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By P. Barnes

The subdivisions of this account are numbered 27, 28, 29, 30, 31, 32, and 33, in the general series of construction accounts, and give the details of cost of the various items of the work, as noted below: Accounts 32 and 33 relate to hand-tools and to heaters, and, being quite small in total amount, are omitted in this statement.

Jan 1, 1879

By W. W. Yankie, A. T. Chatas

This paper is written as a discussion of the paper, "Buckling of Tubing in Pumping Wells, Its Effects and Means for Controlling It" by Arthur Lubinski and K. A. Blenkarn, which war published in the March, 1957, issue of Journal oP Petroleum Technology. An analogy is drawn between the buckling of tubing in pumping wells and a fiube, fitted with frictionless pistom, linked by an inelastic rod, and which is subject to an internal pressure. A simple derivation shows that the critical internal pressure exerts a hydrostatic force on the pisfon which is close to the Euler load for compression buckling of the same tube. While the results agree with those of Ref. I, the basis of calculations has been changed and clarified. The presence of internal upsets at the pistons is discussed. INTRODUCTION In the Appendix, Lubinski and Blenkarn state that a tube with ends closed by frietionless pistons connected by an inelastic rod (Fig. 1) will behave as a column loaded with a force equal to the tension force in the rod. They note that, while the fluid may not resist a shear force, the moment in every cross section is piston force multiplied by the elastic line deflection (c.f., the loaded column). Since the equations of the elastic lines are similar in the two cases, the solution is carried over from the loaded column. On the contrary it is suggested that while the method of solution remains unchanged from the column case, the actual stress distribution is different, a fact which is taken into account in this note. A simple method of approximating the buckling pressure is given, and their reasoning in our mathematical language is continued. GENERAL EQUATIONS The equation of an elastic line, initially straight in the x direction (Fig. 2), is given by In the case of a loaded column, this may be written: For the pressurized tube it was shown, by analogy with the loaded column, that tion has a solution that, for P, = EI/P, any deflection is stable (a criterion for buckling). An attempt will be made to describe more precisely, the forces acting on the tube, and to analyze the buckling condi,tions. DISCUSSION If the tube assumed a deflected position, the volume between the pistons would increase so that in deflecting, the energy of the fluid would decrease. When the increase in elastic energy of the tube (due to bending) is equal to the decrease of fluid pressure energy, buckling conditions exist. Analyzing the forces on the tube (Fig. 3), two transverse forces, T,, T,, exerted by the pistons, are balanced by a resultant of the pressure elements which are linearly dependent on the local curvature of the elastic line (Fig. 4). Unlike most buckling cases, the forces depend on the shape of the elastic line, a condition that makes a rigorous mathematical treatment difficult. Several approximations may be used to clarify the problem.

By M. A. Dayananda, R. E. Grace

Vapor-solid diffusion couples were employed in a study of ternary diffusion in the single-phase copper-rich corner of the Cu-Zn-Mn system Interdiffusion coefficients were measured at three different compositions corresponding to the intersections of diffusion paths determined at 850°C. Intrinsic diffusion coefficients were determined at two compositions by the Philibert-Guy method. New relations between the various intrinsic diffusion coefficients are also presented. MOST of the investigations of ternary diffusion have been made with "sandwich" couples formed by welding together two homogeneous solid solutions with or without markers placed at the interface. With such couples Kirkaldy and his coworkers1,2 have determined interdiffusion coefficients which describe ternary diffusion in the substitutional alloy systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy3 have reported intrinsic diffusion coefficients for Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.4 The use of semi-infinite diffusion couples, for example, vapor-solid couples, where the diffusing species are supplied from a vapor source in contact with a diffusion disk, has so far been confined to studies of binary diffusion. Balluffi et a1.5,6 have successfully determined the interdiffusion as well as the intrinsic diffusion coefficients in several binary metallic systems employing vapor-solid couples with markers initially placed at the vapor-solid interface. They have also discussed the general advantages and limitations of such couples. Vapor-solid diffusion couples can successfully be employed in ternary diffusion studies. The importance of such couples in ternary diffusion lies in the fact that inert markers lie close to the vapor-solid interface, and the composition of the marker plane is virtually known before experimentation begins. Another minor advantage is that the method of Philibert and Guy4 may be used with three alloys instead of four. Lastly, the diffusion paths need not be S-shaped, as pointed out by Meijering7 for "sandwich" couples. The Cu-Zn-Mn system is convenient for ternary diffusion studies because of the large single-phase field in the copper-rich corner. The vapor pressure of zinc above such alloys is known, and X-ray measurements indicate that the molar volume is nearly constant over a wide range of compositions.8,9 It is the purpose of this paper a) to extend the analysis of Balluffi and seigle5 to permit an evaluation of interdiffusion coefficients in ternary vapor-solid couples, b) to use the method of Philibert and Guy to determine intrinsic diffusion coefficients with such couples, and c) to present experimental data on both interdiffusion and intrinsic diffusion coefficients for the Cu-Zn-Mn system at 850°C. INTERDIFFUSION IN TERNARY VAPOR-SOLID COUPLES The analysis of Balluffi and seigle5 is extended in this section to a vapor-solid couple where two solutes diffuse from a vapor source into a ternary solid solution. To take into account the expansion of the diffusion disk caused by the absorption of mass from the vapor phase, the total fluxes are expressed on the basis of a coordinate system that moves with the velocity of the vapor-solid interface; thus. where D3ij are the intrinsic diffusion coefficients,4 v(x, t) is the local Kirkendall velocity of mass flow, and F(t) is the negative velocity of the vapor-solid interface (x = 0). Both these velocities are based on a fixed coordinate system far removed from the diffusion zone. Using the continuity relations and Darken's method1' for a ternary system in which components 1 and 2 diffuse from the vapor phase into a solid of negligible vapor pressure, one obtains

