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By P. D. Gorsuch, D. L. Newhouse, Irvin R. Kramer

ALTHOUGH many methods have been suggested for the calculation of tensile strength and yield point from chemical composition, their usefulness has been limited to a particular cooling rate or section size. Further limitations have been imposed by failure to take into account many of the alloying elements that exert a considerable influence on the tensile strength or yield point. These systems, nevertheless, have filled an important need in many instances. The value of a system for the calculation of the tensile properties from the chemical composition and cooling rate is that it permits the prediction of the effect of alloying elements and heat-treatment on the mechanical, properties, so that more efficient use of alloying elements may be made. Furthermore, it aids in the choice of steel for a given application and tends to decrease the number of steels that otherwise would have to be tested. It is the purpose of this work to present a method of calculating tensile strength and yield point from the chemical composition and to suggest a method of correlating the tensile-strength and yield-point factors and cooling rate. Steelmakers have been interested for many years in the calculation of the tensile strength of hot-rolled steels. Quest and Washburn' summarize several of the attempts that have been made to devise formulas. They show the inadequacy of each of these formulas and present one of their own. It is apparent from their work that a simple additive equation of the type TS = A + BX + Cy + DZ + ? ? ? , where A, B, C, D, etc. are experimentally determined constants and x, y, z, etc., are the percentages of alloying elements present in the steel, is not adequate to analyze fully the situation encountered in the calculation of tensile strength. For example, it was found that the difference between the calculated and observed values became progressively greater as the carbon and manganese contents were increased. Therefore, the effect of manganese was given as a function of the carbon content. Grossmann,2 in his work on the hardenability of quenched steels, and Walters,3 in his method of calculation of tensile strength of normalized steels, present two cases in which multiplying factors were successfully used to express the combined effect of alloying elements. The factors in both cases were obtained from the fractional increase in hardenability or tensile strength with increase of alloy content. Yield point often is more important in design than tensile strength. For quenched and tempered steels a linear correlation exists between yield and tensile strength .4 This is not true, however, for normalized

Jan 1, 1946

By Paul Beck

IT is well known that the hardness of metallic single crystals, like that of polycrystalline metals, increases during deformation (hardening by cold-work). It is also known that, as a consequence of deformation, the metallic material acquires an evident thermodynamic instability, revealed, for example, by the fact that the increased hardness gradually decreases with time, especially at elevated temperatures (softening by annealing). The temperature at which the stabilizing process begins is different for various metals, and for any metal it depends on the amount of deformation. Such stabilization of deformed metals may proceed in two different ways: through recovery, and through recrystallization. The former process allows the unstable deformed metal body to approach stability gradually and without visible change in the grain structure; the latter process, like an allotropic transformation, yields directly the undeformed stable "phase" in the form of new undeformed crystals, which, starting out of a certain number of nuclei, grow into and' consume' the deformed hard material. The extent of stability attainable through recovery is limited, espe-cially if the deformation of the metal crystal or crystals involves not only the gliding along slip planes, but also the bending of the slip lamellae, or at any rate the bending of comparatively large parts of the crystal lattice. In such cases, for instance in bent single crystals or poly-crystalline metals subjected to any deformation, recovery will not as a rule be able to restore the "straight" undeformed lattice, and stability can be attained only by recrystallization; that is, by the consumption of the bent crystal lattice parts by new, undeformed crystals-a much more drastic process. It is evident that the part of the surplus free energy stored in deformed crystals, which is present in the form of the elastic energy of the bent lamellae, is in these instances not considerably involved

Jan 1, 1937

E. E. THUM, * Salt Lake City, Utah (Written discussion ?).-Dr. Fulton's paper sheds a great deal of light upon questions which have perplexed many who have studied the metallurgy of zinc, and have fruitlessly brought forth several hypotheses and reams of discussion. It would be a bright day if others would follow Dr. Fulton's example, for, as a

