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By H. R. Thresh, A. F. Crawley, D. W. G. White

The densities of liquid tin, lead, and Sn-Pb alloys have been measured over a range of temperature above the liquidus. In all cases, data can be adequately represented by an equation of the type p = a + bT. For pure tin, the values of a and b are, respectively, 7.139 and 7.125 x 10-4, and for pure lead, 11.060 and 12.220 x 10-4. At constant temperature, molar volumes in the Sn-Pb system vary linearly with composition. DURING the course of a long-term program at the Department of Energy, Mines and Resources, Ottawa, Canada, the densities of liquid tin, lead, and Pb-Sn alloys were studied. The work reported herein draws on two sets of results independently achieved by Thresh, on the one hand, and by Crawley and White, on the other. EXPERIMENT The method and apparatus were originated by Thresh and have been described in detail in Mines Branch reports.172 In operation, the 14 cu cm graphite pycnometer is put in the furnace as shown in Fig. 1 after a machined charge has been placed inside the pycnometer and the lid screwed down. The dimensions of the charge are such that, upon melting, a small excess of liquid metal is discharged through the capillary hole to displace the weighted float above. When the pycnometer has been equilibrated at the experimental temperature, the

Jan 1, 1969

By J. H. Swisher

The solubility of graphite in CaO-S2O2-Al,O3 slags was measured by equilibrating slag samples with graphite crucibles and CO gas. Carbon contents as high as 2 ut pct were obtained in CaO-saturated, CaO-A1,O3 slags, and 1.3 wt pct in slags of the composition CaO.Si0,. Although the observed conditions for Sic formation were in agreement with those predicted from thermodynamic data, CaC, was found to form at a lower temperature than predicted frotn thermodynamic data. From measurements of the equilibrium carbon content as a function of CO Partial pressure, it was found that carbide ions dissolve in CaO-A12O3 melts with a valence of minus two. The carbon content increased with CaO concentration in Ca0-Al,O3 melts and increased with SiO, content along the CaO'AlO3-CaOSi0 join in the ternary system. When solid CaC2 was added to CaO-A12O3 and CaO-SiO2-A12O3 slags, it was found that one of the oxides in the slag was reduced by the carbide (Al2O3 in the forrner and SiOz in the latter). In electric furnace steelmaking, a double-slag practice is frequently used to meet alloy specifications. Initially a flush slag, which is oxidizing in nature, is used to remove phosphorus and carbon from the steel bath. Later in the refining period, the flush slag is replaced by a highly reducing carbidic slag. When calcium carbide is formed in or added to a finishing slag, the slag is effective as a desulfurizing agent and also permits alloying elements such as chromium, vanadium, and tungsten to be added to the slag in the form of oxides. The oxides are readily reduced by calcium carbide, thereby minimizing the use of expensive ferroalloys. More work has been done on the thermodynamics of silicon carbide in slags than on calcium carbide. Baird and alor' and Kay and alor' determined the free energy of formation of Sic by measuring the partial pressure of CO in equilibrium with solid silica, silicon carbide, and graphite. Using a similar technique, they determined SiOz activities in CaO-SiOz and Ca0-Si0,-A1203 slags. Rein and chipman3 also determined the free energy of formation of Sic using slag-metal equilibrium measurements. A literature survey has uncovered only one experimental study of the behavior of CaC, in slag systems. Shanahan and cooke4 report the results of some preliminary experiments on the solubility and stability of CaC, in a CaO-A1,03 and a Ca0-Si0-A1,03 slag at a temperature of about 1500". The carbon solubility as CaC, in a slag containing 50 pct CaO and 50 pct A1203 was reported to be 0.6 pct. They also review earlier work on the binary CaO-CaC, system. A eutectic exists in this system, but various investigators disagree on the eutectic temperature and composition. eal has given an explanation for carbide furnace erruptions in terms of the thermodynamic properties of CaC,; his analysis is not based on experimental data, but on compiled data for the free energies of formation of CaC, and CO.' , These data for steel-making temperatures are all extrapolated from the results of low-temperature measurements. In the experiments described in this paper, slag samples were equilibrated with graphite crucibles and with mixtures of CO and argon or with CO gas at 1 atm total pressure for measurement of the carbon solubility. Most of the work was done on Ca0-A1203 binary slags, although in some experiments CaO-SiO, and Ca0-Si0,-A1,03 slags were used. EXPERIMENTAL Slag samples of the desired composition for the solubility measurements were obtained by blending pre-fused master slags. The master slags were prepared by fusing mixtures of reagent-grade CaC03 with either A1,03 or Si0, in a graphite crucible. The master slags were crushed, then decarburized in air in a muffle furnace at 1200O C. A schematic diagram of the apparatus is shown in Fig. 1. The source of carbon for the solubility meas-

