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By C. N. Garman

Homestake-New Mexico Partners operate a 750-tpd carbonate leach uranium concentrate mill near Grants, N.M. The highly mineralized water available as process water leaves much to be desired. The 628 ppm as CaCO 3 makes the use of raw water very troublesome in pipes and on filter cloths. However, the residual sodium carbonate in the final filter cake going to tails makes an ideal softening agent. To take advantage of this fact, all makeup water used in the mill is first used as tailing slurry dilution water and comes to the mill from the tailings pond. The 5-acre tailings pond serves as a thickener and 100 to 150 gpm of nearly clear solution is decanted to a pump to be returned to the mill. Since this tailings water has small quantities of uranium in the solution an ion exchange scavenger unit was installed to remove as much uranium as possible. The ion exchange raffinate is then used as final filter wash ahead of the tailings slurrying step. In spite of the large settling area this return water is not clean enough for ion exchange feed. The solids present are very fine and composed of approximately 15 pct (by weight) burnable carbonaceous material common to the sandstone uranium ores in the area, 40 pct SiOz plus 45 pct CaC03. Laboratory work showed that this material responds very well to flotation. Before deciding to use flotation, various clarifying systems such as pressure leaf filters, sand filters, and continuous vacuum pre-coat filters, were considered. Each of these could have solved the problem but with much more operating labor, more reagents and greater installation costs than the flotation step. About 100 to 150 gpm of fouled water is fed to two 66-in. Fagergren cells, in series. Reagents used at the beginning were Arquad 2HT75 and Arquad C50, at the rate of about 1% lb per 8-hr shift, or about 0.0053 lb each per ton of ore. This did not completely remove the solids but does an acceptable job. Approximately 75 pct of the slimes are a size that can be caught on a 41-Whatman Paper are removed. Removal of these slimes also allows much better settling of the coarse nonfloatable material. Advantage is also taken of this fact in a small settling tank ahead of precipitation. Removal of this amount of the slimes makes the ion t:xchange feasible. PREGNANT SOLUTION CIRCUIT The carbonate? leach-caustic precipitation method of uranium concertration does not provide for any process purification step ahead of precipitation. Therefore, any fine solids getting into the pregnant solution through the filter cloth show up in the final concentrate. This, of course, lowers the grade, and, at times, the slimy nature of these very fine solids rendered final filtration of the concentrate difficult if not impossible At Homestake-New Mexico Partners a 75-ft thickener was available for gravity clarification of 100 to 120 gpm of this pregnant solution. However this did not sufficiently remove the slimes. Laboratory investigation of the whole range of flocculants that were suggested by literature, salesmen, and friends failed to turn up anything of consequence. A continuous vacuum pre-coat filter would do the job and was investigated. The capital cost and the operating labor and materials made this a last chance choice. Following work done in the metallurgical laboratory on the tailings return water, it was found that some changes in the reagent strengths and combinations made a very definite decrease in the solids in the pregnant solution. Concentrate grade improved about 5 pct anti the final product after drying had an appreciably greater bulk density. Compared to a cost of about 2.2e per ton for pre-coat filter opelation for cleaning just one circuit, flotation costs less than 1.0 per ton of ore for cleaning two circuits. While a pre-coat filter would do a more thorough job, the flotation does all that is required for either circuit. Gravity causes the froth produced to run back into the leach circuit. This does not appear to result in a build-up of objectionable slime. No extra manpower is required; the operators in the separate areas can observe the operation of the cells and mix the small quantities of reagents as needed. Normally the 66-in. Fagergren cell requires 15 hp per cell, but this very dilute slurry needs only 10 hp for both cells. Originally, a combination of the two Arquads mentioned previously served as frothers and promoters. As further testing

