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

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

Jan 1, 1966

By William C. Peters

The pre-production interval, beginning with the recognition of an orebody's best potential and ending with significant production, contains time-dependent conditions well appreciated by miners but not always understood or appreciated by the landowners, investors, and legislators with whom a miner must deal. The expression persists, even outside of Western fiction, that someone has "found a mine." From a slightly more knowledgeable position, the question is asked "How long does it take to make a mine?" and an all-encompassing answer is expected. By scanning the discovery and development history of hundreds of mines and rejecting those which involve rehabilitation or expansion of older mines, some generalizations can be attempted. It should be kept in mind that while physical conditions involving the geology of the orebody and the geographic surroundings do not change markedly with time, technologic and economic conditions do change from year to year. The new methods, facilities, markets, land tenure, and politics form a pattern in which today's mines are made and which do sometimes modify the pre-production interval.

Jan 8, 1966

By H. D. Peterson, G. E. Butts, J. F. Spisak

In 1978, Anschutz Mining Corp. began efforts to develop the Madison Cobalt Project in southeast Missouri. Preliminary metallurgical studies indicated that intermediate grade cobalt products, suitable for shipment to existing refineries, could be recovered from the sulfide mineralization of the ore body. However, tolling and freight charges were significant, as the refineries were located outside the US. These refineries would not satisfy the goal of strategically insulated production of superalloy-grade cobalt. The acquisition of proven, readily available refinery technologies was then evaluated. However, licensing costs were substantial and the "proven" technologies were not directly applicable to the unique chemistry of Madison materials. Faced with these challenges, Anschutz, in conjunction with the Colorado School of Mines Research Institute, embarked on an effort to develop a sulfate-based separation and refining process. CSMRI performed bench-scale and continuous pilot experiments on solutions generated through other pilot campaigns conducted by Lurgi, Hazen Research, and Sherritt Gordon. The results indicated that cobalt could be selectively extracted from sulfate media using a new generation of organophosphates. The solvent extraction system produced a solution suitable for electrolysis of high-purity cobalt. Preliminary cost studies indicated the novel process was competitive with other refinery systems. Plans to develop the detailed engineering-design information required to commercialize the process were abandoned when the price of cobalt collapsed to less than $17.64/kg ($8.00 per lb).

Jan 1, 1985

By William N. Poundstone

To forecast the future of coal intelligently, one must first consider the market outlook. Coal can be used for many purposes, but currently about 25% of it goes into metallurgical coke, while 75% serves as fuel. Coal for metallurgical coke should show a modest growth for at least the next decade, primarily because of increased exports, but the important factor in the coal outlook is energy. Today, this country faces a serious shortage of energy, and its requirements are growing at an almost unbelievable rate. Last year the United States consumed 68 quadrillion Btu, or double the energy it consumed in 1950, and, if projections are correct, this figure will grow to 150 quadrillion Btu by 1990. Thus, in one working lifetime, the nation's energy consumption is expected to increase by roughly five times. The future of coal hinges on its degree of participation in meeting this energy need. The Federal Power Commission predicts that coal consumed by electric utilities will increase about 4-576 per yr, reaching 472 million tons by 1980 and 615 million tons by 1990. If this projection proves correct, 1980 consumption will be double that of last year and, even more startling, the utility industry alone will use more coal in 1990 than the entire coal industry produced in 1970. This is a tremendous increase, but in view of the projected energy growth, it is difficult to see how this country's needs can be satisfied with- out a coal contribution of this magnitude. Unless some new source such as solar energy is discovered, it must be assumed that the projected energy will come principally from the present-day sources-oil, gas, nuclear materials and coal.

