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By Craig S. Hartley

An approximate expression is obtained for the energy of a closed dislocation loop in equi1ibriu)n with a constant net stress. The result obtained is valid for loops in isotropic or anisotropzc materials provided that they are suJficiently large that the energy per unit length of a segment of the loop can be approximated by that of an infinite straight dislocation tangent to the loop. It is shown that this approximation leads to very close agreement with a more rigorous calculation of the elastic energy of a circular glide loop. The Gibbs-Wulff Form, GWF, of a dislocation is the closed planar loop which has the smallest elastic self-energy of all possible loops having the same Burgers vector and enclosing a fixed area, A.' The energy of such a loop is related to the net resolved shear stress* required to expand the loop and to the stress required to activate a Frank-Read source.223 In the following sectiorls the problem of determining the form of the GWF is discussed and an approximate method for calculating its elastic self-energy is presented. It is demonstrated that the approximations employed lead to no serious errors when applied to a calculation of the elastic energy of a circular glide loop. This method is then used to obtain a closed form expression for the energy of GWFs in isotropic and anisotropic materials. THEORY Burton, Frank, and cabrera4 have proved that the relationship of the equilibrium shape of a two-dimensional array of atoms under the influence of the Gibbs free energy associated with unit length of its boundary, G(O), is that the polar plot of G(0) vs 0 is proportional to the pedal of the GWF.* The angle 0 is measured "The pedal of the polar graph ofG(0) vs0 is the envelope of tangents to the eraph.relative to some crystallographic reference direction. The difficulty in applying this result to a closed dislocation loop arises from the self-interaction of the loop. For a dislocation the energy analogous to G(0) is a function of the total configurati~n.~ Consequently the relation which determines the GWF is an integro-differential equation rather than the simple differen- tial equation which results when G(8) is a function of 0 alone. Mitchell and smialek3 and Brown~ have used the self-stress concept introduced by ~rown' to calculate the shapes of dislocations in equilibrium with an applied stress. In this approach the glide force on an element of the dislocation loop due to the interaction of the element with the rest of the loop is equated to the glide force exerted by the local applied stress. The shape of the loop is then adjusted so that the two forces above are equal at all points on the loop. It is possible to calculate the energies of such loops by noting that, for equilibrium with an applied stress, the energy is equal to pijbiAj (summation convention) where bi is the Burgers vector, p.. is the local net stress tensor, and Ai is a vector directed perpendicular to the plane of thd loop with magnitude equal to the area of the loop. Also Brown' has calculated the energy of a hypothetical polygonal GWF using the above technique and anisotropic elasticity. However, his indicated solution for the energy in the general case of an arbitrary GWF is only slightly less involved than an iterative solution of the integrodifferential equation referred to earlier. In the present work the approximation employed by DeWit and Koehler' is used to calculate the energy of a closed loop in equilibrium with an applied stress. That is, the energy of a loop segment, ds, is approximated by the product of ds and the energy per unit length of an infinite, straight dislocation in a cylinder coaxial with the tangent to the loop at the angular position of the segment. This is known as the "line tension" approximation. The inner cutoff radius of the elastic solution defines the core radius, while the outer cutoff radius is determined by some characteristic dimension of the loop. Actually, both of these radii vary with the edge-screw character of the segment. The effective core radius changes because of the orientation dependence of the Peierls width of a dislocation,8 and the outer radius should be the radial distance from the circumference of the loop to the center of symmetry of the area enclosed by the loop.g However, since the energy varies logarithmically with the ratio of these radii while depending directly on the effective elastic constants, only the effect of the latter is considered. This approximation also neglects the self-interaction of the loop segments. For small loops this will doubtless be extremely important, but for large glide loops produced by plastic deformation the self-interaction is not nearly so important in determining the energy of the loop. This point is illustrated by the following calculation of the energy of a circular loop. Consider a circular loop of radius R which lies in the XI - x, plane of an infinite isotropic continuum and whose Burgers vector makes an angle $ with xs. The first-order solution for the elastic self-energy is:'

