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By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

By M. A. Schimmelpfennig, A. D. S. Gillies

Loss of visibility due to the occurrence of atmospheric fogging in underground mine airways can lead to longer travel times and loss of production efficiency, an increase in the frequency of vehicular and foot traffic accidents and difficulty in checking rock surfaces for instability and loose material. Where hot and humid surface air meets colder underground air, conditions for fog formation may be present. Further, suspended particulate matter from diesel exhausts or stoping operations together with slow movement of air along passageways may contribute to formation. This study describes an investigation being undertaken with the cooperation of Kennecott&apos;s Ozark Lead Co. to identify causes of the problem.

Jan 1, 1984

By ELLSIVOKTH DAGGETT

THE Berlin gold quartz mine is situated in Nye county, Nevada, on the west flank of the Shoshone range, about 40 miles south and 30 miles west from the town of Austin, the county-seat of Lander county. The distance from Austin is about 60 miles by stage-road. The outcrop of the vein, at the top of the incline-shaft, is situated just at the base of the mountain proper, almost exactly at the intersection of the mountain-side with the gravelly bench that slopes for about three-quarters of a mile to the flatter sage-brush plain, or desert valley, below. The -vein itself consists almost entirely of quartz, with perhaps 2 per cent. of sulphide of iron, copper, lead, zinc and antimony, and perhaps a trace of some of the compounds of tellurium with gold and silver, although none of the latter have been as yet positively identified. The relative proportion, by weight, of silver and gold in the ores, varies in different parts of the vein, from 12 silver for 1 of gold, to 7 silver for 1 of gold. The quartz vein-filling is usually frozen fast to the walls, and is very hard and compact, seldom showing the friable, fissured, or shelly structure often to be found in quartz veins. Comparatively little evidence of relative motion of one wall of the vein upon the other is to be found-a fact indicating that during the formation of the vein, and prior to the extensive movements herein described, little disturbance had taken place. No evidence whatever of metasomatic origin has been observed. On the other hand, occasional occurrences of comby structure, in which the axes of the quartz crystals are at right angles to the plane of the vein, rather indicate deposition from solution in a pre-existing fissure. Spurs, or branches, and small parallel veins, while not en-\

Mar 1, 1907

By J. Armanet

THREE MINING colleges are maintained in France; the École Nationale Supérieure des Mines, of Paris; École Nationale Supérieure des Mines, of Saint Etienne; and the École Supérieure de la Metallurgie et des Mines at Nancy. Besides graduates of these schools, a few graduates of the École Centrale des Arts et MIanufactures and of the École Polytechnique are employed as ]nine managers or engineers; however, most of the latter have taken a graduate course at one of the mining schools.

Jan 1, 1939

By FLOYD T. TAYLOR

IN 1833, less than one hundred years ago, Michael Faraday discovered and stated the laws of electrolysis. His discovery formed the foundation of a new use of metals which has now reached a variety of application not ordinarily appreciated. Furthermore, things can be done with electro-deposited coatings which have thus far defied other methods. Some of the uses of electro-deposited coatings are interesting. The tonnage of metals already finding an outlet through such a channel is considerable. In general electro-deposits have two characteristics: ornament plus utility; utility plus ornament. Both these factors are usually found associated in electro- deposits. Ornament plus utility was probably the first use. For example, the silver-plating of tableware, having its real birth in Birmingham, England, about 1844. However, this same ornament plus utility retarded the development of electro-plating, because in the beginning, electro-plated articles were branded with the odium of imitation and shunned accordingly. The gold brick of the swindler may be an exception to this statement.

