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By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By B. H. Bergstram, C. L. Sollenberger

When glass spheres are crushed by slow compression loading, the outer lune-shaped fragments resulting from the fracture consistently fly outward at high velocity. About 45 pct of the strain energy fed into the sphere-platen system reappears in the form of the kinetic energy possessed by these fragments. These measurements were obtained from high-speed photographs. This kinetic energy can be utilized for addtional comminution if the fragments are allowed to impact against a suitable structure. Comminution theory has advanced considerably in recent years by the study of this unit operation under laboratory conditions. Some of the parameters have been isolated, but the experimental measurements of the pertinent quantities, such as energy, particle size, etc., are still only made prior to and after the conclusion of a fracture sequence. The catastrophic fracture process itself has not been adequately studied from a comminution point of view. It has recently been suggested by Gilvarry that the fragments which result from the free crushing of a single glass sphere by slow compression contain a considerable amount of kinetic energy after fracture. This kinetic energy, if properly directed, possibly can be partially utilized to cause additional fracture. In this paper a hypothesis will be presented which suggests that this kinetic energy is necessarily present and that its dissipation is the process by which a large part of the thermal energy imparted to the crushed product is generated. Evidence supporting the existence of kinetic energy and its utilization for secondary fracture will also be presented. THEORETICAL A previous paper4 has shown that the load-deformation curve of a system composed of an elastic sphere gripped by a pair of parallel platens, can be predicted by a consideration of the theories of Hertz as summarized by Timoshenko.' The deformation A, of one half of the system is given by which states that the deformation is a function of the mutually applied load, P, the radius of the sphere, R; and the respective physical properties of Poisson's ratio, v, and Young's modulus of elasticity, Y. The shape of experimental load-deformation curves conform to this relationship. The energy input to the sphere-platen system, can be predicted from the integral of the load acting through the appropriate distance, dA. Since dA can be evaluated in terms of P from the derivative of Eq. 1, this integral can be integrated between limits of 0 and P. The test sphere, however, is loaded at not one but at two points of contact, i.e., at both ends of a diameter, and hence the total energy input, E, is twice the energy input at each end, or The energy input to the system calculated from this equation corresponds to the energy computed from the measured area under the load-deformation curve. Timoshenko, considering the impact of two perfectly elastic spheres, has shown that the inter-penetration distance A is given by - m f (D (^ * ^t w as modified for the special case where one sphere is of infinite radius, i.e., its surface is a plane; where M is the mass of the finite sphere of radius R, and V is the velocity of approach at the start of an impact and also equals the final velocity of separation for perfectly elastic bodies. Because A is also a function of the load and the elastic properties, as shown in Eq. 1, the velocity, V, can also be calculated in terms of the elastic properties and maximum load, P, or

Jan 1, 1961

By H. M. Davis, T. S. Jones

A methodfor accelerating the reduction of a metal oxide by carbon monoxide is to incorporate in the reduction system a nonreducible oxide which has a strong affinity for carbon dioxide and will remove it from the product gases. The effectiveness of this method was investigated by veduction experiments on specially prepared powder mixtures of SrO-ZnO ("active'.) and SrCO3-ZnO (reference). Measurements at 750o and 677°C showed that the rate of reduction of ZnO by CO was as much as an order of magnitude greater in the presence of SrO. Under the experimental conditions at least as much CO2 as generated by veduction was absorbed when SrO was present. Enlzancernent of the veduction rate by SvO resulted from modification of' gaseous djfitsion processes. THE specific question posed in this investigation was whether the reduction reaction CO + ZnO - Zn(g) + COa [1] could be accelerated by incorporating strontium oxide into the oxide charge undergoing reduction. Provided the strontium oxide was active enough, it could remove carbon dioxide from the product gases of ( 11 and form strontium carbonate, thus modifying Reaction [ 1] to CO + ZnO + SrO = Zn(g) + SrCO3 [ 2] This study of the comparative rates of Reactions [ I] and [2] can be considered as a particular case of a general scheme for increasing the rates of reduction of metal oxides by carbon monoxide. The limits of applicability of this scheme are indicated in the simple thermodynamic analysis presented in the appendix. This analysis primarily dictated the choice of the system, CO-ZnO-SrO, employed in this investigation. In addition, it was thought that a study of this scheme by use of the CO-ZnO-SrO reaction system would be of special interest in view of indications in the literature1-3 that the gaseous reduction of zinc oxide is prone to rate control by diffusion in the gas phase. The distinction should be pointed out between this and other efforts to increase the rates of reduction reactions through the use of addition agents. Additions of a wide range of chemicals have been tried with de- grees of apparent success varying from slightly negative to highly positive. The reasons for making additions have included the use of salts to produce effects akin to catalysis,4, 5 the alteration of the microstruc-tural details of the reduction process (including solid-state diffusion),6-8 and the conversion of an en-dothermic reaction into one that is exothermic or autogenous.9-12 The means used to attempt alteration of the enthalpy change has commonly been to incorporate lime into the charge, so that heat is generated by reaction with either of the reaction products, carbon dioxide or water. The use of lime in this way makes endeavors such as that of Edstrom and Wiberg similar to the present one. Furthermore, the basic principle behind the present work has previously been set forth.13 However, a detailed investigation of the type of reaction described in this work does not appear to have been conducted. EXPERIMENTAL PROCEDURE From both conceptual and physical standpoints, Reaction [2] is to be considered as the sum of two reactions:

