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By Tormod Forland

FROM equilibrium measurements on the system NaF-Na 3A l Fo-A 1 2 O 3-Na CO 3-CO 2 with high contents of NaF, Forland, Storegraven, and Urnesl concluded that complexes are formed containing two oxygen, three aluminum, and a less defined number of fluorine per complex. The same number of oxygen atoms per complex was also found by cryoscopic measurements for mixtures high in NaALF 6. In a recent paper by Stokes: some other complex ions, Al2O2F42- and AlOF2-, have been suggested. Here an additional argument in favor of the complex ALO2F. suggested by Forland, Storegraven, and Urnes will be given. When fused Na3AlF6 containing some A12O3, is cooled slowly, the solid phase will consist of the two components as separate phases. The melting point and the heat of fusion of Al2O3 are so high that this component will form the stable solid phase even though in the liquid state the complex may have a high stability. If, however, the fused mixture is quenched, the decomposition of the oxygen-containing complex and the formation of solid Al2O3 does not proceed fast enough, and a solid solution of A12O3 in Na3AlF6 is obtained. Zintel and Morawietz3 obtained cryolite containing 10 pct AL2O3 in this way. The density and the lattice parameters of the A12O3 containing cryolite were also measured, and from this it was concluded that the Al2O3 enters the cryolite lattice as Al3AlO0 groups replacing Na3AlF6 groups. However, the experimental data could as well be explained by assuming that one Na+ ion and two of its neighboring F- ions are replaced by one Al3+ ion and two O2- ions. This may be pictured schematically as: F F F F F F F Al F Na F Al F ,-Na+ + Al8+ F Al 0 A1 0 A1 F F F F —2 F- + 2O2- F F F solid cryolite cryolite-alumina solid solution This means that the complex in the solid solution, derived from X-ray and density measurements, is the same as that which Forland, Storegraven, and Urnes derived from equilibrium measurements in the liquid state. References IT. Forland, H. Storegraven, and S. Urnes: Ztsch. fur anorgan-ische und allgemeine Chemie, 1955, vol. 279, p. 205. 2J. J. Stokes: AIME Trans. To be pubhshed. s E. Zintel and W. Morawietz: Ztsch. pubhshed.fur anorganische und allgemeine Chemie, 1939, vol. 240, p. 145.

Jan 1, 1958

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By W. H. Smith

IN the course of an investigation on chromium containing minor amounts of alloying elements, the information herein has been obtained on the crys-tallographic orientations resulting from arc melting, rolling, and annealing. The chromium used in this investigation was electrolytic flake obtained from the Electro Metallurgical Co. This material was heated for 20 hr at 1600°C in hydrogen with a dew point of about — 100°C. The oxygen and nitrogen content of the chromium after this treatment was 0.0003 pct 0 and 0.005 pct N. Five pounds of this chromium were arc melted in a water-cooled copper crucible. After arc melting, the oxygen and nitrogen contents were 0.002 and 0.025 pet, respectively. A section of this ingot is shown in Fig. 1. By means of a back-reflection Laue technique, the crystal habit of the cast ingot was determined. As expected, it was found that the [loo] was approximately the axis of the columnar grains. In this respect, chromium behaves like other body-centered-cubic metals in that a cubic axis is normal to the cold surface of the mold. A slab cut from this ingot was rolled at 600°C as follows: four 30 pct reductions were made with intermediate anneals at 1200°C for 15 min. Rolling was done with the [loo] of the columnar grains in the rolling direction. Following the final anneal, an 80 pct reduction was taken at 600 °C. The final sheet thickness was ten mils. By polishing and etching, the thickness was reduced to four mils and the grain orientation determined by the transmission Laue method using molybdenum radiation with a zirconium filter. Fig. 2 is the (110) pole figure for this material with the ideal (100) [011] and (111) [112] orientations indicated. The orientation is typical of most cold rolled body-centered-cubic metals having the [llO] of the grains approximately in the rolling direction and the (100) planes approximately in the plane of the rolled sheet. There is also evidence of some 10) [1 orientation. The grain orientation of sheet rolled 40 and 80 pct in the same direction as before at 600°C followed by recrystallization at 12000 C for 15 min was determined by a back-reflection Laue technique. A random texture was found in both cases. This 1200°C 15 min anneal was found to give complete recrystallization and some grain growth.

