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UP TO and including 1931, the twelve mines that were treated in THE PORPHYRY COPPERS had produced 17.4 billion pounds of copper worth $2,820,000,000. With a little help from six others (three of them did not start output until 1954) that record had been increased at the end of 1955 to 60.5 billion pounds worth $10,440,000,000. Today, ten billion dollars is not as impressive as it once was; but it still represents a lot of value. It must be remembered that this is newly-created wealth, produced entirely from material considered worthless when the Porphyry era started about fifty years ago. At that time "rock" that contained less than forty pounds of copper per ton was regarded by competent mining engineers as value- less. It was not "ore" in the economic sense. Today, ore is being successfully exploited that contains less than twelve pounds of copper per ton. Also, in Peru, a typical Porphyry operation is being launched by a partnership of four United States mining companies that will involve an initial capital investment of $200,000,000 for mine development, plant construction, and the provision of related facilities. Of this project more will be said at the end of the chapter. The point I want to make now is twofold: (1) that phenomenal progress has been made in Porphyry engineering and technology; and (2) that exploitation of an important Porphyry copper deposit has become an industrial enterprise of truly great magnitude. Much had been accomplished by 1931; but that progress has been dwarfed by the achievements of the past 25 years- a fact that, in the nature of things, is as it should be.

Jan 1, 1957

By Nicholas J. Grant, Chih-Chung Wang

TO phase of the Ti-0 system has the structure of NaCl and has a wide range of solid solubility.' In the course of studying the Ti-Cr-0 ternary system, binary alloys were made of iodide titanium and high purity TiO,. It was found from X-ray studies of the binary alloys that a transformation of the TiO appears to take place at a temperature near 925°C. Evidence of this phase change is best seen in Fig. 1. Fig. 1A shows the X-ray spectrometer pattern (CUKa radiation) of an alloy of 25 wt pct 0 corresponding to the stoichiometric composition of TiO.

Jan 1, 1957

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat's' The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K'(tn), related by K(m) = K'(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K'(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K' (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K' (m)] is a streamline of value $[K(m), K' (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K' (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

By R. J. McNally

THERE are three primary plant nutrients—nitrogen, phosphorus, and potassium—expressed in any fertilizer compound as percent N, percent P 2 O 5, and percent K 2 O, in that order. This article will be concerned with the first two. The chief source of P 2 O 5 is phosphate rock. As found in the western states phosphate rock is essentially tricalcium phosphate-calcium fluoride (fluor-patite). As such, it is quite water insoluble.

Jan 1, 1957

By S. M. Brisbane

THE life of refractory linings in rotary cement kilns can be shortened by uneven or inadequate support of the kiln and its shell and by variations in the conditions of operation. Alteration of these factors may, according to their nature, bring about mechanical deterioration of the lining or promote chemical attack. Chemical attack has been described elsewhere.1-4 The distortion of cement kilns has been discussed in a general manner by Rochow,6 ho indicates the amount of distortion which may occur in an unlined shell, and by Rosenblad: who states that the deformations of the shell are greatest above the trunnions. The present article indicates the extent of the distortion of a kiln to an oval shape in certain selected positions and the deviation from a straight line of the kiln along its length between two supports. The cement kiln is a long, hollow, rotating cylinder consisting of steel plates which may be either welded or riveted together. This shell is supported on tires, frequently 60 ft apart, which roll on trunnions. The large mass of the kiln causes distortion of its cross-section; it becomes slightly oval, i.e., diameters lengthen as they become horizontal and shorten as they become vertical. There is also a tendency for the shell to bow between supporting tires; this bowing may be upwards or downwards depending on the position of the weight forces and the supports. The extent of the deviations from the ideal kiln shape was investigated. Observations described in this paper were made on the shell of the clinkering zone between the first and second tires of two of the kilns at the Geelong works of Australian Portland Cement Pty. Ltd. The kilns were both 400 ft long and 10 ft diam with a welded enlarged burning zone 11 ft 6 in. diam. The shell was fabricated from mild steel and in this section its thickness was 1 in. It was lined with 41/2 in. of chemically bonded magnesite-chrome bricks which were jointed with mild steel plates. The kilns operate on a 4 pct slope and the speed may be varied between 0.75 and 1.68 rpm. The wet process is used; kilns are coal fired and are fitted with integral coolers. Temperatures within the kiln are difficult to determine with any accuracy because of the absence of black body conditions, but surface temperatures are probably in the range 1420° to 1470°C. Average shell .temperatures at the two positions at which the deformation studies were made were 370°C and 355"C respectively. Methods: In determining the ellipticity it was necessary to measure the lengths of the vertical and horizontal diameters while the kiln was in operation; data obtained from a stationary kiln would not have the same practical significance. For this purpose the four points V, W, X, and Y at the ends of two mutually perpendicular diameters were marked on one kiln. The point X is shown in Fig. 1. For the measurement of the length of the vertical diameter a vertical column, to which a horizontally aligned telescope was attached, was placed 10 ft from the kiln. The telescope could be racked up and down in a vertical plane. Two sets of readings were taken, one set when each of the points V, W, X, and Y was at its maximum height above the

