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By W. N. Hiatt

The mathematical theory of the flow of two-phase, incompressible fluid through porous media is clarified, and the development of a general fluid displacement equation for two-phase, incompressible vertical flow through porous media is outlined. The relationship between the three components of the equation — the "fluid drive effect", the "gravity effect", and the "capillary effect'' — is discussed, as well as implications of the analysis in connection with the study of certain types of petroleum reservoirs. INTRODUCTION The purpose of this paper is to clarify and summarize the mathematical basis of the theory of two-phase incompressible fluid flow through porous media, particularly as it pertains to vertical flow, and to present a qualitative* exposition of the controlling factors involved in circumstances where this type of flow may exist. Although the generally accepted theory of heterogeneous fluid flow through porous media was developed a number of years ago by Muskat,1 and Buckley and Leverett2, 3 using the basic premise of Darcy, (and since then expounded upon by many others) there is a need for an over-all summary and clarification of this theory, especially regarding certain types of applications in connection with so-called "gravity-drainage-type reservoirs". The source and derivation is outlined for what is referred to here as the "General Fluid Displacement Equation for Incompressible Vertical Two-Phase Flow through Porous Media''. This equation would apply under the condition where the pressure drop along the path of flow is negligible in comparison with the pressure level on the system, or where compressibility and solubility effects are negligible. These conditions exist ordinarily in gravity-drainage-type reservoirs. Specifically, it will be shown that this general equation may be developed directly from the basic equations, which, according to present theory, govern the general case of viscous heterogeneous flow through porous media. This general equation has appeared in the literature previously, but in most cases its development from basic theory is not indicated clearly, or the equation is presented in terms of groups of constants and variables involving reduced or dimensionless quantities. This presentation is expedient in cases of experimental or computer applications; but it may make it difficult for the practicing petroleum engineer to identify all the factors involved or to understand the relationships between them. Therefore, in the following development, only ordinary mathematical parlance will be used, and no terms involving groups of other equations or reduced or dimensionless quantities will be used. DERIVATION The following equations for two-phase oil and gas flow result from analogy with Muskat's general equations,** if solubility and compressibility effects are neglected, and if all volumes are considered in terms of reservoir conditions, and the water phase, if present, is considered to be immobile (or effectively a part of the porous medium.) In this case, the sum of the oil and gas saturations may be taken as unity, and the saturation of each phase is in terms of the total hydrocarbon saturation. Note that in Eqs. 1 and 2, and in the derivation following, z is taken as positive in the vertically downward direction,

Jan 1, 1969

By Robert R. Walden, LeMont West

K ENTUCKY'S first acid-grade fluorspar flotation Kmill, shown in Fig. 1, was placed in operation Aug. 1, 1952, by the Pennsylvania Salt Manufacturing Co. at Mexico, Ky. During 1951 a critical shortage of acid-grade fluorspar developed and it became necessary for the company to produce part of its fluorspar requirements. In 1951 the company purchased the Crider and Lennen metallurgical fluorspar mill and an adjacent stockpile of tailing at Mexico, Ky. The tailing, assaying about 26 pct calcium fluoride, originated from log washer and jig mill concentrators in the area. As the mill did not have a fluorspar dryer or convenient rail facilities, the company leased the Burleson concentrator at Marion, Ky., where these facilities were available. At Marion, Ky., on the Illinois Central Railroad, dry acid-grade fluorspar is transported direct to the company's Calvert City, Ky., hydrofluoric acid plant. The Mexico flotation plant was reconditioned and designed to produce acid-grade fluorspar from the jig tailing stockpile. The new plant flowsheet is shown in Fig. 2. The ore feed, old tailing, which contains 10 pct of waste rock and coarse gravel assaying approximately 8 pct CaF,, is bound together by sticky clay