Jan 1, 1956

By R. E. Maringer, A. Schwope

IT has been recognized that oxygen in minute quantities is extremely detrimental to the room-temperature ductility of molybdenum. Early fracto-graphic studies' of the cast metal indicated that oxides are formed preferentially at the grain boundaries. Additional verification of this preferential segregation has been obtained from internal friction studies on poly crystalline molybdenum (average grain diameter varied from 0.039 to 0.065 mm) and from observations of the effect of oxygen on specimens of extremely large grain size. Specimens A, B, and C, of 0.040 in. diameter commercial molybdenum wire (Lot FW 13-40) were heat treated in the vacuum furnace described by Few and Manning according to the specifications given in Table I. Internal friction studies of these specimens were carried out using a low frequency (approximately 1 cycle per second) torsional pendulum completely enclosed in a vacuum tank. As the pressure of oxygen in the heat treating atmosphere changed, the portion of the internal friction vs temperature curves ascribed to grain boundary relaxation changed correspondingly, Fig. 1. The decrease in the damping capacity at high temperatures as the pressure of oxygen in the heat treating atmos-

Jan 1, 1955

By W. Rostoker, S. Spachner

A N alloy of 50 pct Ni-50 pct Fe is currently manu- factured in tape thickness down to 1/8 mil. In the annealed form, this alloy produces an almost square hysteresis loop. This has generally been related to the fact that by proper rolling and annealing practice a sharp cube, (100) [OOl], texture can be developed. As part of a program directed toward an understanding of the relationships between magnetic properties and structure of tape core materials, analyses were made of preferred orientations in tapes of various thicknesses. Annealed tapes of this alloy in 2, 1, 1/2, ¼, and Y' mil gages were acquired from commercial sources. Pole figures constructed for the 2 and 1 mil tapes showed the expected sharp cube texture. However, the ½, ¼, and ? mil annealed tapes showed no evidence of any preferred orientations. A comparison of two transmission patterns is shown in Fig. 1. The origin of the absence of texture in the tapes of less than 1 mil thickness was explored in some detail. The basic questions were whether the heat treatment for the thinner tapes was wrongly selected, whether the initial cold worked textures were different, or whether the actual thickness of the tape exercised some influence on its annealing characteristics. Quantities of the five gages of tape were acquired in the as-rolled condition just prior to the final anneal. Pole figures of the cold worked textures were constructed for each of the tapes. Eye estimates of in-

Jan 1, 1956

By H. Papazian, Robert A. Lad

SINCE it can be shown both theoretically'' : and experimentally that disordered Cu3Au has a greater internal energy than the ordered alloy, it might be expected that its chemical reactivity would be greater. Experiments were initiated' to test this hypothesis. This note will describe some recent results obtained in the study of the rates of corrosion of ordered and disordered polycrystalline Cu3Au by aqueous FeCl., The work of Robertson' has indicated that the attack by such solutions is intergran-ular and highly orientation dependent. It was of interest to see whether the order-disorder effect was great enough to overcome the variations from specimen to specimen which would arise from this type of attack. The polycrystalline alloy specimens (0.020 in. wire, 1¾ in. long) were preannealed in ½ atm H, at 700°C for 2 hr. The subsequent heat treatments to produce order and disorder were performed in M atm He. Disordered specimens were obtained by heating at 450°C for 2 hr and quenching in water. Ordered specimens were produced by heating for 2 hr at 450°, furnace cooling to 380°, and soaking at 380°C for 80 to 90 hr. Room temperature was reached by cooling to 150" at a rate never exceeding 7" per hr, and water quenching from 150°C. The specimens so produced exhibited electrical resistivities characteristic of the two states; of the order of 11.27x10 ohm-cm for the disordered, and 4.28x10 ohm-cm for the ordered specimens. The corrosion rates were studied at 30°C in ferric chloride solutions of several concentrations (?,¼, 1.5, and 1 molar). The specimens were attached to a stirrer during the tests. Tests were interrupted at intervals, and the specimen weight change was determined after washing and drying. Analysis of the solutions showed that the attack was limited to the copper. The higher corrosion rate for the disordered alloy, as illustrated in Fig. l, is typical of the results obtained. The effect of variation in ferric chloride concentrations is indicated in Table I for typical specimens. The variations in the ratio of reactivity for disordered and ordered specimens at the different concentrations are within experimental error, and the best value is estimated to be near 1.4. The experimental variation was due in part to the mode of attack, as mentioned, and in part to the fact that films were formed on the specimens under some conditions. Electron diffraction patterns of the films were very complex and indicated the presence of metallic iron, as did chemical analysis. In an attempt to eliminate the difficulties arising from the mechanism of attack, single crystal specimens were used. A greater reaction rate was again measured for the disordered specimens, but the reproduci-bility was no better than that for the polycrystalline metal. This would indicate that film formation was primarily responsible. It was concluded that the reaction with aqueous ferric chloride served to demonstrate that the reactivity of disordered Cu3Au is greater than that of the ordered alloy. However, the difficulties with film formation did not permit determinations of a precision great enough to warrant extension of the study to partially ordered alloy systems.