Jan 1, 1957

By T. M. Morris, W. E. Horst

W. E. Horst—In regard to the flotation rate being described as "first orcler" for flotation of quartz particles below 65 p in size (or any size studied in this work) in this paper, it appears that the authors' conception of rate equations is not in agreement with cited references. A first order rate equation has as one of its forms the following: a In.=a/a-x=kt where a = initial concentration, a—x = concentration at time t, t = time, and k = constant. The constant, k, has the dimension of reciprocal time which is similar to the specific flotation rate, Q. described by Eq. 2 in the authors' article, as has been previously discussed by Schumann (Ref. 1 of original article). The plotted data presented in Fig. 4 of the article utilizes the specific flotation rate, Q (min.'); however, there is not adequate data given to indicate the order of the rate equation which describes the flotation behavior of the quartz system studied. Results from the experimental work indicate that the relationship between rate of flotation (grams per minute) and cell concentration (provided the percent solids in the flotation cell is less than 5.2 pct and the particle size is less than 65 p) is described by an equation of the first order (R, = k c+", n being equal to 1 in this size range) and the use of the first order rate equation does not apply. Similarly the relationship for other particle size ranges studied is expressed by equations of the second or third order depending on the magnitude of n. T. M. Morris—The authors are to be commended for the experiments which they performed. As they state in their discussion the concentration of collector ion In solution did change with change in concentration of solids in the flotation cell. Since for a given slze of particle, flotation rate increases with concentration of collector until a maximum is reached, the effect of concentration of particles in their experiments was to vary the concentration of collector ions. A collector concentration which insures maximum supporting angle for all particles eliminates the unequal effect of collector concentration on various sized particles and the effect of size of particles and concentration of particles upon flotation rate could be more clearly assessed. I believe that if the authors had increased the concentration of collector to an amount sufficient to attain a maximum supporting angle for all particles they would find that the specific flotation rate of particles coarser than 65 p would be constant with change in the concentration of solids in the flotation cell, and that a first order rate would apply to the + 65 as well as to the —65 p sizes. It might also be discovered when this change in collector concentration was made that the maximum specific rate constant would be shifted toward a coarser fraction than when starvation quantities of collector are used since this practice favors the fine particles and penalizes the coarse particles. P. L. de Bruyn and H. J. Modi (authors' reply)—The authors wish to thank Professor Morris for his kind remarks and for mentioning the influence of equilibrium collector concentration on flotation rate. With a collector concentration sufficient to insure maximum supporting angle for all particles, a first order rate equation may indeed be found to be generally applicable irrespective of size. Such a concentration would, however, lead to 100 pct recovery of the fine particles and consequently defeat the essential objective of the investigation to derive the maximum information on flotation kinetics. To establish absolutely the validity of any single rate equation for a given size range, the ideal method would be to work with a feed consisting solely of particles of that size range. Use of such a closely sized feed would also eliminate the possibility of the interfering effect of different sizes upon one another. The authors do not believe that increasing the collector concentration would shift the maximum specific flotation rate (Q) towards a coarser fraction. Experimentation showed Q to be independent of solids concentration for all particles up to 65 µ in size, whereas the maximum value of Q was obtained in the range 37 to 10 p. Professor Morris contends that the addition of starvation quantities of collector favors fine particles at the expense of coarse particles, but the reason for this is not entirely clear to the authors. The comments by Mr. W. E. Horst are concerned only with the concept of the term "first order rate equation." According to the usage of this term in chemical kinetics, time is an important variable, as is shown in the equation quoted by Mr. Horst. All the experimental results reported by the authors were obtained under steady state continuous operations when the rate of flotation is independent of time. To be consistent with the common usage of the "first order rate equation," it would be more satisfactory to state that under certain conditions the experimental results show that the relation between flotation rate and pulp density is an equation of the first order.