Jan 1, 1929

By W. C. Hauber

Techniques previously published to predict the production performance of a water flood when the mobility ratio is not unity have been primarily restricted to a five-spot well pattern. When other types of well patterns are considered, the prediction of performance has required either a model study or a complex numerical solution of a multiple-fluid system with a high-speed digital computer. Simple methods are developed in this report for predicting the areal sweep efficiency and injectivity history of a water flood for arbitrary well patterns and mobility ratios. The effect of an initial gas saturation can be incorporated into this method of prediction. With the layer superposition concepts published by Prats, et al.,1 these methods can be used to predict the production performance of a water flood in a reservoir having a wide range in permeability. A reasonably good agreement is shown by comparisons of the results calculated by this method with those obtained either by model studies or by complex numerical solution of multiple-fluid systems. Therefore, it has been concluded that a reasonably accurate method has been developed for predicting the production performance of a water flood employing an arbitrary type of well pattern for any given mobility ratio. A medium-speed digital computer can be used in applying this method. INTRODUCTION Production performance of multi-fluid five-spot water floods can be predicted by the techniques published by Prats, et al.1 This technique takes into account the effects of initial gas saturation, mobility ratio and vertical variations in horizontal permeability. A basic assumption in applying this technique is that unit displacement efficiency does not vary with time after the passage of the flood front. Prats, et al. demonstrated that this assumption is valid for normal waterflood applications with small mobility ratios. To extend Prats&apos; technique to other types of well patterns has required either an experimental model study or a numerical solution of a multiple-fluid system to describe the performance of an individual homogeneous layer. Sheldon and Dougherty2 presented an exact numerical solution employing any arbitrary well pattern. This technique is complex to apply, requiring (1) numerical solution of the single-fluid system, (2) conformal mapping of the streamlines and iso-potential lines to form a new grid network, and (3) a numerical solution of the multi-fluid system on the new grid network. A method was developed in this paper to approximate areal sweep efficiency and injectivity as functions of time for an individual homogeneous layer for arbitrary well patterns and mobility ratios. Analytic expressions were derived to directly apply this method to five-spot and direct line drive well patterns. For other types of well patterns, this method is similar to the approach of Higgids and Leighton,6 in that it utilizes the stream tubes and iso-potential lines obtained by the solution of differential equations when the mobility ratio is unity. However, this method is easier to apply than the Higgins-Leighton method since it does not require knowledge of the variation between oil and water relative permeabilities and saturation. Using the relationship between areal sweep efficiency, injectivity and the volume of water injected into an individual homogeneous layer as obtained by the method presented in this paper, and Prats&apos; technique for the superposition of individual layers, one can predict the production performance of any water flood. ASSUMPTIONS GENERAL Basic assumptions made in this report are that fluids are incompressible and the layers are horizontal, homogeneous and uniformly thick. It is assumed that as water is injected into the layer, three distinct regions are formed —a water bank, an oil bank, and an unflooded region. Each region is assumed to displace other regions in a pis-tonlike manner, with only one fluid flowing in each region, so that there is no change in unit displacement efficiency with time after the flood front has passed in the reservoir. Therefore, the residual oil saturation in the water bank and the oil saturations in the unflooded region are constant throughout the layer. The ratio (F) of the bulk volume of a layer occupied by the oil and water banks at any time before oil breakthrough, to the corresponding bulk volume of a layer occupied by the water bank, is given&apos; by the equation BREAKTHROUGH AREAL SWEEP EFFICIENCY To predict the behavior of any type of waterflood pattern, one must know the breakthrough areal sweep efficiency Eb(Mc,o, F) for the pattern for any water:oil mo-