Jan 1, 1955

By Leonard R. Weisberg

The general properties of diffusion in GaAs are reviewed. A total of .fourteen atoms have been studied to date, and activation energies for eleven reported are (in ev): Ga (5.6), As (lo), Zn (2.49), Cd (2.43), Sn (2.5). Mn (2.75). S (4.0). Se (4.2). Ag (0.33), Cu (0.52). and Li (1.0). The dijfusion of the first eight atoms, as measured by Goldstein using radiotracer techniques, established the principle of sub lattice diffusion for both host and impurity atoms, since atoms substituting for gallium have lower activation energies than those substituting for arsenic. The diffusion constant of interstitial copper has been determined for the first time by Hall and Racette using heavily doped p-type samples in which interstitial copper predominates. The anomalous behavior of zinc, which has an abrupt diffusion front and a strong dependence on zinc concentration, has recently been quantitatively explained in terms of an interstitial-substi-tutional equilibrium-diffusion mechanism. Lithium and silver diffuse mainly interstitially, while the diffusion of phosphorus is complicated by the continual formation ofGap. Junction-migration measurements indicate diiferent results than radiotracer techniques, and this is one problem that still remains, together with discrepancies in cadmium-diffusion results, and an unexplained dependence of impurity diffusion on arsenic pressure. BESIDES the usual insights into the behavior of atoms in solids, studies of diffusion in semiconductors have additional importance for device applications. In fact, the amount of diffusion studies performed on a semiconductor might serve as a simple barometer of its technological importance. Thus, the information accumulated for GaAs is not yet quite comparable to that for germanium or silicon, but considerable knowledge is available. The diffusion of at least fourteen atoms has been investigated for GaAs, and the diffusion constants have been determined for eleven of these. Interesting results were found for GaAs that elucidated problems not previously solved for germanium or silicon. For example, the interstitial-diffusion constant for the very fast diffusant, copper, was first measured in GaAs. Also, solutions for interstitial-substitu-tional equilibrium diffusion in extrinsic material were provided first for GaAs, although they are ap- plicable to germanium, silicon, and other semiconductors. Studies in GaAs firmly established the concept of sublattice diffusion, which should have application in many different compound systems. The purpose of this paper is to review briefly the general state of knowledge concerning diffusion in GaAs. First some general aspects of diffusion will be covered, and next attention will be given to the results mentioned above. Diffusion in GaAs has been measured both by radiotracer and junction-penetration techniques, and some discussion will be given of differences in the two sets of results. The comprehensive work of oldsteinl-' has served as the primary reference for the diffusion of well-behaved substitutional atoms in GaAs. Since a review has recently been presented of many of these reults, details of the diffusion data will not be repeated. Neither will any discussion be given of the experimental techniques of diffusion measurements, except to note here, in passing, the simplicity and effectiveness of the precision lapping device employed by Goldstein.' I) EXPERIMENTAL RESULTS AND DISCUSSION A) Summary of Experimental Results. Diffusion constants D = Do exp(E/kT) have been determined for eleven atoms in GaAs: a,' AS,' n,'" Cd,'" n,' n,8 s, e,' Ag,O CU," and i." These results are summarized in Table I. In addition, diffusion was investigated for phosphorus,4'12 germanium,I3 and ilicon,' but Do and E were not determined. Radiotracer techniques were used for most of the studies except for lithium, where a combination of chemical and electrical techniques was employed, and germanium and silicon, where junction-migration techniques were applied. The diffusion of zinc, manganese, sulfur, and tin was also measured using junction migration.13'14 Goldstein demon-

Jan 1, 1964

THE first session was held in the rooms of the American Philosophical Society, on Tuesday evening, February 26th. The President, Dr. T. Sterry Hunt, called the meeting to order, and after a few introductory remarks concerning the importance of theoretical and speculative science, which often involves principles of the highest economic value, and, more than all that, serves to enlarge our conceptions of the universe, and ennoble us, by the cultivation which it affords to our most exalted faculties, proceeded to discuss some points in the chemistry of the atmosphere. It is known that there is in the crust of the earth a great amount of oxidized carbon, not only in the shape of coal, but also in the graphite or plumbago of the crystalline rocks, in the various bituminous shales or pyroschists, which are found in all succeeding rock-formations, and also in the forms of bitumen and petroleum. All the analogies of nature lead us to conclude that these various carbonaceous substances have had an organic origin, and have been generated by the deoxidation of carbonic acid, a process effected by the growing plant, and attended with the liberation of oxygen. He showed that the carbon of a layer of coal covering the whole earth's surface to the thickness of one meter, would, in its production from carbonic dioxide, liberate an amount of oxygen equal to that now present in our atmosphere. But bituminous coal contains also a large amount of hydrogen, derived from the deoxidation of water, which implies the liberation of a farther portion of oxygen. The amount from this latter source would equal, for the various coals and asphalts, from one-eighth to one-fourth, and, for the petroleums, one-half of that set free in the deoxidation of the carbon which these hydrocarbonaceous bodies contain. From what we know of the composition of the stratified rocks, it is probable that they include an amount of deoxidized carbon and hydrogen many times greater than that contained in a layer of coal one meter in thickness, and, consequently, that the disengaged oxygen in past ages must have far exceeded that now present in our atmosphere. To this must be added

