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By C. A. Siebert, S. H. Bush

Isothermal temper-embrittlement studies were conducted on a 5140 steel at various temperatures for times as long as 3000 hr. Specimens from the embrittled steel were subjected to impact tests, metallographic examination, microhardness, and lattice-parameter measurements. SEVERAL of the steels in the low alloy group are subject to a pronounced decrease in impact energy if held within, or cooled slowly through, a range of temperatures below the lower critical. This phenomenon, known as temper embrittlement, is quite pronounced in the chromium steels of which AISI 5140 is typical. This study considered the response of one heat of 5140 steel when embrittled isothermally at various temperatures for times as long as 3000 hr. Excellent reviews of the work done in the field of temper embrittlement have been written by Hollomonl and Woodfine.' Both authors list the various theories which have been advanced to explain temper embrittlement. Some of the mechanisms considered were: 1—a transformation below 700°C; 2—an allotropic modification of iron; 3—precipitation from the ferrite of such compounds as carbides, nitrides, phosphides, or chromium oxides; 4—decomposition of retained austenite; 5—modification of special carbides; 6—grain-boundary segregation; and 7—selective distribution of carbides. The present study investigated the changes in hardness, Meyer's number, impact properties, micro-structure, and lattice parameter which occurred on embrittlement. Previous studies considered the influence of microstructure and of prior austenitic grain size3 on the response of 5140 steel to temper embrittlement. Equipment and Procedure All samples were taken from one heat of 5140 steel; the chemical composition of this steel was: 0.43 pct C, 0.86 pct Mn, 0.020 pct P, 0.019 pct S, 0.27 pct Si, 0.84 pct Cr, 0.10 pct Ni, 0.06 pct Mo, 0.10 pct Cu, and the remainder Fe. The material was received as % in. rounds. This stock was cut down to blanks measuring approximately 0.425~0.425~2.196 in. Heat Treatment: The rough blanks were normalized at 1600°F (870°C) for 1 hr, then austenitized at 1600°F (870°C) for 1 1/2 hr, and quenched into an agitated oil bath. The specimens were tempered at 1275°F (690°C) for 5 hr and water quenched. These tempered specimens were designated as the toughened state. Embrittling Treatments: The tempered bars were divided into sets and subjected to the various embrittling treatments listed in Table I. Temperatures from 750" to 1050°F were investigated for times of 1 to 3000 hr. Special tests to determine the effect of heating a short time at a higher temperature after long-time embrittlement at some lower temperature were also conducted. All specimens were water quenched at the end of the embrittling cycle, then ground and notched to obtain standard Charpy V-notch specimens. Impact Tests: The bars were fractured in a 260 ft-lb Charpy impact unit; specimens were fractured at temperatures ranging from —315°F to room temperature. Fixed temperatures used consisted of —315°F with liquid nitrogen, —115°F with dry ice and acetone, and 32°F with ice and water. Intermediate temperatures were obtained by suspending the bars in a jig over the liquid nitrogen, dry ice and acetone, or ice and water.

Jan 1, 1955

By D. G. Westlake

NUMEROUS hydride habit planes in zirconium, Zircaloy-2, and Zircaloy-4 have been observed by various researchers and have been compiled by Louthan and Angerman.1 While only partial agreement exists on the identification of these habit planes, there is a growing consensus that a tensile stress applied on a polycrystalline rod during slow cooling will cause the hydride platelets to lie perpendicular to the tensile axis. walters2 agrees with Louthan and Angerman who reason that "The particular plane on which precipitation will occur is the plane that will result in the maximum relief of stress by precipitation of the low-density hydride." The experiment described below was initiated to test this hypothesis on a single crystal of zirconium. A single-crystalline tensile specimen of zone-refined zirconium, designated number 13 in a previous study,3 had a square cross section with one pair of parallel faces only 4 deg from the basal plane of the hcp structure. The tensile axis was about 86 deg from the (0001) pole, 14 deg from the (1010) pole, and 16 deg from the (1150) pole. The specimen was charged to 50 ppm H by allowing reaction with the correct amount of hydrogen at 1073°K, homogenizing at this temperature for 2 hr, and cooling in the furnace. Two- surface analysis revealed that hydride platelets had precipitated parallel to the three {1010} prism planes. The specimen was heated to 673°K, in air, for 16 hr to bring the hydrogen back into solid solution, and furnace-cooled to 573°K.* It was then stressed in ten- sion at 1.2 kg per sq mm. (This produced a resolved shear stress of 0.6 kg per sq mm for glide on the prism plane with the highest Schmid factor. A higher stress would have produced significant strain at this temperature because the critical resolved shear stress for prism-plane glide in this crystal was only 1.0 kg per sq mm at ambient temperature.) The poles of the three prism planes were at angles of 14, 46, and 74 deg to the tensile axis so that an applied stress would exert normal stresses on the three planes in the approximate ratios 10:5:1, respectively. As soon as the stress was applied, the sample was furnace-cooled to room temperature. It was ground on wet Sic paper and chemically polished in 50 parts HNO3, 50 parts water, and 7 parts HF before examination. The result of the experiment was negative; i.e., the three (1010) planes were of equal importance as hydride habit planes.* It must be admitted that the ex- periment is not entirely comparable to those performed by walters,2 Louthan,5 and Louthan and Marshall6 on polycrystalline materials. They have found that some critical stress (below the macroscopic yield stress) is required for stress-orienting the hydrides. The applied stress in the present experiment was, by necessity, smaller by an order of magnitude than the critical stresses they report for the various materials. If the critical stress was related to the microstructure, one might postulate that it should be decreased by increasing the degree of perfection of the metal lattice and by increasing the grain size. But the experiment above suggests that, for the extreme case of a zone-refined single crystal of zirconium, the critical stress lies above that which one can apply without introducing gross plastic strain as another variable.

