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By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By E. F. Northrup

THESE brief notes respecting the properties of pure tin that make it useful as a pyrometric substance summarize information gathered by the writer In an extensive experimental investigation on the electrical properties of metals in the molten state. Tin in quantities sufficient for pyrometric purposes may be obtained at relatively low cost and in a state of high purity. The metal melts at 232° C. and, according to determinations made by Greenwood,. 1909, does not begin to boil until a temperature of 2270° C. is reached. The writer can assert, from personal observations carefully made, that tin shows no tendency to boil at a temperature of 1680° C. If Greenwood's observations are correct the temperature interval, 2038° C., in which tin exists as a liquid under atmospheric pressure, exceeds that of any other substance. It has never been observed, as far as the writer is aware, that tin forms any chemical union, as carbide, with carbon at the highest temperatures at which it can exist as a liquid. It is quite certain from the writer's personal observation that tin heated in Acheson graphite to 1680° C. remains chemically uncontaminated. Wires of pure tungsten do not dissolve in molten tin at temperatures at least as high as 1680° C. Tungsten wires or rods may, therefore, be used as electrodes dipping into molten tin when required for measuring the resistance of the molten metal at very high temperatures. When tin is raised to a high temperature in a covered graphite container, the CO atmosphere that exists above its surface has a reducing action, which maintains this surface of mirror brightness. Incidentally, tin maintained molten in a crucible of Acheson graphite makes a most excellent bath into which may be inserted several pyrometers that are to be intercompared at the same temperature.

Jan 8, 1919

By Charles W. Chesterman

Perlite is a glassy volcanic rock which will, upon rapid controlled heating, expand or "pop" into a frothy material of low bulk density, valued as a lightweight aggregate. The term perlite also is applied to the expanded product. The chemical composition of perlite ranges from that of rhyolite to that of andesite; the water content ranges from 2 to 5%. Most perlite is pale gray, but some is black, brown, or even green. Inclusions in perlite are common and include phenocrysts of quartz, feldspar, biotite, and hornblende, and miscellaneous rock fragments. Occurrences of perlite are restricted to areas of Tertiary and Quaternary volcanic rocks. Perlite occurs as flows associated with thick accumulations of pyroclastic debris and other flow rocks, as dikes, sills, domes, and as selvages of intrusive bodies of volcanic rock. Individual flows of perlite range in thickness from a few feet to as much as 100 ft and commonly cover several square miles. Dikes and sills of perlite generally are small, but domes generally are substantial in size and may be as much as several miles in diameter. Most perlite deposits are large enough and topographically situated so as to lend themselves to low-cost open pit mining methods. Conventional equipment is employed in the mining of perlite. Although milling procedures may appear to be simple, care is exercised in order to produce a carefully sized product and to minimize the production of excessive quantities of fine materials, which have limited use and are considered as waste. Perlite is processed, or "popped," in one of two basic types of furnaces: horizontal rotary or vertical stationary. Both types of furnaces include product collection and dust control systems. Many commercial deposits of perlite are known to occur throughout the world, and although no exact estimate of reserves is available, there appears to be an adequate supply to meet current and future worldwide requirements. End Uses The uses of expanded perlite are many and varied and are based primarily upon its physical and chemical properties. Because of its (1) low bulk density, which generally ranges between 2 and 20 lb per cu ft; (2) low thermal conductivity "K" factor (Btu per hr per sq ft per OF per in, of thickness), which ranges between 0.267 for loosely packed perlite (bulk density of 4.48 lb per cu ft) to 1.25 for perlite gypsum plaster; (3) high resistance to fire; and (4) low sound transmission, expanded perlite is used to a great advantage as aggregate and insulating material in the construction industry. Early uses of perlite were related exclusively to the construction industry, which now consumes about 60% of the domestic production. The primary use of perlite now is as aggregate in insulation boards. Other uses of perlite in 1971 were as aggregate for plaster, horticultural aggregate, low-temperature insulation (cryogenics), and concrete. Because of its low thermal conductivity ("K" factor), high adsorption of sound, low bulk density, and fire resistance, perlite aggregate plasters hold many advantages over conventional plaster. Perlite aggregate plaster lends itself to machine applications, dries quickly, and has relatively high elasticity which reduces cracking after drying. These same features make perlite useful as aggregate in portland cement concrete and asphalt concrete for construction wherever weight reduction, insulation, and acoustics are of prime importance. Perlite-portland cement concrete offers up to 20 times more thermal insulation than conventional concrete, and because of this it finds wide application in roof decks and floor fill in multistory buildings, in

