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By J. L. Huitt, J. L. Pekarek, D. K. Lowe

In a theoretical study of hydraulic jetting, the velocity of the abrasive material relative to the velocity of the fluid in the jet stream is analyzed as the jet stream moves through the convergent and straight sections of the nozzle and the region between the nozzle exit and target. The results revealed that the abrasive material exits from the jet nozzle at a lower velocity than the fluid. The exit pmticle velocity can be increased by increasing either the density of the fluid or the length of the nozzle, and/ or decreasing either the particle density or particle diameter. In the divergent jet stream, there exists a point after which the particle velocity exceeds that of the fluid. The relative velocities were considered in the derivation of an equation to predict cutting rate of a circumferential notch and maximum notch depth. Data of a general nature and data which substantiate the theoretical results were obtained experimentally. INTRODUCTION The use of a fluid containing an abrasive material has been an established technique for cleaning and cutting for many years. In the petroleum industry, the early effort to use this technique1 to perforate and/or to overcome wellbore damage met with only limited acceptance because of the short life of the jet nozzle. With the introduction of improved perforating techniques, and later, hydraulic fracturing, the use of hydraulic jetting as a well completion technique became even less appreciated. It was only in recent years that interest in hydraulic jetting was revived. Once this interest was revived, the results of surface tests stimulated the interest of the industry even more than the state of the technology probably warranted because many of the tests were not appropriate for down-hole conditions. However, because of the stimulated interest, the development of the jet nozzle progressed very rapidly to the point where the nozzle life was no longer a prob- lem. With this accomplished, the use of hydraulic jetting in well completion became an accepted practice in a short time. The purpose of this paper is to present a theoretical analysis of the hydraulic jet stream as it passes through the nozzle and travels to its target. With a better understanding of the jet stream and the effects of various parameters, the performance of the process can be predicted more accurately. Equations are presented for cutting rate as applied to circumferential wellbore notching that relate the jet stream make-up, notch configuration and formation material. Also, experimental data are presented on some factors pertinent to hydraulic notching that are not theoretically analyzed. RELATED STUDIES Most of the studiesl-5 reported in the recent literature have pertained to the more practical aspects of hydraulic jetting; i.e., the effects of certain parameters as interpreted from experimental results, and the application of hydraulic jetting in well completion. In reviewing the effects of various parameters, it is interesting to note the reported depths of penetration obtained under various imposed conditions. In general, the depths vary from a few inches to several feet; however, a depth of penetration of less than 6 in., as reported by Thompson,4 seems more realistic for the usual field practice of hydraulic jetting with sand in water for a period of 20 to 30 minutes. In addition to the practical aspects, the study of Brown and Loper5 included a theoretical approach to hydraulic jetting. Their study resulted in the development of a theoretical expression for the maximum depth of penetration if jetting were continued for an infinite time. An analysis of the equations presented reveals that the initial cutting rate is infinite. The equation expressing centerline velocity is that of Forstall and Gaylord,6 which is applicable for a jet stream exiting in a large stationary medium. Since practically all of the fluid pumped into a perforation (or cut) must flow back through the perforation prior to re-entering the wellbore, a description of the medium as finite and non-stationary seems more reasonable. Thus, in this

By M. F. Williams, L. G. Hendrickson

IN classification of pulps bearing magnetized ferromagnetic particles, depolarizing is of great importance. If size separation is to be effective, particles must be individual rather than in floes. Depolarizing is also practiced in heavy medium separations in which ferrosilicon or magnetite is the medium. When particles of ferromagnetic material have been removed from a magnetic field, residual magnetism causes agglomeration. The term depolarizing refers to the operation of reducing or eliminating this residual magnetism and may thus be considered magnetic deflocculation. The terms demagnetizing and randomizing are also used. At the Research Laboratory of Oliver Iron Mining Div. in Duluth a method was developed for measuring depolarization of the pulp of ferromagnetic material. Experiments were made with Mesabi taconite,' a natural magnetite of low coercive force. Ferromagnetic materials of higher coercive force, such as lodestone or the artificial magnetite produced by reduction roasting of hematite, present a more difficult problem, which was not within the scope of this investigation. It is possible, however, that some of the techniques evolved for measuring and calculating electrical characteristics of alternating current coils would be of use in depolarizing high coercive force material, particularly in conjunction with high-frequency alternating current, as proposed by Hartig and others.'," Properties of Ferromagnetic Materials:'7 Experimental work, described below, has shown that if a sample in the magnetized state is heated above the Curie point and cooled, much of the preferred orientation is destroyed and the sample is substantially depolarized. It has been thought that when the sample cools below the Curie point the domains cancel each other, leaving a zero net moment. However, such particles still exhibit a tendency to cohere, and undoubtedly this is caused by the forces of residual magnetism. -AS measured by the percent depolarization, this tendency is reproducible for any sample upon repeated heating above the Curie point and subsequent cooling and is independent of the initial state of magnetization. It is postulated, therefore, that as the material is cooled below the Curie point the domains in any particle do not completely cancel each other, but rather are preferentially oriented to some extent. Mechanism of Depolarizing with Alternating Current Magnetic Fields: It is believed that when ferromagnetic material is passed through an alternating magnetic field, depolarizing occurs in the decaying portion of the field. As the particles pass through the portion of highest intensity they become magne- tized. If the particles are not free to move, the polarities of the particles will be reversed (by a mechanism similar to that described above for magnetism) at a frequency equal to that of the applied field. As the material moves through the decaying field, intensity levels become such that a domain does not completely reverse, but stops on an axis of easy magnetization. By the time the material reaches the point of zero field intensity, a state of fairly random orientation of domains is achieved. If conditions are such as to give a completely random orientation, the particle will have little or no external magnetic field, and a pulp of such particles will be depolarized. Previous Work In 1918 E. W. Davis was granted a patent for demagnetization of magnetite pulps.' His method consisted of passing the pulp through a tapered coil, activated by alternating current of normal frequency (60 cycle). This method, with minor modifications, has been used almost universally in all pilot plants and commercial installations in which depolarization of low coercive force materials has been required. Hartig, Onstad and Foot2,3 avd made a detailed study of the factors involved in depolarizing both low (below 100 oersteds) and high (above 100 oersteds) coercive force material. They developed a method for evaluating the relative degree of depolarization of any pulp based on the settling characteristics of the pulp. Their standard of comparison was a sample heated to above the Curie point and cooled in a zero field, all in a neutral atmosphere.* For low coercive force material they found treatment.Thisprocedure is subsequently called, in this report,theCurie that results equivalent to Curie treatment could be

Jan 1, 1957

By David Cornell, D. L. Katz

Procedures for computing turbulent flow of gas in steady state near the well bore and a graphical method for predicting unsteady state laminar flow at distances from the well have been combined to compute pressure gradients in gas reservoirs. Methods are discussed for predicting single and multiple transients at constant flow rate in an infinite reservoir, predicting constant How rate. in a finite reservoir, reproducing and interpreting back pressure test data, and prediction of the behavior of a closed-in gas well. An example of the graphical method is given for a single transient and the results are compared to a published analytical solution. A typical calculation of the pressure gradient in a reservoir and the production of gas is made .starting with data from a hack pressure test. INTRODUCTION The calculation of pressure gradients throughouse a ga-reservoir at any point in its production history is a complex problem involving turbulent flow near the well bore and unsteady state flow of the gas from the reservoir. The problem is complicated further by the variety of boundary conditions that may be imposed upon the flow. Such boundary conditions include finite or infinite reservoirs. constant or variable rates of production, constant or varying bottom hole pressures, complex initial pressure distributions throughout the reservoir, and pressure maintenance through cycling. In addition to these problems there are the practical difficulties associated with natural gas reservoir analysis These might include: (1) variation. in the permeability and porosity throughout the formation. (2) variations in the thickness of the formation, (3) communication of the producing formation with other producing zones. (4) radial variations in permeability due to influx of drilling fluid. acidizing. or the buildup of liquid in the formation around the well, (5) partial penetration of the producing zone. (6) water flood, and many others. These problems will be considered eventually. In the mean- time, it is necessary to present methods of handling the case of radial flow through a homogeneous, regular, producing stratum to a single well uncomplicated by other factors. The idealized case of steady state, radial flow from a natural gas reservoir was studied by Elenbaas and Katz5 and by Mac-Koberts.' An analysis of the unsteady flow of gases through porous media has been made by Aronofsky and Jenkins' for the one dimensional laminar case with the boundary conditions of constant downstream pressure and uniform initial pressure. Solutions for the partial differential equation for unsteady state radial flow of liquids through porous media have been given by Van Everdingen and Hurst" for the constant bottom hole pressure and constant production rate cases for laminar flow in a reservoir initially at a constant pressure. The analogous heat transfer equation has been treated by Perry and Berggren9 for the case of quenching a cylindrical hole in an infinite medium to a constant temperature. The back pressure curve, which involves the variation of the bottom hole pressure as it is determined by the behavior of the reservoir as a whole. has been studied by Rawlins and Schellhardt,10 Binck-lev,' Baumel and Breitung,' and others. No complete. adequate treatment has been given for the unsteady state, radial flow of gases into a cylindrical hole from a porous medium with or without the presence of turbulent flow and for any set of boundary conditions. If one relies only on analytical solutions of the basic equations, a new solution must be obtained for each new boundary condition. Furthermore, the complexity of the mathematical expressions for boundary conditions other than the very simple cases limits the use of analytical solutions. Graphical methods exist, however. that are general in nature, accurate, and readily employed. The analysis of steady and unsteady, laminar and turbulent, radial flow for various boundary conditions with application to specific natural gas well problems by means of graphical procedures forms the content of this paper. STEADY STATE RADIAL FLOW EQUATION FOR LAMINAR AND TURBULENT FLOW A steady state radial flow equation for laminar and turbulent flow through unconsolidated sands has been given by Muskat as discussion of the work by Elenbaas and Katz.5 This equation is based on the properties of unconsolidated