Jan 11, 1918

By D. R. Pratt, R. W. Hanks

The method of Caldwell and Babbitt for detennining Bingham plastic rheological constants from engineering pipe flow data has been erroneously used in many previous applications. A reanalysis of extensive pipe flow data from the literature is performed. Critical Reynolds numbers corresponding to the laminar-turbulent transition calculated from these data are found to agree with theoretically calculated values for the entire flow range studied. Similar agreement is found for the authors&apos; own data&apos; for flow of 10 slurries between parallel plates. The Bingham plastic model is shown to be a reliable representation of the flow of non-Newtonian slurries provided it is properly applied. If the Hedstrom number He = pD2 t0/?2 > 104, then the linear approximation method of Caldwell and Babbitt is invalid for pipe flow data obtained in systems of ordinary engineering interest, and the complete nonlinear form of the pipe flow Bingham plastic equation must be used in determining rheological parameters. INTRODUCTION Many materials of engineering interest must be handled and transported as slurries or suspensions of insoluble particulate matter in a Newtonian liquid. These suspensions frequently exhibit non-Newtonian rheological behavior which is reasonably well described by the simple Bingham plastic rheological equation1 Using this particular equation to describe the laminar flow characteristics of slurries was discussed at length by Caldwell and Babbitt2-4 who considered the flow of various clay slurries and sewage sludges. The model has since been used by many others.5-7 More recently the problem of predicting the laminar turbulent transition Reynolds number for Bingham plastic fluids has been treated8 for the case of flow in pipes. This paper points out errors which have existed in the analysis of Bingham plastic flow since the work of Caldwell and Babbitt2-4 and presents a reanalysis of the laminar turbulent transition calculatiod for Bingham plastic flow in pipes. In addition, new data obtained for flow of Bingham plastic slurries between parallel plates, both in laminar flow and in the laminar turbulent transition region, will be presented and compared with the theoretical analysis of laminar turbulent transition for flow between parallel plates. THEORETICAL ANALYSIS PIPE FLOW The mathematical analysisl-4 of laminar flow of a Bingham plastic fluid leads to the following equation. where q = <v>/R is a pseudoshear rate, rw is the wall shear stress Eo = r0/rw, r0 is the yield stress and 1 is the coefficient of rigidity or plastic viscosity from Eq. 1. Caldwell and Babbitt2-4 recognized that the quartic term in Eq. 2 was small compared to the other terms whenever 5, « 1, and that for large values of 7, a plot of Eq. 2 becomes linear. The slope of such a plot with rw as ordinate is 4? and the intercept is (4/3) ro. This approximation is illustrated schematically in Fig. 1. The shaded region between the true curve and the straight-line approximation near the origin represents the contribution of the quartic term. In principle, therefore,

By Simon D. Strauss

The world appetite for minerals in the, third quarter of this century grew at a higher rate than had been anticipated. To illustrate, consider the experience of four, commodities. Excluding the Communist bloc, sometimes referred to as the centrally planned economies, demand for aluminum increased at a compound rate of 8.6% between 1950 and 1975,; copper rose by 4.4%; iron ore by 5.5%; and tin, the laggard in the group, by 2%. Except for tin, the figures are substantially greater than growth rates anticipated in 1950 in the Paley Commission report and other studies. The growth rate was not evenly distributed in geographical areas. Professor Wilfred Malenbaum of the University of Pennsylvania did an interesting study breaking these figures down as among three principal sources of demand -- the United States, other industrialized nations (which he referred to as the "rich lands"), and the developing world (which he referred to as the "poor lands").

Jan 1, 1982

By C. H. Mathewson, A. U. Seybolt

As is well known, many questions affecting the properties and uses of a metal cannot be answered without careful consideration of the state of purity realized in the various operations of preparation, refining, or special treatment that have brought the product to its final state. The occurrellce of an impurity in minute quantity offers no guarantee that its effect will be inconsiderable because dissolved substances often modify the properties of a metal quite out of proportion to their concentration. In such cases the determination of solid solubility must be accepted as a problem of considerable difficulty, requiring the use of especially purified materials and methods not ordinarily used in the metallurgical laboratory. This aspect of the equilibrium between metals and their oxides is especially important and a search for fundamental data reveals little except conflicting opinion even concerning the systems of common occurrence and interest. Rhines and Mathewson1 in 1934 studied the solubility of oxygen in solid copper by annealing to equilibrium in air and gave reasons for the failure of other methods, notably the ordinary procedure of heat-treatment followed by microscopic examination, to yield reliable results. In this paper, a similar study has been made of the solubility of oxygen in cobalt. The simple theory of this method is outlined below. Conditions of Equilibrium between a Metal and Dissolved Oxide at Different Temperatures and Pressures The general conditions of equilibrium in any system are conveniently summarized in a projection of the triple curves of the P, T, X space