Jan 1, 1968

By I. Tamura, J. O. Brittain, T. Mura

Plain carbon steel in the cold worked or marten-sitic conditions has an internal friction peak at about 250 oC at a frequency of I cps. The influence of substitutional alloying elements on this peak was examined experimentally. The alloys were vacuum melted Co-, Cr-, Mo-, Ni-, and Si-iron (about 3 pct alloying elements), and carburized Si-iron. The internal friction of the alloys in the temperature range 30o to 500 OC was determined by means of a torsion pendulum. The 250 oC peak of the cold-worked alloys was lower in height than that observed in plain C-iron and steel. Carburized Si-iron in the quenched condition had a peak which occurred at a slightly lower temperature than in quenched plain C-steel, but the height of the peak was substantially greater than that found for the same alloy in the cold-worked condition. The activation energy of this peak for martensitic Si-steel was about 35 kcal per mol. ANNEALED a iron has two internal friction peaks due to nitrogen and carbon at 20o and 40o C respectively, at a frequency of 1 cps. If a iron is cold worked, these diffusion peaks become smaller and a new peak appears at about 250o C. The activation energy for the 250o C peak is in the range of 32 to 44 kcal per mol and has an average value of 38 kcal per mo1. It has been experimentally verified that both interstitial solute atoms and dislocations are necessary for the 250o C peak. 3 Wert has also shown that an incubation period precedes the appearance of the 250 C peak.4 With regard to quenched martensitic steel, Ke et al.596 observed two peaks at around 130o and 250o C. They conjectured that the 250o C peak in martensite was due to the same mechanism as the 250°C peak in cold worked a iron, and the 130°C peak was due to the nature of tempered martensite. They did not report the activation energy for these peaks. Chernikova7 found only one peak at about 200° C in tempered martensite. In a previous paperS we reported an activation energy of approximately 40 kcal per mol for the 250° C peak in plain carbon martensitic steels. Ichiyama8 found the activation energy to be about 36 kcal per mol for the 250° C internal friction peak in steels in the martensitic condition. The present authors proposed a theory for the 250°C peak for cold worked and quenched iron and steel.= The theory for the peak is based upon the addition of a strain-energy term to the free energy for the formation of a carbide precipitate due to the presence of a disclocation. The model employed for the relaxation process consists of the growth and solution of a carbide precipitate of critical size as a consequence of an oscillating dislocation. In this report, the influence of substitutional alloy ing elements on the 250° C peak is examined and the experimental results are discussed in terms of our theory for the peak. Most of the experimental work on the alloy steels was confined to the Fe-Si-C alloys.

Jan 1, 1962

By D. G. Westlake

Resistance was measured as a function of temperature, 77° to 350°K,for niobium with hydrogen concentrations up to 3.76 at. pct. Cooling curves exhibited a discontinuity in slope that was attributed to the initiation of hydride formation. A thermal hysteresis was explained in terms of diffusion and the effects of mechanical constraint on nucleation and growth. The heat of solution of hydrogen in saturated Nb-H solid solution was 2. 737 * 0.045 kcal per g-atom, including an unknown stress contribution. The critical ternperatures for hydride formation during cooling and for embrittlement are correlated but not coincident. This, too, has been explained in terms of mechanical constraint and stress-itlduced tratzsfomtation. Nb-H alloys undergo a ductile-brittle transition with decreasing temperature.'-3 Similar behavior has been noted for v-H.1,5 For the latter system, there is evi-dence6 suggesting coincidence of the temperature of minimum ductility and the critical temperature T, for initiation of metal hydride precipitation during cooling. A decrease in ductility due to the presence of brittle hydride particles is readily explainable. The fact that ductility begins to decrease at some temperature higher than T,4,5 has led us6 to suggest that precipitation may be strain-induced locally during tensile testing. Wood and Daniels' have reported that a plot of temperatures for 10 pct reduction in ductility vs hydrogen concentration in niobium is not coincident with, but parallels, the solvus.7,8 They believe this indicates a correlation of precipitation and embrittlement. Unfortunately, the two reported solvuses 7,8 to which Wood and Daniels refer are not in agreement with each other. Furthermore, neither solvus was determined experimentally: each was a plot of calculated solubilities. Thus. neither is highly dependable for determining whether embrittlement coincides with initiation of hydride precipitation. Longson 9 studied phase relations in the Nb-H system between 77° and 473°K by dilatometry. Comparison with metallographic observations convinced him that discontinuities in the slopes of his dilatometric plots were coincident with the initiation of hydride precipitation. Plotting the logarithm of the hydrogen concentration vs the reciprocal of the temperature at which precipitation was initiated during cooling, he obtained a straight line shown in Fig. 1. Walter and chandler,'' using X-ray techniques to detect the for mation of a second phase? have obtained three experimental points in the temperature range 295° to 338°K which fall within Longson's experimental error for this plot. A similar plotg of temperatures at which dissolution was completed during heating was a parallel line shifted toward higher temperatures. A straight-line plot was obtained, also, for the temperatures of the ductile-brittle transitions,9 but it was shifted toward still higher temperatures. Longson calculated an activation energy of 2.980 * 0.300 kcal per mole for the hydrogen embrittlement mechanism, compared with 3.180 * 0.400 kcal per mole for hydride formation. Despite this agreement, he concluded, "It seems unlikely that embrittlement results from hydride formation..." because hydrogen embrittlement was observed at temperatures above the solvus. It is our contention that embrittlement is correlated with precipitation of the hydride.6 Because only Longson has investigated Nb-H phase relations at sub-ambient temperatures, we deemed it advisable to re-determine the temperature dependence of the solubility using the resistometric technique already proven successful for the V-H system.6 Coincidence of our solvus with temperatures for embrittlement would