Jan 1, 1975

By Clarence Zener

The heat-treatment of steels will not pass from the stage of an art into that of a science until the mechanism of the phase transformations associated therewith is thoroughly understood. Such an understanding will involve two distinct types of inquiry: (I) the direction of the transformation, (2) the speed of the transformation. The first type of inquiry, which involves only the equilibrium relations between the various phases in steel, is the subject of the present and of a succeeding article; the second type, which involves the kinetics of transformations, will be the subject of a later article. In order that a theory of equilibrium relations may give useful information, certain experimental data must be put into the theory. It is customary for these data to be of a thermal nature. In the system discussed herein—steel—such thermal data are very scarce. In medium-alloy steels another type of data might possibly be used. In these steels the concentration of solute is so low that it may be possible to use the approximation of dilute solutions, an approximation that leads to linear relationships. The unknown functions, or constants, may then be determined in some cases from the binary iron-alloy system and in other cases from the ternary iron-carbon-alloy system. From the functions, or constants, so determined may then be computed the equilibrium relations in more complex medium-alloy steels. In the present article this second approach is used, the necessary experimental data 'being obtained from the simple binary and ternary equilibrium diagrams. Fundamental Equations In this article are derived the equilibrium relations between the gamma, alpha and cementite phases. In these three phases all important alloying elements except carbon form substitutional solutions, each alloying atom occupying a potential site for an iron atom. Carbon, on the other hand, forms an interstitial solution. In the face-centered cubic gamma phase, the interstitial positions are at the center of the unit cube and at the centers of the cube edges. There are therefore four interstitial positions per unit cell, or one per iron atom. In the body-centered cubic alpha phase, the interstitial positions are probably at the face centers, and also at the centers of the edges, which are crystallographically equivalent to the face centers. There are therefore six interstitial positions per unit cube, or three per iron atom. In cementite, (Fe, Alloy)3C, the carbon atoms may. be regarded as filling all the lattice positions of a given type. The introduction of the fundamental the of equilibrium has presented the author with a quandary. These equations are formally so similar to other equations that have been derived1,2 for related systems that they may appear to some readers

Jan 1, 1947

By Clarence Zener

The heat-treatment of steels will not pass from the stage of an art into that of a science until the mechanism of the phase transformations associated therewith is thoroughly understood. Such an understanding will involve two distinct types of inquiry: (I) the direction of the transformation, (2) the speed of the transformation. The first type of inquiry, which involves only the equilibrium relations between the various phases in steel, is the subject of the present and of a succeeding article; the second type, which involves the kinetics of transformations, will be the subject of a later article. In order that a theory of equilibrium relations may give useful information, certain experimental data must be put into the theory. It is customary for these data to be of a thermal nature. In the system discussed herein—steel—such thermal data are very scarce. In medium-alloy steels another type of data might possibly be used. In these steels the concentration of solute is so low that it may be possible to use the approximation of dilute solutions, an approximation that leads to linear relationships. The unknown functions, or constants, may then be determined in some cases from the binary iron-alloy system and in other cases from the ternary iron-carbon-alloy system. From the functions, or constants, so determined may then be computed the equilibrium relations in more complex medium-alloy steels. In the present article this second approach is used, the necessary experimental data 'being obtained from the simple binary and ternary equilibrium diagrams. Fundamental Equations In this article are derived the equilibrium relations between the gamma, alpha and cementite phases. In these three phases all important alloying elements except carbon form substitutional solutions, each alloying atom occupying a potential site for an iron atom. Carbon, on the other hand, forms an interstitial solution. In the face-centered cubic gamma phase, the interstitial positions are at the center of the unit cube and at the centers of the cube edges. There are therefore four interstitial positions per unit cell, or one per iron atom. In the body-centered cubic alpha phase, the interstitial positions are probably at the face centers, and also at the centers of the edges, which are crystallographically equivalent to the face centers. There are therefore six interstitial positions per unit cube, or three per iron atom. In cementite, (Fe, Alloy)3C, the carbon atoms may. be regarded as filling all the lattice positions of a given type. The introduction of the fundamental the of equilibrium has presented the author with a quandary. These equations are formally so similar to other equations that have been derived1,2 for related systems that they may appear to some readers

Jan 1, 1947

By Clarence Zener

THE heat-treatment of steels will not pass from the stage of an art into that of a science until the mechanism of the phase transformations associated therewith is thoroughly understood. Such an under- standing will involve two distinct types of inquiry: (I) the direction of the trans- formation, (2) the speed of the transformation. The first type of inquiry, which involves only the equilibrium relations between the various phases in steel, is the subject of the present and of a succeeding article; the second type, which involves the kinetics of transformations, will be the subject of a later article. In order that a theory of equilibrium relations may give useful information, certain experimental data must be put into the theory. It is customary for these data to be of a thermal nature. In the system discussed here in steel such thermal data are very scarce. In medium-alloy steels another type of data might possibly be used. In these steels the concentration of solute is so low that it may be possible to use the approximation of dilute solutions, an approximation that leads to linear relationships. The unknown functions, or constants, may then be determined in some cases from the binary iron- alloy system and in other cases from the ternary iron-carbon-alloy system. From the functions, or constants, so determined may then be computed the equilibrium relations in more complex medium-alloy steels. In the present article this second approach is used, the necessary experimental data being obtained from the simple binary and ternary equilibrium diagrams. FUNDAMENTAL EQUATIONS In this article are derived the equilibrium relations between the gamma, alpha and cementite phases. In these three phases all important alloying elements except carbon form substitutional solutions, each alloying atom occupying a potential site for an iron atom. Carbon, on the other hand, forms an interstitial solution. In the face-centered cubic gamma phase, the interstitial positions are at the center of the unit cube and at the centers of the cube edges. There are therefore four interstitial positions per unit cell, or one per iron atom. In the body- centered cubic alpha phase, the interstitial positions are probably at the face centers, and also at the centers of the edges, which are crystallographically equivalent to the face centers. There are therefore six interstitial positions per unit cube, or three per iron atom. In cementite, (Fe, Alloy)3C, the carbon atoms may be regarded as filling all the lattice positions of a given type. The introduction of the fundamental equations of equilibrium has presented the author with a quandary. These equations are formally so similar to other equations that have been derived1,2 for related systems that they may appear to some readers

