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By D. Y. F. Lai, R. J. Borg

Tracer diffusion of Fe59 has been measured in the a-stabilized Fe-1.8 at. pet V alloy from 700° to 1500°C. The activation energies are obtained in both the presence and absence of magnetic order. Furthermore, it is established that diffusion in the alloy is identical to that in pure iron and consequently the values of Do and Q accurately represent the temperature dependence for self-diffusion. The purpose of this investigation is to obtain an accurate estimate of the temperature dependence for self-diffusion in bee iron in both the presence and absence of magnetic order, and, in so doing, to establish the temperature range of the magnetic effect.&apos;" As the temperature interval suitable for diffusion measurements is severely limited in both bee phases of pure iron because of the intervening fee ? phase, the experiments were performed on an a-stabilized alloy containing 1.8 at. pet V. This alloy is bee over the entire range from room temperature to the melting point. Although there have been several independent investigations of self-diffusion of iron in a, iron,1, 3-6 there still exists considerable disagreement regarding the values of Do and Q for the paramagnetic region. The two systematic studies of diffusion in 6 iron6, 7 previously reported are also only in fair agreement; but in view of the extremely small temperature range available for diffusion studies, i.e., 1390o to 1535oC, this is not surprising. It is comparatively easy to obtain accurate values of Do and Q for the a-stabilized alloy inasmuch as measurements can be made over the entire temperature range -700o to 1500°C. However, in order to assume that these same values apply to pure iron requires careful comparison of the data in the a, and 6 regions in both the alloy and pure iron. We have made several measurements in the appropriate temperature ranges and are unable to establish any systematic difference between the diffusion coefficients of iron in pure iron and in the alloy. We therefore conclude that the values obtained for the alloy are truly applicable to pure iron; the complete evidence favoring this conclusion will be discussed later in this paper. EXPERIMENTAL The experimental methods will be given here only in barest detail since they have been thoroughly de- scribed elsewhere.l, 7 The alloy was prepared by induction melting and chill casting under argon. Diffusion samples were machined from the ingot and annealed in hydrogen for several days at 900°C to give an average grain diameter of 1 to 2 mm. The penetration profiles of the tracer were established by a sectioning technique, the residual activity being counted after the removal of each section. The tracer used is Fe59 which emits two high-energy ? rays of 1.098 and 1.289 Mev, respectively; these were detected by a ? scintillation counter equipped with a pulse-height analyzer. For the measurements in the temperature range -700o to 1130°C the samples were vapor-plated with Fe59, encapsulated in quartz under vacuo, and annealed in resistance-heated furnaces which are controlled to ±1°C. The specimens diffused at higher temperatures are prepared as edge-welded couples, the two halves being separated by a thin washer of the alloy to prevent sintering. The diffusion anneal is then carried out by inductive heating under a dynamic vacuum. The temperature is monitored pyrometrically. RESULTS The diffusion coefficients are obtained from the penetration profiles in the usual way using the error-function complement relationship. The results over the entire temperature range are shown in Fig. 1. In the linear region, 900o < t > 1500°C the least mean squares (lms) values of the diffusion coefficients are given by D = 1.39 exp[-(56.5 ± 1) x 103/Rt] cm2/sec [l] The average departure of the measured diffusion coefficients from the values given by Eq. [1]In order to determine whether or not the slope is truly constant over the entire range from 900" to 1500°C, the data are arbitrarily divided into two groups, the first containing values between -900" and 1133°C and the second between -1133o and 1500°C. The lms values for the two groups are given by Eqs. [2] and [3]: D = 0.519 exp[-55.7 x 103 /RT](900° to 1133°C) cm2/sec [2] D = 1.45 exp[-56.7x103/RT] (1133° to 1500=C) cm2/sec [3] Thus, there is no significant difference between the high- and low-temperature segments of the linear region. This not only assures us of the consistency of the values obtained by induction heating as compared to those obtained from the resistance-heated

Jan 1, 1965

By T. Koulomzine

The theory of the Askania magnetometer, as well as a complete discussion of all factors influencing magnetometer readings, is very ably described by J. Wallace Joyce. We will assume that the reader is thoroughly familiar with this theory and we will use whenever possible the same notations for the physical values involved in the theory. On the other hand, we believe that the principal formulas of the magnetometer can be deduced much more easily by the use of differential calculus than by the methods employed by Joyce. Consequently, we are presenting herewith a resume of the theory of the vertical magnetometer in order to determine the correct formula of the temperature coefficient which we propose to compensate.

Jan 1, 1949

By G. L. Chierici

Starting from Muskat&apos;s theory of water and gas coning, maximum permissible oil production rates without water and/or free-gas production have been determined, in a broad range of reservoir and well parameters, using the potentiometric model technique. The main assumptions made are as follows: (1) the reservoir rock is homogeneeous (either isotropic or anisotropic); (2) the volume of the aquifer underlying the oil zone is very small, so that it does not contribute to reservoir energy; and (3) the gas cap expands at a very low rate, so that it can be assumed to be in quasi-static conditions. The results obtained are presented in the form of diagrams which can be used for solving two types of problems: (1) given the reservoir and fluids characteristics, as well as the position and length of the perforated interval, determine the maximum oil production rate without water and/or free-gas production; and (2) given the reservoir and fluids characteristics only, determine the position and length of the perforated interval which optimize the maximum permissible oil production rate, without water and/or free-gas production. INTRODUCTION In oil reservoirs where the oil-bearing formation is underlain by an aquifer which does not participate in the production mechanism, water-coning is a limiting factor to the flow rates of producing wells. Production rates are usually kept to a value that will prevent the water from entering the wells. The entry of water into a well lowers its productivity by increasing the weigbt of the fluid column; moreover, the separation of water from the effluent, at the surface, may constitute a very difficult problem in cases of heavy viscous oils. A similar situation is encountered in oil reservoirs with a gas cap overlying the oil-saturated zone; here a downward gas cone is induced by the flow of oil towards the producing wells. Production rates must be low enough to prevent the gas from being produced; producing gas from the gas cap would be a waste of energy. Of course, water-coning and gas-coning phenomena can occur at the same time in the same reservoir if the oil-producing formation is both overlain by a gas zone and underlain by a water zone. Due to its relevant practical importance, the mechanism of coning was studied by many people.2,3,5-8 Defining the conditions for getting the maximum water-free and/or gas-free oil production rate is a difficult problem, often encountered under one of the following aspects: 1. Predict the maximum flow rate that can be assigned to a completed well without the simultaneous production of water and/or free-gas. 2. Define the optimum length and position of the interval to be perforated in a well, in order to obtain the maximum water and gas-free production rate. A systematic study of these problems was made by means of the electrical analog technique. The results of this study are presented here, under the form of a set of curves providing solutions for the above stated problems. These curves are valid only for homogeneous forrnations, either isotropic or anisotropic. Should the formation be non-homogeneous (by horizontal or vertical variation of permeability, shale diaphragms, fractures, etc.), a specific potentiometric study would be required for each specific case. Especially when shale diaphragms of some radial extension are present, the critical rates observed are much larger than would be expected from the diagrams. STATEMENT OF THE PROBLEM In the present study the aquifer is supposed to be of such limited volume that it does not contribute to the energy of the reservoir. Moreover, the gas cap is supposed to expand at such a low rate that the potential gradient in the gas cap is negligible. Under static conditions water-oil and gas-oil interfaces (T1 and T2) are both horizontal. When the reservoir production starts, below each well these interfaces take a cone-like shape (Fig. 1) having as an axis the axis of the well. This shape results from the equilibrium between potential gradients in the oil zone and gravitational forces due to density differences between oil and water and between oil and gas. Assuming the oil-bearing formation to be homogeneous and the oil to be incompressible, the analysis of the problem (see Appendix) shows that the oil-water and gas-oil interfaces are stable only if the oil production rate of the well is not higher than the following values.