Jan 1, 1971

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy's law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-

By D. J. Schmatz, H. I. Aaronson, H. A. Domian

Diffusion kinetics in disordered hcp Cd-Mg alloys have been investigated by means of the Kirkendall effect and concentration-penetration curves determined with an electron-microprobe analyzer. Self-diffusion coefficients of both species were determined at the three marker compositions obtained, averaging 27.6, 46. 7, and 78.1 at. pct Mg, by means of the Darken analysis. These coefficients were then corrected for the unequal and concentration-dependent partial molar volumes of the two elements with the Balluffi analysis, and for the vacancy flux effect by the Manning analysis. The latter correction reduced the Balluffi correction produced larger changes in the self-diffusiv-ities; neither, however, produced statistically significant changes in the Do's or the H'S. The most striking result of this investigation is that at all three compositions and at all temperatures studied both the uncorrected and corrected self-difjusivities of magnesium are higher than those of cadmium. The Cd-Mg system is the first one found in which the higher melting, lower vapor pressure element diffuses more rapidly. Both an empirical correlation due to Toth and Searcy and considerations of the atomic mechanism of diffusion indicate that this anomaly is probably due to a comparatively low value of the activation energy required for a magnesium atom and a vacancy to exchange sites, perhaps occasioned by the higher compressibility of magnesium atoms. KIRKENDALL effect studies have been previously reported for only two hcp solid solutions: the E phase of the Zn-Cu system1 and the a phase of the Cd-Hg system.' In neither investigation were the marker-movement studies supplemented with the concentration-penetration curve determinations necessary to evaluate self-diffusivities by means of the atano and the Darken analyses. The present program was undertaken to obtain both types of data on a hexagonal solid solution in order to provide more detailed information relevant to the mechanism of diffusion in this type of lattice. The Cd-Mg system was chosen for this study because the disordered solid solution extends across the entire phase diagram at temperatures above 253"c5 and the substantial difference in the melting points of the component pure metals promised that marker movements would occur at reasonably rapid rates should the diffusivities of the two species be as unequal as might be anticipated. The experimental convenience of the relatively low melting points of cad-miun and magnesium and the availability of extensive and accurate activity data6 (required for application of the Darken analysis) were additional reasons for selecting this alloy system. Since the anisotropy of diffusion is not large in either pure cadmium7 or pure magnesium,' the diffusion couples were prepared from polycrystalline components. The presence of a well-defined texture in the couples—the c axis of individual crystals tended to be normal to the diffusion direction— however, provides a fair degree of crystallographic definition to the data obtained. The principal (and entirely unexpected) finding of this investigation, that magnesium, the high-melting low-vapor pressure element, diffuses more rapidly than cadmium, in contradiction to a broad range of results in fcc and bcc alloys, as well as in the previously studied hcp alloys,172 makes the self-diffusivity determinations of immediate interest in understanding the origin of this anomalous result. EXPERIMENTAL PROCEDURE The cadmium (Belmont Smelting and Refining Co.) and magnesium (Dow Chemical Co.) used in this study were both of 99.99 pct purity. Alloys containing 51.0 and 65.6 at. pct Mg were prepared from these materials by melting under a MgC12-base flux in a high-purity graphite crucible. These alloys were subsequently hot-worked and then homogenized in a helium atmosphere at temperatures close to their solidus points. Sandwich-type diffusion couples of the type g/d/g were prepared from the pure metals by solid-state diffusion. Two-piece alloy couples of Mg/65.5 at. pct Mg (Mg/gCd) and Cd/51.0 at. pct Mg (Cd/CdMg) were welded by a liquation technique. The individual components of both types of couple were initially cylinders 1.27 cm in diam and in length; the ends of these cylinders were machined accurately flat and parallel. For both welding techniques, the pure cadmium cylinders and the alloys were chemically polished in a mixture of 40 pct ethyl alcohol, 40 pct hydrogen peroxide (30 pct conc), and 20 pct nitric acid,g while those of pure magnesium were polished in a solution of 10 pct nitric acid in ethyl alcohol.' Immediately afterwards, both metals were rinsed in freshly distilled acetone, and then in similarly purified methanol.' The Mg/Cd/g couples were assembled in a carefully cleaned stainless-steel welding fixture, in which a screw operating through a self-centering arrangement permitted a controlled pressure to be exerted upon a couple prior to welding.'' Tungsten marker wires 0.005 cm in diam were placed at the d:g interfaces of some of these couples, and imbedded in the couples during the application of pressure. As soon as a couple had been assembled, the welding fixture was inserted into a Pyrex capsule containing a packet of zirconium chips at each end. The capsule