Jan 1, 1969

By R. E. Smallman, I. Milne

The deformation behavior of single crystals of Nb-Mo alloys has been investigated with particular reference to the influence of composition, orientation, and temperature. Strong solid-solution hardening was observed reaching a maximum at the equiatomic cotrlposition and can be attributed to the difference in atomic size between niobium and molybdenutrz. Changes in the form of stress-strain curve, as shown by a high work-hardening rate and restricted elongation to fracture, were observed at a composition of Nb-85 pct Mo and are attributed to the presence of MozC DreciDitate. Conjugate slip was only extensive in dilute alloy samples; at the 50/50 composition deformation rnainly occurred by primary slip, and the onset of conjugate slip gave rise to failure by cleavage on (100). The variation of yield stress of Nb-50 pet Mo with orientation was consistent with slip on (011)(111) slip systems. The temperature deperndence of the yield stress between -196" and 250°C was similar to that of pure bcc metals, but at a much higher stress level; no evidence for twinning %as found. IN recent years the deformation behavior of various pure metals in groups VA and VIA has received considerable attention, but surprisingly little work has been carried out on binary alloys made by mixing metals from the two groups. Such an investigation would be of interest since single crystals of metals of group VA have been shown to deform characteristically with a multistage deformation curve1"3 while a parabolic type of deformation curve has been reported for most of the group VIA metals.4'5 It has been suggested by Law ley and Gaigher~ that the difficulty encountered in obtaining multistage deformation curves for molybdenum in group VIA was possibly because of the presence of a microprecipitate of MozC which they observed even at carbon contents as low as 11 ppm. Recently a multistage deformation curve has been reported for molybdenum ," although the stages are not so definitive as those for group VA metals. The binary alloys of the particular refractory metals which have been investigated in single-crystal form include Ta-w,' Ta- Mo,' and Nb- Na." While a large amount of hardening was observed for alloys of the Ta-W and Ta-Mo systems, associated with room-temperature brittleness for alloys approaching the equiatomic composition, Ta-Nb remained ductile over the complete composition range with little or no solution hardening. Other systems have been investigated by hardness measurements on polycrystalline material and a discussion of the hardening of these alloys has been presented by ~udman." The purpose of the present investigation was to examine the deformation behavior of Nb-Mo alloys in detail, with particular reference to alloy composition and single-crystal orientation. In this way it was hoped to shed some light upon the restricted ductility of these alloy specimens. 1) EXPERIMENTAL PROCEDURE The starting materials were obtained in the form of beam-melted niobium rod and sintered molybdenum rod of suitable dimensions. Since niobium and molybdenum form a complete solid-solution series at all temperatures, alloy single crystals were produced by melting the two constituents together in an electron bombardment furnace (EBM). To produce specimens free from segregation a molten zone was passed over the length of each rod six times in alternate directions at a speed of 10 in. per hr. Typical specimens were analyzed for interstitial impurities by gas analysis and for metallic impurities by spectrographic analysis. The results of this analysis are shown in Table I. Many of the tensile specimens were also analyzed (after testing) by scanning the gage length in an electron beam microanalyzer, from which it was found possible to predict the approximate composition of a specimen from the original proportions of each element in the EBM. The tensile specimens were made with a gage length of 0.5 in. and diameter of 0.075 in., using a Servomet Spark machine. By careful machining on the finest range for the final i hr of this technique, surface cracks could be reduced to the level where they were easily removed by electropolishing in a solution of nitric and hydrofluoric acids. The specimens were strained at a rate of 10 4 sec-' using friction grips designed to prevent accidental straining and maintain a good alignment before straining. The orientations of the individual specimens tested are shown in Fig. 1 and the corresponding compositions listed in Table I1 together with collated experimental data. 2)RESULTS a) General Deformation Behavior. The effect of composition on the room-temperature deformation curves of similarly oriented specimens is shown in Fig. 2. The yield stresses of the pure constituents, while not the lowest reported to date, were at least comparable with existing data. Although the solution hardening was large for alloys at either end of the phase diagram, and comparable with the Ta-W solution-hardening data of Ferris et a1.,8 the low work-hardening rate characteristic of niobium was sustained until a composition of Nb-85 pct MO had been reached. Associated with the peak yield stress ob-

Jan 1, 1969

By L. Yarborough, L. R. Smith

This paper presents results of a laboratory study of retrograde condensate recovery by revaporization into dry injection gas. Flow tests were performed in 10.6-ft long sand packs at 100F and 1,500 psi. In three runs methane revaporized the liquid from a n-pentane-methane mixture in the presence of immobile water. TWO of these tests were water-wet, and the third was totally oil-wet. In the three runs n-pentane recovery was complete after 2.5 hydrocarbon PV of injection. There was no significant performance difference between the two wettability extremes. In a fourth experiment, a methane-hydrogen sulfide mixture revaporized a synthetic light, sour condensate. No water saturation was present. Equilibrium compositions and volumetric data were obtained for the four-component condensate. The heavy component, n-beptane, was removed after 6 PV production. Comparison of the effluent fluid compositions with known equilibrium data shows that the flowing fluid was equilibrium vapor and that the mixing zone between equilibrium vapor and dry injection gas was short. Data indicated that complete recovery of retrograde liquid occurred after it was contacted by a sufficient quantity of dry gas. INTRODUCTION When pressure declines below the fluid dew point in a gas condensate reservoir, a liquid phase forms. In this process, referred to as retrograde condensation, the quantity of liquid formed is frequently small enough that the liquid is not a flowing phase. To prevent loss of valuable retrograde liquids, the process of dry gas cycling has been employed for several years as a more or less standard practice. In this procedure the reservoir pressure is maintained above the fluid dew point so that the liquid components may be produced as vapor and then separated at the surface. Although full pressure maintenance by gas cycling seems ideal in terms of preventing liquids loss, several factors can reduce the atuactiveness of such an operation. From a study of a condensate reservoir in Alberta, Canada, Havlena et a1.1 con-cluded that cycling under conditions of declining pressure leads to economic advantages and to a high recovery of hydrocarbon liquids. This study considered effects of volumetric sweep efficiency, retrograde behavior of the original wet gas and revaporization characteristics of the retrograde liquid when contacted by dry gas. The first major work concerning revaporization of liquid in a gas condensate system is that of Standing et a1.2 Calculations based upon the PVT behavior of a recombined gas condensate fluid indicated that all retrograde liquid can be recovered if it is contacted by a sufficient quantity of dry gas. The paper considered the effect of variable permeability upon the recovery of retrograde liquid. Standing et al. concluded that recovery of heavier components in the retrograde liquid is greatest if reservoir pressure is allowed to decline below the dew point prior to dry gas injection. Since the work of Standing et al., several laboratory studies have been reported which show that recovery of hydrocarbon liquids by vaporization into dry injected gas can contribute to increased recovery above that obtained by ordinary production practices. Vaporization from retrograde condensate,3 conventional oil4-7 and volatile oil8 reservoirs has been considered. There is little work that deals with revaporization recovery from condensate reservoirs. This study demonstrates that vapor-liquid equilibrium exists when a dry gas is injected into a porous medium containing retrograde condensate; investigates the effect of wettability on revaporization of retrograde condensate; and provides an indication of the amount of dry gas necessary to