Jan 1, 1962

By K. Takahashi, I. Iwasaki

it is well known1 that racemic mixtures of optical isomers can be separated by passing their solutions through a column packed with r- or 1-quartz powder so that one of the isomers becomes adsorbed selectively on the asymmetric quartz surfaces. Although the natural occurrence of r- and 1-quartz is more or less equally distributed, some localities show enough deviations toward a higher proportion of l-quartz2 to suggest that optical isomerism might influence quartz flotation. Beta-amines have an asymmetric carbon atom, and therefore optical activity may be expected. Beta-amines are reported to behave quite differently from alpha-amines in the flotation upgrading of certain oxidized iron ores.3 It is of interest, for both practical and theoretical reasons, to determine whether or not optical isomerism plays a role in the amine flotation of quartz. In this article the results of Hallimond tube flotation tests and of adsorption measurements using d-beta-phenylisopropylamine on both r- and 1-quartz are compared. D-beta-phenylisopropylamine was chosen for the tests because it is commercially available in optical isomers. MATERIALS AND METHODS Brazilian quartz crystals were hand-sorted according to the difference in trigonal trapezohedral faces, and each crystal was further checked by the Airy's spiral.4 The respective crystals were then crushed, and the -150 + 200-mesh fractions were screened out for the Hallimond tube tests. The samples were cleaned by brief leaching with warm, dilute hydrochloric acid, and then by repeated rinsing with distilled water. In preparation for the adsorption measurements, they were then dry-ground in a pebble mill for several hours, washed a few times with distilled water, and finally dried in a vacuum desiccator. By means of the Krypton gas adsorption method, the specific surfaces of r- and 1-quartz samples were determined to be 27,700 and 19,800 sq cm per gm respectively, the difference being due mainly to the decantation procedure rather than to the inherent difference in their grindability. D-beta-phenylisopropylamine was the only collector used in the study. It was solubilized by neutralizing with 110% of the stoichiometric requirement of 0.1 N hydrochloric acid. The specific rotation of the d-beta-phenylisopropylamine was determined with a polari-meter using sodium D line to be, Although the d-beta-phenylis~prop~lamine showed absorption maxima in the wave length region of 250 to 270 millimicrons, due presumably to the phenyl group, these peaks were too sensitive to be used for colorimetric determination of the residual concentration in the adsorption measurements. The amine-picrate method, used in the colorimetric analysis of dodecylammonium chloride,' was found to work satisfactorily for the d-beta-phenylisopropylamine. The adsorption densities were thus determined after equilibrating 40 gm of the ground quartz sample with 300 ml of solution by tumbling in separate glass-stoppered Erlenmeyer flasks for one hour. EXPERIMENTAL RESULTS Fig. 1 presents the adsorption densities of d-beta-phenylisopropylamine on the r- and 1-quarts in the pH range of 6 to 7.5. In agreement with data reported in the literature, the adsorption density of d-beta-phenylisopropylamine was slightly higher on the r-quartz than on the 1-quartz, although the difference was not as pronounced as one might expect from the capacity of r-quartz and 1-quartz to separate racemic

Jan 1, 1969

By Walter Rose

It is the purpose of this note to call attention to the circumstance complicating the attainment of uniform gas-liquid distributions in multi-phase flow systems, and especially in those of the so-called Hassler type.' Although the complication arises directly as a consequence of gas compressibility and the dependence of fluid distributions on interfacial curvature phenomena, little reference to the problem has yet appeared in the literature.' In fact, it is only the paper of Geffen et al.3 which gives any experimental evidence that a problem exists. On the other hand, previous authorsl,4,5 have made the tacit, albeit fallaceous assumption that uniform gas-liquid distributions automatically are established in linear flow systems by the expedient of maintaining the pressure gradients equal in the flowing gas and liquid phases. Such a device, it can be shown, will succeed only if the immiscible fluids are both equally compressible or both essentially non-compressible. Another necessary condition required before uniform fluid-fluid distributions can be achieved is that the porous matrix is isotropic. Uniform fluid saturation distribution conditions obtain in isotropic media only when the curvature of each interface of contact between wetting and non-wetting fluids is everywhere the same throughout the interspaces. This is a necessary condition which follows from the consideration that variation in interfacial curvature gives rise to finite capillary pressure gradients and therefore to variation in the saturation distribution. That this is not a sufficient condition follows from the consideration that hysteric possibilities allow for different saturations even though the capillary pressure gradient is zero. In any event, it will- be recalled that it is the intent in the Hassler scheme of relative permeability determination' to obtain initially (by the capillary pressure drainage or imhibition process) uniform conditions of fluid distribution in the core sample, and then to maintain this uniformity during mixture flow so that the resultant fluid mobilities which are calculated will refer to steady-state transfer under fixed conditions of uniform saturation. If the flowing fluids are incompressible, it is recognized that employment of the same value of the pressure gradient in each fluid will result in maintenance of the initially obtained condition of zero capillary pressure gradient. On the other hand, the consequence of gas compressibility is that the gradient in the gas pressure varies from point to point in the flowing stream. and since the pressure gradient in an incompressible liquid is constant it is thus impossible to maintain zero capillary pressure gradient during the simultaneous flow of gas-liquid mixtures. Therefore, one would expect to observe a variation in the gas-liquid saturation in the directions of the capillary pressure gradients, depending in magnitude on the particular way saturation changed with capillary pressure. In order to formulate the manner gas compressibility effects prevent the attainment of uniform gas-liquid distributions during mixture flow, consider a linear flow system of unit length. As noted, it is necessary to assume an isotropic medium (viz. one where permeability is independent of position and direction). One then can arbitrarily set the pressure