Jan 1, 1970

By E. C. van Reuth

FIFTY-three alloys have been examined in the Fe-W and Co-W alloy systems in an attempt to verify the finding of o phases in these systems as reported by Goldschmidt.' The alloys were examined metallographically and by X-ray diffraction. The 10-g specimens were made by powder metallurgy techniques. Very fine, high-purity powders were compressed in a double-acting die at 120,000 psi after hydrogen reduction. All compacts were then sintered for 200 hr at 950°C in a helium atmosphere. Metallographic investigation and X-ray diffraction proved this time to be sufficient to allow complete homogenization before the subsequent high-temperature anneal. Each specimen was then sealed into an evacuated silica capsule and annealed at 1400"or 1500 C (except two) for 25 hr. (The 60 pct Fe and 55 pct Co alloys taken to 1610"and 1680°C respectively were held at these temperatures for 1hr. However, since these structures were at equilibrium before the anneal, and in view of their resultant structures, it is assumed that they reached equilib-

Jan 1, 1960

By R. H. Jacoby, V. J. Berry

Future depletion performance and ultimate oil recovery from reservoirs producing under volumetric control are often predicted with the aid of a material balance equation. When the reservoir fluid is very volatile, however, certain assumptions implicit in the use of the conventional methods are no longer valid. This is became laboratory differential vaporization test procedures do not adequately represent the reservoir depletion process and the performance of surface separation facilities. In such cases recovery of stock tank oil per unit of pressure decline can be predicted only from a detailed knowledge of the separator conditions and the over-all composition of the fluid entering the wellbore at each stage of depletion. Surface recovery is not simply related to the total quantity of liquid flowing into the well under reservoir conditions. In order to improve predictions for reservoirs which produce volatile oils, a step wise method of calculation has been developed. This method uses relative permeability data and multicomponent flash calculations to predict oil and gas production as a function of reservoir pressure. Calculations are presented for a reservoir containing a volatile crude oil, and predicted tank oil recovery by primary depletion is more than twice that predicted by conventional methods which are known to be adequate for ordinary black crude oils. Calculated maximum produced gas-oil ratio is less than one-fourth of the conventional prediction. Wellstream compositions have also been used to determine variation in stock tank oil composition and liquid content of the separator gas. This information is of particular importance for crude stabilization calculations and for design of gasoline plant facilities to recover LPG and natural gasoline. INTRODUCTION The estimation of oil reserves and the prediction of future recovery performance of petroleum reservoirs is a frequent task of the petroleum engineer. If the reservoir produces under volumetric control, performance calculations for primary depletion are made by combining oil and gas material balances with the gas-oil flow characteristics of the reservoir rock. For black oil reservoirs, the Schilthuis1 type material balance is commonly employed. For gas or gas-condensate reservoirs, where only one phase is flowing under bottom-hole conditions, a more simplified material balance is used. In the period in which these material balance methods were conceived and put into practice, it was common to classify reservoirs according to the type of fluid produced as (1) black oil reservoirs, or (2) gas or gas-condensate reservoirs. Recently, however, deeper drilling and more extensive studies of reservoir fluid properties have led to the recognition of reservoir fluids with phase characteristics between those of ordinary black oils, and gases or gas-condensate fluids. These intermediate fluids contain relatively large amounts of the hydrocarbons ethane through decane and are found in deep, high temperature (250°F) reservoirs. Such fluids are often referred to as high shrinkage crudes or "volatile oils." They are usually characterized by tank oil gravities above 45° API. high solution gas/oil ratios,