Jan 1, 1965

By Robert F. Mehl

Jan 1, 1944

By Robert F. Mehl

Jan 1, 1944

By G. D. Van Arsdale

This paper describes a series of experiments leading to the development of a method for leaching the mixed ores of the Inspiration Consolidated Copper Co., containing chalcocite and silicates of copper, by the use of solutions acidified with sulfuric acid and carrying ferric sulfate. Iron is added to the solutions and ferric iron is regenerated electrolytically to a percentage high enough to act as an effcient solvent. The decreased yield is partly compensated for by a higher current density. An important problem in modern copper metallurgy, particularly in the Southwest, has been to obtain good recoveries from what are commonly known as mixed ores; that is ores in which the copper occurs partly as oxide and partly as sulfide compounds. The dividing line between mixed ores and ores commonly accepted as concentrating is not definite. In other words, much ore now being concentrated carries considerable copper in non-sulfide form, on which recoveries are not so good as on ores carrying less of these constituents. While treatment by concentration may be commercially profitable on ores carrying oxide copper within certain limits, there are large deposits for which the application of concentration could not be considered, and yet which have not been considered amenable to leaching because they carried too much sulfide. The Inspiration Consolidated Copper Co. has large amounts of such mixed ores, and this paper is an account of the experimental work by which a method was developed for their treatment, and for which a large plant is now being erected by the Inspiration Co. It is not claimed that the method is a general solution of the problem of mixed-ore treatment but it is apparently well adapted for leaching the ores of the Inspiration Co., for which it was designed. The work done has covered preliminary laboratory and test-plant investigation, and a pilot-plant run, extending from March to the middle of December, 1923. Thoroughly consistent and satisfactory results were obtained continuously for more than six months in the pilot plant; and it is believed that the results and probable costs that can be had on a large scale have been definitely proved. The method, however, was designed for local conditions; and while the basic principles are general, there are ores on which it will not work and other ores for which considerable modification may be required.

Jan 1, 1926

By John E. Murphy, Ernest L. Ohle

Hematite-magnetite ore bodies at Iron Mountain, Missouri, have produced nearly 9 million tons of iron ore concentrates since 1844. The ore minerals occur principally as open-space filling in fractured and brecciated andesite porphyry with very minor replacement of the wall rocks. The enclosing rocks are Precambrian in age and consist of a series of dacite, rhyolite, and andesite flows aggregating about 2000 feet in thickness. All of the ore is in andesite and the mineralization is Precambrian in age. The shape of the ore bodies, the breccia character of the ore, and the gangue mineralogy are believed to be unique. One of the two main ore bodies is crudely dome-shaped with a tendency for development of concentric mineralized shells; the other is an elongated lense in plan but hook-shaped in cross section. Both have strong linear elements striking northeast, east-west, or northwest. Various modes of origin for the structures and for the tension breccias have been suggested, but none is completely satisfactory. Hematite is the main ore mineral; magnetite is subordinate. Important gangue minerals are andradite, quartz, calcite, actinolite, apatite, epidote, and chlorite. Although some evidence favors injection of an iron-rich melt, other evidence suggests ore formation by a high temperature, water-rich solution.

Jan 1, 1968

By M. G., Corson

1. In addition to the alloys of copper with iron previously found by Hanson and Ford to show an increase in the concentration of the alpha range with increase in temperature the following binary and ternary systems have been found by the author to exhibit: the same feature: (a) Copper-chromium. (b) Copper-cobalt. (c) Copper-silicon. (d) Copper-nickel-silicon and its pseudo-binary section Cu-Ni2Si (formula of compound definitely established). (e) Copper-cobalt-silicon and its pseudo-binary section Cu-Co2Si (formula of compound established with some probability but not as definitely as for Ni2Si). (f) Copper-chromium-silicon; formation of a compound definitely established (compare Figs. 1 and 2). The formula of this compound may be either Cr2Si or Cr3Si. (g) Copper-iron-silicon; presence of a phase containing both iron and silicon established in an indirect way only. No definite microconstituents observed. 2. RANGES OF SOLID SOLUBILITY (percentage at various tempera¬tures). (a) For copper-chromium: 0.8 at 1000° C.; 0.5 at 900° C.; 0.25 at 800° C.; 0.05 to 0.1 at 500° C. (b) For copper-cobalt: 3.4 at 1000'C.; 2.4 at 900'C.; 1.7 at 800'C.; 0.9 at 600°C.; 0.35 at room temperature. (c) For copper-silicon (Fig. 3) : 6.8 ± 0.1. per cent. at 800° C.; 3 per cent. at 400° C. and probably below 2 per cent. at room temperature if sufficiently long annealed. (d) For copper-cobalt silicide: 3.3 at 1000° C.; 2.4 at 900° C.; 1.6 at 800° C.; 0.7 at 600° C.; 0.3 at 300° C. (e) For copper-nickel silicide (Fig. 4): 8.2 at 1000° C.; 5.5 at 900° C.; 3.6 at 800° C.; 1.6 at 600° C.; 0.7 at 300° C.