Jan 1, 1957

By M. B. Bever, J. E. Reynolds

IN several alloys of iron, copper, and lithium as well as in some pure metals, martensite formed on cooling reverts to the parent phase upon heating to a temperature below the equilibrium temperature at which the parent phase becomes stable.' These martensitic transformations, therefore, are thermally reversible, although appreciable hysteresis may be involved. The martensitic reaction has long been

Jan 1, 1953

By A. L. Titchener, M. B. Bever

FROM their investigation of the martensitic transformation in Cu-Zn alloys, Greninger and Mooradian' concluded that there was no critical temperature at which martensite formation began in this system. Recent unpublished work by Gen-evray With two compositions of brass revealed the existence of a critical temperature, which is a function of composition and stress. In the work reported here the temperature range of the martensitic reaction was studied as a function of composition in high purity Cu-Zn alloys. The specimens were about 4 in. long with a diameter of 1/16 in.; their compositions are given in Table I. They were heated under vacuum for 5 min at 5" to 10°C below the temperature of incipient melting, and quenched into brine at about — 10°C. Specimens of alloys C, D, E and F were obtained with little or no precipitated a phase. Many attempts yielded only three usable specimens of alloy B, and even these contained appreciable amounts of a. All efforts failed to preserve metastable p in alloy A (containing 38.02 pct Zn and 0.002 pct each of Pb and Fe). The transformation was studied by measuring the electrical resistance during continuous cooling and heating of each specimen at similar rates. The cooling media were alcohol with dry ice from room temperature to — 78°C and a bath of petroleum ether and methyl cyclohexane (75:25), cooled by liquid nitrogen, from —78" to about —150°C. Readings were also taken at —195 °C in liquid nitrogen. Fig. 1 illustrates a typical experiment. The relative resistance is obtained by assuming the known

Jan 1, 1955

By O. Katz, A. Spilners, M. Simnad

THE oxidation of titanium has been studied in recent years by a number of investigators.'-W ne of the most important aspects of the reaction of titanium with oxygen, which has been observed by several of the investigators, is the extremely high solubility of oxygen in the metal. A detailed study of the Ti-0 systeml% as shown that the solubility limit of oxygen in a-titanium is approximately 14.5 wt pct 0 from 800" to 1700°C. The unusual oxidation behavior of titanium may be ascribed to this phenomenon, since part of the oxygen uptake enters into solid solution in the metal and only a part is available for scale formation. A more complete study of the kinetics of oxidation of titanium would require information on the influence of oxygen in solution in the metal upon the oxidation rate. Such information would also be of interest in regard to the theory of oxidation of metals. The authors have measured the oxidation rates of oxygen-saturated and oxygen-free titanium between 800" and 1200°C and have found appreciable differences in their rates of oxygen uptake and in the activation energies. The experimental set-up was similar to that described in a previous paper.u The course of oxida-dation was followed continously by attaching the specimen to a sensitive spring balance and observing the extension of the spring with time of oxidation. High purity electrolytic oxygen was used and precautions were taken to purify the gases employed. The specimens were prepared from iodide titanium and were ground on metallographic polishing papers to a fineness of 4/0. The furnace was first evacuated and filled with argon; the specimen was lowered into the furnace, which was then evacuated and filled with oxygen, after the specimen had reached the oxidation temperature in argon. The samples were presaturated with oxygen by means of the following procedure: Each specimen was first heated in oxygen at 1200°C until its increase in weight indicated 13.8 pct by weight uptake of oxygen. The furnace was then immediately evacuated and filled with purified argon five times. The specimen was heated in the argon atmosphere for a period of 72 hr at 1200°C in order to saturate the metal with oxygen by complete absorption of the scale. The temperature was lowered to the oxidation temperature, the furnace was evacuated and filled with oxygen, and the oxidation rate was followed by noting the extension of the spring balance. No oxide film was visible on these specimens at the start of the oxidation experiments. Titanium samples in the oxygen-free as-received condition were also oxidized and their oxidation rates measured. The results are shown in Figs. 1, 2, and 3, which indicate that the initial rates of uptake of oxygen by both the oxygen-saturated and oxygen-free specimens are parabolic at these temperatures. The rate of uptake of oxygen is, however, appreciably lower