Jan 1, 1935

By A. U. Seybolt, C. H. Mathewson

As is well known, many questions affecting the properties and uses of a metal cannot be answered without careful consideration of the state of purity realized in the various operations of preparation, refining, or special treatment that have brought the product to its final state. The occurrellce of an impurity in minute quantity offers no guarantee that its effect will be inconsiderable because dissolved substances often modify the properties of a metal quite out of proportion to their concentration. In such cases the determination of solid solubility must be accepted as a problem of considerable difficulty, requiring the use of especially purified materials and methods not ordinarily used in the metallurgical laboratory. This aspect of the equilibrium between metals and their oxides is especially important and a search for fundamental data reveals little except conflicting opinion even concerning the systems of common occurrence and interest. Rhines and Mathewson1 in 1934 studied the solubility of oxygen in solid copper by annealing to equilibrium in air and gave reasons for the failure of other methods, notably the ordinary procedure of heat-treatment followed by microscopic examination, to yield reliable results. In this paper, a similar study has been made of the solubility of oxygen in cobalt. The simple theory of this method is outlined below. Conditions of Equilibrium between a Metal and Dissolved Oxide at Different Temperatures and Pressures The general conditions of equilibrium in any system are conveniently summarized in a projection of the triple curves of the P, T, X space

Jan 1, 1935

By John C. Branner

No precise geographic limits can be given for the zinc- and lead-region of North Arkansas. In general terms it lies N. of the Boston mountains and W. of the St. Louis, Iron Mountain and Southern railway; but the prospecting and the development of the ore-deposits have not gone far enough to outline more than vaguely the areas over which workable deposits are to be expected. The tardiness of the development of the region is due in part to its topography, as a hilly and partly mountainous country, through which there have been no railways until recently. There is no longer any doubt, however, about the existence in that region of large bodies of zinc-ores. I. General Geology. The general geology of the region is, in the main, quite simple, but that of the ore-deposits is less so. The zinc-regions of North Arkansas lie about the southern flanks of the Ozark dome. The rocks are approximately horizontal, but have a gentle southward dip away from the axis of this dome. Figs. 1, 2 and 3 show the broad features of the to-. pography and geologic structure. South of the zinc-region, the sandstones and shales of the lower Coal-Measures form the north-facing escarpment of the Boston mountains. Beneath the Coal-Measure rocks are the limestones and cherts of the Lower Carboniferous; and these rest upon Silurian and Ordovician beds. The uppermost beds (Coal-Measures) have been cut into by erosion along the mountain-slopes so that their edges or outcrops have a meandering or dendritic form. The same thing happens with the Lower Carboniferous beds; but these, haying been more or less protected by the overlying Coal-Measured, have broader bases, and cover a much larger area. In places,

Jan 1, 1902

WE must begin by defining what we mean by the Copperbelt. This term is generally used to denote that region of Northern Rhodesia in which the copper mines of that territory are situated. The first published use of the term Copperbelt we have been able to trace dates back to 1905. The African World of December of that year contained an article entitled "The Great Northern Copper Belts of Rhodesia." The next reference we have traced is in 1909 in an article in the Transactions of the Geo- logical Society of South Africa. It began to be used generally in the late twenties and by 1929 was in common use to denote the region which today contains the existing large copper mines of Northern Rhodesia. The first of three accompanying maps is a very simple outline map of Africa showing where Rhodesia is within Africa, and where the Copperbelt is within Rhodesia. The second is a larger scale map of the Copperbelt itself. It will be seen that within the present Copperbelt there are six producing mines. Two of these are new and four are relatively established, having started operations between the two world wars. The Copperbelt also includes a town- ship called Ndola, which is not a mining town, but a railhead on the main line. This town has developed primarily as a result of the mining industry in the neighborhood. It describes itself as the Gateway to the Copperbelt and is shortly to become a refining center.