Jan 1, 1953

By Leendert de Witte

Conventional resistivity logs consisting of a short normal, a long normal, and one or more long lateral curves do not give data that allow a complete quantitative interpretation in beds thinner than 20 ft. Reservoir rocks usually exhibit zones of continuous homogeneity of quite limited thickness where the long lateral curves become useless because of adjacent bed effects and boundary phenomena. If the beds are 12 ft or thicker, the short and long normals may be used for qualitative interpretation, which can be streamlined by the application of simplified departure curves. For beds of a thickness less than twice the long normal spacing, this procedure breaks down. The combination of the limestone curve, the later-olog or guard electrode log, and the microlaterolog permit quantitative interpretation for beds that are at least 10 ft thick, provided the mud resistivity and the hole diameter are known with sufficient accuracy. For beds thinner than 10 ft, combinations of the microlaterolog with short spaced laterologs and pseudo laterologs appear to be promising. Interpretation of these curves again requires the application of simplified departure curves. Resolution of various possible combinations was analyzed using departure curve data calculated on the Whirlwind I computer at the Massachusetts Institute of Technology. A field example is shown using the microlaterolog-microlog combination, and the combination of a 6-in. modified laterolog plus a 6-in. pseudo laterolog. INTRODUCTION For the purpose of quantitative interpretation of resistivity logs in porous formations, we want to obtain two essential quantities from the logs, namely, the true resistivity of the undisturbed formation, Rt, and the resistivity of the part of the formation invaded by mud filtrate, Rt. The apparent resistivities of all conventional logging devices are functions of these two parameters and are also influenced by a third unknown parameter, the diameter of the invaded zone, d. It has been shown' that from the normal curves alone it is impossible to arrive at a unique solution for the three unknowns, Rt, R1, and d1. In very thick homogeneous beds, if invasion is not too deep, we can obtain a fair approximation to Rt from the long lateral curves and then use the two normal curves to find Rt and d1 Even under the most favorable conditions, the resolution of this system is not very good. The short normal does not give a reasonable approximation to R1 unless invasion is very deep (dl>16 hole diameters). For very deep invasion, however, the long laterals no longer approximate Rt. For bed thickness between 20 and 40 ft, the long laterals are affected appreciably by the adjacent beds; and the curves are distorted by boundary anomalies to the extent that they lose their quantitative usefulness in most cases. For the same bed thicknesses, the normal curves still function reasonably well. Although it is impossible to find unique solutions Lor R1 and Rt using the normal curves alone, we can obtain a reasonable approximation for the ratio R1/Rt through the use of simplified departure curves. This fact was brought to our attention by A. J. de Witte, geologist with Continental Oil Co. As the magnitude of Rl/Rt is a major clue to the presence of oil in formations, this method can be used to good advantage for qualitative analysis and will be discussed in somewhat greater detail. With the aid of suitable bed thickness corrections, the analysis of the normal curves may be used for bed thicknesses larger than 12 ft. For thinner beds, the method rapidly loses its resolution; and we have to resort to different types of resistivity logs if we want to attempt to analyze the curves quantitatively. The inadequacy of conventional resistivity curves in thin beds is far more serious than generally realized. Fig. 1 shows a conventional E. S. with a 16-in. and 64-in. normal and a 16-ft lateral through a section of Lansing-Kansas City lime, in comparison to a guard electrode survey through the same section in a neighboring well. The porous zones, which show up as low resistivity breaks on the guard electrode log, are completely masked by adjacent bed effects and boundary anomalies on the conventional curves. Even the short normal shows most of the porous Zones only as Vague deflections and in many cases fails to register Their

Jan 1, 1955

By C. K. Dumbauld, B. E. Morgan

The need for a low-strength cementing composition for use in well cementing is reviewed and results are presented of laboratory and experimental field tests of a modified cement having a controlled ultimate tensile strength of approximately 200 psi. The modified cementing composition may he prepared from either high early strength or normal portland cements by the addition of bentonite clay and a suitable agent for dispersing and controlling the set of the slurry. Substitution of the modified cement for conventional slow-set cements may give better completion results in many wells because the modified cementing composition has lower set strength, lower slurry density, and greater slurry stability than conventional cement slurrieh. The lower ultimate strength allows greater penetration with less shattering of the set cement when perforating casing and cement. The lower elurry density allows the placement of longer columns of cement slurry, and the greater slurry stability reduces the possibility of having an uncemented section caused by the settling of cement particles before the cement set.. INTRODUCTION High strength lias always been one of the accepted criteria of a good cement. During the early use of portland cement in well cementing. emphasis was placed upon securing cements with higher strengths. In 1931, Barkis' reported that, "Normal oil well cements have been improved to develop greater strengths and uniformity of product, which has aided in producing successful jobs in cementing the deeper strings." As long as most wells were completed by the open-hole method. the use of cements having high strengths seemed desirable, and there was no objection raised against high-strength cementing compositions. For a number of years. how-ever, the industry has been completing a large numher of wells by setting and cementing casing through productive horizons and then obtaining production by gun-perforating the section of casing opposite the desired interval. Although this method has been generally successful, difficulties have been experienced in some cases in completing or recompleting wells because of apparent lack of adequate penetration by the bullets through the casing and surrounding sheath of cement and into producing formation. In addition to the penetration trouble: there have been indications that fracturing and shattering of the set cement by perforating might he a contributing factor in causing the failure of some jobs to exclude water or gas from oil producing zones. The possibility that cements having high set strengths were contributing to til difficully ill obtaining satihfartory perforating results has re. ceived attention during recent years. Gun perforating tests conducted in 1944 showed that the depth of bullet penetration into set cement varied with the hardness of the cement, the greater the strength of the cement the less being the penetration. In 1946, Farris2 pointed out that high strength cements were not needed in well cementing, and in 1947, data published by Oliphant and Farris3 showed that set cement was perforated without shattering at approximately 150 psi tensile strength. whereas at approximately 300 psi tensile strength severe cracking and shattering occurred. Oliphant and Farris suggested that wells be perforated at the proper time interval after placement of the cement so that the set cement would have the desired strength. Several difficulties may he encountered in trying to perforate a cement job at the correct time to catch the tensile strength near 150 psi. The rate of strength development of different cements varies considerably. This fact is illustrated by results of tensile strength measurements presented in Fig. 1. These data show that at 175°F the tensile strengths of three conventional slow-set cements varied from 75 to 235 psi at the end of 12 hours. After 24 hours, the tensile strengths varied from 200 to 455 psi. The rate of strength development is affected. also. by the temperature of the forniation, and this adds to the uncertainty of perforating at the rorrect time, since accurate well cementing temperatures may not he known in many cases. Furthermore, in the recomple-tion of wells it is sometimes necessary to perforate cement which has set for a long period and has developed maximum or final strength. In view of the apparent need for a cementing composition having a controlled ultimate strength, an investigation was