Jan 1, 1956

By L. D. Wooddy, Robert Moscrip

The simultaneous solution of the volumerric balance and the unsteady-state equation has been used for several years to make performance calculations for combination drive reservoirs. This method makes possible the calculation of volumetric changes of fluids in the gas cap, oil zone, and aquifer which occur as a result of withdrawals and reservoir pressure changes. It does not provide a means for the determination of reservoir fluid distribution changes corresponding to these vollrmetric changes. A knowledge of the fluid saturation distribution in the reservoir at various stages of depletion is important for the determination of the efficiency of gas and water as oil-displacement media and, therefore, for the reliable predicrion of ultimate oil recovery. To provide this knowledge, the displacement equations are solved simultaneously with the volumetric balance and unsteady-state equations. The described calculation procedure has been used satisfactorily to analyze the past performance and to predict the future behavior of combination drive reservoirs under both primary and pressure-maintenance operations. INTRODUCTION The three basic mechanisms by which oil is displaced from a reservoir are: (1) dissolved gas drive—the displacement of oil by the expansion of liberated solution gas, (2) water drive—the displacement of oil by water which enters the oil zone from the aquifer, and (3) gas cap drive—the displacement of oil by gas which ex- pands into the oil zone from the gas cap. The action of gravitational forces may be effective in increasing the efficiency of the basic drive mechanisms. Gravitational forces favor the segregation both of gas and oil and of oil and water, thus tending to shorten the transition zone between oil and displacing fluids. Most reservoirs produce under the influence of a combination of these drives and are designated "combination drive reservoirs". Fig. 1 is a cross section of a typical combination drive reservoir. A calculation procedure for analyzing the performance of combination drive reservoirs has been developed by combining the displacement equations' with the volumetric balance equation' and the unsteady-state equations. The pressure-production performance and the positions of the gas-oil and oil-water contacts are calculated for several stages of reservoir depletion by solving these equations simultaneously, thus affording a basis for: 1. Determining instantaneous and ultimate oil, gas, and water production under various operating conditions. 2. 'Establishing a maximum efficient rate of production, 3. Determining the advantages of pressure maintenance and unitization, and 4. Designing surface installations necessary for primarv and pressure-maintenance operations. DEFINITIONS The calculation procedure for combination drive res-

Jan 1, 1957

By F. D. Wright, H. D. Fara

The solution to the plastic and elastic stresses around a circular shaft in a hydrostatic stress field that has appeared in two editions of a widely used book on rock mechanics1 is in error. Although this is a relatively minor matter, the correct solution was not found by a literature survey, so it appears worthwhile to present it. For a homogeneous, isotropic, rigid plastic-elastic body in plane strain which obeys Tresca's yield criterion the following equations must be satisfied:'," In the plastic zone,

Jan 1, 1963

By B. L. Averbach, M. Cohen, G. P. Conard

IT has been frequently observed that, when metal crystals are bent and annealed or when they are bent at elevated temperatures, the asterism of the Laue spots is split discontinuously into tiny intensity maxima. This finding indicates that segmented crystallites or subgrains are produced, which are relatively undistorted within themselves but which differ slightly in orientation from their neighbors. The following viewpoints have been put forward concerning the nature of this segmentation process: 1—Crussard' has described the phenomenon as "re-crystallization in situ." According to this mechanism, the deformed lattice recrystallizes on heating into an aggregate of comparatively strain-free subgrains separated from one another by low-angle boundaries and having nearly the same orientation as the original crystal. This process differs from the classical type of recrystallization in that the latter involves the formation of grains having quite different orientations from that of the mother crystal. 2—A similar but more detailed picture has been advanced by Cahn' who adopted the term "polygonization." In this interpretation, the plastic bending of lattice planes results in an excess of dislocations of one sign, but at suitable temperatures these dislocations migrate along slip planes and collect in localized regions to form an array of low-angle boundaries. Concurrently, the lattice segments between the boundaries lose their curvature and elastic strain. 3—The "cell formation" concept of Wood and co-workers: unlike the two hypotheses cited, postulates that the segmentation of the lattice is basically a mode of deformation and is not an annealing phenomenon. Cell formation appears to compete more effectively with respect to the normal slip process as the deformation temperature is increased and as the strain rate is decreased. The present work was performed on 3.2 mm diameter 99.99' pct Zn single crystals, grown from the melt in a gradient furnace. The major impurity was 0.003 pct Fe. The crystal orientations ranged from those with basal plane parallel to the rod axis to those with the basal plane almost perpendicular to the rod axis. The specimens were bent on templates to effective radii varying from 14.2 to 1.3 cm at the temperatures from —196" to 100°C. In each case, the axis of bending was parallel to the basal plane. Subsequent annealing was carried out at temperatures from —196" to 400°C. Back-reflection Laue pictures were taken on the convex surface of the bent specimens, before and after annealing. This procedure was found to yield better resolution of the detail in the diffraction spots than did the previously used Laue transmission technique. Some X-ray pictures of rods bent at —196" and —78°C were taken at these respective temperatures without intermediate warming to room temperature. In addition, bent crystals were acid cut" parallel to the basal plane, and double-crystal spectrometer rocking-curves were obtained from the etched (0001) face before and after increment an-