Jan 1, 1965

By H. R. Froning, R. O. Leach

In wertability alteration flooding, a chemical agent is rnoved through a reservoir by the flood water to increase oil recovery by decreasing the degree of wetting of the rock by the oil. Substantial amounts of the chemical may be lost during movement through the reservoir. The extent of the loss, and therefore the economics of the process, depends in some cases on factors which are difficult to reproduce in the laboratory. Therefore, a short-duration, low-cost field test method is needed to permit evaluation of chemical requirements under actual field conditions. This paper describes a small scale rest conducted at a single well for measuring chemical requirements, thereby giving a more reliable evaluation of this important factor in the applicability and economics of the process. In the rest a small wafer slug containing the chemical agent and a nonadsorbed tracer is displaced into the reservoir by a known volume of wafer. The well is then placed on producrion. Chemical loss per barrel of pore volume contacted is calculated from [he fractional recoveries of the agent tested and the nonadsorbed tracer. The method has been used to determine within the actual reservoirs the chemical requirements for both a sandstone and a dolomite reservoir. Several chemical agents are potentially available for wettability alteration flooding, although none is universally applicable. For some applications of the method, chemical costs per barrel of additional oil recovered can be substantially less than one dollar. INTRODUCTION Wettability alteration flooding provides a means of increasing oil recovery from reservoirs by decreasing the degree of wetting of the rock by the oil and increasing the displacement efficiency of the flood water. Earlier studies demonstrated a relationship between oil recovery during waterflooding and the degree of wetting of a rock surface by an oil. The application of wettability alteration flooding to the Harrisburg field of Nebraska provided a field test&apos; of this recovery process. Subsequently, additional laboratory and field tests have developed additional procedures for evaluating wettability alteration flooding, and have indicated where the process may be applicable. Applicability of this process to specific reservoirs is determined by a progression of tests to determine sus- ceptibility of the reservoir to alteration of its wettability, to indicate the degree of recovery improvement and to estimate the amount of chemical required to process the reservoir. The economics of applying improved oil recovery processes depends not only upon the degree of improvement in oil recovery achievable by the process but also upon the process costs and the timing of the income and the investment. Emphasis in this paper is on the expenditure aspects of the process. The work reported in this paper indicates that the chemical investments required for wettability alteration flooding are substantial. For evaluating the economics of a potential flooding application it is imperative that a sound estimate of the chemical requirements be made for the reservoir. Generally, true reservoir conditions are not adequately simulated in laboratory chemical propagation tests. Because of wide well spacings, many years might be required to obtain chemical propagation data from conventional pilots or inter-well tests. Consequently, n short-duration, low-cost method is needed to determine chemical requirements in the field. The potential applicability of wettability alteration flooding is discussed, as well as the economics of wettability alteration with respect to the inherent and imposed restrictions on the timing of income and investments. DETERMINATION OF CHEMICAL REQUIREMENTS In the process of moving a chemical bank through reservoir rock, some of the chemical agent lags too far behind the flood front to be effective or is otherwise lost to the reservoir system. The extent to which these losses occur overshadows the reductions in chemical concentration due to diffusion and to mixing with the reservoir fluids. Experience indicates that almost without exception, chemicals which induce a wetting change undergo either sorption reactions or chemical reactions with mineral constituents of the pore surfaces. Other reactions may occur between the added chemical and the reservoir oil and water. Even in limiting consideration to reactions of the relatively inexpensive inorganic salts, bases and acids, the reactions may be exceedingly complex. Reservoir pore surfaces consist of more than silica in sandstone reservoirs, and more than calcite or dolomite in carbonate reservoirs. Many mineral species are present, each exhibiting specific tendencies to react with an injected chemical. The reactions which occur can consume enough of the agent to have an important effect on economics. These reactions can cause a change in pH of the chemical bank, or may remove some of the active chemical by precipitation, adsorption or reaction to form a new chemical which may or may not be effective in

By Jerry L. Straalsund, D. Bruce Masson

A dew-point technique was used to determine the thermodynamic activity of zinc at 430°C in a series of e phase Ag-Zn alloys. The composition of the alloys ranged from 72 to 88 at. pct Zn. This range included the composition at which Massalski and King3 found a reversal in the composition variation of the crystallo-graphic c/a ratio, which they attributed to an overlap of the Fermi surface across the (002) faces of the Brillouin zone. The data is presented in a graph in which RT In yz,, where yz, is the activity coefficient of zinc, is shown as a function of atomic percent zinc. This curve has an unmistakable change in slope at the same composition that Massalski and King observed the beginning of the reversal in the c/a ratio. This change in slope of the thermodynamic data is also attributed to a Brillouin zone overlap. Equations are presented to demonstrate that the thermodynamic activity can be related to the density of states of the conduction electrons, and that the observed phenomena are consistent with this model. It is also demonstrated that the contribution of the density of states can be related to the excess stability, a phenomenological parameter recently shown by Darkeen" to be significant in the interpretation of thermodynamic data of metallic phases. The data seem to indicate that zone overlap has caused a spinodal point, and the resulting misci-bility gap, in the phase diagram. THE problem of developing an adequate thermodynamic model of solid solutions has proven to be difficult, and is still only partially solved. The main approach has been to develop a statistical model, such as that of an ideal solution, regular solution, and so forth, to which can be attached corrections for electronic, vibrational, magnetic, ordering, or other contributions. Such corrective terms are usually derived on an ad hoc basis, and it is difficult to predict in advance what their relative importance will be. This problem has been discussed in general terms by Oriani and Alcock,&apos; who have reviewed several thermodynamic models and a few empirical correlations. The measurements described in the present paper were made to demonstrate in a special case the importance of one such corrective term, the contribu- tion of the energy of the conduction electrons of an alloy. It was our premise that the contribution of the energy of the conduction electrons to the thermodynamic activity of the alloy components could be detected; further, that such an effect would be observed at alloy compositions where other phenomena, also ascribed to the energy and density of states of the conduction electrons, are observed. The idea of the importance of the conduction electrons is hardly new. Hume-Rothery and his adherents have developed the well-known theory of alloy phases in which the sequence of phase fields in binary equilibrium diagrams, especially those involving the noble metals with the IIB, IIIB, and IVB subgroups, can be correlated by replacing the composition variable with the ratio of conduction electrons to atoms, e/a. Jones and others have developed a physical explanation for this correlation, in which they consider the solubility limits of phase fields to be restricted by an intersection between the Fermi surface and a Brillouin zone. The general features of the model are also quite well-known—presumably zone intersection causes the density of states to decrease at critical alloy compositions. The attendant increase in energy of conduction electrons in the original crystal structure allows an alternate structure to become more stable as the concentration of polyvalent solute is increased. In spite of the wide acceptance of these ideas on phase stability, there is only indirect* evidence, such as the variations in lattice parameter recorded extensively by Massalskizy3 and others, that Brillouin zone interactions occur. There are few experimental measurements, other than the correlations of the phase sequence, that substantiate the premise that the energy of conduction electrons affects the solubility limits of alloy phases. Much thermodynamic data of alloys has been found to be consistent with the theory; yet there is a lack of detailed data at compositions where zone intersection and overlap are thought to occur. One would expect that the energy of the conduction electrons would make a measurable contribution to the thermodynamic properties of alloys at compositions near zone intersection and overlap if the theory of Hume-Rothery and Jones is correct. This conclusion cannot be avoided, because the phase boundaries are determined by the requirement that the chemical potential of the components be equal in both phases at equilibrium. An electronic effect large enough to alter the stability of a phase should also affect the thermodynamic activity by a measurable amount.