Jan 1, 1878

The first session was held in the rooms of the American Philosophical Society, on Tuesday evening, February 26th. The President, Dr. T. Sterry Hunt, called the meeting to order, and after a few introductory remarks concerning the importance of theoretical and speculative science, which often involves principles of the highest economic value, and, more than all that, serves to enlarge our conceptions of the universe, and ennoble us, by the cultivation which it affords to our most exalted faculties, proceeded to discuss some points in the chemistry of the atmosphere. It is known that there is in the crust of the earth a great amount of oxidized carbon, not only in the shape of coal, but also in the graphite or plunlbago of the crystalline rocks, in the various bituminous shales or pyroschists, which are found in all succeeding rock-formations, and also in the forms of bitumen and petroleum. All the analogies of nature lead us to conclude that these various carbonaceous substances have had an organic origin, and have been generated by the deoxidation of carbonic acid, a process effected by the growing plant, and attended with the liberation of oxygen. He showed that the carbon of a layer of coal covering the whole earth's surface to the thickness of one meter, would, in its production from carbonic dioxide, liberate an amount of oxygen equal to that now present in our atmosphere. But bituminous coal contains also a large amount of hydrogen, derived from the deoxidation of water, which implies the liberation of a farther portion of oxygen. The amount from this latter source would equal, for the various coals and asphalts, from one-eighth to one-fourth, and, for the petroleums, onehalf of that set free in the deoxidation of the carbon which these hydrocarbonaceous bodies contain. From what we know of the composition of the stratified rocks, it is probable that they include an amount of deoxidized carbon and hydrogen many times greater than that contained in a layer of coal one meter in thickness, and, consequently, that the disengaged oxygen in past ages must have far exceeded that now present in our atmosphere. To this must be added

Jan 1, 1879

SHORTLY after Ambrose Swasey suggested the creation of the Engineering Foundation in 1914, the World War broke. upon the scene. Consequently all eyes were soon turned to national security problems. In 1916 the newly-organized Engineering Foundation and the four National Societies joined with the National Academy of Sciences in establishing the National Research Council. From then until 1923 the Engineering Foundation devoted the greater part of its resources to the support of the Research Council and the Council's division of engineering. Since 1923, how-ever, it has turned to the original intention for which it was created, of cooperating with the national societies in proj-ects affecting engineering at large, though it still retains a connection with the Research Council. Mere enumeration and tabulation of work undertaken can of course lend but a vague idea of actual accomplish-ments. The reports of the Foundation give information of its widespread activities.

Jan 2, 1928

By R. A. Stauffer

THE chief ore of lithium is spodumene, a lithium-aluminum silicate containing up to 3 pct lithium. The preparation of lithium salts from spodumene is costly because of the low concentration of the metal and the difficulty of separating it from the other alkali metals present. Dr. Kroll's and Dr. Schlecten's recent paper' has reviewed various methods proposed for preparation of lithium. It will be seen from this paper that the methods proposed to date have required one or another of the lithium salts as a raw material. The high cost of these salts has been the chief item of expense in the lithium metal produced. This situation has made it interesting to investigate the possibility of producing the metal directly from spodumene. When spodumene is calcined at 1000°C in the presence of lime, lithium oxide is replaced in the ore as is evidenced by the fact that it may be leached from the reaction mixture with water.2 Free energy calculations suggested that lithium oxide might be reduced with aluminum or silicon and the lithium produced distilled from the reaction mixture by heating to about 1000°C in a vacuum. These facts taken together suggested that it might be possible to prepare lithium metal directly from spodumene by heating a mixture of the ore, lime, and a suitable reducing agent in vacuum and distilling off the lithium metal as formed. THE REPLACEMENT OF Li20 IN SPODUMENE A series of experiments were undertaken to determine the ratio of lime to spodumene necessary to free substantially all the lithium oxide present in the ore. The spodumene used in these experiments was supplied by Foote Mineral Co. in the form of powder of about 200 mesh. Analysis of the spodumene was as follows: [ ] Lime (cp -200 mesh) was added in various ratios to spodumene and thoroughly mixed in a ball mill. Two hundred gram samples of spodumene-lime mixtures were charged loosely in fireclay crucibles and held at 1000°C in a gas-fired furnace for 5 hrs. The product in each case was ground to pass 140 mesh and then placed in a thimble in a soxhlet extractor. Extraction with water was carried on for 6 hrs. After this period the extract was reduced in volume by evaporation in order to precipitate dissolved lime and was then filtered and titrated with 1/4 normal hydrochloric acid. After correcting for residual calcium oxide in solution, the alkali present was calculated as lithium oxide. The results of these experiments are shown in Table I and Fig I. At lime-spodumene ratios less than 1.5, the products were invariably fused. At the ratio of 1.5 and above, the product was loosely sintered with little evidence of fusion. When the ratio of lime to spodumene was three, replacement of alkali oxides in the

