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By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By J. W. Harden

APART from the merits of the respective systems of mining under conditions alike, there is much in the nature of the coal and the measures with which it is associated, to make that system which is successfully practiced in one locality ill adapted to that of another ; the structure of the coal itself, the roof, the floor, the depth and character of the overlying strata, each exercising more or less controlling influence. Again, in the highly bituminous districts, and with such as have caking coals, where the size of the coal as it comes off the face does not affect its value, as the very smallest of it may be utilized, and in the hard, the open and free-burning coals, in some of which the round only (large coal) is merchantable,

NEW MEMBER, The following list comprises the names of those persons who became members during the period Mar. 10 to Apr. 10, 1915: Members ADAMS, Louis WINFIELD, Supt., Rolling Mills, Lehigh Plant, Bethlehem Steel Co., So. Bethlehem, Pa.. ALLEN, ARTHUR WATTS, Mine Mgr Rodeo, San Juan, Argentina., BALL, EDWIN MARCOTTEL, Mine Supt., Ishkooda. Mines, Care Tenn. Coal, Iron & R. R. Co., H.F.D. 1, Birmingham, Ala. BOLN, CHARLES A., Oil salesman 135 S. 2d St., Philadelphia., Pa. BOYD, DAVID F., Naval Officer Navy Department, Washington, D. C. CAPERTON, GEORGE HENRY Charleston, W. Va. COGGESHALL, GEORGE W., Chem. Engr., Institute of Industrial Research, Washington D C

Jan 5, 1915

By A. A. Smith, J. S. Smart

THE controlled amounts of phosphorus, arsenic, sulphur or selenium found in commercial coppers perform a variety of highly useful functions. Indeed, a large segment of modem copper technology is essentially dependent upon the presence of one or more of these elements. Consequently, the literature contains many references to their effects but the scope is broad and has been only partly covered. New data are presented herewith directed toward a better understanding of the basic behavior of these elements in copper, with particular emphasis on the composition range 0 to 0.05 per cent. These data are a part of a general program of research on the effects of impurities on the properties of oxygen-bearing and oxygen-free copper, other portions of which have been reported previously.1-2-3 Schematically, the behavior of individual elements is determined from measurements of conductivity and softening temperature,1, 2 and the binary alloys employed are synthesized from high-purity copper in order to eliminate interference from the effects of extraneous impurities. Alloys of selected composition were first prepared in the oxygen-free form by continuously casting the melts in the form of 3/8-in. diameter rod. Oxygen was added subsequently to portions of the alloys, either by remelting or by diffusion at 850°C. from a surface scale. Test wires were drawn one B. and S. number per pass, using four 30-min. 600°C. anneals at o.3125, 0.257, o.204 and o.162 in., and a final cold reduction of 95 per cent t0 0.081 in. Oxygen-bearing slugs made by remelting were hot-rolled to 5/16 in., drawn to 0.162 in., annealed for 30 min. at 600°C. and cold-drawn 95 per cent to 0.081inch. The alloys containing phosphorus, having been compounded very early in the program, were prepared in the form of 5/16-in. rod, and processed to wire with only the last three intermediate anneals listed above, all of these having been conducted in commercial nitrogen. In addition, the conductivity anneals on these alloys were also performed in the same atmosphere, and the small amount of oxygen present as an impurity in the gas resulted in some loss of accuracy at temperatures of 700° to 800°C., as will be shown later. Subsequently, the anneals for all oxygen-free alloys were conducted in hydrogen to prevent oxidation, and purified nitrogen was employed only for oxygen-bearing samples. All conductivity anneals were of one hour duration followed by a rapid quench in 10 per cent H2SO4. EFFECT OF PHOSPHORUS The widespread use of phosphorus as a deoxidant has resulted in universal appreci-