Jan 1, 1957

By R. W. Cahn, C. D. Graham

The rate of growth of a single grain growing into a strained aluminum single crystal, measured by the conventional heat-cool-etch technique, is shown to decrease with time at temperature. The growth rate measured by means of X-rays, with the sample continuously at temperature, is found to be linear. Evidence is presented to show that the decreasing growth rate obtained by the conventional technique is due to abnormal recovery in the strained grain, and that the recovery in turn results from the heating and cooling cycles, rather than from the effects of etching. The experimental apparatus is described in an appendix. FREQUENTLY, the rate of grain boundary motion during recrystallization is determined by heating a sample to a known temperature for a given time, cooling to room temperature, and etching to reveal the boundary position. The cycle of operations is repeated as many times as necessary to establish the rate of boundary motion. Although this heat-cool-etch technique has been used by a number of workers over a period of many years,'-!' other investigators have encountered difficulty with the method."'. " They have attributed the erratic results to the effects of repeated heating and cooling, or of etching, or both, and have adopted an alternative experimental procedure in which a number of identical samples are employed, each sample being cooled and etched only once. This alternative method ove1.comes some difficulties, but introduces others. In particular, the incubation periods of the observed grains are unknown: any effect of crystal orientation on growth rate cannot be determined easily. A preferable method would be to measure the motion of a recrystallizing grain boundary with the sample at temperature without etching," but such measurements have in the past been restricted to nonmetals. This paper describes the construction and operation of a device, the goniometer furnace, with which the position of a moving grain boundary between a recrystallizing grain and the strained single crystal into which it grows can be measured by means of X-rays, with the sample maintained continuously at temperature. Goniometer Furnace The operating principle of the goniometer furnace is shown in Fig. 1. The sample, in the form of a bicrystal strip, is surrounded by a furnace, not shown in the sketch, and can be rotated about the two axes A and B which intersect at the point where the X-ray beam strikes the strip. The strip is oriented so that one of the two grains gives a strong Bragg reflection, which is detected by a suitably placed Geiger-Miiller counter coupled to a counting-rate meter When the strip is moved parallel to its own length in the furnace, arrow C, so that the X-ray beam strikes the second grain, there is in general no strong reflection. By noting the position of the strip at which the drop in Geiger counter reading occurs, it is possible to determine the position of the boundary. Measuring the change in boundary position with time at temperature gives the rate of growth of the recrystallizing grain. Details of the construction and operation of the goniometer furnace are given in the Appendix. Measurements showed that the temperature in the furnace was uniform within ±10°C over its working length of about 28 cm. The temperature at the measuring position, i.e., at the point where the X-ray beam struck the sample, was estimated to be constant within ±2oC. Using the goniometer furnace, the position of a stationary boundary could be measured with a reproducibility of ±0.3 mm. At elevated temperatures, 500" to 625"C, with the boundary in motion and the X-ray reflection less sharp, the estimated accuracy of each measured boundary position dropped to about ±1 mm. Experimental Results The test pieces were single crystals of 99.6 pet A1 —principal impurities 0.19 pet Fe and 0.12 pet Si— 1 mm by 1 cm in cross section and 6 to 10 cm in length, grown by the strain-anneal method. This relatively low purity material was used because of the difficulty encountered in producing strain-anneal single crystals of very high purity—99.996 pet—

Jan 1, 1957

By J. M. Schopt

COAL petrology is the study of the lithologic composition and texture of coal and includes megascopic as well as microscopic differentiation. Coal petrography is a quantitative study, principally (but not exclusively) microscopical in nature. The distinction between coal petrologic and coal petro-graphic studies usually is not important, but it is important to recognize that these studies differ materially from other types of petrology that deal primarily with minerals. The petrologic entities* of coal are less clearly distinguished than most minerals and the basis of distinction is not always clearly expressed. The relation of coal petrology to geologic, mining, and technologic problems is most evident when results of coal petrologic studies can be stated quantitatively. The chemical and physical composition of coal and the determination of its quality and properties are continuing problems. The source of these problems lies in the heterogeneity of coal and in its almost complete insolubility in ordinary solvents at normal temperatures. The empirical and comparative character of standard chemical coal analytic values is one of the consequences resulting from heterogeneity and insolubility of coal. Nevertheless, these coal analytic methods are highly technical and diversified. Coal petrol.ogy employs a group of similar analytical methods which provide information about coal that the other methods cannot supply. The heterogeneity of coal is most clearly demonstrated by means of petrologic studies. The properties utilized in coal petrologic studies are related to texture (size, form, and association), hardness, light reflectance, and light absorption and transmission (color). Size relations are most evident but are commonly overlooked. Coal is classed chemically as a mixture, and chemical analyses thus show the composition of the sample as a whole. Geologically coal is an organic clastic deposit, derived from diverse plant fragments and particles having a size range comparable to that of a conglomerate or breccia. The mixture of different materials that compose coal, large and small, can be realized only by microscopic study. This is because the fundamental cellular units of plants, from which coal is formed, are microscopic in size. The kinds of altered plant particles and fragments in coal have specific differences in hardness, reflectance, and color that signify differences in composition. These differences must be taken into account in evaluating the aggregate properties of coal. Terminology and Texture Full discussion of terms applied by various petro-logists in analysis of coal is beyond the scope of this article. For convenience the simpler types of petrologic entities that are defined without reference to lithologic occurrence or texture will be called coal components. Fig. 1 lists reactive and relatively inert