Jan 1, 1927

By H. E. Cline

Calculations of the formation and growth of faults caused by a variation in lumellar widths were made for a two-dimensioml three-plate problem. The angle between the a-ß boundary and the growth direction was allowed to vary and the time evolution was studied using a quasisteady state approach. At spacings smaller than a critical spacing given by X V = AO variations in the larrlellar widths grow in time to produce faults that coarsen the structure, while at spac-ings larger than this critical spacing, variations in the lamellar widths decay in time. If small plates are introduced into the structure they may grow only at large spacings to refine the structure. The time evolution and shape of faults were calculated for the three plate-problem and then the three dimensional problem and rod-like eutectic were qualitatively discussed. UNDERSTANDING of the mechanism by which the spacing of directionally solidified eutectics is determined may allow one to control their structure better. Steady state solutions for the growth of lamellar structures have been found for a range of lamellar spacings A and growth velocities V. To obtain a unique solution for the isothermal growth of pearlite, Zener1 assumed that growth occurs at a maximum velocity, while Tiller2 assumed that a eutectic alloy, grown under an imposed velocity, will choose a spacing corresponding to minimum undercooling. These assumptions are equivalent and have been referred to as "extremum growth". The extremum condition predicts the observed relation between velocity and spacing as given by V = constant [I] but does not provide a mechanism for changing the lamellar spacing. Jackson and Hunt3 calculated the interface shape by using solutions to the diffusion equation for a planar interface and a relation of the interface composition to the local curvature. If the spacing is much larger than the extremum spacing, the interface breaks down catastrophically to form forked plates. However, the catastrophic breakdown cannot account for the small adjustments in spacing that must occur in practice..3 Direct observations during the growth of organic eutectics4 and the Pb-Sn eutectic5 show that spacing changes occur by the formation of faults. A fault in a plate-like eutectic is the edge of a plate. Once the faults form, they may move to make small adjustments in the spacing.6,3 The motion of faults intersecting the growing interface was shown by an approximate analysis to give Eq. [I].6 A perfectly regular lamellar structure should be able to persist over a range of lamellar spacings. However, during growth small perturbations in the structure may occur. If the amplitude of the perturbation increases in time the structure is unstable, while if all possible perturbations decrease in time the structure is stable. In a previous paper7 variations in the shape of the solid-liquid interface were considered, while this paper considers only variations in lamellar widths while maintaining a macroscopically planar solid-liquid interface. Previously, theories of lamellar growth1"3 have artificially contrained the growth to give a regular periodic structure. To allow for a variation in spacing, the three phase intersections and groove angles were allowed to change with time as determined by assuming local equilibrium. THREE-PLATE PROBLEM Since the spacing changes in eutectics by local formation of faults,4'5 it is suggested that local variations in spacing are responsible. The interaction between neighboring plates will be greatest because they have the smallest diffusion distance. For simplicity, as a nearest neighbor approximation, a three-plate problem will be considered, as illustrated in Fig. 1. The structure consists of a periodic array in which all the plates are allowed to vary in width. As in steady state growth it is assumed that the average composition in the solid remains constant. A variation in plate widths, that maintains the composition in the solid, was introduced by making the first a-phase plate thinner by an amount A, keeping the width of the second B-phase plate constant, and increasing the width of the third a-phase plate. If the structure were not perturbed, as in the regular two-plate problem previously described,' then the groove angles at the three-phase junctions are the equilibrium angles, 0, and ? B, and the solid-solid boundary is normal to the interface. In the three-plate problem with a variation in plate widths the phase boundaries are assumed to be related to the three-phase junction by equilibrium angles, but the a/B boundaries may be rotated by an angle 0 from the growth direction. The angle H be-tween the tangent to the a/B boundary and the growth direction may vary during growth and determine the —> — — —.A_ Q-0 / 0 x, X2 Fig. 1—Schematic of the three-plate problem showing a variation in the spacing and the effect on the angles at the three phase intersections.

Jan 1, 1970

By Robert M. Weidenhammer

For years before the war, Coal had the reputation of being a sick industry. Currently it is operating at peak production and succeeding pretty well in keeping out of the red. But, says Mr. Weidenhammer, it will have a relapse as soon as the war ends unless (1) working capital can be built up; (2) it gets the support of the people and Congress; and (3) a truly long-range national fuel policy is formulated.