Jan 1, 1954

By L. M. Howe, J. Gordon Parr, E. Saarema

THE decreasing solid solubility limit at the titanium-rich end of the Ti-Cu constitutional diagram,' Fig. 1, suggests the possibility that titanium-rich alloys may be age-hardenable. However, results obtained by Holden et al. reproduced in Fig. 2 show that after quenching from 790°C the age-hardening of an alloy containing 1.7 pet Cu is very slight, while a 0.8 pet alloy decreases in hardness, during heat treatment at 400°C. It was believed possible that powder samples of alloys might show different results from the lump samples used by Holden et al., since small particles are often more sensitive to diffusion processes than larger samples. Consequently, a 1.9 pet (by weight) Cu alloy was made by the technique of levitation melting," checked for homogeneity, and filings of 48-65 Tyler screen size were cut from it for aging experiments. The filings were helium-quenched (by a technique described previously)' from 790°C, sealed in vacuo in silica tubes and aged at temperatures of 400°, 450°, and 500°C. Microscopic and X-ray examinations failed to reveal any structural changes during the aging process. This is not too surprising since early stages of precipitation do not usually manifest themselves in ways that are readily detectable by metallographic methods, and the extent of precipitation on overaging a 1.9 pet alloy is very small. However, hardness readings (taken on a Bergs-man micro hardness tester, using a 25 g load applied to a diamond indenter) do show a hardness peak at each aging temperature, Fig. 3. About a dozen readings were taken on each heat treated sample; the highest reading and the lowest reading were ignored and an average taken of the remaining values. In

Jan 1, 1957

By Carl E. Johnson

INTRODUCTION A method for predicting water-flood oil recovery was reported by H. Dykstra and R. L. Parsons' in 1950. It is now generally known as the Dykstra-Parsons method and is widely used by petroleum engineers. The method is semiempirical and consists of a correlation of four fundamental variables. These are: V, vertical permeability variation;' a, mobility ratio; Sw initial water saturation; and R, fractional recovery of oil in place at a given producing water-oil ratio. The correlation extends over a wide range in each of these variables, and may be applied to all formations with initial oil saturations of 45 per cent or greater. The method of calculation originally outlined by Dyhtra and Parsons closely follows their derivation. And this is a convenient way of illustrating the development of some rather complicated ideas. However, in actual use it is more cumbersome than necessary. The purpose of this note, therefore, is to provide a simplified method for making Dykstra-Parsons predictions. A SIMPLIFIED GRAPHICAL SOLUTION The correlation between V, a, Sw and R, corresponding to a given producing water-oil ratio, can be shown on a single graph. This is best done by plotting V against a to show lines of constant R(1 - S, . WOR-0.2). Figs. 1, 2, 3, and 4 show these plots

Jan 1, 1957

By J. W. Fredrickson

VERY little information is available in the literature concerning the solubility of magnesium in titanium. Aust and Pidgeon&apos; report the solubility of titanium in magnesium to be 0.0025 pct at 650°C and 0.015 pct at 850°C. X-ray diffraction studies failed to detect any evidence of solid solubility. Based on the fact that the addition of titanium to magnesium increases the c/a ratio of magnesium, Busk&apos; suggested that the Mg-Ti system, like the Mg-Zr, is a peritectic. Eisenreich- eported the solubility of titanium in magnesium to be 0.003 pct at 655°C and 0.064 pct at 760°C. Removal of hydrogen from the melt increased the solubility of titanium to 0.115 pct at 800°C. Eisenreich proposes a peritectic-type diagram for the high magnesium side of the system. Recent work&apos; with Ti-Mg diffusion couples indicate that the solid solubility of titanium in magnesium is extremely small and that there is limited solid solubility of magnesium in titanium. Experimental work on the Ti-Mg system is complicated by the fact that the boiling point of magnesium is considerably below the melting point of titanium. Consequently, the usual alloying methods are impractical. Alloying was accomplished in this investigation by sheath-rolling compressed compacts." The alloys were made from titanium sponge and high purity magnesium. Chemical analysis of the sponge showed 0.04 pct Mg, <0.005 pct Al, <0.001 pct Cu, 0.05 pct Fe, 0.022 pct Mn, <0.0025 pct Ni, 0.007 pct Si, <0.005 pct V, and <0.01 pct Zn. All heat treating was conducted in a protective atmosphere by encapsulating the specimens in fused silica ampules under a partial pressure of helium. Equilibrium was achieved by holding the specimens at temperature for periods of 24 to 120 hr. The alloys were hot rolled, cold rolled, and annealed prior to solution heat treatment. Fig. 1 shows the constitutional diagram obtained for the Ti-Mg system up to 1.5 pct Mg. Oxygen was known to be present in the alloys; therefore, it is necessary to consider the alloys as ternary rather than binary and the diagram should be viewed as a plot of a section through the Ti-Mg-0 system. Other investigatorso have shown that the addition of oxy- gen to titanium stabilizes the a phase. The data presented in Fig. 1 indicate that the addition of magnesium to titanium tends to stabilize the p phase. Armour Research Foundation7 has shown that the addition of magnesium to zirconium lowers the a transus and is classified as a p stabilizer in that system. Magnesium is soluble in solid titanium to the extent of at least 1.5 pct in both the a and /3 phases. No intermetallic compounds or magnesium-rich phases were observed either by light microscopy or X-ray diffraction. However, this does not negate the possibility that such phases exist at higher alloy concentrations.