Jan 5, 1957

By H. C. Chang, N. J. Grant

Creep of very coarse grained, high purity aluminum was studied at 400° to 1100°F with an initial stress range of 50 to 1200 psi. The process of boundary sliding and migration was studied. The driving force of boundary migration under creep conditions is shown to be a combination of strain energy migrationand surface energy. A theory is presented regarding the strainenergyrole the grain boundaries play under creep conditions. From this thetheory intercrystalline failure of commercial alloys can be explained. Also from this theory an optimum grain size should exist for good high temperature properties of high purity materials. IN the investigation of the creep of very coarse grained, high purity aluminum previously reported,&apos; the cyclic nature of the process of grain boundary sliding and migration has been established by microscopic observation of the actual creep process as well as metallographically. It was also substantiated by measuring localized strains across the grain boundaries. In addition, it was shown how extensive subgrain and fold formation may result from boundary sliding and how the slid grain boundary may become sharply wavy as a result of subgrain formation. Since the publication of those results, additional information on the process of grain boundary sliding and migration has been obtained. It is the purpose of this paper to report on the direction and driving force of boundary sliding and migration, the effect of grain size, and the effect of temperature. Finally the effect of decreasing purity (alloys 2s and 3s) on the process of boundary sliding and migration is noted. From these results, an explanation is presented for the intercrystalline failure of alloys under creep conditions. The effects of grain size on the creep properties of impure and high purity materials are discussed in the same light. The experimental procedures and technique have been presented elsewhere.&apos; It is only necessary to state how the 2s and 3s aluminum specimens are prepared. Machined specimens were first annealed at 600°F for about 12 hr. In order to produce a large grain size the specimens were then stretched 3 to 8 pct. The specimens were marked with reference marks, electropolished, annealed at 900°F for 24 hr and at 1150°F for 12 hr, and repolished. The grain size of 2s aluminum produced by this treatment is comparable to that of high purity aluminum in the direction of its width of the specimen, i.e., there are 2 to 4 grains across the width of the specimen. However, the grains of 2s aluminum are 3 to 10 times longer in the direction of the specimen axis. On the other hand, the grain size of coarse grained 3s aluminum ranges from 10 to 20 grains across the width of the specimen due to the treatment just outlined and therefore is much smaller than that of both high purity and 2s aluminum. As in 2s aluminum, the grains are about 3 to 10 times longer in the direction of the specimen axis than in the direction of the width of the specimen. The arrangements of the grains in 2s and 3s aluminum were generally irregular; therefore it was difficult to follow the course of the grain boundaries. Results Method of Presentation: In order to show the arrangement of the grains, especially the direction and positions of the grain boundaries, traces of the grain boundaries on the four surfaces of the specimens were unfolded and mapped out after macroetching. Figs. 1 and 2 show the structural development drawings of specimens P-3 and P-8 respectively. The two flat surfaces (of which the front one faces the microscope) and the round-edged surfaces will be called the "front surface" and "back surface" and

Jan 1, 1954

By Waldemar Lindgren

No one would maintain that all ore deposits or all deposits of useful minerals have been formed by the same processes. Generally they have originated by special processes of concentration but these may be of many different kinds. Some deposits have their origin in chemical or biochemical processes of concentration in rivers, lakes or seas, others developed on land by means of chemical reactions of surface waters on various forms of rocks. Certain insoluble substances remained behind; others were dissolved and precipitated in favorable places. This action proceeded in the realm of the oxidizing surface waters or in the deeper zones to which the waters from the surface could find their way. Examples of the latter kind may be found in the extensive copper and vanadium deposits of some sedimentary beds or in the lead and zinc deposits of certain broad limestone strata. In these instances the evidence for any other mode of origin would seem to be very weak indeed.&apos; Nor does it seem possible to deny that circulating waters may form deposits of the more common metals along fissures after having dissolved many constituents from paths traversed. Another very large class has been formed by magnetic processes of concentration. The last 40 years have been a period of intense activity in the investigation and description of a vast number of deposits; all modern methods have been employed and the result is an accumulation of data, difficult or impossible to master. It has been a period similar to that in petrography. The generalizations, the able deductions, have lagged behind. Evidently several geologists have become weary of this "infinite detail" and a mistrust of the microscope seems to have arisen. Although this feeling of being swamped in microscopic detail is a painful experience, nevertheless only through the detail in combination with the large features, and only by utilizing all the related sciences shall we