Jan 1, 1945

By R. S. Hooper

IN attempting to describe recent mining developments at the Bunker Hill mine, it may be well to recall first the old days of hand mining when holes were laboriously drilled by hand to a maximum depth of three feet, and were shot one or two at a time, in order that the miner could take advantage of every slip, crack or bedding plane, and so save as much drilling as possible. Broken muck, of course, was loaded by hand shoveling into wheelbarrows or small cars, and heading advances or stope ton¬nages were governed by the number of men that could find room to work in any given place. The first big improvement over these old methods was the introduction of the reciprocating type of air-powered rock drill. This innovation, crude as it was, enabled the miners to set up a machine and drill a complete round of holes in one shift; but broken muck was still loaded by hand, and the size and rate of advance in headings were limited by time required to remove the broken rock. The next improvement of consequence was the appearance of the hammer-type rock drill, which greatly increased drilling speed over the reciprocating type, and made possible the completion of a full cycle in one shift, by the use of crossbars in headings, and permitted drilling and mucking to be carried on at the same time. Rock drills continued to improve as time passed, and finally the smaller and more efficient mucking machines appeared on the scene, and it became possible to muck out a round of broken rock and have a clean setup for one or more drill columns and machines. A complete cycle of mucking, drilling, and blasting was completed in one shift with an average advance of five feet. These conditions prevailed for several years, but as the mine grew deeper, the distances to transport the workers grew longer, and this fact together with the shortening of the working day, soon presented the problem of attempting to complete a cycle of operations in a shift of only six hours at the working faces. Anticipating this condition, the operating heads at the Bunker Hill had started an intensive study of more and better mechanization, and over a period of comparatively few years have adopted and placed in service methods and machines that make it possible for a three-man crew to consistently advance headings seven by nine feet in cross section, at the rate of eight feet, and more, per shift, doing all the mucking, switching, drilling and loading. These improvements consist of the following major items: I. The development of a light, flexible, easily transported jumbo equipped with pneumatic columns (Fig I), that has decreased the "setting up" and "tearing down" time an average of 1 1/2 hr per shift, or 25 pct of the available working time. These jumbos were developed at the Bunker Hill mine by members of the staff and consist of two pneumatic columns attached to a suitable carriage. They fold

Jan 1, 1947

By H. R. Aldrich

This paper is not a treatise on the theory and practice of magnetic surveying. It presents a diagram upon which have been plotted observations taken with the simplest form of magnetic instrument, the lowly dip needle, over a large area astride the Lake Superior syncline of northern wisconsin. The exposures of the underlying formations are not sufficiently great in number nor fortunate in distribution to have provided the fuller understanding of the geology which has been secured by the use of the magnetic observations as an auxiliary tool or accessory in the hands of the geologist. The diagram (Fig. 2) in large part speaks for itself if studied in connection with the geological map (Fig. 1) for which it is the main control. It is presented to demonstrate the extent to which the use of such methods may aid in the solution of geological problems in a covered country. The diagram is probably unique in assembling the expression of such a wide range of formations, affected by so wide a range of secondary processes, and deformed by so many different structures in terms of magnetic variation. Few geologists outside of the Lake Superior country have had any first-hand experience in the taking of magnetic observations and the interpretation of the results in terms of geological conditions; nor have the Lake Superior men gone with the methods far afield from the mere tracing of iron formations. In more recent years the oil companies have gone heavily into investments in magnetometers, balances, and dip needles in the quest of concealed structural anomalies which are the favorable loci of petroleum accumulation. But these geophysicists come back from the fields with their collections of observations facing the question of interpreting the geological meaning of their magnetic anomalies. It is considered probable therefore, and certainly it is the hope of the writer, that the appended charts, or magnographs, which show how character of the country rock and its changes, structural strike and dip and their changes, depth of burial and its variation, contact metamorphic

Jan 1, 1929

By L. L. Wyman

Since the presentation, by the writer, of the initial paper on the embrittlement of copper,1 the subject has been investigated further along two separate lines. The first series of investigations involves the "double-deoxidized" coppers, while the second series is devoted to single deoxidizers other than those used in the investigations reported upon last year. The object of these experiments is to develop a type of copper that will show the minimum of detrimental effects after having been exposed to alternate oxidation and reduction. The fabrication of this material necessitates the use of alternate oxidizing and reducing atmospheres, at temperatures ranging up to 900" C. Following this treatment it is essential that the soundness and strength of the copper be unimpaired, even in sections of only a few thousandths of an inch in thickness. Materials The ensuing report embodies three separate groups of materials, which may be classified as follows: 1. Double-deoxidized copper using silicon and calcium boride. 2. Copper deoxidized with calcium. 3. Double-deoxidized copper using constant calcium content (0.075 per cent) plus silicon, or calcium boride. Last year, T. S. Fuller, of the General Electric Research Laboratory, suggested that if a properly deoxidized copper had sufficient deoxidizer residual in the material, this excess material might increase the resistance of the copper to the oxidation reduction cycle. In consequence of this suggestion, two small lots of "double-deoxidized" copper were prepared. The first, lot A, was made by adding 0.03 per cent silicon as the deoxidizer, following this by an addition of 0.55 per cent calcium boride immediately before pouring. The second, lot B, contained the same ingredients, but these were added in the reverse manner. Inasmuch as these lots were tested separately from the materials about to be described, it must be borne in mind that the materials cannot be grouped together, and are not directly comparable.