Jan 1, 1947

By R. F. Stilwell

There are three things that all coal consumers look for when they burn coal: (1) suitability for their particular requirements and burning equipment, (2) uniformity of shipments, and (3) quality as expressed by heating value and other chemical and physical tests. Suitability, or proper application, is determined generally from previous buying experience. It is a function of (1) the reliability and integrity of the shipper and distributor, (2) of a certain coal field or seam and of (3) uniformity and quality. Quality is limited by the location and geology of the seam and mine, the mining and preparation methods and equipment and the knowledge and ability of the personnel. Uniformity of shipments is in many ways the most important factor in coal selection. Lack of uniformity in chemical quality, size consist and treatment cause most of the customer complaints that arise from faults of the coal shipper. Lack of uniformity destroys suitability and quality standards, causing a large customer turnover, and greatly increases sales expense and reduces the net return to the operator. Oil and gas fuels are more uniform in quality than solid fuels, and there will be more gas and oil competition for coal markets after this war than before, because the size of their market is a direct function of the dimensions of their pipe lines, which have been greatly increased during the war. Present mechanical coal-cleaning equipment based upon gravity concentration has gone a long way toward giving us a coal of uniform ash content. The chart in Fig. I, by Hebley,1 shows the greater uniformity of the ash content of washed coal as compared with that of raw coal. Wide variation in the nature and amount of ash in the coal feed to the washer leads to a coal of non-uniform ash content. Mechanica1 cleaning equipment does not understand such terms as ash-softening temperature, coking properties, size consist and sulphur content. Unless the feed to the washer is uniform, the washed coal probably will not be uniform. Table I shows the ash, sulphur and ash-softening temperature of two mines in the Pittsburgh bed, both raw and washed, loaded over the same tipple; also No. 3 and No. 4 Pocahontas seams, both raw and washed, loaded from the same preparation plant. It is obvious that they must be blended or loaded separately if a uniform product is to be obtained. Why Is Blending Necessary? It was natural for the operators of captive mines producing by-product coals to recognize the necessity for blending raw coals of different quality and coking characteristics. They have had many years of experience with blending high, low and medium volatile coals at their oven plants. They have found that careful blending gives a coke of more uniform quality and better structure. Coals that could not be

Jan 1, 1947

By R. F. Stilwell

There are three things that all coal consumers look for when they burn coal: (1) suitability for their particular requirements and burning equipment, (2) uniformity of shipments, and (3) quality as expressed by heating value and other chemical and physical tests. Suitability, or proper application, is determined generally from previous buying experience. It is a function of (1) the reliability and integrity of the shipper and distributor, (2) of a certain coal field or seam and of (3) uniformity and quality. Quality is limited by the location and geology of the seam and mine, the mining and preparation methods and equipment and the knowledge and ability of the personnel. Uniformity of shipments is in many ways the most important factor in coal selection. Lack of uniformity in chemical quality, size consist and treatment cause most of the customer complaints that arise from faults of the coal shipper. Lack of uniformity destroys suitability and quality standards, causing a large customer turnover, and greatly increases sales expense and reduces the net return to the operator. Oil and gas fuels are more uniform in quality than solid fuels, and there will be more gas and oil competition for coal markets after this war than before, because the size of their market is a direct function of the dimensions of their pipe lines, which have been greatly increased during the war. Present mechanical coal-cleaning equipment based upon gravity concentration has gone a long way toward giving us a coal of uniform ash content. The chart in Fig. I, by Hebley,1 shows the greater uniformity of the ash content of washed coal as compared with that of raw coal. Wide variation in the nature and amount of ash in the coal feed to the washer leads to a coal of non-uniform ash content. Mechanica1 cleaning equipment does not understand such terms as ash-softening temperature, coking properties, size consist and sulphur content. Unless the feed to the washer is uniform, the washed coal probably will not be uniform. Table I shows the ash, sulphur and ash-softening temperature of two mines in the Pittsburgh bed, both raw and washed, loaded over the same tipple; also No. 3 and No. 4 Pocahontas seams, both raw and washed, loaded from the same preparation plant. It is obvious that they must be blended or loaded separately if a uniform product is to be obtained. Why Is Blending Necessary? It was natural for the operators of captive mines producing by-product coals to recognize the necessity for blending raw coals of different quality and coking characteristics. They have had many years of experience with blending high, low and medium volatile coals at their oven plants. They have found that careful blending gives a coke of more uniform quality and better structure. Coals that could not be