Jan 1, 1969

By A. McLean, D. W. Gomersall, R. G. Ward

An experimental study has been made of the solubility of nitrogen in liquid iron and liquid Fe-C alloys using levitation melting and a rapid quenching device. Iron alloy droplets were equilibrated with nitrogen gas at 1 atm pressure, quenched, and analyzed. Previous techniques for studying the Fe-C-N system have produced data which me in marked disagreement. This disagreement is due largely to errors caused by reaction between the molten alloy and the crucible material. With the levitation procedure, errors from this source have been eliminated and precise solubility data obtained for temperatures between 1450° and 1750°C. C-N interactions in molten iron have been expressed in terms of first- and second-order free energy, enthalpy, and entropy parameters. ALTHOUGH the solubility of nitrogen in iron base alloys is in general small, the effects of nitrogen on the properties of steel may be quite profound. For most purposes nitrogen in finished steels is undesirable, particularly in the low-carbon grades, since on cooling to room temperature the solubility limit of nitrogen in the steel may be exceeded and this can lead to embrittlement and loss of ductility on aging. On the other hand, nitrogen can improve the work-hardening properties and machinability of steels while in certain stainless grades nitrogen is important in order to stabilize the austenite phase. It is, therefore, desirable that one should be able to predict the solubility of nitrogen in liquid iron alloys. To do this, information is required concerning the interactions between nitrogen and the various alloying elements which may be present in liquid iron. There have been several investigations of these effects in recent years1"7 and the interactions between nitrogen and many elements dissolved in liquid iron are now known to a high degree of precision at steel-making temperatures. Unfortunately, a number of iron alloy systems which are of interest in steelmaking have been difficult to deal with by the experimental techniques generally used for this type of investigation. Among the most important of these are the Fe-C alloys. In the past, two methods have been widely used for determining nitrogen solubilities: the Sieverts&apos; technique, in which the amount of nitrogen required to saturate a given mass of liquid metal at a particular temperature and pressure is measured volumetrically, and the sampled-bath technique in which liquid metal held in a crucible is equilibrated with a gas phase containing a known partial pressure of nitrogen, and samples drawn from the melt are quenched and analyzed. These two methods have been discussed in detail elsewhere.5,8 With the Sieverts&apos; technique, errors may be introduced from the following sources: i) Gas adsorption on metal films which have condensed on the cooler parts of the reaction chamber. ii) Uncertainty in the determination of "hot volume" calibrations. iii) Crucible-melt interaction, particularly if a gaseous reaction product is formed or if the melt becomes contaminated with material from the crucible walls. The sampled-bath method may also suffer from errors due to reaction between the melt and the crucible material. In addition, there is the possibility that gas may be lost from the sample during solidification and cooling. In the present investigation, the solubility of nitrogen in liquid iron alloys has been studied by means of a new technique based on the use of levitation melting equipment and a rapid quenching device. In addition to the fact that problems of the type outlined above are avoided, this particular approach has the following advantages: i) The high-frequency current induces vigorous stirring within the levitated droplet so that gas-metal equilibration is rapidly attained. ii) The gas phase surrounding the melt can be changed very quickly and is easily controlled. For example, a droplet may be levitated in helium, deoxidized in hydrogen, equilibrated with nitrogen, and quenched, within a period of 15 min. ii) Melts can be readily under cooled or superheated, thus extending the effective temperature range of an investigation and allowing temperature-dependent data to be determined with a high degree of precision. Excellent reviews of levitation melting techniques and their application to physical-chemistry studies at high temperature have been published recently by Jenkins et al.,9 Peifer,10 and Rostron.11 In the present investigation a levitation melting technique has been used to obtain data for the solubility of nitrogen in pure liquid iron and liquid Fe-C alloys at temperatures between 1450° and 1750°C. The solution of nitrogen in liquid iron can be described by the reaction:

Jan 1, 1969

By T. S. Lovering

The use of geothermal energy is expanding very rapidly. This type of energy has proven commercially profitable for generation of electricity, for space heating, process heating, auxiliary heating of water in conventional steam power plants and for recovery of chemicals contained in natural hot water and steam. Two types of geothermal energy sources are recognized: 1) hot springs in regions of nearly normal heat flow that tap a deep reservoir through which water moves slowly to a hot springs conduit and then rapidly to the surface; 2) hyperthermal areas in which the water is heated by a relatively concentrated heat source related to volcanicity. If there is a geologic trap that provides a geologic analog to a steam boiler, as at Larderello, Italy, the hyperthermal area will have a convecting system that develops superheated water at relatively shallow depth and may provide natural steam in large quantities. If a hyperthermal area is to be productive for a long time, the underflow into the reservoir should be slow enough to allow the heat source and convective system to heat the underflow to the working temperature, and the production rate must not exceed this rate of underflow. A model based on a typical aquifer suggests that the rate of movement of water through the reservoir be such that a few years are spent in transit between isotherms that are spaced about 2°F apart. The possibility of finding blind geothermal areas is illustrated by discussion of the techniques developed in evaluating the subsurface temperatures in the East Tintic district of Utah where a map of isotherms at water level (2000 to 2000 ft below the surface) shows that a hyperthermal area may exist a short distance southeast of the mining district. Very nearly all of the energy that man currently uses comes ultimately from the sun&apos;s radiation. This includes water power, fuels such as wood, peat, coal and petroleum, the wind and all our animal power. In the paper summarizing a conference on solar energyl6 the average amount of solar energy received daily on the earth is taken at about 1 cal per m2 per min or slightly less than 2 pcal per cm2 per sec; this is almost exactly the amount of energy on the average that the earth liberates in regions of normal geothermal gradient due to its own internal heating. In many places, however, the energy released is many times the average and in some of these hyperthermal areas, geothermal steam is used for generation of electricity, and hot springs are used for heating buildings and private dwellings, process heating, auxiliary heating of water in conventional steam power plants, and chemicals may be recoverable from both hot water and steam. The use of hot springs waters for heating houses goes back hundreds of years but until recently was confined to a few dwellings close to the hot springs. In Korea, some houses had hot spring water channeled through conduits in the floor centuries ago and thus the Koreans can be credited with pioneer development of radiant heating. In Iceland at present nearly a third of the population uses natural thermal water for domestic heating." The Reykjavik system pipes hot spring water at about 94°C throughout the city and has devised insulated double pipes that allow the water to be piped for some 25 km with a drop of only 1°C for every 5 km. The actual cost to the Icelandic consumer is only one-third the cost of heating by imported coal and yet the industry is one of the most profitable in Iceland. The most profitable use of geothermal energy has been its conversion into electricity which can be transmitted economically much greater distances than hot water. The largest installation at the present time is that at Larderello, Italy, where the Count of Larderello began to experiment in the production of electricity from geothermal steam 60 years ago — in 1904. He installed his first steam turbine, with a capacity of only 250 kw, in 1912 as the result of a local quarrel with the power company which furnished the current required in the Larderello chemical industry - an industry that then dated back nearly a century. As experience was gained in drilling deep holes to tap geothermal steam and in converting it to electric power, the capacity of the installation of Larderello gradually increased, but was all destroyed by the Germans during their retreat from Italy in the closing