Jan 1, 1927

By Charles H. White

Methods in colorimetry are based on the assumption that the intensity of the&apos; color of a definite volume .of solution is directly proportional to the quantity of the color-producing substance present. In the preparation and examination of colored solutions there are three ways in which the depth of color may be varied. These variables are : (1) the quantity of&apos; the coloring matter; (2) the quantity of the solvent, or the dilution ; and (3) the thickness or depth of that portion of the solution examined. With these three variables as a basis, three general methods in colorimetry have been devised, all of which have been used in the determination of carbon in steel. In the first method, the quantity of the solution is kept the same for both the unknown steel and the standard, and the sections compared are of equal thickness, while the quantity of the standard is varied until the color obtained is of the same intensity as that produced by a definite quantity of the unknown steel. In laboratories where this method is used there is prepared and kept for permanent use a series of solutions with varying amounts of the standard, representing the percentages of carbon from the lowest to the highest demanded in that laboratory. These standard solutions are kept in bottles or test-tubes of equal diameter, and are arranged in series from the faintest to the most intense color, so that it is a simple matter to find the place of the unknown steel in the series, when the solution is of a definite volume and is contained in a tube of the same diameter as the standard tubes. In the second method, equal quantities of the standard and of the unknown steel are dissolved, the standard is diluted to a definite volume, and the solution of the unknown steel is di-

Jan 1, 1907

By H. J. French

Within the past few years, particularly because of the rapid growth of the airplane industry during the war, considerable attention has been paid to the manufacture of light-wall cold-drawn seamless and welded steel tubing for structural purposes. While the manufacture of such tubing is not, in itself, a difficult matter, some difficulties have been encountered in producing the same under specifications requiring definite physical properties. It is the purpose of this paper to describe the methods of manufacture and the properties that may be obtained by such methods for tubing coming within about 1/2 to 2 in. (12.7 to 50.8 mm.) outside diameter and 10 to 22 Birmingham wire gage (0.134 to 0.028 in. wall thickness). Such tubing is largely used as structural material in the aircraft industry, and it is of the utmost importance that the physical and chemical properties should be known, and also that the various factors entering into the manufacture should be under such control as to allow these properties to be varied and held within definite limits. In general, tubing may be divided into four classes: namely, specialty tubing, such as riveted-sheet or plate, lock jointed, etc.; brazed tubing; welded tubing; and seamless tubing. Welded tubing may be divided into hot product, such as lap welded and butt welded, and cold product, such as acetylene and electric welded. Seamless tubing may be hot rolled or cold drawn. Specialty Tubing The first two classes present mainly mechanical or structural engineering problems. A simple form of tube is made by riveting together the overlapping edges of rolled sheets or plates formed into a cylinder. Because of the nature of its construction, such a tube is necessarily limited to relatively large sizes. Lock-jointed tubing is produced by passing low-carbon strip through a forming machine having suitable rolls and dies, its manufacture is almost entirely a question of design of the forming machine and its satisfactory operation. The chief application of such tubing is in the manufacture of bedsteads.

