Search Documents

By H. J. Snyder

Both the room-temperature and 600°F (315°C) primary solid-solution phase boundaries for the silver comer of the Ag-Cd-In temary system have been determined using X-ray diffraction and metallo-graphic techniques. Solid solubility of indium in silver at room temperature and 600°F (315°C) is shown to be between 20.3 and 21.7 wt pct, and corrects the previously extrapolated value of 18 wt pct appearing in the literature. The solid solubility of cadmium in silver at room temperature, not previously established, is shown to be between 34.9 and 41.3 wt pct. The solid solubility of cadmium in silver at 600°F (315°C) is confirmed as 43.2 wt pct. The shape of the primary phase boundary line for the subject temary system appears straight at room temperature and curves con-vexly towards the solvent (silver) comer at 600°F (315°C). THIS investigation was undertaken to initiate development of the Ag-Cd-In ternary diagram by establishing the primary solid-solution phase boundary in the silver corner of the diagram. At the present time, a diagram for this ternary system is not available, while this system appears to offer potential for a variety of uses. One alloy in the system has already proven to be useful as a control rod material in nuclear reactors.1"3 To encourage additional exploration of the potential of the system an understanding of its ternary diagram would be beneficial. It is towards this end that the present study is directed. LITERATURE SURVEY In undertaking this study, a comprehensive literature survey was first conducted to find information that would be useful for guidance. Useful knowledge did result from investigating the respective solubilities of indium and cadmium in silver as indicated in the binary constitutional diagrams of the systems Ag-In and Ag-Cd and also reviewing possible shapes of ternary primary phase boundaries. Weibke and Eggers~ used metallographic techniques to establish the system In-Ag as illustrated in Fig. Is This diagram shows that silver in the solid state is capable of dissolving approximately 18 wt pct In. This solid solubility of indium in silver holds true from room temperature up to 1276°F (691°C), then decreases continuously up to 1'761°F (960.5"C), the melting point of the silver. The solid-solubility limit of indium in silver established by Weibke and Eggers has been confirmed by Hume-Rothery and Reyno1ds. G Durrant' used a method which consisted of microscopic examination of quenched specimens to establish the Cd-Ag system as displayed in Fig. 2.' The primary phase boundary of Fig. 2 proved to be in good agreement (ie., within 1 wt pct) with other studies*'1' of the Ag-Cd system made using X-rays and metallog-

Jan 1, 1968

By J. Szekely, V. Stanek

Steady state heat transfer and fluid flow rates are predicted for the counter-current contacting of gas and solid streams. For a .fixed pressure drop across the bed the convective heat transfer rate is affected by the gas flow rate, which in turn is affected by the temperature distribution in the system. Variations in bed voidage and in particle size were found to change the predicted temperature profiles quite markedly, in particular when the thermal capacities of the gas and solid streams were equal. IN Part I we examined the effect of step and pulse changes in the inlet gas temperature on transients in the flow of gases through fixed packed beds. Here we shall discuss heat flow and fluid flow interactions in the counter-current heat exchange between packed solids and a gas stream. Counter-current heat exchange in packed beds has been extensively studied. In his now classical paper, Furnas' assumed constant property values and developed a simple analytical. expression for the temperature profiles in the gas and in the solid stream. A highly sophisticated analysis of counterflow systems, allowing for transients and interparticle conduction was developed by Amundsen. In preparing a very readable review of this topic Elliott' also presented a number of elegant solutions, including the case involving heat generation. A great deal of work has been done on the application of these concepts to the modelling of the blast furnace. However, in all this previous work the mass flow of the gas was regarded as a quantity independent of the gas-solid heat exchange process. In the following we shall consider counter-current heat exchange between a gas stream and a packed bed of solids, under conditions where the pressure drop across the bed is specified, rather than the mass flow of the gas. FORMULATION Consider a packed bed, extending from y' = 0 to y' = L, in which moving solids and a moving gas are contacted in a counterflow arrangement. Let cold solids, with an initial temperature Tsi and mass flow GA, enter at y' = L, and hot gas with an initial temperature of Tgi and mass flow Gg enter at y' = 0. In contrast to the problems considered in Part I this system has a nontrivial steady state and we shall restrict our attention to the study of the pressure drop flow relationships and the resultant temperature distributions for steady state conditions. Under these conditions the formulation of the problem requires the statement of the following: 1) heat balance on the gas 2) heat balance on the solids 3) the mechanical energy balance equation and in addition the knowledge of the equation of state, and a functional relationship between viscosity and temperature and an expression for the heat transfer coefficient in terms of the other parameters. On neglecting temperature gradients within the solids and for a constant mass flow of the gas, the solution to this problem is well known.'" The expressions for the temperature profiles of the gas and solid streams may be put in the following form: where Tg and T, denote the dimensionless gas and solid temperatures respectively, y is a dimensionless distance, and R is the ratio of the thermal masses. These quantities are defined as follows: For the particular case of equal thermal mass capacities by the gas and the solid, that is R = 1, the Eqs. [1]and[2] simplify to Eqs. (71 and[8], respectively: i.e., the resultant profiles are linear. As for most practical cases , solutions given by Eqs. [7] and [8] will contain only the inlet temperatures as parameters. For a fixed, predetermined value of C;b the above

Jan 1, 1970

By C. Land, R. Hultgren

Heat contents of four Cr-Ni alloys were determined in a diphenyl ethev calorimeter. Aside from ferromagnetic effects, Kopp's law of additivity of heat capacities is approximately fol-lowed, in disagreement with earlier results of A. W. Foster. In 1934 Foster1 reported heat-capacity measurements of dilute solutions of chromium in nickel, primarily as a study of the effect of alloying on the ferromagnetic Curie temperature. He found that, apart from the Curie temperature effect, the general level of heat capacities was reduced 10 pct by the addition of 1 pct Cr; 20 pct by the addition of 2 pct Cr. His measurements of pure nickel essentially agreed with accepted values. These results indicate that small amounts of dissolved chromium cause an increase in the Debye temperature of nickel, presupposing a change of frequency of interatomic bonding vibrations which is much larger than should be expected. If Foster's results were verified, therefore, they would have important implications for bonding theory. The only other heat-capacity measurements in this system seem to be those of Taylor and Hinton,' who studied anomalies which they attributed to super-lattice formation at 25 at. pct Cr. At temperatures above the anomaly, Taylor and Hinton found heat capacities at this composition were quite normal, approximately obeying Kopp's law of additivity. EXPERIMENTAL WORK In order to verify or disprove the remarkable results of Foster, the heat contents of four dilute solid solutions of chromiunn in nickel were measured in a diphenyl ether calorimeter. This instrument, described elsewhere,, operates on the principle of the Bunsen ice calorimeter, but uses diphenyl ether as the working substance. Diphenyl ether melts at the convenient temperature of 26.S°C and supplies a more sensitive measure of heat than ice. The hot sample, in an atmosphere of argon, is dropped from a furnace at a measured temperature into a chamber which is surrounded by a mixture of solid and liquid diphenyl ether. The heat from the hot specimen melts some of the solid without chang- ing the temperature of the calorimeter. The amount of solid melted, and therefore the number of calories released by the specimen, is measured from the increase of volume of the mixture, which pushes mercury down a graduated capillary tube. The apparatus has been standardized against the known heat content of pure platinum. Heat loss during the dropping of the specimen was estimated by comparing the heat content of an empty platinum capsule with a solid platinum ball of the same radius and degree of polish of the surface. Repeated tests demonstrate the precision of measurement to be closer than *0.3 pct. Smoothed experimental results are listed in Table I. The tabulated values for pure nickel are taken from kelley, several measurements were made which agreed closely with this tabulation. For chromium, however, no similar agreement was found. The values tabulated were taken from a thorough study of chromium with the diphenyl ether calorimeter which will be published elsewhere.= Suitable plots of the data showed the expected ferromagnetic anomalies in the low-chromium alloys, while the 11 pct alloy shows no ferromagnetic anomaly, but a different, small anomaly below 900°K. This is perhaps the same anomaly found in CrNi, which was once attributed to superlattice formation,' but is probably due to some other cause, such as antifer-