Jan 1, 1969

By Laurance L. Oden

The Bureau of Mines studied three processes for preparing NaAl(OH)2C03) the intermediate compound which is calcined to produce alkalized alumina: (1) Mixing of Na2 C03 and of A12 (S04)3 solutions, (2) digestion of aluminum hydroxide in solutions of Na2C03 and NaHC03 at 90° C, and (3) addition of CO2 at 25° C to caustic solutions of aluminum to precipitate aluminum hydroxide followed by digestion at 90° C. The first process had the highest raw material consumption and washing requirements, and successful application of process 2 depended upon the availability of active aluminum hydroxide. Process 3 was the most effective, considering both process technology and raw material requirements. Procedures were also investigated for washing, filtering, drying, and calcining precipitates. Analytical methods included X-ray diffraction, atomic absorption spectroscopy, differential thermal analysis, and thermogravimetric analysis.

Jan 1, 1969

By L. R. Weisberg, E. A. Miller

Single-crystalline films of silicon of good quality were vacuum-deposited on sapphire. The improved crystallinity was achieved by the strict exclusion of oxygen from the evaporation system, including the use of a "oxygen-free" silicon source. To minimize possible contamination of the source, the silicon was sublimed from the solid at about 1390° C. using a simple electron bombardment system to heat the silicon. This resulted in deposition rates of about 5 to 7 µ per hr and film thicknesses of 4 to 20 µ. The vacuum during deposition was ordinarily about 5x 10-8 Torr, DESPITE the success achieved in the chemical vapor deposition of silicon on sapphire using Silane,1-4 vacuum deposition has not provided comparable properties. For example, Chu et a1.5 vacuum-deposited silicon on single-crystalline substrates of A12O3, Sic, ThO2, and other compounds, and, although some epi- but the use of ultrahigh vacuum (about 1 to 3 x10-9 Torr) during deposition did not significantly improve the results in the oxygen-free system. The crystalline quality of films deposited on (0001) sapphire was found to be considerably superior to (1102) sapphire surfaces. Using (0001) sapphire, single-crystalline films were deposited at temperatures as low as 780° C and as high as 1075°C, with the best crystalline quality obtained at about 1000°C. At this temperature, hole mobilities over 250 sq cm per v-sec were achieved. taxy was indicated, single-crystalline films were not produced. More recently, Salama, Tucker, and young6 evaporated silicon on single-crystalline sapphire, but only poor crystallinity was observed, and low carrier mobilities were measured. In the present experiments, good-quality single-crystalline films of silicon on sapphire have been achieved by specifically excluding oxygen from the evaporation. This included not only the use of a "clean" vacuum system but, of special importance, the use of an oxygen-free silicon source. This has also been shown to provide a dramatic improvement in silicon homoepi-taxy.7 As a result, silicon-on-sapphire films with hole mobilities over 250 sq cm per v-set were achieved, and single-crystal films were grown as low as 780°C and as