Jan 1, 1946

By William C. Marshall, Frank G. Norris

THE term "total operation" is meant to include problems that cannot be answered from the standpoint of either the blast furnace or the open hearth separately but must be studied by considering the interrelations of these two processes. There are other ways of expressing this idea, such as reference to the blast furnace and the open hearth as an integrated process or by emphasizing the interrelation and interaction of the two processes. Much progress has been made in metallurgy and other fields by breaking complicated processes and reactions into simpler parts and studying each of these intensively. This intensive study frequently is done under the controlled conditions of the laboratory experiment. The entire process is understood better by this specialized study of each of its parts. This procedure is so satisfactory that an understanding of unit operations is a fundamental requirement of chemical engineering. Much discussion of the open-hearth process is in terms of one heat or one furnace. By this is meant that the conclusions apply to one furnace, wherever it may be. Furnaces seldom occur singly; they are located in groups and these groups are located in steel plants having characteristic blast-furnace equipment. Problems that are affected by the number of furnaces operating, by the number of blast furnaces in the plant and by the fact that the open hearth shop is dependent on the blast-furnace capacity rather than on its own needs for the amount of iron available are among those which, in contrast to "unit operations," we have chosen to call "total operations," Many of these problems, such as charging delays and the general mechanical problem of material handling, are so familiar that merely to define "total operations" brings them to mind. These problems are of such importance that already they have received careful thought and study and probably will merit further study. As will be shown later, these mechanical problems are so intimately related to metallurgical problems of total operations that the effect of certain changes cannot be ascribed with certainty to either a mechanical or a metallurgical cause entirely. Although the problems coming under the general term of "railroading" are included in the problems of total operations, two others are selected for the discussion of this paper. One of these is strictly a problem of composition; the other is strictly a problem of tonnage production. The problem of phosphorus is present whenever basic open-hearth slag is used in the blast-furnace burden. This practice has not secured universal acceptance chiefly because of difference in preference for high-manganese or low-manganese pig iron. If high-manganese (2.00 per cent) iron is to be made, open-hearth slag as a source of manganese is usually cheaper than man

Jan 1, 1943

By L. Grånäs, B. Aronsson

In a recent study of Fe-Si alloys Walter and Koch' observed pairs of dislocations in Fe-6.25 pct Si crystals rolled to reductions of 10 pct and subsequently annealed for 1 hr at 650°C. They interpreted these pairs as being due to stacking faults. From the spacing of the dislocations a stacking-fault energy of 15 to 19 ergs per sq cm was calculated. These authors did not pay any attention to the order -disorder phenomena in Fe-Si alloys. It is the purpose of this communication to report some preliminary results from a study of ordering and its influence on the plastic deformation of Fe-6.0 pct Si alloys. Our results suggest that the dislocation pairs observed by Walter and Koch may have been due to long-range order rather than to stacking faults. The alloys used in this investigation were prepared from pure electrolytic iron and silicon and were melted in argon. After hot working, strip tensile specimens were machined to a gage length of 70 mm and a thickness of 1 mm. The specimens were heat- treated for 2 hr at 1000°C, furnace-cooled, and subsequently deformed 2 pct in tension at 400°C. The strain rate was 5.6 X lo-' sec-'. Thin foils of the deformed specimens were prepared by means of the Bollman technique and examined in a Siemens Elmis-kop I at an accelerating voltage of 100 kv. In the Fe-Si system long-range ordering occurs at a silicon content of about 6 pct Si. In our alloys evidence for ordering is given by selected-area diffraction patterns which show extra reflections consistent with a super lattice of the D0 9 type. In addition, the dislocation arrangement in deformed specimens indicates that long-range order is present. A typical mi-crophotograph of a thin foil is shown in Fig. l. The dislocations are usually straight and parallel and laying in distinct directions. In the commonly observed (111) zone the projections of the dislocations are close to (113) and (oil). Observation of the image position indicates that the two dislocations in a pair have the same Burgers vector and hence constitute a superlattice dislocation.~ According to theory3 a superlattice dislocation in the DO3 structure consists of four ordinary dislocations connected by two types of antiphase boundaries as shown in Fig. 2. In our specimens only two dislocations in each pair have been observed, Fig. 1. The problem is to decide whether the area between these is a NN or a NNN antiphase boundary. Dark-field images using the (200) reflexion (the indices are defined with respect to the DO3-type superlattice) can

