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By M. J. Buerger

POSSIBLY the most puzzling features observed during a single-crystal deformation test are the appearance of slip striae on the surface of the crystal and the strengthening of the specimen.1 While the first phenomenon is mainly of theoretical interest, the latter is fundamental to all strain-hardening and cold-working processes in which the deformation occurs by translation. The plastic deformation of crystals has received considerable discussion2 and need not be reviewed here in, any great detail. It has been observed, essentially, that after a certain amount of initial stress is applied, the surface of the crystal becomes covered with sets of parallel striae or rings which appear to divide it into thin slabs or slip blocks.3 The striae are the traces of rational crystallographic planes along which shearing movements are localized, these movements providing the strain which accompanies stress applied beyond pure elasticity. As deformation under the applied stress proceeds the slip blocks shear past one another, although the essentially single-crystal character of the specimen is unimpaired. All of the shearing apparently takes place in the immediate vicinity of the original slip striae without the appearance of new planes of movement.4 Since each increment of strain is attended by an increased stress requirement to continue the deformation, the crystal strengthens during the process.

Jan 1, 1928

By Pierre Hines

THESE notes are based on observations made while on a recent trip through the West, for the purpose of studying the practical operation of the ball-mill. The writer takes this opportunity to express his thanks for courtesies extended at the many plants visited as well as for the valuable data received. While there are several types of ball-mill on the market, particular attention will here be given to the diaphragm type, as the open-trunnion type, especially the conical mill, has been thoroughly discussed in the Transactions. There is a prevailing impression that the ball-mill is a recent development; however, ball-mills were used extensively in Montana and other western states for crushing ores for concentration as far back as 1898. Its present prominence is due in part to its recent successful application by one of the large copper companies. Without any reference to dry grinding, the first successful ball-mill for wet crushing, which is still in operation, was built 10 years ago.1 This mill, designed by Erminio Ferraris for crushing Sardinian ores for concentration, is of more than passing interest. It embodies the peripheral discharge with grates, large forged-steel balls, and the principal features of the modern ball-mill. The results approach present-clay practice, the chief differences being that the mechanical construction has been improved in the modern types.

Jan 2, 1918

Increased world consumption of crude and products coupled with the trend toward supplying this demand from the nearest and most economical source of supply had the economic effect of broadening the demand for Venezuelan crude. As a result of this, Venezucla produced more in 1934 than in 1929, the previous peak year. During 1934 Venezuelan output is estimated at a total of 139,382,000 bbl., a daily average of 381,868 bbl., against 120,442,000 bbl. in 1933, a daily average of 329,978 bbl. This is an increase of 51,890 bbl. per day. It is interesting to note from the comparison of production for the past 10 years (Table 1) that in spite of the fact that Venezuela produced more in 1934 than in 1929 its share of world production is slightly less than in 1929 and 1930. During the latter part of 1934 Vcnezuela produced its first billionth barrel of crude. Only three other crude-producing countries of the world have attained this distinction; namely, United States, Russia and Mexico. Venezuela still ranks third in the producing countries of the world, being surpassed by the United States and Russia. Exports of crude and products from Venezuela for 1934 are estimated at 133,400,000 bbl. This is an increase of 16,107,000 bbl., or 13.73 per cent as compared with 1933.

Jan 1, 1935

By D. Walton, W. C. Winegard, W. A. Tiller, J. W. Rutter

It is shown that the cellular substructure observed in binary alloy crystals grown from a melt of known concentration can be eliminated by the proper choice of growth conditions. For a given solute concentration, there exists a critical ratio of temperature gradient G in the melt to the rate of solidification R of the crystal, i.e., of G/R, which must be exceeded before the cellular structure can be eliminated. A secondary substructure is observed which is related to the cellular substructure. IN crystals grown from the melt, a prismatic substructure has been observed by Buerger,1 Pond and Kessler,2 and Rutter and Chalmers." This structure is columnar in the direction of growth and appears as a network of hexagonal cells in the plane of the solid-liquid interface. Rutter and Chalmers3 have shown that this substructure occurs as a result of the presence of a layer of high impurity concentration in the melt adjacent to the solid-liquid interface. The formation of the substructure is accompanied by a redistribution of this impurity in the neighborhood of the interface. The structure can be controlled by proper adjustment of the variables in the solidification process such as a rate of solidification and the temperature gradient in the liquid. The redistribution of solute during the solidification of metal crystals has been treated theoretically

