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By Lyman Johnson

Single crystals qf copper in "single slip" orientatiorzs have been deformed in compression. During defortnation all of the independent deformation parameters have been measured. These parameters consist of thefive strain components and three components descrihing the lattice rotation. By a finite strain analysis these pararmeters , forrming a deformation gradient martrix, are related to the amounts of slip on each of the twelve slip systems. The results show that the amount of secondary slip is about equal to the amount of primary slip. This is an order of magnitude larger than has been believed previoutsly. ACCORDING to early theory and experiments, when a single crystal of a fcc metal is deformed in tension or compression it should deform by slip on only one slip system until the stress axis reaches a symmetrical orientation.' However. the observation of a large increase in the secondary dislocation density during ..single slip" makes it clear that some slip does occur on secondary systems. Knowledge of the amount and distribution of this secondary slip is essential to a complete understanding of the mechanisms of single-crystal deformation. Ahlers and Haasen 2 and Mitchell and Thornton1 have tried to detect the amount of secondary slip in single crystals of silver and copper, respectively. Each simultaneously measured the angle A, between the tensile axis and the primary slip direction and the length 1 of a gage section of the specimen after incremental amounts of deformation in tension. The measured A, was then compared with the theoretical single slip angle hp. given by sin Ap = j sin . hO where ?o was the initial angle between the tensile axis and the primary slip direction and lo was the initial gage length. In both sets of experiments a small but systematic difference between ?e and ?p was found. This difference must be due to the occurrence of secondary slip. However, as Mitchell and Thornton1 pointed out. nothing quantitative can be said about the amount and distribution of this secondary slip from the measurements that they made. The reason that no quantitative conclusions could be made is because no unique solution for the distribution of slip on the twelve fcc slip systems can be determined from only two measured deformation parameters such as A and 1. There are, in fact, eight independent macroscopic deformation parameters that can be measured when a single crystal undergoes a homogeneous deformation. Physically these can be thought of as the five finite strain components and the three angles describing the crystal lattice rotation. All eight of these parameters were measured by Taylor4,5 for aluminum deformed in tension and compression. At that time the concern was to show that slip occurs on {111 (110) systems in fcc metals, and the mathematics were not available to determine what slip distributions were compatible with the measurements. In this paper the mathematics6,7 are developed that allow the slip distribution to be determined from these measurable macroscopic deformation parameters. The analysis is applied to the measurements of the strain and lattice rotation of copper single crystals deformed in compression. The results show that the amount of secondary slip is an order of magnitude larger than had previously been thought. CRYSTALLOGRAPHIC DESCRIPTION OF A HOMOGENEOUS DEFORMATION The deformation of a solid body can be represented by a transformation matrix F that transforms the un-deformed state into the deformed state. Consider a vector X connecting two material points in the unde-formed material and the vector x connecting the same two material points after deformation, where both vectors are referred to the same set of Cartesian axes. The final vector x is related to the initial vector X by the equation: X = FS. [2] Eq. [2] can be considered as the equation defining F, which is called the deformation gradient matrix. Its components are: If the deformation is homogeneous, the transformation is linear and the components of F are constants. Using subscript notation, if P is the unit vector in the initial direction of a material line, the components of the unit vector p in the direction of the same material line after deformation are given by:

Jan 1, 1970

By J. L. Walter

Extra-low carbon iron sheet, when deformed and annealed, undergoes exaggerated or abnormal grain growth in the critically deformed regions of the sheet. This exaggerated pmth occurs, for low strains (3 to 6 pct), only in sheet which has a fine dispersion of precipitates in the subsurface region of the sheet and fewer and coarser precipitates in the sheet interior. These particles have been identified as manganese sulfides. Wing the anneal, grains near the surface are gvowth-inhibited by the fine particles but the grains in the interior are free to grow normally. With the additional driving force provided by the strain energy, the interior grains first grow into the small subsurface pains. Eventually, these growing grains grow completely through the sheet. Calculations of limiting grain sizes at various values of strain indicate that a volume fraction of precipitates in excess of 10-' would be required to eliminate exaggerated growth in material strained to 10 pct. OPEN-COIL annealing has made decarburization of sheet steel both efficient and economically practical. Use of such material for porcelain-enameling stock is one of many possible applications of low-carbon iron since carbon in steel is deleterious to porcelain-enameling properties.' However, the extra-low carbon iron presently available presents another problem, that of exaggerated grain growth in regions where the sheet has been deformed as by bending or stretching. In exaggerated grain growth a few grains start to absorb their neighbors and these may become very much larger than the average grains of the sheet. Other names for exaggerated grain growth are coarsening, critical grain growth, secondary recrystallization, abnormal grain growth, or discontinuous grain growth. While this grain growth does not affect the enameling qualities of the low-carbon iron sheet, their presence results in a marked reduction of tensile-yield strength in the region of the sheet containing the large grains. The loss of tensile yield strength may render the material unsuitable for many applications . This report describes the results of a study undertaken to determine the cause of the exaggerated grab growth in extra-1ow carbon iron and, if possi- ble, to prescribe practical procedures for its prevention. GENERAL THEORY The driving force for exaggerated grain growth is the grain boundary free energy. This driving force is proportional to (l/rl + l/r2) where rl and r2 are the mutually perpendicular radii of curvature of the boundary between the growing grain and the grain being consumed. Thus, the greater the difference in size between the growing grain and the matrix grains, the higher the driving force for grain growth. If, however, the matrix grains are free to grow simultaneously, the driving force for exaggerated growth will be diminished. Stability toward growth of the matrix grains may be caused by a) a strong single orientation texture (texture inhibition),' b) a dispersed second phase,3"5 c) the thickness effect,' or d) intergranular segregation.7"9 As exaggerated growth occurs when growth of the matrix grains has been slowed by the stabilizing processes mentioned above, there must be an additional factor acting to promote growth of a few of the grains to the point where they are enough larger than the matrix grains that boundary energy driving forces are sufficient to cause continued growth. For instance, at the annealing temperature, growth-inhibiting inclusions may slowly dissolve and coalesce. Eventually, a grain boundary becomes unlocked and migration occurs at the expense of neighboring grains. Or, an additional driving force may be supplied to some of the grains if the material is strained. Then, since some grains will be strained less than others, the difference in strain energy between adjacent grains may be sufficient to overcome boundary locking and allow growth of the grains with lower strain energies. In the present study, therefore, such factors as the presence or absence of dispersed phases, the nature of the exaggerated growth, and the effect of strain have been considered. EXPERIMENTAL PROCEDURE I) Material and Processing. Three types of low-carbon iron were used in this study; types A and B were commercial grades, each from a different supplier.* The precise details of the processing of

Jan 1, 1963

By R. R. Angel

Drilling rate is a parameter that should be considered in determining the volume requirements for air and gas drilling. The use of past methods which ignore the effects of the solids content upon the pressure and velocity of the annulus flow stream can result in undercalculation of the required volurne by as much as 50 per cent. A vertical-flow equation is presented for determining volume requirements. This equation includes the effect of the solids that are transported up the annulus in the flow stream by incorporating the drilling rate as one of the parameters. The effect of down-hole temperature on required circulation rates is also ana-lvzed. A simple approximate method of determining volume requirements is presented. This method is more accurate than the methods used in the past. Hole cleaning difficulties are analyzed for a recent air drilling job where past methods indicated that - excess air was being used. Sample curves of calculated boitom-hole pressures are presented for air and gas drilling in several hole sizes. INTRODUCTION In certain areas the use of air or natural gas as a circulating medium for drilling oil and gas wells is becoming a common practice. Large increases in penetration rate and bit life are achieved through the use of these media in preference to mud or water. Drilling rates as high as 90 ft/hr have been obtained in shales. The importance of maintaining adequate circulation rate is generally recognized; however, much disagreement exists among drilling operators as to what constitutes "adequate" circulation rate. In quarry drilling, where annular velocities can be accurately determined, an annular velocity of 3,000 ft/min of standard air is required for best results in rocks having approximately the same density as those commonly penetrated in drilling oil or gas wells'. Although this standard air velocity has proven satisfactory for quarry drilling, some oil and gas well drilling operators believe that an equivalent annular velocity of more than 4,000 ft/min is required; others believe that as little as 2,000 ft/min . is sufficient. Much of this disagreement results from determining the required circulation rates with methods which fail to incorporate the drilled solids in an equation which is applicable to vertical flow. Hughes Tool Co. Bulletins No. 23' and 23-A3 present data for determining circulation rates based on the Weymouth formula. These data do not include the drilling rate as a parameter and, therefore, neglect the effect of the solids being transported up the annulus. In spite of this apparent defect and the fact that the Weymouth formula is not applicable to vertical flow, the Hughes data have well served the drilling industry in many areas and are important and timely contributions to the science of air and gas drilling. The Hughes data purposely omit a correction for increasing down-hole temperature. At slow drilling rates this effectively compensates for the use of a formula which is not valid for vertical flow; however, volumes determined by the Hughes method are not sufficient to support rapid drilling rates at moderate and great depths. For example, Phillips Petroleum Co.'s Cauthorn "D" No. l in the Vinegarone field for Val Verde County, Tex., was air drilled from 1,500 to 9,300 ft using a compressor delivering 1,400 cu ft/min. The 8 3/4-in hole was drilled with 5-in. drill pipe, and drilling rates as high as 90 ft/hr were obtained between 7,000 and 9,300 ft. No water or caving hole was encountered. At 7,728 ft it was necessary to wash-out 60 ft of cuttings to reach bottom after a trip to change bits. At 8,130 ft a twist-off occurred and the drill col-lars were stuck in drill cuttings. These difficulties indicate that the 1,400 cu ft/min of air was not sufficient to keep the hole clean. Hughes data indicates that 1,180 cu ft/min is sufficient to produce an annular ve-