Jan 1, 1933

By James W. Shaffer

Aluminum is the most abundant metallic element of the earth's crust and is a constituent of nearly every type of rock (Clark, 1924, p. 13). The sources of aluminum and aluminous material most commonly used by modern industry are the bauxitic raw materials consisting of bauxite, bauxitic clay, and aluminous laterites. These are mixtures of hydrated aluminum oxide minerals and mineral impurities. End Uses Bauxite is used as an aluminum ore and in the manufacture of refractory products, aluminous chemicals, and abrasives. Other raw materials are used for aluminum ores, but their use is minor compared to bauxite. Refractory products made from bauxite are synthetic mullite, high-alumina fire bricks, castables, monoliths, cements, and ramming mixes used by the iron, steel, and cement industries. Chemicals made from bauxite are aluminum sulfate and sodium aluminate for water treatment and aluminum chloride used in refining crude petroleum. Among the abrasive products made from bauxite are coated abrasives, sharpening stones, and grinding wheels. Special grades of bauxite are used in the decolorization and clarification of raw sugar and lubricating oils. Bauxite has been used for road surfacing but mainly because other material was not more readily available. Perhaps the oldest use of bauxite and aluminous laterite is for a building stone. Ancient temples and more recent structures in India have been made from these and some varieties are suitable for decorative stone. Geology Mineralogy and Properties – Bauxite is a mineral raw material composed principally of one or more hydrated aluminum oxide minerals and impurities of silica, iron oxide, titania and elements in minor or trace amounts. The hydrated aluminum oxide minerals are gibbsite, boehmite and diaspore. Corundum is not included as a bauxite mineral although it does occur in some bauxite deposits. Boehmite and diaspore are both alumina mono-hydrates and have essentially the same composition, but diaspore has a greater hardness and a higher specific gravity because of a more tightly bonded and compacted atomic structure. Gibbsite is an alumina trihydrate mineral. Properties of bauxite minerals are shown in [Table 1].

Jan 1, 1975

By J. S. Woodward, F. B. Plummer

The measurement of the rate of flow of liquids through sands dates back to 1856, when H. d Arcyb, a French physicist, carried out his classic experiments on the flow of water through sand layers. The earliest recorded data on relationships of pressure to flow of fluids through porous rocks in this country are those of Newell 23 in 1885. The first comprehensive studies of flow were made in 1898 by King15, who measured the rate of flow of water and air through consolidated and uncon-solidated sands and published the results. From 1900 to 1920 there appears to have been little interest in permeability. In 1920 the increase in demand for oil led the U. S. Bureau of Mines to begin a series of experiments to determine subsurface relationships of oil and water and the characteristics of their flow. Mills18 studied the relationship of flow of liquids to text- and structure of the sands, and Melcher17 in 1925 made a quantitative study of effect of changes in pressure on rate of flow of crude oil through Oklahoma oil sands. Since 1930 the importance of flow measurements to production of oil and gas has been emphasized by a large number of excellent investigations. Among these the works of Fettke9.10, BarbI.2, Cloud6, Nutting24-", Bot-set4, Nevin22, Tickell32.33, Fancher, Lewis and Barnes8, Moore, Schilthuis and Hurst19, and Wyckoff, Botset and Muskat"-39 have contributed much to our knowledge of the technique of permeability measurements and to the laws of liquid and gas flow through porous sands. The application of their work has led to the establishment of laboratories for measuring the permeability and porosity of oil sands by most of the large companies. All the investigations, except those of Wyckoff, Botset and Muskat, and Moore, Schilthuis and Hurst deal with linear flow; that is, flow in a more or less straight line through a given cross-sectional area of sand. Three years ago, at the University of Texas, experiments were started to measure radial flow of liquids through sands; that is, flow from all directions toward a central opening—the conditions that operate in a

Jan 1, 1937

By John H. Hollomon, C. Zener

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By C. Zener, John H. Hollomon