Jan 1, 1967

By M. A. Dayananda

Based on the Kirkendall frame of reference, a method is proposed for the determination of atomic mobilities of all the diffusing species in a multicorn-ponent system with a single diffusion couple. The method is based on an atomic mobility model developed on the concept of negligible interactions among the intrinsic fluxes. It is shown in the model that mobilities can be obtained directly from the cumulative intrinsic fluxes past the Kirkendall interface. The proposed method replaces the need for a prior determination of interdiffusion coefficients far the calculation of mobilities. Relations between intrinsic diffusion coefficients and mobilities are derived and the mobility calculations are illustrated with diffusion data in Cu-Zn-Mn alloys at 850°C. ThE concept of "intrinsic flux" with respect to a fixed lattice was introduced "i Darken1 to explain toa Kirkendall effect2 demonstrated by the motion of inert markers during isothermal diffusion in single-phase binary solid solutions. Based on this concept, intrinsic diffusion studies have been made in various binary metallic systems3,4 employing such a lattice frame of reference, commonly referred to as the Kirkendall interface. Similar approaches, both theoretical and experimental, have been presented5"10 to study intrinsic diffusion in multicomponent systems. Based on the direct integration of Fick's law extended to multicomponent diffusion, Philibert and Guy8 proposed a method for the determination of intrinsic diffusion coefficients. For an n-component system, this procedure requires an experimental study with (n — 1) diffusion couples, all having their Kirkendall interfaces at the same compositio;, where n(n — 1) intrinsic diffusion coefficients are defined. This technique has been employed for ternary diffusion studies by Dayananda and Grace" and Guy and Leroy.11 A different approach is recommended by Ziebold and Cooper,12 who have derived relations between interdiffusion coefficients and atomic mobilities employing fluxes referred to the local center of volume. Their analysis is based on the simplifying assumption of negligible interactions among intrinsic fluxes. This assumption has been considered satisfactory for dilute solutions.5"7 The use of this analysis for the calculation of mobilities requires an initial determination of interdiffusion coefficients with a set of diffusion couples having intersecting diffusion paths. It is the purpose of this paper to propose a method that would permit a direct determination of mobilities of all components of a multicomponent system from a single diffusion couple. This method is based on a mo- bility model developed with diffusion fluxes referred directly to the Kirkendall interface, generally identified by inert markers. gen erall, like that of Ziebold and Cooper,12 employs the simplifying assumption that the flux of each component relative to a fixed lattice is caused only by the driving force of its own chemical potential gradient. THE KIRKENDALL INTERFACE Inert markers are employed in diffusion couples to locate experimentally the position of the Kirkendall interface. They are initially placed at the weld interface for "sandwich" couples, or at the original vapor-solid interface for vapor-solid couples. Studies of marker motion in binary systems3'4 with both types of couples indicate that markers remain in a plane of constant composition and move with this plane para-bolically with time. Parabolic marker movements were also observed in ternary Cu-Zn-Mn couples by Dayananda and Grace.10 It is reasonable to expect a similar marker behavior even for diffusion couples with a higher number of components.