Jan 1, 1960

By H. C. Fiedler

SILICON-IRON strip with a cube-on-edge secondary recrystallization texture is made commercially as thin as 10 mils. With inclusions present to inhibit normal grain growth, a few grains, and these have the (110)[001] orientation, grow very large at the expense of the matrix grains. In the absence of inclusions, only normal grain growth occurs and the texture is not as strong as when it is developed by secondary recrystallization.1 Strip for use at frequencies of 400 cps and higher is made in thicknesses of 1, 2, and 4 mils by a process developed by Littmann.2 Attempts to develop a strong texture in these thin gages by the same methods as were used for the 10 mil and thicker strip were unsuccessful,2 and Littmann's solution to this problem was to cold roll the grain

Jan 1, 1963

By E. E. Underwood, L. L. Marsh

Aluminum single crystals, alloyed with 0.042 atomic pet Cu and 0.11 and 1.1 atomic pct Mg, were subjected to constant stress creep tests, tensile tests, and hot hardness measurements within a temperature range of 300° to 866OK. Calculations based on Dorn's temperature-compensated time parameter, 6, gave a value of DH, = 27,000 cal per mol for the activation energy of early creep in aluminum single crystals. Correlations have been obtained for aluminum alloy single crystals with the parameter E for solid solution strengthening, as well as with the parameter F for solid solution hardening, by using a valence of three for aluminum. Limited measurements on tensile specimens show that the slip band density tends to decrease with increasing temperature and with decreasing solute concentration. INCREASING interest is being shown in the mechanisms of plastic deformation in single crystals during tensile and creep testing. The complexity of deformational processes in polycrystalline materials has led to a search for simpler experimental conditions. Numerous creep and tensile investigations have been conducted with pure, metallic single crystals. To a lesser degree, the effects of alloying elements on the tensile properties of single crystals have been determined. However: the literature dealing with the effects of alloying additions in single crystals under creep conditions is vanishingly small. This paper represents an attempt to narrow this gap in the knowledge of the subject. Previous investigations of creep behavior at the Battelle Memorial Institute1-1 have been of great value in the analysis of the present single crystal data. It is equally desirable, however, to ascertain the extent of correspondence between the behavior of single crystal and polycrystalline materials. For this purpose, correlations, similar to those developed for polycrystalline aluminum alloys by Dorn and co-workers, have been made with the single crystal data. The results from this study have tended to confirm and extend those correlations to the case of alloyed single crystals. Materials and Procedures Three dilute binary aluminum alloys were prepared for this investigation from 99.99 + wt pct Al, 99.8 wt pct Mg, and 99.92 wt pct (electrolytic) Cu. The nominal compositions of the alloys were 0.042 atomic pct Cu, and 0.11 and 1.1 atomic pet Mg. Precautions were taken to avoid contamination of the stock during melting and casting of the alloys. After a heat treatment of 8 hr at 925°F the alloys were extruded, then machined into) threaded tensile specimens with a 3 in. reduced section and a 0.505 in. diam. Spectrographic examination showed less than 47 ppm metallic impurities in each alloy. The single crystals were grown by the strain-anneal method, with a critical strain of about 11/4 pet giving the optimum results. In general, 3 in. crystals were obtained with the Al-Cu alloy, but smaller crystals in the magnesium alloys necessitated the use of 2 in. and 1 in. gage lengths with the low and high magnesium alloy specimens, respectively. After an electrolytic polish, the orientation of that portion of the specimen containing the largest single crystal was determined from Laue back-reflection photographs. Tensile tests were conducted at a constant load rate of about 2 lb per min. Creep runs were made in a constant temperature room, under constant stress at the higher creep temperatures, and constant load at the lower temperatures. The eloneation was measured to within ±5 microin. by a specially designed capacitance extensometer. The ex-tensometer arms were attached to the 3 in. specimens at the shoulders of the test piece or, where the crystals were smaller than 3 in., by knife-edge grips.

Jan 1, 1957

By William H. Waggaman

CURTAILMENT of the mineral industry as a whole undoubtedly will follow world peace, but the output of certain minerals should pursue a course well above the average on any curve of probable output projected beyond the trends exhibited through 1939. Without speculating on industrial conditions in the pending recomversion period, demand for fluorspar should be greater than before the war because of these factors, introduced by or resulting directly from military necessity: (1) Discovery and development of new deposits. (2) Improved technology in benefication. (3) New and expanded uses for fluorspar and its derivatives. The steel industry has been and continues to be the greatest consumer of fluorspar, and it wag largely to meet the wartime needs for steel that the domestic fluorspar industry has been expanded so greatly. Not only were the search for and development of new deposits of this mineral considered esstinal but the marginal nature of some of the,c- domestic deposits made it necessary to improve mineral dressinc and processing techniques to utilize them

Jan 1, 1945

By N. A. D. Parlee

The diffusion rate of hydrogen in liquid iron has been measured by a gas-liquid metal diffusion cell technique. The diffusion cell was formed by immersing an alumina tube containing hydrogen gas at 1 atm in a bath of stagnant liquid iron. The change in the composition of the melt in the cell was determined by measuring the rate of absorption of the gas in the cell. The appropriate solution to Fick's second law was used to examine the data and calculate diffusivi-ties. The absorption of hydrogen in stagnant pure liquid iron has been found to be diffusion-controlled. The results show that the chemical diffusion coefficient, D, of hydrogen in pure iron in the range of 1547" to 1726°C can be represented by the following Arrhenius relation: D(sq cnz per sec) = 3.2 x X exp(- 3300 i 1800/RT) where the uncertainty in the activation energy corresponds to the YO pct confidence level. Oxygen in the melt (above 0.015 pct 2) increased the apparent rate of absorption of hydrogen. The importance of diffusion data on liquid metals for predicting the rates of certain metallurgical processes has been recognized for a long time. Moreover, these data are much needed to test and develop theory for diffusion in liquid metals. Despite this practical and theoretical interest, however, relatively little reliable information about diffusion in liquid metals is available in the literature. This is particularly true for gas components such as hydrogen, oxygen, and nitrogen in liquid metals, where almost no data on chemical diffusion coefficients are to be found. This is probably due to a multitude of experimental difficulties particularly associated with high-temperature melts. In an effort to fill this gap in information, a research program was undertaken to study the diffusivities and rates of solution of gases in liquid metals. This paper presents the results of a study of the diffusion of hydrogen in liquid iron. EXPERIMENTAL METHOD Two methods for the study of the kinetics of dissolution of gases in liquid metals are being employed in this laboratory. Both involve the measurement of the volume of gas absorbed by the melt as a function of time and as such both avoid the uncertainties involved in chemical analyses of quenched samples for relatively small amounts of gas. In the first method, the gas dissolves in an inductively stirred melt and, in the absence of a slow surface reaction, the results are often interpreted in terms of mass transport across a liquid "boundary layer" between the homogeneous gas phase and well-stirred part of the melt. Other interpretations of the results of such experiments have also been described in the literature.1'5 In the second method a gas-liquid metal diffusion cell is used.' The gas dissolves in a cylindrical column of stagnant liquid metal and, in the absence of a slow surface reaction, the results are interpreted in terms of a non-steady-state diffusion solution to Fick's second law. The weakness of the first method is that while it gives information on the mechanism of absorption by stirred melts it yields an overall rate constant which even in the simplest cases depends on the nature and the thickness of the "mass transport layer" or "boundary layer". It yields no values of diffusion coefficients. The second method was used in this research because in many cases it is possible to determine the diffusion coefficient of the gas component in the liquid metal. In this research it has been utilized to measure diffusion coefficients of hydrogen in liquid iron. The apparatus used was essentially the same as that described by Mizikar, Grace, and par lee but certain modifications have been introduced to meet the elevated temperatures and special conditions of this research. Fig. 1 is a schematic drawing of the apparatus and Table I gives the identification of various parts in this figure. The diffusion cell, shown in detail in Fig. 2, was formed by immersing an impervious alumina tube (hereafter called absorption tube) in a bath of pure liquid iron contained in an alumina crucible. Two types of tubes were used, Morganite triangle RR and McDanel AP35. The crucible was contained in a vertical impervious alumina combustion tube (32 mm ID by 914 mm long) which was closed at both ends by water-cooled brass heads employing O-ring compression seals, Fig. 1. A protection tube enclosing a Pt, 5 pct Rh-Pt, 20 pct Rh thermocouple was introduced through the lower end of the combustion tube