Jan 1, 1958

By G. B. Thomas

Several methods of analyzing pressure build-up data in wells have been presented by various authors. This paper reviews the theory and method of D. R. Horner and presents example calculations performed on data obtained by testing several different types of wells. These calculations include, (1) graphical estimation of final static pressure, (2) determination of the productive capacity of the pay away from the well bore and. (3) the degree to which the formation adjacent to the well bore has been damaged by completion or other causes. The methods of testing and precautions which should be taken to assure the best data possible are discussed. Limitations and reliability of calculated results are also treated. INTRODUCTION Pressure testing of wells is generally limited to the determination of producing and static mean formation pressures. The so-called "static" pressure determination.. along with PVT, electric log and production data, enable the reservoir engineer to determine, within reasonable limits, the drive mechanism of the reservoir and in some cases. the amount of edge water encroachment. Producing pressure tests enable calculation of productivity indices and allow the engineer to plan the systematic production of a pool for optimum conservation of suhsurface energy. The radial flow formula advanced by Muskat' has been based on the assumption of incompressible radial fluid flow. It has been known that reservoir fluids do not behave in an ideally incompressible manner. For example, incompressible flow theory indicates a simple logarithmic relationship between the difference of the instantaneous and static well pressures when plotted against time. 'The latter stages of this type of plot of pressure build-up data generally show a marked devia-, tion from the earlier straight line trend. which deviation may be shown to be due to the compressible flow of fluids toward the well bore. Shut-in times of 24, 48. 72. or at most 96 hours are currently in wide use for determining so-called "static" reservoir pressure. Due to the continuation of compressible flow of fluids into the well bore long after this arbitrarily taken shut-in time, the determination of static pressures has almost invariably resulted in lower than equilibrium values. Materials balance calculations made early in the life of a reservoir often result in a calculated reserve which later observations prove to be too low. Failure to obtain reliable "static" reservoir pressures within the prescribed 24 or 48-hour build-up period has undoubtedly been a major factor in obtaining these low estimates. Comparison of theoretical and actual productivity performance has indicated that formation damage and not being able to attain true static pressures have been partially responsible for the observed discrepancies. Research into the theory of compressible flow behavior has resulted in methods of applying these theories to the testing of wells. Application of the developed theories to pressure build-up performance indicates that in many cases the following can be estimated. 1. The static reservoir pressure. 2. The in-place effective formation permeability away from the well bore. 3. The degree or extent by which the formation has been damaged adjacent to the well bore, either through completion methods or subsequent damage due to fluid entry. REVIEW OF THEORY Horner2 has shown that the pressure build-up within a "point source" well is approximated by the following formula: Equation (1) is the approximate "point source" solution to the radial compressible flow equation advanced by Muskat. The solution assumes the following: 1. A point source well is producing at constant rate from the center of an infinite reservoir with a constant pressure at its external boundary. 2. The fluid flowing is present in one phase only. 3. The compressibility and absolute viscosity of the fluid remain essentially constant over the range of temperature and pressure variation encountered. 4. The well i.; shut-in at the sand face arid there is 110 after production into the well bore. 5. The formation permeability is homogeneous in the direction of flow. From Equation (1) it can be seen that if an ideal well were shut-in while producing from a reservoir under the conditions assumed, the pressure build-up would be a logarithmic func-

Jan 1, 1953

By Michael Hoch, Walter C. Wyder

The Cr-Ni system was investigated between 900" and 1400°C and 45 to 100 wt pct Cr. The Cr-Fe system was studied between 1200" and 1385°C and 70 to 100 wt pct Cr. Powdered alloy compacts were produced from high-purity chromium, nickel, and iron poulders. The compacts were sintered in an argon atmosphere and then machined into small, 0.030-in. diam cylindrical specimens. These were then heated by induction in the high-temperature X-ray diJfractwn camem under a helium atmosphere and irradiated with copper Ka radiation. From the results of the high-temperature X-ray diffraction patterns it can be concluded that chromium exists only in the bcc form, and that no eutectoid reaction occurs in the Cr-Ni system in the temperature interval 900" to 1400°C. The X-ray diffraction patterns are in agreement with the Cr-Ni phase diagram of Bechtoldt and Vacher, and Williams. It is possible that chromium undergoes one or more allotropic transformations between room temperature and its melting point. Most of the evidence was gathered from the study of the chromium-rich ends of the Cr-Ni and Cr-Fe binary systems. All the investigations rely heavily on indirect methods: thermal analysis, electrical resistivity, and micro-graphic inspection of quenched samples. In the present work the chromium-rich side of the Cr-Ni and Cr-Fe binary systems is studied, using high-temperature X-ray diffraction techniques. Thus the coexistent structures can be observed directly at temperature. PREVIOUS INVESTIGATIONS ~ansenl shows two possible Cr-Ni phase diagrams 1) a simple eutectic [Liquid =a-Cr(bcc) + y-Ni(fcc)], 2) a eutectic [Liquid+ P-Cr(fcc) + y-Ni(fcc)] and euctectoid [p-Cr(fcc) ==a-Cr(bcc) + yNi(fcc)]. The latter is based on the work of Grant and co-workers.2 Stein and rant'" placed the eutectoid composition at 1215°C and 68 wt pct Cr; their diagram is shown in Fig. l. Similarly, Sully3 also discusses the two proposed diagrams. Price and Grant,4 working on an isothermal section of the Cr-Ni- Fe ternary diagram at 1300°C, made no mention of a ß-chromium phase (fcc). The ß-chromium structure was also reported by Misencik 5 in the Cr-Nb(Cb) system. Williams 6 studied the Cr-Ni system using precipitation techniques. His work included the chromium and nickel solvus lines below 1250°C. He reported no ß structure nor any eutectoid reaction. The solvus lines which he produced were very similar to those of Jette, et al 7 below 1000°C. He concluded that Grant and coworkers2 had misinterpreted their data, and that effects which they had reported were actually due to the rapid and extensive precipitation of the nickel-rich phase. Bechtoldt and vacher8 used sintered powdered alloy compacts in an attempt to find the ß phase. They used metallographic and room-temperature X-ray diffraction techniques and also failed to detect the fcc chromium phase. They attributed the low slope of the chromium solvus at approximately 1150°C as the probable cause of the abundant precipitation obtained. They also stated that the precipitation was the probable cause for the abrupt discontinuities in the thermal analysis and electrical resistivity data which led to the conclusion that a eutectoid reaction existed. Fig. 1 also shows their diagram. Grigor'ev and coworkers9 investigated the polymorphic changes of chromium in the Cr-Ni phase diagram. Using standard microstructural and thermal analysis techniques, they published a phase diagram which contained five polymorphic forms of pure chromium and four eutectoid reactions. They stated that the room-temperature bcc chromium transformed to a fcc structure at 930°C, to bcc at 1300°C, to hcp at 1650oC, and then finally to bcc at 1830°C. The eutectoid reactions were placed at 850°, 960o, 1140°, and 1220°C. Also to be noted was the fact that the uppermost phase, the bcc above 1830°C, was different from the upper phase of Grant and coworkers,2 the fcc above 1840°C. Their eutectoid reactions, temperatures and compositions fall