Jan 1, 1965

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for OFHC copper, and for a series of binary solid solutions of high purity copper with zinc, gallium, germanium, arsenic, and silicon, to investigate the effect of alloying elements in substitutional solid solution on grain boundary viscosity. The apparatus used was of the torsional pendulum type developed by KeI1 modified so that the specimen and vibrating system could be maintained in a high vacuum. The activation energy for grain boundary relaxation in copper is 33,000 cal per mol. This is considerably less than the activation energy for self-diffusion, in disagreement with Ke&apos;s theory2 that the two activation energies should be the same. All the alloying elements increase the activation energy for grain boundary relaxation to approximately 44,000 cal per mol, increasing the grain boundary viscosity at a given temperature. The results are discussed in terms of theories of grain boundary slip put forward by MottQ and by Ke.+ Experiments have also been made to investigate the effect of small amounts of oxygen on the variation of internal friction with temperature for copper. EXPERIMENTS described in this paper were designed to investigate the effect of alloying elements in substitutional solid solution on grain boundary viscosity, using the internal friction method developed by Kel for measuring grain boundary viscosity. It was considered desirable to make the system under investigation as simple as possible by making experiments on a comprehensive series of binary alloys of copper with the elements immediately following it in the periodic table, i.e., zinc, gallium, germanium, and arsenic. These elements are within the range of favorable size factor for solution in copper, and the systems have been extensively investigated by Hume-Rothery and his co-workers." Later, in order to study the effect of the relative size of the solvent and solute atoms, experiments were made on a series of Cu-Si alloys, since the apparent atomic diameter of silicon when in solution in copper—the diameter necessary to assign to the solute atoms to account for the lattice constant of the solid solutiona—is almost the same as that of the solvent atoms. Preliminary experiments were made to measure the variation of internal friction with temperature for pure copper. Ke made some experiments on copper," but found that the curves obtained were not reproducible in consecutive experiments. The copper was maintained in an argon atmosphere during the experiments but, although he took precautions to exclude oxygen, Ke came to the conclusion that the precautions were not entirely satisfactory, and that the lack of reproducibility must be due to absorption of oxygen by the copper. Experiments have therefore been made to investigate the effect of small amounts of oxygen on the variation of internal friction with temperature for copper. Previous Work Ke made extensive experiments on high purity aluminum and was able to show that the grain boundaries behave viscously at high temperatures. He found that the relative rate of movement of the grains could be expressed as Where v is the velocity of slip, A is the constant, u is the shear stress, H is the activation energy, R is the gas constant, and T is the absolute temperature. By assuming that the boundary layer was one atom thick, he obtained a value for the viscosity which, when extrapolated to the melting point, gave good agreement with the viscosity of the liquid metal at the melting point. Ke also made experiments on other high purity and commercial purity metals:, and on some alloys." " He came to the conclusion2 that the activation energy for grain boundary slip was the same as for self or volume diffusion and for steady state creep in single crystals. Rotherham, Smith, and Greenough" have shown recently that the activation energy for grain boundary slip is not the same as for self-diffusion in tin,

Jan 1, 1957

By E. D. Glass, R. C. Hessing

The volume of gas in storage reservoirs may be compuled from estimates of hydrocarbon pore volume and gas density. However, both are dificult 10 estimate accurrately. Further, no adequate method has been presented for estimating reservoir performance during operation for Volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area conr(zilliitg the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usally surrounds, and is in communication with, tile permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir. INTRODUCTION Depleted gas reservoirs arc often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells arc located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply. DISCUSSION For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. l&apos;wo solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is Eqs. I and 2 ore superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BDa and c are ohtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone. The values of the constants found from curve-fitting Eq. 1 to the early time data may then be used in Eq. 2 that only the coefficient- L containing the unknown

By James P. Kimball

Jan 1, 1885

By W. S. Morris

PETROLEUM&apos;S importance in World War II can perhaps be better realized by the recitation of a few facts and figures: Gasoline needs in this war are already eighty times greater than in the last war. It takes nearly three pounds of gasoline to deliver one pound of bombs, filled with petroleum explosives, on an enemy objective. Every American soldier overseas requires an average of more than fifty gallons of petroleum products per week, with the oil used by Navy and supply ships and America&apos;s Allies boosting the consumption of oil per soldier to an even higher figure. Every oil well in the United States now must produce each day an average of four barrels of oil for war and combat jobs. More than fifty million gallons of gasoline, fuel oils, lubricants, and other petroleum products are now going directly to the fighting forces every day.

Jan 1, 1945

By Robert J. McKay, F. P. Huston, WILLIAM G. HUMPTON

THE manufacture of nickel-clad steel plate and the fabrication of articles from it has progressed far enough to permit a general description of the working methods used. The manufacture of sheets made up of layers of nickel and steel is not new as a sheet of this character was patented in Germany in 1893. Present development differs mainly in the size and finish of the product. The earlier light-gage highly finished products have been limited in their application due to their similarity, in certain respects, to electro-plated and highly finished alloy sheets. The new product is a relatively heavy plate 1/4 or 3/s in. thick and heavier, with one side coated with nickel, the weight of nickel being of the order of 10 per cent of the whole. The finish is that of hot-rolled steel plate.