Jan 1, 1970

By James E. Lawver, James L. Wright

This paper describes the design of a cell used to measure the electrical conductivity, or the reciprocal resistivity, of granular materials. It also establishes a quantitative relationship between the electrical conductivity and the electrical separation of selected mineral samples. It is estimated' that the free world produces about 13 million tons of mineral concentrates a year by electrostatic or electrodynamic methods. At least 95% of these concentrates are produced by corona discharge type machines that separate minerals by exploiting the differences in their electrical conductivity. But, what is meant by the electrical conductivity of a mineral? How large a difference in the electrical conductivity of two mineral species is necessary to effect a separation? Just what is the role of conductivity in electrical separations with regard to capacity and selectivity? There is a considerable amount of information in the literature on both the mechanisms of conduction and the values of the electrical conductivity of pure single-crystal mineral specimens. In addition, some insight into the role of mineral conductivity can be obtained by referring to a Bureau of Mines publication' in which 95 minerals have been grouped as conductors or insulators as a function of temperature. The classification was made on the basis of the percent of weight that reported as "conductors" in an electrical separator. But, as is often the case in the mineral industry, practical application leads theory — and there is little useful information in the literature giving any kind of quantitative relationship between electrical conductivity and electrical separations. The problem is a bit complex because electrical conductivity per se — which can be rather easily measured on large, single grains — is not sufficiently informative to permit quantitative predictions of the separability of the mineral system. Practical "high-tension"* separations are made at such feed rates that the band of minerals on the rotor is multilayered in thickness. Thus, the effective conductivities of minerals as seen by a high-tension machine include particle-to-particle contact resistance, which is often a controlling factor in making a separation. This is particularly true when the mineral grains are coated with slime or with a dielectric surface film. From a high-tension separation viewpoint, one is actually concerned with the time required for corona-charged grains to lose enough charge so that the centrifugal force acting on the particles exceeds the image force holding the grains to the rotor. This calculation requires a knowledge of the effective mineral conductivity s. (The conductivity of the metal rotor is sufficiently greater than that of the minerals so that it need not be considered in charge decay calculations.) The charge density at time t can be approximated by the relaxation equation.3 where t 5 charge density at time t r, - charge density when t = 0 cr e total electrical conductivity £ = permittivity The time required for the charge density to fall to l/e of its initial value is called the relaxation time and is numerically equal to €/n. AS defined here, u is the conductivity of an element of homogeneous grains making contact with each other and with a grounded rotor. This paper deals with the design of a conductivity cell used to measure a, or its reciprocal p, the electrical resistivity. CELL DESIGN Initial test work was performed with a cell recommended by ASTM.4 Since the reproducibility with the ASTM cell was not satisfactory, it was decided to

Jan 1, 1970

By P. K. Koh

Isothermal salt bath annealing of 0.014-in. thick 3 pct Si-Fe sheet was conducted at temperatures ranging from 927" to 1260°C in order to investigate the grain-growth behavior. Within the temperature range studied normal grain growth did not take place; instead nucleated grain growth prevailed. The nucleation frequency was found to increase with the annealing temperature, with corresponding decrease in grain diameter of ultimate secondaries after long-time annealing. Large secondaries grown by low-temperature isothermal annealing are essentially of (110)[001] orientation, and the (110)[001] texture is strong. The relatively small secondaries grown by high-temperature isothermal annealing also have orientations near (110)[001] as an average but widely scattered; thus the amount of (110)[001] texture is found to decxease with isothermal annealing temperature. Grain growth and texture development at various annealing temperatures can be described by families of sigmoidal curves with the time axis. ThE cube-on-edge (110)[001] texture and predominating large secondaries in fully annealed 3 pct Si-Fe are customarily produced by a 1100°C annealing of a primary recrystallized sheet. On annealing the primary recrystallized sheet above the temperature at which secondary recrystalliza-tion starts May and turnbull' have demonstrated that secondary grains decrease in size as the temperature is increased. The phenomenon was attributed to a decrease in the (G/N) ratio where G is the growth rate of secondary grains and N is their nucleation frequency. In addition, the growth of grains in orientations rather far from (110) [0011 occurred. The present investigation is devoted to detailed rate studies of the same phenomenon. Mi-crostructure, magnetic anisotropy, and texture data were obtained on strips of 3 pct Si-Fe isothermally annealed for various lengths of time in a BaC12 salt bath at temperatures ranging from 927' to 1260°C. The texture results are reported elsewhere.2 EXPERIMENTAL PROCEDURE Commercial 0.014-in. cold-rolled silicon-iron strip (3.16 pct Si), prepared by two stages of cold rolling with an intermediate short anneal, was given a decarburizing 3-min anneal at 800°C. Metallo- graphic studies indicated complete recrystallization. In order to provide a protective atmosphere and to obtain a rapid rise to an elevated temperature, a BaC12 and NaCl fused salt bath was used to heat samples isothermally at temperatures from 927" to 1260°C for various lengths of time. Torque magnetometer measurements were made on 1-in.-diam disc specimens before and after annealing, since magnetic torque curves supply information on textures and texture changes. Surface layers of the strip samples were polished and etched to reveal the grain structure. The diameters of grains were measured from micrographs at X100. The average value of diameters of matrix grains was established. Individual grains in the micrograph were cut out separately along grain boundaries. These grains were classified either as matrix grains or growth grains. The percent weight of growth grains in the cut-out patterns was reported as percent growth. Manv of the individual grains in the annealed samples were large enough to be X-rayed with a 5-mil beam for Lauegrams. Complete (110) pole figures were obtained for the primary recrystallized structure and short-time annealed structure with CoKa radiation at 30 kv in the back-reflection range, such as (220) for (110) poles, as described recently by Newkirk and ~ruce.~ Both the X-ray optics and the technique for pole figure differed slightly from those adapted previously.4