Jan 1, 1951

By Walter Rose

It is the purpose of this note to call attention to the circumstance complicating the attainment of uniform gas-liquid distributions in multi-phase flow systems, and especially in those of the so-called Hassler type.' Although the complication arises directly as a consequence of gas compressibility and the dependence of fluid distributions on interfacial curvature phenomena, little reference to the problem has yet appeared in the literature.' In fact, it is only the paper of Geffen et al.3 which gives any experimental evidence that a problem exists. On the other hand, previous authorsl,4,5 have made the tacit, albeit fallaceous assumption that uniform gas-liquid distributions automatically are established in linear flow systems by the expedient of maintaining the pressure gradients equal in the flowing gas and liquid phases. Such a device, it can be shown, will succeed only if the immiscible fluids are both equally compressible or both essentially non-compressible. Another necessary condition required before uniform fluid-fluid distributions can be achieved is that the porous matrix is isotropic. Uniform fluid saturation distribution conditions obtain in isotropic media only when the curvature of each interface of contact between wetting and non-wetting fluids is everywhere the same throughout the interspaces. This is a necessary condition which follows from the consideration that variation in interfacial curvature gives rise to finite capillary pressure gradients and therefore to variation in the saturation distribution. That this is not a sufficient condition follows from the consideration that hysteric possibilities allow for different saturations even though the capillary pressure gradient is zero. In any event, it will- be recalled that it is the intent in the Hassler scheme of relative permeability determination' to obtain initially (by the capillary pressure drainage or imhibition process) uniform conditions of fluid distribution in the core sample, and then to maintain this uniformity during mixture flow so that the resultant fluid mobilities which are calculated will refer to steady-state transfer under fixed conditions of uniform saturation. If the flowing fluids are incompressible, it is recognized that employment of the same value of the pressure gradient in each fluid will result in maintenance of the initially obtained condition of zero capillary pressure gradient. On the other hand, the consequence of gas compressibility is that the gradient in the gas pressure varies from point to point in the flowing stream. and since the pressure gradient in an incompressible liquid is constant it is thus impossible to maintain zero capillary pressure gradient during the simultaneous flow of gas-liquid mixtures. Therefore, one would expect to observe a variation in the gas-liquid saturation in the directions of the capillary pressure gradients, depending in magnitude on the particular way saturation changed with capillary pressure. In order to formulate the manner gas compressibility effects prevent the attainment of uniform gas-liquid distributions during mixture flow, consider a linear flow system of unit length. As noted, it is necessary to assume an isotropic medium (viz. one where permeability is independent of position and direction). One then can arbitrarily set the pressure