Jan 1, 1943

By R. C. McFarlane, T. D. Mueller, J. E. Walstrom

In evaluating uncertainty, experiments are usually performed repeatedly and then conclusions are drawn from the distribution of results. With the advent of high-speed electronic computers, it is possible to perform experiments using mathematical models constructed to simulate complex experiments or operations. Statistical methods are then applied to the results of the simulated experiments. This procedure forms the busis of this paper. Demonstrated is the need for properly accounting for uncertainty in petroleum engineering problems. How uncertainty affects solutions is evaluated in three example illustrations. The method used to evaluate uncertainty in petroleum engineering studies is the Monte Carlo simulation procedure.'-" INTRODUCTION The solution to most technical problems may be derived from interrelationships among several quantities called variables or parameters. There may be only a few variables or several hundred. Interrelationships among parameters may be explicit or implicit, well established or only approximate. Some variables that fully or partially depend on the magnitude of others are called dependent variables. Input variables for most practical problems are not precisely known; there is usually an uncertainty in their value. The degree of uncertainty may vary from one variable to another. Variables that are known accurately are called determinates.' For instance, the gravity of crude obtained from a particular pool may be known precisely, and therefore is a determinate. The degree of precision with which a quantity can be determined increases as data describing the pool are accumulated during the development of the field and the producing life of the pool. The uncertainty of a parameter may result from difficulty in directly and accurately measuring the quantity. This is particularly true of the physical reservoir parameters which, at best, can only be sampled at various points, and which are subject to errors caused by presence of the borehole and borehole fluid or by changes that occur during the transfer of rock and its fluids to laboratory temperature and pressure conditions. Uncertainty may also result in attempting to predict future parameter values. This type of uncertainty is particularly evident in investment analyses involving future costs, prices, sales volumes and product demand. Uncertainty in the solution to investment problems is often called risk, and its study is called risk analysis.' Uncertainty also enters into biological and sociological analyses in which indeterminate factors are often important due to limited control of the experimental material. It is customary, in evaluating uncertainty, to perform repeated experiments and to draw conclusions from the distribution of the results of these experiments. With the advent of the high-speed electronic computer, it is possible to construct mathematical models which simulate complex experiments or operations and to perform the experiments repeatedly, utilizing the models. Statistical methods are then applied to the results of the simulated experiments This method forms the basis of the investigation reported here. PROBABILITY DISTRIBUTIONS FOR VARIABLES The uncertainty in the value of a variable may be indicated by a probabilistic description accomplished by expressing the quantity by a probability distribution. Many recognized probability distributions can be used to describe physical quantities. Recent studies used various types of distributions to describe core analysis data.',' However, for the examples in this paper, the uniform and triangular distributions are believed to reasonably approximate the data used (Fig. 1). The uniform distribution confines the variable between an upper and a lower limit. The variable may lie anywhere between the two limits. This distribution is used when no one range of values for a variable is more probable than any other, but information or intuitive reasoning indicates the variable will lie somewhere between the chosen limits. The triangular distribution is used for a variable when more data are available to indicate a central tendency of distribution. This allows postulating a "most likely" value to the distribution and upper and lower limits. In this case, as for the uniform distribution, the variable is not expected to assume a value less than the lower limit or greater than the upper limit. However, with improved quality of data it can be postulated that the variable will tend to assume a value close to the most likely value, and that there will be a decreasing probability for values away from the most likely value. The area under either of these probability distributions is equal to unity since it is assumed that there is a 100 percent probability that the variable will lie somewhere under the curve. An ordinate erected at any particular value of the variable divides the area under the curve into two parts: the area to the left of the ordinate represents the probability that the value of the variable will be equal to or less than the value of the variable at the position of the ordinate, and vice versa. The probability is zero that the variable will have any specific deterministic value. If two ordinates are drawn for any two values of the variable, the probability that the variables will have a value lying between these ordinates is equal to the area under the curve lying between the ordinates.

By CARLE R. HAYWARDC

BEFORE discussing this subject it is necessary to define somewhat the meaning of the tern metallurgical.. When I was a student at M. I. T. ore-dressing was not thought of as metallurgy in any sense of the word, but it was considered as more closely allied to mining, enabling the miner to market an otherwise unmarketable product, or at least to market it to better advantage. Progress in ore-dressing has gradually allied it more closely with smelting, for at present the raw material received by the smelter is predominantly concentrates and smelting practice has been profoundly affected by the products of the concentrating mill. It is not surprising therefore that in many schools ore-dressing is frankly considered as metallurgy and although there may be some dissenting opinions it will be considered as such in this discussion. Twenty-five years ago at M. I. T. metallography was taught in a few optional lectures. This subject has developed rapidly and been expanded into the new and increasingly important field of physical metallurgy. To many metallurgists the -term metallurgy means only physical metallurgy. They know little or nothing about smelting and leaching and even less about ore-dressing. Having then broadened the scope of the term metal¬lurgy to cover ore-dressing, smelting, leaching and phys-