Jan 1, 1958

By G. Y. Chin, M. T. Dolan, W. L. Mammel

The least work analysis of constrained deformation, first proposed by Taylor and recently modified by Chin, Hosford, and Mendorf to include twinning, has been applied to the problem of axisynmetric flow. Calculations were made, for the case of (111}(110) slip and {111}(112) twinning applicable to fcc deformation. The solutions were obtained by linear programming techniques and with the aid of computer methods. The results show that in axisymnzetric tension the onset of twinning tends to decrease the plastic strength anisotropy as compared with the case of defortnation by slip alone. In compression, however, the strength anisotropy is increased as a result of twinning. The [100] and 11111 orientations and their vicinity are unfavorable for twinning in tension and compression, respecticely. With slight modifications, the present results may be applied to bcc metals deform ing by {110}(111j slip and (112} (111) twinning. Implications of present results to wire texture development of low stacking fault energy fcc materials arc discussed. PREVIOUSLY we' have applied linear programming techniques to obtain solutions to Taylor's least work analysis2 of constrained deformation of single crystals undergoing axisymmetric flow, such as occurs in an axially loaded polycrystalline aggregate. These solutions yielded values of the parameter M = o/.r = Y/w which relates the external stress-strain (u-c) curve to the shear stress-shear strain (7-y) curve for the crystal. The value of M is dependent on crystal orientation and hence enters significantly in texture strengthening considerations.3'4 Recently the Taylor hypothesis was modified by Chin, Hosford, and Mendorf' to include mechanical twinning. The latter has now been applied to the problem of axisymmetric flow and the results are reported in this paper. Calculations have been made for {111 )( 110) slip and {111 )(112) twinning applicable to fcc crystals. With minor changes in the indices of the slip and twin systems, the present results are also applicable to bcc crystals which slip on (110) (111) and twin on {112)(111) systems.

Jan 1, 1970

By R. J. Marcotte, C. T. Eddy, R. J. Smith

The objectives of the investigation herein reported were to determine: (I) the S-curves for certain selected cast steels, (2) whether or not the published S-curves for wrought steels are satisfactory for use on cast steels of similar composition, and (3) to prepare hardenability curves of the selected cast steels. In order to make the final comparisons between cast and wrought steel more completely tangible, it was deemed advisable not only to determine S-curves for the steels submitted in the cast condition but also to roll some of the cast-steel test bars and determine comparison S-curves on such wrought material. This procedure eliminates the composition variable and makes it possible to reveal the differences resulting from plastic deformation of the cast structure in addition to providing the comparison with published data on wrought steels. Cast Steels The cast steels selected for the preparation of S-curves, or time-temperature transformation curves, were similar to S.A.E. series 1030, 2330, 4130 and 4330. Of these the 1030 was supplied by The Crucible Steel Casting Co., Cleveland, Ohio, and the other three by The Sawbrook Steel Castings Co., Lockland, Ohio. The steels were furnished in the as-cast condition. The manufacturers supplied the chemical analyses and the properties that could be obtained in the heat-treated condition—all of which is summarized in Table I. The metallographic and dilatometric procedures and equipment were in general standard. The specific technique employed was described in a report of the Steel

Jan 1, 1945

By G. W. Binkley, G. K. Dumbauld, F. A. Brooks, B. E. Morgan

In recent years, oil well cementing compositions have been developed with low densities, controlled set strengths, and satisfactory thickening times. With the introduction of the permanent-type well completion method for cementing wells, another property—that of rate of filtration or water loss to permeable formations— has become important. Laboratory data show that cement slurries prepared with oil, water, bentonite, and calcium lignosulfonate possess satisfactory thickening times, strengths, and filtration properties for primary cementing of casing and for squeeze cementing with the permanent-type well completion technique. Cementing compositions have been prepared with oil-in-water emulsions varying in composition from 60 cc water and 20 cc oil per 100 gm cement to 90 cc water and 45 cc oil per 100 gm cement. These compositions have contained from 0.4 to 5.0 per cent calcium lignosulfonate by weight of dry cement. Slurries prepared from these compositions weigh 11.4 to 13.1 lb/ga1 and have filtration rates of from 10 cc to approximately 100 cc in 30-min API tests at room temperature. The unfiltered emulsion cements develop one-day tensile strengths of 60 to 220 psi; and the filtered mass sets to tensile strengths of 60 to 150 psi in 12 hours and develops strengths of 320 to 515 psi in seven days when cured at 125° F. Field experience gained from 13 field mixing jobs demonstrates the utility of the emulsion cement for permanent-type squeeze cementing operations. INTRODUCTION In recent years, research in oil well cementing composition has been directed toward the development of cements having low densities, controlled set strengths, satisfactory thickening times, and low rates of water loss by filtration. Two well cementing compositions that have been developed with these properties are the modified cements containing, respectively, 12 and 25 per cent bentonite clay and various concentrations of calcium lignosulfonate1,2 In a search for other ways to incorporate these characteristics in a cementing composition, consideration was given to the rheological properties of oil-emulsion drilling fluids. Many of the desirable properties observed in oil-emulsion drilling fluids are equally advantageous in a cementing composition. For example, low water loss by filtration and low density, which are inherent characteristics of these oil-in-water emulsions, are desirable for many oil well cementing operations. Furthermore, oil-emulsion slurries have lubricating properties similar to those of oil-emulsion muds, a factor which should provide ease of rotation of casing during primary cementing operations. The properties of lubrication and low filtration may be of special value in both primary and squeeze cementing operations encountered in slim-hole drilling. Studies in the preparation of oil emulsion systems have pointed out the need for violent agitation in order to disperse the oil into the water phase. It was thought, therefore,