Jan 1, 1920

By Edwards Wichers

The purpose of this paper is to set forth the matters of principal interest in connection with work done in the past few years on the purification of the metals of the platinum group, including the study and modification of methods already in the literature and the development of new procedures. For the most part, the results will be given in summary form, reserving the publication of detailed data and directions for a forthcorning paper to be issued by the Bureau of Standards. In recent years increasing interest has been shown in the preparation of the pure platinum metals, both by those concerned with the manufacture of the metals and their alloys for scientific and industrial purposes and those who are engaged in the study of the chemical or physical properties of the elements. The purification of the metals usually has been regarded as a matter so involved and difficult as to require the attention of specialists. It is hoped that this paper will show that any of the metals can be prepared in any desired degree of purity by relatively simple straightforward chemical methods. For the most part, it is thought that the methods given are suitable for small-scale refineries as well as for the laboratory; also, that they will bring the time required for the purification of any of the metals within reasonable limits. The new procedure suggested for purifying platinum should prove to be much shorter than any methods described in the literature. Treatment of Platinum Ore As is well known, the principal source of the platinum metals is a mixture of several native alloys of the metals, found chiefly in naturally concentrated deposits in stream beds or alluvial material. Without attempting to enumerate all of the minerals present, it may be said that the concentrated ore from such sources contains all of the six platinum

Jan 1, 1928

By Frank Tolonen

IRON-ORE beneficiation is becoming of vital importance to the Lake Superior region, since only a few decades will be needed to exhaust the direct shipping ores even if generous allowances are made for discoveries of new orebodies. If the region is to continue as the chief source of ore to the steel industry of the United States, it must concentrate or otherwise beneficiate the enormous tonnages of available iron formations. A beginning along this line has already been made. About one-fifth of the total shipment, even now, is the product of some sort of concentrating process, while another fifth is improved in physical structure by crushing, screening, drying, sintering, or some other similar method. The amount of material amenable to these processes is limited, however; and, in order to be able to utilize the billions of tons of iron formations that cannot be so beneficiated, an intensive study of their nature and concentration possi-bilities is necessary. As long as high-grade ores are available in ample quantities, ore dressing is economically impossible, but as soon as the supply nears exhaustion it becomes necessary. At first the products of ore dressing must meet as nearly as possible the same specifications as the rich ores in order to be adapted to the reduction processes already established. The future requirements as to quality will depend on the one hand upon the ability of the ore dresser to eliminate undesired constituents and charac-teristics in the material, and on the other upon the adaptation of the reduction processes to the product that can be economically supplied. A better understanding of the blast furnace and other reduction reactions, and improvements in the preparation of raw materials, should enable the Michigan districts to continue to supply ore for a long time to come. The study and testing of the iron formations necessary to bring a utilization of the low-grade ores, though requiring time and effort on the part of all concerned, should not be postponed, especially since the economic situation forces the use of the highest grade ore in preference to the leaner material.

Jan 1, 1933

By T. T. Read

In discussing the taxation of mining enterprises, it is desirable to place limits of both time and space on the field of discussion. For our present purposes it seems best to limit consideration to taxation of mining enterprises in the United States, and to further limit the subject to taxation under approximately current conditions. Even with such limitations the field is large enough, since in this country we have, in most regions, a number of taxing powers; so that state, county and village tax systems must ordinarily be considered, in addition to our national or federal taxes. Nor is it possible, in discussing United States mineral taxes of today, altogether to pass by similar taxation in earlier periods, or related systems in other countries. It is perhaps hardly necessary to remind you, at the outset, that each age in the history of the world displays its own system of public revenues, and that the taxation systems of today are everywhere different from those of older times. Theories as to taxation have varied according to the economic basis of the society in which they were formulated, and our ideas as to justice in taxation fluctuate with changes in social conditions. The word taxation is used in a fairly definite sense today, but you have only to glance into the history of taxation to find that the paragenesis of ore deposits is a fairly simple subject as compared to the paragenesis of taxation systems.