Jan 1, 1951

By J. M. Uys, T. B. King

The solubility of water in silicate melts of various compositions was measured. The basicity of the silicate did not appreciably affect the water solu-bulity at low-base content (acid compositions). Near the orthosilicate composition the solubility increased with basicity for silicates in which the cation displayed a weak ion-oxygen attraction and apparently decreased for those in which the cation showed a strong ion-oxygen attraction; metasilicates of the former class dissolved more water than those of the latter. Temperature had little effect on water solubility. The experimental results are interpreted on the basis of two modes of solution, the contribution of one decreasing, and that of the other increas -ing, with increased melt basicity. In the former, solution occurs through interaction with doubly-bonded oxygen atoms and in the latter, through interaction with singly-bonded oxygen atoms, or, in very basic melts, through reaction with free oxygen ions. THE hydrogen content of a steel melt is in a large measure determined by water dissolved in the slag. In some glasses water may be a major cause of "seeds". Water vapor in the furnace atmosphere is the primary source in both instances. A knowledge of the mechanism of water solution in silicate melts should help in assessment of practical methods for its control in steelmaking and glass refining. Walsh et a1.l measured the water content, expressed as hydrogen, of 40 pct lime-20 pct alumina-40 pct silica and 62 pct manganese oxide-38 pct silica melts as a function of the steam partial pressure, in equilibrium with the melt. Tomlinson 2 and, also, Russell3 investigated this relationship for a molten 30 pct soda-70 pct silica glass. In all three investigations, the solubility of water was found to be proportional to the square root of the partial pressure of steam. Moulson and Roberts 4 confirmed this relationship for a silica glass. On the basis of the square root relationship, Tomlinson2 and Russell3 interpreted the solution reaction as "network-breaking", similar to that expected on the addition of metal oxides to silica. Walsh et al.' postulated two possible modes of solution, one the mechanism suggested by Tomlinson and Russell and the other the reaction of the water molecule with an oxygen ion to form hydroxyl ions. These two modes of solution suggest opposite effects of melt basicity on water solubility. However, little appears to be known about the effect of melt basicity on water solubility. Walsh et a1.l found, in the lime-silica system, that the water content increased slightly with increased basicity. As these authors pointed out, this does not appear to be in accord with their further observation that slags containing little or no silica dissolve very little water. Kurkjian and Russell5 measured the effect of basicity on water solubility in alkali silicates in the composition range 15 to 45 mole pct alkali oxide. They found a minimum in the water content at about 25 mole pct alkali. This was interpreted on the basis of two concurrent solution reacZions; one in which solubility was proportional to the activity of doubly-bonded oxygen and, in the other, proportional to the activity of singly-bonded oxygen. The present work was aimed at establishing the effect of basicity on water solubility in silicate melts over as wide a range of compositions as practical. APPARATUS AND EXPERIMENTAL PROCEDURE The silicate melt was equilibrated with a "carrier-gas" of accurately known water content, quenched, and analyzed for water by a vacuum fusion technique. Some pertinent details of the equilibration procedure, analysis technique, preparation, and handling of the silicates are given below. Gas-Silicate Equilibration. The apparatus used to equilibrate the melt with the gas mixture was similar to that used by Walsh et al.' but with some important modifications.6 Purification trains were provided for nitrogen and hydrogen; whenever air or oxygen was used as carrier gas the nitrogen purifiCation train was used with the copper furnace at room temperature. Gas flow rates were measured with capillary flow meters; bleeders filled with a mixture of dibromo and tribromo ethyl benzene (density about 2 g per cc) were used for convenience in controlling flow rates.

Jan 1, 1963

By J. T. Norton, Pekka Rautala

The phases and equilibria in the W-Co-C system have been studied by X-ray diffraction methods, metallographic technique, and thermal analysis. In addition to the 7 phase, two double carbides, called 8 and have been revealed. The compositions correspond to CO3 W6C2 and Co3-W10C4. The reactions leading to these phases have been explained and tentative diagrams of stable and metastable equilibria proposed. The basic reactions in sintering cobalt cemented tungsten carbides are discussed. THE W-Co-C system is of fundamental importance in practical carbide manufacturing as well as for the understanding of the sintering mechanism. Surprisingly little is known about this system, for the probable reason that all the important alloys are of two-phase structure and that the diagram Co-WC has been treated as a quasi-binary. This obviously is incorrect, because WC decomposes before melting. One ternary phase, 7, of composition Co3W3C has long been known. It was first studied by Adelskold, Sundelin, and Westgren,1 although the isomorphous iron-tungsten carbide was known earlier. There have been in the literature several reports of two 7 phases.' " Also the 7 phase has been considered unstable by Takeda4 and Westgren.1 The Co-WC diagram has been studied by Wyman and Kelley5 and a quasi-binary diagram has been published by Sandford and Trent.2 Takeda has published a tentative Co-W-C diagram, considering both metastable and stable equilibria. However, the lines of two-fold saturation are shown only partially and it seems impossible to complete the diagram without violating the phase theory. Therefore it seemed desirable to examine the system in more detail. Experimental Procedure The alloys used in the present investigation were made of powders of tungsten, tungsten monocarbide, cobalt, and carbon and were of the grade used in manufacture of commercial cemented carbides. The powders were ground and mixed in small stainless steel ball mills, using balls of the same material. Benzene was used as a dispersing agent. The mixing period was 1 hr, since this was shown to give suffi- ciently good mixing of the powders without too great a contamination from the mill. After ball milling, the specimens were pressed in cylindrical or rectangular dies. No paraffin or other lubricant was used and the small compacts had sufficient green strength to be handled without difficulty. Several sintering furnaces were employed. The most satisfactory arrangement was a vacuum furnace based on the Arsem principle which employed a graphite helix as the resistance heating element. Specimens were placed on graphite stands and there was generally a slight carburization or decarburiza-tion of the specimen surface, depending on the carbon content of the alloy. The evaporation of the cobalt at a sintering temperature of 1400°C was not significant, but became severe at 1500°C and higher. The sintering time was 1 hr at 2000°C and 2 to 4 hr at lower temperatures. It was not possible to quench the specimens, but the cooling rates were rather fast, greater than 300°C in the first minute. In the system under investigation, the reactions are sluggish, and it is believed that the high temperature structures are satisfactorily retained. The principal method of investigating the sintered specimens was X-ray diffraction by the Norelco recording spectrometer. Approximate determinations of the phase boundaries were made by the disappearing phase method. Ternary Phases To study the phase formation in W-Co-C system, a series of specimens was sintered at 1400°C. In this experiment two ternary phases, called here ? and k were formed in addition to the well-known 7 phase. The 7 phase, which has been completely described by Westgren: showed a range of homogeneity from 7 to 20 pct C and from 38 to 48 pct Co. At 1400°C the 7 phase was found to be in equilibrium with monotungsten carbide, 8, tungsten, 8, #?, and liquid. The boundaries toward #? and liquid were difficult to determine and appeared to be very temperature sensitive. The other boundaries are believed to be well fixed. The homogeneity range of 7, as measured in this work, is considerably smaller than the one

Jan 1, 1953

By Orville R. Lyons

This paper presents a method whereby the amount of misplaced material and the difficulty of the separation can be used to compare coal cleaning equipment of all types, from effectiveness and capacity standpoints. The correlations presented do not include all types of equipment currently available, but the method can be used to evaluate any make or type of coal cleaning equipment, both old and new. THE relative performance of coal washing equipment, or the effectiveness with which any type or make of equipment removes impurities from coal, has been most difficult to evaluate in the past. The most widely used yardstick is the Frazer and Yancey efficiency formula developed in 1922,' but Yancey in a later article states that "washers treating coals of different density composition or operating at different densities of separation cannot be compared directly on the basis of this criterion."' Prior to and since 1922, a variety of other methods has been used for comparison purposes, including the distribution curve, the error area, and the "ecart probable" or probable error. Yancey and Geer in discussing these methods conclude, "Performance can be evaluated in a number of different ways, with the choice of the proper method to use being dictated by the objectives of the investigation and the data available."' It is true that performance can be evaluated in a variety of ways, but if the equipment is to be evaluated on an effectiveness basis, there should be only one universal comparison method. Varying methods have been used because one universal comparison method has not been found or developed. In the article previously quoted, Yancey and Geer state in clear terms the primary concept for a universal comparison method: "One of the simplest, and certainly one of the most obvious evaluations of washery performance is the quantity of sink material in the washed coal and the float material in the refuse. If the washery products are tested at the density at which the washing unit is operated, the sink in the washed coal and the float in the refuse represent material that has been misplaced." The quantity of misplaced material was used as a criterion of washery performance by Lincoln in 1913," by the United States Bureau of Mines in 1938,' by Hancock in 1947," and by the national French research agency Cerchar in recent years.' In 1950 Andersone proposed the use of this criterion as an efficiency value to replace the Frazer and Yancey formula. However, none of the above-mentioned investigators used the misplaced material concept in a manner that would provide universal coal-cleaning equipment comparisons. The Correlation Theory The ideal coal cleaning process would treat all sizes and would make a perfect separation at any given specific gravity. All material lower in density than the desired value would report in the coal product and all material higher in density would report in the refuse product. Unfortunately, no known cleaning process achieves this goal and there seems little likelihood that any process yet to be invented will do more than approach it. When coal is treated in volume under operating conditions, it is impossible to avoid mechanical entrapment, fluctuations in throughput and effective gravity of separation, and the creation of turbulent currents, even when a true heavy-liquid bath is used and the feed is closely sized and contains little intermediate gravity material. This being so, it is possible to appreciate the difficulties inherent in trying to obtain a perfect separation when treating a wide range of sizes and a feed containing high percentages of intermediate material, using turbulent currents to help create the effective separation gravity, under operating conditions which normally tend to be on the overload side. When coal is separated from refuse in any coal cleaning equipment, some refuse always reports to the coal and some coal to the refuse; the writer therefore assumed that there should be a relationship between the total amount of misplaced material produced by any given piece of equipment and the difficulty of separation as represented by the percentage of near gravity material in the feed. With small amounts of near gravity or k0.1 material in the feed there should be less misplacement of material than would occur with large amounts of near