Jan 1, 1930

By R. A. RAGATZ

THE preparation of specimens for microscopic examination from metal articles of relatively large cross-section offers no particular difficulty. It often happens, however, that articles submitted for examination are so thin that specimens satisfactory for microscopic examination can not be successfully pre- pared by the methods commonly employed when working with larger articles. Ordinarily, the preparation of metallographic specimens involves the following operations : (1) cutting the small specimens to be examined out of the larger mass of metal, (2) cleaning and electroplating, (3) mounting to furnish support during the grinding and polishing operations, (4) grinding and polishing to produce a scratch-free surface, (5) etching and drying. All of these operations must be carried out in such a manner that when the specimen is finally examined under the microscope, the structure seen is a true and well-defined representation of the structure that the larger mass of metal possesses at the place where the small specimen was removed. It is important that the deformation involved in cutting out the specimen be as slight as possible, in order that the subsequent grinding and polishing operations will completely eliminate the cold- working effects in the vicinity of the cuts. It is also important that the specimen never be allowed to attain a temperature high enough to alter its structure; the maximum permissible depends on the metal being handled. With some metals, zinc for example, consider- able care must be taken to avoid heating; with other metals, annealed steel -for example, no particular pre- cautions need be observed because there is no tendency for structural change to occur at relatively low temperatures.

Jan 1, 1929

By R. W. Guard, M. E. Fine

By treating the dislocation like a surface and ap-plying the usual thermodynamic treatment to the adsorption process a Gibbs adsorption equation for dislocations was derived. For extended dislocations in binary solutions the adsorbed concentration on the fault, X2a, may be computed from (jo/da2b) where a2b is the activity of the solute in the bulk material and s is the stacking-fault energy. Using the data of Howie and Swann for s the adsorption concentration goes through a maximum at 2 at. pct Al in Ag-Al, 10 at. pct Zn in Cu-Zn, and 8 at. pct A1 in Cu-Al. The pinning stress calculated from this concentration difference goes Ihrough a maximum at the same concentration us the peak in X2 a. The computed pinning stress thus does not vary with composition in the manner predicted by Suzuki, as was also pointed out by Hendrickson. The results are compared with the stress increment which can be attributed to Suzuki locking in Cu-Zn and Cu-Al stress-strain curves. They both agree in magnitude and in the location of the maximum. The predicted and observed maximum values for the Cu-Zn system (where activity data are available) are 700 g per sq mm (predicted) and 1000 g per sq mm (measured, laking into account the orientation factor of 2.2 to convert poly-crystalline to single-crystal data). CERTAIN simple internal surfaces may be regarded as dislocation grids. This fact suggested that it might be profitable to consider certain phenomena related to segregation of solute atoms at dislocations from the point of view of the thermodynamics of surfaces and surface adsorption. A general treatment of this type is given and then the results are applied to Suzuki segregation and pinning. Confirmation of the results is obtained from comparison of stress-strain behavior for copper and copper-base alloys. Two kinds of dislocations need be treated: perfect and extended dislocations. In either case the line tension of a dislocation, ?. the work which must be done to increase the length of dislocation by a unit length, is analogous to the surface tension. For an undissociated dislocation ? is the self-energy of a unit length of dislocation; for an extended dislocation where is the self-energy per unit length of a pair of partials far enough apart so that there is no interaction energy, is the interaction energy per unit length, is the stacking fault energy per unit area, and w is the equilibrium separation of the paired partials. In the absence of an applied stress the force pushing the dislocation partials apart in a close-packed structure is Gb2/12p where G is the shear modulus, b is the Burgers' vector of the complete dislocation, and is the separation of the partials. At the equilibrium separation, w this force equals s. Thus

Jan 1, 1965

By D. E. Peacock, B. Harris

The mechanical behavior of a niobium (columbium)TUNG alloy containing 20 wt pet Ta. 15 wt pet W, and 5 wt pct Mo has been studied in the temperature range 77° to 423°K. All specitrzens tested, apart from those into which oxygen was introduced deliberately, were fully recrystallized at 1500°C, had an average grain diameter of approximately 0.03 mm, and a combined carbon, ox-vgen. nitrogen, and hydrogen content of not not more than 250 ppm The meckatnical behavior of this alloy was found to be similar in seine respects to that of unalloyed bcc transilion metals. Both yield and flow stresses were sensililae to changes in deformation rate and both increased rapidly as the temperature was lowered below 150°C. A detailed examination revealed, however, that most of the temperature dependencc of the yield stress could be accounted for by the temperature dependence of the elaslic, modulus, whish is not true of the unualloyed metals. In lension at moderate strain rates, the trunsition fvom ducfile to hvittle behavior occurred just belour room teunperature bur incveasing the oxygen content from 190 to 200 pptn raised the transition temperature to about 4000K. TUNGSTEN and molybdenum have been found to be very effective high-temperature solid-solution strengtheners of niobium, but the amounts of these elements that can be added are limited if the alloy is to retain useful room-temperature ductility. It has been shown, however, that partial replacement of niobium with tantalum lowers the ductile-to-brittle transition temperature of such alloys and allows larger additions of molybdenum and tungsten to be made. Some of the high-temperature properties of niobium alloys containing these elements have been reported by Bartlett et al.,' and the work presented here describes the low-temperature behavior of one of these, a solid-solution alloy containing, by weight, 20 pct Ta, 15 pct W, and 5 pct Mo. The elastic modulus, the temperature and strain-rate dependence of the yield and ultimate tensile stresses, and strain-hardening effects are discussed and compared with those of unalloyed niobium. EXPERIMENTAL MATERIAL AND PROCEDURE The material used in this investigation was produced from a 6-in.-diameter, double arc-melted ingot. This was can-extruded at about 1150°C to a 3-in.-diameter billet, and after annealing for 1 hr at 1345°C the billet was heated to 1315OC and part rolled and part forged to 0.5-in.-thick plate. The resulting material exhibited a cold-worked structure