Jan 1, 1967

By R. T. Mishler

I WISH to express my keen appreciation of the article on the above subject by Coe and Clevenger.1 It has been doubly interesting to me, for the reason that the experience recorded and the principles evolved practically parallel the results of similar investigations made by myself and others at The Lucky Tiger Mine, El Tigre, Sonora, Mex. An outline of the work at El Tigre may aid in confirming the principles expressed by Coe and Clevenger. El Tigre has the unenviable distinction of possessing a slime with a much lower settling rate than any recorded in the article discussed. Under most favorable conditions the settling rate is about one-third that reported for the Liberty Bell mill, and one-tenth that reported for the Nipissing, Golden Cycle, and Presidio mills. This slow settling characteristic of Tigre ore has necessitated careful investigation of settling phenomena throughout the various evolutions of the plant. PREVIOUS SETTLING INVESTIGATION AT TIGRE During construction work at the mill, the Metallurgical Engineer in charge, D. L. H. Forbes, ran a series of experiments on settling. His tests proved that deep settling tanks were not ordinarily necessary. The use of tanks 2 or 3 ft. in depth was suggested.2 Later experiments demonstrated that the following principles of settling applied to Tigre pulp.3 1. In settling dilute pulp, settling rates are independent of pulp depth. 2. In settling thick pulp, settling rates are approximately proportional to pulp depth.4

Jan 3, 1917

By Kenneth C. Vincent, A. M. Gaudin

TEN years ago Taggart, Taylor and Ince1 described a workable, convenient apparatus for the measurement of contact angles between cleaved, ground or polished particles and captive bubbles. Wark and Cox2 and Wark and Sutherland3 have done an immense amount of experimental work with this apparatus. Their work has had as principal object the determination of "contact curves." Contact curves are cartesian charts in which pH (or some other variable) is plotted against quantity of modifying agent. The rectangular area is broken into two or more curvilinear areas separated by the contact curve. The curve indicates that a sharp demarcation exists between conditions that bring about sticking of particles to bubbles and conditions that do not produce sticking. The type curve appears in the TRANSACTIONS as Fig. 1, page 248, volume 112. Wark and Cox offer data to show that the contact angle has a value determined by and characteristic of the agent used. Wark and Cox also make the statement that they believe this value is independent of concentration (ref. 2a, p. 209). They say: It is suspected that, given sufficient time and provided that there are no disturbing factors, the full ethyl xanthate angle (corresponding to a complete xanthate film) would be obtained in every case where contact occurs. Such a conclusion, if correct, would tend to substantiate the hypothesis of flotation collection by metathesis championed by Taggart and his associates4-8 and would argue against the adsorption hypothesis now adopted by Wark7 and by one of us.8 However, the data of Wark and Cox do not bear out the conclusion that there is a sharp passage from conditions of contact to conditions of noncontact. Rather, they indicate the existence of a transition zone of reagent concentration across which the contact angle varies with changes in reagent concentration from zero to a value near the maximum. This may be seen, for example, from Fig. 195 in the new text by one of us (ref. 8, p. 380), which presents the data of Wark and Cox in graphical form. The object of this study has been to explore the nature of the transition from conditions of contact to conditions of noncontact. The data of Wark and Cox to which reference has been made as showing that a gradual transition exists are marred by the fact that the region of critical-agent concentration is at an extremely small concentration. This condition suggests that diffusion may have played such a preponderant role that equilibrium was not reached within the time alloted. In the Wark and Cox data, the critical concentration was at about one part of xanthate per million parts of water. To form a monolayer of xanthate on the mineral surface would therefore require depletion of xanthate in the liquid to a depth of the order of

Jan 1, 1940

By W. W. Anderson

A formula for quantitative efficiency is proposed, in which the efficiency value is a function of the improperly distributed material at the, gravity of separation effected by the cleaning equipment. The misplaced material is expressed as a percentage of the total material discharged from the equipment. Numerous examples are given, demonstrating application of the formula to various types of separation, including multiple-product separations.