Jan 1, 1968

By S. J. Prison, C. R. Smith

The effect of fluid injection to control water coning in oil and gas wells was investigated. Analytical and model techniques were employed. The factors investigated were the position and length of the completion interval, the point of fluid injection, the viscosity of the injected fluid and the relative thickness of the oil and water sections. The resulting influence of these factors on the net producing water-oil ratio was determined. Several important conclusions can be drawn from the study. In general, it was found that the net producing water-oil ratio can be reduced by fluid injection. The magnitude of this reduction depended on the factors listed above. An important practical consideration is that the injection fluid may be either oil or water. If the injected fluid is less dense than the connate water of the reservoir, the fluid will not be lost. This fact is reassuring when valuable oil is being injected. Efforts to suppress water production were more successful when the injection fluid was more viscous than the reservoir oil, or when a zone of reduced permeability existed in the vicinity of the point of fluid injection. Under test conditions, little benefit was derived through the use of impermeable barriers or cement "pancakes". INTRODUCTION The occurrence of water coning has been known for at least 60 years. In thin oil or gas pay sections, the presence of an oil-water or gas-water contact hinders production and often causes early abandonment of the afflicted well if a completion is even attempted. Even when relatively thick pay sections are found, the encroachment of water when a water drive is present will eventually pose serious water coning problems. This water is often corrosive, expensive to separate from the oil or gas and is costly to dispose of. The theory of water coning has been discussed by a number of authors. 1,2,3,4 Briefly, water coning to the producing interval in a well is due to pressure gradients resulting from the production of fluid from the reservoir. These pressure gradients will cause a water cone to rise toward the bottom of the producing interval if a water-oil or water-gas contact exists. The tendency of the water to cone is offset or partially offset by gravity forces since the water has a higher specific gravity than the oil. A balance then exists between two forces, gravitational forces arising from the difference in specific gravities of the oil and water, and the pressure gradients causing the flow of fluids to the wellbore. If the pressure gradient exceeds the gravitational force, water coning to the wellbore occurs and water production results. Through the years considerable thought has been given to the water coning problem. More than 50 U. S. Patents have been granted to inventors on the subject. A relatively complete literature review of the water coning problem has been made. 5 A number of these patents hold considerable promise for the solution or the partial solution of the water and/or the coning problem. Very little has been written describing field tests of techniques for the suppression of water coning. A notable exception is the paperby West. 6 He reports success in reducing gas coning by a combination of gravel packing and oil injection above the oil-producing interval. He also describes a comparable method to prevent water coning, but provides no field examples. This study experimentally and analytically verifies the benefits of oil injection as a means of partially or completely suppressing the water cone. While the gas coning problem was not treated, it is anticipated that results comparable to those obtained in water suppression could be obtained with reduced oil injection since the viscosity contrast between oil and gas exceeds that between oil and water. For the purpose of this study, the conventional potential flow theory was applied to the water-coning problem. The experimental verification centered on both a radial and a linear model. The model study permitted the investigation of complex flow configurations and the use of fluids of differing densities and viscosities. No analytic expressions are available to permit a solution of the problem as stated (see Fig. 1).

By C. A. Stickels, C. M. Yen

Secondary recrystallization was investigated in vacuum-melted electrolytic iron to which 70 pm N was vacuum-meltedadded. The secondary texture is "near {554}<225>" for material cold-rolled 75 to 90 pct, the sharpness of the texture increasing with increased rolling reduction and with decreased annealing temperature. At reductions of 95 and 97.5 pct the secondary texture is &apos;"near {322)(296)". Both secondary orientations also exist as major components of the primary re-crystallization texture. Development of a strong "near {554) (225)" secondary texture appears to depend on the evolution of the Primary texture to a transition texture depleted in orientations near the secondary orientation before the onset of secondary growth. A variety of qualitative experinzents have been used to show that nitrogen is important in limiling primary grain growth. The presence of nitrogen does not seem essential for the establishment of a transition texture, but a loss of nitrogen during annealing may facilitate growth of grains in the secondary orientation. Secondary grains we shown to form initially at the specimen surface. This is not thought to indicate that surface energies are important in the growth process. It is proposed that the quasi-two-dimensional character of surface grains permits discontinuous growth parallel to the surface before secondary growth of interior grains is possible. An earlier study of recrystallization textures in 90 pct cold-rolled electrolytic iron showed that secondary recrystallization occurred after annealing for several days at 700C1 This type of secondary recrystallization, which had not been reported previously, results in the formation of a strong texture, best described by the indices "near {554}(225)". The purpose of the present work was to investigate the effect of various processing variables on secondary recrystallization in this material and determine the mechanism of secondary grain growth. LITERATURE REVIEW An understanding of the mechanism of a secondary recrystallization process depends on knowing: 1) how grains in the secondary orientation come to be in the primary recrystallization texture; 2) why normal grain growth does not occur; and 3) what factors determine the strength of the secondary texture. For secondary growth of grains of a particular orientation, a certain minimum fraction of the grains must be in that orientation after primary recrystallization. This requirement is apparently satisfied "naturally" in certain systems, i.e., when the primary texture obtained by rolling and recrystallizing material initially randomly oriented contains a sufficient fraction of primaries in the secondary orientation. However, in other cases, e.g., {110}<001> and {100}<001> secondary growth in silicon iron,2 it is necessary to enhance the fraction of primary grains in the secondary orientation by rolling and recrystallizing textured material. In the present case, the "near {554}<225>" orientation is contained within the spread of orientations found in the primary recrystallization texture of iron or bbc iron-base alloys. In systems where the main driving force for secondary growth is the reduction in total grain boundary energy, secondary growth is observed only when normal grain growth is minimized. Four ways in which normal grain growth can be limited are: 1) Limitation by a strong primary texture. When a very strong primary texture consisting of a single component or twin-related components develop, most primary grains are separated from one another by relatively immobile small-angle grain boundaries. The classic instance of this is secondary growth into the primary cube texture in some fcc metals. 2) Limitation by precipitates. Precipitates present in the proper volume fraction with a suitable dispersion will limit primary grain growth. The role of MnS inclusions in impeding normal grain growth in Si-Fe is well-documented.5 3) Limitation by sheet thickness. Normal grain growth slows drastically when the mean grain diameter is of the same order as the sheet thickness. This effect has been used to obtain secondary recrystallization in thin sheets of high-purity silicon iron.&apos; 4) Limitation by solute impurities. It is well-established that certain impurity elements in solution can have a large effect on grain boundary mobility.&apos; However, there does not seem to be any secondary recrystallization process in which primary grain size stabilization has been shown to be due to the drag exerted on grain boundaries by dissolved impurities. In certain systems, e.g., secondary recrystallization in silver,&apos; the means by which normal grain growth is limited has not been identified, and solute-impurity limitation might be suspected. In order to understand the factors which determine secondary texture strength in three-dimensional growth, it is necessary to examine in more detail the current picture of general secondary recrystallization processes. Following Cahn,9 it is assumed that the primary grains have a range of sizes and that secondary growth of one of the large grains in this distribution is possible when it exceeds a critical size with respect to its neighboring grains. The critical size depends on the ratio ?S/?p, where ?s is some sort of average grain boundary energy between the potential secondary and the primary grains and ?p is some sort of average grain boundary energy between primary grains. For a constant primary grain size, the critical size for secondary growth increases as ?$/?p increases. May and Turnbull5 have incorporated the