Jan 1, 1932

By G. S. Cole, G. F. Bolling

Fluid flow strongly influences ingl structure and the columnar -to-equaaxed transition. Artificial flow patterns siwzilar to the nuturul ones act to induce this transition, while dampening forces act to suppress this transition. It is shown here how simple mechanical forces can be applied to a systerrz in order to induce or slipPvess relative fluid flow and the change both the structure transition and the exact structures obtained. The example used is the effect of slow rotations and oscillations 012 a cooling- ingot (of laboratory scale). The details of rotution and oscillation for various cooling rates, lenlperal~ire gradients, and sizes of ingot are related to other solidzfication variables. THE grain structure of a casting can be changed by altering the fluid motion during solidification. Just how important these changes are depends directly upon the degree to which the fluid motion can be controlled. An early step in understanding the nature and influences of fluid motion was taken by studying natural thermal convection; when a static mechanical device was used to suppress natural flow the result was opposite to that obtained when an electromagnetic device was used to augnlent flow in a pattern similar to the natural one. &apos;&apos;2 Suppression allowed more columnar growth to occur, but "augmented natural convection" brought about an earlier columnar-to-equiaxed transition (CET). Since the solidification of a free ingot must have characteristics somewhere between those displayed during suppression and augmentation, we know that natural convection must influence the CET. Further, since heat transfer in the liquid is always some time-dependent combination of convection and conduction, it can easily be guessed that the temperature gradient in the liquid is the vital factor affecting the CET.1,2 It is obvious that the structure arising from the unadulterated solidification of an ingot, without external influence, is rarely if ever the best possible one. Although the pattern of the natural fluid flow may be considered efficient, the magnitude of the flow and the heat transfer decrease freely from the outset. For a

Jan 1, 1968

By R. G. Treuting, W. C. Ellis

D. Whitwham, M. Mouflard, and P. Lacombe (British Council Research Fellow, Labratoire du Professor Chaudron, Vitry-sur-Seine; Inqenieur de Recherches, Labratoire de Vitry; and Maitre de Recherches, Labratoire de Vitry, Professeur Adjoint de Metallurgie, Ecole des Mines, Paris)—The authors&apos; work is of great interest in bringing out the geometrical relations existing between twinned lattices, and for the notion of a coincidence super lattice developed from this. We should like to point out that a similar idea was put forward by Friedel8 in his book on the subject of lattice merohedrism "merihedrie réticulaire:"—When two crystals A and B are twinned with respect to a mirror plane, there exists a common superlattice, "réseau periode," which is independent of the contact surface between the two crystals. The volume V of this superlattice is a simple multiple of the volume v of the lattice of crystals A, or B, (Fig. 5). This "multiple cell" is defined by the twin plane (p q r) and a row of atoms [h k l] normal to this plane, the base being taken as the smallest unit (two-dimensional) of this plane. Two cases must be considered. First when the multiple cell, as defined, has no atom site at its center nor at the center of its faces other than (p q r), v the twinning index is defined by —. In the second v case, when one of the two above conditions does not v apply, then the twinning index is V 2v A more intuitive definition of the twinning index would be the proportion of atoms of C, which would coincide with those of C1 when the C, lattice is imagined to extend on the other side of the contact surface. In the case of cubic crystals, the twinning index