Jan 1, 1957

By J. B. Murdoch, John G. Jackson

The many mechanical, geological, and economic factors which influence the planning of a directional drilling program are thoroughly discussed and analyzed. It is demonstrated that the planning of a directionally drilled multiple-well artificial island location is a complicated undertaking and that it is imperative that complete planning and engineering analysis be undertaken before the program is started. Complete planning is profitable because all of the factors influencing the directional work are in general interrelated and many time compromises have to be made before a harmonious program results. The engineering control necessary to accomplish a complicated directional drilling program is outlined. Various means by which engineering control can be increased, such as cylinder drilling specifications, are given. A hypothetical example is developed for a complete offshore artificial island of ten wells to demonstrate the more important factors involved in the planning. Included with this example are special charts and tables which make more rapid the drafting of directional drilling proposals and maps. Introduction A petroleum engineer must consider many and varied factors when planning a long range directional drilling program for an offshore or inaccessible location on an oil structure. The basic principles of direc- tional drilling planning and operation must be reconciled with his company's drilling practices, and frequently special concessions to standard drilling and production practices should be made. The field techniques and tools used in directional drilling are well known and widely used, but the deliberate, careful planning of a complete directional program is in the main a recent innovation. This development, plus the increased demand for oil resources and the consequent exploitation of inaccessible structures and offshore locations, has placed this problem before many engineering departments for the first time. Directional drilling programs of a very complex and difficult nature have been successfully carried out in the Mid-Continent and Pacific Coast regions. The planning itself of a directional drilling project, however, has not had the careful analysis it deserves and we can reasonably expect widespread future progress along thesc lines. Data and experience gained in these programs by the directional drilling service companies and the oil producers have been studied with the objective of giving the engineer a better conception of the factors which govern the various steps in planning a series of directional wells. The newest engineering procedures are the result of recent careful analysis of years of directional drilling work accomplished under the supervision of directional drilling service companies working with the oil companies. The purpose of this paper is to illustrate

Jan 1, 1949

By H. H. Keller, E. J. Couch

Damage to production wells subjected to the high temperatures associated with in-situ combustion projects has been a problem since the advent of this thermal recovery technique. Injection of water down the annulus of hot wells has been successfully utilized for cooling and prolonging the life of such wells. A mathematical model that is suitable for predicting the effectiveness of cooling water in a particular application is developed. Typical results for practical ranges of the various parameters involved are presented. INTRODUCTION In the normal course of in-situ combustion operations, highly damaging conditions develop in the production wells as the combustion zone approaches, and these wells are subjected to high temperatures (up to 1500F). The resulting well damage is recognized as one of the more serious operating problems unique to the in-situ combustion process. Even in operations where well completions have been specifically designed to cope with this problem, the question arises as to how this destructively high temperature can be kept within tolerable limits. A simple and economical approach to this problem is to circulate cooling water down-hole. This method has been used with some success in shallow reservoirs. At greater depths, however, the heat exchange with the overburden surrounding the well and between the fluids in the tubing and the annulus tends to equalize the temperatures of the two fluid streams so that the cooling capacity delivered to the bottom of the hole decreases with well depth. This method would provide no appreciable control over the bottom-hole temperature at great depths. In order to delimit the condition under which cooling by water circulation is effective, the wellbore temperature must be related to the water inlet rate and temperature; to the reservoir depth, production rate, and initial temperature; and to the combustion at at bot tom-hole depth. A model that meets these requirements and that will offer an approach for developing engineering solutions to practical design and operating problems is described in this paper. MATHEMATICAL MODEL Previous studies of temperature distributions include those for flowing wells1p2 and those for hot fluid injection. Adams and Haddenhorst 6 presented solutions for the down-hole circulation of hot oil in the treatment of paraffin-deposition problems. In this paper the thermal model presented by Ramey 4 is adapted to the flow system shown schematically in Fig. 1. Water at temperature Ti is injected at a rate wi and flows down the annulus outside the tubing. It mixes at bottom-hole depth D with the fluids produced at race w from the hot reservoir at temperature T. This mlxtureJ. of injected water and reservoir fluids flows up the tubing and is produced at the surface at TI,. In order to describe the temperature response in this system, we make use of the usual conservation of