Jan 1, 1969

By K. T. Koone, R. J. Blackwell

One of the more important problems to be solved in designing a miscible flood is related to the size of the solvent bank used. Size of the bank may be critical to economic success. Too large a bank loses money; too small a bank may deteriorate and fail to maintain the miscibility needed for high recovery. An important factor in deterioration of a small bank is permeability channeling. In a highly stratified reservoir, solvent speeds ahead in the more permeable zones and mixes laterally with fluids bypassed in adjacent, low-permeability strata. Numerical solutions have been obtained .for the differential equations that describe the movement of a slug through a two-layer system in which mixing occurs both in the direction of flow and transversely. The solvent slug is assumed to have the same density and viscosity as the resident fluid and the pushing fluid. These solutions have been verified by comparing them with similar concentration profiles obtained in the laboratory in a 36-ft stratified model packed with glass beads. The theoretical study revealed that when the dominant mechanism causing a bank to fail is lateral mixing the bank size needed for a given recovery may increase with length rather than decreasing as the square root of reservoir length, as suggested by one-dimensional mixing theory. From a comprehensive examination of the variables, a generalized correlation is developed that relates strata thicknesses, bank size, fluid velocity, mixing coefficients, system length and simple solvent-resident fluid phase behavior to the area miscibly swept. INTRODUCTION Miscible displacement, or solvent flooding, continues to receive widespread attention as a method for increasing oil recovery over that possible in conventional gas-drive or waterdrive projects. A basic economic requirement in the application of such processes is the use of as little solvent as possible. A basic physical requirement is that enough solvent be used to maintain miscibility. Economics places an upper limit on the size of a solvent slug, and physical considerations establish a lower limit. Consequently, the practicality of any given miscible process requires that the economic limit be greater than the lower limit imposed by physical requirements. Procedures exist for determining the economic limit; however, procedures for determining realistic minimum bank sizes exist for only special reservoir situations. In the past, bank size has usually been selected on the assumption of a piston-like displacement for which only longitudinal mixing is important. This assumption leads to the favorable conclusion that bank size, expressed as per cent of pore volume, is inversely proportional to the square root of length. Collins considered the problem of transverse mixing of solvent with fluids in bypassed zones with the assumptions that no forward mixing occurs and that the concentration is uniform in the permeable stratum of interest. 1 Lauwerier considered a mathematically similar problem in thermal recovery operations.2 Their work suggests the much less favorable conclusion that bank size could be directly proportional to the length or even higher powers of the length. This paper considers the physical behavior of a small solvent bank as it moves through a real reservoir, without imposing many of the restrictive assumptions of past treatments. To facilitate mathematical description, an idealized, two-layer model that permits mixing both laterally and in the direction of flow will be considered. A calculation procedure for solving the descriptive equations will be developed for a displacement involving fluids of equal density and viscosity. In addition, laboratory experiments designed to check the computational results will be described, and the coincidence of calculated and observed results will be discussed. The use of many solutions for a variety of bank sizes, strata thicknesses and characteristic system lengths to develop a usable correlation between

Jan 1, 1966

By A. Totani, S. Nakajima, H. Okazaki

The phase diagram for the SnTe-SnSe system has been studied in the temperature range from 300° to 900°C by differential thermal and quenching techniques. The X-ray measurements were made on quenched specimens. High-temperature diffraction was also made to study the phase transition in SnSe. The system is proved to be of a eutectic type in which no intermetallic compound exists. The eutectic point is at the composition SnTeo.55 Seo.45. the eutectic temperature being 755°C. Solid solubility limits are SnTeo.6Seo.r and SnT eo. 3s Seo.6s at the eutectic temperature, and change almost linearly to SnTeo.aaSeo.lz and SnTeo.18 Seo.az as temperature decreases to 300°C. It was shown that the SnSe phase has a phase transition of the second order at about 540°C and that the transition temperature decreases with increase of the SnTe content. THERMOELECTRIC properties of tin telluride (SnTe) and tin selenide (SnSe) have been studied extensively in recent years. The variation of physical properties with composition could be of interest if these compounds form an appreciable crystalline solution. The purpose of present investigation is to confirm the formation of crystalline solution or intermetallic compound, if any, and to establish the phase diagram for this system. The crystal structure of SnTe is NaCl type with a cubic unit cell1 (a = 6.313A). The crystal of SnSe having an orthorh2mbic unit cellz (a = 11.496, b = 4.1510, and c = 4.4437A) is isomorphous with tin sulfide (SnS) which has a distorted sodium chloride structure. It has been known that SnSe has a phase at at 540°C; the transition has been assumed to be of the second order. As far as we know, only two studies on the SnTe-SnSe pseudobinary system have been reported. The conclusion obtained in these papers is that, in the composition regions near SnTe and SnSe, the system forms a crystalline solution of the SnTe structure and the SnSe structure, respectively, and that, in the intermediate region, both phases coexist. However, neither the variation of the solid solubility vs the temperature nor the liquidus and solidus were investigated. Hence present writers have attempted to determine the phase diagram of the system by differential thermal analysis (D.T.A.) and X-ray diffraction. EXPERIMENTAL Sample Preparation. Starting materials, SnTe and SnSe, were prepared by the direct fusion of commercially available high-purity (99.999 pct) elements. Stoichiometric amounts of each couple Sn-Te or Sn-Se were weighed into a clear fused silica ampule. After evacuation to a pressure below 10-3 mm Hg, the am- pule was sealed, and annealed at 900°C for 5 hr. The melt was quenched in water. X-ray analysis confirmed the formation of a single phase of SnTe or SnSe. The other samples, SnTel-,Sex were synthesized from these SnTe and SnSe by mixing them in the required ratio, followed by annealing at 900°C and quenching. These samples were used directly for D.T.A. For X-ray measurements, samples were annealed at 700°, 600°, or 500°C for 100 hr or at 300°C for 150 hr, and then quenched in water. It was found that the lattice constants of the SnTe phase annealed for 150 hr at temperatures above 500°C did not differ from those annealed for 100 hr at the same temperatures. However the X-ray phase analysis showed that at 300°C the annealing for 150 hr was necessary to attain a true equilibrium state. D.T.A. The solid-liquid equilibrium temperature was determined from D.T.A. measurements. The sample was sealed in an evacuated silica tube and molybdenum powders sealed in an another tube were used as a reference material. The sample and the reference tube were placed in a nickel block and were heated from room temperature to 900°C at a rate of 3°C per min and then cooled down at the same rate to 600°C. Thermocouples for these measurements were Pt-Pt. Rh (10 pct) and the error of temperature measurements was within + l0C. D.T.A. curves were obtained on a two-pen recorder and an automatic controller (PID type) was used for the program of heating and cooling. When temperature reaches the solidus from the low-temperature side, there appears an endothermic peak. The solidus temperature was determined by extrapolation of the straight portion of the starting flank of this peak to the base line. In a similar way, the liquidus temperature was determined from an exothermic peak on D.T.A. cooling curve. In the case of supercooling, if any, its degree can be estimated from the magnitude of the abrupt temperature rise. X-Ray . X-ray powder patterns were taken by a diffractometer using CuK, radiation. Since the SnSe crystal is cleaved easily, the powders become flaky when SnSe-rich samples are ground in an agate