Jan 1, 1950

By O. J. Kensok

THE literature contains three previous studies of the chemical activities of Cd-Mg alloys: Trumbore, Wallace, and craigl obtained chemical activities of magnesium at 543" by performing electromotive-force measurements; Borg and irchenall calculated activities at 590°K based on vapor-pressure measurements of cadmium over Mg-Cd alloys by the Knud-sen effusion method; and Terpilouski and arcka measured the chemical activities of magnesium in the liquid state by means of electromotive-force measurements. In this study the vapor pressure of cadmium was determined over nine solid Cd-Mg alloys in the temperature range 571" to 697°K by the Knudsen effusion method. This study was prompted by the lack of precision in the data reported by Borg and Birchenall. Knudsen cells used during this study were fabricated from 0.020-in.-thick tantalum tubing. The tops and bottoms of the cells were cut from 0.010-in.-thick tantalum sheet, press-fitted, and welded in place. The orifice was drilled in the cell top and subsequently reamed to a knife-edge thickness. The diameter of the orifice was measured with a traveling microscope capable of reading 0.0001 cm. The sample was heated by means of a resistance

Jan 1, 1967

By Margaret Dienes, Karl L. Fetters

It is recognized that ingot structure is important in determining the quality of finished steel. Such elements of ingot structure as the size, shape and distribution of primary crystals; the size, shape and distribution of shrinkage cavities; the degree and kind of segregation (both macro and micro); the distribution of nonmetallic impurities and gas cavities are each the result of solidification phenomena. 'These structural features vary with variations in ingot practice. Their control requires a knowledge of their correlation with the variables of ingot practice. The structures of full-sized commercial steel ingots have been studied extensively by the Steel Ingots Committee of the Iron and Steel Institute.l This work has contributed much to our knowledge of ingot structure and the factors that control it. These investigations of necessity have been limited in scope because of their costliness and the great amount of time required. Studies of the structure of small steel ingots have not been very satisfactory because of the rapid rate of freezing of the ingots. Their structures are thus difficult to resolve and to interpret. Medium sizes of steel ingots in the ranges of 150 to 500 lb. do offer opportunity for study, but their cost also becomes greater and their use less expeditious. Experimental models for the study of steel-ingot structure have been made of nonferrous metals. Gathmann2 used lead-tin alloys and reported that they were satisfactory for determination of the location of the major shrinkage cavities and the Liplanes of weaknessv resulting from the pattern of crystallization. Certain features of mold design have been illustrated by these results. Bezdenezhnihk3 has used copper and aluminum ingots similarly and has shown the effect of mold-wall thickness on the depth of columnar grains. These studies of nonferrous models have been useful, but their results have been limited because the analogy with steel ingots obviously is not a close one. Model wax ingots have also been useful in pointing out important features of mold design. Gathmann4 watched the solidification of wax ingots, through a glass-walled mold, and has reported the effects of mold type on the location of the shrinkage cavities. Segregation was simulated by using a mixture of paraffin and stearine and adding a red dye that on freezing segregated preferentially to the stearine. Brearley5 also used wax models to determine the effects of some of the principal features of mold design. Carlsson and Hultgren6 dsed stearic acid to show that the columnar crystals of ingots tend to slope upward progressively from the mold wall toward the center of the ingot. As with the nonferrous ingots, the wax ingots have