Jan 1, 1965

By J. P. Heller, H. B. Bradley, A. S. Odeh

It is an accepted procedure to represent oil field displacement problems in which the pressure is relatively constant by a potentiometric model. Variations in reservoir permeability thickness product are represented in the model by proportional variations in electrolyte depth. It is shown that significant errors are present wherever these variations are of such magnitude that the consequent differences in the electrolyte depth in the model or any regions therein are appreciable in comparison with their respective horizontal dimensions. To demonstrate the order of magnitude of this error, a hypothetical linear oil field in which permeability varies linearly with distance was treated both analytic.ally and by potentiometric model. The results obtained from the model are compared with the exact solution for various configurations of linear geometry. Deviations in flow times up to 11 per cent were observed. It is confirmed that these discrepancies can be reduced by increasing the areal scale and/or decreasing the vertical scale of the model. It is the purpose of this work to assist in the design of potentiometric models by indicating the relationship between this error and the chosen scale factors. INTRODUCTION The fundamental geometrical criterion which determines whether the pressure distribution in an oil or gas reservoir may be simulated in a conventional potentiometric model is the requirement that all reservoir parameters be constant along any vertical line between its upper and lower boundaries. This situation never obtains exactly; nevertheless, it is usually assumed that there is no permeability stratification within the section of interest, that all wells completely penetrate the sand, that there are no gravitational effects, and that variations in thickness of the sand are small compared to the horizontal extent of the field. In these ways the reservoir problem is reduced to two dimensions in which there is no variation of pressure in the vertical direction within the limits of the sand. Variations in sand thickness and/or horizontal pesmeability may be taken into account as described by Muskat, by considering the fluid conductivity of the reservoir in its horizontal plane to be proportional to the product of permeability and sand thickness. If the variations in sand thickness are small compared to the horizontal dimensions of the reservoir, then it is a good approximation to consider the reservoir problem to be essentially two dimensional. The same approximation, however, is made in the simulation of the assumed two-dimensional reservoir by the electrolytic model. The model, if it is to take into account variations of permeability-thickness product, must of necessity be made in three dimensions, that is, with variable depth. Most potentiometric model studies and theoretical treatments reported in the literature to date2,3,4,5,6,7,8 are those in which either an average permeability was used or a constant permeability was assumed. This is understandable since detailed permeability data are not usually available for the majority of reservoirs. Many investigators have recognized that the failure to incorporate permeability variations within a reservoir in model studies leads to serious error in predictions made

Jan 1, 1957

By G. Borelius

ABOUT the turn of the century, Gibbs' thermo-dynamic theory of heterogeneous equilibrium, on the one hand, and the experimental methods of thermal and microscopic analysis, on the other, gave to the physical metallurgist his first scientific tool, the equilibrium diagram. The classical equilibrium diagram of a binary alloy system shows the boundaries between ranges of homogeneous and heterogeneous equilibrium in their dependence of concentration and temperature. A homogeneous solid sohtion which on cooling passes such a boundary is assumed to precipitate, forming a mixture of two phases with different concentrations. The equilibriunl diagram and the equilibrium theory, however, give no information about the time scheme of the process or the intermediate states passed during precipitation. For this reason it satisfies neither the practical need of the metallurgist nor the curiosity of the physicist. As a matter of fact, in the heat treatment of alloys for technical use the objective very seldom is the equilibrium state. Thus good mechanical properties of construction material are connected, for the most part, with some intermediate state. As these intermediate states are thermodynamically unstable, there is, from a theoretical point of view, always to be expected a decay of the good properties with time; and it is a matter also of practical interest to know whether this natural life time of a material is of the order of, say, ten or thousands of years. Thus, for many reasons, there is a current demand to complete our knowledge of equilibrium through knowledge of the kinetics of the precipitation phenomena. From the point of view of the physicist, the most interesting question in this case is whether there are any general laws governing the kinetics. According to a generally accepted view, precipitation is ruled by two more or less independent phenomena, the formation of nuclei of a new phase and the growth of these nuclei. It is also commonly accepted that there is a tendency for the velocity of growth to increase with increasing temperature because of the increasing mobility of the atoms. There is also a tendency for the velocity of growth to decrease in the neighborhood of the two-phase boundaries. So far, however, very little is known quantitatively about this fundamental phenomenon in the case of solid metallic systems. In our laboratory attention has been directed especially toward the nucleation phenomena, and a series of measurements have been carried out with the guidance of a work- ing hypothesis (based on experiences from previous work on order-disorder transformations in alloys) about the influence on the nucleation of thermo-dynamic potential barriers. However, before discussing the experiments, the theoretical ideas will be considered. In a binary solid solution the arrangement of atoms on the lattice points approaches with increasing temperature a state of full randomness, as illustrated by the ball model of Fig. 1, that might represent a [111] plane of a face-centered alloy with 30 pct "black" and 70 pct "white" atoms. In reality the atoms are changing places continually with their neighbors so that the picture should rightly have been a moving one. On account of this thermal motion the concentration of black atoms within a certain group of, say, a hundred or a thousand lattice points fluctuates with time around the bulk concentration of 30 pct in a manner governed by statistical laws. With decreasing temperature two independent changes in this state grow more and more important. First, the mobility of the atoms decreases, and second, the forces between the atoms will have an increased influence on the fluctuations. In alloys with a tendency for precipitation, which are the concern of this lecture, the distribution function of concentration fluctuations will broaden, so that the relative probability of great local variations from the bulk concentration increases. Fig. 2 gives an example of such a fluctuation. When the alloy is supercooled below the solubility limit into the range of two-phase equilibrium, the fluctuations will now and then at some point give rise to a state that resembles the equilibrium state and thus will form a stable nucleus that is capable of growing by diffusion processes. In discussions with colleagues and in the literature, I have often encountered the idea that three or four atoms of the dissolved metal could form a nucleus of the new phase. A look at the ball model might be enough to indicate that this cannot be true. If it were true, there should be nothing but nuclei, whereas we know from experiment that nucleation must be a rather rare occurrence. In fact we have, as will be mentioned later, certain reasons to believe that the nuclei are formed by fluctuations containing some hundreds of atoms, which should be the order of the number of black balls in the fluctuating group of the figure, if it were extended into three dimensions. As a working hypothesis we have assumed that the fluctuations producing nuclei, though large and rare, still are ruled by the distribution laws of fluctuations of the supercooled solid solution in its initial state. Thus the probability of nucleation will be connected to the thermodynamic properties of the solid