Jan 1, 1969

By G. H. Alani, H. T. Kennedy

One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the Inolal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heary hydrocarbons expressed as c The equatious are similar in form to van der Waals equation. hut the constants a and b tire considered as furnctions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydro- When comptired with experimental values jound in the literal the. the average absolute deviation in the calculated molal volumes is found to be a Maximum of 0.33 per -cem for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubbl-point ro 10,000 psis. The equations expressing the correlation for. mixrurrc were developed from 647 experimental measure-rilents of volume on 47 bouom-hole samples covering ; temperature range of 72" to 250°F and a pressure znge from bubble-point ro 5,000 psig. The average absotute deviation was found to he 1.6 per cent with the maximum for any measurement of 4.9 per cent. INTRODUCTION Accuratc information of the pressure-volume-temper-iiture behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state. Equations of state for gases have been developed based on the ratio of pressure, temperature and volume to the pressure, temperature and volume at the critical points of the hydrocarbons. These equations have been successful in yielding values fairly accurate for reservoir engineering purposes. For liquids, however, relations of this type are more complex and have not yielded useful results. The composition of reservoir liquids is normally expressed in terms of the moles of hydrocarbons C,? C,. C,. elc, per mole of mixture. The composition must include the fraction of a mixture such as C,,, which cannot be separated with reasonable time and effort into specific hydrocarbons. Although there are several equations of state having variable degrees of accuracy applicable to pure liquid hydrocarbons, none includes a means for estimating the volume of mixtures as a function of temperature. pressure and composition expressed in this manner.

By J. J. Beeson

The second part of the paper includes a detailed account of the processes of secondary-enrichment which have been effective in producing the disseminated ores. While both parts present new features, it is hoped that the discussion on secondary chalcopyrite and bornite may be of interest to those who are engaged in the study of secondary processes in other districts. The excellent work' Economic Geology of the Bingham Mining District, by J. M. Boutwell, was published in 1905. Since that time the extensive development work-surface cuts and underground drifting-of the Utah Copper Co. has made possible the collecting of samples for more detailed microscopic study. The writer has taken advantage of this fact and presents the following work, not as a criticism, but as a' continuation of the work which was begun by Mr. Boutwell. b. Acknowledgments.-The present study was undertaken at the suggestion of Dr. A. F. Rogers; to him, and to Prof. C. F. Tolman and Prof. S. W. Young, the writer wishes to express his thanks for criticism in the preparation of this paper. The writer also expresses his thanks to D. C. Jackling, Vice-President and Managing Director of the Utah Copper Co., for permission to publish this paper, and to William Spencer, D. W. Wadleigh, T. S. Carnahan, J. A. Caulfield, Percy Dayer, and Edward Norsefall, for the courtesies extended to him while a co-worker in the mines.