Jan 1, 1951

By Rex E. Cheek, Donald E. Menzie

The fluid mapper, a model relatively new to the petroleum industry, was used to study the effect of various mobility ratios on the areal sweepout efficiency for two typical spacing patterns. The experiments indicated the areal sweepout for the five-spot pattern varied from 51.8 per cent at a mobility ratio of 0.093 to 89.1 per cent for a ratio of 24.4. In the direct line-drive pattern, the areal sweepout varied from 58.7 per cent at a mobility ratio of 0.089 to 92.0 per cent at a ratio of 24.8. The fluid mapper may prove useful to determine quickly the effective areal sweepout for any well spacing. INTRODUCTION The effect of the mobility ratio on the areal sweepout efficiency during primary depletion of a water drive reservoir and during secondary recovery operations has recently become more widely recognized The mobility ratio, M, is defined as: _ kjp (displaced fluid) k/u (displacing fluid) where k = effective permeability u = viscosity When the displacing fluid is miscible with the displaced fluid, the permeabilities are equal and the mobility ratio may be expressed as a ratio of viscosities: u (displacing fluid) u (displaced fluid) The mathematical analysis for calculating the areal sweepout efficiency with mobility ratio other than unity is quite tedious.5,11 An experimental method by using a potentiometric model2 in a step-wise manner and in using an X-ray shadowgraph model3,12 with continuous fluid flow has been published. Several types of models have been used to study oil and gas reservoir performance. These models may be classified as physical, electrolytic, potentiometric, X-ray shadowgraph, and fluid mapper. The X-ray shadowgraph and fluid mapper are models relatively new to petroleum engineering and have not been used extensively for specific applications. The theory of the fluid mapper indicates it may be adapted to a study of areal sweepout efficiencies for various mobility ratios as well as other complex problems in petroleum engineering. The use of the model and results obtained when using displacing and displaced fluids of equal densities but different viscosities are discussed. FLUID MAPPER DEVELOPMENT H. S. Hele-ShawV eveloped a fluid mapper model based on the hydrodynamic theory. This theory is that in the steady flow of a viscous fluid between horizontal parallel plates spaced a very small distance apart, the effect of viscous shear is of such magnitude in the vertical plane that the motion in the horizontal plane is practically undisbrted streamline flow. Techniques developed by Hele-Shaw were not expanded and no additional developments in fluid mapper models were forthcoming until A. D. Moore, University of Michigan, published a series of papers starting in 1949, which describe the construction of a flexible and inexpensive model'h nd the fluid mapper technique for the solution of certain problems.' The essential components of the fluid mapper as developed by Moore are::.ln 1. A base slab. made of dental stone (calcium sulphate and water). which is shaped to represent the prototype. 2. Plate glass slightly larger than the slab and spaced

Jan 1, 1956

By T. G. Sieber, T. D. Tiemann

The extraction of quartz from siliceous iron ores by dissolution in sodium hydroxide solution has been described in detail in AIME Transactions. l923 data reported covered the temperature range from 230-416°F, where a continuous increase in the amount of silica extracted with increase in temperature was found. It is the purpose of this paper to describe some unexpected results of more recent work exploring principally the range of 500600°F where higher rates and greater amounts of silica extraction were antici-p ted. In brief, the experimental procedure consists in digesting the ore under pressure in solutions of sodium hydroxide, filtering the suspension and weighing and analyzing the dried residue for iron content. The amount of extraction is calculated from the weight loss or from the iron analysis of the residue and that of the original ore.

Jan 1, 1969

By L. S. Castleman, L. L. Seigle

IN a recently reported investigation, J. B. Clark and F. N. Rhines1 used a diffusion couple technique to determine the number of intermetallic phases which should be present in the Al-Mg equilibrium phase diagram. Their method was an application of the following generally accepted principle. If a diffusion couple made up of two metals is annealed at a given temperature for a long time, all the phases of the binary system which exist under equilibrium conditions at the diffusion temperature will form intermetallic layers. It is important that the diffusion temperature be high enough and the diffusion time be long enough to permit the nuclea-tion of all thermodynamically stable phases at the interface of the couples and their growth to observable thicknesses. These simple time-temperature criteria are at times difficult to satisfy, and it is the purpose of this note to point out a situation in which this is the case. The authors are currently studying diffusion bonding in the Al-Ni system." It is well established

Jan 1, 1958

By E. J. Dulis, G. V. Smith

AS reported several years ago,' nitrogen may be taken up from the atmosphere by austenitic Cr-Ni steels during creep or creep-rupture tests. This was indicated by chemical analysis and by the appearance of a new microstructural phase, or phases, tentatively identified as chromium nitride (S), at the surface or at the intergranular cracks associated with fracture. The nitrogen pickup was observed to be dependent on time, temperature, and deformation. In a more recent investigation, a sample was obtained in which there was sufficient of the precipitate to suggest that it could be readily identified by X-ray diffraction. This sample had been taken from a 1/4 in. diam creep-rupture specimen of annealed, type 304L stainless steel of the following initial composition: C, 0.03 pct; Mn, 0.65; P, 0.010; S, 0.019; Si, 0.54; Cr, 19.50; Ni, 12.02; N, 0.031; and Al, 0.005. The specimen had ruptured after 10,470 hr at 1500°F (2000 psi). In this case nitrides were distributed across the whole section of the sample, Fig. 1. The precipitate occurred both at the grain boundaries and within the grains; the latter precipitate had in some cases the appearance of pearl-ite, and in others was distinctly Widmanstatten. Chemical analysis of the sample after test showed 0.64 pct "soluble" nitrogen (soluble in 1:1 hydrochloric acid: water) and 0.18 pct "insoluble7' nitrogen (insoluble in the hydrochloric acid solution but dissolved by fuming sulphuric acid). For identification of the precipitate by X-ray diffraction, the matrix in the surface layer of the specimen was dissolved by prolonged attack in an alcoholic solution of picric and hydrochloric acids. The appearance of the specimen surface after such etching is shown in Fig. 1c. The diffraction pattern of the surface-concentrated precipitate was obtained with a recording spectrometer in both the forward and back-reflection regions (the latter by adapting a special fixture to the conventional X-ray unit). The observed X-ray diffraction lines, Table I, show the presence of Cr,N and CrN; the agreement with interplanar spacings calculated from reported data2,3 is quite good. Since it has been suggested' that CrN dissolves only in concentrated sulphuric acid, whereas Cr2N dissolves in dilute hydrochloric or sulphuric acids, an effort was made to distinguish between the two nitrides. This proved possible, inasmuch as etching in a dilute solution of hydrochloric acid gave a sample in which microscopic examination showed that much of the Widmanstatten-pearlitic precipitate within the grains had been eaten out, leaving the grain boundary precipitate in relief, and which, when examined by X-ray diffrac-