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By L. S. Darken, H. A. Wriedt

An investigation has been made of nitrogen absorption by the lattice defects in a low-carbon steel afte~ Plastic deformation. Specimens in which defects were distributed by various combinations of cold rolling and vacuum heat treatment were equilibrated with controlled ammonia + hydrogen mixtures at 300° to 450°C to study the relation between the solubility and the thermodynamic activity of nitrogen. The results are interpreted in terms of nitrogen being absorbed upon two different types of defect sites, called A sites and B sites. The concentrations of these sites are calculated for specimens with various histories of straining and annealing; and the thermodynamic relations descrihing the equilibrium distribution of nitrogen among the A, B, and ordinary interstitial sites in ferrite are evaluated as follows: THE generalization that the solute atoms in a solid solution interact with imperfections in the solvent lattice is now universally recognized and the subject of an extensive literature. All types of imperfections—point, line, or surface—exhibit these interactions, but the relative importance of each type depends upon its concentration, the strength of its interaction with the particular solute atom, and whether the interaction is attractive or repulsive. The strength and sign of the interaction vary with the vectorial displacement of the solute atom from the imperfection in the crystal. The concentration of lattice defects increases during plastic deformation and the effect of the imperfections upon the solute atoms is usually perceived only after cold work or irradiation. Two experimental methods have previously been used to observe the effects of interaction between nitrogen atoms and lattice imperfections in a iron. Internal friction, which was first used for this purpose by Dijkstra,1 has been applied more often than the electrical-resistivity method of Cottrell and Churchman.2 The method of the present investigation has not been used before.* Uniform specimens of steel with a metastable defect structure are produced by cold rolling and subsequent heat treatment below the recrystallization temperature. Variations in the defect structure are obtained by varying the amount of strain and the heat-treatment conditions. The specimens are then saturated with nitrogen at moderately elevated temperatures in ammonia + hydrogen mixtures having various thermodynamic activities of nitrogen below saturation with Fe4N. From the nitrogen contents of analyzed samples, the metastable equilibria of interactions between the defects and nitrogen can be established and the concentration of sites for nitrogen atoms in the lattice defects calculated. A steel was used in the present experiments instead of purified iron or iron alloys because the amount of nitrogen absorbed at defects is larger in the steel over a much wider range of experimental conditions and could therefore be measured more accurately. The effect of alloy composition is discussed in Part II of this paper; it is sufficient to say here that impurities and phase heterogeneity in ferritic alloys favor the generation and/or retention of larger defect concentrations during plastic deformation and annealing at 300° to 500°C. MATERIALS AND EXPERIMENTAL PROCEDURE The experimental specimens were prepared from stock of a low-carbon steel, which will be called "X steel" here, with the composition: C, 0.12 pct; Mn, 0.43 pct; P, 0.010 pct; S, 0.034 pct; Si, 0.007 pct; As, 0.086 pct; Cu, 0.022 pct; Ni, 0.009 pct; Cr, 0.003 pct. The stock was all from a single ingot made by the basic open-hearth process, which was hot-rolled to strip 0.080 in. thick.. This hot-rolled strip, given the code designation "XH", was the starting material for preparing a series of cold-rolled sheets. The latter are designated "XC27",