Jan 1, 1952

By J. Szekely, V. Stanek

Heat and gas flow interactions in nonisothermal packed beds were examined in the paper. A study was made of the response of the system to a step or pulse change in the inlet gas temperature, with a fixed value of the overall pressure drop across the bed. Under these conditions the heat flow and fluid flow transients are coupled because the convective heat transfer rate is alfected by the mass flow rate of the gas which, in turn, for a fixed pressure drop will depend on the temperature profile in the system. The Problem was stated in terms of differential equations, which were integrated numerically. The parameters used in the computation were so chosen to reflect the operation of the stack region of blast furnaces and sinterbeds. The computed results showed that the pressure drop-flou1 relationships and the rate of progress of the temperature fronts (waves) were strongly interrelated and were also markedly affected by variations in particle size and in void fraction. MANY metallurgical processes involve the contact of solid particles with a gas stream in a packed bed arrangement under nonisothermal conditions. Examples are shaft furnaces, regenerators, pebble heaters, and the sinter process. Although the heat and mass transfer aspects of packed bed processing have been extensively studied, the associated flow phenomena and in particular the effects of nonisothermality on the flow, have received little attention to date. :In fact, most of the previous workers considered the flow rate of the carrier gas time invariant and independent of the heat or mass transfer processSzekely and carr2 have shown that the pressure drop-flow relationships in nonisothermal packed beds may be strongly affected by the temperature profile within the system. These authors have devised a method for relating the pressure drop to flow for a given temperature profile. thus providing an extension of the Ergun equation to steady nonisothermal systems. Finally, in a recent paper willmot3 examined the response of regenerators to externally imposed changes in the gas flow rate. Both these investigations were somewhat specialized since, in general, neither the temperature distribution nor the gas flow rate may be regarded as truly independent variables, thus the heat transfer and the fluid flow problems have to be solved simultaneously. The work reported here is divided into two parts: in Part 1 the general formulation is given and a detailed discussion is presented of fixed bed systems. Part is devoted to systems in which a gas and particulate solids are contacted in a counter flow arrangement. FORMULATION Consider a nonisothermal fixed packed bed, extending from through which a gas is flowing. The problem is to develop a relationship between pressure drop and gas flow (with the gas flow being the dependent variable) and to evaluate the rate at which a change in the gas temperature, imposed at the inlet, travels through the system. Let us consider an infinitesimal section of the bed and establish differential heat, mass, and mechanical energy balances over this region. In addition, relationships are needed describing the temperature dependence of gas density (equation of state) and the temperature dependence of viscosity. These may be written as: where c, and are constants. It is noted that in this formulation we neglected any temperature gradients within the solid particles, thus assuming these to be either sufficiently small or of sufficiently high thermal conductivity to meet this condition. The justification and consequences of this assumption will be mentioned in the discussion.

Jan 1, 1970

By C. C. Miller, C. A. Hutchinson, A. B. Dyes

This paper presents a simple and practical method for the estimation of effective permeability and reservoir pressures from the rise in bottom hole pressure when a well is shut in. The equations on which the method is based consider a stabilized well producing from a uniform formation when flow is shut off at the sand face followed by the unsteady state flow of a compressible liquid from regions far from a well to points closer in during the build-up period. An approximation for extending the method for two-phase flow in the reservoir is also presented. In order to compare the effects of extremes in the conditions existing at the external boundary of the reservoir, two general equations defining the build-up characteristics of the reservoir are shown: first, for a reservoir with constant pressure maintained at the radius of drainage, and second, for a reservoir with no influx over the radius of drainage. These equations define the build-up characteristics for the shut-in well as functions of time, the permeability and porosity of the drainage area, the viscosity and compressibility of the fluid flowing, the production rate prior to shut-in, and the radius of drainage of the well. When a well is shut in at the surface, rather than at the sand face, flow will continue into the well bore after shut-in due to the compressibility of the fluids in the bore. The effect upon the build-up characteristics of this flow into the well after shut-in has been studied by means of the electrical analyzer. From the basic relationships and consideration of the limitations due to continued flow after shut-in, methods have been developed for the estimation of the effective permeability of an area from the plot of the build-up characteristics of the well producing that area. Likewise, equations are presented for the estimation of the reservoir pressure from an early portion of the build-up curve. By means of the electrical analyzer, studies have been made concerning the variations in the build-up characteristics resulting from damaged or improved permeability in the immediate vicinity of the well bore. These studies show that the permeability estimated from the build-up curves represents the average effective permeability of the majority of the drainage area and that the permeability in the immediate vicinity of the well does not affect this estimate. Since the major portion of the drawdown is in the immediate vicinity of the well, variations in the permeability of this area greatly affect the productivity of the well as expressed by the productivity index. From pressure build-up and productivity index tests the ratio of the permeability of some arbitrarily specified area immediately surrounding the well and the effective permeability in the majority of the drainage area can be computed. This ratio is a measure of any damage to the well incurred in drilling or reworking and likewise any benefits as a result of remedial measures. In build-up tests and many other tests that are made on a producing well it is at least desirable, if not absolutely necessary, that the well be stabilized prior to testing. A method is presented here for relating the time required to stabilize a well and the reservoir and fluid properties. An equation is also presented for approximation of the length of shut-in time required to obtain sufficient build-up data for the estimation of permeability and reservoir pressure.

Jan 1, 1950