Jan 1, 1960

By N. J. Grant, A. W. Mullendore, Y. Ishida

Creep tests were performed at 500°F on polished specimens of A1-3 pct Cu at stresses of 2000, 4000, and 6000 psi. The effects of the size and distnbution of the second phase were studied in connection with the mechanisms of deformation, especially grain boundary sliding. Although the amount of grain boundary sliding varied considerably for the different heat treatments, yestriction of grain boundary sliding is not due primarily to precipitate on the grain boundary. NUMEROUS prior investigations of grain boundary sliding, notably those of McLean, 1 Rachinger, 2 Rhines, Bond, and Kissel, 3 and Brunner and Grant,4 have established the importance of this phenomenon in the deformation of pure aluminum and its solid-solution alloys at elevated temperatures. An extension of this kind of study to the case of a simple two-phase structure is an important step towards understanding the deformation behavior of more complex alloys. A two-phase A1-3 pct Cu alloy was selected for this study. The creep behavior of alloys in this system has been studied by Sully and Hardy,5 by Underwood, Marsh, and Manning,' and by Pelloux, Chaudhuri, and Grant.7 In these studies, the prior heat treatments were such that some precipitation took place during the tests in most cases. Pelloux, Chaudhuri, and Grant7 studied the creep of A1-2 and 3 pct Cu alloys in the overaged condition. Their results indicated that the structure most effective in promoting high-temperature strength consisted of a fine, closely spaced grain precipitate and large, widely spaced particles on the grain boundary. The present work consists of quantitative meas- urements of grain boundary sliding during creep of an A1-3 pct CU alloy with four different precipitate distributions. The aims were to quantitatively define the role of the second phase on grain boundary sliding, and to obtain information regarding the mechanism of grain boundary sliding. MATERIALS AND PROCEDURE A high-purity A1-3 pct Cu alloy, kindly supplied by Alcoa, was used in this investigation. The composition of the alloy in weight percent was as shown in Table I. This composition is such that A12Cu exists as a second phase at temperatures below 850°F. A homogeneous grain size of 0.6 to 0.8 mm was obtained by annealing the machined test bars for 5 min at 1000°F, furnace cooling to 930°F, and homogenizing for 5 hr. Following the recrystalli-zation and homogenizing anneal, four different heat treatments shown in Fig. 1 were utilized. The F7 and F5 treatments utilize a furnace cool to the aging temperature while Q7 and Q5 have a water quench from the homogenization temperature before aging. Figs. 2 to 5, and Table 11, show the size and shape of precipitate dispersions obtained with the above heat treatments. The heat treatments produce variations in the dispersion both in the grains and along the grain boundaries. Precipitate particles along the grain boundaries are rounded and large (about 1.5 p diameter) in the F5 and F7 structures (Figs. 3 and 5). The grain boundary precipitate was somewhat smaller (0.9 p diameter) in the Q7 structure and no grain boundary precipitate was detected in the Q5 structure using light microscopy. The pre-

Jan 1, 1964

By Gareth Thomas

The analysis of Kikuchi pattersns of exct ovientalions from single cryslals and paired Kikuchi lines from single and overlapping crystals is shown to be useful and quanlitalve and is applied to Phase transfovnzcitions including ordering, spinodals, mavten-silic, and nuclealion and growth pyocesses. 112 pinciple, the analysis of exacl orientations enables the crystal system and the Bravais lattice of a crystal to he determined. The advantages of the davk-field imaging technigure for detecting vevy small precipitates are also described. ALTHOUGH Kikuchi electron-diffraction patterns were first observed nearly 40 years ago,' little systematic application seems to have been made of them, until fairly recently during electron microscopy, when their usefulness in contrast experimen and for determining exact orientations8'9 has been pointed out. With the availability of gonio-metric specimen tilting stages it has now become possible to make much wider use of diffraction patterns, particularly the Kikuchi pattern, which is the main subject of this paper. The treatment presented here is not exhaustive but it is hoped that it will stimulate more use of Kikuchi patterns during electron-microscopy investigations. The Kikuchi pattern is formed as a result of Bragg diffraction of the inelastically scattered electrons produced during the interaction of the beam and thick specimens, The important feature of these patterns is that they give an accurate representation of the symmetry of the crystal being investigated, so that it is possible to identify crystal systems and even the Bravais lattice. This means that new structures, e.g., formed in phase transformations, may be identified during normal electron microscopy, so that Kikuchi-pattern analyses considerably extend the uses of the electron microscope. Recent work has also shown that dark-field images are more informative than bright-field images, particularly, for observing small precipitates. The second part of this paper discusses some applications and advantages of dark-field imaging in studies of two-phase systems. 1) DIFFRACTION PATTERNS 1.1) Spot Patterns. Electron-diffraction spot patterns have their limitations because of the importance of the form factor on the intensities and shape of the reciprocal lattice points. Because of the extension of these points into relrods, reflections are possible over a large angular range (+5 deg) and the patterns from thin regions can be complicated because second-layer relrods intersect the reflecting sphere. Spot patterns can thus give only an approximate idea of the crystallography unless the foil is tilted into exact orientation. In this case the spot pattern is symmetrical, with equal numbers of spots on the positive and negative zone directions about the origin. Such cases are necessary for structural analyses and have been used recently to determine the crystal structure of the ordered Ta64C phase." Exact orientation means that the plane of the reciprocal lattice lies exactly normal to the incident beam as shown in Fig. 1(b). It should be noted that in exact orientations the angle of reflection is less than the exact Bragg angle 9 so that the reciprocal lattice points lie to the outside of the sphere, Fig. 1(b). This deviation is denoted by the parameter s and in the usual convention4 s is negative for exact orientations and, of course, zero at the exact reflecting position shown in Fig. l(a). In order to avoid secondary reflections from thickness relrods it is advantageous to work in thicker regions of foils. Diffraction from thick regions may also produce Kikuchi patterns and as dis-

Jan 1, 1965

By C. F. Cockrell, H. E. Shafer, J. W. Leonard

A significant technological development is discussed for the processing of certain power plant flyashes that are a problem because they contain a high water-soluble mineral content and yield inferior flyash-based brick. This development is based on the addition of hydrochloric acid to the flyash-bottom ash-sodium silicate blends used for the production of flyash-based structures. Favorable changes are evi-dent in sodium silicate consumption, where about half the amount used for making brick from normal flyash is required, processing costs, and strength and appearance of the resulting freshly formed green and fired structural products. In some high cost in-stances (above the $30 or less per thousand brick estimated for normal flyash), hydrochloric acid additions can replace or reduce other costly additives normally required for problem flyashes. This results in savings of as much as $9 per thousand brick. These developments offer promising possibilities for utilizing problem flyashes as well as flyashes which may come into contact with water soluble sulfur as a result of the eventual application of certain experimental air pollution control processes. Much of the research datal-6 accrued through work by the Coal Research Bureau of West Virginia University for the Department of Interior's Office of Coal Research on converting waste power coal ash to valuable brick and other structural products, can be categorized as follows: (1) general ash-to-brick tech- nology; (2) specific ash-to-brick optimization; (3) pilot plant progress; (4) production cost estimates. A summary of the progress on bench-scale experiments indicates that coal ash can yield two types of brick. An acceptable brick is obtained by mixing 73.6% fly-ash, 23.5% bottom ash and 2.9% sodium silicate solution (dry basis). Depending on the flyash and bottom ash used, optimum brick can be manufactured by mixing 72-77% flyash, 20-25% bottom ash and 2.3-3.0% sodium silicate (dry basis) with Na2O : SiO2 ratio varied according to the composition of the flyash used. These blends are thoroughly mixed and mechanically formed into green brick shapes at pressures ranging from 1000 to the more usual 3000 lb per sq in. The green shapes then are dried and fired at temperatures ranging from 1975-2150°F using clay brick cycles that are shorter than standard. Other findings reported to date indicate that when making optimum brick, it is necessary to carefully control the top size of the moisture-releasing bottom ash so that it falls between 8 and 30 mesh, depending on the flyash used. Moreover, the chemical composition of bottom ash and flyash have been found to be of little significance with the exception of a few problem flyashes which are the subject of this paper. Finally, the pilot plant, which was previously reported under construction, is now in operation. This will indicate, among other things, the cost of brick production, which was earlier estimated for non-problem flyashes at $30 or less per thousand brick. The foregoing bench-scale technology is applicable to all the initially tested ashes as well as to the majority of ashes examined during the course of research. However, a few of the ashes yield green and fired products that may be structurally inferior or unacceptable, necessitating excessive and diverse reagent addition, and/or may be coated with unsightly surface deposits. These problem ashes generally originate in certain areas of Illinois, western Ken-