Jan 1, 1963

By M. Hoch

Equations are derived from statistical considerations to represent the activities of each component of an interstitial solution, and of a compound with a wide homogeneity range as a function of composition and temperature, based on the interaction energies between the various components, Eij. The equations are checked on the binary systems Fe-C, Ta-H, and Y-H, the ternary systems Ti-O-H, liquid Fe-C-0, and the compounds TiO, MnO, COO, and YH,. In all cases the present model represents the experimental data well. THE aim of this paper is to derive from statistical considerations the thermodynamic behavior of non-substitutional solid solutions. "Nonsubstitutional solid solution" means either an interstitial solid solution (carbon in iron, oxygen and hydrogen in hexagonal and bcc titanium, and so forth) or deviation from stoichiornetry in compounds (introduction of vacancies—removal of atoms in one or both lattice sites of compounds FeO, MnO, TiO, NbO, YH2). wagnerl and Fowler and Guggenheim considered the theory of compounds with small deviation from stoichiometry; Anderson includes larger deviations from stoichiometry, the defect being present in one component only, as vacancy and interstitial. Rees considers only vacancies in one of the components and introduces various kinds of sites for the component where the defect occurs; the various sites interact with different energies, thus giving isotherms with two or more plateaus. Both Rees and Anderson are mainly occupied in determining the limits of two-phase regions, and the defect interaction energy is determined from the critical point. Darken and Gurry5 gave a brief treatment of carbon solution in iron; Speiser and spretnak calculated the configurational entropy for binary interstitial solid solutions by assuming that each interstitial atom in the solution excludes a certain number of neighboring interstitial sites from occupancy. Use will be made of this concept later. Hoch et al treated transition metal oxides of the NaCl-type structure, and also oxygen solution in titanium.' The main aim was to determine the behavior of the activity of one of the components as a function of the composition in the single-phase region. In the present paper, the various interaction energies are discussed in detail and the similarity between interstitial solid solutions and deviation from stoichiometry in ionic compounds is shown. Both types of systems have in common that at least on one kind of lattice site only one kind of atom occurs; this gives a fixed frame to the system, permitting a much easier statistical treatment than for the substitu-tional solid solutions. (The theory is also applied to ternary systems.) The difference between an interstitial solution and deviation from stoichiometry can be explained as follows. In an interstitial solution in the pure or standard state the host atom or host structure is present alone and all the interstitial sites which are going to be filled when the interstitial atom is introduced are empty. The interstitial solution is now created by introducing atoms into this empty lattice. In the deviation from stoichiometry, both kinds of lattice sites are already occupied in a special fashion (all lattice sites occupied, or the same fraction of lattice sites empty, or one kind completely filled, the other only two-thirds). Deviation from stoichiometry removes atoms from lattice sites, adds them, or removes atoms from one kind of lattice site and introduces them on the other lattice site. Though both cases (interstitial solution and deviation from stoichiometry) lead almost to the same equations, they are treated separately. The treatment given below corresponds to the "regular solution"10 treatment of substitutional solid solutions. Speiser and spretnak's6 treatment is similar to the athermal solution in the substitutional use. a) INTERSTITIAL SOLID SOLUTIONS Theory. It will be assumed that there are N lat-tice sites occupied by the host atom (denoted by 1). Corresponding to those N lattice sites there are N octahedral and EN tetrahedral interstitial sites. If only one kind of interstitial atom is added, this in-

Jan 1, 1964

By F. F. Schmidt, H. R. Ogden, E. S. Bartlett

Continuing tantalum alloy development studies have been concerned with a more detailed investigation of promising binary, ternary, and more complex tantalum alloys containing Groups IV-A, V-A, VI -A. VII-A, and VII-A metal additions. A primary objective of these studies was to improve the elevated temperature strength of tantalum with minimum degradation of fabricability and low-temperature ductility by alloying. Several alloys were found to exhibit hot tensile strengths in the excess of 25, 15, and 10 ksi at 2700°, 3000°, and 3500°F, respectively, combined with excellent cryogenic toughness and ductility. Particularly outstanding in this respect are alloys in the system Ta-Mo-W. Ternary parameter curves describing hot-strength, low-temperature ductility, recrystallization temperature, weld ductility, and fabricability are presented for the Ta-Cb-V, Ta-Hf-W, Ta-Mo-Hf, Ta-Mo-V, Ta-Mo-W, and Ta-V-W systems. At present, only four metals qualify for large scale structural applications at temperatures above about 1800°F. These are tungsten, tantalum, molybdenum, and columbium. Research and development work on these refractory metals has progressed to the point where efforts are now primarily directed toward the improvement of high- and low-temperature mechanical properties through alloying. High melting point combined with excellent low-temperature ductility, fabricability, toughness, weldability, and high solubility and tolerance for both substitutional and interstitial solutes are important attributes of tantalum. Conversely, its high density and relative scarcity compared with other refractory metals are the major deterrents to the use of tantalum. Early studies in the Battelle alloy development program established base line data on the mechanical and metallurgical properties of high-purity tantalum.' These studies were extended to include a preliminary investigation of the effects of various alloying elements on the established base properties.2,3 Recent studies involved a more detailed investigation of promising binary alloys containing Cb, Hf, Mo, Os, Re, Ru, and W, and ternary Ta-Cb-V, Ta-Hf-W, Ta-Mo-Hf, Ta-Mo-V, Ta-Mo-W, and Ta-V-W alloys. Results of major importance obtained are given in this article. EXPERIMENTAL PROCEDURES Electron-beam-melted tantalum (Wah Chang) and high-purity alloying elements were consolidated as 150-g ingots by multiple nonconsumable arc melting under a partial atmosphere of helium. Homogeneity of the button ingots was checked radiographically. Alloy buttons measured about 1-1/2 to 1-3/4 in. in diam by about 0.35 and 0.50 in. thick. Nominal alloy compositions were checked on each alloy button by weighing after arc melting. In most instances, weight losses were within 3 pct of the total weight charged. Subsequent chemical analyses on a number of selected alloys showed interstitial contents to range as shown below: Range of Interstitial Content, ppm 0 C N H 25-75 50-100 10-50 1-5 Metallic alloying additions were found to agree well with nominal compositions based on weight change data. Fabrication directly from the cast button to sheet was conducted at low (75° to 900°F), intermediate (1800° to 2000°F), or high (3000°F) temperatures, depending upon alloy content and hardness. Evacuated stainless steel or molybdenum packs were used for fabrication at intermediate and high temperatures, respectively. The temperature required to complete recrystal-lization in one hour was determined by hardness measurements and metallographic observations (longitudinal test sections) after vacuum annealing at 180°F intervals in the range 2010° to 2910°F. All mechanical property evaluations were conducted on recrystallized sheet, nominally 0.04 in. thick. Weldability of the various alloys was screened using manual TIG welding techniques. Bend ductility (bend axis perpendicular to weld axis) was the criterion used for evaluation. Tensile specimens employed 0.200 by 1 in. gage lengths, and bend test specimens measured about 1 by 1/4 in. Low-temperature tensile tests were conducted using a crosshead speed of 0.02 in. per min up to the point of yielding, and 0.05 in. per min to fracture. High-temperature tensile tests were conducted in vacuum using a crosshead speed of 0.01 in. per min

Jan 1, 1963

By J. Lohrenz, C. R. Clark, B. G. Bray

Procedures to calculate the viscosities of in situ reservoir gases and liquids from their composition have been developed and evaluated. Given a composition expressed in methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide together with the molecular weight and specific gravity of the heptanes-plus fraction, the procedures are capable of calculating the viscosity of the gas or liquid at the desired temperature and pressure. The procedure for reservoir liquids was developed using the residual viscosity concept and the theory of corresponding states, and was evaluated by comparing experimental and calculated results for 260 different reservoir oils ranging from black to highly volatile. The average absolute deviation was 16 per cent. This is the first known procedure for calculating the viscosity of reservoir liquids from their compositions as normally available, i.e., including the heptanes-plus fraction. The procedure for reservoir gases uses a sequence of previously published correlations. Evaluation of the procedure was accomplished by comparison of 300 calculated and experimental viscosities for high-pressure gar mixtures in the literature. The average absolute deviation was 4 per cent. The calculations are useful for (I) determining viscosities in compositional material balance computations and (2) predicting the viscosity decrease which occurs when gases, LPG, or carbon dioxide dissolve in reservoir oils. INTRODUCTION Methods to predict viscosities of reservoir fluids from the normally available field-measured variables have been presented. Beal,1 Standing,2 and Chew and Connally3 orrelated oil viscosities with temperature, pressure, oil gravity and gas-oil ratio. Carr, Kobayashi, and Burrows4 and Katz et al.5 have presented correlations for reservoir gas viscosities as a function of temperature, pressure and gas gravity. Lie all intensive physical properties, viscosity is completely described by the following function: Eq. 1 simply states that viscosity is a function of pressure, temperature and composition. These previous correlations1- hay be viewed as modifications of Eq. 1, wherein one assumes more simple functions may be used. The assumptions are practical, because the composition is frequently not known. Further, the assumptions are sufficiently valid so that these correlations are frequently used for reservoir engineering computations. In compositional material balance"' computations, the compositions of the reservoir gases and oils are known. The calculation of the viscosities of these fluids using this composition information is required for a true and complete compositional material balance. For reservoir gases, Carr, Kobayashi and Burrows4 have presented a suitable compositional correlation. For reservoir oils, no correlation is available, and data from reservoir fluid analyses have been used7-9 for compositional material balance calculations.* From a theoretical point of view, this is entirely invalid. The reservoir fluid analysis, whether flash, differential, or other process, does not duplicate the compositions which occur during the actual reservoir depletion process, therefore the viscosities measured during reservoir fluid analysis are not those which occur in the reservoir. From a practical point of view, the "error" of using viscosities from reservoir fluid analysis is of varying and unknown significance. One can say qualitatively that the error is greatest where compositional effects are greatest, i.e., for volatile oil and gas condensate reservoirs and pressure maintenance operations. The first requirement to obtain a quantitative estimate of the significance of the error is to develop a reliable compositional correlation for the viscmities of reservoir oils. No such correlation has been available. Consistent with this requirement, the objective of this study was to develop a procedure to predict the viscosity of reservoir fluids from their compositions. Normally, the compositions of reservoir fluids are available expressed as mole fractions of hydrogen sulfide, nitrogen, carbon dioxide and the hydrocarbons methane through the heptane-plus fraction, with the average molecular weight and specific gravity of the latter. The final correlation was to use the composition in this form. While the more challenging objective of the study was the development of a correlation for the viscosities of reservoir oils, the viscosities of reservoir gases were also studied. The end result of the study was a procedure to calculate the viscosities of reservoir gases and liquids suitable