Jan 1, 1969

By Charles L. Mantell, George Ferment

This investigation determined the jeasibility of current-potential curves as an analytical tool for monitoving manganese electroicinning solutions for metallic impurities. Nine metallic impurities were studied: trickel, cobalt, silver, copper, zinc, molybdenum, catlmiun magnesium, and sodium. The individual effect of each metallic irzplrl,iLy on the standard point-izatiorr was determined for a range of &apos;concentration. Not all of Ihe impurities affected the polarization curve; correlation between transition current and cotrcetztration of impurity. Molybdenum had an uncorrelated effect on the polarization curie. The effects of binary mixtures of impurities were studied to see if the transition current of the mixture could be predicted. Interactions occurred between impurities which prei&apos;etzted the pvecliction the transition current of tile rrlisLitr.e by additive laws. The polarization curve was shown to be sensitive to metallic impurities which affect the current efficiency of a manganese cell. THE application of current-potential curves in manganese electrowinning is not new but played an important part in the conversion of an inoperative large-scale pilot plant into a continuous comnercial operation.1"" The effects of trace metallic impurities in manganese electrowinning solutions on cathode current-potential curves,5-19 specifically nine impurities (nickel, cobalt, silver, copper, zinc, molybdenum, cadmium, magnesium, and sodium) were studied for a range of concentrations. Cadmium, magnesium, and sodium had no effect. Nickel, cobalt, silver, copper, and zinc yielded a correlation between transition current and concentration of impurity: molybdenum had an uncorrelated effect. Binary mixtures of impurities were studied to de-termine if the transition current could be predicted from the values for the individual constituents. Interactions between impurities prevented the prediction of the transition current of the mixtures by an additive law. The polarization curve was shown to be sensitive to metallic impurities which affected the rurrent efficiency of a manganese cell. The electrowinning of manganese relies upon maintaining a high-purity electrolyte. Purification schemes were developed to remove all of the heavy metals, the magnesium and calcium. Concentration limits have been established for single impurities. With high-purity electrolytes, favorable cell efficiencies are consistently obtained; but with impure solutions there is a reduction in efficiency. With the rapid rise to commercial prominence of electrochemical processes, there has been a lag in developing rapid methods for determining whether an electrolyte is sufficiently pure for efficient electrolysis. The most sensitive test for impurities is the behavior of the electrochemical cell. Impure electrolytes will cause a serious reduction in cell efficiency, and in many cases metal deposition will be prevented or reversed. The effects of impurities are not usually evident until after long periods of electrolysis, resulting in a disruption of the process. A method which could predict the behavior of an electrolyte in terms of cell efficiency prior to reaching the commercial cell is needed. Van Arsdale and Maier," Allmand and Campbell,a1&apos;22 and others attempted to develop an electrochemical process for manganese,"3"29 but all met with some degree of difficulty. Jacobs et a studied the effects of metallic impurities in manganese electrowinning. Plant methods were based on a 2-hr plating in a small electrolytic cell. The final method was based on a 24-hr plating run, performed in a relatively large test cell. Here, current efficiencies were calculated with and without impurities in the electrolyte, and the critical concentration was established as the maximum amount of impurity that the electrolyte could tolerate before there was a serious loss in efficiency. The amount of impurity that could be tolerated decreased as the plating time increased, indicating deposition of the impurity. This test duplicated the conditions of commercial practire, and was sensitive to impurities. Small amounts of impurities significantly affect the hydrogen overvoltage at a metal surface, increasing or decreasing it depending upon the nature of the impurity. ockris established the limit for the onset of poisoning at 10-l moles per liter. The effects of impurities were studied by potential-time curves at a constant current density. The technique did not lend itself to rapid analysis in that several hours were needed to establish stable potential-time curves. Serfass and coworkers3&apos; developed calorimetric and spectrophotometric techniques for analyzing for trace impurities. Our method4&apos;" is based on current-cathode potential curves produced by continuously changing the cell voltage at a programmed rate. Starting with a clean stainless-steel cathode, the cell voltage was initially adjusted to yield zero current: the program was then started and the current was plotted as a function of the cathode potential. Fig. 1 is a typical current-potential curve. In initial region A the hydrogen-evolution reaction predominates and the polarization curve

Jan 1, 1967

By O. D. Gonzalez, R. A. Oriani

A thermo-osmosis technique has been used to measure the heat of transport, Q* , of hydrogen and of deuterium dissolved in a iron and in nickel, and of hydrogen in Feo.6Nio.4 in the tempevature range 400° to 600°C. For all these systems, Q* is negative and has a large temperature coefficient; an isotope effect can be established for the solutes only in nickel. The magnitude of Q* is considerably larger than the activation energy, E , for migration in the case of these isotopes in a iron, so that all variants of the Wirtz model must be rejected. The phenomenological definition of Q* is developed to show that Q* is related to the mechanisms by which the activation energy is dissipated back into the lattice, and that Q*/E is a function of the ratios of the mean free paths of electrons and of phonons to the distance of jump of the diffusing atom. A correlation is shown to exist between the sign of Q* in thermal diffusion and that of the effective charge in electro migration, and may be understood as due to the large ratio of the mean free path of electrons to that of phonons. THE study of nonisothermal diffusion in the solid state is of interest because certain aspects of the mechanism of diffusion are made manifest which remain concealed though still present in the isothermal case. The thermodynamics of irreversible processes characterizes nonisothermal diffusion, known as thermal diffusion or as the Ludwig-Soret effect, by a quantity, Q*, called the heat of transport, which essentially measures the sign and the magnitude of the steady-state concentration gradient produced by the imposed temperature gradient. The problem then is to understand the quantity Q* at the atomistic level. There does not exist a theory for the atomistic interpretation of the heat of transport. There are, however, two classes of simple models which seem to afford some physical insight into Q*. Wirtz&apos;s model1, z and its subsequent generalizations partition the activation energy, E, for the migration of the atom spatially about the region of the migrating atom, so that Q* is the difference between the portion of the activation energy centered about the original site of the jumping atom and that portion about the arrival site. Clearly, the magnitude of Q* cannot on this model be larger than the activation energy for migration. The model of Oriani3 also considers the spatial distribution of E not only before but also after the atomic jump, and Q* is related to the variation of the spatial distribution of E that is produced by the jump. The simplest kind of system with which to compare the consequences of these ideas is the interstitial solid solution, since one may easily choose a temperature at which only the interstitial component moves, the solvent lattice serving as a completely satisfactory frame of reference. Thus, one avoids complications arising when both species in a binary system move. In addition, one avoids the necessity of knowing the energy for the formation of a vacancy, something which is needed for the analysis of thermal-diffusion data on metals which diffuse by the vacancy-exchange mechanism. However, the number of well-measured interstitial systems is extremely small, and, in particular, there are almost no data in the published literature for the temperature dependence of the heat of transport. If one works with solutes which are gases in the pure state at ordinary temperatures, one may use the technique of thermo-osmosis4 which permits thermal diffusion to be measured over a small temperature difference so that the temperature dependence of Q* can be more easily determined. The choice of dissolved hydrogen in iron and nickel was based on these considerations as well as on the desire to look for an isotope effect associated with localized