Jan 1, 1969

By Clark L. Corey, Bogdan Lisowsky

Electrical resistivity, X-ray line positions, degree of order, and microstructures have been investigated for Ni-A1 alloys near the Ni3Al composition. The results indicate that Ni3Al undergoes disordering between 1250oC and the mp; also supersaturated y, produced in y + y' alloys by gas quenching, is extensively ordered prior to y' (Ni3Al) phase separation. The latter reaction, if not both, must follow the cooperative phenomena model. Shifts in line position as a function of quench-indulced super satulration are shown. Lattice pavarneters of equilibriunz and nonequilibrium phases are given. THE objective of this investigation was to determine the mechanism and kinetics of the reactions which occur in Ni3A1 and hypostoichiometric Ni3A1 alloys. The results are of particular significance relative to pre-precipitation phenomena. Early work on Ni-A1 binary compositions near the Ni3A1 composition (13.6 wt pct Al) has been adequately reviewed by Hanssen,1 whose phase diagram is presented in Fig. 1. williams2 verified the suggestion made by Taylor and Floyd3 and others4 that y', Ni3A1, may precipitate coherently on (100) planes of the y phase (see Fig. 1 for phase nomenclature); he further suggested a two-step precipitation mechanism consisting initially of probably short-range ordering followed by actual precipitation of y'. The precipitation stage in low-aluminum hypo-eutectic compositions has been studied by a number of investigators;*"7 short-range order or "zone" formation have been suggested as explanations for various diffuse X-ray scattering effects. The ordering reaction in Ni3A1 alloys is characterized by a) a very rapid rate of ordering in nonstoi-chiometric compositions, b) absence of a disordered phase region for the stoichiometric compound, y', or Ni3A1, c) precipitation phenomena as a dominant aspect in hypoeutectic alloys, and d) an increase in elec-trical resistivity on ordering.' The latter two factors were found by Newkirk to characterize ordering in Co-Pt, for which an extensive and detailed analysis was made.' An electrical-resistivity increase on ordering has also been reported for cuAu3.10 PROCEDURE Ni-A1 alloys in the form of 1300-g chill-cast ingots were prepared by vacuum melting electrolytic nickel and high-purity (99.99 pct) aluminum. Very small heats prepared from high-purity carbonyl nickel, supplied through the courtesy of Dr. Goff of the Naval Research Laboratory, were used for comparison with the larger ingots and no differences were noted. The cast material was homogenized in purified argon for a minimum of 72 hr at 1200°C and water-quenched from 1350°C. Compositions studied are given in Table I. The 10 pct A1 alloy was both hot- and cold-rolled. X-ray superlattice line intensities and peak positions were obtained from -270 mesh filings, using CuK, radiation with a LiF crystal monochromat adjusted to receive both 01 and a2. One-degree slits and a 1/8 deg per min scan rate were used to record line traces. A standard tungsten powder, obtained through the courtesy of G.E. Research Laboratory, was used to calibrate line positions.

Jan 1, 1968

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

The kinetics of crack propagation in a hydrogenated high-strength steel at subzero temperatures indicated that cracking progressed in a discontinuous fashion. The delayed failure process thus involves a series of crack initiations rather than the continuous growth of a single crack. The incubation time required for the initiation of delayed failure was controlled by the diffusion of hydrogen. The activation energy for the process was 9120 cal per g-alom. As the test temperature was lowered the incubation time constituted a greater percentage of the total tinze to fracture, and al -50°F the incubation and fracture times were essentially coincident resulting in instantaneous, catastroplzic fracture. A unique feature of hydrogen embrittlement is the delayed failure process in which the material fails under the action of a sustained load even though it is capable of supporting a higher load for a finite period of time.')' Delayed failure of steel and titanium is characterized by an incubation time, preceding the initiation of a crack in a highly localized region, and the subsequent growth of the crack to ultimate failure.3-5 The kinetics of crack growth in hydro-genated high-strength steels have been studied through the use of resistance measurements and have an important bearing on the mechanism of delayed failure. Delayed failure is believed to be merely a facet of hydrogen embrittlement in which sufficient time is allowed during a test for hydrogen diffusion. The current theories employed to explain hydrogen em-brittlement can be grouped into two types. one6-8 explains the embrittlement on the basis of the pressure exerted by molecular hdrogen in lattice voids or defects while the other9-10 attributes the embrittlement to the influence of hydrogen in the lattice. The mechanism used to explain the nature of the crack kinetics in delayed failure is based on the stress-induced diffusion of hydrogen to the area of maximum triaxiality.3 When the hydrogen concentration in this region reaches a critical value, a crack is nucleated. This initial crack propagates instantaneously until stopped by the higher fracture stress of the adjacent material of lower hydrogen content. The continuation of cracking must then await the further diffusion of hydrogen to the new region of triaxiality near the base of the crack where another initiation will occur. From this mechanism it follows that crack propagation is nothing more or less than a series of initiations with limited fracture. The purpose of this investigation was to examine the kinetics of crack growth in an effort to determine whether or not the process was discontinuous. Studies of crack propagation were conducted at low temperatures to retard the diffusion of hydrogen which is presumed to be the rate controlling process in delayed failure. MATERIALS AND PROCEDURE Specimen Preparation—A commercial heat of air-craft quality SAE-AISI 4340 steel, designated as Heat G, was furnished by the Republic Steel Co. in the form of %-in. hot-rolled bars. The material had the following chemical analysis: Composition of 4340 Steel—G Heat C Mn Si Ni Cr Mo 0,395pct 0.82pct 0.29pct 1.76pct 0.85pct 0.25pct Notched tensile specimens with less than a 0.001 in. radius, Fig. 1, were used throughout the investigation. The specimens were heat treated to a 230,000 psi strength level according to the following sequence: a) Normalize bar stock at 1650°F for 1 hr, b) Stress relieve at 1200°F for 4 hr and furnace cool,