Jan 1, 1957

By Y. C. Liu

Both the habit plane of martensite and the orientation relationship between the matrix and martensite platelets of different habit planes have been investigated in binary titanium alloys with molybdenum, chromium, and iron. The effect of the mode of deformation on the martensite habit plane was studied. A micrograph of an exposed mar-tensite platelet is presented. IN the study of martensitic transformation in Ti-Mn alloys,' two martensite habit planes—{334), and {344)8—were reported. The {334), habit was also observed in unalloyed titanium upon transformation,' although there is disagreement with respect to the exact indices. The other habit plane, {344),, has not been reported in martensitic transformation in any other alloys. The present investigation was made to determine whether other binary titanium alloys with P-stabil-izing elements would exhibit a crystallography of transformation similar to that of Ti-Mn alloys. Furthermore, since martensite platelets can be induced by deformation under certain conditions, it was of interest to investigate whether the mode of deformation, compressive or tensile, would influence the formation of martensite platelets on a specific plane in an alloy system which possesses two martensite habit planes. Experimental Procedure The material used for the preparation of the binary alloys of iodide titanium with molybdenum, chromium, and iron had the following purities: 99.99 pct iodide titanium, 99.9 pct molybdenum, 99.423 pct chromium, and 99.9 pct iron. The compositions of alloys listed in this paper are in nominal weight percentage. All specimens used were prepared and treated according to the procedure described in reference 1, unless stated. For the subzero temperature treat,ment the following experimental schedule was followed. After specimens had undergone the grain-growth treatment, they were quenched into an ice-water bath and were then metallographically examined. In specimens of higher alloy content, no martensitic transformation was observed. In those in which mar-tensitic transformation did occur, only specimens in which the martensite platelets existed as fine needles in localized regions were used. All specimens were reannealed 17 hr at 1200°C, quenched into ice water. and the capsule was broken. They were held in the ice water for from 5 to 10 sec, then transferred to a liquid-argon bath. This stepped quenching procedure was found to be more efficient than direct quenching into liquid argon. In the latter case, as soon as the hot specimen was immersed in the liquid argon, a protective, insulating layer of argon gas formed, and the specimen continued to glow vividly in the bath for some time. In the study of the habit behavior of martensite produced by deformation, specimens were deformed at room temperature either by compression, tension, or rolling. Martensite habit planes were determined by the two-surface analysis procedure described in reference 1. A stereographic net of 153/4 in. diam was used throughout the investigation. The method for determining the orlentation relationship between martensite and the matrix follows that used by Greninger and Troiano.' A diamond-polishing table with its auxiliaries was used in order

Jan 1, 1957

By R. E. Hoffman, R. A. Ward

The self-diffusion coefficient in high purity nickel has been measured over the temperature range 870' to 1248°C. The results are described by the relation D = 1.27 exp[—-66,800/RT 1cm2ec-1. The measured activation energy correlates satisfactorily with absolute melting point, heat of fusion, and heat of sublimation. KNOWING the rates of self-diffusion is important in the understanding of many metallurgical reactions. However, in spite of the rather widespread interest in nickel, both commercially and in fundamental investigations, no measurement of the self-diffusion in solid nickel has previously been re- ported." In connection with a program of measuring rates of diffusion in some nickel alloys, self-diffusion in pure nickel has been investigated over a rather wide temperature range by combining a sectioning technique and a surface counting technique.

Jan 1, 1957

By R. H. Raring, F. E. Martin

A high speed gas quenching dilatometer useful in studying phase transformations in low alloy steels is described. Changes in specimen length are measured by means of an electrical micrometer tube. The maximum instantaneous cooling rate is approximately 5000°F per sec; the maximum average cooling rate from 1650' to 950°F is approximately 2900°F per sec. Data for steels of 0.11 pct and 0.67 pct C content are included. KNOWLEDGE of phase transformations as they occur in an alloy under conditions of continuous cooling affords valuable insight into its properties. The transformation characteristics during continuous cooling of steels of high hardenability, which decompose entirely to martensite at fairly slow cool-