Jan 1, 1965

By W. W. Mullins, F. A. Nichols

Solutions are developed, assuming surface diffusion and both internal and external volume diffusion, for the relaxation of bodies slightly perturbed from spherical and cylindrical geometries. Combined with those previously published for the nearly planar case, these results provide a means of gaging the relative contributions of the two diffusional proc-cesses in any given case. It is shown that in all sintering experiments to date, and probably in any attainable in practice, surface diffusion has played the dominant role, although most previous authors have assumed otherwise. It is also shown that surface diffusion predominates in normal field-emission tip blunting and also for the coalescence of gas bubbles introduced into metals by a bombardment. The surface-diffusion solutions for a perturbed sphere are combined with previous results for volume diffusion to show that the inclusion of interface diffusion permits considerably larger spheres to develop in diffusion-controlled precipitate growth before the onset of instability. A mechanism is also proposed for the spheroidization of precipitate platelets as well as rods. In a previous paper1 the relaxation of a nearly plane surface to flatness by the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion has been analyzed under the assumption that all surface properties are independent of orientation. In this treatment, criteria were developed for deciding which process predominates, and solutions valid in the latter stages of the sintering of small wires and particles to a plane were obtained. A numerical solution, valid throughout the entire particle-sintering process for the case of surface diffusion, was subsequently obtained by the present authors.&apos; It was found that the analytic solution (which assumed small slopes everywhere) is accurate to within -10 pct when the maximum slope of the profile is less than 0.3; the wire-sintering problem has also been solved nu- merically for the case of surface diffusion and here again the results converge to the analytic small-slope solution at late stages of the process, the two solutions agreeing in this case to within 10 pct when the maximum slope of the profile is less than -0.6. The purpose of this paper is to extend the perturbation solutions to nearly spherical and nearly cylindrical geometries. We treat only the two principal diffusional processes, i.e., surface and volume, but for these geometries we discuss volume diffusion both inside and outside of the solid. Our results, when coupled with Mullins&apos; solutions1 for nearly planar surfaces, provide criteria for gaging the relative contributions of surface and volume diffusion to the over-all transport process in three basic geometries. A very interesting feature in the cylindrical case is the occurrence of instability for longitudinal perturbations with wavelengths greater than the cylindrical circumference, a classical result. This instability of the cylindrical surface is applied to give a quantitative explanation for the often-observed "erratic" pore closure in the late stages of the sintering of wire compacts; also, the theory previously presented for the spheroidization of rod-shaped precipitates by surface (interface) diffusion&apos; is expanded now to include volume diffusion inside and outside of the particle. The results for circumferential perturbations on a long cylinder allow quantitative estimates for gaging the relative importance of surface or volume diffusion in the early stages of the sintering of spheres or wires. The results here demonstrate clearly that surface diffusion has played a very important, if not dominant, role in all sintering experiments discussed in the literature, although the surface-diffusion contribution to the kinetics has usually been ignored. The results for the sphere (surface-diffusion case) are added to the results obtained previously by Mullins and sekerka3 concerning instabilities of a growing spherical precipitate particle (with interface diffusion disallowed) to obtain a general solution to this problem including interface diffusion. The inclusion of interface diffusion is found to increase significantly the range of stability of a growing spherical precipitate for typical metallurgical cases. The following assumptions are made: (i) the initial surface lies everywhere near and has a slope differing only slightly from that of the reference

Jan 1, 1965

By F. G. Miller

Earlier studies of the mechanism of flotation showed that coal flotation products are contaminated by composite coal and mineral particles. The mineral matter of these particles has the dual effect of increasing the specific gravity and decreasing the coal surface of the particle available for bubble attachment. The present study showed that these particles are more loosely held in the froth column than the high grade coal particles, especially in the coarser sizes. Consequently, it is possible in the laboratory to produce a secondary concentration of the product by sprinkling the froth product with water to wash these loosely held particles from the froth during formation and recovery. To improve coal flotation, Bethlehem Steel Corp.&apos;s research department has been working on a number of related problems based on both physical and chemical factors. The ideal is of course full understanding of the interrelated effects of both sets of factors. However, detailed studies1 of each physical factor have produced immediately usable results in commercial coal flotation and are providing the basis for our current work on the effect of chemical factors. Since these detailed studies provided the basis for the present investigation of froth sprinkling, their key results are highlighted here. For example, for a highly floatable bituminous coal, particle floatability was shown to be directly related to the percentage of coal surface available for bubble attachment and inversely related to particle mass. The data also underscored that in a given size range the addition of mineral matter to a particle makes flotation more difficult both by adding to the mass of the particle and by decreasing the amount of coal surface available for bubble attachment. Size also affects particle floatability in that as the size of particles of a given specific gravity increases, mass increases and the ratio between coal surface area and mass of the particle decreases. Flotation tests showed that any recovery of the coarsest particles in a coal feed is accompanied by progressively higher recovery of finer and finer particles. Consequently, fine high-specific-gravity particles are recovered with the coarse good coal. As a result, when the entire 14 mesh x 0 size range is processed by froth flotation, the good coarse coal is contaminated with high-specific-gravity fines. It is the small quantities of these fines that must be rejected from the froth product if flotation efficiency is to be increased above its present level. These principles and findings, together with work by Professor V. I. Klassen,&apos; led to the froth sprinkling investigation reported in this paper. Working with Russian coals, Klassen had shown that froth sprinkling washes loosely held refuse particles from the froth and compensates for the water lost in the upper froth layers and increases its stability. As a result, the coal particles are retained in the froth and the loss of coarse coal from the froth is prevented. Decreases in ash of 0.1% to 1.5% were reported by Klassen. Working with a 28 mesh x 0 American coal, the author of the present paper found that single-stage flotation coupled with froth sprinkling produced a product comparable to that obtained by the more expensive method of roughing and cleaning.3 The investigation reported in the present paper expanded study of the effect of froth sprinkling to include each of the standard size fractions of a bituminous coal. The main findings are as follows: (1) For those size fractions between 48 mesh and 150 mesh, froth sprinkling produces a marked reduction in both sulfur and ash. In the case of those sizes coarser than 48 mesh, while this reduction is not as significant, the additional benefit of shorter retention time is still a plus for froth sprinkling. Furthermore, when froth sprinkling is coupled with normal fast flotation, the product purity approaches that obtained by starvation reagent feeding, i.e., gradual feeding of flotation reagent to float the recoverable coal from the pulp slowly in several increments. The specific results for these two size groups are: (a) 14 x 48 Mesh. By using froth sprinkling with fast flotation, product sulfur can be reduced to a level