Jan 1, 1947

By Thomas M. Barczak

This paper describes a computerized simulation system developed by KETRON, Inc., in cooperation with the US Bureau of Mines. The system is designed for use by mine managers and engineers rather than computer specialists and allows the novice user to arbitrarily create room-and-pillar mine plans, with the computer illustrating the simulation of face activities on a video screen. Extensive visibility of the simulation is provided by visual display of the machine elements and their movement in the section to accommodate the extraction, roof control, place changing, and haulage operations. Performance statistics are also generated to analyze the operations. Both conventional and continuous mining methods can be simulated. In addition to simulating arbitrary scenarios, the system can also be used to display actual time-studied operations and maintain a file of these activities. Practical applications and case studies are provided in the paper to demonstrate the usefulness of the system. The system is designed to operate on a desk-top mini computer and is currently installed on a Hewlett-Packard 9854B system with 450 K bytes of memory.

Jan 1, 1983

By W. G. Pfann

THE problem of forming points on wires that were from 0.002 in. to 0.010 in. in diam arose in the recent appearance of silicon and germanium point contact rectifiers as elements in microwave radar.1 In these devices a pointed tungsten wire makes a delicate contact with the surface of a semiconductor. Because the quality of such rectifiers is largely determined by the nature of this contact, considerable attention has been given to the formation of the metal point. Reproducibility of contour and freedom from burrs and even microscopic irregularities are considered essential. The operations involved must be simple and rapid enough for mass production. Previously tungsten wires had been provided with conical points by a grinding method which involved rotating a wire about its axis and causing it to bear at an oblique angle against a spinning abrasive disc. This was later complemented with an electrolytic polishing treatment which removed irregularities from the ground point and also rounded it off at the tip-a desirable feature. Finally, these operations were supplanted by the electrolytic pointing method described here. MECHANISM OF POINT FORMATION The wires to be pointed are partially immersed- in an electrolyte in a .vertical position whereupon they are provided with smooth rounded points entirely by electrochemical action. The process is independent of the depths to which the wires penetrate the electrolyte because the points are formed at the surface level. It may be used to point a single wire or many of them simultaneously and is applicable to wires of different diameters within a limited range. Solution of the immersed portion of a tungsten wire is accomplished by making it the positive electrode in an electrolytic cell, as shown in Fig I. While the wire is maintained at constant voltage the current through the cell falls continuously, principally because of the decrease in wetted area which results from solution of the tungsten. This increase in resistance occurs in a reproducible manner and is used as a control in the process. As the immersed portion of the wire dissolves, it remains cylindrical in shape except for the short section which is wetted by the meniscus. Here the rate of solution is lower and decreases as the top of the meniscus is approached. The result is the formation of a tapered section inside the meniscus. As solution continues, the cylindrical section either dissolves entirely or drops off just before complete solution, leaving only the taper which is now sharply pointed. Further action causes this point to become rounded and then quite blunt, until finally the end of the wire is almost plane. Fig 2 shows the stages in this development. Contour PF is most representative of those used in point contact rectifiers. Thus a variety of point