Jan 1, 1957

By T. M. Geffen, F. F. Craig

Laboratory model flow tests have been made to simulate field conditions of partial pressure rnaintenance by dispersed gas drive on rocks having sandstone-type porosity. In this production method there is a significant saturation gradient between injection and production wells. A means of calculating relative permeability characteristics. from partial pressure rnaintenance flow tests has been developed. This method takes into account the saturation gradient. These kg/ko characteristics are identical to those for solution and external gas drives. This method of calculation, which has been proved experimentally, has limitations; however, it is valid for cases likely to be encountered in field prediction of partial pressure maintenance performance. The production performance of a hypothetical reservoir has been calculated for several different injection programs, involving both full and partial pressure maintenance. Results indicate that the maxinum oil recovery by these gas injection programs is obtained by full pressure mainte- nance at the original bubble point. Correspondingly lower oil recoveries are obtained by postponing gas injection and/or by reducing the degree of pressure maintenance. INTRODUCTION Dispersed gas injection is an important method of recovering additional oil beyond that obtainable by pressure depletion alone. The injected gas acts as a source of additional energy to displace oil from the rock formation as well as to retard oil shrinkage in the reservoir. In practice, gas injection is usually started after the reservoir pressure has fallen below the original bubble point. For various reasons sufficient gas is generally not injected to completely maintain the pressure in the reservoir. So, injecting gas at a declining reservoir pressure results in a combined external and solution gas drive. These two oil displacement processes are characterized by different gross saturation distributions in the reservoir. The external gas drive, like all frontal drive processes, inherently results in an oil saturation which increases from the injection wells to the producing wells. In the solution gas drive there is essentially a uniform oil saturation throughout the reservoir, provided the field is being depleted uniformly. It has been customary to predict oil recovery performance under partial pressure maintenance by a method which does not take into account the saturation gradient1. It has been shown2 that neglecting the presence of a saturation gradient can cause considerable error. It is the purpose of this paper to develop and present an improved method of predicting partial pressure maintenance performance of reservoirs including, where necessary. the effects of well arrangement. From the laboratory standpoint, this problem involves the measurement of the basic flow behavior (relative permeability characteristics) under partial pressure maintenance conditions. Recent research- as shown that for rocks having sandstone-type porosity, the relative permeability characteristics are identical for solution gas drive and complete pressure maintenance external gas drives. Since both solution and external drives have the same basic flow behavior, it was speculated that partial pressure maintenance, being a combination of the two, would also

Jan 1, 1957

By H. Papazian, Robert A. Lad

SINCE it can be shown both theoretically'' : and experimentally that disordered Cu3Au has a greater internal energy than the ordered alloy, it might be expected that its chemical reactivity would be greater. Experiments were initiated' to test this hypothesis. This note will describe some recent results obtained in the study of the rates of corrosion of ordered and disordered polycrystalline Cu3Au by aqueous FeCl., The work of Robertson' has indicated that the attack by such solutions is intergran-ular and highly orientation dependent. It was of interest to see whether the order-disorder effect was great enough to overcome the variations from specimen to specimen which would arise from this type of attack. The polycrystalline alloy specimens (0.020 in. wire, 1¾ in. long) were preannealed in ½ atm H, at 700°C for 2 hr. The subsequent heat treatments to produce order and disorder were performed in M atm He. Disordered specimens were obtained by heating at 450°C for 2 hr and quenching in water. Ordered specimens were produced by heating for 2 hr at 450°, furnace cooling to 380°, and soaking at 380°C for 80 to 90 hr. Room temperature was reached by cooling to 150" at a rate never exceeding 7" per hr, and water quenching from 150°C. The specimens so produced exhibited electrical resistivities characteristic of the two states; of the order of 11.27x10 ohm-cm for the disordered, and 4.28x10 ohm-cm for the ordered specimens. The corrosion rates were studied at 30°C in ferric chloride solutions of several concentrations (?,¼, 1.5, and 1 molar). The specimens were attached to a stirrer during the tests. Tests were interrupted at intervals, and the specimen weight change was determined after washing and drying. Analysis of the solutions showed that the attack was limited to the copper. The higher corrosion rate for the disordered alloy, as illustrated in Fig. l, is typical of the results obtained. The effect of variation in ferric chloride concentrations is indicated in Table I for typical specimens. The variations in the ratio of reactivity for disordered and ordered specimens at the different concentrations are within experimental error, and the best value is estimated to be near 1.4. The experimental variation was due in part to the mode of attack, as mentioned, and in part to the fact that films were formed on the specimens under some conditions. Electron diffraction patterns of the films were very complex and indicated the presence of metallic iron, as did chemical analysis. In an attempt to eliminate the difficulties arising from the mechanism of attack, single crystal specimens were used. A greater reaction rate was again measured for the disordered specimens, but the reproduci-bility was no better than that for the polycrystalline metal. This would indicate that film formation was primarily responsible. It was concluded that the reaction with aqueous ferric chloride served to demonstrate that the reactivity of disordered Cu3Au is greater than that of the ordered alloy. However, the difficulties with film formation did not permit determinations of a precision great enough to warrant extension of the study to partially ordered alloy systems.