Jan 1, 1968

By D. J. Schmatz

DISCUSSION OF RESULTS The qualitative correlation between low-temperature ductility and prior high-temperature creep strain in nickel obtained in this investigation confirms the result obtained on high-purity brass by Chen and Machlin. However, the quantitative effect is much smaller in nickel. Comparison can be made on the basis of a prior high-temperature strain that is a certain percentage of the total high-temperature elongation to rupture. In the research of Chen and machlin, the prior high-temperature strain of 1/2 pct equaled 8.5 pct of the total high-temperature elongation at rupture. For nickel, in our experiments, 8.5 pct of 21.2 pct equals 1.8 pct. For eh = 1.8 pct, the loss in ductility in percent equals x 100 = b.5 pct. That is, for equivalent bo Formation of Beta Manganese-Type Structure in Iron-Aluminum-Manganese Alloys D. J. Schmatz IRON-aluminum alloys have gained much interest in the past few years for use as a base material for elevated-temperature alloys because of their excel- high-temperature strain the loss in low-temperature ductility is 8.5 pct for nickel as compared to 60 pct for pure a, brass. It is also interesting to note the observation that in nickel the low-temperature fractures, even at the most extreme high-temperature pre-strain, were partly trans crystalline and partly intercrystalline. In the case of a brass, these fractures were completely intercrystalline. According to the data on the percent of the grain boundary area that is cracked, at 22 pct high-temperature elongation, about 12.5 pct of the grain boundary area does not carry load. Thus, the inter-crack areas are carrying a stress that is about 11 pct higher than the nominal stress. A simple model predicts that the overall elongation, which is primarily the elongation in the bulk of the specimen, will correspond to the nominal stress when the stress in the intercrack area equals the tensile strength. Quantitatively this model predicts the equation The form of this equation will agree with that found if the strain-hardening exponent, n, equals unity. Actually this model is too gross an approximation to yield good quantitative results. The question naturally arises as to whether in ordinary hot-working, such as hot-rolling, intercrys-talline cracks are introduced that affect the low-temperature properties. It appears that the answer is that such a possibility cannot be overlooked, if the hot-working induces tensile stresses at temperatures above the equicohesive temperature and if the material tends to be notch sensitive at low temperature. ACKNOWLEDGMENT This research was supported by the Aeronautical Research Laboratory, Directorate of Research, Wright Air Development Center, United States Air Force. REFERENCES lC. Zener: Fracturing of Metals, 1948, Cleveland, ASM. 'H. C. Chang and N. J. Grant: Mechanism of Intercrystalline Fracture. AIME Trans., 1956, voL 8, p. 544; lownal of Metals, May, 1956. 'E. S. Machlin. CreepRupt ure by Vacancy Condensation, AIME Trans., 1956, vol. 8, p. 106; lownd of Metals, February, 1956 'C. Chen and E. S. Machlin: On a Mechanism of High-Temper at ure Inter-crystalline Cracking, lownd of Metals, July. 1957. p. 829. Alloys lent oxidation resistance. Binary alloys of aluminum in iron are ferritic and consequently have poor hot strength. Alloys of iron-aluminum-manganese were made in an attempt to produce an austenitic alloy containing sufficient aluminum to retain the oxidation resistance of binary alloys of iron-alumi-

Jan 1, 1960

By James E. Harding

The usual method of sampling mineral deposits is to drill holes and assay the sludge or core. Though the results thus obtained may not represent the true average value of the deposit, it is on these results that estimates of practically all large orebodies are made. In a large number of cases, the results of exploitation fall far short of the estimated value of the orebody. The standard method of making these estimates is to find the cubic contents of triangular prisms, in the apexes of which the drill holes are placed, by. multiplying the surface area by the average depth of the ore in the three drill holes and then multiplying the cubic contents by the specific gravity of the ore or rock to find the tonnage. The assay value is found by dividing the sum of the products of the depth of ore in each hole and the corresponding assay value by the sum of the depths of the ore in the three holes. As the latter part of this method is subject to many mathematical errors, it should not be depended on. Some engineers, therefore, use a discount factor, but as this factor is either arbitrarily selected or is obtained by obscure methods, the results are no better than guesswork. The standard method is correct when the drill holes are so laid out that the triangular prisms are equilateral in cross-section. But as ore deposits cannot always be drilled into at regular intervals and because of the human factor, if many holes are drilled, triangular prisms of all degrees of angularity are produced. In such cases it is necessary to assume that the influence of the different holes is not the same in all directions, which assumption of course is absurd. The area of the triangular prism is usually found by scaling; an ore-body of sufficient size to justify churn drilling is too large to be handled conveniently on maps having a scale larger than from 1000 to 1 to 1,500 to 1 and maps of such scales cannot be accurately measured. A variable is thus introduced in the first operation. In addition, the scaling is frequently done from blueprints, which sometimes shrink as much as 4 per cent. between printing, washing, and drying. The error due to scaling may be eliminated by surveying the location of each hole and