Jan 1, 1953

By J. S. Kasper, R. M. Waterstrat, B. F. Decker

THE existence of v phase in the Mn-Mo system was discovered in this laboratory several years ago,' but neither the conditions of its formation nor its composition were known, and preliminary attempts to reproduce the phase were unsuccessful. We wish now to specify the information appropriate to phase formation on the basis of experiments performed since that time. The starting materials were in every case electrolytic manganese and high purity molybdenum. Two methods of preparation were employed: l—arc-melting varying combinations of the elements in an inert atmosphere and subsequent heat treating, and 2—sintering compressed mixtures of finely divided powders of the elements. In the latter method, the powders were first passed through 200 mesh screen and then compressed into cylinders of % in. diameter and % in. length, which were sintered at elevated temperatures in an atmosphere of dry hydrogen. For some samples, the sintering temperature was 1200°C (for 1 hr), and these were then heat- treated at lower temperatures for times up to 24 hr. Eventually it was found, for the proper composition, that essentially pure a phase could be produced by sintering at 1125°C for 3 hr. Quenching to room temperature was effected by means of a stream of cold, dry hydrogen in a water-cooled chamber. The arc-melting procedure was found to be unsatisfactory after an investigation of many samples at different compositions and temperatures. Large quantities of manganese were vaporized during melting and none of the products were homogeneous or contained extended regions of pure phase. Nonetheless, these experiments established that no formation occurs in the Mn-Mo system below 1115oC, and indicated, at least roughly, the composition range of interest for further exploration. The more definite results obtained from samples produced by the second method are given in Table I. A portion of sample 2 heated for 16 hr at 1000°C in a Vycor tube transformed to molybdenum plus unidentified phases of complex X-ray pattern. From these few results it appears that the region of phase is quite narrow in composition. It is of interest that the composition is such as to make for difficulties in correlating this structure on an electron atom basis with other a structures of iron, cobalt, and nickel. In that respect Mn-Mo shows the same anomaly as Mn-Cr and Mn-V systems.' A second feature is that in common with the two other known molybdenum (Fe-Mo and Co-Mo), Mn-Mo v exists only at elevated temperatures. The X-ray powder pattern of the pure a phase of Mn-Mo is given in Table 11. It agrees well with the patterns established for other structures, especially with that for Fe-Mo as given by Goldschmidt.An attempt is being made to establish whether an ordering of the respective atoms occurs and such information will be reported in a future publication. Acknowledgment The authors acknowledge gratefully the assistance of Mrs. J. R. Belanger in some portions of this work. References 'J. S. Kasper, B. F. Decker, and J. R. Belanger: Journal of Applied Physics (1951) 22, p. 361. 2 A. H. Sully: Journal Inst. Metals (1951) 80, p. 173. H. J. Goldschmidt: Research (1949) 2, p. 343.