Jan 1, 1969

By Richard J. Fruehan

ThE thermodynamic activities of nickel and chromium in liquid Ni-Cr alloys have not been previously reported. There have been several investigations on the solid alloys.1-3 In the present investigation the activity of chromium in liquid Ni-Cr alloys at 1600° C was determined by the use of the following galvanic cell, The use of galvanic cells employing solid oxide electrolytes for determining the activity of metals in solid alloys was first demonstrated by Rapp and Maak4 on Cu-Ni alloys between 700° and 1000°C. Recently Schwerdtfeger5 tested the performance of the ZrO2(CaO) electrolyte at 1600°C and found it satisfactory for oxygen pressures as low as 10"12 atm. He also demonstrated the use of solid oxide electrolytes for determining the activities in liquid metal systems in measuring the activity of manganese in Fe-Mn alloys at 1500°C. Extensive investigations have been carried out in this laboratory, exploring the oxygen partial pressure lower limit at which ZrO2(CaO) electrolyte can be used satisfactorily in oxygen galvanic cells at 1600°C. In a paper to be published at a later date,9 it is demonstrated conclusively that ZrO2(CaO) exhibits insignificant electronic conductivity at oxygen pressures down to about 3 x 10"13 atm which is lower than the oxygen partial pressure in equilibrium with Cr-Cr2O3 at 1600°C. Therefore, the activity of chromium can be related to the measured reversible electromotive force of the cell in the present investigation since no electronic short circulating will occur. Fig. 1 is a schematic diagram of the cell used. The Cr-Cr2O3 electrode was made of equal weights of chromium and Cr2O3 powders which were mixed and packed into a recrystallized alumina crucible. A Pt-wire lead was embedded into the Cr-Cr2O3 compact to insure good contact. A ZrO2(CaO) crucible, supplied by the Zirconium Corp. of America, contained the Ni-Cr melt equilibrated with solid Cr2O3. The ZrO2(CaO) crucible was placed on the Cr-Cr2O3 electrode and additional Cr-Cr2O3 mixture was packed around it. Contact with the Ni-Cr alloy was made with a Cr2O3 tube, which is a weak electronic conductor. A platinum wire lead was attached to the Cr2O3 tube. The galvanic cell was lowered slowly into the hot zone of the furnace tube in order to avoid too large a thermal shock which could break the ZrO2 (CaO) crucible. The furnace was con- tinuously flushed with purified argon during the experiment. The temperature was measured with a Pt-Pt/10 pet Rh thermocouple and maintained at 1600° ± 5°C. The electromotive force was measured with a recording potentiometer. The furnace was turned off when measurements were being made in order to avoid induction effects and the reversibility of the cell was demonstrated in the usual manner. The electromotive force was measured several times over a period of approximately 1 hr. During that period the electromotive force remained constant within ± 3 pet and did not continuously drift in any one direction. After the experiment the alloys were analyzed for chromium in the usual manner. The measured electromotive forces of the cell at 1600°C, (2912°F), are listed in Table I. The activity of chromium, with solid pure chromium as the reference state, (a), was calculated using Eq. [l], , n F E I, n lna RT- U] where E is the measured electromotive force, F is the Faraday constant, and n is equal to 3, the number of equivalents per mole, (nF/RT = 18.59 volts'1 at 1600°C). The resulting activities are listed in Table I. The activity of chromium relative to pure liquid chromium was also calculated. The free energy of fusion of chromium at 1600° C was calculated using

Jan 1, 1969

By C. W. Schultz

The distribution of material passing a screen, or a set of screens, is described by the equation [ ] where p = the probability that a single particle will pass the screen on a single presentation k = number of layers of screen cloth n = distance from head of screen expressed as number of screen openings. This model can be used to predict the performance of conventional screening operations (i.e., k = 1) as well as the so-called "statistical screening" operations. Using this technique, in which multiple identical layers of screen cloth are employed, screening can be carried out at a finer size than is possible with conventional techniques with no loss of separation efficiency.

Jan 1, 1969

By Andrew J. Gaber

Beginning in 1961 the Coal Research Bureau of the West Virginia University School of Mines began a program of research to investigate the potential of the magnetic separation process to remove sulfur of the pyritic form from pulverized coal. Using a so-called isodynamic magnetic separator (1) it was demonstrated that significant quantities of pyritic sulfur could be removed from coal. Pulverized coal samples representing several different coal seams were individually screened into sizes in the 48 mesh by 200 mesh (297 to 74 microns) range, and untreated and steam-air treated samples of each were processed by the magnetic separator. The results of the investigations to magnetically remove pyrite from coal were published in two separate reports issued by the Coal Research Bureau (2,3), The isodynamic magnetic separator was designed about 30 years ago for use in geological and mineralogical laboratories (1,4,5) to isolate one or more minerals exhibiting only small differences in their magnetic propertiese Specifically, to accomplish this, the air gap of the unit was designed to provide a nearly constant magnetic gradient both laterally and longitudinally in the separating zone. It is reported that mineral concentrates of 99.5 percent purity can-be produced on closely-sized fractions after several cleanings through the unit. The isodynamic magnetic separator, therefore, was not expected to process coal containing sizes smaller than 200 mesh, or to demonstrate commercial capability to process pulverized coal. The primary purpose of the Coal Research Bureau in using the unit was that of determining if the magnetic process could remove pyrite from coal, and thereby encourage further research directed toward development of acceptable full-scale processing equipment.