Jan 1, 1952

By S. F. Shaw

Tars paper is a review of the principal details of cyanide practice in several of the modern plants in America, mainly during the year 1908. Two of the mills, the Goldfield Consolidated and the Vets, Colorado, are not yet prepared to give data, the former having started about Jan. 1, 1909, and the latter not yet being completed. These two mills embody most of the latest methods and are therefore described as far as possible. I. CRUSHING. The principal methods of crushing ores for treatment by the cyanide process are with gyratory and jaw-crushers, stamps, Bryan and Huntington mills, and tube-mills. The first stage is usually done by gyratory or jaw-crushers, in a few cases sup-\

Jul 1, 1909

By Paul F. Kerr, Raymond F. Robinson

Uranium mineralization occurs in the footwall of the Sunshine vein from the 2900 to the 3700 level. Veinlets of uraninite associated with pyrite and jasper have been so extensively divided and recemented that units more than a few feet in length are seldom observed. The wall rock is St. Regis quartzite of the Belt series. The age of the uraninite, on the basis of isotopic analyses, is 750 * 50, which agrees with geological data suggesting that phases of the Sunshine mineralization are pre Cambrian. THE Sunshine mine in the Coeur d'Alene district, Idaho, is well known for its silver-bearing veins but prior to the summer of 1949 had not been recognized as a possible source of uranium. At that time, during a geiger counter reconnaissance by T. E. Gillingham, R. F. Robinson, and E. E. Thurlow, high radioactivity was noted and radioactive specimens were collected from the footwall of the Sunshine vein.' The detection led to the identification of uraninite-bearing veins, since explored jointly by the Atomic Energy Commission and the Sunshine Mining Co. After the occurrence was noted, the geology of the uranium deposit was studied by the Sunshine staff, and a laboratory examination of the ores was conducted at Columbia University. Several types of laboratory work were undertaken. Differential thermal curves were made of selected siderite samples and results from many more were secured through the work of Mitcham.2 X-ray diffraction and X-ray fluorescence analyses were employed on uraninite, jasper, and siderite. Chemical analyses were made through the cooperation of the Division of Raw Materials of the Atomic Energy Commission. General Geological Features Several silver-bearing veins cut the overturned north limb of the Big Creek anticline as mapped by Shenon and McConne1,³ while the Osburn fault, a long-recognized regional feature about a mile away, marks the north boundary of the Silver Belt. The Sunshine vein, Fig. 1, has a south dip more or less parallel to the 60" axial plane of the fold and cuts rocks of the Belt. Series, starting with the Wallace formation near the surface, continuing downward through the St. Regis formation, and probably extending into the Revett quartzite which lies below the bottom or 3700-ft level. The limb of the anticline is locally modified by secondary folds, one being prominently exposed in the uranian area along the Jewel1 crosscut near the Sunshine vein. Crumpling of the limb resulted from compression which formed the anticline and probably preceded the faults in which the vein deposits accumulated. Evidence of drag along these faults points to reverse movement in the uranium-bearing area and elsewhere. This is true of major faults in the mine workings, and the majority of faults which can be mapped, as pointed out by Robinson.' The St. Regis formation, as measured in the mine, appears to have an initial thickness of some 2000 ft, but the apparent thickness due to thickening during folding is some 3400 ft. Along the Sunshine vein the purple and green rocks characteristic of the Wallace formation in the nearby Military Gulch section p. 37 of ref. 5) have been completely bleached because of introduced sericite. Hydrothermal solutions acting on the wall rock have substituted for the original color a pale greenish cast, although no pronounced mineralogical change has resulted, as Mitcham has observed.' The silver and the uranium depositions appear to belong to distinct epochs resulting from several periods of emplacement. Likewise, multiple periods of deformation account for the faulting. Uraninite is generally associated with silicification, while silver . mineralization accompanies carbonate veins. Rarely, uraninite may be found in a matrix of siderite. Ordinarily uraninite formed prior to ar-gentian tetrahedrite. Where clusters of veins form a stockwork, uraninite-jasper veins often favor one trend while tetrahedrite-siderite veins favor another. During deformation, brecciation of the St. Regis quartzite provided openings between broken rock fragments for precipitation from vein-forming solutions. Fractures due to major breaks were filled during the first stages of vein formation, while later deformation displaced the first veins and provided new channels along which further mineralizing solutions proceeded. The uraninite veins, as the first formed, have suffered fracturing, displacement, and segmentation. Uranian vein segments uncut by faults and more than a few feet in length are rare or nonexistent. Siderite veins are more massive and often extend without a break for tens and even hundreds of feet. In general they show much less segmentation. While the siderite is usually later, there is an overlap in the periods of deposition, some earlier siderite veins being extensively segmented in much the same way uraninite veins have been broken. Vein silica is more extensively distributed than the uranium and iron mineralization it carries. Along the vein course concentrations of uraninite frequently fade away and barren white quartz continues, the transition often occurring within a few feet along strike or down dip. An example appears on the 3700-ft level where a uraninite vein, see Fig. 2a,