Jan 1, 1947

By L. W. Pommier, F. B. Brien

The Rheological properties of pulps are non-Newtonian in character and more than one viscosity parameter is necessary to describe their behavior, therefore, the single term 'apparent viscosity' which has been used in the past may be misleading. The study reported in this paper uses a dimensional analysis based on the Ostwald-de Waele shear stress-rate of shear model for non-Newtonian liquids to develop velocity and resistance equations for falling spheres. An electronic monitoring apparatus was assembled for determining the velocity of metallic bodies as they fall through opaque liquids and suspensions. By means of this apparatus the behavior of the viscosity parameters of the Ostwald-de Waele model and the applicability of the proposed equations were examined for a number of non-Newtonian liquids. The validity of the equations for these liquids was confirmed. Preliminary data collected using solid-liquid suspensions established the validity of the form of the basic equations for these systems. The differential movement of solid particles through solid-liquid pulps and suspensions is very important LO many branches of engineering, such as minerals processing, soil mechanics, ceramic slip processing, oil well drilling-mud technology, materials-handling in pipelines, and many others. There is a dearth of fundamental knowledge on the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The resistance offered by Newtonian liquids to the movement of free settling spheres is well described for laminar and turbulent conditions by Stokes' and Newton's Laws, respectively. However, problems are encountered when attempts are made to extrapolate these simple relationships into solid liquid suspensions. The rheological properties of pulps are such that they are non-Newtonian in character;'" that is, the applied shearing stress and resulting rate-of-shear are related by non-linear functions, and thus, in the simplest case two viscosity parameters are necessary to describe their rheological properties. For this reason the single term 'apparent viscosity' which has been commonly used to explain the flow resistance of suspensions and non-Newtonian liquids may be misleading. It is realized that a rigorous analysis of the rnechanisms of momentum transport of liquid-solid systems is complex indeed. There are many variables that affect the rheological properties of the systems such as density, size, shape, and surface energy of the suspended solid and density and viscosity of suspending liquid, as well as the solid to liquid ratio. However, it was felt that a useful contribution to the knowledge of the behavior of suspensions could be made by examining the systems in terms of the basic fundamentals of nowNewtonian flow. This has led to the development, by means of dimensional analysis, of velocity and resistance equations, using two viscosity parameters to describe the velocity of penetrating bodies and the flow resistance encountered by these bodies, as they pass through non-Newtonian systems. THEORY In order to examine the effects of the rheological properties of solid-liquid suspensions on the movement of immersed bodies it is appropriate to start with non-Newtonian liquids and develop equations, analogous to those of Stokes and Newton, for laminar and turbulent flow respectively, from which quantitative information may be obtained. Further investigation would then be directed at the complex suspension systems, and the effects of the many variables on the velocity and resistance equations. Liquids are classified on a basis of viscosity which may be defined as the relationship between applied shear stress and resulting rate of shear?-'* Pure single phase liquids composed of small light molecules behave as Newtonian liquids, having a single viscosity parameter since the shearing stress and rate-of-shear are related by a linear function. Bingham plastics are similar but have a yield stress. Of particular importance in our investigation are dilatant (shear thickening) and pseudoplastic (shear thinning) non-Newtonian liquids, with and without yield values.

Jan 1, 1968

By T. H. Alden

T. H. Alden (General Electric Research Laboratory)—This paper as well as earlier ones of Dr. Wood represent an important contribution to the experimental description of fatigue fracture. The mechanism of fracture proposed by the authors, however, is not established by this data nor supported by other data existing in the literature. Although taper section metallography provides a rather detailed picture of fatigue crack geometry, photographs so obtained must be interpreted with care. The narrow bands revealed by etching, frequently associated with surface notches, are labeled by the authors "fissures". Measurement shows, taking into account the 20 to 1 taper magnification, that the depth of these structures is at most 2 to 3 times the width. This distinction is important in the conception of a mechanism of crack formation. It is difficult, for example, to imagine a deep, narrow fissure arising from a "ratchet slip" model. A surface notch, on the other hand, may form easily by this mechanism. The notches observed in the present work are the subsurface evidence of the surface slip bands or striations in which fatigue cracks are known to originate.4-6 It is clear that an understanding of the structure of these slip bands is of key importance in understanding the mechanism of fracture. The evidence presented shows that these regions etch preferentially, possibly because they contain a high density of lattice defects, or as the authors state equivalently, because they are "abnormally distorted." However, it is not possible to conclude that the distortion consists of a high density of vacant lattice sites. The fact of a high total shear strain in itself does not assure a predominance of point defects as opposed to other defects, for example, dislocations. Other evidence in the literature which suggests unusual densities of point defects formed by fatigue7-' refers not to the striations or fissures, but to the material between fissures (the "matrix"). If a choice must be made, the preferential etching would seem to be evidence for a high dislocation density, since dislocations are known to encourage chemical attack in copper;g no such effect is known for the case of point defects. A third alternative is that the slip bands are actually cracked, but that near its tip the crack is too narrow to be detected by the authors' metal-lographic technique. In this case the rapid etching can be readily understood in terms of the increased chemical activity of surface atoms. Unless a vacancy mechanism is operative, the motion of dislocations to-and-fro on single slip planes will not lead to crack growth. Point defect or dislocation loop generation are the principal non-reversible effects predicted by this model. In any case, the nonuniform roughening of the surface in a slip band6 requires a flexibility of dislocation motion which is not a part of the to-and-fro fine slip idea. The same is probably true of crack growth by a shear mechanism. Either some dislocations must change their slip planes near the end of the band and return on different planes,'0 or dislocations of opposite sign annihilate." The mechanism by which these processes occur in copper at room temperature or below is that of cross slip. Thus cross slip appears to be essential to fatigue crack growth.6'10"12 The fact that a tensile stress opens the slip bands into broad cracks does not indicate the structure of the bands or the mechanism by which cracks form. The charactersitic concentration of slip into bands during fatigue shows a low resistance to shear strain in these regions. (This fact in itself may be inconsistent with a high concentration of vacancies.) The authors contend also that continuing shear produces an additional mechanical weakening so that the bands fracture easily (are pulled apart) under the influence of the superimposed tensile stress. It is equally possible that the only weakness is a weakness in shear, that the crack propagates by a shear mechanism, and that subsequently the tensile stress pulls the crack apart. Even the direct observation of bands opened by a tensile stress would not be conclusive since, as argued above, they may be fine cracks. The same argument applies to internal cracks, their existence in the presence of a tensile stress not indicating the mechanism of formation. Internal cracks originating in regions of heavy shear have also been seen following tensile deformation of OFHC copper,13 so that this mode of fracture is not unique to combined tensile and fatigue straining. The authors point out in their companion report14 that 90 pct of the cracks formed during pure tor-sional strain were within 8 deg of the normal to the specimen axis. If the tensile stress were an important factor in crack propagation, it is surprising that the cracks cluster about the plane in which the normal stress vanishes. Similarly, a study of zinc single crystals showed that for various orientations the life correlated well with the resolved shear stress on the basal plane,'= and was not dependent on the normal stress across this plane. W. A. Wood and H. M. Bendler (Authors' reply) -Dr. Alden's discussion emphasizes the essential point in the relation of slip band structure to