Jan 1, 1956

By E. R. Brownscombe, Francis Collins

The pressure distribution in a reservoir producing an incompressible fluid by radial flow in a horizontal structure is a simple logarithmic function&apos; used daily by reservoir engineers. The assumption of an incompressible liquid is equivalent to assuming that pressure is maintained constant at the well radius and at some external "radius of drainage," or, in other words, that the entire flow into the well passes across the external radius. In most cases a well is surrounded by other wells draining adjoining areas so that the "radius of drainage" is not a line of constant pressure with flow equal to the flow into the well but rather a contour of zero pressure gradient across which no flow occurs, production being due to the expansion of the liquid within the area. The radial flow steady state pressure distribution for this case does not seem to be extensively used despite the fact that the mathematical analysis has been given in detail&apos; and the results are simple and generally applicable. &apos;The object of this discussion is to develop this result from a physical rather than a mathematical viewpoint, thereby aiding intuition in judging circumstances to which it may be applicable. If the production rate at a well in an unsaturated reservoir is maintained constant while no flow occurs across the outer radius a steady state will soon be reached in which the flow rate or pressure gradient is constant with time at all points in the reservoir. To preserve such a condition it is necessary that the pressure decline at the same rate at all points in the reservoir, that is, the curves of pressure versus radial distance at successive times are all parallel. Then each unit volume of oil is expanding at the same rate and contributing an equal share to the production. The rate of flow q across any circle r is thus proportional to the volume of the reservoir between r and the external radius re, or q = qw (I-r2/r2e) ......(1) where q, is the production from the well and it is assumed that rw is very small compared with re. This equation can be combined with the differential form of Darcy&apos;s law for radial flow, 2phkr dp q =—— ........(2) aµß dr ( where q is not a constant as in the incompressible flow case but is a function of r given by Equation (1). If Equation (1) is substituted in Equation (2) the variables p and r can be separated and the result integrated to obtain the pressure distribution p = pw +--------In------------- 2pkh[ rw 2re2] ......(3) This equation differs from the incompressible case only in the addition of the term proportional to the square of the radius

Jan 1, 1950

By F. G. Stone

A strain anneal process has been developed for the production of iron tensile test specimens, the gauge length consisting substantially of a single crystal. Since the method has been quite successful and the results of general interest, the process will be described in detail. The essential feature of the method is the continuous, slow increase of furnace temperature during the grain growth annealing treatment. Briefly, the procedure is as follows: I. Heat machined bars to 950°C in vacuum, hold I hr, furnace cool. 2. Strain to 3.5-3.8 pct elongation (axial loading). 3. Anneal, continuously raising furnace temperature from 450 to goo°C at a rate of so0 per day. 4. Hold at 900°C for 100 hr, furnace cool. Tensile test bars with a 1/4- X I-in. gauge section have been machined from 35 in. Armco iron plate and from 3/8 in. rounds of Puron, a high purity laboratory iron. The axes of the test bars were parallel to the rolling direction. During the machining operation the bars were polished in the lathe with No. 600 emery paper, and this polished surface proved satisfactory for subsequent macrographic examination. A micrographic examination of the materials showed that both were high in FeO inclusions, those of the Puron being smaller but much more numerous. An initial vacuum anneal of I hr at 950°C followed by furnace cooling resulted in a ferritic grain size of ASTM No. 3 for Armco and No. I for Puron. Special heat treatments which reversed these initial grain sizes produced no marked improvement in single crystal production after subsequent treatments. The strain for subsequent grain growth was determined by measuring the decrease in diameter of the tensile bar during elongation. The change in diameter could be measured with a micrometer to +0.0001 in., corresponding to an accuracy of 0.08 pct for the elongation. The accuracy of the diameter measurement is also dependent on grain size because of surface roughening during elongation, and for this reason, a No. 3 grain size is preferable. Optimum grain growth was obtained for strains between 3.5 and 3.8 pct elongation. Once this critical range had been cstablished, all tests were held within it, and thus only meager data were obtained on grain growth following strains outside this range. In general, grain size decreased with increasing strain to about 5.5 pct elongation. Grain growth was occasionally ohserved with less than 3.5 pct elongation although this may have been the result of error in measurement. The program control device for the grain growth anneal consisted of a I rpm motor and worm gear drive, operating the dial shaft of a pyrometer controller through a pulley. Dial speeds of 33 and 50°C per day were tried, but the results at the slower speed were not sufficiently better to warrant the increased furnace time. The furnace tube was evacuated at intervals during the run and kept sealed the remainder of the time. When the controller reached 900°C, it was stopped and the temperature held for 100 hr. This eliminated most of the numerous minute crystallites of about 0.5 mm dimension usually visible on the etched surface of the single crystal. Since recrystallization occurs at the A3 point, the top temperature of 900°C provided a 10"