Jan 1, 1956

By Robert L. Fleischer

A well known but unexplained experimental fact is the observation1 that aluminum shows a pure <111> wire texture, in contrast with other fcc metals, which have a mixed <100> <111> texture at moderate reductions. A possibly related single crystal observation on aluminum is the following:2 under tensile deformation <111> single crystals are stable (maintain their original axial orientation), while <100> crystals are unstable at room temperature and become stable at lower temperatures. This suggests that at room temperature, as proposed by Yen and Hibbard,3 the single <111> texture obtains be- cause <100> orientations are unstable in the poly-crystal. It also implies that for wire drawing at lower temperature a <100> component of the texture might be expected since that orientation is then stable. This possibility has been examined by wire drawing at temperatures near 77°K. The apparatus was designed to be used with an existing draw-bench, a steel trough acting as die holder and containing sufficient liquid nitrogen to immerse the wire entering the die. The trough is insulated by a styrofoam container to prevent excessive boiling of the bath. The wire emerging from the die enters a polyethylene tube, into the far end of which the grips are inserted. Liquid nitrogen is funneled into the tube to maintain the low tem-

Jan 1, 1962

By M. J. Salkind

In discussing the possible contribution of plastic deformation to neck growth during sintering, Wilson and Shewmon State that Lenel, Ansell, Salkind, and Early34, 35 concluded that dislocation flow is the rate-controlling process in sintering under zero external load. The experiments cited34, 35 were done with applied external loads, and the conclusions were that the same kinetics could be controlling sintering due to the force of gravity with no additional applied load. The effect of gravity on sintering behavior was previously cited.34, 31 In addition, Wilson and Shewmon argue that the conclusions of Refs. 34 and 35 are doubtful because the strain rate is proportional to stress for plastic flow. This assumption is true only for certain kinds of plastic flow such as Nabarro-Herring Microcree38 As Early, Lenel, and Ansell point out3&apos; plastic flow, based upon dislocation movement, can exhibit strain rates which exhibit a power law relationship to the applied stress.39, 40 Wilson and Shewmon also doubt the results of Refs. 34 and 35 because the stresses in the necks are too small for x/a > 0.1. This is true, and the experiments described in Refs. 34 and 35 were done for small values of %/a. The conclusion was that plastic flow by dislocation movement was important during the early stages of sintering when x/a is small.

Jan 1, 1968

By G. L. F. Powell

TURNBULL and Cech1 reported undercooling small droplets (approximately 50 mp in diam) of a large number of metals by approximately 0.18 TE (TEoK = the equilibrium freezing point). This was considered to be the undercooling for homogeneous nucleation in

Jan 1, 1968

The following list contains the names of members of whose deaths notices have been printed in MINING AND METALLURGY during the year ending April 1, 1940. Biographical sketches published in MINING AND METALLURGY are indicated in the last two columns. [ ]

Jan 1, 1940

Volume LIV has been shipped to all members whose clues were paid on or before Feb. 10, 1917. The next shipment will be made the latter part of April to all those whose dues were paid on April 1, 1917.

Jan 4, 1917

The following list contains the names of members of whose deaths notices have been printed in MINING AND METALLURGY during the year ending April 1, 1939. Biographical sketches published in MINING AND METALLURGY are indicated in the last two columns.

Jan 1, 1941

The following list contains the names of members of whose deaths notices have been printed in MINING AND METALLURGY during the year ending April 1, 1939. Biographical sketches published in MINING AND METALLURGY are indicated in the last two columns.

Jan 1, 1942

The following list contains the names of members of whose deaths notices have been printed in MINING AND METALLURGY during the year ending April 1, 1939. Biographical sketches published in MINING AND METALLURGY are indicated in the last two columns.

Jan 1, 1944

The following list contains the names of members of whose deaths notices have been printed in MINING AND METALLURGY during the year ending April 1, 1939. Biographical sketches published in MINING AND METALLURGY are indicated in the last two columns.