Jan 1, 1970

By R. J. Charles, G. Agar

Experiments on single particles show that the amount of material created during impact that is finer than any chosen size is proportional to the energy of the impact. As the underlying principle of comminution, it might be stated that each unit of energy input to a given comminution system tends to add to the system an identical assembly of new particles and subtract an equivalent volume of larger particles. Thus, two of the consequences of the fact that each unit of energy tends to add identical assemblies of new particles to the system are: 1) on continued application of energy the total charge in any batch comminution system tends to assume the characteristics of this assembly, and 2) the process of comminution may be described by a relationship such as E = Ak-a. Recently Schuhmannl presented a theory of comminution which puts rational perspective on the extensive controversy surrounding most of the existent theories of comminution. With hindsight the origin of controversy can be ascribed to a relatively simple circumstance. In general, a progressive shift of a size distribution curve towards finer sizes is observed as energy is added to a comminution system. It is also observed that, with continued grinding, the size distribution curves usually change and appear to approach some constant shape. Inves-tigators generally felt that an appropriate method of relating and generalizing such data would be to consider the hypothetical case where particles in the system were uniformly subjected to comminution such that each of these particles, receiving its proportion of input energy, was transformed into a number of smaller particles of uniform size. Since the changes in shape of the size distribution curves during size reduction were clearly associated with the coarse particles in the system, it was also assumed that these changes accounted for little of the input energy and one could deal solely with the equilibrium shape towards which the size distribution curves tended. Although the unrealistic nature of the foregoing points of view was realized some justification was felt for such treatments since, in most cases, the resulting mathematical formulae could, by the adjustment of at most two parameters, satisfactorily describe experimental observation. Difficulties arose, however, in that the formulae required a specific influence of the feed size on the comminution process. In actual fact, the application of a feed size term in fitting experimental data was often found to be unnecessary or contrary to the above formulae. Secondarily, much discussion arose concerning the appropriate energy number that would relate the size change of one particle to the amount of comminution energy it received. As has been previously shown3 all the above theories that treat comminution as a continuous process of size reduction may be related to a proposition of the following form: dE = -Cfn [1] where dE is the increment of energy, dx is the size change, x is the particle size, and C and n are constants. It is now clear, as pointed out by Schuhmann, that Eq. 1 is inapplicable to comminution processes, since comminution cannot be considered other than as a discontinuous mixing process in which the overall size distribution of the product results from mixing, in various proportions, finished material with unfinished, and sometimes untouched, material. A striking illustration of this mixing phenomena may be obtained by comparing the size distributions of grinds in a typical batch ball mill with size distributions calculated on the basis of mixing various proportions of feed material with a ground material which obeys a power law size distribution relationship. Figs. la and lb illustrate such a comparison and the similarity of these figures indicates that mixing plays an important role in determining the overall shape of the product size distributions. Figs. la and lb illustrate, additionally, the underlying basis of the comminution theory presented by Schuhmann.&apos; In the preliminary grinding of relatively close sized feed particles in a batch ball mill, one may visualize that, when a successful encounter of a ball with a feed particle occurs, then the particle undergoes severe size reduction and the size range in which the resultant particles reside is far removed from the size of the feed particles. After a number of feed particles are reduced by independent but similar impacts and one examines the size dis-

Jan 1, 1961

By H. W. Winkler, Discussion, V. L. Forsyth

The development of a new gar lift valve has removed many of the obstacles limiting over-all gas lift efficiency. The valve is pressure charged in place in a well, and operating pressure can be changed without pulling. Temperature and gas gradient compensation have been eliminated. Intermitting and constant flow installations, using conventional pressure-charged valves, are compared with designs incorporating the new automatic stabilizer controlled valve. Specific well performance data are presented. The means of obtaining and controlling multiple-point injection of gas are explained and contrasted with single point injection. The effect on small diameter strings and multiple string installations is discussed. The effect of flowing temperature gradient on a design using conventional pressure-charged valves, the limitations imposed by such temperature, and the obvious benefits which result from the use of automatic stabilizer controlled valves are shown. Reduction of gas requirements is stated mathematically and demonstrated with specific examples which are identified as to oil company and well. Increased fluid recovery resulting from greater drawdown is illustrated. The economic advantages are mentioned with emphasis on reduction of capital expenditures, as well as reduction in operating expenses. INTRODUCTION Much of the engineering and research work performed with gas lift has been based upon the supposition that under producing conditions gas would be injected at a single point in a well. Many tests were performed in determining the optimum size of the opening through which gas would be passed and the exact placement of the valve equipment. The objectives in a gas lift installation are to unload the well and to efficiently produce the well after it is unloaded. Until recently, the function of upper valves was simply to unload the well. An operating valve located at a proper place in a well served as a single injection point for lifting liquid to the surface. The basic problem in using such equipment is to arrive at operating depth with sufficient operating pressure to efficiently lift the liquid. Few gas lift installations are designed with all required well data available. However, regardless of the quality and availability of data, and regardless of the accuracy of the design, there is the practical problem of preparing and placing gas lift equipment in the well in exact accordance with the plans and intentions of the engineer. In recognition of these and many other problems, attention was directed toward a means of removing the need for temperature and gas gradient compensation, a way to change the gas lift installation to meet the changing requirements of the well itself, and a manner of compensating for changes in oil-water content, fluid volumes, PI, and bottom-hole pressure resulting from flood or repres-suring activity. A device which could actually set and change the operating pressure of gas lift valves in the well would meet most of these needs. There now exists a new gas lift valve which fulfills the original objectives and in so doing actually accomplishes much more. With this device, called an Automatic Stabilizer Controlled valve, there is an exact matching of valve operating pressure and well conditions. Gas is injected at more than one point in the well, thereby making controlled multiple-point injection of gas a reality. Installation calculations are materially simplified and the need for basic temperature and gas gradient data no longer exists. Section I—The Automatic Stabilizer Controlled Valve The operation of the ASC valve is more easily understood by first studying a conventional pressure-charged valve and then inserting the stabilizer element to observe the changes which result. Fig. 1 is a schematic of a conventional precharged pressure-operated valve. The pressure in the dome pd, acts downward, against the area of the bellows A,, to hold the valve closed. The resulting force Bf plus the spring effect of the bellows Sf represents the total force acting to close the valve. Correspondingly, the tubing pressure ptbg works upward against the port area Atbg and the casing pressure pc works upward against a portion of the area of the bellows

Jan 1, 1965

By H. Leslie Bullock

From aluminum to zirconium, the quantitative preponderance of quartz as a gangue material is well recognized. lf this material is to be efficiently removed, its variations must be understood. Variations with temperature are especially important. Too little attention has been given to the thermal polarization of quartz. Under closely controlled conditions, electrostatic upgrading is very reliable. For efficient separation, contact charges must be fostered and charges due to radiation, surface coatings, or thermal polarization avoided. This paper lists thermal transition points of quartz and shows their effect on actual separations. Simple separation tests with all factors except temperature held constant are recommended for determining transition points. With silica making up more than 27% of the earth&apos;s crust, its oxides comprising more than 59% of all igneous rocks, and quartz accounting for most of the main free oxides, the mining engineer is in constant contact with quartz, which may occur as a valuable mineral to be purified or, far more frequently, as a gangue material to be removed as completely and economically as possible. As a means of effecting such purification or removal, dry beneficiation is becoming more and more desirable owing to local water scarcities, wet waste disposal problems, or freezing conditions. One method that has been gaining particularly rapid acceptance is electrostatic beneficiation, or the separation of dry free-flowing materials by means of opposite surface charges, differences in potential, or differences in conductivity. Electrostatic beneficiation dates back to the 1870&apos;s, but only in recent years have newly developed methods and apparatus and a growing knowledge of solid-state physics widened the field for its economical application. Because the term "electrostatic beneficiation" has been rather loosely used in the literature, it has come to include both electrostatic and electrodynamic procedures. Attracting type separators, however, in which oper- ation is based on differences of surface charge or potential, are truly electrostatic, because the separation occurs in a substantially static field set up between oppositely charged surfaces. Separations with this type of equipment may occur at potentials as low as 1000 v and seldom require potentials as high as 30,000 v. In the new contact charge dielectric separators1 the variation in charge is produced by continuous contact and separation of the particles in the moving feed stream and these charges are fostered by the use of non-conducting support and feed surfaces and by handling the feed in the form of streams of appreciable depth. This favors uniformity of feed and allows higher production rates. The distinctive surface charge differences are set up on the separation of the particles according to Coehn&apos;s Law,2 which states that equal and opposite charges are generated on the separation of any two materials in contact and that the substance having the highest dielectric constant will be positively charged. The basic contact charge concept is reliable, but all electrical charges are transient and modified by the electrical conditions of the surroundings. Pyro-electric, photoelectric and radiant effects may modify or totally destroy the contact charges necessary for efficient separation, or contact with conducting surfaces may neutralize them. Such hostile conditions must be carefully guarded against, since they have led to many costly failures in the past. The most consistent difference in surface charges to insure good separation is produced by repeated uniform contact and separation of particles in the moving stream. The thickness of the feed stream possible with this method reduces the effect of contact with the supporting surfaces, but as some contact is inevitable, the best results may be assured by having the dielectric constants of the supporting surfaces between the dielectric constants of the substances to be separated. In general, the hard smooth surface of quartz makes it an ideal substance for electrostatic separation from most minerals. For instance, with calcite, starting with a feed containing 1.9% acid insolubles, one can produce a concentrate containing 0.30% acid insolubles with a tailings containing 21.7% acid insolubles and a yield of 92.8%. The color can be held at 92 or above and the tint at 1.7 or lower. Working with specularite iron ore, laboratory work has given a concentrate of 68.8% Fe., with an iron unit recovery of 96.7%. Excellent results are also in pros-

