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By Elmars Ence, Harold Margolin

The titanium-aluminum system has been investigated in the composition region 0 to 34 pct Al in the temperature range 800" to 1450°C. The phases encountered in this region were: a,ß, TiAl3, The reactions observed are as follows: 13 ; L - 6T. A1, 0 (15 pct Al) + 6 (18 pct Al) - yTi Al (16.5 pct Al) at -1170°C andP (7 pctpct Al) + y (9.2 pet Al) - ah(9 pct Al) at - 1060°C. A eutectoid reaction: y — a +d belm 700°C is postulated. THE Ti-A1 system has been the sub.ect of a number of investigations. Several of these1-3 have indicated extensive solubility of A1 in both a and ß titanium. Ence and Margolin, as a result of work on the Ti-A1-0 system:'5 have shown that the a solubility ofalumi-num is considerably restricted, and found that a compound, Ti2A1 existed in the region formerly designated as Q a This structure was identified as hexagonal with c/a = 0.803. Pietrokowsky confirmed the existence of this phase7 and pointed out that the structure was isomorphous with Ti3Sn.8 Although the existence of Ti,A1 has been confirmed by others,9-12 there has been considerable disagreement regarding the composition and mode of formation. A detailed reinvestigation of the Ti-A1 system has been published by Sagel et al.13 The tentative diagram indicated two phases, a, and e, occurring in the former all a region. The a, phase has the same structure as Ti2A1 and was indicated as having a broad region of solubility. Epsilon, a tetragonal phase, was shown to form within the a, solubility region. AS a result of unpublished work,14 Ence and Mugy3 olin disagreed with the interpretation of Sage1 et al., although some common features existed. The present study was conducted in an attempt to clarify prevailing uncertainties. EXPERIMENTAL PROCEDURE Alloy Preparation—Alloys were prepared from iodide titanium (99.9 pct Ti with less than 0.01 pct Zr) or Bureau of Mines electrolytic titanium (BHN-73) and high purity aluminum (99.99 pct). Alloys were arc-melted in argon or helium atmosphere as 15-g buttons in the composition range up to 34 pct Al. Depending on need, alloys were made in increments varying from 0.25 to 2 pct Al. Up to five 15-g buttons of some compositions were made. Weight losses during melting did not exceed about 1 pct of the charge and chemical analysis revealed that both titanium and aluminum were evaporated. In general, nominal and analyzed compositions agreed within 0.5 pct and therefore nominal compositions were used in plotting the data. Unavoidably, some overlap of composition occurred, particularly where small increments of A1 were used. The small increments were primarily used to obtain alloys which would fall into the narrow a -, r region and this purpose was achieved. In general, the data obtained from Bureau of Mines base titanium and iodide titanium alloys were in agreement. Forging—Both as-cast and forged samples were employed. Samples were heated for hand forging by an oxygen-hydrogen torch to the region 1200" to 1300°C. A titanium anvil and cover plate were used to prevent any iron pick-up and consequent formation of a low melting point compound. Frequent reheating kept the temperature in the desired range. Under these conditions, alloys containing up to 15.5 pct could be successfully forged. To check on the depth of contamination, forged alloys were heated slightlybelow the ß transformation temperature. Metal was removed to a depth below the contaminated surface so revealed, and the subsequent results obtained from these samples agreed closely with those secured from as-cast material. Heat Treatment—Prior to heat treatment, all alloys were vacuum annealed to remove hydrogen. Samples

Jan 1, 1962

By L. S. Birks

The bainite transformation in a 3.5 pct Ni-1.25 pct Cr steel was studied under various conditions of cooling and stress. Several characteristics may be specified: 1) transformation in the bainite region (925° to 575°F) is very little affected by the manner of cooling from the austenitizing temperature at 1600°F to 575°F)tothe upper limit of bainite transformation at 925°F; 2) starting time for the bainite transformation is the same order of magnitude for either isothermal transformation or continuous cooling, but the rate of transformation is somewhat greater for isothermal transformation; 3) tensile stress accelerates both isothermal and continuous cooling transformation, and 32,000 psi stress changes the form of the isothermal transformation diagram to correspond in appearance to the continuous cooling diagram; 4) transformation for nonlinear, continuous cooling may not be determined directly from the linear, continuous cooling transformation diagram, but may be predicted by assuming first that the fractional amount of austenite transformed in a given small temperature interval depends on the approximate linear cooling rate during that temperature interval and then by summing stepwise over the whole temperature range. IN a previous publication' an X-ray spectrometer was described with which the X-ray diffraction from a specimen could be observed continuously under controlled temperature and tensile stress. This instrument has now been applied to a study of the austenite-bainite transformation in a Ni-Cr steel for both isothermal and continuous cooling conditions, with and without stress. Certain characteristics of the transformation lead to a method of predicting the amount of transformation to be expected at a given temperature for any type of cooling curve. Material and Specimen Preparation The steel chosen for the investigation was a Ni-Cr steel having the composition in the following percentages: 0.30 C, 0.27 Mn, 0.019 P and S, 3.50 Ni, and 1.25 Cr. In order to fabricate specimens suitable for the X-ray spectrometer, a 1/4 in. plate was ground down to 0.060 in. and then cold rolled to about 0.035 in. Next it was heat treated by quenching in oil from 1650°F and tempering at 1200°F for 1 hr. Then it was etched in dilute nitric acid to reduce its thickness to 0.014 in. and cut into blanks in the shape of flat tensile specimens 3 1/4 Vi in. long, 7/16 in. wide, with a notch % in. long and 7/32 in. wide; see Fig. 1. X-Ray Technique Since the X-ray spectrometer has been described in detail elsewhere,' only a brief outline of the principles will be repeated here. A focusing, pow- der-diffraction arrangement' was used, as shown schematically in Fig. 1, and the specimen was mounted vertically in a vacuum furnace (not shown in the figure). The X-rays, moving in a horizontal plane, enter and leave the furnace through beryllium windows. As shown in the figure, X-rays diverging from the line source A are diffracted by the specimen B and converge at the detector slit C. The detector D and the slit C may be set at the proper angle in the horizontal plane to receive X-rays diffracted by either the face-centered phase (austenite) or the body-centered form (ferrite, bainite, martensite). The specimen is heated by electrical conduction between connectors E, and E,, and a Pt—Pt-10 pct Rh thermocouple spot-welded to the center of the notched region on the side away from the X-ray beam indicates the temperature continuously on a Brown recorder. Temperature control is exercised manually with a variable transformer on the input to E,-E,. Any desired time-temperature relationship is easily obtained by first drawing the desired curve on the temperature recorder chart and then adjusting the variable transformer during the run so that the thermocouple