Jan 1, 1957

By N. Brown, M. Herman

ORDERING'S effect on the creep strength and other plastic properties of metals is unknown at the present time. Sachs and Weerts' attempted to compare the mechanical properties of the ordered and disordered state by comparing a quenched specimen with one annealed for a long time at a low temperature. This experiment is unsatisfactory because it introduces a possible effect from quenching. Barrett' used a hot impact test, but his method was not sufficiently sensitive to indicate any discontinuity in plastic behavior in the neighborhood of the critical temperature. On the theoretical side, Fisher9 as suggested that short range order would strengthen an alloy, but he gives no conclusions as to the effect of long range order. Cottrell" has discussed the interaction between long range order and dislocations, but does not indicate whether slip in a completely ordered alloy without domain boundaries is appreciably more difficult than slip in the disordered state. Because order exists in so many alloy systems, it is most important to prove experimentally whether long range order weakens or strengthens a metal. This investigation used -brass because: 1) it orders

Jan 1, 1957

By Walter J. Karplus

By means of a finite difference expansion a fluid flow field in cylindrical coordinates with axial symmetry, is simulated by a network of electrical resistors. A series of DC analog computing units, connected to the network bounrlary corresponding to the free surface effectively adjust the network parameterr to satisfy simultaneously Laplace's equation and the borrndary conditions. The system automatica1ly "re1axes" to the correct boundary shape in a fraction of a second. A detailed application of the method to the water coning problem in oil wells is presented. INTRODUCTION The water coning problem in petroleum production is a prime example of a class of problems known as free surface problems. A free surface arises in fluid flow regions when the shape of the boundary of a single phase flow region is affected in some manner by the pressure or potential gradients within the region. When there exists an interface of two fluids of different densities, the shape of this interface will be determined by the relative velocities of the two fluids and will therefore comprise a free surface. Other free surface problems of interest to petroleum engineers include the gas coning, water injection, and gravity drainage probIcms. In each case it is desired to predict the shape of the boundary of the oil zone as a function of the flow rate, the well penetration and the physical parameters and dimensions of the system. Such problems do not lend themselves to the classical analytical treatments of boundary value problems because in this case the boundary of the potential field and the potential distribution within the field are interdependent and must be calculated simultaneously. A further difficulty arises from geometric considerations. Since the fluid flow is of the radial type in most cases, such effective methods as conformal transformation and the hodograph are not applicable. It is the purpose of this paper to present a method whereby free surface problems of this type may be solved rapidly to the desired order of accuracy by means of a combination of a network of electrical resistors and conventional analog computer units. The water coning problem is treated in some detail. Then the procedure for extending the technique to other free surface problems is indicated. FORMULATION Most commercial oil reservoirs consist of an oil-saturated sand, bounded above by an impermeable strata and below by a water-saturated sand. Gravimetric separation results in a horizontal oil-water interface. When an oil well is drilled so that it partially penetrates the oil zone, and production is initiated at a constant rate, the oil-water interface will assume a new shape as a result of the pressure gradients in the oil zone. It should be emphasized that this is a steady phenomenon. After an initial transient period the water phase will be completely static and only the oil will be in motion. The new steady-state shape of the interface, as shown in Fig. 1, depends upon the depth of penetration, d, the thickness of the oil zone, I, the production rate, q, the hydraulic permeability zone of the sand, k, the viscosity of the oil, µ, and the densities of the oil and water, p.,. and pw.. The problem is to determine this relationship. Darcy's law + = - (P f g p z).....(1) it.