Jan 1, 1965

By W. O. Philbrook, H. E. Burner, F. S. Manning

The equation of continuity for the hydrogen reduction of hematite in a fixed bed of closely-sized particles is solved assuming a flat velocity profile, negligible temperature gradients, md negligible axial diffusion. A kinetic expression from the literature is used which assumes the reduction process is controlled at the oxide-metal interface. The integral fractional conversion is computed, and the importance of particle diameter, flow mte, temperature, bulk axial diffusion, and inter- and intra-particle mass trarnsfer is predicted. Comparison with experimental data suggests one or more additional undefined variable(s) is significant. Equipment modifications are suggested for fidture experimentcll work. WITH the increasing desire to "design" the ore feed of a blast furnace, it has become necessary to define more quantitatively the process variables and to evaluate the extent of their control upon the reduction process. The bulk of the work reported in the literature has centered about the reduction of single particles; however, the blast furnace process more closely resembles reduction of a fixed bed than that of single particles. To simplify this analysis, the isothermal reduction by hydrogen of a natural hematite in a fixed bed of closely-sized particles is examined. With appropriate modifications in the kinetic and flow rate expressions, the approach employed should be extensible to mixtures of carbon monoxide, hydrogen, and inert nitrogen, and to adi-abatic conditions, thus approaching the blast furnace process more closely. The fixed bed variables which are investigated in this study are particle diameter, flow rate, temperature, and bulk axial diffusion, as well as inter-and intra-particle mass transfer. Of particular interest is the effect of particle size upon fractional conversion for a bed operating under constant pressure drop. The constant pressure drop concept bears a close resemblance to the blast furnace process, where regions of larger particles may provide a greater permeability to divert most of the reducing gas flow from the regions of smaller ore particles. Under such conditions one would expect qualitatively that, for sufficiently small particle sizes where the flow rate is small and the total surface area is large, the reduction rate would be limited by the gas flow rate. Initially the gas entering the bed reacts very rapidly and the composition approaches the equilibrium conversion value a short distance from the reactor inlet. This concentration "wave-front" then moves up the bed as the flow of reducing gas is continued, leaving in its wake an ever increasing layer of reduced particles. Providing that the reducing gas leaves the bed at equilibrium concentrations, conversion is expected to increase with an increase in flow rate, and hence with an increase in particle diemater. Conversely, for sufficiently large particles the flow rate will be high but the surface area available for reaction will limit the reduction rate. Since the total surface area decreases with an increase in particle size, conversion, in this case, is expected to decrease as the particle diameter is increased. It is clear then that between these two extremes an optimum particle diameter must exist. THEORETICAL DEVELOPMENT Above the temperature where wiistite is stable (about 560°C) the reduction of hematite proceeds through the series Fe2O3/Fe3O4/FeO/Fe. On the basis of microstructural studies and earlier work, Edström1 has postulated a mechanism for the reduction of an ideal hematite lattice: 1) Iron phase formation at the boundary between wiistite, iron, and gas (for sufficiently porous iron). 2) Diffusion of iron across a wustite layer. 3) Phase boundary reaction of Fe3O4 to FeO. 4) Diffusion across a dense magnetite layer. 5) Phase-boundary reaction of Fe2O3 to Fe3O4. According to the mechanism postulated, gaseous reaction product has to be removed only at the boundaries between wüstite and iron or gas, the only possible exception being enveloped Fe3O4 specks. On this basis McKewan2,3 has proposed that one may consider the hematite reduction process as a simple two-phase system of oxide/metal. If, for FeO and Fe3O4 layers of negligible thickness, the hypothesis is made that the rate of formation of a

Jan 1, 1963

By N. J. Grant, D. Carne, J. B. Seabrook

IT is unnecessary to review much of the literature on hydrogen embrittlement of steel since several excellent reviews and bibliographies exist.1-3 Hot acid pickling and cathodic charging have been known to cause hydrogen embrittlement of steel and have been used as laboratory methods to charge steels with hydrogen.4-8 Experimental Procedure The problem of prime concern in all instances, except in the work of Sims and coworkers,10 is that at no time was there a definite known hydrogen value reported which could be related to a particular value of the degree of embrittlement. It was the purpose of this research to determine the relationship between hydrogen content and degree of em-brittlement quantitatively. The 1020 stock used for the specimens was hot-rolled 7/16 in. diam rod of the following analysis: 0.19 pct C, 0.40 pct Mn, 0.012 pct P, 0.036 pct S' Vacuum-fusion analyses for nitrogen and oxygen gave 0.014 pct O2 and 0.0011 pct N2. Cathodic charging was used to cause embrittle-ment. The advantages of this method were that no quenching was necessary, the impregnation was reasonably controllable, and representative samples for analysis could be prepared simultaneously with the charging of the tensile bars. Analyses for hydrogen were made in a vacuum-fusion type of apparatus which extracted gas from the samples by fusion in a molten tin-iron bath' This apparatus, which has recently been described in detail elsewhere, will not be discussed here.". " Consecutive samples can be analyzed every 15 min with an accuracy of 0'03 ppm. A A from an electrolytic or pickling bath can be charged for analysis in about 3 min, and analysis completed in 15 min. Samples of as-received 1020 stock were analyzed and found to contain a negligible amount of hydrogen (0.06 ppm). Preliminary pickling and electrolytic charging gave highly variable results. Cold-worked samples showed higher values but ranged from 0.6 to 6.0 ppm of hydrogen. Charging at 90°C gave higher values of charged hydrogen, but troublesome films on many of the specimens resulted. It was not until a few drops of a catalytic poison, prepared from 2 g of yellow phosphorus dissolved in 40 ml of carbon disulphide,8 was added to the electrolytic cell that fairly consistent high values of hydrogen could be charged into the as-received 1020 steel at room temperature. The cell used is sketched in fig. 1. The anode and fixture for the tensile specimens were fastened to the cell cover as shown, and the specimen was screwed in place, centrally located with respect to the anode. At first, anodes of lead and graphite were tried, but they contaminated the electrolyte and gave a slight deposit on the specimen. Later, a platinum wire was used in the form of a uniform helix. A current of 2 amp, corresponding to about 0.5 amp per sq in. of cathode, was used for most specimens. The electrolyte was 4 pct H2SO4 solution. Fig. 1 shows the form of the special tensile bar, the main portion of which was an ordinary 1/4 in. diam, 1 in. gauge length test bar, except that two to four small cylinders of stock were left attached by small links to the bottom end of the tensile bar for the purpose of providing samples for hydrogen analysis. Thus the bars and samples were charged with hydrogen simultaneously and an analysis could be made while the bar was being tested mechanically. Experiments were performed to determine how representative the test cylinders were of the middle of the test bar proper. While the bar center was being analyzed, the small cylinder was stored in dry ice, since it had been shown that such storage prevents loss of hydrogen for many hours.12 The results of these checks are shown in table 1. The checks are very good (0.3 ppm) and indicate that it is permissible to use the small end cylinders to establish the hydrogen content of the tensile test bar proper-