Jan 1, 1969

By Charles E. Lundin

The character of the Er-D system was established by determining pressure-temperature-composition relationships. A Sieuerts&apos; apparatus was employed to make measurements in the temperature range, 473" to 1223"K, the composition range of erbium to ErD3, and the pressure range of 10~s to 760 Torr. The system is characterized by three homogeneous phase regions: the nzetal-rich, the dideuteride, and the trideuteride phases. These phases and their solubility boundaries were deduced from the family of isotherms of the system zchich relate the pressure-temperature-composition variables. The equilibrium plateau decomposition relationships in the two-phase regions were determined from can&apos;t Hoff plots to be: The differential heats of reaction in these two regions are AH = - 53.0 * 0.2 and -20.0 *0.1 kcal per mole of D2, respecticely. The differential entropies of reaction are AS = - 36.3 * 0.2 and - 31.0 * 0.2 cal per mole D2. deg, respectively. Relative partial molal and intepal thermodynamic quantities were calculated from the pure metal to the dideuteride phase. The study of the Er-D system was undertaken as a logical complement to an earlier study of the Er-H system.&apos; The primary interest was to compare the characteristics of the two systems and relate the difference to the isotopic effect. Studies of rare earth-deuterium systems by other investigators have been very limited in number and scope. Furthermore, there is even less information available wherein an investigator has systematically compared a binary rare earth-hydrogen system with the corresponding rare earth-deuterium system. The available information consists primarily of dissociation pressure measurements in the plateau pressure region of a few rare earths. Warf and Korst&apos; determined dissociation pressure relationships for the La- and Ce-D systems in the plateau region and several isotherms for each system in the dideuteride region. They compared these data with those of the corresponding hydrided systems. The study of these systems as a whole was very cursory and did not give sufficient data for a thorough comparison of the effect of the hydrogen vs the deuterium in the respective rare earths. The heat capacities and related thermodynamic functions of the intermediate phases, YH, and YD2, were determined by Flotow, Osborne, and Otto,~ and the investigation was again repeated for YH3 and YD3 by Flotow, Osborne, Otto, and Abraham.4 This investigation studied only these specific phases. Jones, Southall, and Goodhead5 surveyed the hydrides and deu-terides of a series of rare earths for thermal stability including erbium. They experimentally determined isotherms of selected hydrides and plateau dissociation pressures for deuterides. These data allowed comparison of the enthalpy and entropies of formation of the dihydrides and dideuterides. To date, no one rare earth has been selected to thoroughly establish the complete pressure-temperature-composition (PTC) relationships of binary solute additions of hydrogen and deuterium, respectively. The objective in this investigation was to provide the first comparison of a complete family of isotherms of a rare earth-deuterium system with those of a rare earth-hydrogen system. This would allow one to determine what differences exist, if any, in the various phase boundaries and the thermodynamic relationships in various regions of the systems. I) EXPERIMENTAL PROCEDURE A Sieverts&apos; apparatus was employed to conduct the experimental measurements. Briefly, it consisted of a source of pure deuterium, a precision gas-measuring buret, a heated reaction chamber, a mercury manometer, and two McLeod gages (a CVC, GMl00A and a CVC, GM110). Pure deuterium was obtained by passing deuterium through a heated Pd-Ag thimble. A 100-ml precision gas buret graduated to 0.1-ml divisions was used to measure and admit deuterium to the reaction chamber. The reaction unit consisted of a quartz tube surrounded by a nichrome-wound furnace. The furnace temperature was controlled by a recorder-controller to . An independent measurement of the sample temperature in the quartz tube was made by means of a chromel-alumel thermocouple situated outside, but adjacent to, the quartz tube near the specimen. Pressure in the manometer range was measured to k0.5 Torr and in the McLeod range (10~4 to 10 Torr) to *3 pct. The deuterium compositions in erbium were calculated in terms of deuterium-to-erbium atomic ratio. These compositions were estimated to be *0.01 D/Er ratio. The erbium metal was obtained from the Lunex Co. in the form of sponge. The metal was nuclear grade with a purity of 99.9+ pct. The oxygen content was reported to be 340 ppm and the nitrogen not detectable. Metallographically the structure was almost free of second phase (<i vol pct). A quantity of sponge was arc-melted for use as charge material. The solid material was compared with the sponge in the PTC relationships. They were found to be identical. Therefore, sponge material was used henceforth, so that equilibrium could be attained more rapidly. The specimen size was about 0.2 gr for each loading of the reaction chamber. The procedure employed to obtain the PTC data was to develop experimentally a family of isothermal curves of composition vs pressure. First, a specimen

Jan 1, 1969

By J. C. Martin

Equations for three-phase, three-dimensional, compressible flow (including capillarity) are reduced to two-dimensional relations by a partial integration. This reduction allows three-dimensional flow problems to be treated with mathematics for only two spatial dimensions. The results can be used to formulate flow equations for two-dimensional reservoir simulators in which the effects of capillarity and fluid segregation in the third dimension are represented. Such reservoir simulators would retain many of the aduantages of two-dimensional simulators while simulating three-dimensional effects. The principal restriction of the method is that the thickness of the reservoir should be small, compared to the distance across the reservoir. INTRODUCTION In recent years, computers have been used to calculate the performances of many reservoirs. Most of the detailed calculations, however, are based on finite difference solutions of the flow equations, and present day computers are seldom able to handle a sufficient number of cells to produce entirely satisfactory solutions, even for reservoirs represented by two-dimensional arrays of cells. The situation becomes much worse when one wishes to approximate the reservoir by a three-dimensional array. A great saving in computation or a more detailed solution can be obtained for many reservoirs by using the partial integration of the equations of flow presented in this paper. The integration reduces the three-dimensional equations to two-dimensional relations; and, for studies of two-dimensional flows in vertical cross-sections, the equations are reduced to one-dimensional relations. Most reservoir performance calculations currently are based on one- or two-dimensional flow re1ations.l-3 In some cases flow in the third dimension is approximated by assuming a particular type of vertical saturation distribution, such as gravity segregation.l.2. The relations developed in this paper approach those for segregated flow as the capillary pressures approach zero, and they approach those for uniformly distributed saturations as the capillary pressures are increased. For this analysis, the ratio of the reservoir&apos;s thickness to the maximum distance across it must be small. The capillary pressures between the oil and water should also be small compared to the maximum pressure difference in the reservoir. This requirement is met by most reservoirs. It is assumed that the capillary-pressure curves are well defined, whether or not hysteresis effects are included. Also, the reservoir must have sufficient vertical permeability to allow the fluids to segregate. The results presented here provide a firm theoretical foundation to Coats&apos; et aL5 assumption of vertical equilibrium and extend the relations to three-phase flow. Coats&apos; assumption of vertical equilibrium, which he verified by calculations and experiment, is developed here mathematically from basic flow equations. DISCUSSION SATURATION AND PRESSURE DISTRIBUTIONS Appendix A presents a mathematical analysis of fluid flow in reservoirs where the ratio of thickness to maximum distance across the reservoir is small. The results indicate: (1) that the fluids along any line perpendicular to such a reservoir&apos;s upper surface are in static capillary equilibrium (vertical equilibrium); (2) that, to a first approximation, the fluid pressures and properties are functions of only areal position in the reservoir and time; and (3) that hydrostatic pressure gradients exist along any line perpendicular to the reservoir&apos;s upper surface. The results might be expected after studying several physical considerations. First, no flow is allowed normal to the upper and lower reservoir boundaries, which are relatively close together.