Jan 1, 1953

By P. G. Winchell, M. Cohen, J. Woodilla

The kinetics of stabilization have been studied with respect to the isothermal component of the martensitic reaction in ivon-nickel alloys. Although the carbun (or nit-vogen) content may be very low in these alloys, it plays an important vole in the stabilization phenomenon. In fact, if these interstitial elements are removed by moist-hydrogen treatment, no evidence of stabilization is found. In the pvesence of 0.007 wt pct C, the activation energy for the stabilization process is comparable to that -for the diffusion of carbon (or nitrogen) in ferrite) rather than in austenitc. This suggests that the interstitial diffiision controlling the stabilization occurs within the martensitic embryos rather than in the matrix of the parent phase. The kinetics furthev indicate that the interstitial atoms tend to diffuse -from the embryos toward the suvroundings, thereby immobilizing the interface. This appears to be the origin of the stabilizing effect -found in these alloys. PHILIBERT' has shown recently that interstitial elements play an important role in the stabilization of martensitic transformations in iron-base alloys. However, determination of the temperature dependence for this stabilization process has produced values (- 11,000 cal per mol) that cannot be readily identified with the activation energy for diffusion of carbon (or nitrogen) in either ferrite or austenite. In the present work, the isothermal mode of the martensitic reaction was employed to derive the activation energy for stabilization, and this was found to agree fairly well with that for diffusion of carbon (or nitrogen) in ferrite. An iron-nickel alloy with 30.8 wt pct Ni and 0.007 wt pct C was used in these experiments, the specimens being in the form of rods 0.074 in. in diam and 2 1/2 in. long. The specimens were sealed in evacuated vycor tubes and austenitized at 1100°C for 1/2 hr prior to quenching in water. A second series of specimens was decarburized (and denitrogenized) prior to the above austenitizing treatment by annealing in moist hydrogen for 182 hr at 1215°C. In order to achieve a "standard" condition in the austenitic state, all the specimens were transformed to martensite by cooling to - 195°C before the final austenitizing. Both the 0.007 pct C and the decarburized series then had an Mi temperature of about - 30°C. The isothermal martensitic transformation was carried out at a reference temperature of -88"C, and was traced by means of electrical resistance measurements. Each resistance value was normalized by dividing by the resistance of the austenitic specimen at O°C, thus giving a resist- ance ratio R. The rate of decrease of the resistance ratio (-dR/dt) provided a measure of the transformation rate. It was found that a plot of R vs log t at the reference temperature resulted in a slightly curved line which could be closely approximated by two straight lines intersecting at a time of 10 min, as shown in Fig. 1. If G = dR/dlogt is the linear slope of either straight segment, the rate of transformation at any given time is: The ratio of G for 1 less than 10 min to that for t greater than 10 min was 1.19 for the 0.007 pct C series and 1.24 for the decarburized series. These ratios made it possible to compute the transformation rate at any time greater than 10 min, knowing the transformation kinetics prior to 10 min. The stabilization treatment was introduced by up-quenching from the reference temperature, usually after 10 min of isothermal transformation: to one of four stabilizing temperatures between 0" and 22"C. After holding for various times, the specimens were down-quenched to the reference temperature for additional isothermal transformation. In this way, it was possible to compare the transformation rate (- dR/dt), immediately after stabilization with the transformation rate (- dR/dt)U in the unstabilized condition. The degree of stabilization was defined as: Ordinarily, Gs and Gu would be measured after the same time of prim isothermal transformation.

Jan 1, 1960

E. A. Loria (Product Metallurgical Engineer, Crucible Steel Co. of America, Pittsburgh)—In this interesting paper, our introductory work was quoted. We would like to call attention to our sequel paper on the experimental determination of oxygen in cupola-melted cast iron,20 which was not mentioned. Vacuum-fusion oxygen values (as well as hydrogen and nitrogen) were reported for nine heats of cast iron melted in the Battelle 10-in. cupola under normal operating practice and under oxidizing conditions. The oxygen analyses ranged from 12 to 68 pprn compared to the author's computed range of 10 to 80 ppm. The average amount of oxygen found in our irons was about 20 pprn and changes in the silicon content of the iron from 1.32 to 2.35 pct had no consistent effect on the oxygen content of the iron. The gas determination specimens were poured in split steel molds that produced a clean pin, 3/8 in. diam and 2 in. long. Because freezing was almost instantaneous, the pins were entirely white iron (nongraphitic). In the early stages of the investigation, the pins were transferred to a mercury-filled trap system immediately after pouring. This was done to collect gas evolved between pouring and analysis. However, it was found that during storage for 4 weeks gas evolution was negligible. Because the vacuum-fusion analysis was usually completed within 4 days of pouring, pins from later heats were not stored in the mercury-trap system. We found some evidence that cast iron picks up oxygen during long storage, because of rusting. Earlier work by the British Cast Iron Research Association has shown that cast irons may be stored for a long time without significant change in their oxygen content. The practical significance of this study (and our own) would be in the improvement of cast-iron quality. Has the author investigated this aspect and reached any conclusions on the effect of oxygen on the mechanical properties of cast iron? The second phase of our study was to determine the properties of the test bars poured simultaneously with the gas analysis specimens. We realize that there may be complicating factors attendant in this procedure.21 Results from many test specimens measuring chill depth, transverse flexure and deflection strength, spiral fluidity, and sensitivity to hardness of gray irons ranging from 12 to 68 pprn oxygen showed that the lowering of transverse strength was the only significant undesirable effect of high oxygen content. A statistical study of the chill test results21 showed that the iron containing 22 to 46 pprn oxygen had forced chill depths that were 2/32 in. below the expected value from their composition, and irons containing less than 16 ppm oxygen had forced chill depths averaging 1/32 in. greater than the expected chill depth. Higher oxygen contents, within the range of 12 to 68 pprn did not increase forced chill depth. With the wedge tests, there was a good linear relationship between carbon equivalent of the irons and their chill depth. The results indicated that oxygen contents below 50 ppm in the iron did not affect chill depth. With 50 to 70 ppm oxygen in the iron, oxygen appeared to have a slight graphitizing tendency. These results are in disagreement with the common belief in gray iron foundries that "oxidized irons" produce high chill depths. It would be appreciated if the author would comment on this subject. Gustaf Ostberg (author's reply)—In Fig. 1 the legend of line I should read 2 pct C, 1 pct Si. The author wishes to thank Mr. Loria for calling attention to his later work, which was published after the present paper was concluded. The range of oxygen contents quoted seems to agree well with the author's values. The lack of response to variations in silicon content is probably due to the fact that the oxygen content in most cases was below the saturation level. The absence of temperature dependence, even in the case of saturation, is understandable if the difficulty in formation and escape of the deoxidation products is taken into account.