Jan 1, 1951

By R. Taggart, D. H. Polonis, W. C. Gallaugher

In the Ti-Cu system, the a' phase can be produced over a wide range of alloy composition witJwut the retention of measurable amounts of the ß or ? phases. This paper reports on the decomposition of this hexagonal martensite phase front the standpoint of solute corzcentratiorz, tempering temperature, and coherency strain condition. The mechanism of precipitation during tempering comprises localized precipitation which is followed by discontinuous precipitation if sufficient coherency strains are present. The localized precipitation process in hypoeutectoid alloys is described by the generalized Johnson-hiehl equation and an activation energy of 46,000 cal per mole. In hypereutectoid alloys the corresponcEing activation energy is 51,000 cal per mole. The rate-controlling process has been proposed as the difision of copper along a' platelet interfnces. SEVERAL investigations have been reported concerning the kinetics of decomposition of the mar-tensitic a' phase in titanium binary alloys.' In the Ti-Mo system,' two modes of a' decomposition have been observed in the presence of /3 phase; one of these involves the precipitation of fine a from a', and the other involves diffusion across the a'-ß interface. In studies of the Ti-Cr system, Rostoker2 did not detect the formation of TiCr2 during tempering. In Ti-Ni alloys,3 the intermediate phase Ti2Ni has been found to precipitate directly from a' along the interfaces between plates. With the exception of the study of Ti-Ni alloys the previous investigations of tempering phenomena in substitutional martensites are mainly qualitative and do not present a detailed description of the precipitation processes. The following limitations restrict the correlation of the microstruc-tural processes and reaction kinetics during tempering in most binary-alloy systems. 1) A mixture of at least two phases characterizes the constitution of quenched alloys. 2) Difficulties have been encountered in obtaining uniform structures throughout quenched samples. 3) The reaction products, and in particular their morphology. have not been clearly resolved. 4) The martensitic a' phase forms over only a limited composition range for most titanium-base binary alloys. Gomez and polonis4 showed that the Ti-Cu system provides an excellent basis for investigating the tempering of a' over a range of composition without the complication of retained P or the transition w phase. In the present work the effects of solute concentration, tempering temperature, and coherency strain conditions are considered with reference to the over-all precipitation process in quenched alloys of the Ti-Cu system. Both microstructural observations and kinetic data are correlated to define the rate-controlling processes which govern the observed localized and discontinuous precipitation reactions. An earlier paper5 was devoted to a discussion of the modes of heterogeneous nucleation of Ti2Cu from the martensitic a' structure. The present paper will therefore emphasize the progress of the tempering reaction beyond the initial stages. EXPERIMENTAL METHODS The Ti-Cu alloys for this study were prepared by conventional arc-melting procedures. Chemical analysis revealed that the alloy buttons contained approximately 0.02 wt pct 0, 0.04 wt pct N, and within 0.1 wt pct of the intended copper concentration. The progress of the tempering reaction was followed by means of electrical-resistance measurements utilizing a Kelvin double bridge, microhard-ness readings with a 400-g load, and X-ray dif-fractometry patterns to reveal line-broadening effects. Metallographic specimens examined at magnifications greater than X1000 were shadowed with germanium to reveal fine structural details. Direct carbon replicas were prepared for the electron-microscopy studies. EXPERIMENTAL RESULTS Property Changes. The changes of microhardness that accompany the precipitation of Ti2Cu from a' are shown in Figs. 1 and 2. As the solute concentration increases the peak hardness, for a given tempering temperature, increases. In alloys of given composition the time to reach the peak hardness agreed with the time to attain maximum X-ray diffraction peak breadth, as shown in Fig. 3. The maximum hardness and the maximum line breadth increased with lower tempering temperatures, and the time to reach the maximum also increased. The a' peaks broadened during the initial stages of tem-

Jan 1, 1965

By D. W. Fuerstenau, P. C. Kapur

The kinetics of green pelletization in a laboratory balling drum have been studied, using pulverized limestone as a model system. The growth characteristics of green pellets were found to be extremely sensitive to the moisture content of the material. Empirical kinetic equations, which incorporate a function of specific surface of the pellets as the criterion for growth potential, have been found to describe growth in a nucleation region and in a ball growth region. The rate constants in the kinetic equations are strongly dependent on the moisture content of the material being pelletized. Size distributions of the balls at different stages of pelletiz-ing are also discussed. In many industrial chemical processes, particulate matter can only be utilized if it is in an agglomerated form, such as pellets. Pelletizing is now widely used in iron ore technology1, and it has also been applied to a number of diverse fields such as the production of cement-kiln feed2, fertilizers3, and fluorspar4. Recently, it has been proposed to pelletize dispersion-type ceramic nuclear fuel elements5. In iron ore technology, for example, the production of agglomerates by pelletizing involves two major steps: 1) the preparation of green balls by rolling particles in a suitable balling device and 2) the firing of the green balls to form compact, strong bodies upon sintering. The critical step in a successful iron ore pelletizing operation is generally considered to be the balling operation1. In this paper, which is not concerned with the sintering of green pellets, the words green pelletizing and balling will be used interchangeably. Green pelletizing, or balling, will be defined as the process of forming larger bodies by rolling fine particles on a surface without the application of direct pressure. Two recent literature surveys6" indicate that in spite of the considerable amount of industrial pelletizing, very little is known about the fundamental principles of balling and its kinetics. The first reported research on the kinetics of pelletizing is the work of Newitt and Conway-Jones8. Using silica sands of different sizes in a batch laboratory balling drum, they found that the average green pellet diameter increased linearly with time at constant drum speed, and qualitatively the growth rate increased with moisture content. Generalized conclusions cannot be drawn from their research since the materials which they pelletized were sand and sand-silt mixtures rather than comminuted materials. Moreover, Newitt and Conway-Jones used testing sieves to estimate the size distribution of the green pellets, and this technique limited the range over which they could study the growth kinetics of the pellets. Bhrany and co-workers9 investigated the kinetics of balling iron ore fines on disk pelletizers ranging in diam from 1 to 18 ft. In their investigation, balling was carried out as a continuous operation, and growth kinetics were studied in terms of retention time of the material on the disk. Although the feed material in their study was quite coarse (the maximum size being about 1/2 in.), they also found qualitative relationships between pellet growth and water content, and feed size. In the present investigation, a number of innovations were introduced that refined the experimental measurements and established the reproducibility of balling experimentation. This enabled extension of the range of measurements to include study of agglomerate nucleation phenomena in the fractional mm size. This paper presents a detailed analysis of the nucleation and growth of green pellets in a laboratory balling drum. MATERIALS AND METHOD Pulverized limestone of specific gravity 2.72 was used as a model system in these studies. It has already been established that the balling characteristics of limestone and silica are similar to those of iron ore concentrates 2,8,10, depending on physical, rather than chemical, properties of the particles. The size distribution of the limestone was determined by a wet-dry sieving technique in the sieve range and by a sedimentation balance in the sub-sieve range. Fig. 1 presents the size distribution of the limestone used in this research. This figure shows that the material is finer than 200p (65 mesh) and that 25% of it is finer than 12. The specific surface area of this powder, as measured by BET gas adsorption methods,

Jan 1, 1964

By P. Somasundaran, D. W. Fuerstenau

The length of the collector is found to influence the flotation of the mineral even at incipient conditions, which are below the concentration at which interaction at the solid-liquid interface begins to take place to form hemi-micelles. To study this dependence, concentration for incipient flotation of quartz was determined as a function of pH with collectors of various chain lengths. The observed effect of chain length on flotation is ascribed to that of collector adsorbed on the bubble surface. In previous studies, it was shown that at low concentrations the alkyl collector ions adsorb at the solid-liquid interface as individuals.''2 At higher concentrations, the collector ions adsorbed at the solid-liquid interface associate with each other to form two-dimensional aggregates called hemi-micelles. Above the hemi-micelle concentration, the length of the hydrocarbon chain is extremely important since the hydrocarbons are in effect removed from water during the association, making the energetic conditions more favorable for adsorption at the interface. Because of this enhanced adsorption, one observes a very rapid increase in flotation associated with the hemi-micelle formation at the solid-liquid interface. However, a dependence of flotation on the chain length at concentrations below that required for hemi-micelle association was also observed,' and this cannot be explained by the above mechanism which postulated hydrocarbon chain interactions only at the solid-liquid interface. This prompted an investigation into other possible reactions of the hydrocarbon chains and an examination of the conditions at the bubble surface involved in the flotation system and how these observations might explain the reactions at the solid-gas interface which cause the particle-bubble attachment required for flotation. To obtain more information on chain length effects, flotation, under incipient conditions, was tested by vacuum flotation techniques. The collector-concen-tration-pH relationships for flotation of quartz with alkyl ammonium acetate collectors was delineated by observing the pH at which quartz particles begin to float to the liquid surface. By investigating flotation as a function of pH, it was also possible to study the effect of neutral molecules on incipient flotation conditions, since the aminium ions hydrolyze to amine molecules at higher pH values. EXPERIMENTAL WORK Brazilian quartz specimens were crushed and sized, and the 270 x 400 mesh fraction was used for flotation studies. The samples were leached with concentrated hydrochloric acid until no coloration of the acid occurred. The leached material was washed free of chloride ions and stored in distilled water. The vacuum flotation technique developed by Schuhmann and prakash3 was used to determine the critical pH-concentration curves. This method, which can be used to delineate conditions for incipient flotation, is fairly simple and rapid. About 0.5 gm of 270 x 400 mesh quartz was placed in a 100 ml graduated cylinder which was then filled to the 100 ml mark with the collector solution made from high-purity alkyl ammonium acetate salts. The water used for the test was conductivity water saturated with air that had been passed through a cleansing train consisting of Drierite, Ascarite, a water wash bottle, and a trap. After the pH was adjusted, the cylinder was then conditioned for thirty minutes. In the tests where an acid pH was desired, sufficient acid was added before the collector solution to avoid any effect due to slow desorption of collector from the quartz surface. After conditioning, vacuum was applied to the system and the flotation or nonflotation of the quartz was noted. The pH at which the quartz particles began to float to the liquid-gas interface was taken as the critical PH. Critical pH curves were thus determined for different concentrations of the various collectors. Hallimond tube flotation data were taken from the authors' previous publication1 for correlation with that from the vacuum flotation. RESULTS AND DISCUSSION The results of vacuum flotation studies for determining critical pH-concentration curves, i.e., curves which delineate conditions for incipient flotation, are shown in Fig. I. In generaI, all the curves exhibit an upper and lower pH limit between which flotation will