Jan 1, 1943

By Y. C. Liu, G. A. Alers

The effect of rolling reduction on the textures of Cu-A1 alloys has been investigated both by pole figure and by modulus methods. In alloys which exhibit complete copper or brass types of rolling texture, the rolling reduction has little effect on the texture except to increase the degree of preferred orientation. In alloys which exhibit a transition texture, however, increased rolling reduction increases the amount of brass-type texture at the expense of the copper-type texture. The present experimental results show that there is no one-to-one correspondence between the SFE and the rolling texture of fcc metals. Additional data taken from the literature for fcc metals also support this conclusion. On the other hand, the present and previous experimental results are shown to be in good agreement with the suggestion that the texture transition occurs at a critical value for the separation distance between two partial dislocations—a consequence of the "dislocation interaction" hypothesis for texture. formation. This critical separation occurs when the parameter .r/ub is 3.75 x 10&apos;3. From this, a value for the SFE of 39 ergs per sq cm may be deduced for a Cu-2.85 at. pct A1 alloy. ThE correlation between the rolling texture of fcc metals and the stacking fault energy, SFE, was one of the first attempts to relate atomistic properties with the type of rolling texture.&apos; This correlation gives a qualitative explanation for the experimental observation that the addition of alloying elements, which generally lower the SFE, changes the copper-type texture to a brass-type texture. The simplicity of this correlation had led to its general acceptance and even its quantitative use.&apos; However, it is only a correlation and is largely based on descriptive features of pole figures, and on the poorly known SFE values in dilute alloys. Quantitative verification of this phenomenologi-cal correlation is, in fact, completely lacking. One purpose of the present study is to test this correlation. Another atomistic description for the formation of rolling texture is the "dislocation interaction" hypothesis of texture formation.3 In this hypothesis, the factor controlling the type of rolling texture depends on whether or not the separation distance between two partial dislocations exceeds a critical value. Materials having a separation of less than the critical value are supposed to exhibit a copper-type texture while those with a separation above the critical value are supposed to have a brass-type texture. At the critical value, it is expected that the material should show equal amounts of copper- arid brass-type orientations in their textures, i.e., a 50 pct transition texture. The SFE appears in this hypothesis as only one of several factors which determine the separation distance between partial dislocations. It is possible to test the validity of these two concepts by studying the rolling texture as a function of rolling reduction. Since the SFE per se is an intrinsic property of the metal, it should not, by definition, be influenced by local irregularities, such as variable stress conditions. Thus, no change in texture-type is expected to occur with changes in rolling reduction. On the other hand, according to the "dislocation interaction" hypothesis, any factor that effectively influences the separation distance of partial dislocations would be expected to change the rolling texture. Since the separation distance between partial dislocations is known to depend upon local stresses,4-6 it is anticipated that there would be an effect of the degree of reduction on the texture-type. Also, since applied stresses are more likely to increase, rather than to decrease, the separation between partials,4&apos;5 the overall effect would be to increase the amount of material in the brass-type orientations as rolling reduction is increased. Furthermore, this reduction dependence would be most prominent in alloys exhibiting the transition texture since the distance between partials in those alloys is thought to be close to the critical value. Experimental data in the literature is insufficient to distinguish between these two alternatives. Haessner studied the effect of rolling reduction on textures in a series of Ni-Co alloys by means of the X-ray intensity-ratio technique,&apos; and found that while one texture parameter indicated no reduction dependence the other indicated a slight dependence of the rolling texture on reduction in the range of 96 to 99 pct. As has been noticed previously, the intensity-ratio technique is a convenient but controversial method7 because there is no a priori reason to suggest which intensity-ratio would describe the texture most meaningfully. A more quantitative method of describing textures is found in terms of the orientation dependence of Young&apos;s modulus. Here, the type of modulus aniso-tropy associated with the copper-type texture is sufficiently different from that observed for the brass-type texture to allow the two types to be easily distinguishable and a quantitative measure of the amount of each can be deduced from the numerical results. This ability to provide quantitative data is particularly valuable when the two textures occur simultaneously in one alloy as is the case for the transition textures. In this paper the modulus method, supplemented by pole figure data, is used to look for an effect of roll: ing reduction the texture. Also by combining the texture measurements with recent determinations of the SFE in Cu-A1 alloys&apos;0&apos;" it should be possible to test for a relationship between the SFE and textures.