Jan 1, 1960

By W. J. Helfrich, C. L. Sollenberger

Many present direct reduction processes utilize iron ore concentrates for the production of sponge iron and the sponge iron is usually preferred as an agglomerate. Pelletizing a high grade iron oxide concentrate prior to reduction is a simple approach to the high capacity production of a uniform and agglomerated sponge iron product. The present paper describes the effect of different atmospheres and physical characteristics on the reduction of pelletized iron oxide concentrates. The kinetics of iron oxide reduction have been I studied by numerous investigators1-4 and a rate equation for the hydrogen reduction of hematite and magnetite has been proposed. Mc Kewan' obtained kinetic data for the reduction of hematite spheres sintered at 13'70°C (2498'F'). The kinetics of magnetite reduction was studied by Quets. He compacted the oxide at a pressure of 1 ton per sq cm and sintered the specimens to densities of 95 to 96 pct of theoretical. These studies demonstrated that the reduction of iron oxide is a topochemical process and that the rate of reduction is proportional to the receding surface area of remaining iron oxide. Thus, the measurement of the kinetics of iron oxide reduction depends upon the development of a measurable and well defined interface between metal and reacting oxide. It is evident that the reduction rate will be constant only when the rate of formation of the reaction product layer is constant. It was recognized by Joseph' and Edstrom' that the physical character of the oxide will determine the configuration of the interface between oxide and metal. The reduction of oxides which exhibit few pores or no interconnected pores should proceed by topochemical processes. However, if a massive or dense crystalline ore cracks during the reduction of the oxide, thus allowing the reduction to Proceed away from a well defined oxide/metal interface, then the observed reduction rate will vary or change during reduction. From a process standpoint, it would be difficult to apply absolute reduction rates determined for crystalline or nonporous iron oxide to the direct reduction of a porous pellet of iron ore concentrate. Most present direct reduction processes are attempts to utilize iron ore concentraates in the production of sponge iron. The sponge iron is usually preferred in an agglomerated form for subsequent melting practices. Pelletizing a high grade iron oxide concentrate prior to reduction is a simple approach to the high capacity production of a uniform and agglomerated sponge iron product. One process for preparing such a product has already been de-scribed. This paper describes the effect of different atmospheres and physical characteristics on the reduction of pelletized iron oxide concentrates. ORE CONCENTRATES STUDIED A magnetite concentrate from Reserve Mining Co. and a hematite concentrate from U.S. Steel Corp. were used in preparing pellets for these experiments. A head analysis of these concentrates is given in Table I. To compare the reduction rates of pelletized concentrates, it was necessary that each pellet contain equal amounts of oxygen which could be removed by reduction, regardless of the oxidation state, i.e., Fez% or Fe304. Also, because of the difficulty in preparing spherical pellets of uniform size, weight, density, and porosity for experimental purposes, pellets of a cylindrical shape were formed in a press.

Jan 1, 1961

By H. P. Stuwe

It is investigated whether a model of sphere packing permits the computation of the lattice parameters and their variation with concentration in various a phases; it does, except in phases containing silicon. Several observations indicate that a particular role is played by the "E-atoms" in the lattice. THE phase is formed by many alloys of the transition elements.'-' Its structure has been described by Bergman and Shoemaker,5,8 Dickins, Douglas, and Taylor,7 and Kasper, Decker, and elanger.' There are five kinds of crystallographically equivalent positions for the 30 atoms in the unit cell which have been designated by these authors I, 11, 111, IV, and V or, in the same sequence, A, B, C,D, and E, as shown in Fig, 1. For the purposes of the present paper two elements of the lattice will be discussed separately: The lattice planes perpendicular to the c-axis which are made up by the atoms A, B, C, and D and which determine the a-parameter; and the close-packed "vertical rows" of E-atoms which determine the c-parameter. asper,9 and Frank and kasper10 described the a phase and other complex structures as sphere packings. In these papers particular attention is paid to the coordination polyhedra. Lattice positions with an equal number of nearest neighbors are considered equivalent regardless of their crystallo-graphic description. This seems to work very well for the explanation of ordering phenomena in the a phase as far as information on this is available." If the description of the phase as a sphere packing is valid it should be possible to draw two further conclusions: 1) It should be possible to calculate the lattice parameters from the atomic radii of the components, and 2) It should be possible to predict the variation of the lattice parameters with concentration within one phase field. Both points are discussed in this paper. PROCEDURE Measurements of lattice constants were done with a symmetrical back-reflection X-ray camera. With Cr-radiation, about a dozen a1 lines could be observed with most samples. From the (550/710)- and 720-lines the a-value was computed. With this value the c-parameter was calculated from the (333)- and (413)-lines. Finally, the position of all the other lines was computed from the lattice parameters thus obtained. In this way the validity of the indexing could be checked and, at the same time, this proce- dure gave an estimate of the accuracy of the lattice parameters. A correction was made for film shrinkage. The atomic radii used in the computations are the Goldschmidt radii for coordination number 12. Actually, some of the atoms have a coordination number of 14 or 15, but the error thereby introduced is small. * For the computation of lattice constants from the atomic radii an "average atomic radius" of all components was used, i.e., complete disorder was assumed. Although this seems to be true for some systems like OS-Cr,4 it is not true in others.11,13,14 The ordering model, however, which has been suggested by Kasper on the basis of extensive research lets both kinds of atoms contribute to both the ''vertical rows" and the lattice planes perpendicular to them, so that even with ordering of this kind the assumption of complete disorder cannot introduce a very serious error in calculating lattice parameters. RESULTS Bergman and shoemaker6 gave a table of the interatomic distances in the Fe-Cr phase. If we disre-