Jan 1, 1969

By L. B. Harris

Continuous cyclic unloading during tensile work hardening of polycrystalline zinc at room temperature enables specimens to sustain greatly increased extension. Such enhanced ductility is associated with creep-type extension, during which the cyclic component appears to promote relaxation of internal strains. It is possible to trace the transitions from tension, through enhanced cyclic extension, to fatigue and relate the observed behavior to simpler types of deformation. DISTINCTIVE deformation behavior has been shown to occur when loading includes both cyclic and unidirectional components. For aluminum and copper extended by a sequence of progressively biased strain reversals, coffin1 observed greater fracture ductility and lower flow stresses than during monotonic tension. This may be compared with the reduction in hardness obtained from conventional fatigue softening. But fatigue softening is accompanied by enhanced fatigue life,' whereas Benham3 found that fatigue life was reduced when copper continuously extended during axial load cycling. The corresponding specimen elongation, for large cyclic load amplitudes, was greater than during normal tension. Under different conditions, Bendler and wood4 found that torsional fatigue initiated extension in copper under low tensile loads previously in equilibrium with the specimen; fatigue life was again reduced. Thus there is a type of cyclic softening which is associated with reduced fatigue life and which occurs when the cyclic loading is accompanied by a unidirectional strain component. Further, the fracture ductility or extension obtained from the unidirectional component can exceed that obtained in the absence of cyclic load. Specimen extension was not initiated by axial fatigue at small load amplitudes;3 hence Benham's work distinguishes between fatigue at large and small amplitudes, the former often being linked with unidirectional deformation because of similarities in strain Structure. The initiation of tensile extension during torsional fatigue,4 however, occurred with small amplitudes. Comparable changes in behavior have been ob- served during creep. kennedy' found that combined cyclic and creep stresses on lead at 32°C increased the rate of elongation over that for simple creep, the consequence being a reduction in creep life. It was also demonstrated that small cyclic stresses applied after creep deformation initially increased recovery, but that prolonged application produced only normal fatigue hardening. It is clear that physical properties can be changed by interaction between the cyclic and unidirectional deformations, but owing to the number of different ways in which the deformations can be combined and the large number of possible variables for each combination, trends of behavior become easily obscured. One definite conclusion is that enhanced ductility or increased extension can be obtained by cyclic action, and it is this process that has been investigated for the tensile test by measurements of the extra tensile strain produced by the addition of a cyclic tensile component. EXPERIMENTAL PROCEDURE Material. Specimens were 99.99 pct Zn wire of 1.6 and 2.0 mm diam. Mean grain diameter was 0.02 mm, sufficiently small to give a ductile necked-down fracture under all loading conditions. All experiments were conducted at an average temperature of 20°C. Normal Tension. Unidirectional tensile curves at different strain rates were obtained from an In-stron testing machine, on which load-time curves were recorded autographically, using gage lengths of 5 and 10 cm. Straining was at constant cross-head velocity, and quoted strain rates are with reference to initial specimen length. Measurements of total elongation under simple tension were also made on the tensile machine that had been modified to incorporate an added fluctuating load. Combined Tension and Rapid Cyclic Load. An electromagnetic vibrator was coupled to the elastic beam of a Hounsfield ensometer- and driven sinus-oidally from a power amplifier at frequencies from 20 to 360 cps, the flexible connecting links on the tensometer being replaced by rigid fixtures to eliminate lateral vibration in the specimen. One end of the specimen was pulled by the normal extension drive of the tensometer while the other end, fixed to the elastic beam and vibrator, was subjected to rapid oscillations of load. It was thus possible to apply cyclic load to a tensile test without altering the rate of extension of the specimen

Jan 1, 1964

By J. E. Andersen, J. Halpern, C. S. Samis

In the presence of oxygen, galena is oxidized in an aqueous medium containing sodium hydroxide, in accordance with the following reaction: PbS + 2O2 + 3OH ? HPbO2 + SO4 = + H2O A novel method was devised for following this reaction which takes place in an autoclave under oxygen pressure, by measuring the concentration of HPbO2- in the solution with a cathode ray polarograph employing stationary platinum electrodes. Using this procedure a study was made of the kinetics of the reaction, in which the effect of a number of variables, including temperature, oxygen pressure, NaOH concentration, and agitation, on the rate, were determined. The results of this study are described and discussed, in terms of possible mechanisms for the reaction. IT is known that sulphide minerals can be oxidized in aqueous media in the presence of oxygen under pressure. Reactions of this type can be classified in two categories depending upon whether the products of oxidation are insoluble or soluble in the aqueous medium. An example of the first type of reaction is the oxidation of pyrite in alkaline solutions, giving rise to an insoluble iron oxide. The kinetics of this reaction have been investigated and its mechanism established.' It has been applied in the oxidation of iron sulphides present in refractory gold ores to improve the subsequent recovery of gold by cyanida-tion.' The second type of reaction finds application where it is desired to recover the metal by leaching during oxidation. In this case a medium is selected in which the oxidized mineral is soluble. For example, nickel, copper, and cobalt sulphide ores can be treated by oxidation in the presence of a solution of ammonia dissolving the nickel, copper, and cobalt as the metal ammine sulphate salts.:' A similar treatment has also been reported to apply to zinc sulphide ores.' It is known that lead sulphate is soluble in solutions of sodium hydroxide or ammonium acetate. It should therefore be possible to dissolve the lead from galena ores by aqueous oxidation with oxygen under pressure using either of these solutions. The applicability of the ammonium acetate treatment has been investigated and confirmed in a recent study.' The present paper describes the results of a similar study in which the kinetics of the oxidation of galena in sodium hydroxide solutions have been investigated. The object of this investigation was pri- marily to obtain information of a fundamental nature relating to the kinetics and mechanism of this reaction. The use of pulps of comminuted ore in a study of this type is undesirable because of the difficulty in controlling and measuring the surface area. The measurements were therefore made using galena crystals of measured surface area and in this way absolute reaction rates were obtained. The reaction was found to proceed as follows: PbS + 2O2 + 3OH ? HPbO2 + SO4 + H2O [I] The products are sodium plumbite and sodium sulphate salts which dissolve in the aqueous solution. The reaction studies were carried out in an autoclave in which a desired pressure of oxygen was maintained. The reaction was followed by measuring the concentration of lead in the solution with a cathode ray polarograph. The results obtained in this investigation are presented and discussed in the present paper. Experimental Materials: The crystals of galena were obtained from Violamac Mines, Sandon, B. C. The following impurities were indicated by spectrographic analysis carried out by the Provincial Assay Office, Victoria, B. C.: Sn, 0.02 to 0.2 pct; Sb, 0.07 to 0.7; Zn, 0.01 to 0.1; Si, Fe, Mg, As, less than 0.05 pct; Ag, 126 oz per ton, the latter determined by standard fire-assaying procedure. After cutting a specimen measuring approximately 5x7x12 mm, the crystal surfaces were ground parallel to the 100 axes using No. 2 emery, washed with water, and the dimensions were measured with a micrometer. Oxygen gas was of commercial grade and supplied in cylinders by Canadian Liquid Air. Solutions were made up with chemicals of chemically pure grade and distilled water. Equipment: Autoclave: The autoclave used in these studies was constructed of stainless steel and