Jan 1, 1969

By R. F. Jones, N. E. Truitt, M. Prats

In most published discussions and theories of in situ combustion, the combustion fronts are assumed to be vertical. However, evidence from field tests leaves no doubt that combustion fronts often advance more rapidly along the top than near the bottom of a formation as a result of difference in density between injected air and formation liquids. The approximation proposed in this paper to determine the movement of the resultant tilted combustion surfaces states that the vertical rate of movement of combustion surfaces is proportional to the horizontal oxygen flux. Where self-ignition is possible, the proposed method demands that a secondary combustion surface exist around production wells which produce some oxygen. These secondary combustion surfaces may be formed long before the primary combustion surface can advance from injection to production wells. Heat liberated near production wells at these secondary combustion surfaces can contribute to an early increase in production rate. Results indicate that significant oil recoveries cannot be obtained from the usual flood patterns (five-spots, seven-spots, etc.) without producing large volumes of unused oxygen. Ideally, to increase oxygen- consumption efficiency, well patterns should allow oil production from a first line of production wells and gas production from more distant lines of producers. However, it may be desirable to produce some gas at all wells to support (and benefit from) active secondary combustion surfaces. Results indicate that the well spacing through which combustion can be advanced is larger than that predicted by other methods. A large number of production wells may still be desirable to take quick advantage of gravity drainage. From a comparison with results at South Belridge field, California, it appears that this method adequately describes oxygen concentration and temperature histories and combustion-front shapes. However, this method does not accurately locate the most advanced point of the combustion surface. There is some field evidence to substantiate the actual presence of secondary combustion surfaces at South Belridge. Use of the proposed method appears warranted at this time when lay-over of the combustion surface can be anticipated. INTRODUCTION The assumption of vertical combustion fronts has been embodied in all previous publicationsl-6 which use the movement of combustion fronts away from injection wells to determine the temperature and fluid distributions in the reservoir. The only paper concerned with a mathematical model of the combustion process in which a nonvertical combustion front is used was written by Gottfried.11 Actually, nonvertical combustion fronts have been observed in most in situ combustion field tests for which adequate data are available.7, 8, 6 In practice, the typical vertical extent of the burned zone decreases with distance from the injection well, and this burned zone is at or near the top of the sand body. In some cases, such as at South Belridge field near Taft, Calif., the combustion surface is almost horizontal over a very large area.8 Thus, for some years an obvious and serious gap has existed between theory (vertical fronts) and practice (tilted fronts). This is indicated in Fig. 1. Tilted combustion fronts such as observed at South Belridge8 sometimes result from the natural tendency of injected gases to rise to the top of an oil sand. An initially present gas cap, even if thin, would make apparent the effect of gravity segregation from the first, particularly since formations considered for in situ combustion field operations are generally selected for their

Jan 1, 1969

By C. E. Violet, R. J. Borg, E. M. Howard

The miscibility gap in the Au-Ni system has been determined by Mossbauer spectroscopy, with used as a probe. The phase boundaries were determined from the compositional dependence of both the isomer shift and Curie temperature. X-ray diffraction measurements were also used to confirm the Mossbauer results. 1 HE purpose of this research is to demonstrate the application of Mbssbauer spectroscopy to the determination of phase boundaries and to redetermine the miscibility gap by an independent and novel technique. The techniques evolved in this study are readily applicable to other polyphase systems and are generally as quick and accurate as the more conventional methods, e.g., metallography, X-ray diffraction, thermal analysis, and so forth. To be sure, not all polyphase systems will lend themselves favorably to Mijssbauer investigations, but this is a problem met in the use of conventional methods as well. The Mbssbauer spectrum responds to a different set of physical parameters, and consequently provides an entirely independent method of analysis. It is especially useful if the system has either a ferromagnetic or an antiferromagnetic transition. The Au-Ni system was selected because alloys containing more than -60 at. pct Ni become magnetically ordered at low temperatures; also the miscibility gap is quite well established (see Ref. 7 for a compilation of pertinent references, also Fig. 11, and thus provides a reliable test of this novel procedure. As Fe is the most commonly used Mijssbauer isotope, there exists a wealth of information concerning its behavior in iron-containing alloys and compounds. However, as yet there have been relatively few experiments using it as a probe to investigate nonferrous systems. By choosing a nonferrous alloy system, we are able to demonstrate that its use is not restricted to systems containing iron as one of the major constituents. Wertheim and ~ernick&apos; have used the same method to investigate Cu-Ni, and demonstrated that one can obtain a systematic variation in the isomer shift and magnetic hyperfine field. However, we believe this to be the first time these techniques have been used to establish phase boundaries. Two hyperfine interactions were measured and used to determine the phase boundaries, viz., the magnetic hyperfine splitting and the isomer shift which in this alloy system are both strong functions of composition. Calibration curves were established based upon single-phase solid solutions obtained by quenching from temperatures well above the maximum of the miscibility gap, see Fig. 1. Solid solutions containing 25, 50, 65, 75, 85, 92, and 96 pct Ni as well as pure nickel were used in the calibration procedure. Fig. 2 shows the Curie temperature, TC, and the isomer shift, v,, as determined from the Mbssbauer spectra, and variation in lattice parameter as determined by X-ray diffraction, as functions of composition. The compositions of the two-phase systems quenched from temperatures within the miscibility gap are obtained by comparing their respective values of TC and v0 with the calibration data. I) EXPERIMENTAL Mbssbauer sources were made by fusing the component metals in a tungsten arc melter, which has a water-cooled copper hearth. Both nickel and gold were 99.999 pct pure, and the melting was done in an atmosphere of purified argon. The alloys were rolled, diced,