Jan 1, 1969

By C. W. MacGregor

IN the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Prob-ably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section AO at the start of the test, as a function of the strain ?o, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwik1, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area Ao a fictitious stress is obtained, which does not actually exist; (2) that the strain ?o = ?Lo /Lo is not an exact expression for the true strain for large values of ?Lo in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and ?o does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would he thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937

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 William H. Baer, George M. Carlton, Blake M. Loring

IT is a well known fact that age-hardening alloys remain in a supersaturated, or partially supersaturated, condition only for limited periods of time at temperatures below the solvus. In order to develop optimum properties by subjecting the quenched alloy to precipitation or age-hardening treatment at a specified temperature, it is necessary that the cooling rate be sufficiently high to maintain the required degree of supersaturation of the solid solution. In practical applications the size and shape of the specimens obviously have considerable influence on the rate of cooling and there is need for more information on the effects of various rates of cooling. Cooling rates of quenched aluminum alloys generally have been established by the type of quenching medium, the temperature of the medium and the dimensions of the specimen.1,2,3 Except for the work of Roth3 little quantitative information is available on the measurement of cooling rates of aluminum alloys and the significance of the influence of various cooling rates upon the mechanical properties. The purpose of the present investigation was to study the use of the Jominy test for aluminum alloys (Table I). EXPERIMENTAL PROCEDURE The material for this investigation consisted of extruded rods 1 ¼ to 1 ½ in. in diam. The chemical compositions were as follows: [ ] The modified L-type Jominy specimen with dimensions shown in Fig I was selected as the most convenient means for obtaining a wide range of cooling rates. The standard Jominy specimen was not satisfactory because its cooling rate was not sufficiently high. The four flat surfaces machined at right angles along the length of the L-type specimen to a depth of 0-015 in. facilitated the hardness measurements. The specimens were machined from the extruded stock with no intermediate forging. New specimens were used for each aging experiment. The specimens were given solution treatments of 2 hr duration at recommended temperatures in a Hoskins furnace (Table 2). The temperature of the furnace was maintained constant to ±3°C. No protective atmosphere was necessary because the thin film of oxide that formed on the surface of the specimens had no effect on the hardness measurements.

Jan 1, 1948

By P. Pollard

A method has been developed for evaluating acid treatments in fractured limestone fields by breaking down pressure drawdown into three component parts: (I) pressure differcntial across "skin" near the borehole face, (2) pressure differential due to flow resistance in the coarse communicating fissures and (3) pressure differential between the fine voids and the coarse fissures. It is apparent that in most successful acid treatments the first term, skin resistance, has been reduced or eliminated. Further, it is often possible to estimate the volume of coarse fissures associated with the second term, coarse fissure flow resistance. In cases where this volume is comparable with practical acid volumes it seems likely that this resistance also may be attacked with a suitably retarded acid. INTROD UCTION Acid treatment has been successfully applied as a general practice in the limestone wells in the Mara/ Maracaibo districts of Venezuela for some 10 years. At the same time the need has been felt for a more precise method of: (1) evaluating the effect of an acid job and (2) selecting wells which should benefit from an acid treatment. The following method, based on an analysis of build-up curves for wells producing from fractured limestone, provides a means of forecasting the effect acid will have on a well and in many cases the probable order of production rate increase which may be expected. In certain cases it is also possible to calculate the fissure volume through which the acid has to be displaced for best results. Various approximations are introduced in the method, but within the limitations of these the analysis gives an indication of how a well, whether previously acidized or not, may be expected to respond to acid treatment. Suitable build-up curves cannot be obtained on "tight" wells which do not give sustained production and the method is not applicable to such wells. Figs. 1 through 7 illustrate various types of build-up curves obtained from limestone wells in Western Venezuela. Curves are included showing (1) both skin and coarse fissure resistance, (2) skin resistance only, (3 and 4) reduction of skin resistance by acidization, (5) fissure resistance only, (6) reduction of coarse fissure resistance by acidization, and (7) acidization failure. This theory has been successfully applied for over three years during which 22 acid treatments have been carried out specifically to reduce skin resistance and three treatments to reduce coarse fissure resistance. The method has been found to be a useful aid in the selection of wells for acidization.

By William J. Craig, Harold L. Walker

INDUSTRY has for many years recognized the dependence of certain mechanical and physical properties, as well as workability, upon grain size variations in brass. Although the dependence of properties upon grain size has been recognized there are not many instances where a planned program of testing has been conducted and where the only intentional variable has been grain size. In particular the literature is limited with respect to the effect of grain- size on the endurance limit, though there are many industrial applications where the brasses are subjected to cycles of repetitive stresses. LITERATURE A number of the physical and mechanical properties of a given brass sheet, in the annealed condition, will depend upon: (I) The ready-to-finish grain size before final rolling, (2) the percentage deformation by cold working, and (3) the time and temperature of annealing, The first and second variables affect the recrystallized grain size, and the third variable affects the coalesced grain size. Gibbs1 has shown the effect of two different ready-to-finish grain sizes upon the tensile strength and hardness of deep drawing brass strip after a definite amount of cold rolling. The smaller the ready-to-finish grain size, the higher the tensile strength and hardness, but with lowered ductility, Gibbs also demonstrated, for a given time and temperature of anneal, that the tensile strength, hardness, and elastic limit are higher for the smaller ready-to-finish grain size, but the elongation is lowered, Townsend and Greenall2 have reported data which show that cold working increases the tensile strength, hardness, and load carrying ability of deep drawing brass sheet under reversed stress. Greenall and Gohn3 have reported data which show that the smaller grain sizes have higher tensile strength and hardness properties, and the data also show that increased cold working increases the tensile strength and hardness properties of deep drawing brass sheet. Kommers4 has reported data for tests of brass of known ready-to-finish grain size, a specific amount of cold reduction, and annealed at different temperatures above and below the recrystallization temperature. Kommers' results indicate that annealing below the recrystallization temperature does not change the tensile strength and hardness properties, but the endurance limit may be increased from 22,000 to 28,000 psi. The increased endurance limit is explained as resulting from the reduction of internal stresses by a stress-relief anneal. Burghoff5 and associates have reported data on creep tests, over