Jan 1, 1949

By E. R. Morgan, J. C. Shyne, V. F. Zackay

NITROGEN used as an alloying element in steel has received increased attention in recent years. Its merit as an austenite stabilizer and hot strengthener has long been recojinized, particularly by European investigators.&apos; Recent work&apos; indicates that nitrogen contents of 1/2 pet or more allow the addition of several percent of ferrite-forming hot strengtheners, such as molybdenum, without subsequent austenite decomposition at elevated temperatures. The room temperature properties of such alloys are characterized by high yield and tensile strengths with excellent ductility, even after cold working, as shown in Tables I and 11. The 1350°F creep-rupture properties of Cr-Mn-Mo-N steels are comparable to those of commercial alloys such as Timken&apos;s 16-25-6, containing 16 pct Cr, 25 pct Ni, and 6 pct Mo, as shown in Table 111. Cr-Mn steel containing 1/2 pet N must be made under pressure if ingot gassing is to be avoided. However, there are difficulties attendant to this practice. Pressure melting restricts the ingot size, and the equipment required is costlier and more complicated than comparable air melting facilities. An effort was made, therefore, to determine more economical methods of adding nitrogen. The pressures generated in centrifugal casting usually range from 5 to 10 atm and are sufficient to prevent the gassing of high nitrogen Cr-Mn steels. A centrifugal casting was made of an alloy containing 16 pct Cr, 18 pct Mn, 2 pct Mo, and 0.73 pct N. A risk, 8 in. diam and 11/2 in. thick, was cast at 1000 rpm. It has been calculated that a pressure of 9 atm was developed at the periphery of the disk at this speed. Metallographic inspection of specimens taken from the disk revealed no gas holes or other defects. The elevated temperature properties of radial and circumferential specimens taken from this casting are given in Table IV. The creep-rupture life of this cast nickel-free austenitic steel was equivalent to that of the wrought Cr-Mn-Mo-N steels. Although centrifugal casting appears to lend itself to the manufacture of high nitrogen austenitic steels, its applicability is limited to relatively small sizes. A process applicable to the production of large ingots of high nitrogen steels is suggested by low carbon rimming steel practice. Gas holes formed during ingot solidification are not detrimental so long as they weld shut during hot rolling. An economic advantage of gassing ingots is the increased ingot-to-slab yield, especially if the ingots are mechanically capped. Also, it is probable that higher nitrogen levels can be achieved with mechanically capped ingots than with hot-topped ingots. A series of gassy heats was made under both atmospheric and higher pressures, as indicated in Table V. Several of the air melted ingots were mechanically capped by chilling the molten ingot tops with a steel plate. The ingots were allowed to freeze in steel molds without hot-tops unless otherwise indicated. A comparison of Table 111 with Table V shows no significant difference in the creep-rupture properties of the gassy and the nongassy ingots after hot work- ing nor between the gassy ingots produced under different conditions. References 1 F. Rapatz: Application of Stainless and Heat Resisting Steels Alloyed with Nitrogen. Sinhl and Eisen ( 1941) 61, pp. 1073-1078. &apos;V. I?. Zackay, J. F. Carlson, and P. L. Jackson: High Nitrogen Austenltlc Cr-Mn Steels. Trans. ASM 119551 48, PP. 509-523.