Jan 1, 1943

By Margaret Dienes, Karl L. Fetters

It is recognized that ingot structure is important in determining the quality of finished steel. Such elements of ingot structure as the size, shape and distribution of primary crystals; the size, shape and distribution of shrinkage cavities; the degree and kind of segregation (both macro and micro); the distribution of nonmetallic impurities and gas cavities are each the result of solidification phenomena. 'These structural features vary with variations in ingot practice. Their control requires a knowledge of their correlation with the variables of ingot practice. The structures of full-sized commercial steel ingots have been studied extensively by the Steel Ingots Committee of the Iron and Steel Institute.l This work has contributed much to our knowledge of ingot structure and the factors that control it. These investigations of necessity have been limited in scope because of their costliness and the great amount of time required. Studies of the structure of small steel ingots have not been very satisfactory because of the rapid rate of freezing of the ingots. Their structures are thus difficult to resolve and to interpret. Medium sizes of steel ingots in the ranges of 150 to 500 lb. do offer opportunity for study, but their cost also becomes greater and their use less expeditious. Experimental models for the study of steel-ingot structure have been made of nonferrous metals. Gathmann2 used lead-tin alloys and reported that they were satisfactory for determination of the location of the major shrinkage cavities and the Liplanes of weaknessv resulting from the pattern of crystallization. Certain features of mold design have been illustrated by these results. Bezdenezhnihk3 has used copper and aluminum ingots similarly and has shown the effect of mold-wall thickness on the depth of columnar grains. These studies of nonferrous models have been useful, but their results have been limited because the analogy with steel ingots obviously is not a close one. Model wax ingots have also been useful in pointing out important features of mold design. Gathmann4 watched the solidification of wax ingots, through a glass-walled mold, and has reported the effects of mold type on the location of the shrinkage cavities. Segregation was simulated by using a mixture of paraffin and stearine and adding a red dye that on freezing segregated preferentially to the stearine. Brearley5 also used wax models to determine the effects of some of the principal features of mold design. Carlsson and Hultgren6 dsed stearic acid to show that the columnar crystals of ingots tend to slope upward progressively from the mold wall toward the center of the ingot. As with the nonferrous ingots, the wax ingots have

Jan 1, 1943

By Kung-Lee Wang, Brian W. Mackenzie, Warren E. Morrison, DeVerle P. Harris, George F. Sharrard

The term "mineral economics" is applied to a wide range of activities in the mineral industries. Earlier chapters have described the application of economic concepts to the mineral industries-supply, demand, conservation, tariffs, etc. The solution of mineral economics problems is often assisted by the application of quantitative methods. The purpose of this chapter is to describe a number of quantitative methods-econometric, operations research, and management science techniques-which find application in the analysis of mineral economics problems. These methods include input-output analysis, trend analysis, forecasting techniques, simulation, multivariate statistical analysis, mathematical programming, and market research techniques. The purpose of this introductory section is to provide a mineral economics framework for the application of these methods. Mineral economics is a subdivision of economics that is justified by a sufficient number of economic problems in the mineral industry requiring special experience and an unusual combination of skills. These problems are concerned with the conversion of minerals as geologic resources to minerals as economic goods. The mineral conversion process is outlined in Fig. 8.A.1. The physical occurrence of mineral deposits in nature and the market demand for mineral products in the economy provide the basic stimuli. The conversion process embodies a number of sequential stages-exploration, the development of mineral deposits, and mineral processing facilities and, consequently, productive activity to supply market demand. Changes in demand and the depletion of deposits illustrate the dynamics of the process. Mineral economics applies economic con-

Jan 1, 1976

J. E. Stead, Middlesborough, England (communication to the author): Prof. Howe's valuable paper on cast-iron brings forward most prominently the correct explanation of the part played by combined carbon in pearlite and cementite, in determining the strength and hardness of cast-iron. On a previous occasion I haveoshown that castings made by melting a white Cleveland iron and glazed iron, one containing 1.5 and the other from 4 to 5 per cent. of silicon, and each about 3 per cent. of carbon, were stronger than those made of ordinary foundry-iron; the difference in the final castings being a differ-

Jan 1, 1902

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained-the isothermal growth of the phase follows a simple parabolic equation: [1 = ki [I]] where X is the thickness of the alloy layer, k the reaction rate constant, and [t] the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation: [k = Ae-QIRT [2]] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By Wm. A. Haven

As soon as the likelihood of American participation in the war was established, and in spite of the fact that we can produce almost as much as all other countries combined, the demand for prompt deliveries of iron and steel products from American factories began to exceed their utmost capacity, and, after fifteen months of practically full operation, has continued to do so. Therefore, it would seem worth while to review some of the aspects of the supply and demand for steel as well as the efforts that are being made to bring them into balance. It is still being debated as to whether the situation should be defined as a real shortage that will persist through the emergency period or as a temporary one than can be relieved by less drastic measures than a Government-sponsored program of expanding existing plants and building new ones.