Jan 1, 1965

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By Victor A. Phillips

A series of strips of a Ni-12.7 at. pct A1 alloy were Prepared containing cubical y'(NisAl) precipitates with edge lengths from 60 to 500A. A particle-free solution-tveated strip was included for cornparison. They weve cold-rolled 95 pct and the effects of particle size on the isochronal (1/2 hr) annealing behavior between 300° and 950°C studied (by hardness and light and electron microscopy). It ulas inferred that the particles deformed with the lnatvix becoming lamellae which remained coherent. Comparison with published data fov pure nickel showed that aluminum greatly re-tavded softening and recrystallization, but it made little difference whether or not particles were present. The presence of pakticles led to a heterogeneous distribution of precipitates after annealing at 700" to 750°C. Recovery was not detected. Recrystallization occurred by the growth of new grains into unrecrys-tallized material. In a previous study by the author,' the growth of Ll2-type ordered yl(Ni3Al) precipitates was followed in Ni-12.7 at. pct A1 alloy as a function of aging at 600" and 700°C. The particles were showo to be cubical in shape in all sizes from 50 to 3000A and remained coherent. This work was used as a guide in preparing the starting structures for the present study of the effect of these particles on the annealing behavior of heavily cold-rolled strip. Another question of present interest was whether dislocation and particle hardening were additive, since the structures before rolling ranged from solution-treated to peak-aged to overaged. Also, precipitation might occur on annealing after cold-rolling. Reference may be made to other papers2"5 for previous work in this relatively unexplored field and only some recent work will be mentioned her:. phillips2 studied the effect of deformable 0 to 590A-diam cobalt particles on a Cu-3.23 pct Co alloy rolled 95 pct and found that the particles, which rolled out into thin lamellae, impeded softening and recrystallization. Tanner and servi3 likewise studied the annealing of cold-swaged Cu-2 pct Co alloy containing 150A-diam particles and found impeding effects. Haessner et a1.,4 on the other hand, found that incoherent 2-p-diam non-deformable particles of B4C (0.04 vol pct) tended to increase the rate of recrystallization of copper rolled up to 95 pct reduction. They attributed this to the formation of new grains at the particle interfaces. Humphreys and artin' found that nondeformable silica particles in copper rolled to 30 pct reduction accelerated recrystallization if the particle spacing was large and retarded it if the spacing was smaller. Haessner et a1 4 also studied a rolled Ni-Cr-A1 alloy; however, the particles of y'(Ni3Al)-type precipitate were not put in before rolling, but separated during the isothermal annealing at 750°C. No previous work appears to have been carried out on the effect of y' (Ni3A1) particles on the annealing of Ni-A1 alloy. Hornbogen and ICreye7 redetermined the solubility c of aluminum in nickel as a function of temperature T and showed that it was given by c = 32.6 exp(-1940/RT). This relation gives aluminum solubilities of 15.1, 14.2, 12.0, and 10.7 at. pct at 1000°, 900°, 700°, and 600°C, respectively. The phase precipitated from the nickel-rich solid solution is fcc y1 (Ni3A1) which has a Cu3Au -type ordered structure8 and remains ordered up to 1000°C.B EXPERIMENTAL PROCEDURE The alloy used was identical with that used before. Chemical analysis showed 6.27 wt pct (12.71 at. pct) Al, the principle impurities being 0.065 pct Fe, 0.022 pct Co, 0.020 pct Cu, and 0.004 pct C. Bar stock of 1 in. diam was cold-swaged to % in. diam, cold-rolled to 0.300-in.-thick strip, and annealed at 900°C in dry hydrogen. It was cold-rolled to 0.100-in. thickness and solution-treated for 1 hr at 1000°C while sealed in a quartz tube in argon, quenching in iced brine with the aid of a device to snap off the nose of the tube. Lineal analysis gave an average grain size of 0.055 mm. Pieces of strip were aged at 700°C in vacuo for 30 min, 51/4 hr, and 1 week to produce nominal average particle widths of 60, 150, and 500A, respectively, as known from the previous work.' The average diamond pyramid hardness was determined. The heat-treated strips were rolled from 0.100 to 0.005 in., a reduction of 95 pct, and the rolled strips stored at about -5°C. Small pieces were annealed within 1 week for 30 min at temperatures from 300° to 950° ±2°C in a horizontal vacuum furnace. Strips were withdrawn into a cooling zone, giving an estimated initial cooling rate from 950°C of about 50°C per sec. Average diamond pyramid hardnesses were determined on a lightly electropolished spot on the surface of each strip using 300-g load. Each point on the softening curves represents a separate annealed specimen. Sections containing the rolling direction were examined by optical metallography. Selected specimens were electrothinned to the center plane' and examined by transmission at 100 kv in a Siemens Elmiskop I electron microscope. It is well-known that changes in the structure tend to occur when a deformed strip is electrothinned below a thickness of a few hundred angstroms, although this is less serious with a material such as nickel which has a high melting point, and also is apt to be less serious when particles are present. Observations were nevertheless confined to thicker regions of the foils with estimated thicknesses over 1000A. No changes were observed due to beam exposure.