Jan 1, 1922

By Webster Hodge

MALL generators and motors are required to Soperate, in some critical applications, at temperatures where cold-worked silver-bearing copper re-crystallizes. Copper containing up to 30 oz Ag per ton has been used for many years to build the highest grades of commutators and slip rings. With failure of commutators impending because silver-bearing copper cannot withstand the stresses imposed at these higher temperatures, Cr-Cu was tried as a substitute with varying degrees of success. Cr-Cu proved difficult to fabricate because a critical heat treatment was necessary to obtain sufficient ductility. Besides, its rupture strength was shown to be low at operating temperatures, its electrical conductivity lower than desired, and its cost high. Furthermore, it often contained hidden flaws. The Nippert Electric Products Co. set out to find a better material by undertaking a research project with the stated objective of providing a material suitable for commutators that would have 1) a softening temperature above 750°F (400°C), 2) a minimum electrical conductivity of 90 pct of that of pure copper, 3) a strength not less that that of cold-worked silver-bearing copper, and 4) a materials cost of not over 1.5 times the cost of copper containing 25 to 30 oz Ag per ton. No commercial alloy met these specifications. However, it was found that copper containing from 0.18 to 0.35 pct Zr could be produced quite easily in the laboratory, and promised to fulfill the major requirements noted above. Interest naturally centered in the lower part of this composition range, since such alloys gave somewhat better electrical conductivities, and were lower in

Jan 1, 1958

By Joseph S. Malesky

As essential as the discovery of coal was to our state of advancement, the discovery and development of explosives marks one of the most important findings in the history of civilization. For this reason explosives are rightfully referred to as the forerunner of progress. Without explosives our vast economic enterprise concerning the mining of coal, copper, iron, aluminum, and various other ores could not function. Explosives are used in all kinds of construction works, in the razing of old buildings, blasting of trenches, driving of tunnels, and in many other instances common to our everyday life. An explosive may be defined as a substance (usually a mixture) that, where flame or shock is applied, yields readily to rapid combustion or oxidation, accompanied by the formation of such relatively large quantities of gases as to produce much violence and pressure which, in turn, react against their surroundings and cause what is termed an explosion. By their very nature the action of explosives is destructive and disruptive of adjacent materials. Decomposition of explosives can occur through deflagration, which is rapid burning or combustion, as in the case of black powder, or through detonation, which is an almost instantaneous disruption, as in the case of dynamites and blasting agents. HISTORY OF BLASTING WITH EXPLOSIVES At one time workmen obtained stone blocks for building by grooving the rock with crude picks, driving wooden wedges into niches in the rock, and pouring water on the wedges; the swelling of the wood forced out the blocks. As late as the 17th century, fires were placed against the face of rock to crack it, and water was sometimes dashed on the heated rock to shatter it by sudden cooling. The progress of our country is synonymous with advancement of the improved manufacture and extended use of explosives. Coal had been

Jan 1, 1973

By W. S. McCain, B. A. Wilcox, A. H. Clauer

The creep and creep-fracture behavior of a Ni-200-2Th0, alloy has been studied over the temperature range 816° to 1038°C and stress range 4000 to 19,000 psi Specimens having their axes either parallel or transverse to the final sheet-rolling direction were tested in air, and the apparent activation energy for creep was found to be 92 kcal per mole, regardless of specinien orientation. The stress dependence 01- the steady-state creep rate, was satisfied by where n depended on orientation; n = 9.7 for rrzaterial transverse to the rolling direction and n = 24.3 for material parallel to the rolling direction. In the latter case, the relation was also valid. The rupture strength of material parallel to the rolling direction was -1.5 times gveater than the transverse rupture strength. Several tests in vacuum revealed that here the creep rate was higher and rupture life lower than for comparable tests in air. THERE is an increased interest today in producing improved dispersion-hardened alloys for high-temperature structural applications. This had led various materials designers to modify existing alloys, such as thoriated nickel. One system that has received considerable attention is based on chromium additions to Ni-ThO2, with the obvious motive of improving the oxidation resistance. Another effect of chromium is that of lowering the stacking-fault energy, y, of nickel. For example, the addition of 30 wt pct Cr decreases y from -225 erg per sq cm for pure nickel1 to -70 erg per sq cm.' This decrease in y could have several effects on the deformation behavior. There is some evidence that cross slip of dislocations around Tho2 particles is a mechanism of tensile3 and creep4 deformation in TD Nickel (Ni + 2 vol pct ThO2) at temperatures below 0.5 the absolute melting point of nickel, T,. A decrease in ? by chromium additions should increase the difficulty of cross slip. Also it has been suggested that the high-temperature (T > 0.5Tm) rate-controlling creep process in "recrystallized" Ni-Tho2 alloys is the climb of edge dislocations over Tho2 particles.5 According to weertman6 a decrease in the stacking-fault energy should decrease the dislocation climb velocity resulting in a decreased steady-state creep rate. Thus, chromium additions to recrystallized Ni-Tho2 alloys would be expected to decrease the creep rate, all other conditions being constant. However, a difficulty arises when the stacking-fault concept is applied to high-temperature creep of dispersion-strengthened metals which are produced on a commercial or semicommercial scale. This occurs because the materials are processed so that they have a high-stored energy of cold work, and the other substructural effects could obscure any influence of stacking-fault energy per se. An example of an alloy with a high stored energy of cold work is TD Nickel bar. This material has a fibrous grain structure (1 I diam by 10 to 15 p long), and the structure is stabilized by the ThO2 particles. Annealing at high temperatures, e.g., 3 hr at 1300°C, causes no recrystallization or grain growth.4 Previous work by the authors4 showed that the high -temperature creep behavior of TD Nickel could not be related to any simple dislocation theory of creep, and this probably was associated with the complex initial structure of the material.