Jan 1, 1954

By Carl A. Zapffee

FOR a number of years a puzzling phenomenon of brittleness in Class II ferritic stainless steels, developing in the temperature range near 475C, has received increasing attention, but its nature remains essentially unknown. During an investigation of the fractographic structures in stainless steels, conducted in the author's laboratory the past several years, principally under sponsorship of the Office of Naval Research, some observations of a new kind were found for "475 °C embrittlement." While the details of the study cannot be given here,' three fractographs will suffice to carry the

Jan 1, 1952

By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958

By S. R. B. Cooke, C. E. Thurston, G. Kudo

The trend toward utilization of low grade iron ores means that more efficient methods must be developed for their concentration. The collecting ability of fatty acids derived from fish oils has been extensively investigated by Cooke.' Tuna oil, a byproduct of the tuna canning industry, is one of the lower priced fish oils. Utilization of tuna oil fatty acids as collectors in the flotation of iron ore might be economically feasible under certain market conditions, especially if their efficiency were high. Crude or unfractionated tuna oil fatty acids, and five fractions derived therefrom, were tested for their ability to concentrate a commercial specularite ore from northern Michigan. A commercial fatty acid derived from tall oil, and commonly used in nonsulfide flotation, was used as a reference. The crude fatty acids were obtained by simple saponification of tuna oil. Fractions A and B were obtained by acetone precipitation of the crude acids at -5O and -2S°C, respectively. Fraction C was obtained by a partial fractional distillation at 12S°C and at a pressure of 3y in a centrifugal molecular still in order to remove the shortest and longest chain fatty acids of tuna oil as well as oxidation products present in the original mixture. Fractions D and E were prepared by a chilling process in order to precipitate the unwanted saturated fatty acids. Yields and iodine values of the materials used are listed below: The seven samples were used as collectors in a laboratory procedure patterned after the commercial process for flotation of Michigan specularite ore. The outline of the procedure is that previously described1

Jan 1, 1962

By C. W. Schultz, R. B. Tippin

Statistical screening is so named because a particulate feed is separated into "size" intervals on the basis of the probabalistic behavior of the individual particles (i.e., their probability of passing the screen) rather than by physical restraint. To illustrate this statement, consider a conventional screening operation. A particle which is larger than the openings in the screen cloth is physically restrained from passing through and is repeatedly reflected from the surface until it is discharged as oversize. Of those particles smaller than the screen openings, the very smallest tend to pass the screen near the feed end while those nearer in size to the screen opening tend to pass at a greater distance from the feed end. Alternatively, we could say that the particles with high probability of passing through the screen are concentrated near the feed end while particles of low probability of passing are dispersed from the feed end. This tendency to segregate is the basis for size separation by statistical screening. The purpose of this note is to: 1) Show that the distribution of material passing an array of screens can be described by a modified binomial distribution. 2) Demonstrate that an efficient size separation can be made by this technique. 3) Relate some of the more important screening parameters to the efficiency of the size separation. The Distribution Function The distribution of undersize products along the length of a screen can be derived with the help of a few simple definitions and assumptions. 1) First, we must assume that each particle has some probability of passing a screen on a single presentation. Further, we must assume that this probability is constant and is not affected by the position of the particle on the screen. It must also be acknowledged that several factors enter into this probability. Among them are the "action" of the screen, the slope of the deck, the shape of the openings, etc. The relationship between these factors, however. is not the subject of this paper. 2) To simplify calculations, all particles falling within a size range on the Tyler scale, e.g., —x + x/ mm, are assumed to have the same probability. 3) It is assumed that particles which do not pass the screen on a presentation are reflected a unit distance forward, i.e., the direction of material travel. A unit distance is defined as the distance between the centers of consecutive wires in the screen cloth.

Jan 1, 1971

By W. Vickers

SALKOVITZ1 has given a number of useful angles between planes for use with the Laue method in determining the orientation of bismuth single crystals. Bismuth is usually considered as having a face-centered-rhombohedra1 structure with its axial angle 87°34', Fig. 1. A similar figure given by Sal-kovitz appears to be in error in that the angle there marked as 87°34' should be 92°26. The primitive cell is a single rhombohedron of axial angle 570 14. The structure is almost face-centered-cubic and hence high accuracy in measurements is essential if there is to be no confusion in indexing poles or zone axes. It is easier to get this accuracy if zone axes are plotted on the stereogram because they will lie near the basic circle where the net has a more open scale. The zone axes can be read from the film, using a Greninger chart, and can be plotted more accurately than poles. Also, the angles between points near the basic circle can be read more accurately than those between poles near the center. In order to use the zone axes the angles between directions have been calculated from a formula given by Niggli,2 and are given in Table I. Miller indices