Jan 11, 1915

By J. E. Chappelear

We are concerned with the problem of calculating the forces produced by passing waves on a submerged object (in particular a drilling barge) located on the ocean floor. We employ the linearized theory of waves (the Airy1 theory), since solutions are generally more easily obtained in such a theory. It will be indicated how an approximate solution to the problem can be obtained for waves of finite height by use of a linear combination of Airy waves. We shall assume the submerged object has an infinite length, thus neglecting diffraction and making the problem two-dimensional. We find that there is not a considerable difference between our solution and the usual engineering solution. The force, as a function of time, is plotted in Figs. 4 and 5, together with the usual solution for easy comparison. So far, no experiments have been found to compare with the results. As will be shown, the calculations can be extended to waves of finite height (Stokes2-Struik3 waves) in an approximate fashion. This can be done by calculating the force produced by each Fourier component of the wave, separately, and omitting the coupling between the various harmonics produced by Bernoulli's theorem. The problem and its boundary conditions will be briefly stated. We seek a function, +, the velocity potential, which is harmonic, ?2?=0...........(1) and which satisfies the boundary conditions ??/?n =0 .......(2) (the normal derivative of + is zero) on the ocean floor and the sides of the barge, and s??/?y = ?..........(3) on the ocean surface, where s = g/w2........(4) The physical reasons for these choices and an interpretation of ? are given by Lamb.' As previously stated, we assume also that the problem is two-dimensional. We set up our coordinates such that x = 0 is the center of the barge and y = 0 is the ocean floor. The coordinates are shown in Fig. 1, together with the location of the barge on the bottom. Our solution may be decomposed into a function which is symmetric about x = 0,?e, and one which is antisymmetric, +,, ? = ? + ?o...........(5) Thus directly above the barge we have as boundary conditions that for x = 0, ?o = 0, ...........(6) and ??e/?x = 0........(7) Now, far from the barge, we have that (for x positive and assuming the waves are incident from the left) ?e ? Ae cosh ky cos k (x + a) , . . . (8) and ?e ? Ao cosh ky cos k (x + ß) . . . . (9) where + means ". .. approaches ... for x large." Let us put Ae, Ao, and k equal to one, and remember that, in accordance with the derivation of Eq. 3, a sinusoidal time factor is to be supplied. Then we may rewrite Eq. 8 for ?e, and we find that

Jan 1, 1958

By Paul Torrey

IN his recent article, Stanley C. Herold described some of the principles involved in oil-field rejuvenation. The purpose of this paper is to present certain facts, based upon observations of systematic water flooding of oil sands in the Bradford and Allegany fields of northwestern Pennsylvania and southwestern New York, which, it is believed, will partially substantiate Mr. Herold's opinions. The writer gratefully acknowledges his obligation to the Forest Oil Corpn., the Kendall Refining Co., the Petroleum Reclamation Co., W. J. Healey, of Bradford, Pa., and the Producers Oil Corpn., of Olean, N. Y., for information included in this article; and he is especially indebted to Jerry B. Newby, of the Petroleum Reclamation Co., for helpful suggestions and criticism in the preparation of the paper. It is obvious that, in the calculation of mathematical formulas for the prediction of oil recovery, uniform conditions must be assumed; otherwise, the applicability of the results of such work will be, by necessity, restricted to the area or individual property for which they were designed. Geologic and physical conditions are so variable throughout the fields where water flooding is practiced that it is difficult to devise methods that can be universally applicable. However, it is believed that there are certain fundamental principles which, when applied with specific modifications designed to meet the conditions existing in local areas or individual properties, may yield considerably greater recoveries of oil.

Jan 1, 1927

By Forbes Wilson

IN February 1952 Freeport Sulphur Company started exploration work on a group of lateritic deposits at Moa Bay, Cuba. As a result of successful exploration work and a vast amount of metallurgical research over the past five years, these deposits will soon become a new Free World source of nickel and cobalt. Moa Bay lies on the north coast of Oriente Province, the easternmost part of the island, about 600 miles east of Havana and about 40 miles east of the U. S. Government nickel plant at Nicaro.

Jan 5, 1958

By D. R. Walker, M. C. Shaw

THE laws of comminution of Kick and Rittinger have been debated for many years. Certain data obtained from ball mill and drop tests are found to be in approximate agreement with Rittinger's law while other data would seem to support Kick's law. In all these tests the energy required to produce a wide variety of particle sizes has been studied. Surface area has also been measured with considerable difficulty, at first because it was thought that the energy associated with crushing was that required to create new surface, later because of precedent and because a more fundamental variable was unknown. Tests made with the machine shop type of grinding process show that normally brittle materials that are usually crushed can behave like the more ductile metals. Brittleness is then a relative property largely dependent on specimen size and stress state. The machine grinding operation offers a convenient means for studying the comminution of materials in which the important size variable retains its identity. The energy required to grind a certain volume of material is shown to be strongly de- pendent on size. Kick's law is found to hold very well for particles below 1 micron in size, while Rittinger's law holds approximately in the comminution of larger particles. While a physical origin of Kick's law is established in terms of the theoretical strength of materials having a perfect lattice structure, there is found to be no physical basis for Rittinger's law.