Jan 1, 1960

By J. E. Andersen, J. Halpern, C. S. Samis

In the presence of oxygen, galena is oxidized in an aqueous medium containing sodium hydroxide, in accordance with the following reaction: PbS + 2O2 + 3OH ? HPbO2 + SO4 = + H2O A novel method was devised for following this reaction which takes place in an autoclave under oxygen pressure, by measuring the concentration of HPbO2- in the solution with a cathode ray polarograph employing stationary platinum electrodes. Using this procedure a study was made of the kinetics of the reaction, in which the effect of a number of variables, including temperature, oxygen pressure, NaOH concentration, and agitation, on the rate, were determined. The results of this study are described and discussed, in terms of possible mechanisms for the reaction. IT is known that sulphide minerals can be oxidized in aqueous media in the presence of oxygen under pressure. Reactions of this type can be classified in two categories depending upon whether the products of oxidation are insoluble or soluble in the aqueous medium. An example of the first type of reaction is the oxidation of pyrite in alkaline solutions, giving rise to an insoluble iron oxide. The kinetics of this reaction have been investigated and its mechanism established.' It has been applied in the oxidation of iron sulphides present in refractory gold ores to improve the subsequent recovery of gold by cyanida-tion.' The second type of reaction finds application where it is desired to recover the metal by leaching during oxidation. In this case a medium is selected in which the oxidized mineral is soluble. For example, nickel, copper, and cobalt sulphide ores can be treated by oxidation in the presence of a solution of ammonia dissolving the nickel, copper, and cobalt as the metal ammine sulphate salts.:' A similar treatment has also been reported to apply to zinc sulphide ores.' It is known that lead sulphate is soluble in solutions of sodium hydroxide or ammonium acetate. It should therefore be possible to dissolve the lead from galena ores by aqueous oxidation with oxygen under pressure using either of these solutions. The applicability of the ammonium acetate treatment has been investigated and confirmed in a recent study.' The present paper describes the results of a similar study in which the kinetics of the oxidation of galena in sodium hydroxide solutions have been investigated. The object of this investigation was pri- marily to obtain information of a fundamental nature relating to the kinetics and mechanism of this reaction. The use of pulps of comminuted ore in a study of this type is undesirable because of the difficulty in controlling and measuring the surface area. The measurements were therefore made using galena crystals of measured surface area and in this way absolute reaction rates were obtained. The reaction was found to proceed as follows: PbS + 2O2 + 3OH ? HPbO2 + SO4 + H2O [I] The products are sodium plumbite and sodium sulphate salts which dissolve in the aqueous solution. The reaction studies were carried out in an autoclave in which a desired pressure of oxygen was maintained. The reaction was followed by measuring the concentration of lead in the solution with a cathode ray polarograph. The results obtained in this investigation are presented and discussed in the present paper. Experimental Materials: The crystals of galena were obtained from Violamac Mines, Sandon, B. C. The following impurities were indicated by spectrographic analysis carried out by the Provincial Assay Office, Victoria, B. C.: Sn, 0.02 to 0.2 pct; Sb, 0.07 to 0.7; Zn, 0.01 to 0.1; Si, Fe, Mg, As, less than 0.05 pct; Ag, 126 oz per ton, the latter determined by standard fire-assaying procedure. After cutting a specimen measuring approximately 5x7x12 mm, the crystal surfaces were ground parallel to the 100 axes using No. 2 emery, washed with water, and the dimensions were measured with a micrometer. Oxygen gas was of commercial grade and supplied in cylinders by Canadian Liquid Air. Solutions were made up with chemicals of chemically pure grade and distilled water. Equipment: Autoclave: The autoclave used in these studies was constructed of stainless steel and

Jan 1, 1954

By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemi-sorption. FLOTATION of quartz is of practical importance as something to be avoided in soap-floating many types of ores. Clean, unactivated quartz is not floated with fatty acids and soaps, such as oleic acid and sodium oleate, in the quantities normally used for flotation. However, data in the literature indicate that almost any multivalent cation will activate quartz if given an opportunity. Thus, a common problem is to prevent activation of quartz by the various inorganic cations inevitably present in flotation pulps. Wark and his coworkers1 have demonstrated the reversibility of the chemical reactions and adsorptions involved in the activation, depression, and collection of the common sulphide minerals. The procedure in much of their work was to bring a mineral surface to equilibrium with solutions of known pH, collector concentration, and activator concentration, and then to test the floatability of the mineral by contact-angle measurement. From the data, graphs were constructed with pH and reagent concentrations as coordinates. These graphs show fields of flotation and fields of nonflotation, separated by narrow transition regions whose locations are shown by so-called contact curves. From the shapes and locations of the contact curves, which roughly separate fields of flotation from fields of nonflotation, a quantitative understanding of the interaction of the reagents with each other and with the minerals often can be deduced. The study of quartz flotation to be described in this paper follows in broad lines the approach of Wark and coworkers. That is, pH, activator concentration, and collector concentration were varied to find equilibrium conditions of flotation and non- flotation, and the results are presented graphically by means of contact curves. However, instead of testing for floatability by measuring the contact angle on a polished surface, a simple vacuum flotation technique was developed and used. Purified oleic acid was the collector and terpineol the frother. Barium activation was studied in some detail, and exploratory studies were made of activation with calcium, aluminum, ferric iron, and stannic tin. Preparation of Materials Quartz: Large lumps of high-grade vein quartz were crushed dry in a cone crusher and rolls. The —20, +28-mesh portion was screened out and used in the subsequent steps. This material was passed through a high-intensity magnetic separator to discard iron, then leached twice with hot concentrated HCl and washed repeatedly with distilled water. The cleaned sand was then wet ground with porcelain balls in a porcelain pebble mill, deslimed repeatedly by settling and decantation to discard —800-mesh material, and again washed with hot HCl followed by distilled water. The resulting stock of quartz was stored under water. Chemical analysis gave 99.8 pct SiO2. Table I gives the size analysis of the quartz used for flotation tests. Calculations from these data, using shape factors given by Gaudin and Hukki9 indicate a specific surface of about 500 cm2 per g. Blank flotation tests in distilled water, and in water with added frother, showed the prepared quartz to be completely nonfloatable and thus indicated the absence of organic contamination. Oleic Acid: The preparation of oleic acid was based on fractional vacuum distillation of methyl oleate2,3 followed by regeneration of oleic acid, and finally fractional crystallization of oleic acid from acetone solutions at low temperatures." The pure oleic acid was stored in a refrigerator. The iodine number of the oleic acid was found to be 90.0 (theoretical 89.93). Oleic acid was used in the form of a dilute water solution of sodium oleate, after preliminary flotation tests showed no effects of form of addition and order of addition of reagents when an adequate conditioning time (that is, 30 min) was provided. Other Reagents: Sodium hydroxide solutions low in carbonate were prepared by first making 1:1

Jan 1, 1951

By G. Purcell, S. C. Sun

In an attempt to determine the relative collecting ability of 18-carbon fatty acids, studies were performed on rutile in aqueous solutions of the fatty acid soaps. The preceding article reported the electro-kinetic properties; this article outlines the flotation behavior. Results of these flotation experiments are described and correlated with the electrokinetic results. Recent studies of the electrokinetic1-4 and the electrochemical5,6 properties of a few solid-liquid interfaces have provided a better understanding of the flotation process. A number of investigators have attempted to determine the relative collecting ability of 18-carbon fatty acids, but their published results (even for the same mineral) vary widely. Such lack of agreement indicated a need for further investigation. In an effort, therefore, to resolve the problem, electro-kinetic studies were made on rutile in aqueous solutions of the fatty acid soaps. Following the determination of the electrokinetic properties, the flotation behavior of rutile was studied. Results of these flotation experiments are described in this paper and are correlated with the electrokinetic results. MATERIALS AND EXPERIMENTAL PROCEDURE Materials: Pure -28, + 35-mesh rutile crystals were used for all flotation tests, and nitrogen-saturated conductivity water was used throughout. Sodium hydroxide and hydrochloric acid were added for pH regulation. The methods of purification for these materials and the preparation of the soaps have been described elsewhere. 7 Equipment: A Hallimond cell, constructed in a manner similar to that described by Fuerstenau, Metzger and Seele,8 was used for the flotation of mineral particles; however, a coarse pyrex frit was substituted for the capillary. Procedure: Purified nitrogen was led through a two- way stopcock into a graduated cylinder partly filled with water. The gas forced water from the cylinder back into a header tank until the water level in the cylinder coincided with a predetermined mark. Reversal of the stopcock then allowed water in the tank to force nitrogen into the cell until the water in the graduated cylinder rose to a second predetermined mark. In this way a constant volume of nitrogen under practically constant pressure was used for each flotation test. However, the flotation time varied, depending upon the amount of mineral floated and the pH of the solution. Rutile crystals were transferred under water from a storage bottle by a glass scoop holding 1.7 g. Consistency of the scoop samples was good, varying from a low value of 1.67 to a high of 1.74 g. The water added to the conditioning bottle during mineral transfer was drained off, and then 2 cu cm of either hydrochloric acid or sodium hydroxide were added. The concentration of pH regulator was adjusted to give approximately the final soap solution pH that was required. The order of addition of reagents did not affect the results within the limits of experimental error. Soap solution of the required concentration was added under nitrogen pressure to fill the bottles completely. Conditioning for 1 hr was carried out on rolls rotating at 35 rpm. After conditioning, 2.5 cu cm of solution were run off into the container of a Beckman (model G) glass electrode pH meter. The electrodes were rinsed in this solution, which was then discarded, and 2.5 cu cm more were added for pH determination. The remaining solution and the mineral were transferred to the cell; care was taken to ensure that all mineral was washed out of the bottle by the conditioning solution. With the cell back in its flotation position the liquid just reached the desired level, and the test was started immediately. The amount of agitation in the cell was kept constant, and flotation was carried out without the use of a frother. In each series of ten tests one was run with no collector added to ensure that the mineral had not become contaminated, and two were conditioned at the same pH to check reproducibility. After each test the cell was dismounted, soaked in cleaning solution, washed in hot water and then rinsed with distilled water.