Jan 1, 1963

By James W. Neill

Discussion of the paper of H. 0. Hofman, presented at the Canal Zone meeting, November, 1910, and printed in Bulletin No. 42, June, 1910, pp. 473 to 497. JAMES W. NEILL, Pasadena, Cal. (communication to the Secretary *) :-Professor Hofman's paper brings the art up to . date. As I was one of the pioneers in this business, I beg to give the following incomplete data regarding my efforts in this line. In the year 1883, while I was in charge of the smelting-operations at Mine La Motte, Mo., there was at the concentrator an unusually large production of a middle product, locally called "iron," which carried considerable values in nickel and cobalt, and which it was desirable, for this reason, to treat by itself. The works could not spare a furnace for the purpose; and to handle this product I improvised a "roast-hearth " from an old " lead-hearth." This was a small cast-iron furnace of the usual construction, about 2 by 4 ft. in dimensions, with a hollow cast-iron back, through which the wind circulated before entering the tuyeres. I had a cast-iron grate made to fit this hearth, and placed it flush with the lip, or apron, and above the tuyeres. On this grate, which had round holes about 0.25 in. in diameter, and a total surface of about 20 by 40 in., I roasted the nickeliferous pyrite product; starting the fire with kindling, then adding charcoal, and then gradually feeding the sulphides with a shovel, so as to cover the fire, choke down blow-holes, and get an even bed. Blast at a pressure of 3 or 4 oz. was supplied by a fail-blower. When a cake of roasted material had formed, it was removed with a steel bar, or fork, to the lip of the furnace, and thence into a wheel-barrow.. The fine material which had remained unmelted, but very hot, on top of the cake would promptly ignite when the cake was broken up and removed. The fire would then be covered with fresh material and * Received Aug. 29, 1910.

Apr 1, 1911

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By Sam Tour

OF the new alloys achieving commercial prominence during the year, an aluminum-silicon magnesium casting alloy, which is similar in many respects to the 4 per cent copper alloy, developed about 1921, which has attained such a wide field of service, may be mentioned. The new alloy, like the old, is a heat-treatable type and develops about the same physical properties. The alloy casts easily and is relatively insensitive to high pouring temperatures. Its ability to produce substantially leak- proof castings is noteworthy. A second casting alloy development is the new Aluminum Co. of America No. 132, "Lo-Ex" piston alloy, a result of nearly eight years of research. The alloy contains about 14 per cent silicon and varying amounts of nickel, copper, and magnesium. It exhibits a low coefficient of expansion and thus permits small piston clearances. Its lower specific gravity is a further advantage.