Jan 3, 1954

By Alan T. Gorton, T. L. Joseph, Gust Bitsianes

High-temperature X-ray diffraction techniques were used to determine thermal expansion coefficients of iron and its oxides. Lattice parameters of a and iron, wiistite, magnetite, hematite, and goethite were determined and plotted as a function of temperature. From these results, the true and mean linear thermal expansion coefficients were calculated. In the case of noncubic crystals, the expansion coefficients were determined along each of the crystallographic axes. The effect of the magnetic transformation on lattice parameter was measured for a iron and magnetite at their respective curie temperatures. COEFFICIENTS of expansion for iron and its oxides were determined from the temperature dependence of their lattice parameters. From these data, the true linear coefficients were derived by means of the formula: at =[(l/ao )(dao/dt)] [1] where at is the true linear coefficient of expansion, a, is the lattice parameter in angstrom units, and all variables are referred to the temperature, t, in OC. Thus the true expansion coefficient represents the instantaneous change in lattice parameter on a unit basis and at a particular temperature. A second expansion coefficient is also often used. It is termed the mean linear coefficient and is defined in the following way: am = [ao(t) - ao(O)]/ao(0) l [21 This coefficient represents the average change in lattice parameter on a unit basis but at a specified parameter length, ao at O°C, and over a specified temperature range,1 to 0°C. Generally the true co-

Jan 1, 1965

By Lyall, Zickrick

As a result of the studies on recrystallization and crystal growth made in this laboratory, certain theories have been developed. These are expressed briefly in a paper by Dean and Hudson.' One of the principal points brought out in that paper is that in the deformation of a crystal, the energy supplied is distributed to the atoms of the lattice, probably by the forced formation of molecules. It is found that a Maxwellian distribution of the energy among these atoms will account for the grain growth at various temperatures. According to such a distribution the number of atoms with energy above a certain critical value, E, necessary for recrystallization at the absolute temperature T is given by n = Ne-E/kT where N is the total number of atoms. It is apparent that if this line of reasoning is correct, a metal which has been cold-worked and reheated to a temperature below that of complete annealing will have the atoms with the higher energy recrystallized, that is, reduced to normal energy and there will remain only atoms below a certain energy. If this metal is again cold-worked the peak in the number-energy distribution curve will, as compaied with its position after the first cold-working, be displaced toward the regions of lower energies, that is, the temperature of recrystallization will be higher. By a repetition of this process the position of this maximum and hence the recrystallization temperature of the metal could be raised considerably. In order to check this theory, experiments have been made on copper wire. The wire was drawn from 1/4-in. rod to 22 B & S gage and then sample lots were annealed at 400 and 220° C., respectively. The wire annealed at 400° C. gave an elongation of 34 per cent., whereas that annealed at 220° C. gave only 23 per cent. These wires were then drawn by identical practice to 34 B & S gage and the elongation determined after an anneal of 3 min. in an oil bath held at various temperatures. The figures obtained have been plotted in Fig. 1. It will be seen that the

Jan 1, 1927

By C. T. Cox

The title of this short paper necessarily implies that friction articles comprise a distinct and unique field and are different from the other metal-powder articles, such as bearings, electrical contacts, and magnets. However, this distinction is rather hard to define in that it is really one of degree and not Of kind. It would appear that the main distinction is that friction are are articles of rather large pressing area. In other words, they are articles in which the area Of the mold in which the metal powder is pressed is relatively large. Other articles made from meta1 powders are generally of rather small area, usually a few square inches, while in friction articles the area ranges up to several hundred square inches. The satisfactory production of meta1-powder friction articles involves many production problems and a large number Of these are accentuated by the large area' Since it is impossible in the short space of this Paper to describe adequately all the problems involved, I have thought it best to merely mention some Of them and to place particular emphasis upon a problem that is common to all metal-powder articles, although it is of greater importance in the making of friction articles. This problem has to do with the effect On the properties of a friction article of small variations in the composition. However, before discussing the problems, it is probably appropriate that some mention be made of the limitations on the use of friction articles. Most engineers are familiar with the general field that can be characterized as constituted by clutch facings and brake linings, and undoubtedly have heard many stories of how metal-powder friction articles have had a service life 10 times as long as nonmetallic friction materials, and of instances where metal-powder friction articles have operated satisfactorily where no other material could be used. These instances should not be regarded as criteria for the assumption that metal-powder friction articles are capable of universal use in the friction field and will always outperform other materials. On the contrary, metal-powder friction articles are unsuitable for numerous applications, either on a performance or on a cost basis. Metal-powder friction articles will not replace wooden block brakes for wagon wheels nor cast-iron brake shoes for railway car wheels, to mention just two obvious examples. Metallic friction articles cannot be used where they must act as heat insulatorsl for they have a relatively high thermal conductivity as compared with asbestos. This is a detriment in some uses, as in certain airplane brakes having hydraulic actuators provided with rubber seals. The metallic friction material readily transfers the heat developed at the braking surface back through the material to the rubber seal and destroys it. Within its limited field, metal-powder friction material has proved satisfactory, but many problems are involved in the Selection of the proper material to use in an application and in the commercial pro-