Jan 1, 1968

By J. L. Dumanoir, Maurice Martin

The induction-electrical log is a combination of a SP curve, a short normal curve, and an induction log; all three logs being recorded simultaneously in a single run. The spacing of the short normal is 16 in. The induction log is designated as 5FF40, which means that the sonde involves five coils and a focusing system, and that the distance between the main coils is 40 in. Examples of induction-electrical logs are shown in Figs. 13 and 15. The right-hand track contains the induction conductivity curve. The scale of this curve is linear with the units of conductivity, i.e., mhos/m or millimhos/m (mmhos/m), increasing from right to left. The same curve can be read in the reverse direction as a resistivity log, with a hyperbolic scale. In the middle track, the solid curve represents the short normal. (An amplified short normal is also shown in Fig. 15). The dotted curve is the resistivity curve of the induction log, i.e., the reciprocal of the conductivity curve, recorded with the same linear scale as the short normal. The SP is in the left-hand track. In this combination, the SP curve and the 16-in. normal are the essential correlation curves, as in the conventional electrical log. The induction log provides a more accurate and detailed record of formation boundaries than the conventional log, especially in hard rock territories. Furthermore, the induction-electrical log makes possible the determination of fluid content, particularly in thin beds—at least qualitatively and very often quantitatively. In such thin beds, because of the adverse effect of the adjacent formations, the responses of the conventional devices are generally doubtful and/or incom-plete. Another advantage of the new combination is that the induction log is little affected by the presence of thin hard streaks interbedded within the permeable sections, whereas such occurrences are the cause of serious distortions of the long normal and lateral curves. The evaluation of saturation from any resistivity log implies the knowledge of the true resistivity R, of the bed and of the resistivity R.. of the flushed zone, or at least of the ratio Rxo/Rc. With the induction-electrical log run in fresh mud, the 16-in. nor-mal has a smaller radius of investigation than the induction log, so that the former reads closer to R.. and the latter closer to Rt. Thus, it has been observed that the ratio of the 16-in. normal to the induction log readings can be used as a basis for the interpretation in terms of saturation, with the help of appropriate charts. The purpose of the present paper is essentially to explain this procedure and to provide the corresponding charts. On the other hand, when a formation is deeply invaded, the response of any log (in particular the induction log) depends upon the radial distribution of formation resistivities behind the wall of the hole, which itself is a function of the arrangement of the fluids saturating the formation pore spaces. This paper, accordingly, will begin with a schematic description of the distribution of fluids and resistivities in the invaded zone. Next, some essential characteristics of the induction log will be reviewed. Finally, the determination of the interpretation charts and their application will be explained. The discussion will be confined to the case of fresh muds, i.e., muds whose resistivity is at least five times as great as that of the formation waters. With the present equipment the induction log is not well adapted for logging in salty mud. The Laterolog and guard electrode log are at their best under conditions of low resistivity mud. Accordingly, when these tools were introduced a few years ago, the use of salty mud was recommended. Now, with the introduction of induction logging, spe-

Jan 1, 1958

By A. D. Hodges

The great mining region of Peru is a mountainous belt of country, running nearly the whole length of the republic, and comprising the two grand ranges of the Andes with the elevated table-lands between them. On the east of this belt are the extensive plains and fertile valleys of the Amazon and its tributaries. On the west is a narrow strip of coast 20 to 50 miles wide, for the most part a sandy desert, but producing abundant crops where irrigated ; and here are found petroleum (Department of Piura), salt (at Huacho and elsewhere), nitrate of soda in enormous amounts at the south, silver in a few localities (Province of Tarapaca), copper and other mineral products. The Western Cordillera, running nearly parallel with the shoreline, rises like a wall on the eastern side of the coast-belt, with passes from 15,000 to 18,000 feet high and peaks attaining 18,000 to 20,000 feet. Further east, at a varying distance, is the Eastern Cordillera, composed of broken mountain ranges which, considered as one group, have a general parallelism with the western chain, but individually vary greatly in direction, sometimes running nearly east and west, in places projecting out into the Amazonian lands, or here and there curving around to unite with the western ridge, and with this enclosing immense inter-alpine plains. These general features are indicated in Fig. 1. The surface of these plains is uneven and traversed by lower ranges of hills which surround large lakes, or rolling pampas, or fertile valleys; and through many of these last run rivers of considerable size. The whole country has a high altitude (averaging up to 15,000 or 16,000 feet), and slopes gradually north and east towards the Amazon, into which drain all its waters. Its bounding mountain chains are scored on all sides by narrow, picturesque and pre-