Jan 1, 1932

By L. D. Jaffe

THE data recently published1-" on heat treatment of titanium alloys have not been readily systematized into an overall picture. When the ß titanium phase transforms isothermally at low temperatures, the hardness follows a typical age-hardening pattern, going through a peak as schematized by the "hardness" vs "time of isothermal transformation" coordinates of Fig. 1. As the temperature is raised, the peak will decrease in height and occur at shorter times; slowing must however take place as the /3 transus is approached. The brittle microconstituent in the region of peak hardness has been termed /3'. Its structure is still undetermined but it is clearly a transition stage from soft /3 to the £ + a that is found at the right of the peak. On continuous cooling, high cooling rates correspond to short times on Fig. 1; abscissa labeling has been added accordingly. Extremely rapid cooling will retain soft /3; very slow cooling will precipitate soft a; intermediate rates give hard 8'. Increasing distance from the water-quenched end of a Jominy hardenability bar corresponds to slower cooling (right on Fig. I), but the range of cooling rates covered by a Jominy bar is only a small portion of that shown in the figure. The p-stabilizing alloying elements retard the transformation process, moving the material to the left on Fig. 1. A lean alloy is harder water-quenched (P') than air-cooled (/3 +a); a rich alloy is harder air-cooled (/3') than water-quenched (/3). Examples of the position of various compositions with respect to the curve, based on limited data in the literature, are given at the top of the figure. Oxygen and carbon accelerate the transformation process, moving the material to the right on Fig. 1. If an alloy quenched quickly enough to retain soft /3 is reheated below the £ transus (tempered), it ages, going through a hardness maximum as time increases (moving right on Fig. 1). Material which after cooling from the /3 range lies on or right of the hardness peak, will move still further right on tempering, and so soften. Since the rate of the tempering (aging) reaction increases with temperature, the figure also may be used to represent the variation in properties with tempering temperature, at short tempering times. The simple picture given here neglects martensite transformation, as well as differences between decomposition products of /3 formed by direct isothermal transformation and those formed by quenching and tempering. It may nevertheless be of use as a guide for practical heat treatment and for further research.

Jan 1, 1955

By Gordon E. Frantti

Under the auspices of the Geophysical Committee of Michigan College of Mining and Technology, an investigation was made in Michigan's Upper Peninsula to obtain geophysical data related to the regional subsurface geology in the area covered by Paleozoic sediments. The area surveyed includes that portion of the Upper Peninsula which lies between R18W to R26W and T41N and T49N, covering approximately 1300 square miles. On the index map, Fig. 1, it is represented by the cross-hatched zone west of Munising. Four of the five sites of detailed investigation are indicated by the letters A, B, C, and D. A detailed gravity and magnetic survey had previously been conducted by J. G. Wilson near Perkins, 8 miles north of Rapid River, on a local anomalous area. Results of his work, which showed a large positive magnetic anomaly associated with a gravity anomaly, aroused interest in the possible economic significance of the formations underlying the Paleozoic sediments in this part of the Upper Peninsula.

Jan 1, 1956

By F. A. Forward, J. Halpern

A new process is described for extracting uranium from ores containing sulphidic minerals, which comprises treating an aqueous pulp of the ore with air or oxygen at elevated temperatures and pressures. The acid required to dissolve the uranium is generated during the leach through oxidation of the sulphides. The chemistry of the process is discussed and laboratory results are presented to illustrate the operation of the method and the variables which control it. With most ores, leaching at a temperature of 130°C and an oxygen partial pressure of 10 psi provides uranium extractions of 90 to 95 pct in 4 to 6 hr. The acidity and level of dissolved impurities in the leach liquor can be kept fairly low. The method is characterized by a number of advantageous features including low reagent cost, short retention times, and high recoveries. RECENTLY there have been developed several processes for extracting metal values from ores by pressure leaching techniques;' -' an example is the carbonate leaching process for uranium ores which has been studied in this laboratory.' Leaching is carried out under oxygen pressure to ensure oxidation of the uranium to hexavalent compounds which are soluble in carbonate solutions. During the course of investigations relating to this process, it was observed that sulphide minerals, such as pyrite, usually were oxidized under the conditions of the leach treatment resulting in the formation of iron hydroxides and sodium sulphate, i.e. 2 FeS= + 7Vz O2 + 8 Na,CO3 + 7 H,,O -* 2 Fe(OH)3 + 4 Na2SO4 + 8 NaHCO.,. [1]

Jan 1, 1956

By Edmund J. Pryor

DURING the war years restrictions on travel, pressure of work, and the irregular arrival of technical literature from abroad combined to severely isolate Great Britain in a period of intense war expansion of the art and practice of mineral dressing. Many British technicians were fully occupied with the day-to-day problems of improvising substitutes as regular sources of supply failed. and with mastering the strange demands and working conditions of wartime. After a long day spent between ones laboratory and production work, the rest of the waking hours were often filled with fire watching or home guard patrol activities, substituting for a night-shift manager, or "resting" in a dugout while the bombs came down. There was no time for serious study of such technical literature as survived the Atlantic crossing.

Jan 1, 1947