applications. Machined specimens were degreased, with a final rinse in acetone, prior to the application of coatings. Specimens of each substrate and configuration were pack-siliconizedin a particulate mixture of 80 pct A1203, 17 pct Si, and 3 pct NaF. Specimens were embedded in this mix (contained in graphite retorts) and coated in an electrically heated argon-atmosphere furnace under time-temperature conditions to effect nominal 1- and 3-mil-thick silicide coatings: Coating Thickness, mils Thermal Treatment 0.6 to 1.4 24 hr at 982°C 2.4 to 3.2 48 hr at 1093°C Coating kinetics were similar for both the TZM and D43 substrates. These treatments had little or no visible effect on the substrate microstructure as determined by optical metallography. The coatings on TZM were essentially single-phase unmodified disilicides, while those on D43 showed substantial evidence of modification by proportionate reaction with the respective substrate elements or phases, as shown in Fig. 1. It was recognized that these coatings might not be particularly desirable regarding protective capability. However, it was desired to circumvent possible inter -ferring chemical interaction with the substrate by pack additives such as chromium, titanium, boron, aluminum, and other elements that typify the better protective coatings for these materials.' Thus, the results presented apply specifically to the simple silicide coatings investigated. They may not be rep-

Jan 1, 1967

By Jerome J. English, Gordon W. Powell

An experimental investigation and mathematical analysis of the thermal-dilation behavior of the titanium alloy Ti-7Al-3Cb have shown that the linear dimensional changes associated with the polymorphic transformation need not be isotropic. The absolute magnitude of the linear dimensional change, which may be either positiue or negative, associated with the cr-p transformation is dependent upon the relutzve volumes of different orientations of the transformation product. It is hypothesized that the dilation irregulati-ties that have been observed during the polymorphic transformation of pure, coarse-grained titanium and other titanium-base alloys can be explained in the same manner. When titanium is heated above about 165O°F, the hcp a structure transforms to bcc 0. Thermal-dilatioh measurements have shown that the transformation is accompanied by a decrease in length of 0.16 pct.' Such dilation behavior would be expected because the volume of the hcp unit cell is about 0.3 to 0.4 pct greater than that of the bcc unit cell. A recent investigation2 of the thermal-dilation behavior of an experimental a-p* titanium alloy, Ti- 7A1-3Cb, containing 0.06 wt pct 0 showed that its dilation behavior during the polymorphic transformation differed substantially from that reported for unalloyed titanium. The first time the alloy was cycled through the transformation, the dilation curve closely duplicated that of unalloyed titanium. However, upon repeated cycling through the transformation temperature range, both the magnitude and the sign of the dimensional change associated with the transformation were observed to vary with each cycle. This investigation was undertaken to obtain additional data on the dimensional changes associated with the polymorphic transformation in the Ti-7A1-3Cb alloy and to determine the cause of the dimensional irregularities. After testing, the specimens were examined metallo-graphically. In addition, Laue back-reflection patterns were obtained from selected sections taken perpendicular to the specimen axes to determine the a orientations present in these sections. White radiation from a tungsten target and a 0.1-mm-diam collimator were used to produce the diffraction patterns. RESULTS Dilation Curves. Three types of thermal-dilation curves were obtained when the a-8 titanium alloy was heated and cooled through the transformation temperature range. These three types of curves are illustrated in Fig. 1. The type I curve represents what is considered normal behavior, because the dilation change is what would be expected on the basis of the volumes of the unit cells of a and p. The Type I1 curve is the inverse of Type I. Normal behavior is characterized by an expansion on cooling through the transformation, whereas a contraction takes place in the Type 11 curve. With Type ni behavior, no clearly distinguishable length change occurs during the transformation. No other anomalies that might be indicative of other phase transformations were observed in the dilation curves at lower temperatures. Apparently, the cooling rate was low enough for equilibrium to be reached during the 0 to a transformation. Table I lists the types of dilation curves observed during the polymorphic transformation as a function of the direction of measurement and cycle number. The A1 value was determined by extrapolating the low-temperature (a + 5 pct p) and high-temperature (100 pct p) segments of the dilation curves to a common temperature and measuring the difference in the or-dinates at that temperature, see Fig. 1. The transformation occurs over a temperature range in this alloy, so the magnitude of A1 is not an absolute value but depends on the choice of temperature. A mean temperature, T,, within the transformation temperature range was selected for the measurement. T, on cooling occurred about 100°C lower than T, on heating. The first time each of the three dilation specimens was heated to above the temperature, that is, Cycle 2, normal Type I behavior was observed. In Cycle 3, two deviations from normal behavior occurred. First, during cooling of the longitudinal specimen, a substantially larger expansion, +0.21 pct, was measured as 0 transformed to a compared with +0.03 pct in Cycle 2. Second, the thickness specimen was observed to undergo a contraction instead of the anticipated expansion on cooling. Continued cycling of the three specimens from room temperature to 2500°F produced additional changes in the dilation behavior. These changes did not seem to be related to the fabrication direction of the alloy because the values of a1 for the longitudinal, transverse, and thickness specimens varied unpredictably in magnitude and sign. Furthermore, both the longitudinal and transverse specimens showed all three types of dilation curves at least once during the six cycles that they received. Fig. 2 is a sketch of the transverse specimen after

Jan 1, 1967

By John H. G. Monypenny

The range of chromium content of stainless steel is, in most cases, included in the limits 11 to 14 per cent., or the middle part of the range, 9 to 16 per cent., specified by the discoverer. For some time after the steel was produced commercially, the carbon content was about 0.3 to 0.4 per cent. and occasionally higher; only rarely was material with 0.25 per cent. carbon or less produced. The reason for this is obvious from the nature of the alloys of chromium available for making such steels; as the lowest carbon content generally available was about 1 per cent., and this in conjunction with a chromium content of about 60 per cent., the production of a 12-per cent. chromium steel with less than 0.25 to 0.30 per cent. carbon was impossible. The advent, on a reasonable commercial scale, of carbonless ferrochromium has modified this condition, however, so that for the last three years stainless material containing 0.1 per cent. or less carbon and the normal amount of chromium has been on the market. As far as the author is aware, the material was first made on a commercial scale by the firm with which he is associated in June, 1920, when a 5- or 6-ton cast of material containing 0.07 per cent. carbon and 11.7 per cent. chromium was made and cast into 12-in. ingots. The necessity for using a totally different raw material, carbonless ferrochromium, instead of the ordinary low-carbon ferro (0.6 to 1.0 per cent. carbon) has led to the idea that stainless iron is a quite distinct product and quite different from stainless steel. While this may be true from a commercial aspect, it is wrong metallurgically. The name stainless iron is unfortunate as the material is a very mild stainless steel and forms the lowest carbon member of a series of steels of continuously varying content which are, in many respccts, the counterpart of the series of ordinary carbon steels ranging from "dead soft" to tool steels. In an article on stainless steel in the Journal of the Society of Chemical Industry, November, 1920, the author said "Just as in the far-off days 'steel' was regarded as a hard product of iron, and little or no attempt was made to grade it into harder or softer varieties, so at present stainless

Jan 1, 1924