Jan 1, 1968

By W. M. Reilly, Martin E. True, O&apos

A technique, equipment, and a compound have been developed and field tested for sealing tubing joint thread leaks without removing the tubing from the well. This eliminates the necessity of killing the well with possible damage to the producing formation, which could result if it were exposed to drilling mud. A thread sealing compound, developed and tested in the laboratory, is introduced into the tubing and squeezed into the joint to eliminate the leak. A high percentage of successful field applications have eflected an appreciable cost reduction in repairing leaking tubing strings in East Texas and in the Louisiana Gulf Coast area. INTRODUCTION In producing oil and gas wells the industry has been plagued with a never ending problem of tubing connection leakage. This situation is becoming increasingly more significant as more gas wells are placed on production and as higher pressures are encountered at greater depths of current drilling. Substantial progress has been made in minimizing thread leaks by careful handling and cleaning of joints and by the use of improved sealing compounds in combination with controlled makeup. But even with the use of the best known methods and sealing materials during initial makeup, occasional leaks through tubing joint threads appear inevitable. In some instances, tubing joints in high-pressure gas wells have been found to leak gas at relatively less pressure than that at which the tubing had been tested satisfactorily using liquid. Many expedients have been employed to prevent the physical replacement of tubing when leaks have developed. Perhaps the most commonly used is the sodium silicate treatment in which the solution is lubricated into the tubing to form a crystalline plug in the leak. Generally, any benefit realized is of a temporary nature. In addition to field studies on handling and makeup of tubing, extensive laboratory work has been undertaken on the development and testing of thread dopes.' Also, substantial effort has been devoted to testing tubing joints using high-pressure gas as a pressure medium.' The results of this work have emphasized that tubing joints are susceptible to occasional leaks, especially when subjected to relatively high differential pressures. To cope with the problem of leaking connections, an extensive investigation was undertaken to devise means of sealing leaks without removing the tubing from the well and without reducing the inside diameter of the tubing. The purpose of this paper is to present a technique, together with the associated equipment and compound, which have been developed for effecting a seal of leaking tubing in place. DISCUSSION Work was initiated simultaneously on two ventures: (1) to develop a satisfactory leak sealing compound and (2) to develop tools necessary to find the leak and place the compound. Leak Sealing Compound In the development of a sealing compound, tests were conducted on those compounds commercially available which include: (1) conventional thread lubricants, (2) thermo-setting resins and (3) other materials which held promise of effecting a seal. Although none proved completely satisfactory in their available form, two commercial compounds proved nearly equally effective in sealing leaks during laboratory tests after proportioned quantities of graded silica had been added. Field usage has indicated that the preferred compound is one prepared of an aluminum-stearate base thinned to the proper constituency and carrying a mixture of fine mesh graphite and graded silica. The compound developed by Humble Oil & Refining Co. is designated as Tubing Thread Leak Sealant 800. Placement Tools and Technique In developing tools to detect joint leaks and to place the sealing compound, work was done initially on wireline equipment. Preliminary designs were completed of a tool somewhat on the order of a pressure bomb to test individual joints with gas at high pressure to determine if the joint was leaking. An entirely different tool equipped with opposed packers was intended for placement of the sealing compound at high pressures in each leaking joint. The application of these tools