Jan 1, 1969

By Robert E. Green, Edmund G. Henneke

The velocities of the three possible modes of elastic wave propagation have been calculated for single-crystal copper at 1-deg intervals throughout the standard stereographic triangle. The results are presented as isospeed contours. The deviations between the direction of maximum energy flux and specimen axes are presented as arrows drawn on stereographic projections. The orientation factors associated with dislocation motion on the primary slip system only and also on all twelve slip systems have been calculated for all three elastic waves. The orientation factors associated with a longitudinal standing wave resonant specimen have also been calculated. The results of these calculatians are compared with earlier calculations on aluminum crystals and the relevance of these results to ultrasonic attenuation measurements is discussed. GREEN and inton&apos; have recently outlined a procedure for determining the orientation factors for dislocation damping in single crystals. The stress field associated with a given mode of elastic wave propagation is resolved on the slip systems in which it is assumed the dislocations are vibrating due to this stress field. Since, at room temperature, slip has been observed on a limited number of systems in fcc and hcp metal crystals, it is assumed that these systems are the appropriate ones to use for the resolving process. This procedure has been applied to aluminum crystals by Hinton and hreen&apos; and to zinc crystals by Henneke and Green.3 In the present paper the modes of elastic wave propagation have been calculated for copper crystals possessing orientations at 1-deg intervals throughout the standard stereographic triangle. The deviation of the energy flux vectors from the specimen axis have been calculated for each mode. The stress field associated with each mode has been resolved on the (111)(110) slip systems in order to determine the orientation factors for dislocation damping. MODES OF ELASTIC WAVE PROPAGATION For any direction in a linear homogeneous aniso-tropic material three elastic modes can be propagated. In general, each of these modes has both longitudinal and transverse particle displacements associated with it and thus are not "pure" modes. However, there is always one component which is greatest in either a longitudinal or transverse direction and hence the mode may be referred to as quasi-longitudinal or quasi-transverse, accordingly. For certain axes of high symmetry pure modes may be propagated. The phenomenon of refraction of the energy flux vector is also exhibited by elastic wave propagation in ani-

Jan 1, 1969

By Giovanni Barla

The stress-relief method for the determination of the ground stress tensor is a common procedure in rock mechanics. In particular, the method of applying gauges to the end of a borehole is a well-established technique. Investigations, both experimental and theoretical, indicate that large discrepancies can exist in the determination of the ground stress tensor when the rock substance is not the ideal elastically isotropic material assumed for the reduction of data. The purpose of this paper is to extend the analysis of strain gauges applied to the end of a borehole to rock material more closely approximate to an orthotropic substance.

Jan 1, 1969

By Leon Borgman, Michael P. Lipkewich

Orebodies at or near the surface are generally amenable to open pit mining. The development of a mining program involves designing an ultimate pit and a production schedule. This pit maximizes total profit while the production schedule maximize6 the present value of the property. Optimum pit limits can be approximated by two-and three-dimensional numerical techniques. These techniques presuppose that the mineralized area has been sufficiently sampled to allow a reasonably accurate prediction of grade at any spatial location.

Jan 1, 1969

By V. J. Southey

"This paper reviews the history of Wabana Mines from 1892 to 1966, inclusive, in order to clarify the essential factors involved in the achievement of maximum mining efficiency and in the search for an acceptable product to satisfy changing market requirements. It outlines the progressive steps taken to mechanize both surface and underground operations, and forecasts anticipated performance, assuming certain major plans could have been implemented. Results of extensive research in the treatment of the complex ore are discussed. Selected processing alternatives are compared as to feasibility in a summary incorporating estimated capital and operating costs."