Jan 1, 1954

By M. R. Tek

A new method for correlating the data on multiphase flow through vertical pipe is presented. The correlation is based on a "two-phase f factor" concept which was developed and successfully applied to horizontal multiphase flow by Bertuzzi, Tek and Poettmann. Field data previously published on several flowing and gas-lift wells have been used as the basis for the developed correlation. The application of the method to actual two-phase flow problems indicate that this method is capable of predicting the pressure distribution in vertical multiphase flow strings well within the accuracy range usually desired for common engineering and design calculations. A new working chart developed for calculation of two-phase pressure gradients and a graphical step-by-step procedure for the computation of pressure distribution are presented along with an example problem. INTRODUCTION Multiphase flow through vertical pipe is encountered in many engineering installations. In petroleum, chemical process, nuclear engineering and many other industries, problems associated with simultaneous flow of two or more phases through vertical pipe have been of interest for a long time. This interest has increased considerably during recent years due to applications to new processes in petroleum production and refining and to problems of steam generation and heat removal from nuclear reactors. One prominent example of vertical two-phase flow is provided by the gas-lift process where oil, water and gas flow simultaneously. If the pressure profile in a gas-lift well can be predicted within reasonable accuracy, it would be possible to get good estimates of the power required to lift the oil, the optimum depth, the pressure and the rate at which to inject gas. Furthermore, the effect of production rate and tubing sizes on these quantities can be evaluated before any design decision is made on the installation and operation of the flow string. The majority of experimental work available in the literature deals with two-component systems where individual phase flow rates in and out of the pipe remain constant. The general problem of prediction of pressure drops in multiphase flow systems is very complicated. The co-existence of numerous flow patterns of widely different geometry and mechanism, conditions of surface instability and the nature of force fields acting upon the system are among the major difficulties commonly encountered. The classical approach of fluid dynamics which would be based upon the formulation and solution of Navier-Stokes equations has been found by many investigators completely devoid of any hope of success-—not only because of inherent nonlinearities but also because of insurmountable analytical difficulties standirng in the way of setting up the boundary conditions. The presence and effect of interfacial forces on mu1tiphase flow systems further complicate the theoretical approach. For these reasons, many investigators choose to adopt semi-empirical if not purely empirical approaches in order to obtain solutions of engineering utility. A prominent practical solution has been given by Poettmann and Carpenter' in the form of an empirical correlation. In their paper, total flowing densities of fluids and solubility effects of gas in oil have been taken into account for the correlation of field data covering a wide range of operating conditions for oil wells. They treated the gas. oil and water as a single phase of combined propcrties and correlated the multiphase friction factor as a function of the product (pvd), i.e., density X velocity X diameter of the flow string. However, because the product (pvd) is dimensional while the frictior factor is dimensionless, the generality of their result's is somewhat restricted. It seems that the omission 01 viscosity effect may be one of the reasons for the scatter of data as shown in their correlation chart. The concepts of the "two-phase f factor" and the "two-phase Reynolds' number function" were recently developed and successfully applied to correlate horizontal multphase flow by Bertuzzi, Tek and Poettmann.' Recently, two new methods of correlation by Tek and Chan' have been presented on simultaneous flow of liquid and gas through vertical pipe. These two methods of correlation and the working equations in field units necessary for their application are included in this paper. The extension of the conccpt of two-phasc Reynolds' number function successfully developed for horizontal flow into vertical multiphase flow systems, development and evaluation of working charts permitting calculation of two-phase pressure gradients and