Jan 1, 1965

By M. E. Wadsworth, T. L. MacKay

Sintered UO, samples were leached in sulfuric acid solutions of various concentrations. A pressurized system was used so that it was possible to investigate the kinetics of the reaction to 270°C with oxygen overpressures as high as 900 psi. The rate was observed to be a function of the concentration of hydrogen ions and directly proportional to the partial pressure of oxygen. Evidences are presented which indicate that a UO2 surface site reacts with a molecule of water to form a hydroxyl complex which in turn can dissociate with the characteristics of a weak acid. A rate determining step has been proposed which involves the reaction between an oxygen molecule and the hydroxyl complex on the surface of UO,. ThE 2 principal methods for uranium dissolution are carbonate and acid leaching. The sulfuric acid leach is the more popular and is used for the treatment of the majority of the ores of Africa, Canada, and the United States. Low recoveries in basic leach circuits led investigators at the University of British columbia1 to study leaching of uranium ores in pressurized vessels. Early in the study of dissolution of uranium it was found that only uranium in the hexava-lent state could be leached in acid or basic circuits. Therefore, the use of oxygen over-pressure in an autoclave offered an interesting approach to solving the low recovery problems of carbonate leaching. UO, was used in this study because it could be obtained in high purity and also because it is representative of the most refractory of the primary uranium minerals. A pressurized system was used to provide a means whereby important temperature and pressure parameters could be varied for the evaluation of the kinetic processes. The mechanism for the dissolution of UO2 should be similar for any of the uraninite type minerals. At the present all of the kinetic studies that have been conducted have been in carbonate media. Peters and Halpern2 carried out a kinetic study of the leaching of pitchblende. Their specimens were pitchblende ores selected on the basis of high grade and homogeneity. Pearson and wadsworth3 conducted a kinetic study of the dissolution of UO2 in carbonate solutions with results very similar to those obtained by Peters and Halpern. EXPERIMENTAL The UO2 as received* was found by spectroscopic *Mallinckrodt reagent, supplied by the Atomic Energy Commission. analysis to have a purity of 99.94 pct 0.03. It was ground in a mechanical agate mortar and screened through a 400-mesh sieve. Thin flat disks of UO2 were prepared by pressing the sized powder in a specially constructed die at a total pressure of approximately 25 tons per sq in. The pressed disks were approximately 0.25 cm thick, 1.6 cm diam, and 3.5 g in weight. As pressed, the samples were approximately 65 pct of theoretical density. It was essential that a binder such as poly-vinyl alcohol be added before pressing to prevent formation of cracks when fired. It was found by trial and error that pressed disks sintered close to 1870°C in a hydrogen atmosphere, reach densities between 91 and 91.5 pct of the theoretical density. At this density the samples had no measurable porosity based upon a 2-hr emersion in boiling water. An X-ray examination of these sintered UO2 disks showed them to be identical with the original UO2 received. Reaction of UO2 with the alundum furnace core was prevented by placing molybdenum between the samples and the core according to the method of Corwin and Eyerly.4 Leaching studies were carried out in a specially designed autoclave, the details of which have been presented e1sewhere.6 The main features of the equipment as applied to a kinetic study are: 1) solution samples may be removed during the course of a single run; and 2) temperature and agitation are carefully controlled. Two-ml samples removed from the autoclave during the course of a run were analyzed for U3O8 content with a Beckman model DK-2 spectrophotometer by the method of

Jan 1, 1959

By Thomas R. Mager

An in.t!estigation has been made of the equilibrium conditions at 1200°C in the reaction between hydrogen sulfide gas and sulfur dissolved in Fe-Si alloys From this the equilibrium constant, activity coefficient, and activity of sulfur in solution were calculated. A number of studies of the equilibrium of sulfur with iron and iron alloys have given closely agreeing results from which the activity and free energy of the dissolved sulfur may be found. Sherman, El-vander, and chipman1 discussed the significant researches of dilute solutions of sulfur in liquid iron prior to 1950, and the results of this study indicated that the relationship between the ratio of PH2S/PH2 in the environment and the percentage of sulfur in solution is not a linear one. Morris and williams2 studied the equilibrium conditions in the reaction between hydrogen sulfide gas and sulfur dissolved in liquid iron and Fe-Si alloys, and reported that silicon dissolved in iron has a pronounced effect on the equilibrium conditions. They found that the activity of sulfur in iron is increased by the addition of silicon. At a silicon content of 4 pet the activity coefficient of sulfur was about twice that for sulfur dissolved in pure iron. Sherman and chipman3 investigated the chemical behavior of sulfur in liquid iron at 1600°C through the study of the equilibrium: H2 + S = H2S; K = PH2S/PH2 . 1/as [1] From the known equilibrium constant of the reaction between H2, H2S, and S and the experimental data, the activity of sulfur in the melt was determined. They found that the activity coefficient of sulfur defined as fs = as/%s is increased by silicon and decreased by manganese. Morris4 and Turkdogan5 also reported that manganese decreases the activity coefficient of sulfur in liquid iron and iron-base alloys. A recent technique of sulfur analysis developed by Kriege and wolfe6 of the Westinghouse Research Laboratories permits an accurate sulfur analysis of 0.5 * 0.2 ppm in the range of 0.1 to 3 ppm, whereas in the range of 3 to 50 ppm the accuracy is ±1 ppm. This technique of sulfur analysis was utilized in this experiment. Previous unpublished data reported that sulfur analysis by the combustion technique was not accurate below 20 ppm. EXPERIMENTAL PROCEDURE Five 5-lb ingots of high-purity Fe-Si were prepared. Three of these ingots were prepared without the addition of manganese but with a variation of silicon contents from 2 to 4 pet. The remaining two ingots contained 3 pet Si with the addition of manganese. Ingots were made at each of three silicon levels: 2, 3, and 4 pet. No alloys were made with less than 2 pet Si since below approximately 1.8 pet Si the binary alloy exhibits a to ? transformation. The two additional ingots of 3 pet Si-Fe were made at each of two manganese levels: 0.20 and 0.50 pet. To minimize the effects, if any, of impurities on the activity of sulfur on Si-Fe, the best metals available were used for melting. All ingots were vacuum-melted in magnesium oxide crucibles. After obtaining samples for chemical analyses, the ingots were processed. This consisted of hot rolling and subsequently cold rolling the alloys. Each ingot was hot-rolled at 1000°C, reheating between every pass to minimize grain growth. All heating was done in a protective argon atmosphere. The slabs were hot-rolled to strips 50 mils thick. After hot rolling, all the material was pickled to remove the scale formed on the surface of the strip during hot rolling. The material was then cold-rolled to 12-mil strips. Single strips of the material used in this experiment were hydrogen-annealed at 1200°C for 16 hr in an alumina tube. Chemical analyses of strips M-1, M-3, M-4, M-7, and M-8 are given in Table I. Sulfur, silicon, and manganese analyses were made from the millings from the cold-rolled 12-mil strips. The oxygen analyses were made from slugs of the as-cast material. The hydrogen sulfide used in these experiments was supplied from cylinders containing a mixture of argon and 1 pet hydrogen sulfide. The parts per million of hydrogen sulfide were determined from the analysis of the exit gas of the annealing furnace during each anneal. The flow rate of hydrogen was approximately 1 liter per min in all anneals. The