Jan 1, 1957

By L. D. Jaffe, R. K. Pitler

IT would clearly be advantageous to produce molten titanium, suitable for alloying and casting, directly from the relatively inexpensive tetra-chloride, without using a metallic reducing agent. Accordingly, a preliminary investigation has been made of the production of titanium by hydrogen reduction of the tetrachloride in an electric arc furnace. For the reaction: TiCl4(g) + 2H2(g) ? Ti(s) + 4HCl(g), Lockhart and his colleagues&apos; have calculated equilibrium constants at 800" to 1500°K, based on tables of Brewer.&apos; Extrapolating these data on the assumption that the heat of reaction varies linearly with temperature, and using Brewer&apos;s value for the heat of fusion, there is obtained for the reaction: TiCl4(g) + 2H2(g) ? Ti(l) + 4HCl(g) an equilibrium constant at 2100°K (100" above the melting point) Kp = (PHCl)4/pTlcl4 (Ph2)2 = 0.167 atm. If this is correct, starting with hydrogen saturated with TiC14 at 25°C, where the vapor pressure of the latter3 is 12.6 mm, and maintaining the overall pressure at 1 atm, 99 1/4 pct of the TiC14 would be reduced to Ti at equilibrium. An arc furnace designed for the melting of titanium and lined with water-cooled copper was used for the preliminary experimental check. Its inside diameter was 2 7/16 in. and height 6 in. The water-cooled electrode was tipped with 3/4 in. diam tung-sten. In the one run carried out, the furnace was charged with a starting batch of 293.35 g of scrap titanium,&apos; analyzing 99.24 pct Ti. After the system was twice pumped out and flushed with argon to remove air, the arc was struck in argon and kept at 400 amp dc, electrode negative, for 1 min to melt the starting batch. Commercial tank hydrogen, dried by passing over silica gel and bubbled through technical grade TiC14 at room temperature, was then admitted to the furnace. The inlet tube directed this gas downward toward the arc and melt; the gas outlet was at the top of the furnace. The quantity of gas passed through was not measured accurately but is estimated to be about 50 liters per min at a few mm of mercury above atmospheric pressure. The arc was held in the H2-TiC14 mixture at 400 amp with little difficulty. After 10 min the arc burned through the copper lining above the melt, admitting water and ending the run. (This had happened frequently in straight melting runs under argon, and is not thought due to the atmosphere used.) In the furnace were found an ingot, several small pieces, and a little metallic powder, evidently formed when water entered the hot furnace. Some titanium also clung to the electrode. The portions were weighed and separately analyzed for titanium. Their total weight was 321.76 g of 94.82 pct overall purity. Much of the impurity consisted of tungsten broken off when the titanium was removed from the electrode. No detailed impurity analysis was made because the starting materials were impure and flooding the furnace introduced further contamination. Thus, the metal recovered contained 305.08 g Ti, as compared to 291.12 g in the starting batch. Titanium could not have been carried over from previous melting runs in the furnace, as the interior was sandblasted and the electrode ground clean before the run. Evidently at least 13.96 g of Ti were produced from TiCl4. Since this would require complete reduction of 430 liters of TiCl, gas at 12.6 mm of Hg, the efficiency of the process must have been rather high. Experimental work is continuing. No reason is seen why the process could not be scaled up to the size of a 30-ton steel-melting arc furnace. In a large unit there would be a large molten pool from which liquid metal could be withdrawn for alloying and casting. The problems of electrodes and power supply are similar to those arising in arc furnaces for melting titanium. Unreacted TiC14 and the HC1 in the exhaust gases could be recovered; unreacted H2 could be dried and re-used. The melt would be saturated with hydrogen, whose solubility in liquid titanium is unknown. Small amounts of hydrogen seem to have little effect on the properties of titanium.5 If the amount introduced was so large as to impair properties or cause casting difficulties, it could be reduced by holding the melt under an inert gas or by pumping on it, prior to casting. Acknowledgment The authors would like to thank I. Preble and M. Goldman for their valuable aid in the experimental work and the thermodynamic calculations, respectively. References 1R. J. Lockhart, J. J. Ward, M. J. Hussey, and J. W. Clegg: In unpublished report, "U. S. Air Force Project Rand. Titanium and Titanium Base Alloys." Battelle Memorial Institute (1949) 37-44. 2 L. Brewer et al: Chemistry and Metallurgy of Miscellaneous Materials—Thermodynamics. Ed. by L. L. Quill. pp 13-39, 60-192. (1950). McGraw-Hill Book Co. 3 K. Arii: Scientific Reports. Tohoku Imp. Univ. (1933) 22, 182. 4 R. S. Dean, J. R. Long, F. S. Wartman, and E. L. Anderson: Transactions AIME (1946) 166, 369-381; Metals Technology (Feb. 1946) TP 1961E. * R. I. Jaffee and I. E. Campbell: Transactions AIME (1949) 185, 646-654; Journal of Metals (Sept. 1949) TP 26813.

Jan 1, 1951