Jan 1, 1954

By J. D. Alexander, W. L. Martin, J. N. Dew

This paper presents data obtained using a flood-pot technique to determine the fuel available and the corresponding theoretical air requirements for in situ combustion of crude oils. Since the technique is relatively quick and easy, it is a practical and convenient tool for evaluating reservoirs as fireflood prospects. It is also a research tool which facilitates systematic study of the variables affecting fuel availability and corresponding air requirements. The understanding of these variables is of prime importance to those concerned with the technical and economic development of in situ combustion as an oil-recovery process. The experimental results show conclusively that the fuel available for in situ combustion is not a constant but, rather, varies with crude-oil characteristics, porous-medium type, oil saturation, air flux and time-temperature relationships. Thus, the fuel availability for specified field applications should be determined using actual reservoir crude and core material and the process conditions expected during in situ combustion in the reservoir. INTRODUCTION In situ combustion is a thermal process for recovering crude oil from reservoirs. The thermal energy released during the combustion of a small amount of the oil in place aids in the displacement of the remaining oil. Numerous articles have been published describing the in situ combustion process giving detailed results of laboratory and field experiments.10 In order to engineer an in situ combustion project, a number of important factors must be considered and determined. These factors include: (1) the amount of fuel consumed per unit of reservoir volume swept by the combustion zone, (2) the composition of the fuel consumed, (3) the amount of air required to consume this fuel, (4) the portion of the reservoir swept by the combustion zone, (5) the appropriate air-injection rates and pressures, (6) the amount of oil that will be recovered, (7) the rate of oil production and (8) the operating costs. Nelson and McNiell1 recently have described a procedure which utilizes laboratory combustion-tube data as a basis for the calculation of some of these design factors. Various authors have attempted to describe the in situ combustion process mathematically, and considerable progress has been made. Analytical solutions to the problem of heat transfer from a moving combustion front have been obtained for linear and radial systems."-' All of the published results involve the assumptions that: (1) fuel concentration is constant throughout the reservoir, or that fuel concentration is inversely proportional to the velocity of the front for a given rate of oxygen consumption; and (2) the fuel reacts instantaneously with injected oxygen, while liberating a constant amount of heat per unit weight of fuel at all temperatures. It seems both desirable and reasonable to test the validity of these assumptions experimentally. This paper presents laboratory data which were obtained by means of a "fire flood-pot" method for determining fuel availability and composition, and the corresponding theoretical air requirements for in situ combustion of crude oils under variable conditions. The mechanics of the method are similar to a conventional tube-run experiment.' The important differences involve the size of the reservoir model used and the method for providing the experimental environment. The new method subjects conventionally-sized core samples or unconsolidated sands to a programmed environmental sequence similar to that experienced by a similar volume of rock during the approach and passage of a combustion front in a long tube or in an oil reservoir undergoing in situ combustion. Restored-state samples can also be used. The small samples and relatively simple techniques involved allow an experiment to be set up, run and calculated in about three 8-hour days. This is a considerable improvement over long-combustion-tube techniques which can require several days to run and several more work days to set up and calculate. All the runs presented were run at 40-psig injection pressure. Pressure was not considered as a variable for these experiments, since we previously had found that it had only a small effect on fuel availability up to 600 psig.APPARATUS AND MATERIALS APPARATUS The fire flood-pot apparatus consists of a consolidated

By E. T. Turkdogan, J. H. Swisher

The solubility of oxygen in zone-refined iron was determined in the temperature range.from 881" to 1350°C. The solubility in a iron at 881°C ms found to be about 2 to 3 ppm; in y iron, the solubility was found to increase from about 2 to 3 ppm at 950°C to about 25 ppm at 1350°C. The permeability of oxygen in an iron -0.1 pct Al alloy was determined in the y iron range, using an internal oxidation technique. By combining the permeability and solubility data, the diffzisivity of oxygen in y and a iron was calculated. The oxygen diffusivity in solid iron may be s~immarized as follows: 8820 For 6 iron and IN a recent paper, Hepworth, Smith, and Turkdogan1 reported on the solubility, permeability, and diffusivity of oxygen in 6 iron, together with permeability data for oxygen in a iron. In the present investigation, similar measurements were made in the ? phase region. In addition, a solubility measurement was performed in the a phase region to permit calculation of the diffusivity of oxygen in a, iron. References to early work on this subject are given in the previous publication.' EXPERIMENTAL Solubility Measurements. The oxygen solubility was determined by equilibrating cylindrical samples 0.3 in. diam by 14 in. long of zone-refined iron in water vapor-hydrogen gas mixtures. The zone-refined iron was prepared by B. F. Oliver of this laboratory, using an apparatus and technique described elsewhere.2'3 Six zone-melting passes were used to achieve a total impurity level of about 30 ppm. Of this 30 ppm, the combined nickel and cobalt content was about 20 ppm, oxygen was 4 ppm, and all oxidizable impurities less than 1 pprn each. A vertical resistance furnace wound with molybdenum wire was used for the experiments. The temperature was measured before and after each experiment with a Pt/Pt-10 pct Rh thermocouple. In the gas train, flow rates of hydrogen and argon were measured with capillary flow meters, and the resulting mixtures were passed through a column containing 90 pct oxalic acid dihydrate and 10 pct anhydrous oxalic acid to obtain predetermined ratios of H2O to H2. The vapor pressure of H2O above this mixture as a function of temperature is well-known.4 The exit gas was ana- lyzed periodically for H2O, and good agreement (+3 pct) with the calculated composition was obtained. The zone-refined iron specimens were held in the furnace for a sufficient length of time for equilibration, e.g., 18 hr at 1350°C and 1 week at 881°C, then quenched in a brine solution. After removing the surface oxide from the samples by machining, duplicate analyses were obtained by a combined vacuum fusion-infrared method; oxygen analysis was reproducible within 2 ppm. Permeability Measurements. The permeability of oxygen in alloys containing about 0.1 pct A1 was determined by internal oxidation and measurement of the subscale thickness as a function of time. The experimental alloys were prepared by adding aluminum to electrolytic iron (grade 104A plastiron) that had previously been vacuum-carbon deoxidized. The resulting ingots contained about 20 ppm O, 100 pprn C, 40 pprn Si, 50 ppm Mo, 20 ppm P, 20 ppm S, and 20 pprn Zr as the principal impurities. After hot rolling the ingots to 1-in.-thick slabs, specimens were machined from the stock in the form of rectangular plates, 4 by 5 by 2 in. The general procedure for the permeability experiments was the same as those for the solubility measurements. The specimens were cooled in a reducing atmosphere rather than quenched, however, in order to maintain a clean surface for measurement of the sub-scale thickness. This measurement was made on a polished cross section of each specimen, using a microscope with a micrometer stage. The inclusions formed at the lowest temperature 1033°C were too small to be seen with an optical microscope. An electron micrograph showing the size and shape of individual particles is shown in Fig. 1. The dark band in the picture is a boundary between two subgrains. The subscale thickness in these samples was measured with an optical microscope after heavily etching in 2 pct nital, which gave contrast between the subscale and the unoxidized zone.

Jan 1, 1968

By R. J. Quigg, G. S. Doble

Commercial stress -relieved TD Nickel bar was shown to retain room- and elevated-temperature tensile strength after exposure up to 2501°F. Cold swaging increased both room -temperature and 2000°F tensile strength. After annealing at 2500°F the strengthening due to swaging was retained at 2000°F hilt eliminated at room temperature. Annealing produced changes in hardness and X-ray half peak width indicating the presence of recovery processes as 1071° as 1000°F but no recrystallization of swaged material was noted at any temperature. In contrast to swaging, rolling induced a recrystal-lized structure after annealing. The tensile strength of this recrystallized structure was comparable to the cold-worked condition. High-temperature tensile properties of as -received bar were highly anisotropic with the transverse tensile strength being one fifth the longitudinal value. The aniso-/ropy is affected by working direction and may he partially reversed by changing the direction of metal flow. The divergence in tensile strength, beginning above 550°F or- approximate one third the absolute melting point, is strain-rate dependent. T D Nickel is a commercial dispersion-hardened alloy containing 2 vol pct thoria. The dispersion, consisting of spherical particles 0.030 to 0.050 in diameter with an interparticle spacing of less than 1 is reported to maintain stable properties up to 2400°F.1 This stability of second phase results in maintenance of elevated-temperature strength at higher temperatures and longer times than normal nickel-base superalloys.2 The purpose of this paper is to describe the effect of various mechanical working operations on the strength and microstructural stability of TD Nickel bar. MATERIAL AND PROCEDURES All material used in this study was commercial TD Nickel bar. This material is produced by a chemical process which results in a nickel powder containing a dispersion of thoria particles. The powder is then pressed, sintered, extruded, and subsequently worked to bar stock. Three starting materials from three separate lots were used: as-extruded bar. 1-in.-diam stress-relieved bar, and 1/2-in.-diam stress-relieved bar. Since TD Nickel bar stock is cold-worked without a recrystalliza-tion anneal, the accumulated deformation or degree of cold work in these materials increases as the bar diameter decreases. Some of the 1/2-in.-diam bar was swaged to 1/4 in. diameter at room temperature in order to produce an as-worked condition for comparison with the stress-relieved stock. Tensile testing was performed on an Instron Tensile Tester at a constant crosshead speed of 0.020 in. per min. The 0.2 pct offset yield strength was measured from the load-crosshead movement plot. Specimen gage dimensions were 0.080 in. in diameter by 0.40 in. in length, producing a strain rate of approximately 0.050 min-1. Specimens were tested in air and heated within a resistance-wound furnace controlled to ±5°F. A 15-min soak at temperature was employed before testing. Samples were heat-treated in air and specimens machined after exposure with sufficient material removed to eliminate any surface contamination. X-ray line breadth was determined from a diffractometer scan of a transverse face of a bar using copper K, radiation. Metallographic preparation utilized standard mechanical polishing with Carapella's etch. Specimens for electron microscopy were electropolished in a 1:7 sulfuric/methaol solution and chromium-shadowed collodion replicas prepared. RESULTS AND DISCUSSION I) Effect of Elevated-Temperature Exposure on the properties of TD Nickel. The effect of various elevated-temperature exposures on the room-temperature tensile strength of TD Nickel is shown in Table I. In the unexposed condition the tensile strength, reduction in area, and hardness all increase with increasing accumulated deformation while the elongation decreases. After exposure at 2500°F the strength of all three materials decreases to about 65,000 psi and the elongations increase slightly. The apparent increase in strength of the 1-in. bar after a 2000°F treatment is probably experimental scatter. These results indicate that the room-temperature strengthening due to additional deformation is annealed out upon elevated-temperature exposure. In contrast to the room-temperature data, the 2000°F tensile strengths increase in order of increasing deformation even after exposure. Although some loss of strength occurs after exposure, much of the effect of working is still maintained at 2000°F. The room-temperature hardness after various