Jan 1, 1958

By W. J. West, T. D. Mueller, J. E. Warren

The authors have presented valuable information on the influence of the interfacial tension and the contact angle on the recovery efficiency of the waterdrive process. It is considered, however, that the following points deserve a closer examination. 1. As pointed out by Wyllie and Spangler1 the displacement pressure PD i.e. the pressure required to initiate the displacement of the wetting phase from the core, is a measure of the maximum pore diameter dmax. If the capillary pressure Pe as a function of the wetting

Jan 1, 1956

By J. T. Richards

ELASTIC constants, including E-modulus, G-modulus, Poisson's ratio, and compressibility, are affected by temperature, but not necessarily to the same degree nor in the same direction. Theoretical expressions relating the temperature coefficients for the various elastic constants have been introduced by Gruneisen. In considering the thermoelastic characteristics

Jan 1, 1955

By Paul F. Fulton, Robert K. Estes

INTRODUCTION Relative permeabilities are factual data necessary to any prediction of reservoir production behavior. One important problem in determining relative permeabilities of porous media to gas is the effect of gas slippage on these determinations. Since certain aspects of the slippage phenomenon still remain unknown, this study is particularly concerned with that problem. The validity of the theory of gas slippage as it is applied to the flow of gas through porous media has been well established. 1,2,3 Therefore, in determining the permeabilities of porous media to gas by ordinary laboratory procedure, i.e., at atmospheric pressure, the slippage correction should be considered. Rose3 performed experiments on gas relative permeabilities which indicated that the effect of gas slippage on the measured effective gas permeabilities at various liquid saturations decreased with an increase in liquid saturation. Following Rose, it was substantiated experimentally' that the effective gas permeabilities at the various liquid saturations extrapolated to infinite mean pressure were the same as the non-wetting liquid permeabilities at the same saturations. This same paper also presented data which showed that the magnitude of the slippage between those values of gas effective permeability determined at atmospheric pressure and those found by extrapolation to infinite mean pressure decreased with an increase in liquid saturation. However, these experiments were not performed at liquid saturations above 30 per cent. Therefore, the purpose of this experimental work was to determine the effect of gas slippage on permeability measurements at liquid saturations in excesh of 30 per cent. APPARATUS Five core samples were used In this work: two synthetic Alundum samples (A-1, and A-2). a Nichols Buff sandstone sample (NB-13), and two samples from producing formations, a Soso sandstone (S-1), and a vugu-lar dolomitic limestone (R-7). The core samples ranged in permeability from 32 to 663 md. These cores were chosen because they represented a fairly wide range of permeabilities and probably a considerable difference in pore size and pore size distribution. Fig. 1 is a schematic diagram of the apparatus which consists of an air dehydration filter A, two Moore null-matic sub-pressure regulators B and C, the differential oil manometer D, the core holder E, the flowmeter F, the soap reservoir G, and a mercury manometer H measuring the downstream pressure. The interesting features of the apparatus are the two Moore vacuum-pressure regulators. The regulators permit the rapid establishment and easy control during flow at sub-atmospheric pressures of both the differential and downstream pressures, and prevent the surging action of the vacuum pump from disturbing the system during flow. Provided there are no leaks in the system, these regulators will maintain without measurable change selected downstream and differential pressure. Specifically, regulator B controls the downstream pressure and regulator C controls the differential pressure. In opera-