Jan 1, 1964

By V. S. Gupt, W. H. Somerton

Rock may undergo great changes in physical properties when heated to high temperatures and then cooled, The temperature and intensity of reactions causing rock alterntiorl.s can he controlled by introducing certain chemicals during heat treament. Three typical outcrop sandsone samples were saturuted with common salt solutions, then heated to several maximum temperatures. After cooling, it was found that per-rrreuhilities had increased much more for salt-saturated samples than for samples not saturated with salt but heated to the same temperatures. This was only true, however. for samples heated above the melting points of the particrrlar salts. Potassium chloritle was particularly effective with Bandera sandstone. Samples saturated with potassium chlorirlr. solution and heated to 900C showed an 11-fold increa.se in perrrieahility. Samples without potasrirdrn chloritle but heated to the .same temperature. showed only a 2.7-jold incresre in permecahility. In application, it seems possible that injecting chemicalc into the formations from a wellbore followed by applying intensive borehole heating might promote reactions which would greatly improve permeability of the formalions. INTRODUCTION Great changes in the physical properties of rocks which have been heated to temperatures in the range of 600 to 800C have been reported earlier. Permeability increases of 50 per cent, and equivalent decreases in sonic velocity and breaking strength have been observed. Although there might be some suppression of certain reactions responsiblc for these changes when rock samples are heated under simulated reservoir pressure conditions. recent work has shown that these are more than offset by the increased importance of other reactions at high pressures. The reactions considered responsible for alteration of rock properties by heating include differential thermal expansion. dehydration, phase changes and dissociation of mineral constituents. Ceramists have long known that temperatures at which reactions occur can be raised or lowered by the presence of certain impurities in the sys. tcnl. Thus the possibility exists that by saturating rocks with appropriate solutions. desired reactions might be accelerated and unwanted reactions might be suppressec! when the rock is heated. Purpose of the present work was to investigate the effects of several common salts on the thermal alteration of sandstones. Types of reactions which might occur are reviewed and the findings of a number of thernlochemical alteration tests are presented. THEKMOCHEMICAL ALTERATION OF SANDSTONE MINERALS The most abundant constituent of most sandstones is quartz. Quartz can exist in at least eight different forms, but in the temperature range of immediate interest (to 900C) only two forms are of importance—alpha quartz below 573C and beta quartz above this temperature. Although the alpha-beta inversion of quartz is very important in thermal alteration of rocks. it is not particularly important here because the inversion temperature cannot be changed significantly by the presence of impurities or by the application of pressure. The transition temperature of quartz to tridynlite is 867C. but the transition is very sluggish. Tridymite is considered to be a metastable transition phase between two stable phases: quartz?cristobalite. However. the transition temperature for tridymite to cristobalite is 1,470C.4 The quartz-tridymite-cristobalite transition can be accelerated substantially by the presence of fluxing agents. Finely divided calcium, magnesium and titanium oxides accelerate the conversion while A12O may retard it. A Mixture of NaCl and CsCl reduces the temperature for cristobalite formation by as much as 420°C. Feldspars constitute the second most important mineral in sandstones. The melting points of feldspars range between 1,000 and 1,700°C depending upon the variety. No information available indicated any important role of fluxing agents in the thermal alteration of this group of minerals. Carbonate minerals are subject to dissociation at temperatures within the range of the present investigation. The dissociation of magnesite can start at a temperature of 373°C, but the reaction is sluggish and might not occur untll a temperature of 500°C or ,higher is reached. Dolomite dissociates in two stages at 500°C and 890°C, whereas calcite dissociation temperature is about 885C. Because CO2 is released in the dissociation of carbonates, ail such reactions are somewhat dependent upon CO2 partial pressure. In the absence of CO: in the surrounding atmosphere, the dissociation of calcite starts at 500°C.However. when 1 atm of CO surrounds the sample, the dissociation does not start until 900C. The other carbonates are apparently much less sensitive to a change in partial pressure of CO2. The aragonite calcite transformation can occur an!. where within the temperature range of 357 to 488°C. depending upon the presence of impurities such as barium. strontium. lead and perhaps zinc. The differential thermal analysis (DTA) curves of both magnesitc and dolomite vary with the presence of &apos;impuritics. The presence of iron in particular seems to affect the magnesitc DTA curve

Jan 1, 1966

By J. H. Waxweiler, L. C. Ikenberry, R. J. Bendure

Carbon which is present as insoluble carbides in austenitic stainless steels can be measured quantitatively by dissolving the steel in iodine-methanol and analyzing the residue for carbon. Severe sen-sitization was observed in Type 302 due to precipitation of only 0.003 pet carbon. Both cold work and the presence of delta ferrite caused a marked acceleration in rate of carbide precipitation. Carbide precipitation rates in 17-7 PH were stzulied for the austenite conditioning and also the aging heat treatment. CARBON and its compounds exercise a major influence on the properties of stainless steels and their response to thermal treatment. Sensitization in 18-8 type stainless steels has been the subject of numerous investigations throughout the years. Bain, Aborn, and utherford," and Binder, Brown, Frankss all studied the effects of heating austenitic stainless steels in the temperature range of 1000° to 1500°F. The primary purpose of most of these studies was the investigation of susceptibility to in-tergranular attack in acids due to these sensitizing heat treatments. Intergranular precipitation of carbides was always associated with intergranular attack but it was recognized2 that severe attack could occur with but minute quantities of precipitated carbide. Mahla and ielsen utilized the electron microscope to make a significant contribution in illustrating the appearance and method of growth of chromium carbides during sensitizing heat treatments. However, as they stated, their studies of residues could not be used to obtain a quantitative measurement of the amount of carbon which was actually precipitated. The aim of the present investigation was to devise a relatively fast, simple method for the quantitative measurement of carbides in stainless steel. EXPERIMENTAL WORK The initial investigations were made to determine the best means of separating carbides from the matrix. A number of dissolving media were tried using both chemical and electrolytic attack. Qualitative examination of the extracted residues by X-ray diffraction indicated that solution in iodine-methanol would furnish a good means of separation. Consequently, further work was pursued along this line. The method is quite simple. The sample in the form of millings or nibblings is dissolved in iodine-methanol solution at room temperature (6-g iodine, 25-ml methanol per g of sample). The insoluble residue containing the carbides is separated by suction filtration through an ultra-fine glass filter disc. This is a very fine filter medium that will retain particles as small as 0.1 to 0.2 p in diameter. After washing with methanol and drying, the filter disc and residue are placed in a conventional combustion carbon-tube furnace and the carbon determined gravimetrically. Using this technique it was found that reproducible insoluble carbon values were obtained. However, since such small amounts of insoluble carbon were obtained on Type 302 after sensitizatipn at 1250°F and 1500°F, the values were confirmed by a second method. In the second method the sample was dissolved with copper potassium chloride and filtered through a millipore paper. This treatment dissolves the matrix but leaves undissolved practically all of the carbon irrespective of how it is present in the steel. The amount of insoluble carbon present as chromium carbide is determined by calculation from the analysis of the residue for chromium and iron. The derivation of the formula used for this calculation is discussed later. The values obtained by the indirect copper-potassium-chloride method were in agreement with those obtained by the iodine-methano1 method. See Table I. It should be pointed out that the sensitivity of the direct combustion method is not too high when the amount of carbide present is small. This is due primarily to inherent blanks and to analytical errors such as weighing. For this reason it cannot be stated with any degree of certainty that there is a significant difference between values of 0.002 and 0.005 pct. Having confirmed that the iodine-methanol extraction gave a quantitative measurement of the precipitated carbides in Type 302, exploratory tests were conducted on Armco 17-7 PH stainless steel. Samples from commercial Heat 54807 were solution annealed at 2000°F, water quenched and heated at 1250" and 1500°F, and water quenched. The analysis of Heat 54808 is as follows:

Jan 1, 1962

F. E. Thompson, Pottstown, Pa.: If Mr. Webster&apos;s endeavor to open up the subject of cast-iron should prove as prolific of results as did the discussion on " The Physics of Steel," he must certainly feel richly repaid. His remarks concerning the secretiveness and conservatism of the average foundry-man recall to my mind an instance of a blast-furnace which, for the last year, has been producing much foundry-iron. The manager, believing that much more of his product could be used in the foundry than the foundry-men were will-