Jan 1, 1957

By E. J. Koval

Practical miscible displacement processes will be characterized by lingering of the solvent into the oil. The lingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. INTRODUCTION Theoretical considerations,1 laboratory experiments,2 and pilot tests3 lead to the conclusion that miscible displacements in the field will be unstable In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced. For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding by the usually less dense solvent. Al- though gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids. Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs4 or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. l Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.6 During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks2 and how it is affected by viscosity ratio,7 geometry,7 and slug size.2,* Peaceman and Rachfordg suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected. The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible dis placements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were: (1) The system was linear; (2) The solvent was miscible in all proportions with the oil in place; (3) The solvent was continuously injected into the porous medium; (4) Gravitational effects were eliminated by matching densities and (5) All the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. The use of

By B. J. Reid, J. N. Greenwood

It has been shown1 that cavities are formed in the grain-boundaries of copper and 70:30 brass (as well as in magnesium) by the application of tensile stresses at elevated temperatures. For a given rate of strain, cavities are formed in brass at a lower temperature than in copper, and they are larger; it was thought that this earlier onset of cavitation in the alloy might be caused by the distortion produced in the metal lattice by the alloying element. If the cavitation is caused by the vacancy-migration mechanism, ' the distortion of the lattice would reduce the energy required for vacancy formation, and thus provide vacancies more readily to assist in the cavitation process. It was decided to study a range of alloys to find out whether increasing amounts of an alloying element would cause any progressive increase in, or modification of, the cavitation in copper. Nickel was chosen for this purpose, since it is soluble in copper throughout the whole range of alloys. A further advantage was its low vapor pressure, which enabled the preparation of the alloys in vacuum and the consequent reduction of their hydrogen content. It has been suggested that cavities may be nucleated by the migration of hydrogen atoms to the less regular atomic spacing at the boundary, and their combination to form molecules. The latter being too large to diffuse back into the lattice, form stable cavities into which vacancies could condense. PREPARATION OF ALLOYS All alloys, ranging from pure OFHC copper to 43.7 at. pct of nickel (carbonyl), were prepared in a vacuum furnace employing high-frequency induction heating. When a charge was melted, vigorous gas evolution occurred initially, after which the pressure was reduced to 10-4 mm Hg, using an oil-diffusion pump. After remaining molten for a further 1/2 to 1 hr to aid degassing, the melt was allowed to solidify in the crucible. In this way contamination by gases evolved from the surface of a separate mold was avoided. The list of alloys prepared is shown in Table I. The percentage of hydrogen present in the OFHC copper was reduced from 0.0054 at. pct to 0.0012 at. pct, as measured by a vacuum-fusion method. The alloys were cold-rolled to 0.03-in.-thick strip, and were homogenized in vacuum for 1 hr at 900°C after every 30 pct reduction. At a thickness of 0.05 in., the strip was held at 450°C for 24 hr under high vacuum (10-5 mm Hg) in an attempt to reduce the hydrogen content still further. Tensile specimens were prepared with a gage length of 1 in., and were finally annealed for 2 hr at 800°C to give an average grain diameter of 0.1 mm. TENSILE DEFORMATION The specimens were deformed in a tensile straining machine operated by a synchronous motor at a constant rate, equivalent to 1.7 pct per hr on a 1-in. gage length. The specimen and grips were contained in a vacuum jacket. A pressure of 10-2 mm Hg was maintained, which was sufficient to prevent surface tarnishing of a specimen held at 650°C for 24 hr. Tests were made between 20. and 650°C and the temperature was controlled to within ±3° over the gage length. The load was measured by the deflection of a cantilever spring. a) Mechanical Properties-The ductility curves shown in Fig. 1 fall into two groups. Figs. 1(a) and (b) for copper and the 5 pct nickel alloy, respectively, show a continuous fall in ductility with a steep fall between 200° and 400°C. Figs. l(c) to (f) show the same sudden loss of ductility between 200° and 400°C. With higher temperatures, however, there is a recovery in ductility values to a maxi-

Jan 1, 1959

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

By S. J. Matas, R. F. Hehemann, R. H. Goodenow

The hot-stage metallographic method has been employed to determine radial growth rates of upper and lower bainite. Lower bainite appears to grow as individual plates that increase in both length and thickness while upper bainite grows as sheaves of closely spaced plates or needles. A discontinuity in the temperature dependence of the growth rate appears to be associated with the transition from upper to lower bainite and stepped quenching experiments suggest that lower bainite will not continue to grow when the temperature is raised to the upper range. Thus, a single process does not appear to control the growth of both upper and lower bainite. A tentative model based on the forces acting on a dislocation interface is proposed to account for the slow growth of bainite. It has been recognized since the early studies of Davenport and Bain that a close relationship exists between the martensite and bainite transformations in steels. However, diffusion of carbon during the transformation has lead to considerable controversy concerning the reaction mechanism.1-7 Many studies4,5,7-9 have emphasized the structura and kinetic aspects of the bainite reaction and, in particular, the difference observed between the two forms of bainite—frequently termed upper and lower bainite. A kinetic difference between the two types of bainite has been revealed in the activation energy determined from the overall reaction;4,5 however, many difficulties arise in an interpretation of these activation energies since a number of temperature dependent factors contribute to the kinetics of the overall reaction. The displacive surface relief10 accompanying the bainite reaction permits a separation of the nuclea-tion and growth contributions to the reaction and allows the kinetics of the growth process to be examined. Several investigations of this type have been conducted; however, they have been restricted to the low temperature range.3'6'11 Here, bainite plates are observed to grow slowly in both length and width. The present investigation extends such studies to include the upper bainite range. MATERIALS AND PROCEDURE Materials. The composition of the steels studied in this investigation are presented in Table I. The range of composition permitted a study of the effect of carbon content on the growth rate of upper bainite in the 9 pct Ni steels and consideration of both upper and lower bainite in the higher carbon steels. These steels were received as hot-rolled rounds and were forged to approximately 1/2 in. thick plates for preparation of metallographic specimens. In order to produce an essentially zero carbon steel, Steel A was decarburized in wet hydrogen at 1550°F for 15 days with the result tabulated as Steel AD. Experimental Procedure. In order to study the slow growth of the displacive transformation product, a commercially available Leitz hot stage was modified to permit heating of the specimen by its own resistance in a manner similar to that employed by other investigators.6 The furnace chamber was maintained at a pressure of 2 to 3 X 10-5 mm Hg prior to austenitizing at 2000° ± 12° F for 5 min. Samples could be cooled from the austenitizing to the transformation temperature in approximately 15 sec and the progress of transformation was recorded with a 9 cm by 12 cm single frame camera or a 16 mm movie camera. RESULTS AND DISCUSSION Growth Characteristics. The general growth characteristics observed in this investigation were analogous to those reported previously.3,6,11 Typical growth sequences for the high temperature and low temperature forms are illustrated in Figs. 1 to 5. In both temperature ranges, bainite plates increase in length at slow, temperature dependent rates until interrupted by a grain boundary, another plate, or