Jan 1, 1970

By W. H. Patnode

The effect of suspended solids on the resistivity of slurries is discussed and the relationship between drilling mud resistivity and mud filtrate investigated. It is concluded that it is erroneous to substitute mud resistivity for mud filtrate resistivity in electric log calculations. A recommendation is made that both the bud resistivity and the mud filtrate resistivity be determined when electric logs are run. INTRODUCTION The electric log is influenced not only by the resistvity of the drilling mud in the borehole at the time of logging but also by the resistivity of the drilling mud filtrate. Sherborne and Newtoni investigated the relationship of mud resistivity to mud filtrate resistivity and concluded that, "The resistivity of the mud in most cases closely approximates that of its filtrate," and "In fact, with the exception of Aquagel and its filtrate, the figures for any particular mud and filtrate are almost identical." Present practice is to determine only the drilling mud resistivity and apply this same value to calculations involving the mud filtrate. The purpose of this study is to reexamine the factors governing the relationship between mud resistivity and mud filtrate resistivity. EFFECT OF BOREHO1.E FLUID ON THE ELECTRIC LOG Resistivity Log The resistivity log may be modified by the resistivity of the borehole fluid in two different ways: (1) The apparent resistivity of a for-formation may be different from the true resistivity of the formation because of the flow of some current through the drilling mud in the borehole. Therefore the resistivity of the mud is an important factor. (2) The apparent resistivity may differ from the true resistivity, if a formation is invaded by mud filtrate, because of displacement by the mud filtrate of some of the interstitial fluid in the formation. In this case the resistivity of the mud filtrate rather than the resistivity of the mud is the important factor. Self Potential Log The self potential arises, in part, from electrochemical effects resulting from the interaction of connate waters in porous formations and the fluid in the borehole. Expressed in simple form, E = Klog-p where E is the electrochemical self potential, K is a derived constant, pl is the resistivity of the borehole fluid, and p2 the resistivity of the water in the formation. A theory of the electrochemical component of the self potential in boreholes has been recently set forth by Wyllie.3 In the above equation resistivities have been substituted for activities of the ions in the fluids.&apos; It is therefore apparent that the resistivity of the mud filtrate is more nearly representative of the activities of the ions than is the resistivity of the mud. However, it is possible that in some instances the ionic activities of cations from certain clays may contribute to the total cationic activity of the drilling fluid to such an extent that the mud resistivity is more nearly representative of the activities than the filtrate resistivity. This is particularly the case when the resistivity of the mud is less than the resistivity of the mud filtrate. In addition the apparent self potential may be influenced by the resistivity of the drilling mud because of current flow through the borehole. RESISTIVITY OF SLURRIES Aqueous drilling muds are slurries containing fine-grained solid particles. The solid constituents consist mainly of added clays and weighting materials in addition to solids contributed by the drilled formations. The filtrate is primarily water in which quantities of salts or other chemicals are dissolved. The resistivity of the fiiltrate is a function of the type and quantity of dissolved material whereas the resistivity of the mud is a function of the combined resistivities of the filtrate and the resistivities of the suspended solids. Experiments have been carried out to determine the relationship between the resistivity of solutions and the quantity and type of solid matter insus-pension. Solid materials of high resistivity, as well as solid materials of relatively low resistivity, have been used. The data obtained make possible the evaluation of the probable effect of suspended solids on the resistivity of drilling mud. Procedure Resistivities were determined by means of a conventional conductivity cell with platinized-platinum electrodes. Total resistance between the electrodes was measured by Kohlrausch&apos;s alternating current bridge method using a General Radio Company Type 650-A impedance bridge with telephone. The cell was standardized with potassium chloride solutions of known normalities in order to calibrate the cell so that measured resistances of slurries could be converted to resistivities. Resistivities were determined for mixtures of potassium chloride solution and solid materials by placing a measured quantity of solution in the cell and adding weighed quantities of solid materials in small increments to the solution. The net change in resistance on addition of solid materials was measured. Even distribution of the solid particles was maintained within the cell by a motor-driven glass propeller before measurements were made. Slurries Containing High-Resistivity Solids Powdered silica sand having a maximum diameter of about 60 microns and precipitated chalk of commercial grade were used to make the slurries whose resistivities were measured. Both of these substances have high resistivities, are virtually insoluble, and effectively do not carry current in a slurry. The resistivities of slurries composed of potassium chloride solution and these two solid materials are given in Table 1. The ratio of the resistivity of the solution to the resistivity of the slurries was computed and was found to follow the relationship established by Archie