Jan 1, 1958

By H. L. Luo

SYSTEMATIC investigations of the Fe-Ga system have been reported only very recently."' The maximum solid solubility of gallium in a-Fe is nearly 50 at. pet at 900°C. However, from Ref. 1, it was not evident that the a-Fe solid solution could be retained successfully beyond 17.38 at. pet Ga by solid-state quenching. The present investigation reports the retention of a-Fe solid solution at 50 at. pet Ga by quenching from the liquid. An ordered phase of CsC1-type B2) structure was observed between 34 - 50 at. pet Ga. Since it was considered very probable that the CsCl structure would occur at high temperatures, alloy filings were also quenched by the conventional quenching technique. In addition to the CsCl phase, a second ordered phase of BiF3-type (DO3) structure was found in the range 25 - 30 at. pet Ga. Alloys were prepared from elements of 99.99 pet purity or better, induction-melted in alumina crucibles under hydrogen. After reweighing, the alloy ingots were cast into wires under argon. From the weight losses and the reproducibility of the lattice parameters, compositions were estimated to be within ± 0.3 at. pet. The techniques of quenching from the liquid state were reported before.3-5 Prior to quenching, a small section of cast alloy wire (30 - 50 mg) was melted in an alumina insert under an argon flow. The quenched specimens were in the form of flakes, typically 1 sq mm in area. For solid-state quenching, alloy filings passing 200 mesh were sealed under a reduced helium atmosphere in a thin-bottom silica tube. After heating for -30 min at the desired temperature in a vertical furnace, the sealed tube was rapidly dropped into ice water so that the thin bottom of the tube broke on impact. The quenched alloy filings were always ferromagnetic and could be collected by a magnet. X-ray diffraction patterns were taken with iron-filtered cobalt radiation in a 114.6-mm-diam Debye-Scherrer camera. High-angle lines were always resolved and spacings were computed relative to ? (CoKa1) = 1.78890Å. Lattice parameters were obtained from extrapolation against the Nelson-Riley function. The variation of lattice parameter with composition is shown in Fig. 1, together with the data of Dasarathy and Hume-Rothery.1 Uncertainties in the present measurements are within the dimensions of the symbols or indicated by error bars. X-ray diffraction lines indicative of CsC1-type ordering could be clearly identified for alloys of 34 - 50 at. pet Ga quenched from the liquid and alloys of 35 - 41 at. pet Ga quenched from -975°C. Within experimental error, no difference in

Jan 1, 1968

By J. L. Wyatt

The electrical resistance of titanium as a function of purity and temperature was measured from —325" to 2800°F. Two points of inflection in the data plots were found, and an increase in resistance with increase in temperature above the transformation was observed. IN 1948 Greiner and Ellis' reported on the thermal and electrical properties of titanium, including a study of the effect of temperature on the electrical resistance. The materials used in the research were obtained from the United States Bureau of Mines, where powder metallurgy techniques were being employed for consolidation purposes. These authors found a decreasing resistance with increasing temperature above 1625°F, and concluded that the latter temperature represented the point of transformation from hexagonal close-packed to body-centered cubic structure on heating. They reported a specific resistivity value of 55x10-6 ohm-cm, and showed that dp/dt was positive, decreasing with increasing temperature above ambient. In one of his early texts Hume-Rothery2 mentioned that certain metals, including titanium, exhibited minima in plots of resistance vs temperature. He indicated that this occurred at 212°F. Reporting many years ago on the effect of temperature on the electrical resistance of zirconium, de Boer and Fast³ showed that phase transformation in this sister metal occurred over a range of temperatures, the extent varying with its purity. Graphs of resistance vs temperature, showing transformation effects over a range of several hundred degrees, were presented for relatively impure metal. In the latter case the resistance decreased with increasing temperature throughout the region of partial phase transformation, thereafter increasing as predicted for normal metals by modern theories of the solid state. Since the quality of metal used in previous studies was substandard compared with iodide-type titanium, and in view of the fact that there seemed to be some rather unusual observations in the reported literature, it was decided to undertake a more extensive study of the thermal effects using high purity titanium, and to include temperature ranges beyond those which had been studied in order to ascertain whether or not the characteristics of zirconium would be duplicated. Experimental Materials Materials used in this investigation included commercial quality titanium (Ti-75A produced by the Titanium Metals Corp. of America) in the form of ¼ in. diam rods, and high purity iodide titanium (produced by the Foote Mineral Co.) in the form of crystal bar of irregular size. The latter was cold-swaged into rod form and machined to the desired size. Lead wires to all specimens consisted of 18 gage Ti-75A. Chemical analyses of the stock materials are given in Table I. Experimental Procedures Specimens 2½ to 3 in. in length were prepared with diameters nominally 0.15 to 0.20 in. Two holes,

Jan 1, 1954

VITRIOL is likewise a mineral substance from whose exhalation, according to the opinion of some, are generated and produced the elemental materials or substances which produce metals, particularly gold. It is not a fumosity from metal nor is it a thing from which metal is extracted in any manner, although it shows in certain ways that it is not entirely without metal since it produces a certain trace of it. It is a thing that has a great resemblance to alum; it has a biting substance, is sharp to the taste and pungent to the tongue, and has an astringent nature. It dissolves in water and every damp place in a short time. They say that the reason for this lies, as with every other mineral, in its poorly joined watery substances. Nor does this mean that it does not contain much earthiness; on the contrary it seems to me that there are in it five. [2.9v] different participating qualities, that is, the property of sulphur, the action of alum, the corrosion of niter or of salt, and from the metals, the properties of copper and of iron. Its ore is mined in the valleys of mountains in wild but not too rugged places. It is more a gray earth or soft dead rock than a hard stone. It always has in it some yellow and green spots or near it is some sulphur mineral, either large or small.. When it is beneath the earth it exhales a sharp and very strong foul odor of scorching similar to that of sulphur. And the waters that rise where it is are all foul, earthy, and thick, some boiling with great fumes and others without great fumes, so that they surely appear to be infernal products in many places where there is a large quantity of it. After you have excavated and sorted well the quantity you wish, the ore must be put in a heap in open airy places before the vitriol can be extracted from this soil or ore, however you wish to call it. And it is left thus exposed to the weathering of the rains, the cold, and the sun for five or six months. It must be turned several times in order to bring to the surface that which was underneath; and always when this is done it is broken small with the eye of a mattock so that it is better heated and baked throughout. When it has been brought to this point it is covered over by a shed built above it or it is carried under a hut that has already been made. Here it is left to stand for another six or eight months before it is worked.