Jan 1, 1888

By Francis M. Rich

BEFORE the world-wide depression, the primary purpose of most blast-furnace operators was to produce a maximum tonnage of pig iron per day for each furnace in blast. Some attention was paid to the conservation of labor and raw materials, but the idea was well established that low-cost pig iron was attainable only when each furnace was producing a high tonnage. After the depression had set in, the picture changed considerably. Each blast-furnace operator was forced to run his plant in a manner that best fitted the economical set-up of his company. A great deal of thought was expended on the different methods of operation, always with the idea of making each product in a way that would best serve his company financially. Because of this abnormal condition, the blast-furnace man was compelled to indulge in various practices of which many had been believed to be next to impossible up to that time. The ultimate purpose of these innovations was either one or a combination of the following: 1. To produce only enough pig iron for immediate consumption at a minimum cost. 2. To produce gas for boiler or mill use to supplant some higher priced fuel. 3: To consume the coke produced at the coke plant, which was often viewed as a byproduct. 4. To protect the cash position of the company. These conditions were met by diverse methods, some of which were: 1. Slow or decreased wind. In some instances the blast blown was held as low as 25 per cent of the normal volume. 2. Intermittent operation, in which the furnaces were shut down or "fanned" at frequent intervals.

Jan 1, 1935

By Alexander Squire

A BRIEF study of the effects of material and processing variations upon the tensile properties of steel formed from mixtures of iron and carbon was made in order to provide information regarding the .properties obtainable in iron-carbon compacts as influenced by forming pressure, sintering temperature, and graphite particle size. Sintered steels formed from mixtures of iron and graphite have been studied by Stern,1 who investigated the effect of various percentages of graphite on compacts formed from electrolytic iron that were repressed and heat-treated after sintering. A further study, by Stern and Greenberg,2 is concerned with the heat-treatment of steels formed by the carburization of iron compacts, and Margolies3 has reported work on the simultaneous sintering and carburization of iron-powder parts. Glauch4 investigated the effect of various types of graphite on the properties of iron-carbon powder alloys but did not determine the effect of different particle sizes of the same graphite alloyed with different types of powder. In the investigation reported in this paper, powders typical of those produced by electrolytic deposition and the decarburization of shotted steel scrap were used. The powders were mixed by tumbling in a jar mill with graphite powder ground to an average particle diameter of 2, 4, 6, and 16 microns (as determined by microscopic measurement). The properties of the iron and graphite powders are presented in tabular form as Table I. In order to obtain the maximum information from a minimum number of test specimens, the study was divided into two sections with one set of specimens treated identically in each section as a basis for comparison. In the first section, iron powder produced by the shotting and subsequent decarburization of scrap steel was mixed with 2-micron graphite powder, pressed at 50,000, 100,000, and 200,000 psi, and sintered in hydrogen at 1200°C for the periods of time ranging from 15 to 120 minutes. In the second section of the investigation, electrolytic iron powder was mixed with graphite of an average particle diameter of 2, 4, 6, and i6 microns, pressed at 100,000 psi, and sintered at temperatures ranging from 1000° to 1200°C. for periods of time of 30 to 180 minutes. By following this procedure an indication of the effect of the following variables upon the density and tensile properties of iron-carbon powder compacts was obtained: (I) forming pressure, (2) sintering time, (3) particle size of graphite powder, (4) sintering temperature, (4) type of iron powder.