Jan 1, 1963

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi's solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith' have applied Raimondi's solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,' Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By U. N. Bhrany, N. Arbiter

F. C. Bond (Consulting Engineer, Processing Machin-Dept., AllisChalmers Manufacturing Co., Milwaukee) This is a very comprehensive paper. It deals with 1) size distribution functions, 2) energy-particle size relationships, and 3) criteria for grinding efficiency. The method of analysis used consists of tracing the increase and decrease of successive Tyler scale screen fractions as grinding progresses. The treatment is based upon the assumption that the work done in grinding is concentrated entirely upon the coarse size fractions in the mill. It is postulated that when a feed consisting entirely of particles of one size fraction is batch ground that finer fractions increase at a constant rate as grinding progresses, until finally each in turn begins to be ground and to decrease in amount. It is shown that under these conditions the empirical Gates-Gaudin-Schuhmann log-log size distribution plot can be logically explained. It is difficult to imagine any condition of ball mill operation, or any probability analysis, which would result in no grinding contacts on the finer particles present. However, the authors' postulate must be accepted if their conclusions are to be sustained. They conclude that the equation expressing the for mation rate of each size fraction can be resolved into the G.-G.-S. size distribution equation, and that the curvilinear portion of the log-logsize distribution line represents the only particle sizes which are being ground as well as produced. The author's statement that the G.-G.-S. Eq. 4 applies only to the finer portion of the size distribution while the Rosin-Rammler Eq. 6 applies over the whole size distribution range certainly supports the view that an exponential equation of the Rosin-Rammler type corresponds more closely to actual size distribution than does the power law G.-G.-S. equation. However, the G.-G.-S. equation is used to derive Eq. 8 and Eq. 9, which state that the energy required to grind a ton through a particular mesh varies inversely as the particle size to the exponent -a , whic h is the slope of the extended G.-G.-S straight line. This is stated to apply to both batch and continuous grinding. The G.-G.-S. slope exponent thus becomes very important in all crushing and grinding analyses by this method. The authors include some data which can be used to test their conclusions, as described below: We will consider grinding a feed composed of 14 mesh (1190u) to -200 mesh (74u). The average of 17 Allis-Chalmers grindability tests on quartz gives a work index (Wi) of 12.77. The -200 mesh product should have 80 pct passing 41.6u or P = 41.6. The equivalent 80 pct passing size of the 14 mesh feed particles is considered to be the particle diameter, as is true for spherical particles. Thus F is 1190u. In the work index equation 10 wi 10 wi 127.7 127.7 P f 41.6 1190 = 16.1 kw-hrperton. In Table I the ball mill exponent for quartz is 1.0 and from Eqs. 9 and 10: w=kw-hr/ton =Constan/(do/di) = 16.1 ton so that (1190) Constant/ Constant and the Constant equals 259. The tons per horsepower-hour value is 0.0464, in agreement with Table IV. The exponents for other minerals are listed in Tabl e 11. In Table IIA, the kilowatt hours per ton required to grind these minerals between the same sizes as the quartz, both by the authors' method and the work index equation, are listed. According to the authors kw-hrperton = 259/(16.1)".

Jan 1, 1961

By M. M. Singh, H. L. Hartman

This paper reports on the results of a fundamental investigation of the behavior of rock under impact of a chisel-shaped bit. Drop-tester studies were conducted with strain gauges attached to the rock and striking bit-edge. It was established that rock behaves viscoelastically. Little correlation was found to exist between the strain waveforms detected on the rock surface and in the bit; thus, strain-time curves obtained with transducers mounted on the bit cannot be used to explain the sequence of events in rock breakage. It is estimated that nearly 1 per cent of the total energy of the blow is expended in permanent deformation of the rock. The strain- energy distribution on a rock surface as a result of chisel impact, which follows a simple law, is presented graphically. Experiments also were conducted with gauges embedded in the rock vertically below the line of impact and at an angle of approximately 45' to the vertical. No essential difference was observed in the type of wave obtained with embedded gauges and with gauges on the surface, as may have been anticipated from theory. INTRODUCTION Through the ages great strides have been taken towards improvement of the various techniques applied in the breakage of rock. Indeed, numerous applications of the rock-failure process are an integral part of present-day industry, including oil well drilling. Yet, astonishingly, little is known regarding the behavior of rock under dynamic loading or the mechanism of rock failure. The value of impact loading studies from the point of view of drilling is evident, however, and requires little elaboration because impact of a chisel edge on rock forms the basic action constituting most common methods of drilling. RELATED STUDIES Impact studies of communition and fragmentation conducted by Fahrenwald, et a1,8 Poncelet,l7 Axelson, et a1,2 Piret,16 Hartman and pfleider,ll Charles and deBruyn,5 and others have been of considerable help in understanding rock-breakage phenomena. Further insight into the basic action of drilling and penetration has been obtained by the work of Irving,13 Cherkasov and Shlyapin,6 BOrcherdt,3 Shepherd,19 Shreiner and Pavlova,20 Drilling Research Inc.7 Hartman,10 Appl and Gatley1 and several other investigators. However, knowledge concerning the stresses and strains induced in the rock and bit during impact remains scant. Recent photoelastic studies by Tandanand and Hartman (1961. 1962)22, 23 have shed light on stress distributions and Fracturing produced in plastics by chisel-shaped bits. In the field of transient strain Pulses and their role in rock drilling, the only extensive work has been performed by Drilling Research Inc. (DRI). They attached strain gauges to the shank of a bit and conducted drop-tester studies, using a die-shaped bit to obtain force-time diagrams. Their work led to the conclusion that, for a given rock type, the first peak of force occurs at a fixed level regardless of the total energy in the system, provided it exceeds a certain minimum threshold level. Further, on this basis an explanation was offered for the sequence of events in crater formation as the result of a single blow on rock. PURPOSE OF PRESENT STUDY The investigations reported in this paper were conducted in a manner similar to the DRI approach, but with the objective of determining the strain distribution in the rock around the area of bit impact and, to a limited extent, the strain in the chisel-shaped bit itself. It was expected that a knowledge of the disposition of these strains, along with the rate of attenuation of strain energy in the rock