Jan 1, 1942

By Frank G. Norris, William C. Marshall

The term "total operation" is meant to include problems that cannot be answered from the standpoint of either the blast furnace or the open hearth separately but must be studied by considering the interrelations of these two processes. There are other ways of expressing this idea, such as reference to the blast furnace and the open hearth as an integrated process or by emphasizing the interrelation and interaction of the two processes. Much progress has been made in metallurgy and other fields by breaking complicated processes and reactions into simpler parts and studying each of these intensively. This intensive study frequently is done under the controlled conditions of the laboratory experiment. The entire process is understood better by this specialized study of each of its parts. This procedure is so satisfactory that an understanding of unit operations is a fundamental requirement of chemical engineering. Much discussion of the open-hearth process is in terms of one heat or one furnace. By this is meant that the conclusions apply to one furnace, wherever it may be. Furnaces seldom occur singly; they are located in groups and these groups are located in steel plants having characteristic blast-furnace equipment. Problems that are affected by the number of furnaces operating, by the number of blast furnaces in the plant and by the fact that the open- hearth shop is dependent on the bla furnace capacity rather than on its o needs for the amount of iron available among those which, in contrast to "u operations," we have chosen to call "to operations." Many of these problems, such as cha ing delays and the general mechani problem of material handling, are familiar that merely to define " total op ations" brings them to mind. These pr lems are of such importance that alrea they have received careful thought 2 study and probably will merit furt study. As will be shown later, these mechan problems are so intimately related metallurgical problems of total operati that the effect of certain changes cannot ascribed with certainty to either a mech ical or a metallurgical cause entirely. Although the problems coming under general term of "railroading" are inclu in the problems of total operations, ' others are selected for the discussion of paper, One of these is strictly a problem composition; the other is strictly a prob of tonnage production. The problem of phosphorus is pres whenever basic open-hearth slag is used the blast-furnace burden. This practice not secured universal acceptance chi because of difference in preference for h manganese or low-manganese pig iron hjgh-manganese (2.00 per cent) iron is to made, open-hearth slag as a source manganese is usually cheaper than m

Jan 1, 1943

By William C. Marshall, Frank G. Norris

The term "total operation" is meant to include problems that cannot be answered from the standpoint of either the blast furnace or the open hearth separately but must be studied by considering the interrelations of these two processes. There are other ways of expressing this idea, such as reference to the blast furnace and the open hearth as an integrated process or by emphasizing the interrelation and interaction of the two processes. Much progress has been made in metallurgy and other fields by breaking complicated processes and reactions into simpler parts and studying each of these intensively. This intensive study frequently is done under the controlled conditions of the laboratory experiment. The entire process is understood better by this specialized study of each of its parts. This procedure is so satisfactory that an understanding of unit operations is a fundamental requirement of chemical engineering. Much discussion of the open-hearth process is in terms of one heat or one furnace. By this is meant that the conclusions apply to one furnace, wherever it may be. Furnaces seldom occur singly; they are located in groups and these groups are located in steel plants having characteristic blast-furnace equipment. Problems that are affected by the number of furnaces operating, by the number of blast furnaces in the plant and by the fact that the open- hearth shop is dependent on the bla furnace capacity rather than on its o needs for the amount of iron available among those which, in contrast to "u operations," we have chosen to call "to operations." Many of these problems, such as cha ing delays and the general mechani problem of material handling, are familiar that merely to define " total op ations" brings them to mind. These pr lems are of such importance that alrea they have received careful thought 2 study and probably will merit furt study. As will be shown later, these mechan problems are so intimately related metallurgical problems of total operati that the effect of certain changes cannot ascribed with certainty to either a mech ical or a metallurgical cause entirely. Although the problems coming under general term of "railroading" are inclu in the problems of total operations, ' others are selected for the discussion of paper, One of these is strictly a problem composition; the other is strictly a prob of tonnage production. The problem of phosphorus is pres whenever basic open-hearth slag is used the blast-furnace burden. This practice not secured universal acceptance chi because of difference in preference for h manganese or low-manganese pig iron hjgh-manganese (2.00 per cent) iron is to made, open-hearth slag as a source manganese is usually cheaper than m

Jan 1, 1943