Jan 1, 1949

By W. H. Patnode

The effect of suspended solids on the resistivity of slurries is discussed and the relationship between drilling mud resistivity and mud filtrate investigated. It is concluded that it is erroneous to substitute mud resistivity for mud filtrate resistivity in electric log calculations. A recommendation is made that both the bud resistivity and the mud filtrate resistivity be determined when electric logs are run. INTRODUCTION The electric log is influenced not only by the resistvity of the drilling mud in the borehole at the time of logging but also by the resistivity of the drilling mud filtrate. Sherborne and Newtoni investigated the relationship of mud resistivity to mud filtrate resistivity and concluded that, "The resistivity of the mud in most cases closely approximates that of its filtrate," and "In fact, with the exception of Aquagel and its filtrate, the figures for any particular mud and filtrate are almost identical." Present practice is to determine only the drilling mud resistivity and apply this same value to calculations involving the mud filtrate. The purpose of this study is to reexamine the factors governing the relationship between mud resistivity and mud filtrate resistivity. EFFECT OF BOREHO1.E FLUID ON THE ELECTRIC LOG Resistivity Log The resistivity log may be modified by the resistivity of the borehole fluid in two different ways: (1) The apparent resistivity of a for-formation may be different from the true resistivity of the formation because of the flow of some current through the drilling mud in the borehole. Therefore the resistivity of the mud is an important factor. (2) The apparent resistivity may differ from the true resistivity, if a formation is invaded by mud filtrate, because of displacement by the mud filtrate of some of the interstitial fluid in the formation. In this case the resistivity of the mud filtrate rather than the resistivity of the mud is the important factor. Self Potential Log The self potential arises, in part, from electrochemical effects resulting from the interaction of connate waters in porous formations and the fluid in the borehole. Expressed in simple form, E = Klog-p where E is the electrochemical self potential, K is a derived constant, pl is the resistivity of the borehole fluid, and p2 the resistivity of the water in the formation. A theory of the electrochemical component of the self potential in boreholes has been recently set forth by Wyllie.3 In the above equation resistivities have been substituted for activities of the ions in the fluids.&apos; It is therefore apparent that the resistivity of the mud filtrate is more nearly representative of the activities of the ions than is the resistivity of the mud. However, it is possible that in some instances the ionic activities of cations from certain clays may contribute to the total cationic activity of the drilling fluid to such an extent that the mud resistivity is more nearly representative of the activities than the filtrate resistivity. This is particularly the case when the resistivity of the mud is less than the resistivity of the mud filtrate. In addition the apparent self potential may be influenced by the resistivity of the drilling mud because of current flow through the borehole. RESISTIVITY OF SLURRIES Aqueous drilling muds are slurries containing fine-grained solid particles. The solid constituents consist mainly of added clays and weighting materials in addition to solids contributed by the drilled formations. The filtrate is primarily water in which quantities of salts or other chemicals are dissolved. The resistivity of the fiiltrate is a function of the type and quantity of dissolved material whereas the resistivity of the mud is a function of the combined resistivities of the filtrate and the resistivities of the suspended solids. Experiments have been carried out to determine the relationship between the resistivity of solutions and the quantity and type of solid matter insus-pension. Solid materials of high resistivity, as well as solid materials of relatively low resistivity, have been used. The data obtained make possible the evaluation of the probable effect of suspended solids on the resistivity of drilling mud. Procedure Resistivities were determined by means of a conventional conductivity cell with platinized-platinum electrodes. Total resistance between the electrodes was measured by Kohlrausch&apos;s alternating current bridge method using a General Radio Company Type 650-A impedance bridge with telephone. The cell was standardized with potassium chloride solutions of known normalities in order to calibrate the cell so that measured resistances of slurries could be converted to resistivities. Resistivities were determined for mixtures of potassium chloride solution and solid materials by placing a measured quantity of solution in the cell and adding weighed quantities of solid materials in small increments to the solution. The net change in resistance on addition of solid materials was measured. Even distribution of the solid particles was maintained within the cell by a motor-driven glass propeller before measurements were made. Slurries Containing High-Resistivity Solids Powdered silica sand having a maximum diameter of about 60 microns and precipitated chalk of commercial grade were used to make the slurries whose resistivities were measured. Both of these substances have high resistivities, are virtually insoluble, and effectively do not carry current in a slurry. The resistivities of slurries composed of potassium chloride solution and these two solid materials are given in Table 1. The ratio of the resistivity of the solution to the resistivity of the slurries was computed and was found to follow the relationship established by Archie