Jan 1, 1963

By K. G. Davis, P. Fryzuk

The diffusivity of silver in liquid tin has been determined, using the capillavy-reservoir technique, over the temperature range 250° to 500°C. The new value, D = 2.5 x 10'* exp(-2480/ RT) sq cm per sec, differs from that obtained by other workers in an earlier investigation. The analysis of data from the capillary-reservoir technique is discussed. In a recent investigation of the solidification of dilute alloys, values for the diffusion constant of silver in liquid tin were required in the analysis of the formation of impurity substructures. AS a result, measurements were made of the diffusion constants in the temperature range 250° to 500°C (melting point of tin 232°C), for the alloy concentrations used in the solidification experiments and at higher concentrations, to verify previous determinations.I)2 The capillary-reservoir method was adopted, using experimental procedures similar to those followed by Ma and Swalin,1 with the main exception that radioactive silver was used in the present investigation to facilitate solute-concentration measurements. EXPERIMENTAL PROCEDURE a) 100 ppm Samples. Glass capillary tubes of 2 mm inside diameter and approximately 5 cm- long were sealed at one end, evacuated, and filled with tin of 99.999 pct purity. The region of shrinkage near the mouth was cut off, and the tubes were then placed in a graphite holder and immersed, with the open end up, in an unstirred bath of alloy containing 100 ppm Ag 110, where they remained for periods of up to 30 hr. On removal from the bath they were cooled by an air blower. The bath was kept under a small positive pressure of argon, and the temperature controlled to within +1°C. A 10-hr diffusion period was used in the majority of the tests, scatter on runs of less than 5 hr being rather large. The procedure outlined above was chosen in preference to putting alloy in the capillary and pure tin in the bath, in order to avoid segregation when the tubes filled with alloy were first solidified. To minimize segregation when the diffusion period was complete and the capillaries again solidified, the earlier samples were held in thin-walled silica tubes which could be cooled very rapidly. Later tests were made in precision-bore Pyrex tubes, to eliminate effects caused by variations in the capillary diameter. No consistent differences in diffusivity as measured in the two types of tube were detected. After removal from the glass tubing, the samples were sectioned into 2.5 mm lengths and counted for y activity, using a scintillation counter with fixed geometry. Samples were also drawn directly from the bath and counted, so that values for C/C,, the ratio of the weight of Ag 110 in the sample to that in the bath, could be obtained. b) 5000 ppm Alloy. To check for possible effects of concentration, the silver content of the bath was increased to 5000 ppm. Complete mixing was found to have taken place in the capillary after a 10-hr period at 300°C. It appears that the greater density of the alloy was sufficient for buoyancy forces to cause instability in the alloy-tin interface, leading to rapid convective mixing. For the 5000 ppm alloy, therefore, the bath was of pure tin and the capillary tube was filled with alloy. With this arrangement, values of D consistent with those for the 100 ppm alloy were obtained, Fig. 1. CALCULATIONS OF DIFFUSIVITY The terminology used applies to a capillary of pure tin immersed in a bath of alloy. 1) Error-Function Method. under the present experimental conditions, the rod of liquid tin into which silver is penetrating may be considered semi-infinite. Assuming the concentration at the mouth of the tube to remain constant at Co, the concentration C at distance x from the mouth of the tube at time / is given by3 Plots of the inverse error function of (1 -C/Co) vs .v gave straight lines passing through the origin with slope 1/2-, x being corrected for shrinkage both on solidification and while cooling to the melting point (total correction about 6 pct at 500°C). Values for log D obtained in this manner are shown in Fig. 1. A least-squares fit to the relation D = Do exp(-Q/RT)

Jan 1, 1965

By C. C. Harris

A critical literature review leads to a descriptive model of tumbling mill operation based upon energy partition concepts and the necessary requirements for particle fracture. As grinding proceeds into the ultra-fine region, conditions which are of little significance during normal operations gradually become controlling. These involve increasing resistance to fracture and an increasing tendency to aggregate as particles become smaller, and a growing fraction of the power input being consumed fruitlessly. The result is that fineness asymptotes to a maximum value as comminution proceeds indefinitely; thus where t is time, p and n are experimentally determined parameters, and Ø is a measure of fineness, which is presumed to be proportional to specific surface area, or proportional to the reciprocal of the size modulus (provided that the distribution modulus remains constant with time), or both. Ø, is the asymptotic value of Ø and is a measure of the grind limit. A method for its graphical determination is given. In a previous paper1 the physical and mathematical principles requisite to a study of the role of energy in comminution were reviewed. The micro-process of comminution — or the comminution event — can be investigated in terms of (a) the magnitude of the force-field localized around the individual particles which gives rise to the stresses generated in the particles, which in turn induces their fracture, and (b) the distribution of fragment sizes, should the event prove fruitful. The entire fragmentation operation can be considered to be the totality of its individual events, and in order to obtain a single independent variable of the process it is necessary to transform and sum the local stresses in terms of energy.1 This energy, however, will account for only a fraction of the energy input to the comminution process, the actual magnitude depending upon the kind of mill and several related factors. From the comminution viewpoint the primary function of a mill is that of stressing as many as possible of the individual particles of the charge to failure, with the maximum economy of energy expenditure. This is difficult indeed to achieve, for stressing a particle does not always break it, while the overwhelming portion of the energy input is involved with various internal mill processes which — almost incidentally — determine the magnitude, frequency, and manner in which the forces are applied to the particles. Essentially, these processes depend upon the mill dimensions, loading and speed, and they may be little affected whether fracture occurs or not. These processes must be delineated if a complete description of the role of energy in comminution is to be given; the energy account sheet1 (Fig. 1) in showing how the energy is partitioned for the requirements of the several functions it performs, provides a framework for the development of a model of the comminution process. Actual numerical values for the variables appearing in Fig. 1 will depend upon the mill, materials, and operating conditions. A possible general relationship between the variables will be suggested in this paper. Before proceeding further, a cautionary note must be issued. It was pointed out in an earlier paper' that while energy input is not changed by increasing the power and decreasing the time in the same proportion, and vice versa, the results of the process in terms of particle fineness may be different. Thus, although energy is chosen as the independent variable of a comminution process, it is not absolutely independent, and care must be exercised to ensure that it is used within its range of valid application. Time has the necessary independence, and it will be used in place of energy where it is appropriate. The residence time in a mill is usually of the order of minutes. Under these conditions the particles are subjected to "... a relatively constant fracture producing environment".2 However, under the more rigorous conditions of greatly extended time, which pertain in ultra-fine grinding, indications are that the fracture producing environment no longer remains constant; this is the major subject of this paper. At this extreme limit the mill is probably taxed to its utmost, and at the same time the bulk material properties are becoming closer to ideal, while the physico chemical effects associated with surfaces, edges and corners are multiplying. (The edge length per unit volume is proportional to the square of the specific