Jan 1, 1965

By D. W. White

The kinetics of isothermal transformation of ß-to-u uranium have been studied over a broad temperature range in alloys containing from 0.3 to 4.0 atomic pct Cr. Two modes of transformation are indicated by the existence of two C-curves in the TTT diagram. The upper temperature mode is regarded as a nucleation and growth mechanism, whose rate is controlled by diffusion of chromium in the ß phase matrix. The lower temperature mode is martensitic in nature. The M, temperature increases with decreasing chromium content, suggesting that the two transformation processes become synonymous in unalloyed uranium. URANIUM metal undergoes two allotropic transformations in the solid state. The a phase, orthorhombic in crystal structure,' is stable from room temperature up to about 665°C. The ß phase, characterized by a complex tetragonal structure,' prevails from 665" to about 770°C. The y phase is body-centered-cubic3 and is the stable modification from 770°C up to the melting point (about 1130"). In uranium of reasonable purity, neither of the two high temperature phases can be retained by quenching. However, the addition of certain alloying elements to uranium makes it possible to retain either the y-uranium phase or the ß-uranium phase at room temperature. Chromium alloyed in small amounts with uranium will permit retention of the ß-uranium phase in a metastable state at room temperature upon quenching from a ß-phase temperature.' From available information' on the equilibrium phase diagram for the U-Cr alloy system (Fig. I), it is to be expected that, however sluggish in its rate, the ß phase in such alloys should decompose eutectoidally to a phase and elemental chromium. It was the aim of this investigation to measure the rate and study the nature of this decomposition as a function of temperature and of chromium content. The investigation was reported in classified literature about five years ago and has recently been declassified for publication. In the meantime, there have appeared the papers of Holden,5 Mott and Haines,".' and Butcher and Rowe8 ealing with the metallography and the crystallography of the ß-to-a transformation in U-Cr alloys. These investigators have confirmed several of the phenomenological observations that will be described in the present paper and have examined in considerable detail certain aspects of the transformation and its mechanism. Although all of these investigations have concerned themselves experimentally with U-Cr alloys for the most part, an important consequence has been a clearer understanding of the nature of the ß-to-a transformation in uranium metal itself. Experimental Procedure This investigation dealt with a series of uranium alloys varying in chromium content from 0.3 to 4.0 atomic pct (0.066 to 0.90 weight pct). On five of the alloys, rates of isothermal transformation from the ß to the a phase were measured over a wide temperature range, leading to the development of TTT (time-temperature-transformation) diagrams. Transformation rates were measured over certain narrow temperature ranges on additional alloys. The alloys were prepared by vacuum melting and casting, using zircon or magnesia crucibles and graphite molds. Electrolytic chromium was used as the alloying addition, and the uranium was Mallin-ckrodt biscuit metal that had been vacuum remelted and cropped to remove many of the nonmetallic impurities that had floated to the top of the ingot. The ingots, 3/4 or 1 in. diam, were reduced in size by swaging. Alloys containing less than about 2 atomic pct Cr were swaged at 250° to 275°C, with initial and intermediate anneals at 550°C after every 75 pct reduction in area. Alloys with higher amounts of chromium were swaged at 550" to 600°C, although at the smaller sizes some of them were reduced by the procedure used on the more dilute alloys. Before use as test specimens, the swaged rods were annealed at 700" to 720°C for several hours, followed by slow furnace-cooling. The purpose of the anneal was to achieve the maximum amount of solution of the available chromium into the ß phase, as well as to remove extensive preferred orientation. The isothermal transformation rates were measured dilatometrically, using a quenching dilatometer and an experimental technique similar to those employed by Davenport and Bain in their original work on the transformation kinetics of austenite in

Jan 1, 1956

By F. H. Callaway, W. O. Keller

The various theories as to the well spacing-recovery relationship are reviewed in considerable detail and these theories analyzed in terms of their consistency with modern reservoir engineering concepts. It is concluded that the well spacing problem must be analyzed in terms of recovery efficiency and that a positive answer to the relation between well density and recovery efficiency is not available from direct comparisons of the production histories of wells and fields. The results of an engineering analysis designed to permit approximate calculation of recovery efficiencies as a function of well spacing in a depletion type reservoir from basic reservoir data is presented. Results of this type analysis indicate that the effect of well spacing on recovery efficiency in depletion type reservoirs can be expected to be very small. Limitations of this approach are pointed out, particularly with respect to its application in lenticular reservoirs. Testing techniques are outlined which should indicate whether or not a reservoir is continuous between wells and whether or not satisfactory drainage is being obtained with present spacings. A mass of data of this type indicates continuity to exist in most fields. INTRODUCTION The purpose of this paper is to review critically the engineering aspects of the well spacing problem, both from the standpoint of certain concepts and from the standpoint of reservoir mechanics. The well spacing problem is primarily an economic problem in which the optimum well density for a particular field is that density which will yield the greatest oil recovery consistent with justifiable development costs. The well spacing answer in terms of economic conditions, however, is extremely sensitive to the variation in recovery efficiency with well density. The variation in recovery efficiency with 'References given at end of paper. Manuscript received at the office of the Petroleum Branch October 2, 1949. Paper presented at the Petroleum Branch Meeting in San Antonio. Texas, October 5-7. 1949. well density is properly an engineering problem. Different opinions as to the correct answer to this engineering problem is the basis for most of the wide difference in opinion among various members of the industry as to optimum well spacing. This paper will be confined to the engineering problem of the relation between well density and ultimate oil recovery; economic considerations necessary for the evaluation of optimum well density for any particular field will not be discussed. The paper can be logically divided into two parts. The first part deals with a critical examination of the background and logic of the Cutler Rule and of similar studies by other authors and of related well spacing concepts. It is indicated that the variations in recoveries with well density* observed by Cutler and. others can be logically attributed to regional migration. Theoretical justification of the Cutler type relation wherein observed variations in recovery with well density in the same field is attributed to variations in recovery effiiency, in terms of energy relations, is refuted. The second part consists of a review of concepts of reservoir mechanics with regard to the well density-recovery relation. It is indicated that little variation of recovery efficiency with well density can be expected in a depletion type reservoir, unless lenticular conditions prevent communication between wells. The significance of field test data with regard to the existence or non-existence of lenticular conditions is pointed out. THE CUTLER RULE The first published article concerning the engineering aspects of the well spacing problem to receive wide attention was the work of W. W. Cutler' of the U. S. Bureau of Mines, published in 1924. In a study of decline curves from a large *The expression "well density" as utilized herein refers to the number of acres attributed to each well in a uniform well pattern, and is expressed in acres per well. The term "well spacing" Is utilized to denote the average distance between adjacent wells in a uniform well pattern. †Although the Cutler rule is treated critically in this discussion the authors intend no personal criticism of W. W. Cutler or of his hark The currently accepted concepts of reservoir mechanics were no": existent at the time of Cutler's work, as were even the moat basic tools (such as the bottom hole pressure bomb) for observing reservoir behavior.

Jan 1, 1950