Jan 1, 1948

By J. W. Craig, H. L. Walker

Industry has for many years recognized the dependence of certain mechanical and physical properties. as well as workability, upon grain size variations in brass. Although the dependence of properties upon grain size has been recognized there are not many instances where a planned program of testing has been conducted and where the only intentional variable has been grain size. In particular the literature is limited with respect to the effect of grain size on the endurance limit, though there are many industrial applications where the brasses are subjected to cycles of repetitive stresses. Literature A number of the physical and mechanical properties of a given brass sheet, in the annealed condition, will depend upon: (I) The ready-to-finish grain size before final rolling, (2) the percentage deformation by cold working, and (3) the time and temperature of annealing. The first and second variables affect the recrystallized grain size, and the third variable affects the coalesced grain size. Gibbsl has shown the effect of two different ready-to-finish grain sizes upon the tensile strength and hardness of deep drawing brass strip after a definite amount of cold rolling. The smaller the ready-to-finish grain size, the higher the tensile strength and hardness, but with lowered ductility, Gibbs also demonstrated, for a given time and temperature of anneal, that the tensile strength, hardness, and elastic limit are higher for the smaller ready-to-finish grain size, but the elongation is lowered. Townsend and Greena112 have reported data which show that cold working increases the tensile strength, hardness, and load carrying ability of deep drawing brass sheet under reversed stress. Greenall and Gohn3 have reported data which show that the smaller grain sizes have higher tensile strength and hardness properties, and the data also show that increased cold working increases the tensile strength and hardness properties of deep drawing brass sheet. Kommers4 has reported data for tests of brass of known ready-to-finish grain size, a specific amount of cold reduction, and annealed at different temperatures above and below the recrystallization temperature. Kommers' results indicate that annealing below the recrystallization temperature does not change the tensile strength and hardness properties, but the endurance limit may be increased from 22,000 to 28,000 psi. The increased endurance limit is explained as resulting from the reduction of internal stresses by a stress-relief anneal. Burghoff5 and associates have reported data on creep tests, over

Jan 1, 1949

By B. N. Das, J. B. Darby, P. A. Beck, Y. Shimomura

A POWDER pattern for the (Cr, Mo, Co)R-phase annealed at 1200°C was reported in 1951.1 Through the courtesy of Prof. D. P. Shoemaker of Massachusetts Institute of Technology the authors became aware of inconsistencies of this pattern with that to be expected from the structure of the R-phase, as determined by Komura, Shoemaker, and Shoemaker.' In addition, Professor Shoemaker also noted that the powder pattern reported8 for the (Cr, Mo, Co)D-phase, annealed at 1300°C, agreed fairly well with that to be expected from the newly determined structure of the R-phase. In view of these findings, the previously reported powder patterns of the R-phase and of the D-phase were compared carefully. It was found that most lines in the two patterns (22 lines) were to a fair degree of accuracy related to each other by a single conversion ratio for the corresponding d spacings. The value of the conversion ratio was found to be 1.0058, so that the d spacings of the D-phase pattern previously reported were larger than the correspond- ing d spacings for the reported R-phase pattern by approximately that factor. The intensity relationships between corresponding lines in the two patterns were similar, as judged visually. The following exceptions were noted: Lines Nos. 2, 3, 19, 20, 21, 22, 23, 24 and 25 of the D-phase pattern,:' all designated weak or very weak, were missing in the apparently somewhat fainter R-phase pattern used.' Lines 1, 2, 3, 5, 15 and 34 (all weak or very weak), reported for the R-phase, were missing in the D-phase pattern, Table I. In view of these observations it seemed probable that the two patterns differed from each other mainly by a slight change in lattice parameters (with c/a remaining approximately constant), and that the pattern previously reported for the R-phase contained some weak extraneous lines, most likely to be attributed to impurities. In order to check the foregoing assumption, two specimens of an alloy containing 43 pct by weight of cobalt, 41 pct molybdenum, and 16 pct chromium, which was within the composition range of stability of both the D-phase at 1300°C and of the R-phase at 1200°C, were homogenized at 1200 and 1300°C, respectively, and quenched. X-ray diffraction patterns of the powders of these two specimens, obtained with CrK radiation, were compared carefully with each other and with the D-phase pattern previously