Jan 1, 1960

By A. M. Sarem

For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady - state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two - phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-pbase relative permeability as it does in two-phase flow. INTRODUCTION In the light of increasing demand for three-phase relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis 1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between I/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression for determining the outflow face saturation from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. PROPOSED METHOD The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three - phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

Jan 1, 1967

By A. E. Powers

YEARS of experience and research have shown that molybdenum, tungsten, and vanadium are among the most useful and effective elements in augmenting the high-temperature strength of heat-treatable, ferritic steels. Grün, for example, in conducting an early survey of the strengthening effects of various elements in annealed, low-carbon steel at 750° and 930°F (400° and 500°C), found molybdenum and vanadium to be the most effective.' Holtmann comprehensively studied the strengthening effects of molybdenum and vanadium in quenched and tempered steels at 930°F as a function of microstructure and carbon content.' He found creep strength to be related to the saturation of the austenite at the austenitizing temperature, such that strength is increased by alloying until the y loop is reached—the terminus of complete austenitization. Beyond this degree of alloying, the inability to heat treat will result in lower strength, at least for low and moderate creep temperatures. Tungsten, owing to higher cost than molybdenum, has been little used in ferritic high-temperature steels. As a result, very few investigations have been made of its high-temperature strengthening ability, and reliable data on its effectiveness are not available. Grün rated tungsten far less effective than molybdenum at 930°F (500°C) on a weight-percentage basis.' However, Tammann has found that tungsten is as effective as molybdenum in raising the recrystallization temperature of iron. For this reason Smith, in a review of the subject, has advocated a re-examination of the influence of tungsten on the high-temperature strength of steel.' In any study of the effects of alloying additions on high-temperature properties, recognition must be made of the many variables involved, some of which can be controlled but have been ignored in innumerable investigations of the past, and some of which are difficult or even impossible to control. One cannot, for example, assign a definite strengthening index to any one alloying element, for this will be dependent upon the microstructure (heat treatment and mechanical treatment), testing con- ditions (temperature, time, and stress), and the complete composition of the steel (accompanying alloying elements, impurities, etc.). One ever-appear ing variable, hardness or tensile strength at room temperature, may be eliminated by heat treating all of the alloys to a single hardness level. An attempt may be made to control the variable of primary quenched structure by oil or water quenching the test specimen. The control of such variables may not be possible in cases of widely varying compositions, but at least such deviations should be recognized. Material and Procedure The alloys, made as 30-lb ingots in an induction furnace, all had the same base composition of about 0.18 pct C, 0.85 pct Mn, and 0.48 pct Si. They were grouped as follows: Mo Group—Containing up to 5.2 pct Mo. W Group-Containing up to 6.0 pct W. V Group—Containing up to 3.3 pct V. Mo-V Group—Containing up to 2.7 pct Mo and up to 1.4 pct V. Mo-W Group—Containing up to 2.5 pct Mo and up to 2.5 pct W. The steels, listed in Table I, were forged to ¾ in. sq bars and the material for the high-temperature, rupture-test specimens was further swaged to %-in. round bars.

Jan 1, 1957

By M. J. Blackburn

The ordering reaction and its effect on dislocation awangements in alloys based on Mg3Cd has been studied by transmission electron microscopy. Ordering occurs by the growth of ordered domains until they impinge, thus producing an antiphase domain boundary (APB) network. In the disordered alloy, slip is confined to the basal plane while in the ordered condition slip occurs on the basal, prism, and pyramidal planes. Superdislocations have been identuied on these planes and their origin and expected spacings are discussed and compared with the observations. The APBs between the dislocation pairs have been resolved and have proved useful in the identification of superdislocations. Observed slip structures are related to the changes in mechanical properties produced by ordering. At high temperatures magnesium and cadmium form a continuous series of disordered hexagonal solid solutions. At lower temperatures three ordering reactions occur; two based on the compositions Mg3Cd and MgCd3 are transformations to DO19-type superlattices while alloys based on the composition MgCd transform to a B19 lattice. The ordering process in alloys near the composition Mg3Cd has been studied by several workers'-4 and it has been shown to be a first-order type transformation. The variation of mechanical properties with the degree of order and temperature have been reported in some detail by Stoloff and Davies.5 It was shown that the disordered alloy was stronger and less ductile than the ordered alloy, the differences being attributed to changes in the number of active slip planes and to the presence of short-range order in the disordered alloy. In this investigation the ordering reaction has been qualitatively followed by transmission electron microscopy. The effect of this ordering transformation on the dislocation arrangements in deformed specimens has been studied in some detail. EXPERIMENTAL Alloys were melted in a stainless-steel crucible under a flux and chill cast; both melting and casting were performed in an argon atmosphere. The ingots were hot-rolled and tensile specimens cut from the resultant strips. Some large-grained specimens were grown by the strain-anneal method. Heat treatment was carried out in inert atmosphere furnaces and in oil baths at the lower temperatures. Thin foils for transmission electron microscopy were produced by electropolishing in a cooled solution (temp = -40°C) containing 50 cu cm of nitric acid and 180 cu cm of methanol at a potential of 10 v. The ordering reaction was followed by transmission electron microscopy, X-ray, and electrical resistivity measurements but this paper will be concerned chiefly with the electron-microscopy results. Much of the work described in this paper was performed on an alloy containing 26.10 at. pct Cd although two of the micrographs are taken from work on a 25.55 at. pct Cd alloy. RESULTS i) The Quenched Solid Solution. Specimens which were quenched from above the critical temperature showed diffuse superlattice reflections. sark-field analysis on these reflections failed to reveal the presence of ordered domains and thus the superlattice reflections were assumed to arise from regions of short-range order. Quenching from temperatures of 400" to 450°C results in the formation of dislocation loops and helical dislocations. Such defects have been observed and analyzed in detail in several hexagonal metals6-' and as the crystallography and interactions of such loops appear similar in this alloy they will not be reported in detail. Fig. 1 shows a high density of loops