By T. M. Kegley, J. H. Frye, D. L. McElroy, M. L. Picklesimer, E. E. Stansbury

Measurements of rate of growth, thermodymmic quantities, and partitioning of Mn are reported for high-purity eutectoid Fe-C and Fe-C-Mn steels for the auistenite-pearlite reaction. Evaluztion of the cotnstants of a derived-rate equation with these data indicate that Mn additions cause the decrease observed by increasivg the activation energy and apparent activation entropy or the movenment of complexes at the interface. A diffusion-controlled mechanism is not required. Appreciable partitioning of Mn to cementite occurs entirely behind the austenite-pearlite interface for more than 30°C of subcooling. ThE growth of pearlite from austenite has been extensively studied over a period of years. but the rate-controlling step in the process is not known nor is the mechanisrn of the effect of alloying elements understood. A comprehensive review of the subject has been given by Mehl and Hagel. The present study has been concerned with further considerations of the effects of alloying elements on the rate of growth of pearlite. Analytical relatioriships for the rate of growth of pearlite have been considered by Zener.2 Turnbull,3 Machlin,4 Cahn.5 Frye,6 and Frye et a1.7 The derived expressions in each case involve the free energy of the transformation. the interlamellar spacing. and some rate term of the nature of the diffusion coefficient. mobility or frequency of occurrence of some rate-determining step. The treatments. of course. differ in detail. Further consideration is given in the present paper to the equation of Frye, Stansbury. and McElroy which was derived from modified absolute rate theory without in any way specifying the mechanism of the reaction. This equation is r=c ? T ? F exp -?E*/RT [1] where r = rate of growth in mm/sec c = a constant AT = equilibrium transformation temperature minus actual transformation temperature "C ?F = free energy per mol of austenite minus that of pearlite ?E* = activation energy R= gas constant ?F in Eq. [1] is computed from the following: ?F=?H?T/To - ?T' dT' ?T' ?CdT"/T" [2] To To where AH is the enthalpy per mol of austenite minus that of pearlite at the equilibrium temperature, To, and AC is the difference in specific heat between austenite and pearlite per mol. Subsequently, Darken, Fisher, and Galligan8 have reported that a layer of ferrite separates pearlite from austenite at the growing interface (i,e., the advancing face of Fe3C is in contact with ferrite, not austenite) and the ratio of the thickness of this layer to the spacing of the pearlite has not been found to vary with alloy content or transformation temperature. This observation does not require any alteration in the above equation: however, it may require that a different significance be attached to the factor, AT. The AT term appears in Eq. [I] as a consequence of a factor for the amount of growth per complex transformed at the interface.* It is based *This is not the sole reason for expecting such a relationship. See Ref. 7._______________________________________________________ on a l/2 ?T dependence of the interlamellar spacing. Zener2 has developed a theory which leads to Soa 1/?V where So = the pearlite interlamellar spacing. This relation is as consistent with the data on interlamellar spacing as other relationships, although, as pointed out by Mehl and Hagel,1 the data are not sufficiently precise to consider the relationship as confirmed. The work of Darken, Fisher, and Galligan8 requires that the above be written where f = the thickness of ferrite layer between austenite and pearlite. The present paper is concerned with iron-carbon-manganese eutectoid alloys and reports experimental measurements of the following kinds: 1) the effect of

Jan 1, 1961

By M. T. Hepworth, T. P. Papazoglou

Hydrogen diffusion in hcp and bcc titanium in the temperature range 610° to 900°C was measured by reacting cylindrical specimens of high-purity titanium at constant temperature with small constant pressures of hydrogen of the order of a few Torr. In the range 0 to 6.7 at. pct H in hcp titanium, the diffusion coefficient D in sq cm per sec is given by: where T is in °K and R in cal per g-atom OK. Only three measurements of diffusivity in bcc titanium were made: at 900' : the diffusivity in ß titanium was found to be 1.8 x 10-4 sq crn per sec. McQUILLAN1 has studied the constitution of the Ti-H system and reported the concentration of hydrogen as a function of pressure of hydrogen and temperature. He found hydrogen absorption was reversible and rapid at temperatures above 500°C in both crystallographic modifications, the a (hcp) phase and the ß (bcc) phase, with the latter phase stabilized by hydrogen additions. Wasilewski and Kehl 2 measured the diffusivity of hydrogen in hcp and bcc Ti-H alloys. For bcc alloys, they reacted cylindrical specimens of titanium with hydrogen gas at 1 atm pressure. They measured the rate of absorption of hydrogen isothermally on specimens ranging from zero hydrogen content when above the transformation temperature to hydrogen contents sufficient to stabilize the bcc phase when below the transformation temperature. By integrating Fick's second law for a cylindrical geometry, assuming a diffusion coefficient independent of composition, they calculated diffusivities as a function of temperature. In the range 650" to 1000°C their results in bcc titanium yielded the expression: where D is in sq cm per sec, T in OK, and R the gas constant in cal per g-atom-OK. Their studies on the hcp a phase were conducted by exposing long cylindrical titanium specimens to hydrogen at a sufficiently high pressure to establish a surface layer of fl phase 80 to 120 u thick for the duration of an isothermal experiment. Concentration profiles were then determined by hydrogen analysis from chips obtained upon machining quenched specimens. The diffusivity of hydrogen was then calculated yielding the expression: The present investigation was undertaken principally to redetermine the diffusivity data on a titanium by a direct absorption from the gas phase at sufficiently low hydrogen pressures to avoid the presence of a surface bcc phase and also to check the diffusivity data at low hydrogen concentrations in the bcc stmcture. EXPERIMENTAL PROCEDURE High-purity electrolytic sponge titanium (99.9 pct) of BHN 91 was arc-melted, forged, rolled, and machined into cylinders of final hardness, upon annealing, of BHN 92. Cylindrical specimens of two sets of dimensions were used: 1.524 by 2.931 cm and 1.905 by 3.663 cm diam and length, respectively. The experimental apparatus used for annealing specimens and for admitting known amounts of hydrogen at constant pressure is shown in Fig. 1. In a typical experiment, a specimen was lightly abraded with fine-grain silicon carbide, washed with water and detergent, and then thoroughly degreased with reagent-grade tri-chlorethylene and acetone. The specimen was suspended by a Chrome1 wire in the center of a quartz furnace tube, without contact with the tube, and heated to 925°C (as measured by a thermocouple adjacent to the specimen, outside the tube) for a period of at least 4 hr under a vacuum of from 10-6 to -7 Torr as measured by an ionization gage. The furnace temperature was then adjusted to the temperature chosen for the particular diffusion study and the specimen allowed to equilibrate thermally. Hydrogen was then ad-