Jan 1, 1969

By David, Cole

THE years 1914-15-16 were a pioneering period in mining, milling, and copper metallurgy generally. It was uncertain just what path the crushing, grinding, and concentrating processes would take. This situation was quite embarrassing to the directors of some of our large porphyry properties, then being equipped for production. Inspiration had already made several designs for its proposed 15,000-ton concentrator, incorporating in them the latest devices developed in the art of gravity concentration, only to have the work vitiated by the rapid march of events. In a little improvised plant, built on ground that is now in the crater of subsidence over the Inspiration- Miami orebodies, flotation was being experimentally &apos; applied to Inspiration ore by Minerals Separation engineers in 1914, with results indicating that this process would be of major importance in the concentration of the sulfides. How best to apply it, and especially how to crush and grind the ore to the very much finer sizes required for the new process, was a serious question, properly to be answered only by doing it, in full- sized machines, under regular &apos;operating conditions.

Jan 1, 1931

By R. A. Morse, W. O. Keller

The properties of limestone reservoir rocks such as the distribution and degree of continuity of the pore systems, and the relative volumes and permeabilities of the systems making up the complex cause large variations between performance of individual limestone reservoirs and their susceptibility to secondary recovery methods. The effects of these factors on the mechanism of fluid flow cannot be adequately evaluated with presently developed concepts, laboratory data, and geological information. The observance and interpretation of the performance of individual limestone reservoirs provides, at present, the most adequate approach for evaluating the integrated effects upon performance of the many. now immeasurable variations in the properties of limestone reservoirs. INTRODUCTION The development and application of techniques for increasing the efficiency of oil recovery from natural reservoirs is a problem of primary importance to the industry. During the past several years, a great deal of effort has been expended by the technical personnel of the industry toward the improvement of present known methods of oil recovery. and evaluating the factors which control the susceptibility of particular reservoir types to economic application of secondary recovery methods. Providing adequate and accurate laboratory data on the properties of the reservoir rock and its contained fluids. together with good production statistics, are available, methods have been evolved for estimating with reasonable accuracy the performance of an oil reservoir under either continued natural depletion or conditions imposed by introducing additional displacing fluid into the reservoir from an extraneous source through the injection of gas and/or water. The susceptibility of limestone reservoirs to secondary recovery by gas injection is very much dependent upon gas-oil relative permeability relationships for the reservoir in question. In a rock formation in which the porosity is of the intergranular type such as is found in sand stones and some non-fractured dolomites, a representative sample of the pore structure can be obtained in a small core plug. In this type of reservoir, it has been shown that relative permeability data obtained from laboratory experiments can be Properly applied to evaluate the flow relationships actually observed during the depletion of a reservoir. In addition, a good idea of the fraction of the reservoir which will be swept by the injected gas may be obtained from the spacing pattern used and the permeability profile of cored wells. From these data, it has been demonstrated that reliable estimates of performance and recoveries under gas injection operations can be made for reservoirs in which the Porosity is of the intergranular type. Limestone reservoirs on the other hand often present much more complex problems. One reason that the performance of limestone reservoirs is so variable is that there may be, in reality. two or more pore systems, the integrated performance of which will depend upon the physical properties of each system and their inter-relationship. For instance, in a limestone reservoir, the main pore structure, as far as void spaces for storage of hydrocarbons is concerned, may be represented by the intergranular openings of the rock. Usually in limes and dolomites, the intergranular pore openings are very small and the matrix permeabilities extremely low. Often, as in the case of Many dolomite and oolitic lime reservoirs, this is the only pore system, and performance is observed to be very similar to that of a sand stone of similar permeability. However, in the great majority of&apos; the limestone reservoirs, there is present, in addition to the intergranular pore system, a complementary system of openings caused by fracturing or solution.&apos;,&apos; The openings in the latter system are usually many times more permeable than the intergranular pore system due to their much larger size, and may contribute almost all the fluid carrying capacity of the formation, even though their volume may be a very small part of the total pore space in the reservoir. Obviously, the performance of such a complex under either primary or secondary control will deend upon the distribution and degree of continuity of both systems, the relative volumes and permeabilities of the

Jan 1, 1949

By John D. Verhoeven

A technique has been developed for carrying out normal freezing experiments with a current density of 2000 amp per sq cut passing through the solid-liquid interface. The equation relating the effective distribution coefficient to the equilibrium distribution coefficient in electric field-aided solidification, originally developed by Huckc et al.,1 has been modified for the case of concentrated solutions. Preliminary experiments on the Sn-Bi system give qualitative agreement with the equation. The data are analyzed by a slightly novel use of the normal freeze equation which allows one to determine the effective distribution coefficient more easily. Very extensive mixing in the liquid was found at these high current densities and it is postulated that the mixing results from a vertical component of the magnetic Lorentz force generated by the electric current. In the search for techniques of obtaining ultrahigh-purity metals the inefficient but very effective technique of electrotransport has received little attention. Electrotransport is most effective in the liquid state and a natural application, therefore, is to apply an electric field across the liquid zone of a zone-melting experiment. The present investigation was undertaken to study the effect of an electric field upon solidification of metals, so that the usefulness of electrotransport in such solidification experiments as zone melting could be determined. In zone-melting and normal-freezing experiments it is difficult to achieve complete mixing in the liquid in the immediate vicinity of the solidifying interface. Consequently a solute build-up will occur at the interface in the portion of the liquid where complete mixing does not occur (an equilibrium distribution coefficient, ko, less than one, and unidirectional atom motion will be implied throughout). This local solute build-up produces a corresponding rise in the solute concentration in the solid so that the ratio of the solute concentration between the solid and the bulk liquid is larger than the equilibrium distribution coefficient. This ratio is defined as the effective distribution coefficient, k,. The differential equation describing the solidification process may be derived by applying the continuity equation to an expression for the net solute flux at the interface. The solution to this differential equation then allows one to determine the solute distribution in the liquid and the relationship between k0 and ke. One of the most useful solutions to this equation was first derived by Burton, Prim, and Slichter,&apos; in which they assumed that a) the equilibrium distribution of solute was maintained on the plane of the interface, 11) the solute build-up ahead of the interface in the liquid disappeared at a distance 6 from the interface, and c) the solute distribution in the liquid was invariant with time. The following well-known relation between ko and ke was then obtained, where R is the rate of solidification and D the diffusion coefficient of the solute in the liquid. This equation appears to correlate the data from a number of different types of solidification experiments very well. Application of an electric field across the solid-liquid interface can produce an additional flow of solute atoms as a result of the electrotransport. When the polarity of the field is such as to direct the electrotransport flux away from the interface the solute build-up may be diminished, even to the point of producing a solute depletion and a consequent ke smaller than ko. The quantitative description of this process and the resulting form of Eq. [I] was first given by Hucke et al.1* and then inde- where E is the electric-field intensity and U is the differential mobility, i.e., the velocity of the solute atoms with respect to the solvent atoms per unit electric field. Both authors follow the method of Burton, Prim, and Slichter in their derivation, the only difference being the additional electrotransport term in the flux equation. It has been pointed out1,3 that Eq. [2] predicts the possibility of a noticeable increase in the purification of materials by solidification in an electric field. The validity of Eq. 121 has not been checked experimentally and it is possible that other factors&apos; arising from the presence of an electric field across