Jan 1, 1957

By W. E. Hall

The Darwin mining district of California, 160 miles north of Los Angeles, has yielded an estimated $45 million in lead, silver, zinc, and copper since 1875. The deposits are in silicated limestone of Penn-sylvanian and Permian age close to a stock of horn-blende-biotite-quartz monzonite. Steep left-lateral strike-slip faults that strike N 50o 70o E served as feeder channels for the ore solutions, and minor folds, favorable beds, and faults close to the feeder channels localized the orebodies. The orebodies are irregular, steep, pipe-like replacements that cut across bedding, bedding replacements, and fissure fillings in a calc-silicate country rock consisting mainly of wollastonite, grossularite-andradite garnet, idocrase, and diop-side. Near surface the ore consists of a soft, crumbly mass of cerussite, hemimorphite, jarosite, limonite, and some secondary copper minerals. The primary ore consists of galena, sphalerite, pyrite, pyrrhotite, and chalcopyrite with smaller amounts of andorite, matildite, scheelite, tetrahedrite, and a high silver-lead-bismuth-selenium-bearing galena. Preliminary X-ray fluorescence study of the primary ore has indicated unusually high concentrations of bismuth, selenium, and silver in galena from certain parts of the mine. One phase of this study concerns the distribution of these elements. Twenty-two samples of galena and thirty of sphal- erite have been purified and analyzed or are being analyzed. The selenium in 21 samples of galena ranges from 0.0045 to 2.11 pct; four contain more than 1 pct. These four samples were collected from the Essex orebody, where most of the selenium is concentrated. Three are from high-grade, near-surface ore, and one is from the 700 level. Four of the seven analyzed galena samples from the Thompson workings immediately north of the Essex orebody contain 0.29 to 0.74 pct Se; the others show less than 0.05 pct. Galena from the Defiance workings about 2000 ft south of the Essex has less than 0.03 pct Se. The selenium-bearing galena also contains concentrations of bismuth and silver. Preliminary spectographic analyses indicate as much as 3 pct Bi and more than 1 pct Ag in galena with high selenium content. Antimony is the only other minor element present in galena in amounts greater than 0.02 pct; most galena contains between 0.1 and 0.2 pct and the maximum is 0.72 pct. A second phase of the study is an attempt to determine the temperature range of the formation of the ore. The iron content of sphalerite deposited in equilibrium with pyrrhotite is being used as a geologic thermometer as it is a function of the temperature of deposition of the ore.' Preliminary results indicate temperature range from 430°C in replacement orebodies in the Defiance workings to 180°C in shallow fissure fillings.

Jan 1, 1960

By George F. Sowers

THE geophysical methods of exploration employed so extensively in mining and petroleum investigations are now being used in civil engineering. Requirements differ from those of mineral ex- ploration and therefore modified techniques have been developed. The civil engineer is primarily interested in the uppermost soil and rock strata. In highway engineering the materials affecting design and construction may be found within 15 or 20 ft of ground surface, and data on soils and rocks is seldom needed for more than a depth of 100 ft even for the heaviest structures.

Jan 1, 1954

By Harry Udin

IN 1948, the writer and his associates determined the surface tension of solid copper by balancing the force of surface tension in a very fine wire against an external load.' At that time we, in common with other early workers, assumed that grain boundary energy in a pure metal is very small in comparison to the energy of an external surface. Accordingly, we neglected the internal surface energy of the coarse-grained specimens. Since that time, experimental evidence has accumulated showing that grain boundary energy, far from being small, is generally about one-third of the energy of an external surface.2-4 This is sufficient to introduce a significant error into our determination. The differential equation governing equilibrium is: wdl - yds, + y*ds2 [I] rather than wdl = yds as originally written. w is the balancing force in dynes, 1 the length of the specimen, sl the external and s2, the internal surface area, y the copper/ copper vapor surface tension, and y* the grain boundary tension. Fortunately, we had made for another purpose a careful study of the size and shape of the grains, and found that the boundaries, with rare exceptions, traversed the specimens and were perpendicular to the wire axis. For this case, eq 1 leads to w = rry -(n) r2y* [2] where r is the wire radius and (n is the number of grains per unit length. A count of some twenty 5-mil wires indicated that - n became 80 & 10 after a short anneal near the melting point, and remained nearly constant for as long as 96 hr at temperature. An assumption of y* = 1/3y leads to a defining eauation for r: [31 The term in the brackets may be considered a correction factor applied to eq 11 of ref. 1. Upon applying this factor, the surface tension of solid copper at its melting point is found to be 1650 & 100 dynes per cm, rather than 1370 as previously reported.' The new temperature coefficient is —0.55 dynes per cm per "C. Grain boundary energy is more significant than surface energy to the physical metallurgist. It is evident from eq 2 that a series of experiments with wires of different grain size can lead to an evaluation of y*. The details of such an experiment are being worked out now. References 1 H. Udin, A. J. Shaler, and J. Wulff: The Surface Tension of Solid Copper. Trans. AIME, 185, 186-190; Journal of Metals (Feb. 1949) TP 25303. 2 G. L. C. Bailey and H. C. Watkins: Surface Energies in the System Solid Copper-Molten Lead. Proceedings Physical Society. (London) (1950) 36B, 350. 3 L. H. VanVlack: Inter granular Energy of Iron and Some Iron Alloys. Ph.D. Dissertation, Univ. of Chicago, Sept. 1950. 4 . P. Greenough: Grain Boundary Energies in Silver. R.A.E. Report, No. Met. 52. (May 1950) Fan-borough, Hants, England.

Jan 1, 1952