Jan 1, 1969

By A. F. Witt, A. M. Gaudin, A. K. Biswas

Finite contact angles in the rutile-water-organic liquid system are traceable to contamination or are due to addition of a surface-active agent. Finite contact angles are invariably accompanied by hysteresis.1-7 Besides surfactant concentration and pH, the nature of the organic liquid is found to be a factor influencing the magnitude of contact angle hysteresis. In a recent paper the authors have reviewed principles and applications of measurement methods for contact angles and their hysteresis.22 In this paper, these methods are applied to a system consisting of rutile, an organic liquid (benzene, decane, or dode-cane) and water. Surfactant (dodecylamine hydro-chloride) was used at various concentrations and various pH values. MATERIALS A synthetic rutile crystal supplied by the Linde Co. was used. It is a cylinder 1/2 in. diam, with faces cut perpendicular to the c-axis. The crystal is stated to be alumina-free and to be 99.9% pure. Rutile is a high surface energy solid, its calculated average field strength being 2.7 x 105 e.s.u.,9 its dielectric constant10 is 114. The zero point of charge of rutile was measured11 and found to be at pH 6.0. The atomic distances and bond angles of the tetragonal crystal of rutile have been precisely determined.l2 The organic liquids were specially purified. Reagent grade benzene was repeatedly shaken with concentrated sulfuric acid to remove thiophene, then neutralized with sodium hydroxide solution, rinsed with distilled water, dried overnight over anhydrous calcium chloride and filtered. The refractive index of this chemically purified benzene was 1.4977 (at 25°C) - very close to that of pure benzene (n25 1.4979).13 Both n-decane and n-dodecane were washed with aqueous sodium hydroxide, concentrated sulfuric acid (repeatedly, until the acid layer was colorless) and again with alkali, to free the organic hydrocarbon from fatty acids and unsaturated hydrocarbons. The organic phases were subsequently washed with distilled water and dried over anhydrous sodium sulfate. The filtered hydrocarbons were then distilled under vacuum (9-10 mm pressure). Decane, thus purified, showed traces of unsaturated and of carboxylic compounds. On gas chromatographic analysis the purified n-dodecane showed the presence of two impurities. However, the relative retention times of these components did not change substantially when measured on a polar or a nonpolar column. This indicates that the compounds were probably in the same polarity class, i.e. the components were nonpolar like dodecane. Conductivity water has always been one of the liquids. Conductivity of the water used was 10-6 ohm-' cm". Dodecyl ammonium chloride was prepared from pure amine (supplied by Armour and Co., Chicago), by Li in the MIT Mineral Engineering Laboratory.14 The critical micelle concentration at 25°C is known, 0.0138 mol per liter15 or 3.06 gpl. All our experiments have been done at concentrations lower than the critical micelle concentration. The glass vessels, glass drop holder and the rutile crystal were all cleaned with hot chromic acid followed by distilled water, concentrated hydrochloric acid, and again distilled water, and conductivity water. During the experiments, a nitrogen atmosphere was maintained. For this purpose, commercially purified nitrogen was further purified by passing it over hot copper wire at 450°C, then through columns of acidic chromous chloride solution, concentrated alkali solution and distilled water. APPARATUS AND METHODS Hysteresis was produced by the "captive drop" or constant volume drop method as well as by the "expanding-contracting drop" or variable volume drop method. The image of the drop while it is expanding, contracting or moving is projected on a screen and photographed. The developed film is projected through an enlarger and the contact angles measured with a protractor.

Jan 1, 1964

By N. J. Grant, B. C. Giessen, U. Wolff

With the aid of the splat-cooling technique of rapid quenching, metastable alloy phases based on antimony ad bismuth have been prepared. At room temperature, simple cubic phases were found in the Sb + Au, 56 + Yd, and Sb + Ni systems. Another phase was retained in the Au-Bi system at -190°C; in this systent, a microcrystalline phase and a rhombohedrally distorted phase were also observed. The crystal chemistry of these phases is discussed in terms of their valence electron concentration range. A remarkable five-step Phase sequence was found upon heating and equilibration of certain metastable Au-Bi alloys. USING the splat- cooling technique of rapid quenching from the liquid,' a large number of metastable intermediate alloy phases have been prepared in recent years. Thus, Hume-Rothery phases of the hexagonal type based on the valence electron concentration have been produced in systems where they are missing in equilibrium, e.g., Ag-Ge 1 or AU-Sb. 3 In a comprehensive study of metastable alloys based on tin, simple hexagonal metastable y phases were found, raising the total of stable and metastable y phases from 3 to 13. 4 In the In-Bi system, five new metastable intermediate phases were retained.' In most cases, the new metastable phases have some crystal chemical characteristics in common: a) They have rather simple, elementlike structures with few atoms per unit cell, e.g., y phase,4'5 or the metastable primitive cubic phases in the Ag-Te and and Au-Te systems.= b) Their structures are often related to those of the terminal phases, or to elements that are straddled in their position in the periodic table by the constituent elements; this is the case for metastable ß (In-Bi) with the structure of white ß Sn,' or metastable a (Cd-sn). 4 c) They seem to represent the crystal structures appropriate to certain average group number (AGN) ranges in which no or few single-phase structures exist in equilibrium. These average group number ranges can probably be equated in the case of many elements of the Ba(Zn)-Bs(As) groups with the averaged valence electron concentration. In the present work, the splat-cooling technique has been applied to the alloys of antimony and bismuth. In equilibrium, neither element forms intermediate alloy phases with other B elements from groups Bl(Cu) to B4(Si) that contain more than 66.7 at. pct of Sb or Bi, respectively, e.g., AUSb 2. 7 Thus, antimony- or bismuth-rich phases, which might be closely related to antimony or bismuth, and which would reflect struc- tural changes occurring on alloying with small amounts of addition elements, do not exist. Also, the terminal solubility of antimony and bismuth for all B metals is very small. It was therefore of interest to investigate the influence of enforced, nonequilibrium solid solution of addition elements in antimony and bismuth on their crystal structures. It was found that additions of group B 2-B4 metals act distinctly differently than additions of group T 10 and B1 metals. The latter set of additives will be treated here. EXPERIMENTAL TECHNIQUES Alloy preparation and splat-quenching followed closely the procedures described in Refs. 1, 4, and 5; they consisted of the preparation of master alloys from high-purity starting materials (99.99+ pct) and blast-atomizing of 20-mg quantities onto copper sheets. The resulting approximately 1 to 5 u thick foils were investigated by X-ray diffraction. The cooling rates obtained are of the order of 107 to 10 8 C per set,'" causing solidification to proceed at a rat; of approximately 100 cm per sec.' Powder patterns of the resulting fine-crystalline materials were taken with filtered CuK, radiation. For antimony alloys the substrates were held at room temperature and for bismuth alloys at -190°C both during splat foil deposition and X-ray investigation. Annealing treatments at several