Jan 1, 1957

By M. C. Fuerstenau, D. W. Fuerstenau

Studies of the collection of alkali and ammonium halides utilizing vacuum flotation techniques and contact angle measurements show that ionic size controls the flotation of techniquesthese halides with amine salts measurementsas collector. Contact angles of air bubbles on sylvite in saturated brines were withaminemeasured salts asascollector.a function of such variables as collector addition, length of collector chain, and pH of the brine. No contact occurs between halite and an air bubble in brines containing dodecylammonium acetate as collector. LONG-CHAINED aliphatic amine salts have been used for the separation of sylvite (KCl) from halite (NaCl) by flotation.1,2 It is puzzling how these two minerals, which are so similar chemically and crystallographically, can be separated by this method. Gaudin" has postulated that the difference in floatability of halite and sylvite with salts of primary amines depends on ionic size: In the case of amine flotation, the cation would attach itself to the chloride. I have a speculation there, which I cannot prove, that the ammonium group, that is the —NH3 group in the amine, floats potassium chloride because the dimensions of this grour, as it has been measured in other compounds is almost identically the dimensions of the potassium ion, quite different from the sodium ion, and so it fits where potassium had been, in place of it and not attached to it. Apparently, because an aminium ion (RNH3+) is much larger than a sodium ion, it cannot fit into the lattice of halite. Taggart also has speculated that ionic size may control the floatability of sylvite.4 The object of this experimental investigation has been to test this hypothesis and to study what controls the adsorption of cationic collectors at the surface of sylvite. Since collection is to be approached from the viewpoint of ionic size, the ionic radii that are of interest in this work are presented in Table I. The values of the ionic radii of the ions listed in Table I, except NH4+, are those given by Pauling." Several different values for the radius of the ammonium ion have been given, but that of Goldschmidt6 seems to be preferred. The radius of the charged head of a dodecylammonium ion is assumed to be the same as that for the ammonium ion. Little experimental work has been reported in the technical literature concerning the separation of sylvite from halite by flotation. Guyer and Perren studied the separation by flotation of 50 pct binary mixtures of NaCl, KC1, NH,Cl, NaNO3, KNO3, K2SO4, and Na,SO, using either oleic acid or a sodium sul-fonate as collector.' It is possible to measure floatability under actual flotation conditions where all three phases, air- water-mineral, are present by vacuum flotation tests and contact angle measurements.9 Both of these techniques were used in the experimental approach in this paper. Experimental Method and Materials The vacuum flotation tests were run with glass-stoppered pyrex graduated cylinders. Twenty-five ml graduates were used to test the floatability of all salts studied except rubidium and cesium salts. For each test distilled water containing the desired collector concentration was saturated with the salt to be floated. Sufficient salt (—48 mesh) was added to leave about 2 ml of solids in the bottom of the graduate. After the graduate had been agitated several minutes to saturate the solution with air, a vacuum was applied. If the salt were floatable in the collector solution, the gas bubbles attached themselves to the particles, and the particles floated to the surface. In determining the floatability of the expensive Rb and Cs halides, the experiments were run in 10 ml graduates with about 11/2 ml of collector solution initially. Contact angles were measured in the usual manner except that the solutions had to be previously saturated with the mineral to avoid dissolution of the crystal. Solutions for studying contact angles were made by adding the desired amount of collector to a saturated brine, giving the collector concentration in molarity. The mixture was agitated until dissolution of the collector was complete, with the exception of those concentrations greater than about millimolar. At these high concentrations complete dissolution of the collector was impossible. The face of the mineral to be tested was a freshly cleaved crystal of halite or sylvite. The mineral was placed in the brine and conditioned with collector for at least 15 min, which was found to be long enough to obtain a maximum value for the contact angle. The temperature remained constant during each experiment. The experiments were run at 24°C ±2°C. For contact angle measurements, a crystal of halite from Carlsbad, N. M., was used. Several samples of sylvite were used in this work: a crystal of sylvite from Stassfurt, Germany; a crystal from Carlsbad, N. M.; and a crystal of chemically pure potassium chloride. Saturated brines were made from reagent grade chemicals and distilled water.

Jan 1, 1957

By J. Chipman, N. J. Grant, J. H. Walsh, T. B. King

WITH the development of adequate sampling and analysis techniques, much information has been obtained concerning the behavior of hydrogen in the steel bath during the course of steelmak-ing operations. From studies of this type it has become clear that the slag has an important role to play in determining the hydrogen content found in commercial products. A knowledge of the behavior of hydrogen in slags is necessary to round out our knowledge of hydrogen in steelmaking practice; with this information we are better able to assess practical methods of control. In this paper a method developed for analyzing slags for hydrogen content, studies of the solubility of hydrogen in synthetic slags, and studies of the variation of hydrogen content in slag and steel in industrial heats will be described. Previous Work—While very little has been done in the past to determine the hydrogen content of metallurgical slags, measurements have been made on such slag-like materials as geologic magmas and glasses. Goranson as made extensive studies of the solubility of water in natural and synthetic granites. Many workers have investigated the solubility of gases in synthetic and commercial glasses, but the recent work of Russell" is the most extensive. Russell found that the solubility of water in glass was proportional to the square root of the water vapor pressure in water vapor-oxygen mixtures. It was found that the solubility could either increase or decrease with temperature depending on the glass composition. Wentrup, Fucke, and Rief,' and Piper, Hagedorn, and Backes' have extracted hydrogen by holding a slag at 1300" and 800°C respectively in vacuum. Wentrup et al. reported hydrogen and water vapor as evolved together while Piper et al. passed the evolved gases from the hot extraction treatment over hot ferromanganese to reduce the evolved water vapor to hydrogen and, therefore, reported the analyses in terms of total dissolved hydrogen. Yavoiskii has reported hydrogen and nitrogen analyses on steelmaking slags. Dobrokhotov, Povol-skii, and Khan have studied the hydrogen content of basic open hearth steel under slags of varying viscosity. These authors reported that the hydrogen content of the steel bath increased as the fluidity of the slag was increased by the addition of bauxite. They recommended that a viscous slag be used and the steel tapped without deoxidation in the furnace to ensure a low final hydrogen content. Analysis of Slags for Hydrogen Development of Apparatus—The vacuum fusion analysis equipment described by Shields, Chipman, and Grant" was modified for the analysis of slags." This method depends upon the reduction of water in the slag to hydrogen, which is readily determined by the method used for hydrogen in steel. Preliminary experiments were made with a eu-tectic ferrosilicon melt as the reducing agent. Other experiments included the use of graphite and molybdenum crucibles. The ferrosilicon alloy bath was found to produce a thick coating on the furnace tube which could adsorb hydrogen. Graphite produced CO by the reduction of FeO, MnO, and SiO2 in such quantities that analysis for hydrogen was virtually impossible. Molybdenum, while giving a low blank value, could reduce the slag sufficiently to produce a volatile oxide which again was found to adsorb hydrogen. The arrangement finally adopted is shown in Fig. 1. The molybdenum sheet served as the induction-heated susceptor, and was separated from the escaping gases by alumina guide tubes. An outer jacket of alumina protected the quartz furnace tube, and alumina and quartz stools completed the assembly. The falling sample is shown wrapped in aluminum foil, 0.002 in. thickness, which acted as the reducing agent' This foil was careful'~ washed in acetone and an d and then dried in hot air before wrapping the weighed slag sample for charging into the apparatus. Investigation of the hydrogen content of the aluminum foil itself showed that a small quantity of hydrogen was released in vacuum, but had no relation to the weight of the aluminum charged. This quantity of hydrogen was