Jan 1, 1969

By R. W. Smith, K. H. Lee

Bond type simulated closed-circuit grindability tests and batch grindability tests were run on six pure minerals plus a limestone and a taconite ore. The simulated closed-circuit tests were made at five different meshes of grind. The minerals tested varied widely in hardness and breakage pattern. For all simulated closed-circuit tests both Bond and Holmes work indices were calculated and compared. The Bond grindability testlm6 has been widely and quite successfully used for predictions of such items as ball mill power requirements and as an aid in plant comminution equipment selection. The test is interesting in that although run as a series of batch tests it is over-all a simulated closed-circuit test with a circulating load of 250%. The simulated closed-circuit feature is probably the primary reason for the notable success of the test. Perhaps the major criticism that can be brought against the test is that it is time consuming, since it normally takes a trained technician about an eight-hour shift to perform it.4 For many purposes this is an acceptable time requirement. However, if a grindability test is to be used for mill control purposes it should be performed in as short a time interval as possible, preferably under an hour. Sometimes in industry strictly batch tumbling mill tests are run and an attempt is made to correlate such batch tests with plant mill operation. Then an attempt is made to adjust operating tumbling mills based on data from the tests. The tests, however, frequently do not correlate well with operating data. The purpose of the present work was to explore some of the similarities and differences between a simulated closed-circui.t grindability test and a batch type test. Six different minerals plus a limestone and a taconite ore were tested in the experimentation. These materials varied widely in hardness, breakage characteristics, etc. Standard dry Bond grindability tests were mn on all materials at 48, 65, 100, 150 and 200 meshes of grind. Feed material was prepared by stage cmshing to -6 mesh. Initial feed volume was 700 cc. Care was taken to maintain the standard constant weight (about 20125 gm) and number of balls (283) during all the tests. Rotational speed was 70 rpm. Table I lists the materials studied along with pertinent data regarding the materials and Bond grindabilities obtained. In addition, dry batch tests were performed on all materials. These tests were made in the same mill as was used for the Bond tests. An identical ball charge and an identical feed volume were used. After rotating the mill for a predetermined number of revolutions at the same rotational speed as for the Bond test, the material was removed and separated from the ball charge. A screen analysis was performed on this product. Knowing the original size distribution of the feed and the size distribution of the product, it was possible to calculate the grindability or grams of a particular mesh produced per revolution of the mill. After the screen analysis of the product, the various fractions were recombined and placed back in the mill for further grinding. After grinding for additional revolutions of the mill the procedure was repeated. Thus, it was possible to obtain grindabilities for each material at a number of meshes of grind and for various revolutions of the mill. Grind-abilities obtained from batch tests are shown in Table 11. COMPARISON OF BOND AND BATCH GRINDABILITIES Figs. 1A through 1D show relationships between batch and Bond grindabilities. Figs. lA, lB, 1C and 1D show respectively graphs indicating the relationships for batch tests run for 100, 300, 500 and 700 revolutions of the mill. For a particular material on each graph, points are shown for 200, 150, 100, 65, and 48 meshes of grind except for several missing coarse meshes of grind for galena which did not fall conveniently on the figures. For each material and graph the point nearest the origin is for 200 mesh, the next for 150 mesh, the next for 100 mesh, etc. Considering Fig. lA, it is interesting to note that all relationships shown are essentially straight lines. There are, however, considerable differences

Jan 1, 1969

By L. C. Brown, E. B. Hawbolt

If a single-phase alloy is rapidly cooled such that insufficient time is available for an equilibrium transformation to occur, the high-temperature phase may be retained to room temperature or may undergo a massive or martensitic reaction. The massive or martensitic product develops without a composition change and usually has a crystal structure approximating an adjacent equilibrium phase. The characteristics of a massive transformation are intermediate between the equilibrium reaction in which long-

Jan 1, 1969

By F. A. Crossley

The key to disagreements between Blackburn&apos;s findings and mine is the word equilibrium". My work attempted to define the equilibrium diagram of the titanium-rich end of the Ti-A1 system. It can readily be shown that Blackburn&apos;s conclusions are based primarily on the examination of structures substantially removed from equilibrium. The diagram presented in Fig. 16 is properly labeled a "phase diagram". However, it appears that Blackburn either does not understand or does not accept the difference between "phase diagram" and "equilibrium diagram" as defined in the Metals Handbook.17 The conflict lies not in Blackburn&apos;s data but in his interpretation of it, and his use of "transformation", "phase diagram", and "equilibrium diagram" as synonymous terms. I share his view that the light microscope is much inferior to the transmission electron microscope for the study of transformations; but this fact does not render the light microscope useless or untrustworthy. The difficulties experienced with the Ti-A1 system have not been due to the limitations of the light microscope, but rather to the extreme sluggishness in achieving equilibrium at temperatures below 1000° C. Were it not for the light microscope employed with polarized light, the twin phase syndrome&apos; might still be unrecognized and, as a consequence, still adding to the confusion of Ti-A1 investigations. (Ref. 1 should read ... Contract No. N161-25952 ... vol. 236.) Other, more sophisticated techniques, including electron transmission, simply confirm the erroneous tentative conclusions drawn from observations of structures due to the twin-phase syndrome. By the standards of most of the investigations of the Ti-A1 systems, seven of the fifteen compositions investigated by Blackburn were seriously contaminated with oxygen. The writer has found that 0.1 wt pct 0 shifts the a + Ti3A1 boundary to 1 at. pct lower A1 content at 700°C. At constant aluminum content, this corresponds to a temperature shift of the boundary of +25°c.18 Blackburn advises that the first group of alloys contained 0.1 to 0.15 wt pct 0, bur he does say whether the analyses were performed on as-received material or on specimens in their final state of heat treatment. This is especially important considering the 20-mil-thick starting materials. If specimens had been annealed in the two-phase a + 6 region it would have provided an indication of the final degree of oxygen contamination since up to about 12 at. pct A1 the boundaries of this region are well-defined for low-oxygen alloys. Blackburn questions the capability of light microscopy in determining phase boundaries in the Ti-A1 system. I submit that the a/a + Ti3A1 boundary in Fig. 1 of Ref. 1 over the composition range from 10 to 18 at. pct A1 was determined by dilatometry and supported by electron diffraction. Specimens of alloys containing 8, 10, 12, and 14 at. pct A1 were aged at 550°C for 1000 hr (under stress of 5000 psi to accelerate the tendency to equilibrium) and then fractured in tension at room temperature. Collodion was applied to the as-fractured (unetched) surface and, when stripped, carried away particles identified by electron diffraction as Ti3A1. Perhaps Blackburn will explain why these electron diffraction data were ignored. At this time, a technique for revealing or indicating

Jan 1, 1969