Jan 1, 1945

By Albert D. Pernichele, Wayne C. Smith

Both water pollution and proposed solid waste disposal regulations have a definite effect on the copper leaching industry and some of the major factors affecting the industry are discussed in this paper. New developments of the NPDES are discussed with emphasis on the ‘toxic’ or priority pollutants, and EPA’s philosophy on the control of these pollutants. The protection of groundwater is the prime aim of RCRA through solid/hazardous waste management. Some of the major elements of the RCRA regulations that will effect the copper leaching industry are discussed.

Jan 1, 1980

By W. R. Seyfried

THE -problem of extracting alumina from clay and low-grade bauxites has been the subject of considerable interest for some time. The basic reason, of course, lies in the fact that known reserves of high-grade bauxite are not inexhaustible and that the present commercial process cannot successfully cope with low-grade bauxites or clay. Ultimately it may be necessary to use these poorer raw materials for all commercial operations, An unprecedented demand for aluminum during the war emergency and the constantly threatened shortage of imported bauxite caused the United States Government to take an active role in this problem. Through the National Academy of Sciences, the War Production Board and the Defense Plant Corporation, it investigated processes and finally selected four to be used in the construction and operation of four experimental plants. Each plant was to be designed in such a way as to facilitate its incorporation into a larger commercial plant should the need arise. The Chemical Construction Corporation process, or "Chemico" ammonium sulphate process as it is better known, was one of the four selected. The extensive literature and patents on record before the war generally follow one of two process-types depending upon the extracting reagent used. One group uses an acid reagent, the other an alkali. The Chemico process uses an acid reagent. For those interested in other processes described in literature, there is a short bibliography at the end of this paper, The basic steps of all acid extraction processes are: (I) to make the aluminum silicates acid soluble, (2) to separate the released alumina from impurities and insoluble gangue, and (3) to recover the reaent for re-use. THE PROCESS AS PLANNED In April 1941, a group of chemists and engineers of the Chemical Construction Corp, became interested in the problem of extracting alumina from clays and low-grade bauxites and, under the leadership of Mr. Blakeslee Barnes, Vice President and General Manager of the Company, first drafted a process in July of that year-five months prior to Pearl Harbor. The work continued in our research laboratories and with a small pilot plant, By June 1943, the work had progressed to a point where it was possible to apply for a patent on the process which was U.S. patent 2,405,426, granted August 6, 1946. Immediately prior to the development of the Salem plant, the process was envisaged to be as follows: I. The first step was to make the aluminum silicates acid soluble. It was planned: (a) Clay or low-grade bauxite would be roasted at 700 to 800°C (1292° to 1492°F). (b) The roasted ore would then be leached .with hot aqueous ammonium bisulphate to form a slurry. In this way the

Jan 1, 1948

By C. H. Loux

THIS paper deals primarily, with the advantages realized from the adoption of methods more suitable than those previously used. The improvements noted include: (1) modification of practice in shrinkage stoping, (2) use of sublevel caving over grizzlies, (3) improved haulage and loading, (4) use of contract wages wherever possible. The Washington mine is on Jonestown Hill, one mile south of Oxford, in northwestern New Jersey. It is producing 16,000 tons of concentrates a month, which are being shipped to the Alan Wood Steel Company's furnaces at Swedeland, Pennsylvania.

Jan 1, 1933