Jan 1, 1969

By A. Kenneth Schellinger

DURING the comminution of a brittle material in the presence of dry air, no known phase change or chemical reaction takes place. The energy changes associated with the comminution are those of the transformation of kinetic energy into heat energy and the energy absorption represented by the actual rupture of molecular and/or ionic bonds. The random nature of the actual grinding process in a tumbling-mill often precludes the effective application of a rupture force on each individual particle of brittle mineral present. The result must be a great deal of useless vibration on an atomic scale in both the brittle mineral and the grinding medium below the elastic limit, which vibration is eventually manifested as heat energy in the mill. The actual rupture of molecular, or ionic, bonds creates new surface on the brittle minerals; each square centimeter of this new surface then must possess a number of potential bonds, each of which could reform theoretically with the release of energy. The sum total of this potential energy of bonding per unit of new surface, minus bond satiation effects of the enclosing gas or liquid, must be the surface energy of the mineral. If the comminution of the brittle mineral were carried out within the chamber of a calorimeter, the energy released as heat could be determined rather accurately. Moreover, the total kinetic energy input to the comminuting mass (mineral and medium) conceivably could be derived by a suitable torquemeter and revolution counter if the whole calorimeter were revolved. The difference between these two energy figures should then represent the net energy (gross energy input—heat enerb output) used in creating new surface, gliding or slip on atomic planes, twinning, and possibly other lattice rearrangements within the mineral. If it be postulated further that with a hard, brittle crystalline material, such as quartz, the energy used to produce gliding, twinning, and other permanent lattice movements is a very small fraction of the total net energy absorbed, then this energy absorption within the grinding calorimeter can be ascribed to the creation of new surface energy alone. Such energy is, from the thermody-namic standpoint, the true effective work of the grinding device, in this case a tumbling-medium mill. The ratio of this effective work (in calories) to the total energy input (in calories) should express the thermodynamic efficiency of the comminution taking place under the conditions used in the grinding calorimeter. This approach to the measurement of the energetics of tumbling-mill grinding was suggested by some previous work by Fahrenwald and coworkers' with a laboratory ball mill and a thermometer. They measured the efficiency of grinding based on the formula: Pct Grinding Efficiency = Energy (calories) — Thermal Energy x 100 1npZ Output (calories) Energy input (calories) Efficiencies thus measured, while grinding quartz sand, ranged from 19.7 pct to 7.4 pct. Cook in 1915,' used this approach to the problem of grinding efficiencies in stamp batteries and obtained the energy input by stamp weights times drop distances and the energy output by means of thermometers and pulp flow rates. He calculated that 80 pct of the input energy to the stamp shoes was wasted as sensible heat in the ore pulp. No other studies of comminution by this method of energy differences came to the author's attention. Reasonable agreement as to the order-of-mag-nitude of comminution efficiencies in tumbling-media mills is lacking in the literature. There is a widespread impression among technical workers that the grinding efficiency of the industrial ball mill may be on the order of 1 pct, or even a fraction

Jan 1, 1952

By H. F. Webster, C. G. Dunn

Rolling md annealing procedures are described for developing the (110) preferred orientation in tantalum for use as a thermionic-emission materinl where electrodes of a uniform high work function are needed. The development of a (110) [001] annealing texture is also reported. A preferential growth process due to low (110) gas-metal surface energy is considered in explanation of the observed growth of (110) grains. ThE growth of (110)-oriented grains in thin strips of rolled zone-refined tantalum, previously discussed briefly,' is reported together with more recent information on the formation of a (110)[001.] annealing texture, i.e., one where the [001] direction of each grain lies close to the rolling direction. The development of tantalum sheet with a (110) preferred orientation (position of [001 ] directions unspecified) is of importance as a thermionic-emission material in thermionic-energy converters. Since therm ionic-emission properties of cesium-coated crystals vary over a wide range depending on (hkl) a2-7 a single (hkl) preferred orientation is more useful than either several preferred orientations or none. Furthermore, the (110) preferred orientation yields the highest thermionic-emission density for a cesium coverage of less than a monolayer.5-7 A consideration of the stability of the grain structure needed at high operating temperatures suggests that the preferred orientation itself should be produced by annealing processes. Information on annealing textures in tantalum, however, is rather limited. Pugh and Hibbard 8 obtained (111)[112] and (lll)[112] components in a 1400°C recrystallization texture in 95 pct cold-rolled foil; these components were enhanced on annealing at 2500°C. Muller9 rolled 99.97 Ta to 90 pct reduction in thickness in the final stage and noted only a slight sharpening of the rolling texture, with some intensification of the (111)[112] component upon annealing at 1200°C. The experimental procedure followed in the present work stemmed from the idea of using possible differences in (hkl) surface energies to provide a small driving force for growth of grains having the lowest (hkl) surface energy.l0* This would mean using high-purity tantalum processed into thin sheet form and annealed at high temperatures either in a noncontaminating atmosphere or in one producing additional sample purification. EXPERIMENTAL Zone-Refined Tantalum. National Research Corp. tantalum in the form of 1/8-in.-diam rod and of 99.98 purity (53 ppm 0, 15 ppm N, and 8 ppm C) was zone-melted four times. The traversing speed was 4 mm per min. Such treatment increased the resistance ratio, R293k/R20K , where R293K is the resistance of the specimen at 20°C and R20K the re-resistance at liquid-hydrogen temperature, from a value of 25 for the initial rod to 175 for the zone-refined rod (the increase in the resistance ratio provides a measure of purification11,12). Part of a zone-refined rod was rolled unidirec-tionally to a strip 0.003 in. thick and 0.28 in. wide. Samples were given anneals in the range 1300" to 2100°C using ac conduction heating in an oil-free vacuum system. Recrystallization to small grains appeared to be complete at 1300°C. Large grains were formed at higher temperatures, but these were not entirely strain-free, some grains showing asterism in Laue X-ray patterns and some displaying a range in orientation. Part of the difficulty was caused by thermal expansion of the tantalum strip as it was held between fixed supports. However, in a different arrangement with the tantalum freely suspended in a tantalum can, high-frequency induction heating in vacuo at about l0-6 Torr produced