Jan 1, 1942

By Dale A. Vaughan, Oliver M. Stewart, Charles M. Schwartz

Solid-solubility limits at 1500°, l000q and 500°C for carbon, nitrogen, and oxygen in high-purity tantalum were determined by X-ray lattice-parameter methods. For carbon, the solubility was found to be 0.17 at. pct at 1500°C, and less than 0.07 at. pct at 1000°C. A nitrogen solubility of 3.70 at. pct at 1500° C decreases linearly with temperature to 2.75 at. pct at 1000°C, and 1.8 at. pct at 500°C. In the case of oxygen, the solubility was found to be 3.65 at. pct at 1500°C, 2.95 at. pct at 1000°C, and 2.5 at. pct at 500°C. The phases Ta2C, the low-temperature modification of Ta205, and Ta,N of unknown composition but which has a superlattice structure based upon the original bcc tantalum lattice have been identified as the initial precipitates in the respective systems. Metallographic methods were employed to verify the X-ray analyses. The etching behavior of Ta is discussed in terms of lattice i?rzperfections and precipitate phases. The excellent fabricability, high melting point, and nuclear properties of tantalum are responsible for interest in this refractory metal. Data on the solid solubility of the interstitial elements (oxygen, nitrogen, and carbon) in tantalum and on the precipitate phases are somewhat limited. The significant contributions are discussed below. Because the purity of electron-beam melted tantalum (only recently available) is considerably higher than that used in previous studies, the present investigation was initiated. Gebhardt et all-3 have investigated the tantalum-oxygen and tantalum-nitrogen systems with particular reference to the changes in physical properties and to the rates of reaction between these gases and the metal. The solubility of oxygen in tantalum was reported2 to be 3.7 at. pet at 1500°, 2.3 at. pet at 100O°C, and 1.4 at. pct at 750°C. Schonberg4 reported that several oxide phases (Ta40, Ta,O, TaO and Ta,05) exist while X-ray studies by Gebhardtl showed only two oxides, Ta,05 and an unidentified phase which was associated with a platelet-type precipitate. La-gergren and Magneli,' however, questioned the existence of compounds other than the two allotropic modifications of Ta,05 for the tantalum-oxygen system. In the case of nitrogen, the solubility was estab- lished by Gebhardt3 to be of the order of 7 at. pct at 1800°c. The solubility was reported to decrease rapidly with temperature, and, although no limits were established, a precipitate phase was observed by Gebhardt except when the high-nitrogen specimens were cooled very rapidly from the reaction temperature of 1800c. He reported the initial precipitate phase to be a tetragonal distortion of the bcc tantalum lattice while Schonberg6 reported the phase lowest in nitrogen Jo be a cubic super-lattice with a cell size of 10.11 A. Two other nitride phases, Ta,N and TaN, were reported; these appear to be isomor-phous with the carbides of tantalum. The tantalum-carbon system was investigated by Ellinger7 and by Lesser and Braurer. Two compounds, Ta,C and TaC, were reported to exist, each with a range of composition. The solubility of carbon in tantalum was found to be practically nil at all temperatures. Thus, of the interstitial elements which are present in small amounts in high-purity tantalum, carbon might be expected to form precipitates. The present investigation was initiated to obtain additional data on the solid-solubility limits of these interstitials at 1500°, 1000°, and 500' with particular emphasis on the distribution and the identification of the precipitate phases. EXPERIMENTAL WORK AND RESULTS In the present investigations of the solid solubility and of the precipitate phases in the systems tantalum-nitrogen, -oxygen, and -carbon, high-purity tantalum was reacted with high-purity gases, homogenized at 1800°c, and annealed at and quenched from 1500°, 1000,