Jan 1, 1959

By O. F. Thornton, D. L. Marshall

Results of the determination of the inter stitial water content of several core samples from oil reservoirs are presented. Data obtained by the capillary pressure method, which has recently been developed, are compared with water saturations measured in cores cut with oil-base mud and with values calculated from the electrical resistivity of the formation. The agreement between the capillary pressure and other methods, combined with the fact that similar agreement has been obtained by others, indicates that the capillary method properly applied yields results sufficiently accurate for most engineering purposes. In some cases, it may be possible to extend the utility of data obtained with the capillary pressure method by correlation of interstitial water saturation with more easily measured physical properties of the media. Introduction Several methods are in use for determining or for estimating the interstitial water saturation at given points within oil and gas reservoirs. The direct measurement of the water content of cores obtained with nonaqueous fluid in the hole is believed to be an accurate method under most conditions. The water saturation may be calculated by use of the resistivity curves of the electric log,' although this method is not applicable under conditions that exist in some reservoirs. Recently, a method has been developed and described3.' wherein the interstitial water saturation of cores is measured at a capillary pressure such that conditions existing in the reservoir are simulated. The purpose of this paper is to present data obtained by use of this latter method, and to compare the results obtained with determinations made by other means. Method The theory underlying the capillary pressure method applied to petroleum reservoirs has been discussed adequately in the literature by Garrison,2 Leverett,5 and Others.3,6,7 Briefly, and simply, capillary pressure is defined as the difference in pressure between two contacting fluid phases, such as oil and water. For the simplified sand, water and oil system illustrated in Fig I, the pressure difference can be stated as follows:6 where Pc is the capillary pressure in pounds per square inch, ? is the interfacial tension between oil and water in pounds per inch, r1 and r2 are the radii of curvature of the interface between oil and water in inches. Capillary pressure varies in a given reservoir with depth because of the greater density of the water phase as compared with oil or gas. The following equation expresses the difference in pressure between two points: p1- p2 - h?p/144 [2] where p1 — p2 is the capillary pressure difference in pounds per square inch, h is

Jan 1, 1947

By D. L. Marshall, O. F. Thornton

Results of the determination of the inter stitial water content of several core samples from oil reservoirs are presented. Data obtained by the capillary pressure method, which has recently been developed, are compared with water saturations measured in cores cut with oil-base mud and with values calculated from the electrical resistivity of the formation. The agreement between the capillary pressure and other methods, combined with the fact that similar agreement has been obtained by others, indicates that the capillary method properly applied yields results sufficiently accurate for most engineering purposes. In some cases, it may be possible to extend the utility of data obtained with the capillary pressure method by correlation of interstitial water saturation with more easily measured physical properties of the media. Introduction Several methods are in use for determining or for estimating the interstitial water saturation at given points within oil and gas reservoirs. The direct measurement of the water content of cores obtained with nonaqueous fluid in the hole is believed to be an accurate method under most conditions. The water saturation may be calculated by use of the resistivity curves of the electric log,' although this method is not applicable under conditions that exist in some reservoirs. Recently, a method has been developed and described3.' wherein the interstitial water saturation of cores is measured at a capillary pressure such that conditions existing in the reservoir are simulated. The purpose of this paper is to present data obtained by use of this latter method, and to compare the results obtained with determinations made by other means. Method The theory underlying the capillary pressure method applied to petroleum reservoirs has been discussed adequately in the literature by Garrison,2 Leverett,5 and Others.3,6,7 Briefly, and simply, capillary pressure is defined as the difference in pressure between two contacting fluid phases, such as oil and water. For the simplified sand, water and oil system illustrated in Fig I, the pressure difference can be stated as follows:6 where Pc is the capillary pressure in pounds per square inch, ? is the interfacial tension between oil and water in pounds per inch, r1 and r2 are the radii of curvature of the interface between oil and water in inches. Capillary pressure varies in a given reservoir with depth because of the greater density of the water phase as compared with oil or gas. The following equation expresses the difference in pressure between two points: p1- p2 - h?p/144 [2] where p1 — p2 is the capillary pressure difference in pounds per square inch, h is