Jan 1, 1968

By I. R. Kramer

The delay time for single crystals of iron, zinc, and pre-strained aluminum was measured under conditions of high-speed deformation. The delay time of aluminum was found to be affected by the orientation of the crystal. Under the dynamic conditions employed, tile calculated "activated volume" term appears to be very small for the three metals studied. IN a previous paper,1 it was shown that under dynamic testing conditions at 78° K, there was a delayed yield in single crystals of aluminum and copper which had been cold-worked prior to testing. The experimental results also indicated that the delay-time effect was not due to the interaction of dislocations with impurity atoms or vacancies, but rather to a dislocation-dislocation interaction since aluminum which has not been prestrained shows no delay-time phenomenon. In this paper, some data are reported on the effects of orientation on the delay time of aluminum single crystals; the delay time of zinc single crystals saturated with nitrogen and the delay time of iron single crystals also were measured. EXPERIMENTAL PROCEDURE Aluminum (99.997 pct) and zinc (99.999 pct) crystals, 1/2 in. in diam and 8 in. long were grown by the Bridgman technique. The iron single crystal was supplied by Dr. R. Maddin. The zinc crystals containing nitrogen were prepared by melting high-purity zinc in a graphite crucible and the nitrogen was introduced by additions of ammonium chloride. The liquid zinc was then drawn up into glass tubes of 1/2 in. diam and allowed to solidify. The rods were cooled to room temperature before the transfer to the mold for conversion into single crystals. The orientation of all specimens was determined by the Laue' back-reflection technique, Fig. 2 and Table I. To prepare for the delay-time measurements, the crystals were cut with a fine jewelers saw and the ends carefully machined. The specimens then were electrolytic ally polished to remove the cold-worked metal, mounted in a special fixture and hand-lapped. As a final step, the crystals were annealed in evacuated tubes. Specimens of aluminum crystals, Nos. 24 and 26, were compressed 0.5 and 2 pct, respectively, in the direction of the later impact. The zinc specimens were aged at 50°C for 15 min, In the case of iron, only two specimens could be obtained. To obtain sufficient data, it was necessary to resort to a reaging treatment. After each delay-time test, the specimens were aged at 65° C for 100 min. This treatment, according to Clark,2 is sufficient to restore the original delay time. It is believed that although the specimens were plastically deformed approximately 10-4 pct, after each test the delay-time values are reliable. The delay-time measurements were made in an apparatus similar to that described previously.' Single crystals approximately 1 in. long and having a diameter of 1/2 in. were placed in a pendulum which consisted of a bar 1/2 in. in diam and 8 ft long, designed with a crystal holder to accommodate the specimen at low temperatures. The crystal was held at a position 2 ft from the front part of the pendulum. This portion of the apparatus was supported on a fine molybdenum wire. A projectile bar of the same diameter and length comprised the other portion of the apparatus. This bar was supported on

Jan 1, 1962

By H. C. Chao, W. F. Hosford, L. H. Van Vlack

The negative "plastic Poisson's ratio" suggested in earlier studies of Mus deformation is analyzed, and the results are verified experimentally with NaCl crystals. In the early stages of deformation where the primary {110}(110) slip predominates, compression along. the [001] direction produces contraction along the lateral [011] direction plus a compensating expansion along. the [100] direction. With additional strain, the primary slip is supplemented by secondary {111}(110) slip so that the above contraction diminishes and a more typical deformation appears. THE shape change of bee and fee crystals deformed by compression or tension along [011] has been analyzed in some detail and shown to be responsible for the development of peculiar microstructures in [011] fiber textured polycrystals of these metals.1'3 This paper concerns the unusual shape change accompanying [011] compression of NaCl crystals. It is the direct outgrowth of an earlier investigation of the deformation of manganese sulfide inclusions in steel.3,4 In that investigation, cylindrical specimens of steel containing small oriented crystals of MnS were prepared by powder metallurgy and plastically compressed. The flow of the inclusions was determined relative to that of the steel by sectioning the composite and measuring the length-to-width ratio L/W of the inclusion and diameter-to-height D/H ratio of the steel cylinder on the plane of section. These L/W ratios, normalized by dividing by the initial LO/WO ratio of the inclusion, were compared with the normalized D/H ratio of the steel cylinder. Of particular interest here are the deformation characteristics of an inclusion oriented with [Oil] parallel to the compression axis. When measurements were made on sections parallel to the (100) plane of the inclusion, the L/IV ratios were only slightly in excess of unity, indicating a high apparent hardness of the [011] criented inclusion. However, measurements on a (011) plane of section resulted in L/W ratios which were much larger, Fig. 1. These observations prompted an analysis of the strains resulting from slip in an MnS crystal compressed along [011.]. CRYSTALLOGRAPHIC ANALYSIS Manganese sulfide has the NaCl crystal structure, and the predominant slip system is {110}(110). A secondary system, {111}(110), has also been reported.= {110}(110) Slip. When a crystal is subject to a uni-axial compressive stress 011 along [011], four slip systems, (101)[101.], (101)[101.], (110)[i10], and (110) [ 110], will be equally stressed with a shear stress t = 0.2 011 while the other two {110}( 110) systems will be unstressed. The normal strain En along any reference axis n resulting from slip is given by Schmid's law: en = S COS ?in COS in ?i 111 where ?in and +in are the angles between n and the i slip direction and n and the i slip plane normal, respectively, and where ?i is the shear strain on the i slip system, For the four active slip systems above, the cos ?in cos +in terms are all equal when the reference axes are the [011] compressive axis, [011] and [ 100]. Eq. [I.] therefore reduces to en - cos ?n cos +ny [2] where y =S?i for all slip systems. Substituting the appropriate angles, Eon = 0.25? 110 eon - 0.25y110 [3] €100 = -0.50y 110 The interesting feature of Eqs. [3] is that they predict that the strains in the [011] and [011] directions, resulting from {110}(110) slip, are equal and of the same sign. Thus when a crystal is compressed along [011], it will contract along the lateral [oil] direction

Jan 1, 1967

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper' a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951