Jan 1, 1949

By E. F. Bradley, R. I. Jaffee, H. R. Ogden, E. S. Bartlett, D. N. Williams

The mechanical properties of solid-solution-strengthened columbium alloys have been assessed as a function of alloying additions. Studies included the effects of tungsten, tantalum, molybdenum, and vanadium. Elevated temperature fabrication was required at alloying levels above about 15 pct W or 10 pct Mo. Tungsten, molybdenum, and vanadium additions increase tensile strength at room temperature and 2200°F, but tantalum additions exert little strengthening. Similarly, tungsten, molybdenum, and probably vanadium additions increase the ductile-to-brittle transition temperature, and tantalum additions decrease this parameter. The 2200°F stress-rupture strength is increased by tungsten and molybdenum additions; with 20 to 25 at. pct additions, 100-hr rupture strengths of 30,000 psi are obtainable. Small vanadium additions exhibit mild stress-rupture strengthening, and tantalum additions are innocuous. At 2500°F, tungsten additions retain stress-rutpure strengthening capability, but molybdenum additions are much less effective. Tantalum additions augment the stress-rupture strengthening of tungsten plus molybdenum additions at 2500°F. Of the refractory metals, columbium possesses specific potential for structural use in the temperature range from 2000" to about 2500°F. Desirable features of columbium are its good low-temperature ductility, ease of fabrication, oxidation mechanics (lack of a volatile oxide at moderate temperatures), good availability and reserves, and relatively low density. However, alloying is required to provide attractive strength at elevated temperatures. Published information concerning alloying be- havior of columbium relative to mechanical properties is sketchy, particularly in consideration for long-time applications at temperatures in excess of 2000°F. Only a few stress-rupture data at temperatures from 2000" to 2500°F have been reported;&apos;-&apos; these are too meager to allow rationalization of the effects of various alloying additions on creep or stress-rupture properties. Additional published data do, however, give some insight toward understanding of systematic alloying behavior for columbium relative to low-temperature strength4-&apos; and ductility,&apos; and elevated temperature tensile behavior.4,6 This paper is intended to augment previous knowledge, and to promote understanding of the alloying behavior of columbium for long-time structural service at elevated temperature. BASIC CONSIDERATIONS Solid-solution strengthening is recognized to be of prime importance in improving strength in columbium-base alloys. Other strengthening mechanisms may be (and are, in current alloys) used to augment solid-solution strengthening. As strengthening results primarily from lattice distortion, the strengthening effectiveness per atom depends upon atomic size mismatch between solvent and solute. Another factor in this regard is conformance to ideal solution behavior in the solid solution. Thus, for example, despite appreciable differences in the degree of mismatch between tungsten (5 pct), molybdenum (5 1/2 pct), and vanadium (7 1/2 pct) in solution in columbium, all are about equally effective in straining the columbium lattice at room temperature.&apos;-&apos; Similarly, tantalum additions do not strain the columbium lattice, and little strengthening is expected. Size effects being equal, maximum solution strengthening at high temperatures is anticipated to result from the addition of elements that increase the melting temperature of columbium. This expectation is based on an increase in the electronic bonding forces exhibited in the transition metal series as electronic structures approach those of the Group Vl metals. Of the metals that exhibit ex-

Jan 1, 1963

By G. Rowan, M. W. Clegg

The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including: gravity drainage of depletion-type reservoirs; multiple well systems; well interference. INTRODUCTION A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages — the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov,1 who (a) postulated a disturbed zone in the reservoir, the radius of which increases with time, and (b) replaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following: 1. That the flow is irrotational. 2. That the formation is of constant thickness. 3. Darcy&apos;s Law is valid. 4. The formation is saturated with a single homogeneous fluid.