Jan 1, 1947

By J. E. Hilliard

A procedure is described for determining, from measurements on a section, the moments of any degree n (i.e., the mean value of Dn, where D is a linear dimension) of the size distribution of particles (or grains) in an opaque sarnple. The analysis is applicable to particles of alnzost any shape and to any mixture of shapes. However, if absolute values of the wloments are required, it is necessary to know what shapes are present and the relative frequency of their occurrence. In addition, certain shape-dependent parameters have to be evaluated before the formulas can be used. The measurement required is the distribution of intercept lengths. This can be determined either visually or with an automatic scanning instrument. Corrections me derived for the bias due to instrumental end effects. The proposed analysis has the following advantages over existing ones: 1) Confidence limits are easily estimated for the measured properties or, conversely, the number of counts required to achieve a given accuracy can be determined. 2) The analysis is not restricted to particles of a special shape. 3) The error resulting from any known degree of departure of the actual from the assumed particle shape can be estimated. 4) The computations are simple and, apart from a change in constants, are independent of particle shape. 5) The number of particles per unit volume can be determined by a simple counting procedure. MANY procedures have been described for determining the size distribution of particles from measurements on a section (or plane of polish). They differ from one another in the property measured on the section (radius, intercept length, profile area) and in the method used for the numerical solution of the integral equation relating the property to the particle size distribution. However, all existing analyses share at least two of the following disadvantages. 1) They are limited to a particular shape of particle (usually spherical). 2) It is very difficult to determine how the statistical sampling error is propagated into the computed size distribution. The investigator thus has no means of knowing the reliability of his result and, what is of equal concern, he is unable to estimate how many measurements are required to obtain a result of the required accuracy. 3) It is also difficult to assess the error resulting from any deviation between the actual and assumed particle shape. The foregoing limitations stem from the complex relationship between the particle size distribution and the distribution of the property measured on the section. As will be shown, they can be avoided by defining the size distribution in terms of discrete parameters

Jan 1, 1969

By W. O. Philbrook. K M Goldman, M. M. Helzel

RADIOACTIVE calcium has been used to learn whether calcium can be detected in iron saturated with carbon after it has been melted under CaO- A12O3- SiO2 slags similar to those used in the iron blast furnace. It was hoped that the radioactive tracer technique might make possible a general study of steelmaking reactions in which calcium or calcium oxide are involved. No calcium could be found in the metal under conditions which were favorable for the reduction of calcium, and it has been concluded that the calcium content of the iron was less than 6 x 10 - pct. Some of the problems encountered have been instructive with regard to pitfalls and limitations of tracer methods. Calcium oxide occurs in almost all iron- and steelmaking slags, and it is essential to the success of all commercial basic steelmaking processes. Calcium alloys are sometimes used in the deoxidation of steel and for the innoculation of gray iron. The element calcium is therefore almost as ubiquitous in the steel industry as are carbon and oxygen, but calcium has been thought to be completely immiscible with iron in both the liquid and the solid states.' It does not seem entirely unreasonable to Suppose, however, that some low concentration of calcium might exist in liquid iron under a basic slag with other conditions being favorable, just as silicon and other elements can be introduced into iron by reduction of their oxides from slags under appropriate circumstances. The radioactive tracer technique offered a more sensitive method than chemical analysis of testing this supposition. The reasons for interest in this investigation were strong enough to justify a recognized risk of failure. On the theoretical side, information on the distribution of calcium between liquid iron and a slag and the rate at which the equilibrium distribution is approached would contribute strongly to the general theory of slag-metal interface reactions. Furthermore, any evidence on the presence of calcium in liquid iron might provide a vital clue to the mechanism of the desulphurization of iron by slags. All of the reactions which have been proposed to explain desulphurization postulate that the sulphur ultimately becomes fixed in the slag as calcium sulphide, but the mechanism by which sulphur

Jan 1, 1951

By Murray F. Hawkins

One problem of reservoir engineering is the early estimation of the size of newly discovered reservoirs. Often these reservoirs are the expansion type in which sizeable pressure drops occur incident to the production of small fractions of the oil reserve, above the bubble point, and a material balance equation may be solved to find the reserve. The early form of this equation' considered only the compressibility of the oil. Later Hall2 showed that the compressible nature of the formation rock is a significant factor in production above the bubble point, and he presented a new equation which includes a formation (rock) compressibility term. This note presents a further extension of the material balance equation as applied to volumetric, unsat-urated reservoirs above the bubble point by including a term for the presence and compressible nature of the interstitial water. DERIVATION OF EQUATION During a decline in average reservoir pressure, ?p ?p, — p1 the initial reservoir volume V,, will decrease to some value V, due to the reduction in pore volume as a result of a decline in the hydrostatic pressure within the formation, and v, = V,, [l — cr ?p]......(1) The formation compressibility c, is expressed in terms of change in pore volume per unit pore volume per psi. Simultaneously the connate water within the formation expands from an original volume V,, = S,V,, to a new volume V,, V, = s,v,, [I + c,npl.....(2) The difference [Vp — V,] is the hydrocarbon pore volume at pressure p and may be equated to the volume of the remaining oil, or [N — N,] B, = V,,, [I - C~A;] - S,.Vpi [l + cwnjl.........(3) But the initial oil in place in terms of the initial reservoir volume, connate water, and formation volume factor is Ilividing Equation 3 by Equation 4 eliminates V,, to give,