Jan 1, 1965

By R. A. Morse, W. O. Keller

The properties of limestone reservoir rocks such as the distribution and degree of continuity of the pore systems, and the relative volumes and permeabilities of the systems making up the complex cause large variations between performance of individual limestone reservoirs and their susceptibility to secondary recovery methods. The effects of these factors on the mechanism of fluid flow cannot be adequately evaluated with presently developed concepts, laboratory data, and geological information. The observance and interpretation of the performance of individual limestone reservoirs provides, at present, the most adequate approach for evaluating the integrated effects upon performance of the many. now immeasurable variations in the properties of limestone reservoirs. INTRODUCTION The development and application of techniques for increasing the efficiency of oil recovery from natural reservoirs is a problem of primary importance to the industry. During the past several years, a great deal of effort has been expended by the technical personnel of the industry toward the improvement of present known methods of oil recovery. and evaluating the factors which control the susceptibility of particular reservoir types to economic application of secondary recovery methods. Providing adequate and accurate laboratory data on the properties of the reservoir rock and its contained fluids. together with good production statistics, are available, methods have been evolved for estimating with reasonable accuracy the performance of an oil reservoir under either continued natural depletion or conditions imposed by introducing additional displacing fluid into the reservoir from an extraneous source through the injection of gas and/or water. The susceptibility of limestone reservoirs to secondary recovery by gas injection is very much dependent upon gas-oil relative permeability relationships for the reservoir in question. In a rock formation in which the porosity is of the intergranular type such as is found in sand stones and some non-fractured dolomites, a representative sample of the pore structure can be obtained in a small core plug. In this type of reservoir, it has been shown that relative permeability data obtained from laboratory experiments can be Properly applied to evaluate the flow relationships actually observed during the depletion of a reservoir. In addition, a good idea of the fraction of the reservoir which will be swept by the injected gas may be obtained from the spacing pattern used and the permeability profile of cored wells. From these data, it has been demonstrated that reliable estimates of performance and recoveries under gas injection operations can be made for reservoirs in which the Porosity is of the intergranular type. Limestone reservoirs on the other hand often present much more complex problems. One reason that the performance of limestone reservoirs is so variable is that there may be, in reality. two or more pore systems, the integrated performance of which will depend upon the physical properties of each system and their inter-relationship. For instance, in a limestone reservoir, the main pore structure, as far as void spaces for storage of hydrocarbons is concerned, may be represented by the intergranular openings of the rock. Usually in limes and dolomites, the intergranular pore openings are very small and the matrix permeabilities extremely low. Often, as in the case of Many dolomite and oolitic lime reservoirs, this is the only pore system, and performance is observed to be very similar to that of a sand stone of similar permeability. However, in the great majority of&apos; the limestone reservoirs, there is present, in addition to the intergranular pore system, a complementary system of openings caused by fracturing or solution.&apos;,&apos; The openings in the latter system are usually many times more permeable than the intergranular pore system due to their much larger size, and may contribute almost all the fluid carrying capacity of the formation, even though their volume may be a very small part of the total pore space in the reservoir. Obviously, the performance of such a complex under either primary or secondary control will deend upon the distribution and degree of continuity of both systems, the relative volumes and permeabilities of the

Jan 1, 1949

By T. E. Scott, D. H. Sherman, C. V. Owen

Mechanical properties and optical metallographic characteristics of vanadium containing 53 ppm (wt) H were investigated from, 77° to 298°K. A sharp ductile to brittle transition induced by the presence of hydrogen was observed between 238° and 223°K and a mar-tensitically formed hydride appeared at 200°K. While there appears to be a subtle relationship between the hydride formation and the ductile-brittle transition, it was concluded that the hydride per se was not sufficietzt to cause the severe em brittletnent. On the basis of the metallographic experiments and the results of a Petch analysis it is suggested that the mechanism of the embrittlement involves a reduction of the true surface energy, or cohesion, of the uanadiunz. THAT hydrogen can severely embrittle vanadium is well-documented;&apos;-5 however, the mechanism by which hydrogen induces the observed embrittlement has not been established. It is not known whether the embrittlement of vanadium is caused by the formation of vanadium hydride or by a more subtle role of hydrogen. Until very recently6>&apos; the solid solubility of hydrogen in vanadium at temperatures in the,range of the embrittlement was not known to a useful accuracy. In general, a severe embrittlement of the type produced by the presence of hydrogen in vanadium can be caused by changes in either of two properties of a metal. Either the yield stress of the metal is raised to the extent that plastic deformation at the tip of a crack cannot occur or the cohesive properties of the metal are reduced, at least locally, to the point at which cleavage is the natural response to applied loads. Of course a combination of these is possible. It is not known which of these properties of vanadium is influenced most by the addition of hydrogen. The purpose of this investigation was to determine the role of hydrogen in the embrittlement of vanadium. Accordingly, the solubility of hydrogen in vanadium in the temperature range where embrittlement is most severe was determined, the appearance of vanadium hydride was examined in relation to the initial ductile to brittle transition temperature, and an attempt was made to evaluate the effect of hydrogen on the yield stress and cohesive properties of vanadium. MATERIAL AND PROCEDURES Sample Preparation. The vanadium used in this investigation was prepared by the iodide refining process described by Carlson and owen.&apos; Three ingots, 3 in. diam by 6 in. long, were cold-swaged to 0.096 in. diam, cut into short lengths, and then arc-melted under purified argon into one ingot. This process was repeated to insure a uniform composition in the final ingot. Chemical analysis of the metal is given in Table I. On the basis of work of Loria et a/ .&apos; the following sequence of treatments was performed in order to obtain a uniform equiaxed ultimate grain structure: a) cold swage q-in.-diam ingot to 0.230 in. diam; b) anneal 6 hr at 1000°C in vacuum; c) by cold swaging reduce 81 pct in area in three steps: 0.230 to 0.187 in. diam, 0.187 to 0.150 in. diam, 0.150 to 0.096 in. diam. This sequence provided the desired grain structure after subsequent annealing treatments. Because annealing in evacuated quartz capsules resulted in contamination by oxygen, all anneals in this investigation were performed in a 304 stainless-steel chamber under a dynamic vacuum of 10- I Torr with the vanadium wrapped in tantalum foil. Prior to all annealing treatments the wires were electropolished for 1 min at 16°C in an 80 pct methanol-20 pct sul-furic acid electrolyte at 12.5 v. Following the final reduction the 0.096-in.-diam wire was cut into 2-in. lengths. A 1-in. gage section was reduced to 0.090 in. diam by electropolishing as above. Five different grain sizes were obtained by annealing the 2-in. samples at different temperatures for 8 hr to insure uniform grain size and residual hydrogen removal. The annealing temperatures used and the resulting grain sizes are given in Table 11. The final step in sample preparation was to charge half of the specimens of each grain size with hydro-