By E. H. Citron

CLEANING fine coal in jigs is not new in Europe, where the feldspar jig is being used almost exclusively for this purpose. A feldspar jig operates with an artificial bed made up generally of feldspar or other hard rock material. Dimensions and specific gravity of this material must be of suitable values for good bedding qualities. For good efficiency, the size should range between 1x2 in. and 2x2x½ in. thick. The disadvantage of an artificial bed is that it is not mobile and must be replaced every so often with new material to obtain good cleavage characteristics. A semi-mobile bed has been developed to retain only a part of the feldspar on the sieve screen— the other part is drawn off with the refuse material, from which it is reclaimed and returned to the jig feed. Recirculating this feldspar rock offers definite advantages. However, in time it will lose its original shape because of wear, and new bed material must be added to the jig feed. The latest feldspar jigs arc generally air-pulsated, Baum-type jigs, although more than 70 pct of the feldspar jigs operating in Continental Europe are still of the piston type. These jigs are very popular in Europe, but they do require a great deal of time and attention. New Theory to Eliminate Artificial Bedding: At the preparation plants of Pittsburg & Midway Coal Mining Co. it has always been the contention that a small piston-type jig could be developed to clean fine 1/4x0-in. coal down to 28 to 60 mesh efficiently by obtaining and admitting bedding material from the present plant refuse circuit to the jig feed. This eliminates use of artificial bedding materials. The jig should incorporate these essential adjustable features as follows: Adjustable Sieve Screen A screen that can be raised and lowered to increase or decrease washing compartment depth. The sieve screen also can be set on an incline level, or decline. Adjustable Plunger Eccentric Length of stroke can be adjusted to increase or decrease pulsion and suction. Variable Plunger Speed Variable speed reducer for decreasing and increasing the number of strokes per minute. Water Distribution Adjustable baffle plate separating the plunger and sieve compartment so the water can be distributed uniformly over the entire sieve screen area. Refuse Ejector Special unique rubber-type refuse ejector gate operated by air and electrically controlled (as a conventional jig). Automatic Control Conventional float that measures the specific gravity of the coal-water refuse medium in the jig is of the submerged type. The float is mounted on a vertical stem held in position by two parallel arms. A movable weight regulates the effective specific gravity of the float. The float stem can be raised and lowered, having a graduated scale to indicate the depth of bed for the setting of the float. Hutch Drawoff Hutch material is drawn from the cell compartment to the elevator compartment by gravity. The first one-cell experimental jig incorporating all these features was built in January 1955 by Ore

Jan 1, 1959

By Robert Mehl

PART I. ORIENTATION RELATIONSHIPS IN OXIDE LAYERS Oriented overgrowths and intergrowths among both metallic and nonmetallic substances have been recognized and studied for well over a century. The work of Widmanstätten in 1808 on the geometrical struc-ture in meteorites, a structure known by his name, demonstrated that oriented intergrowths can occur in purely metallic systems. This fact led to much of the early microscopic study of alloys, contributing greatly to the advance of physical metallurgy. The problem has been attacked again in recent years in a comprehensive fashion, with the object of dis-covering what atomic movements may occur during phase changes in alloy systems. Much of this work has appeared in the A.I.M.E. TRANS-ACTIONS in a series of papers published by Mehl and coworkers beginning in 19311. Although many aspects of this general problem remain unsolved, it may be said that the orientation of a new phase forming by precipitation from solid solution or by transformation invariably bears, a unique relationship to the orientation of the phase from which it formed, and that similarity in atomic patterns on atomic planes in the two phases play an important part in determining the orientation relationship. Analogous orientation relationships exist in oriented intergrowths in nonmetallic systems-mineral or inorganic. In 1827 Haidinger2 dis-covered natural intergrowths of hematite and magnetite, and demon-strated that the rough form of the magnetite octahedrons was delineated by small crystals of hematite, of which the basal (00.1) planes lay parallel to the octahedral cleavage planes of the magnetite. The description of this orientation relationship was later completed by von Rath3, who showed that the edge (00-1):(10-1) in hematite lies normal to the [111]

Jan 1, 1937