Jan 1, 1947

By M. Bevis, E. O. Fearon, P. C. Rowlands

Fe-Ni and Fe-Ni-C martensite specimens have been deformed in compression at room temperature and the habit planes of operative deformation twins determined by two-surface optical trace analysis. The full orientations of the martensite crystals were determined from divergent X-ray beam diffraction patterns. The experimental results are in excelled agreement with predicted twinning modes. In particular, the habit planes of some deformation twins in bcc martensites are consistent with a "Type XI compound'' twinning mode with Kl, Kz, 71, 77~ elements given by {5, 8, 11) {ioi}, (33) (ill) Tetragonal derivatives of this mode are operative in bct martensites. UnUSUAL deformation twinning modes have been reported by Richman' to occur in Fe-Ni-C martensites with bcc and bct structures. The twin habit planes were determined by single-surface trace analysis (pole locus method) and the remaining twinning elements were determined from the geometry of twin-twin intersections. The indices assigned to the observed habit planes are (3 101, "(089)" and "{0, 1,13)" or "{1,2,7} ", and only in the first case do the twinning elements correspond to a predicted twinning mode. This is mode 1.4 in the paper by Bevis et al. The results presented in Ref. 2 indicate that previously unpublished bcc and bct modes should be operative in preference to the (130) mode and anomalous modes reported by Richman. In view of these results and the uncertainties involved in determining habit planes from single-surface trace analysis and twinning elements from twin-twin intersections5 a two-surface trace analysis of deformation twins in Fe-Ni and Fe-Ni-C martensites has been carried out. EXPERIMENTAL PROCEDURES Two alloys with compositions Fe-23 pct Ni-0.6 pct C and Fe-30.4 pct Ni were prepared from 4N pure materials by induction melting under a vacuum of 10"5 mm Hg. The alloys were homogenized at 1350'~ for 5 days. Both of these alloys are austenitic at room temperature with M, temperature - — 50"C. The aus-tenite grain size of the Fe-Ni-C alloy was approximately 300 to 400 p. The Fe-Ni alloy was remelted in a vertical tube furnace and the melt lowered slowly from the hot zone of the furnace to produce s ingle -crystal austenite specimens. Specimens approximately 10 by 5 by 5 mm were cut from the ingots and quenched to various temperatures below the Ms temperature. The specimens were elec-tropolished in a 10 pct perchloric acetic electrolyte before being deformed in compression at room temperature. Martensite plates which exhibited profuse deformation twinning were selected for analysis and the specimen polished on a second surface such that the two surfaces which contained the martensite plate enclosed an obtuse angle of approximately 145 deg. The specimens were then electropolished to reveal the traces of the deformation twins on both surfaces. The full orientations of the martensite crystals were determined using a divergent X-ray beam technique (Kossel line technique) employing an AEI SEM2 electron probe microanalyzer. Details of this technique which include a detailed description of the Kossel camera attachment to the microanalyzer used in the present experiments have been discussed elsewhere.3 Only additional details relevant to this investigation are discussed here. The specimens were mounted with one surface normal to the incident electron beam as illustrated schematically in Fig. 1. The martensite plates to be analyzed were located using the normal scanning equipment of the microanalyzer. The position of the electron beam and hence the position of the source of divergent X-rays generated within the crystal could be located to within 1 p. Exposure times of approximately 8 to 10 min were required for back-reflection Kossel patterns and it was found that useful diffraction patterns could be obtained consistently from heavily deformed martensite plates. A reference line (carbon contamination mark) produced on the two surfaces of the specimen by scanning the electron beam in a direction having a known relationship with the reference !ine in the X-ray camera enabled the full orientation of the crystals to be determined. Martensite plates with widths as small as 8 p could be oriented using this procedure. The Kossel line patterns were interpreted using the charts developed by Rowlands and ~evis~ as generally

Jan 1, 1969

By John Buch

NEARLY 25 years ago operating officials in the northern anthracite field were confronted with the problem of profitably mining virgin beds of thin coal (those 48 in. and under) or destroying them by mining under-lying thick beds. To solve this problem costly hand-mining methods were replaced by cheaper mechanical methods, which eliminated the need for the lifting of bottom or the brushing of top in excessive quantities, which was essential if proper height for hand loading' was to be provided. During this period long-face mining was an outstanding development. In its favor in comparison with any other method were the ease with which undercutting machines could be used, a differential in powder cost of about fifteen cents per ton in favor of this method over mining from a solid chamber or pillar face, and a greater production per day from a single working place, resulting in lower capital expenditures for a given total production, closer supervision and lower transportation cost. The long faces were drilled by jackhammer and undercut by machines. The coal from the cut was loaded into mine cars placed on the gangway road by means of a double-drum mechanical scraper engine and a mechan-ical V-type scoop. A tugger hoist was used to spot empty cars at the loading point from a supply placed at the operation by an electric mine locomotive. During loading the roof was supported by vertical wooden props paralleling the face. After the loading was completed the scraper engine and the ropes that had been used to propel the scoop in the loading of coal transferred the props to and along the face. A row of unfilled cogs was then built parallel to the new face and about 6 ft. from it. These cogs were usually made 6 by 3 ft., the longer dimension paralleling the face; they were placed on an average at 12-ft. centers. These wooden cogs were left in place and were buried later by falling roof. Attempts to remove them were never successful. When a new long face was started, the cog spacing would be increased to about 20-ft. centers. As successive cuts were made, weight would begin on the cogs, and they

Jan 1, 1939