Jan 1, 1969

By C. G. Dunn, P. K. Koh

THE primary recrystallization texture in cold-rolled silicon iron, which is the matrix texture for developing the Goss texture or the cube-on-edge texture by secondary recrystallization at temperatures near 900°C,1-5,21 has not been adequately described. Thus from the present available information, it is not possible to explain satisfactorily both the grain-growth selectivity of the matrix and the often observed magnetic torque curve, which itself provides some information on the texture. Also lacking is information on the special annealing texture that develops in this material when the annealing temperature is 1200°C or higher and the rate of rise to temperature is extremely rapid. From the work of May and Turnbull5 and from unpublished work, it was known that isothermal annealing near 1200°C tends to reduce the extent of secondary recrystallization and that a much weaker cube-on-edge texture results if appreciable normal grain growth replaces secondary recrystallization. Koh and Dunn6,7 have obtained additional information on complex primary recrystallization textures from further studies made after normal grain growth. In these instances the initial textures were retained during normal grain growth. A similar result reasonably could be expected in the present study except for the presence of a grain growth ihibitor1-5,8,9.21 and its tendency to allow only a few grains to grow. However, any information on the orientations of grains in the special annealing texture, even if far from representative of the initial matrix texture, would provide useful information on the nature of the matrix texture. In the present texture study the method of Newkirk and Bruce,10 which is based on the methods of Geisler" and Schwartz, 12 is used to obtain a complete (110) pole figure of the primary recrystallization texture. The high-temperature annealing texture is determined simply from the orientations of a large number of selected grains. The kinetic nature of the process that produces the annealing texture is treated elsewhere13 and it is shown that a form of secondary recrystallization with a very high rate of nucleation occurs during rapid annealing at high temperatures. EXPERIMENTAL PROCEDURE Commercial 0.014-in. cold-rolled silicon iron strip (3.16 wt pct Si), prepared by two stages of cold rolling with an intermediate short anneal, was given a decarburizing 3-min anneal at 800°C. Me-tallographic studies indicated complete recrystallization. Short-time anneals at 900° C and at higher temperatures proved that secondary recrystallization had not begun at 800°C, in fact, the short additional anneals were still in the induction period of secondary recrystallization. A rapid rise to an annealing temperature of 1260°C (2300°F) was obtained in a BaC12and NaCl fused salt bath. The structures that resulted from anneals in the range 12- to 1000-sec duration were relatively finegrained, even though the growth was a form of exaggerated grain growth13 or secondary recrystallization with a high nucleation frequency.= Many of the grains were large enough for an X-ray study using a 5-mil X-ray beam. A transmission Laue Camera and an optical-mechanical stage for moving the grains into the X-ray beam were used. A total of 325 grains were X-rayed in this manner and the grain orientations determined. Complete (110) pole figures were obtained for the primary recrystallization texture using CoKa radiation at 30 kv in the back-reflection range, such as (220) for (110) poles, as described recently by Newkirk and Bruce.10 The low voltage serves to reduce the spurious white radiation to a minimum. A filter of 0.001-inch iron foil was located in front of the detector slit for transmission and in front of the beam slit for back reflection. A new and improved specimen holder extended the useful tilting angle range for transmission to 70 deg instead of 60 deg as previously reported.&apos; A torque magnetometer was used to obtain the magnetic torque curves for a number of l-in. diam disk specimens. RESULTS The (110) pole figure of the material after recrystallization at 800°C is shown in Fig. 1. The positions of the pole concentrations are found to be

Jan 1, 1961

By M. J. Scoble, W. J. P. Leigh

This paper aims to characterise the forms of slope instability incident in surface coal mines in Britain. These are related to observed controlling factors, with particular reference being given to slope geometry and structure. The work is based on specific data collection programmes considering actual stable and unstable mine slopes. Reference is made to field examples.

Jan 1, 1982

By Bryan J. Travis, Thomas L. Cook

INTRODUCTION Our growing concern for adequate and secure sources of energy and minerals has stimulated vigorous exploration for new sources, research toward a better understanding of geological processes, and development of new extraction technologies. The need for control, or at least prediction, of subsurface fluid flow is important for many of these technologies for example: primary, secondary and tertiary recovery of oil; ground water and waste management; in-situ fossil energy extraction (oil shale, coal, tar sands); and solution mining of uranium, copper and other minerals. These technologies, especially the last two, are characterized by highly complex systems. A partial list of the physical processes occurring would include flow in porous/fractured media, multi-phase and multi-component flow with heat transport, chemically active fluids and soils, tracers, diffusion and dispersion, fracturing and dissolution. A great deal of understanding of how these processes behave and interact can be obtained from models. MODELS Theoretical models are valuable because they: 1) provide a frame of reference for interpreting results of laboratory and field experiments; 2) once validated by experiments, allow a variety of geometries, injection/production strategies, etc., to be examined (at relatively low cost) for efficiency and stability; 3) can provide guidance to the design of experiments and field operations. Most models are based on the fundamental principles of mass, momentum and energy balance. But from this starting point, many paths can be taken. For example, there is the theory of Payatakes (1973) which concentrates on the microscale dynamics. In this approach, the rock or soil matrix is represented by a complex of characteristic channels (such as periodically constricted smooth tubes). Detail of flow within the characteristic channel is calculated very accurately. A difficulty with this model is that description of a representative channel can require several parameters which may not be easily measured. Also, it is not clear how the channels can be combined practically to model a large scale flow. Another type of model is the "global" one described by Bear (1972). Here, the continuum equations for conservation of mass, momentum and energy are averaged over a distribution of pore channels, resulting in a set of conservation equations in which the small scale structure of the medium is replaced by quantities such as porosity, permeability, dispersion coefficients and tortuosity. This approach allows computation of large scale flows. However, additional constitutive equations are needed which relate averaged quantities such as permeability to observables such as local saturation, particle size distributions, and others. An important difference between models is the way they handle the momentum equation. Payatakes&apos; model solves the full equation. In others, it is replaced by a simpler relation such as Darcy&apos;s law (valid for slow flow rates) or by Forchheimer&apos;s equation which extends Darcy&apos;s law to higher flow rates. These simple relations can nevertheless match a great deal of experimental data (Dullien 1975). The permeability term which appears in Darcy&apos;s law and in Forchheimer&apos;s expression has been related to other quantities such as porosity and particle surface area. The Kozeny-Carmen equation is a well-known example, valid for some ranges of porosity and particle sizes and for some materials. Several other semi-theoretical, semi-empirical formulations have been devised, none of which are entirely satisfactory. One goal of researchers has been the ability to predict permeability of a porous material from basic measurable quantities such as grain size distributions without recourse to adjustable parameters. This effort has proceeded from consideration of distributions of idealized, non-intersecting channels, to intersecting channels, to consideration of both distributed pore radii and pore neck radii. This last approach has been used successfully to predict permeabilities (ranging over several orders of magnitude) in sandstones (Dullien 1975). Additionally, studies on explicit networks of channels (e.g., Fatt 1956) and percolation theory (e.g., Larson et. al. 1981) have been used to examine interconnectivity effects in porous media with the hope of eventually being able to predict permeability accurately. To be of more than theoretical interest, a model must be compared s controlled laboratory conditions where boundary and initial conditions and relevant material properties can be accurately determined. Also, extraneous forces can be eliminated so that the interactions between processes of interest can be clearly seen and flow models can be vigorously tested. In contrast to the well-defined environment and

Jan 1, 1982