Jan 1, 1964

By Robert D. Pehlke, Weldon L. Daines

The reduction of manganese oxide from a basic slag by silicon dissolved in liquid iron at steelmaking temperatures was studied to determine the rate-controlling step for the process. The experiments were carried out under an argon atmosphere in a resistance-heated vertical-tube furnace. The two liquid phases, slag and metal, were held in zirconia crucibles. Sampling and chemical analysis of the slag phase led to time-concentration curves for the system. Results obtained by varying parameters such as temperature, stirring rate, concentration, and melt geometry defined the limiting reaction mechanism. The reduction of manganese oxide by silicon is a fast reaction and reached equilibrium within 90 min. The rate of stirring has a marked effect on the reaction rate, while, on the other hand, the effect of temperature is very small. This identifies the rate-controlling step as diffusion rather than interfaciul chemical reaction. The variation of other parameters revealed that a) diffusion of manganese in the iron phase is the slow step, b) the value of D/6 for manganese in iron at 1550°C is 7x 10-4 cm per sec, c) the energy of activation for the apparent rate constant is 7 kcal per mole, and d) increasing the amount of silicon in the iron decreases the diffusion coefficient of manganese. THE equilibrium relations pertinent to the reduction of manganese oxide from a steelmaking slag by silicon dissolved in liquid iron have been studied, but little is known about the mechanisms that control the rate of the process. The purpose of the present investigation was to study the rate of reduction by silicon and to determine the rate-limiting step. The effects of stirring rate, temperature, composition, and melt geometry were investigated as a means of identifying the controlling step. On the laboratory scale, relatively little work has been done in the area of slag-metal kinetics, primarily because of the problems confronted in attempting to contain liquid slags and metals in laboratory crucibles at steelmaking temperatures. Since graphite is an ideal material for a crucible, several investigations have been carried out on the reduction of various oxides from a slag by carbon in graphite-saturated iron and on the transfer of sulfur between a slag and graphite-saturated iron. Most of this work has been performed in induction furnaces. Studies where the container was not graphite are extremely limited. A single kinetic study of manganese transfer between molten iron and basic slags was carried out by Sano, Shiomi, and Matsushita.' These investigators prepared calcium oxide and titanium oxide crucibles to contain the two-phase system. Only a few experiments were carried out and the results had to be treated qualitatively. Despite the paucity of kinetic data, a large quantity of information is available in the literature concerning the thermodynamics2-12 and physical properties'3-21 of the slags containing manganese oxide and the dilute liquid iron alloys containing manganese and silicon which were involved in this research program. EXPERIMENTAL METHOD A vertical-tube resistance-heated furnace was used in this investigation to study the slag-metal reaction Although most previous slag-metal studies were carried out in induction furnaces, a resistance furnace has several advantages including better control of temperature and stirring rate. Hence, a resistance furnace was selected for this study, and its design is shown schematically in Fig. 1. Slip-cast, fine-grained, low-porosity, lime-stabilized cubic zirconia crucibles were used for the kinetic experiments. The crucibles were 4 1/2 in. high and 2 1/8 in. OD with a 1/16-in. wall. The crucibles were only slightly

Jan 1, 1969

By T. K. Perkins, O. C. Johnston

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in parous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature. Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/D, is about 0.6 to 0.7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as D/Do = 1/FF where F is the for- mation electrical resistivity' factor and 4 is the porosity. If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity. At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces. There are several variables that must be con- trolled to get consistent longitudinal and transverse dispersion results, viz., (1) edge effect in packed tubes, (2) particle size distribution, (3) particle shape, (4) packing or permeability heterogeneities, (5) viscosity ratios, (6) gravity forces, (7) amount of turbulence, and (8) effect of an immobile phase. INTRODUCTION Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes. In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or "fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. 58 Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes. In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. As time passes, the sharp interface between the two fluids will become a diffuse

By T. Szaplonczay, D. E. Light

The auto-oxidation of sulfur dioxide to form sulfuric acid in commercially produced barren and recycle liquors, containing 1.66 and 4.56 gpl Fe respectively, from Elliot Lake was studied. A gas mixture, containing 3.5% SO2 and air was introduced into these liquors through a frit at a rate of 6.0g SO2 per hour per liter of solution. The barren and recycle were heated to 60°C. At the end of the first 24 hours of the process the concentrations of acid produced were 158 and 220 gpl H2SO4 for the barren and recycle respectively. Corresponding conversion efficiencies were 70 and 83%. In the period from 24 to 36 hours the rate of acid production decreased so that the H2SO4 concentrations at the end of 36 hours were 180 gpl for the barren and 260 gpl for the recycle; average conversions for the initial 36 hours were 55 and 68% respectively. Many investigators1'2'3 have considered the oxidation of sulfur dioxide to form sulfuric acid in aqueous solutions containing metallic ions. A summary of the work performed on this subject prior to 1946 has been presented by Keyes4 who described the auto-oxidation process as follows. Keyes also suggested that in this second reaction ferric ion serves as a catalyst for the conversion of sulfur dioxide to sulfuric acid. Neytzell-de Wilde and Taverner5 have reported on the use of auto-oxidation to produce a 4 to 5% sulfuric acid solution for use in a cyclic leach process at South African uranium plants. This paper describes investigations carried out to determine the feasibility of using the auto-oxidation process to produce sulfuric acid solutions of as high concentration as possible using commercially produced uranium plant barren and recycle liquors from the Elliot Lake region of Ontario. These liquors contained 1.66 and 4.56 gpl respectively of iron, chiefly in the ferrous state. This investigation is of particular interest to the uranium producers in Elliot Lake where the ores contain 3 to 4% sulfur, as sulfides. Flotation of these sulfides and roasting of same to produce SO, bearing gases have been successfully demonstrated using conventional methods.6'7 Barren and recycle solutions, as described previously, are also produced in large tonnages by these uranium producers. The experimental method and apparatus used to examine the auto-oxidation process will be described first. Then the tests carried out on laboratory prepared aqueous solutions containing ferric sulfate to determine optimum conditions will be presented. The next section will describe the tests using the commercial barren and recycle liquors. A final section will summarize the conclusions of the work. EXPERIMENTAL APPARATUS AND PROCEDURES Two types of solutions were used in the tests, a laboratory prepared aqueous solution containing definite amounts of ferric sulfate, and commercially produced iron bearing solution obtained from a uranium leaching plant in the Elliot Lake area. Two liters of a solution to be examined were placed in a 3 in. diam by 30 in. long glass cylinder with a cross-sectional area of 7 sq in. A mixture of air, and SO2 supplied from a lecture bottle for convenience, was introduced into the bottom of the vessel through a standard 30 mm glass frit, 700 sq mm in area. The temperature of the apparatus was controlled by a heating tape and variable transformer. Exhaust gases were vented to atmosphere. At the end of the test period the gas flow was shut off and the solution was analysed for H2SO4, Fe ++, and Fe +++, by conventional means. Four variables were examined using the laboratory prepared aqueous solution of ferric sulfate. First, the effect of SO2 concentration, from 1 to 1076, in the feed gas mixture was considered. Second, the temper-