Jan 1, 1956

By G. I. Madden, L. H. Van Vlack

WhEN basic refractories which contain peri-clase, MgO, are used in steel furnaces, they are altered by iron oxide to form magnesiowiistite, (Mg,Fe)O, and an iron-rich magnesioferrite, (Mg,Fe)Fe2O4. Silica, which is usually present, produces a silicate liquid that surrounds the solid phases. The individual crystalline grains of the above two solid phases grow at elevated temperatures. Previous papersL" showed that, if either periclase or magnesiowiistite is present as the only solid phase, its grain size increases in proportion to temperature and in proportion to the square root of time; the growth rate is reduced slightly if the amount of silicate liquid is increased. Similar results have been observed for iron-rich magnesioferrite.3 To determine the effect of the presence of two solid phases on the rate of grain growth, micro-structural studies have been made on samples containing both magnesiowustite and magnesioferrite. The experimental procedure was the same as that followed in the previous studies of this type.'12 Briefly, this included determination of compositions from the available phase relationships4 that would produce the two phases of interest at the firing temperature and using reagent-grade raw materials to prepare mixtures of these compositions. The mixtures were pressed into pellet-size samples and then fired at the desired time and temperature. The samples were water-quenched to preserve the microstructure present at the firing temperature. Standard reflected-light metallographic techniques were used for sample examination and sample analysis. Grain sizes were determined by measuring the mean diameter of a number of randomly selected grains in a two-dimensional microsection. A large cross section of the sample was covered to prevent biased data resulting from such effects as localized differences in the radius of curvature of the crystal grains. Examination indicates that grain growth is restricted when more than one solid phase is present. This is illustrated in Fig. 1 for: (a) magnesiowustite plus a silicate liquid; (b) magnesioferrite plus a silicate liquid; and (c) magnesiowiistite and magnesioferrite plus a silicate liquid. Fig. 2 plots the

Jan 1, 1964

By P. Farrar, H. Margolin

The Ti-Pb diagram was investigated in the region 0 to 58 pct Pb and from 500°C to liquidus temperatures. Three reactions were encountered: I—ß?a+Ti Pb at 725 10°C; 2—ß+L?Ti4Pb at 1305+ 10°C; and 3—the possible eutectic L-+Ti,Pb and y between 1200" and 1300°C. LEAD-RICH alloys have been investigated by Nowotny and Pesl,' who used sintered compacts and studied the region from 37.5 to 100 pct Pb by X-ray diffraction analysis. The only phase found in addition to titanium and lead was the hexagonal compound Ti Pb. Alloy systems of lead with metals of the transition group, such as iron, chromium, tungsten, cobalt, nickel, or manganese, generally show little liquid or solid solubility.' Craighead et al.,3 however, indicated that lead is soluble in a and ß titanium to at least 2.1 pct. They also found that approximately 50 pct of the lead added was lost during the arc-melting of Ti-Pb alloys. In the present investigation, are-melting also was used to prepare Ti-Pb alloys and similarly large lead losses were encountered. Experimental Procedure Alloy Preparation: Considerable difficulty was encountered in the melting of the Ti-Pb alloys and a number of experiments were performed before the method described was developed. Alternate layers of lead and titanium were wrapped with titanium sheet and compacted. This "sandwich" was annealed at 300" to 350 °C and was melted according to the procedure described by Cadoff and Nielsen.' Using a low current, 150 amp, and an argon atmosphere, four to eight 10 to 20 sec melts were made on each alloy, with the button being turned over between each melt to insure homogeneity. In the high lead range, the preliminary sintering was found to be of doubtful value and was eliminated. In the region above the nominal composition of 70 wt pct Pb, the alloys prepared in this manner always consolidated into two phases. The outside appeared to be composed entirely of lead and the inside was a Ti-Pb alloy. In order to determine whether this phenomenon was caused by a miscibility gap, master alloys with a nominal composition of 40 wt pct Pb were machined and mixed with various percentages of lead sheet. This mixture was compacted and melted in the same manner as the other alloys. Although these alloys were not homogeneous, they did not show the layering that was observed