Jan 1, 1968

By W. Rostoker

Single isothermal sections were constructed for the titonium-rich corners of the systems Ti-Fe-O, Ti-Cr-O, and Ti-Ni-0 with a view to locating the shape and disposition of the ternary intermediate-phase fields for the compounds isomorphous with Fe3W3C. IN a previous note,' it was reported that a group of ternary intermediate phases existed which occurred in the general composition range Ti,X,O-Ti&O where X was one of the following elements: copper, nickel, cobalt, iron, or manganese. In two instances, binary intermediate phases occurred (Ti²Cu and Ti²Ni) which appeared to be isomorphous. The X-ray diffraction patterns of the phases could be indexed on a cubic lattice whose cell edge was of the order of 11 kX. Karlsson2 stated that the line extinctions and line intensities indicated that these phases were isomorphous with Fe³W³C and therefore belonged to the space group Oh. This author also noted that no unique phase of this type occurred at the composition Ti,Cr,O. This latter statement was accepted as true at the time the previous technical note was written.' However, work continued along these lines and that reported here has shown that a phase isomorphous with Fe³W³C does exist in the vicinity of the composition Ti³Cr³O but not at or near Ti4 Cr²O. The lattice parameter of this phase was found to be 13.01 kX. Metallographic examination of both as-cast and annealed specimens of these supposed ternary oxide phases disclosed structures which were far from single phase in many instances. It was considered a point of some interest to locate more positively the composition coordinates of the single-phase fields. To this end, single isothermal sections for the systems Ti-Fe-O (1000°C), Ti-Cr-0 (1000°C), and Ti-Ni-0 (900"C) were constructed. Phase relationships were studied by both X-ray diffraction and metallotrra~hic methods. Allovs were prepared as 10 g buttons by melting in a noncon-sumable electrode, water-cooled copper crucible arc-melting furnace using a helium atmosphere. Oxygen was introduced quantitatively by the use of weighed amounts of TiO² or TiO. Iodide titanium and the purest available alloying metals were used. All results are discussed in terms of the nominal composition of the melts. Previous experience with making oxygen-rich alloys had shown that oxygen losses were not significant if a homogeneous melt was produced. Weight-loss measurements were used to check loss in metallics during melting. Anneals were conducted in evacuated Vycor bulbs, and annealing times ranged from 24 hr at 1000 °C to 48 hr at 900°C. To achieve equilibrium in certain sluggish alloys, seven-day anneals were used. Debye-Scherrer powder patterns were taken in a 14 cm diam camera using filtered CuK radiation (K² = 1.541232 kX; K., = 1.53739 kX). Specimens were prepared by crushing and screening previously annealed buttons. In general, the X-ray diffraction results were used to identify the major phases, while the metallographic examinations were more useful in indicating the number of phases present. By the use of the combined results and general fundamental rules governing ternary equilibrium, it was possible to construct isothermal sections in good detail. In some instances where auxiliary lattice-parameter data were available, it was possible to lay down tie lines and to locate more positively corners of three-phase fields. Isothermal Section of the System Ti-Fe-O at 1000°C The binary systems Ti-O³ and Ti-Fe4 have been published. Binary phases, TiO, TiFe, and TiFe2, are likely to be encountered in the titanium-rich corner of the system. The structures are NaCl (Bl), CsCl (B2), and MgZn, (C14) types, respectively. Although preliminary X-ray diffraction studies indicated the presence of a ternary phase in the composition range Ti,Fe,O-TiJ?e,O, metallographic examination of two specimens at these compositions revealed the presence of other phases. Thirty-eight alloys were used to delineate the phase boundaries of the isothermal section illustrated in Fig. 1. The five almost single-phase ter-

Jan 1, 1956

By R. F. Mehl, R. F. Bunshah

A fast amplifier technique has been developed for the measurement of the rate of propagation of martensite in an Fe-29.5 pct Ni alloy. The time of formation of one plate of martensite is 3x10 sec and the rate of propagation is 3300 ft per sec approximately. IT has been known for some time that the plate-like structural unit of martensite forms from austenite with great rapidity. Wiester1 and Hane-mann, Hofmann, and Wiester took motion-pictures of the transformation as it occurs in a 1.65 pct C steel; they demonstrated that a single plate formed fully in the time interval between successive frames, viz., 1/20 sec, thus setting an upper limit. Forster and Scheil,3 using an Fe-Ni alloy with 29 pct Ni, recorded the sonic characteristics of the process electrically, upon an oscillograph, setting the upper time limit at 0.002 sec. Forster and Scheil,~ measuring the change in electrical resistance in the same alloy upon a cardiograph, set a limit of 0.02 sec. Forster and Scheil5 later, employing the same alloy, improved their technique, reporting an upper limit of 7.10 sec. In studying signals of such short duration, it is an important question whether the frequency response of the electrical system used is high enough compared to frequency of the pulse measured, or, put differently, whether the system is able to reproduce without distortion the signal arising, in this case, from the formation of a single martensite plate. Forster and Scheil (referring only to their last paper) obtained signals of a frequency of 30 kilocycles (hereinafter kc); this was about the frequency response of the equipment used; thus, if the signal had a frequency higher than 30 kc, it would still appear as a signal of frequency 30 kc. All of these results thus provided upper limits only. Recent developments in electronics have made available equipment with very high frequency response, very high sweep-speeds, high gain, etc. The electrical characteristics of such equipment, used in the present study, are given in Table I. Such equipment offers obvious attraction in the study of the rate of propagation of a martensite structural unit—and perhaps of other structural alterations proceeding at a very high rate. This paper reports an attempt to develop a technique employing such equipment to measure the time of propagation of a martensite structural unit and the variation of this with temperature, with the mode of formation—athermal and isothermal—in both polycrystalline and single-crystal samples; and from such measurements to obtain the rate of propagation. As will be seen, the results obtained are useful theoretically. Materials All data presented here are for an Fe-Ni alloy of the following analysis: 29.5 pct Ni, 0.027 pct C, 0.135 pct Mn, 0.094 pct Si, balance Fe. There were several reasons for choosing this alloy: 1—it is substantially the one used by previous investigators; 2—it exhibits both the athermala and the isothermal' mode of formation of martensite, both studied in detail by Machlin and Cohen; 3—the subzero temperatures of transformation in this alloy are experimentally very convenient; 4—it exhibits the "burst phenomenon";" 5—the change in electrical resistance upon the formation of martensite, a decrease, is great, approximately 50 pct.' The polycrystalline specimens were in the form of wires of 0.025 in. diameter; the single crystals were 1x1/4x1/4 in. Experimental Methods Electrical Apparatus: Fig. 1 is a schematic drawing of the electrical circuit used. The principle used in these measurements is the same as that used by Forster and Scheil." A small direct current, about 1 to 2 amp, is passed through the sample. When a martensite plate forms, the resistance of the sample changes and a high frequency signal is generated. This signal is picked up by the probes attached to the sample, fed into the bank of amplifiers and thence to the vertical deflection plates of a cathode-ray oscilloscope. The signal itself triggers the oscilloscope trace which flashes across the tube face and is photographed by means of a 35 mm movie camera at the end of a light-tight hood. The camera has no shutter. As soon as the signal flashes

Jan 1, 1954

By W. G. Bearden, P. P. Scott, G. C. Howard

This paper concerns the rupture or breakdown of rock formations as related to drilling, completing, and stimulating production of wells, and comprises data compiled from a study of literature and records of treatment of oil and gas wells. and from tests conducted in bores drilled into rock cores and outcrops of rock. Results of the investigation indicate that the internal pressure to rupture cylinders of rock and to breakdown rock formations surrounding a bore in the earth is dependent upon the extent of intrusion of fluids. the position of bedding planes. the ratio of internal to external diameter, the tensile strength of rock, and magnitude of confining pressure, and is independent of the size of bore, degree of fluid saturation. and temperature of rock within practical limits. It is concluded that the mathematical relationship of pressure in bores and stresses in the surrounding rock must not be limited by the simplifying assumptions of homogeneity. isotropy, and impermeability; that the incidence of lost circulation of drilling fluids to induced fractures may be reduced by preventing intrusion of fluids into the small intrinsic fractures along weak bedding planes; and that the magnitude of the breakdown pressure of wells to be treated may be lowered by removal of mud cake. INTRODUCTION The purpose of this paper is to present and discuss the results of tests which may serve to broaden the understanding of the phenomena of rupture or breakdown of rock and thus contribute to the improvement of the techniques for drilling and completing wells. including such operations as preventing lost circulation, stimulating production, and placing cement. Since the early recognition of the possibility of rupturing rock adjacent to a well by fluid pressure, the distribution and magnitude of stresses around a well and the internal pressure to cause failure have been expressed mathematically by application of the principles defining the elastic and inelastic behavior of thick-walled cylinders of a homogeneous. isotropic, impermeable material. In either the elastic or plastic state, if the conditions of homogeneity. isotropy, and impermeability were the normal characteristics of rock. there would be no reason to question the validity of the above principles when applied to rock. However. since most rock formations are characteristically permeable to some degree, contain bedding planes and small intrinsic fractures. and are heterogeneous, rendering invalid the assumptions of homogeneity, isotropy, and impermeability, the application of the thick-walled cylinder theories to the behavior of rock formations penetrated by a bore appears illogical. Also the failure to consider the effect of the properties of the drilling fluids, which certainly intrude in various degrees into most rock formations. is further cause for questioning the application of these principles. Even in the case of cylinders of hardened chrome-nickel steel, which would he considered relatively homogeneous isotropic. and impermeable, as compared to rock, it has been observed that the internal pressure capable of being withstood by the cylinders varied with the sizes of molecules comprising the rupturing fluid used. Because of these apparent weaknesses in the theories of the behavior of thick-walled cylinders when applied to bores in rock, and the importance of knowing the true behavior of rock under the influence of fluid pressure when planning drilling and completing procedures for wells, tests were undertaken to determine by observation the actual rupturing pressure of cylinders of rock and the effects of such variables as environmental conditions and characteristics of rock formations, fluid properties, and bore dimensions. It was intended that by these tests the validity of the thick-walled cylinder theories when applied to rock would be determined and, if found invalid, mathematical expressions would be derived for predicting stress and rupturing pressure of rock formations under various conditions. Since the derivation of mathematical expressions has been only partially completed, all of the results of the latter phase are not included in this paper. PROCEDURE The investigation was initialed with a study of the theories pertaining to the rupturing of thick-walled cylinders of homogeneous. isotropic, impermeable material and a study of the