Jan 1, 1896

By W. M. Robertson

The formation of grain boundary grooves on surfaces of poly crystalline samples of cobalt and iron immersed in liquid lead has been studied. The grooves form by volume diffusion of the solutes cobalt and iron in the liquid. The diffusion coefficients of the solutes in liquid lead are derived from the measured rate of grooving. The diffusion coefficients are described by the relation D = Do exp (-Q/RT), with, for cobalt, Do = 4.6 x 10-4 sq cm per sec and Q = 5300 ± 800 cal per mole, and for iron, DO = 4.9 x 10-3 sq cm per sec and Q = 10,500 ± 1500 cal per mole. LIQUID metal-solid metal interactions occur at solid-liquid interfaces. Interfacial energy provides a driving force to change the morphology of the interface. Mullins1,2 has derived expressions for the kinetics of interface morphology changes driven by capillarity. These expressions can be applied to an isothermal system of a solid in equilibrium with a liquid saturated with the solid. Surface profile changes can occur by volume diffusion of the solute in the liquid, by volume self-diffusion in the solid, and by interfacial diffusion at the liquid-solid interface. A groove will form at the intersection of a grain boundary with a solid-liquid interface, reducing the total interfacial free energy of the system. The solid-liquid interfacial energy ? must be greater than half the grain boundary energy of the solid ?6 for Mullins&apos; calculations to apply. If ? is less than ?b/2, then the liquid penetrates the boundaries, separating the grains rather than forming grooves. Boundary penetration did not occur in the work described here. where CO is the equilibrium volume concentration of the solid in the liquid, Dv the volume diffusion coefficient of the solid in the liquid, ? the interfacial free energy of the solid-liquid interface, O the atomic volume of the solid crystal, k Boltzmann&apos;s constant and T the absolute temperature. Eqs. [1] and [2 ] also apply to grooving by volume self-diffusion in the solid,1 with CoODv = D Self, where DSelf is the volume self-diffusion coefficient of the solid. For a grooving mechanism of interfacial diffusion at the solid-liquid interface, the groove width is given by2 where CS is the interfacial concentration of the diffusing species, and DS is the interfacial diffusion coefficient. Eqs. [1] and [3] can be used to determine the mechanism of groove growth. A t1/3 dependence of the growth indicates volume diffusion and t1/4 indicates interfacial diffusion. In some cases, volume diffusion and interfacial diffusion both can contribute substantially to the grooving process, causing the time dependence to be intermediate between t 1/3 and t1/4.3 For these cases, the relative contributions of the two processes can be separated.4 However, in many cases, one process will be dominant, and the data can be analyzed on the basis of Eq. [1] or Eq. [3] alone. The time dependences for volume diffusion in a liquid and volume self-diffusion in a solid are the same. However, the self-diffusion contribution of the solid is usually negligible compared to volume diffusion in the liquid. After the grooving mechanism has been determined, Eq. [1] or Eq. [3 ] yields the kinetic parameter A or B. The kinetic parameter can be used to calculate values for the unknown quantities in the product CD?. Usually C is known or can be estimated. If ? is known, then D can be calculated. In a measurement of grain boundary grooving of copper in liquid lead,&apos; the time dependence indicated volume diffusion in the liquid. The quantities Co, Dv, and ? were obtained from the literature, giving excellent agreement between the observed values of A and the values calculated from Eq. [2 ].5 In a study of the grooving of several refractory metals in liquid tin and liquid silver, A1len6 educed that grooves formed by volume diffusion in the liquid. In a study of nickel in a nickel sulfide melt, Steidel, Li, and spencer7 found volume diffusion grooving kinetics. Both Dv and ? were unknown, so they could not obtain either one separately, though they did obtain a reasonable value for the temperature dependence of the product Dv ?. Several methods have been used to obtain surface profiles. It can be done by sectioning through the interface7 or by chemically removing the liquid from the solid surface after solidification of the liquid.6 However, if the liquid dewets the solid on removing the solid from the melt, then the interface can be observed directly. This method was used previously&apos; and was utilized also in the present study. EXPERIMENTAL PROCEDURE Lead of 99.999 pct purity was obtained from American Smelting and Refining Co. Cobalt sheet was obtained from Sherritt-Gordon Mines, Ltd., with a nominal purity of 99.9 pct, the principal impurities being nickel, iron, copper, carbon, and sulfur. The sheet was

Jan 1, 1969

By Morris Muskat

A theory is presented for calculating the performance history of complete water-drive systems producing from idealized stratified formations. The general equations are applied to systems where the permeability stratification is either of the exponential or linear type. Calculations were carried through for different degrees of permeability stratification, but with special emphasis on the effect of the mobility ratio between the produced oil and the invading water on the resultant performance. These results are also expressed graphically as curves for the initial water breakthrough recovery, for the different degrees of stratification, as a function of the mobility ratio, and of the composition of the produced fluid stream as a function of the cumulative oil recovery. For several typical cases the latter has also been plotted as a function of the cumulative oil and water throughflow. The general result is that when the mobility of the oil is lower than that of the invading water the channelling tendency resulting from the permeability stratification becomes aggravated as the higher permeability zones become flooded out. Situations of this type would obtain when producing low gravity or highly viscous oils. Conversely, if the mobility of the oil is high compared to that of the invading water, the flooding of the high permeability zones will lead to a retarding and choking effect, and the gross bypassing phenomena will be partially suppressed. These conditions would correspond to those of flooding high gravity or low viscosity oils. A discussion is given of the various basic assumptions made in the analysis, including that of ignoring the stripping phase of the production history as implied by relative permeability concepts. INTRODUCTION The physical ultimate recoveries from oil reservoirs are basically determined and limited by the physical oil displacement processes associated with the reservoir producing mechanism. In practice, however, the economic ultimate recoveries are further limited by the mobility of the reservoir fluids and the uniformity and continuity of the producing formation. In fact, it is the differential depletion between the component parts of the composite reservoir which ultimately determines the total recovery at the time of field abandonment. While this observation applies to both the solution gas drive and gravity drainage mechanisms, in which use is made only of the energy contained within the original oil-bearing reservoir, it is of even more paramount importance under operations wherein the energy associated with extraneous fluids provides the ultimate oil expulsion mechanism. Whether the invading fluid is the water from an edgewater drive, water injected for pressure maintenance, gas injected for pressure maintenance, or gas returned to the formation in a cycling program, it is often the continuity and uniformity of the producing section which will control the economic efficiency of the operations. The importance of the problem of reservoir non-uniformity does not, of course, lessen its complexity or the difficulties of its solution. In fact, these are inherently such that the concept of a "general" solution is virtually meaningless. About all that can be reasonably hoped for is the analysis of specific and well-defined types of non-uniformity which may give some degree of approximation to actual reservoir conditions. Since variations in the nature of the reservoir which depend only on the position along the streamlines will not lead directly to major differential depletion development within the reservoir, the types of non-uniformity considered thus far have involved stratification assumptions. That is, the producing section has been replaced by a multi-layer "sandwich," each uniform areally, and differing from the others only in its basic physical constants as to thickness, porosity and permeability. The fluid motion in the composite system is thus approximated by a parallel superposition of the independent fluid movements in the individual strata. For the specific application to cycling operations the theory of the effect of permeability stratification has been developed for both discontinuous&apos; and continuous types of permeability stratification. Among the latter, treatments have been given of systems in which permeability distributions are governed by exponential, linear&apos; or probability3 functions. In all these studies complete dynamical equivalence was assumed between the injected dry gas and the displaced wet gas. The overall effective permeability of each stratum was therefore considered as constant and independent of the degree of invasion of the injected fluid. In the case of the displacement of oil by water, the assumption of dynamical equivalence between the water and oil will be strictly valid only by accident. Even if the oil viscosity should be the same as that of the water, the effective permeability to the oil in the presence of the connate water will in general be quite different from that of the water behind the water-oil interface flowing past the trapped residual oil. As a result the effective permeability for the stratum as a whole and rate of water invasion will change with time as the intrusion continues. The differential fluid motion in the individual strata will thus also vary with time. Qualitatively, it is easy to predict the resultant effects. If the permeability to viscosity ratio of the invading fluid exceeds that of the fluid displaced, the stratification and bypassing effect of the perme-

Jan 1, 1950