Jan 1, 1957

By Herty, C. H.

The effect of temperature on the physical properties of structural materials has been the subject of many investigations during the past decade. The literature on the effect of elevated temperatures. is voluminous, and during the last four years a great deal of experimental work has been carried out on the effect of low temperatures on the impact properties of steel. For many engineering purposes it is important to know the shock resistance of steels at low atmospheric temperatures, and with the ever-developing field of refrigeration and separation of materials at low temperatures, the normal limits of atmospheric temperature have been exceeded in practice. Iron and its alloys in the unnotched condition have a high impact strength at low temperatures, but in practice variations in type of notches result either from design or accidentally through scratches and surface or internal defects. A study of notched bar impact tests is, therefore, highly important to the engineer. A survey of the literature on low temperature impact testing indicates that chemical composition, heat treatment and method of testing have been the variables which have been considered in most previous work. In only a few instances has any mention of the steel- making method been mentioned and in these the comparison was between steel-making processes and not between steel-making methods on the same process. In view of the wide variations in impact properties at room temperature, in quench and strain ageing and in grain growth of steels of identical chemical composition, (by this is meant the usual five element analysis reported), it was felt

Jan 1, 1957

By M. T. Simnad, G. Derge, Ling Yang

STUDY of diffusion in molten substances is important in at least two respects. Diffusion data, combined with thermodynamic and kinetic information, throw light on the structure of the liquid state. Moreover, a knowledge of diffusion coefficients and their temperature dependence is useful in ascertaining the controlling step in many metallurgical reactions. Although diffusion measurements have been made on a number of molten salts, slags, metals, and alloys,'-'" the results available are still limited and widely scattered, especially for the high temperature melts. It is the purpose of this investigation to establish reliable procedures for the measurement of self-diffusion coefficients in high temperature melts and to use these procedures to determine the self-diffusion coefficients of iron in molten Fe-C alloys of different carbon contents. Experimental Measurement of self-diffusion coefficients in high temperature melts is usually carried out by using one of two methods. In the first, diffusion takes place between two cylindrical samples of the same material, one of which is made radioactive. The diffusion coefficient is calculated from the radioactivity penetration curve in the solidified sample after the diffusion. In the second method, samples contained in capillaries of an inert substance are immersed in an infinite reservoir of the same material. Either the material in the capillary or that in the reservoir is made radioactive and the diffusion coefficient is calculated from the change of the radioactivity of the sample in the capillary after the diffusion. The second method is simpler because a radioactivity penetration curve is not needed for the calculation of the diffusion coefficient; however,.it is valid only when no convection has occurred in the capillary during the diffusion. A radioactivity penetration curve is therefore always useful in indicating that the required conditions for the diffusion are ful- filled. Towers and Chipman" recently studied the self-diffusion of calcium and silicon in CaO-Al,O,-SiO, melts by using the capillary method. Instead of measuring the change of the radioactivity of the sample in the capillary, they autoradiographed the sample after the diffusion and calculated the diffusion coefficient from the intensity distribution of the autoradiograph. Their method is useful when the radioactive isotopes are weak ß-emitters, but is very difficult, if not impossible, to apply to cases involving strong ß or y-emitters. For such cases, sectioning of the sample according to the method of Morgan and Kitchener' may be used for the construction of the radioactivity penetration curve. The self-diffusion of iron in molten Fe-C alloys has been studied in this manner and the experimental procedures are described as follows: The diffusion apparatus is shown schematically in Fig. 1. The bath consisted of about 200 g of an Fe-C

Jan 1, 1957

Jan 1, 1957