Jan 1, 1953

By P. S. Kotva

Dislocation substructures in superalloy matrices of varyzng co)npositions have been studied. In general, it has been found that the alloys can be classified into ''high", ''medium", and "low" stacking fault energy classes based on the type of dislocation substructure observed in the matrix and that the substructure can be correlated to the stacking fault energy. The effect of different types of dislocation substructure and dislocation reactions on the intragranulur precipitation of carbide phases has been studied. In a Ni-Cv-Mo-Fe matrix, precipitation of MC carbides in association with stacking faults has been observed. In most superalloys, solid-solution strengthening and precipitation hardening are the chief mechanisms employed to achieve strength. The latter contribution to strength is usually achieved by the precipitation of / in certain wrought alloys. Insufficient attention has been given to the problem of obtaining strength in su-peralloys by controlling precipitation of carbides on imperfections within the matrix. The present work was undertaken to investigate the dislocation substructure in various superalloy matrices, to study the effect of such substructure on subsequent precipitation of carbides in the matrix, and to investigate whether certain modes of precipitation of carbide phases found in austenitic stainless steels2"4'6 would occur in nickel-base alloy matrices with dislocation substructures of the same type as those found in austenitic steels. 1) EXPERIMENTAL TECHNIQUES Five-pound heats of the various alloy compositions reported here were vacuum-cast. The ingots were given light deformation by rolling to break up the as-cast structure and then homogenized for 24 hr. HASTELLOY alloy X (nominal composition: Ni-2OCr-17Fe-8Mo-0.05C) was homogenized at 2150°F and In-cone1 625 (nominal composition: Ni-20Cr-5Fe-8Mo-3.5Cb-0.05C) was homogenized at 2280°F. Fabrication of 0.004-in. sheet was achieved by cold rolling with intermediate annealing treatments being carried out at the same temperature as those used for homogeniza-tion. Each solution anneal was followed by quenching. The aim of this procedure was to redissolve as much of the primary carbide phase as possible. Samples of the 0.004-in. sheet were cut and encapsulated in quartz capsules and then heat-treated in the tube furnaces. Thin foils were prepared using an ethanol-10 pct perchloric acid bath at 32°F and at a voltage of 22 v. A "window" technique was employed. Observations were made on a JEM-7 electron microscope operating at 100 kv. 2) EXPERIMENTAL RESULTS a) Types of Dislocation Substructure. Fig. 1 shows a schematic correlation between stacking fault energy, SFE, and the type of dislocation substructure observed in various matrices of nickel- and cobalt-base alloys. A precise quantitative determination of stacking fault energy is not implied in the figure but the correlation between stacking fault energy and the type of dislocation substructure obtained allows alloys to be divided into three classes in analogy with the classification employed by Swann and ~uttin~' for binary alloys of copper. Class I alloys are associated with a "high" SFE and show a cellular substructure of dislocations as typified by the micrograph of a thin foil of pure nickel deformed 4 pct at room temperature in Fig. 2. With decreasing SFE the tendency toward cell formation is lessened and dislocations tend to be arranged in coplanar groupings. Examples of this class of alloys with "medium" SFE are provided by the mi-crostructure of solution-heat-treated, quenched, and deformed thin foils of HASTELLOY alloy X, "Waspaloy" (prior to any aging), and Inconel 625. Fig. 3 shows a thin-foil micrograph of an alloy of Inconel 625 composition, solution-heat-treated, quenched, and deformed 5 pct at room temperatures. No evidence of any cell structure can be obtained in materials of "medium" stacking fault energy, Fig. 3, even after severe deformation. The stacking fault energy of the alloy shown in Fig. 3 is, however, not low enough to make the dissociation of dislocations visually obvious. As stacking fault energy decreases further, with successive addition of solute in the matrix, there is an increased tendency toward dissociation of dislocations and cross slip becomes progressively more difficult. Eventually, when the stacking fault energy is "low" enough, complete dissociation of dislocations is seen to occur as shown in Figs.

Jan 1, 1969

By R. W. Hertzberg, F. D. Lemkey, J. A. Ford

The effect oj unidirectional solidification upon the microstructural, crystallographic and mechanical characteristics of high -purity A1-A13Ni eutectic a1loy specimens has been investigated. varying the growth rate caused the morphology of the Al3Ni phase to gradually change from platelets to rods. In addition, the effect of increasing the rate of planar liquid-solid interlace movement is to decrease the Al3Ni rod diameter and inter-rod spacing. The platelets and rods grow approxinlately parallel to each other and are aligned in a faulted substructure. A single unique crystallographic relationship hetween the A1 and ASNi phases was found and may he descrihed as : interface {001} Al3Ni {331} Al and growth direction <010>Al3Ni || <110> Al The platelet interlace and the aligned rows of rods are both uniquely defined by the above statements. Alignment of the Al3Ni phase by unidirectional solidification has given rise to a threefold increase in strength over that exhibited by specimens with an as-cast microstructure. These results illustrate the possible use of this eutectic alloy as a zohisker -reinforced structure. It has been demonstrated by Winegard et al.,1 Kraft and Albrighht,2 Chilton and winegard,3 Chad-wick,4 Yue,5 Tiller,6 and others that a planar liquid-solid interface may be established in binary eutectic alloys by proper control of heat flow during the solidification process. The unidirectional movement of such an interface results in a eutectic mi-crostructure consisting of an essentially parallel array of the two phases over an entire ingot. Two dominant phase micromorphologies have been produced using this technique: that of substantially parallel alternating lamellae of each phase or long thin parallel rods of one phase imbedded in a continuous matrix of the other phase. While not all eutectics can be controlled in this manner, it has been shown that a "normal" eutectic may, under properly controlled conditions of purity, liquid and solid thermal gradients, and solidification rate, be forced to solidify with essentially parallel phase particles. Kraft and Albright2 have demonstrated that, when the growth rate is too rapid or when the thermal gradient in the liquid at the growing interface is too low, a layer of constitutionally supercooled liquid, formed by impurity build-up, will stabilize a cellular rather than a planar interface. The unidirectional movement of the cellular interface forms the macrostructure of eutectic colonies.7 Chilton,3 Chadwick,4 and Tiller,&apos; studying eutectics of zone-refined Pb-Sn, A1-CuAl2, Zn-Sn, and Cd-Zn systems, noted that in the absence of impurities a planar interface is stabilized even when rapidly solidified. Although it is generally agreed that impurities break down a planar interface to form the eutectic-colony macrostructure, at present the origin of the varying micromorphologies (i.c., plates or rods) in a given normal eutectic alloy is not completely understood. Tiller8 has predicted that the micromor-phology produced may be dependent on solidification rate (i.e., at fast rates a rodlike structure is preferred whereas at slow rates a lamellar structure should form), and also suggested that rod formation may be favored at large phase-volume ratios. yue5 has experimentally verified Tiller&apos;s prediction in the eutectic Mg-Mg17Al12 by observing a lamellae-to-rod transition with increasing growth rate where the phase-volume ratio was approximately 2.3:1. However, Hunt and chilton9 more recently unidirec-tionally solidified over a wide range of growth velocities six different eutectic systems with phase-volume ratios between 12:l and 2.7:1 and observed no lamellae-to-rod transition. chadwickl0 has proposed that the change in micromorphology in some eutectic alloys is due entirely to the presence of impurities and further states that the lamellar structure is the characteristic structure of pure eutectic alloys even when the phase-volume ratio is as great as 12:l. Kraft11,12 has shown that the parallel lamellae in certain eutectic alloys assume a unique crystallographic relationship during unidirectional growth. This preferred crystallography may be developed

Jan 1, 1965