Jan 1, 1956

By R. L. Huntington, Frank P. Vance, George F. Russell, Robert Thompson

With the advent of higher pressures in the operation of natural-gas transmission lines, the removal of water vapor from the gas has become increasingly important in order to prevent condensation or formation of gas hydrate from slowing down or stopping the flow of gas. Intelligent design of these dehydration or gas-drying plants has been hampered through the Iack of experimental data on the water vapor content of natural gas at elevated pressures. In view of this need, this present investigation was sponsored by the Southern Natural Gas Co. in the Chemical Engineering laboratories at the University of Oklahoma Research Institute. Experimental results were obtained on the water-vapor content of natural gas up to 2000 lb. per sq. in. at atmospheric temperatures. The water content at 2000 lb. is approximately two thirds as much as it is at 1000 Ib. Deviations from the ideal gas laws vary directly with pressure and indirectly with temperature. Introduction The removal of water vapor from natural gas is an important operation in connection with the production and transportation of this commodity because: I. Liquid water accelerates internal corrosion of a pipe line. 2. Accumulation of water at low points in a pipe line reduces markedly its capacity. 3. Gas hydrates, icy snowlike growths, form readily under high pressure in the presence of the lower hydrocarbons and water, often plugging up the pipe line. In order to design dehydration plants for stripping the gas of its water content, it is essential that the engineer. have a knowledge of the saturated or equilibrium water-vapor content of the gas to be processed. With the gradual increase of operating pressures around gas-producing wells and pipe lines, it was observed that the quantity of water recovered from dehydration plants or condensed in colder lines was considerably greater than had been expected from calculated contents, based on vapor-pressure data taken from steam tables. This observation prompted a number of investigators, for instance, Laulhere,3 Dea-ton,l and Hammerschmidt2 to carry out experimental work at pressures up to 600 lb. per sq. in. in order to determine quantitatively the water content of various gases. Sage, Lacey, et al.4,5 have recognized more recently the need for such data at higher pressures, but their work was done at temperatures of 100ºF, and higher. Since hydrate formation usually, if not entirely, occurs at temperatures below 100ºF., the present investigation was confined to the . lower temperature range at pressures from 600 to 2000 lb. per sq. in. gauge.

Jan 1, 1945

By Alden B. Greninger

Twinned metal crystals are usually designated as either deformation twins or annealing twins. If twins are to be classified according to the treatment the metal has undergone just prior to the observation of the twins, there are two other possible groups: (1) solidification twins,† when observed in the as-solidified or as-cast condition, and (2) transformation twins,† when observed in a metal which has been cooled from above an allotropic transformation temperature. McKeehan has demonstrated that ferrite does, occasionally at least, contain twinned structures2. The twins, which he studied by optical methods, were obtained during the preparation of iron single crystals by very slow cooling through A3. He proved that the twin relation was actually that which previous investigators had predicted; namely, twinning along three planes of the form (112). Since McKeehan's discovery, little or no attention has been given to this transformation twinning of alpha iron, or to the possibility that it might occur at all speeds of cooling from above A3 instead of merely during the preparation of single crystals. McKeehan's twins were evidently regarded as interesting only in proving that a body-centered cubic metal could form twinned structures—at least under certain conditions. It is generally believed that iron seldom if ever forms annealing twins. Certainly the straight-line banding which is so abundant in annealed face-centered cubic metals is characteristically absent in iron annealed below A3. However, O'Neil13 has studied "twin-like" crystals in annealed alpha iron and concludes that the specimen he studied actually contailled a few annealing twins. Tamura4 as reported "twin-like" crystals both in wrought iron and mild steel; specimens of the latter were annealed above and below A3 and showed "twin-like" crystals after both kinds of treatments.

Jan 1, 1936

By Alden B. Greninger

Twinned metal crystals are usually designated as either deformation twins or annealing twins. If twins are to be classified according to the treatment the metal has undergone just prior to the observation of the twins, there are two other possible groups: (1) solidification twins,† when observed in the as-solidified or as-cast condition, and (2) transformation twins,† when observed in a metal which has been cooled from above an allotropic transformation temperature. McKeehan has demonstrated that ferrite does, occasionally at least, contain twinned structures2. The twins, which he studied by optical methods, were obtained during the preparation of iron single crystals by very slow cooling through A3. He proved that the twin relation was actually that which previous investigators had predicted; namely, twinning along three planes of the form (112). Since McKeehan's discovery, little or no attention has been given to this transformation twinning of alpha iron, or to the possibility that it might occur at all speeds of cooling from above A3 instead of merely during the preparation of single crystals. McKeehan's twins were evidently regarded as interesting only in proving that a body-centered cubic metal could form twinned structures—at least under certain conditions. It is generally believed that iron seldom if ever forms annealing twins. Certainly the straight-line banding which is so abundant in annealed face-centered cubic metals is characteristically absent in iron annealed below A3. However, O'Neil13 has studied "twin-like" crystals in annealed alpha iron and concludes that the specimen he studied actually contailled a few annealing twins. Tamura4 as reported "twin-like" crystals both in wrought iron and mild steel; specimens of the latter were annealed above and below A3 and showed "twin-like" crystals after both kinds of treatments.

Jan 1, 1936