Jan 1, 1964

By Wayne L. Worrell

Thermodynamic data for the stable carbides and oxides of chromium, molybdenum, and tungsten have been critically eualuuted and are used to determine the stable condensed phases at 1 atm total pressure in each metal-carbon-oxygen system. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures neces.see)*y to oblain these metals by corbolhermic redlrction under reduced pressures. USING recently reported data for the carbides and oxides of chromium, molybdenum, and tungsten, the stable phases in the Group VI metal-carbon-oxygen systems at specific temperatures and pressures can be determined. The thermodynamically stable regions in each metal-carbon-oxygen system can be completely pictured using a Pourbaix-Ellingham diagram in which the two coordinates are oxygen potential (-RT In Po2) and temperature. Worrell and chipman' have described and constructed such diagrams for the metal-carbon-oxygen systems of vanadium, columbium, and tantalum. Downing2 has used similar diagrams to provide a description of the reactions in submerged arc furnaces. One of the examples which he cited was the Cr-C-O system; however, an improved diagram is presented in this paper using recently obtained data for the carbides of chromium. Although some of the oxides and carbides of the Group VI metals exist over slight ranges of composition,3 all solid phases are represented as stoi-chiometric compounds in the subsequent diagrams. Any error introduced into the calculated equilibria by neglecting the compositional variation of these phases is less than the uncertainty in the thermodynamic data. In a Pourbaix-Ellingham diagram for a three-component system, the phase rule requires that at equilibrium four condensed phases specify a point, three condensed phases determine a line, and two condensed phases define an area. To obtain a well-defined area at high oxygen potentials and teniperatures, the initial carbon to oxygen mole ratio is specified to be more than sufficient to reduce the oxide but not enough to convert all the metal to carbide. Thus, the lowest regions in the subse- quent Pourbaix-Ellingham diagrams represent areas in which the metal and its carbide are the stable condensed phases. Cr-C-O SYSTEM A) Thermodynamic Data. To simplify the subsequent calculations, all thermodynamic data are presented in the form of linear Gibbs-energy-of-formation* equations which were derived for the temperature range 505° to 2000°K and are reasonably accurate over the entire temperature ranges of the diagrams. The thermodynamic data for the compounds occurring in the Cr-C-O system are summarized in Table I. Several volatile chromium oxides have been reported,4 but their influence is negligible in the Cr-C-O system. Thermodynamic data for CO and CO2 were taken from the compilation of Coughlin.5 The only solid chromium oxide sufficiently stable to exist below 1800°K in the Cr-C-O system is Cr2Os.11 The Gibbs-energy-of-formation equation for Cr2O3 was obtained by revising the data tabulated in Coughlin,5 using the heat of formation of ah' and the high-temperature thermal data for chromium.7 In 1953 Richardson8 re-evaluated the original work of Kelley and coworkers,9 who measured the thermodynamic properties of the chromium carbides. However, the high-temperature equilibrium results of Boericke9 yield values for ?G°f of Cr2O3 which are 2 kcal more positive than the accepted data. His results for the chromium carbides are based on the same questionable equilibria. Gleiser10 recently determined the Gibbs energy of formation of Cr3C2 and the equation in Table I was calculated from her data and the thermal data of Kelley and coworkers.9 Thermodynamic data for the Cr7C3 and Cr23C6 carbides were obtained by combining the Cr3C2 data

Jan 1, 1965

By J. N. Ong

The oxidation of tantalum is assumed to occur by four simultaneous first-order chain reactions; solution of oxygen in the metal, nucleation and growth of a suboxide phase at the metal surface and two phase boundary processes which give rise to two different modifications of Ta2O5. A rate equation is then formulated which accounts for all principal details of oxidation behavior, unifies and correlatss the results of the principal investigations, and expresses the rate as a function of pressure, temperature, and time. For purposes of practical application, the expressions: may be used below and above 700T respectively to determine the regression rate of tantalum in cm per hr, where T is to be expressed in "K and P in atmospheres pressure of oxygm. The equations will reproduce within a factor of two all reported experimental rates in the temperature range 475" to 1400°C and pressure range 0.000026 to 40.8 atm 0. 1 HE oxidation kinetics of tantalum have been investigated thoroughly in the temperature range 50" to 1400 and pressure range 1.32 x l0-' to 40.8 atm pressure of 0,and as a result, the principal features of the oxidation of tantalum are known and have been described in considerable detail. The exposition of the characteristics of the behavior of tantalum in oxygen has been largely descriptive, with considerable attention being devoted to elucidating the structure, composition, and morphology of the resulting oxide products. The weight change vs time results have usually been reported graphically. With the exception of the linear rate below 700 C and the process of diffusion of interstitial oxygen into the metal,6'9 no effort has been made to characterize the reaction rates in functional form. It is the purpose of this paper to demonstrate that when the fundamental principles of chemical kinetics are rigorously followed, the results of the principal investigations will be correlated and unified and the oxidation rale may be expressed as an analytic function of pressure, temperature, and time. In addition to accounting for the temperature and pressure dependency of the oxidation rate, the following minor features will be accounted for as a result of the basic analysis: the initial period of nonline-arity in rate at low temperatures, which decreases with increasing temperature;3'5'7 the rate vs temperature cusps obtained at constant pressure"5 the concentration gradient of oxygen interstitially dissolved in the metal.5'7 The analysis will also be consistent with the overall chemistry of reaction and with all visual, microscopic, and X-ray observations. DEVELOPMENT OF RATE EQUATION As a fundamental basis for the treatment of metal-oxygen reaction kinetics, it will be regarded that the rate of reaction is determined by the concentration and not the activity or chemical potential. It is further assumed that all metal-oxygen reactions are first order complex chain reactions" whose rate is dependent on the concentration of an intermediate species which is a complex function of the oxygen concentration, or oxygen pressure, only. The basic rate equation is therefore: is the weight of oxygen consumed by the reaction, A is that portion of the area of the metal over which the reaction is occurring (cm2), t the time (sec), kf the rate constant for forward reaction, C the intermediate species concentration and f '([Oz]) and f (Po,) are complex functions of oxygen concentration and Oxygen pressure respectively. Reverse reactions may usually be neglected in metal-oxygen systems since a large negative free energy generally accompanies these reactions. Eq. [I] takes different forms when the rate of reaction is controlled by diffusion into or through a phase or at a phase boundary. For diffusion into the metal phase, the rate is given by1' Di is the diffusion coefficient of species diffusing into the metal phase (cm2/sec), and Q is the corre-

Jan 1, 1962