Jan 1, 1962

The Committee on Technical Nomenclature, of which John T. Faig, Professor of Mechanical Engineering at the University of Cincinnati, is Chairman, appointed by the Society for the Promotion of Engineering Education, has recently issued a report advocating uniformity in the use of symbols to designate engineering and mathematical terms: The selection of the symbols was based upon a canvas of a considerable number of engineers, editors of engineering papers, and professors of engineering throughout the United States. The list, as finally accepted by the Committee and recommended for universal adoption, is as follows: Concept Symbol I Concept Symbol Acceleration due to gravity 'g Length L Acceleration, linear a Mass m Area A Modulus of section Z Breadth b Modulus of elasticity, Young's... E Center of rotation 0 Moment of force M Coefficients and constants C, K Moment of inertia, polar J Deflection of beam y Moment of inertia, rectangular.. I Depth : d Quantity of liquid flowing Q Diameter D . Radius r Distance passed over s Radius of gyration k Distance of extreme fiber from Reactions R neutral aids C Revolutions per unit of time.... N Eccentricity of application of load e Stress, unit S Efficiency (hydr., mech., vol.)...er,.em, e9 Time t Force F Torque T Friction, coefficient of f Velocity, angular :. W Head H 'Velocity, linear V Height h Volume V Horsepower : Hp Weight W Hydraulic radius Re Previous lists of symbols have not secured wide acceptance in, this country; some that have been proposed by prominent writers are familiar to very few engineers. The above list is presented in the hope that it will assist in the evolution of a standard list. It is short; it contains no Greek letters; it is mnemonic to a considerable degree, though not by

Jan 1, 1918

By Carle R. Hayward

THOUGH recent months have seen a rapid decline in lead-smelting activity and consequent uncertainty as to the future, the first half of the year showed progress in keeping with similar activity in other metals. Demand for scrap increased and various lead-bearing materials found their way to plants producing secondary lead. Some of these materials introduced complications into normal smelting procedure and were the cause of many conferences among plant officials attempting to find the most satisfactory method of treatment. If a blast furnace is to do itself justice it must be run with an open charge. Troubles inevitably result when materials are added to a charge which tighten it up and pre- vent free burning of the coke and con- sequent rapid smelting with a clean hearth This fact has long been recognized by plants producing primary lead, but only recently only it received the attention it deserves.

Jan 1, 1938

By Evert Hoek

Summarising a conference is never an easy task, but I will try to keep my comments brief and to the point. There are a number of lessons which we have learned from our deliberations together during these past three days, and I will try to give you my impressions of these lessons and of their practical implications in open pit mining. The first thing that has become increasingly obvious during these discussions is that it is no longer acceptable to offer an 'Act of God' as an excuse for a major slope or tailings dam failure. Disasters such as that at Aberfan in the United Kingdom have focussed the world's attention on the activities of the mining industry and the report of the commission set up to investigate the Aberfan disaster clearly showed that adequate knowledge was available and that failure to apply this knowledge did not qualify as an 'Act of God'. The courts and the world's press are certain to impose increasingly harsher penalties and criticism on those held responsible for major failures, particularly of tailings dams, in the future. One of the major problems in applying available knowledge to slope problems is that attempts to apply this knowledge are frequently left too late. To provide an engineering solution in the case of a slope in an advanced state of failure is an almost impossible task, and it is essential that those responsible for the stability of a slope must learn to recognise signs of distress at an early enough stage for effective remedial measures to be taken. As our ability to solve slope problems improves, the time at which slope stability problems are considered in a mining project must move forward to a stage at which these problems can be anticipated and dealt with before they arise. Conferences such as this are important in that they enable us to exchange ideas and advance our knowledge to a level at which such predictive engineering will be possible. It has been encouraging to hear of mining projects such as the Bougainville Copper operation where slope stability studies were carried out as part of the overall evaluation programme and it is hoped that this will become a more common procedure in the future. Providing a safe slope in an opencast mine obviously costs money, either in terms of the reduced ore to waste ratio given by flat slopes or because of the cost of stabilization techniques such as drainage or the use of rock anchors. An optimum slope design will provide maximum safety at minimum cost but achieving this optimum is not an easy task. Any one of us could design a slope which would be stable to the end of time, but it is probable that that slope would be so flat as to be totally uneconomic in most open pit mining situations. On the other hand, if the overall economics of a mining project are so critical as to require slope angles which the engineer responsible for these slopes considers to be unsafe, it is his duty to make us could design a slope which would be stable to the end of time, but it is probable that that slope would be so flat as to be totally uneconomic in most open pit mining situations. On the other hand, if the overall economics of a mining project are so critical as to require slope angles which the engineer responsible for these slopes considers to be unsafe, it is his duty to make

Jan 1, 1971