Jan 1, 1931

By AIME AIME

WITH a brilliance undimmed by hard times, the annual dinner on Wednesday evening, Feb. 17, was a complete success. More than 600 members, friends and ladies gathered early and filled the anterooms of the grand ballroom of the Commodore Hotel, while the president&apos;s reception was in progress, and then at the sound of the gong and with the music of the orchestra, rising above the happy din of conversation thronged to their seats at the tables. Following the "potage Ambassadeur"-probably to eliminate a very real hazard-the usual toy balloons appeared and a gay and lively scene, punctuated by multitudinous explosions, ensued, as the hundreds, of variously colored spheres bounced yon and hither until their gaseous existence was ended on the glowing end of a cigar or cigarette. On the speakers&apos; dais sat C. E. Beecher, Chairman Petroleum Division; J. Vipond Davies, representative of A. I. M. E. on the Alfred Noble Prize Committee; Corbin T. Eddy, Alfred Noble Prize recipient; A.&apos; S. Tuttle, Vice-president American Society of Civil Engineers; W. C. Mendenhall, Director U. S. Geological Survey; George C. Bateman, representing the Canadian Institute of Mining and Metallurgy; Paul D. Merica, Institute of Metals lecturer and Chairman James Douglas Medal Committee; Champion Herbert Mathewson, James Douglas Medalist; Robert E. Tally; retiring President; G. Temple Bridgman, toast-master; Scott Turner, incoming President; F. W. Bradley, William Lawrence Saunders Medalist; Fred Searls, Jr., Chairman William Lawrence Saunders Gold Medal Committee; Arthur Notman, President Mining and Metallurgical Society of. America; Robert J. Grant, Director U. S. Mint; Landon F. Strobel, Chairman New York Section; Howard Scott, recipient of Robert W. Hunt Prize; George. B. Waterhouse, Chairman Robert W. Hunt Prize Committee; F. M. Becket, Chairman Iron and Steel Division; Ora E. Clark, recipient of the J. E. Johnson, Jr., Award; Richard Peters, Jr., Chairman J. E. Johnson, Jr., Award Committee; E. C. Bain, Howe Lecturer; Sam Tour, Chairman Institute of Metals Division; and H. Foster Bain, Chairman. Charles F. &apos;Band Foundation Committee. &apos; Each was heartily applauded when introduced by Mr. Bridgman, as was Mrs. Tally, who also made a bow. The toastmaster made graceful reference in introducing Mr. Strobel, to the large part the latter had taken in planning the meeting.

Jan 1, 1932

By A. W. H. Morris, G. H. Laurie, J. N. Pratt

Using- galvanic cells of the form Sn(liq)/Sn" (LiCl-KC1-SnCl,)/Sn-Ag (alloy), measurements have been made of relative thermodynamic properties of the a, C, E, and liquid phases of the Ag-Sn alloy system. Partial heats of solution of the components in the liquid alloys lzave also been observed by direct cal-orimetric measurement in an isoperibol calorimeter. The thermodynanzic quantities are disczlssed in relation to structural and other properties and the existence of anomalous minor fluctuations in the partial heats and entropies of solution in liquid alloys is tentatively suggested. In the course of a recent electro motive-force study of the thermodynamic properties of Sn-Ag-Pd liquids,&apos; some measurements were also performed on the Ag-Sn binary system. Most previous thermodynamic studies of this system have been concerned with the liquid state. Measurements confined to the limiting heat of solution of silver in liquid tin have been made by many calorimetric workers2 while high-temperature calorimetric measurements of the heats of formation of the full range of liquid alloys are reported in the early work of Kawakami~ (1323°K) and more recently by Wittig and Gehrin~(1248°K). Electromotive-force studies on liquid alloys have been made by Yanko, Drake, and Hovorka&apos; (606" to 686°K; 86 to 99.4 at. pct Sn) and by Frantik and Mc Donald&apos; (900°K; 30 to 90 at. pct Sn). The only known measurements on the solid state are of heats of formation of the a, £, and c phases; these values were obtained using tin-solution calorimetry, at 723"K, by Kleppa,~ whose investigation also yielded heats of formation of liquid alloys containing more than 64 at. pct Sn. The present experiments on the Ag-Sn alloys include a re-examination of the liquid phase and, because of the dearth of free-energy data for the solid state, attempted measurements on the a, c, and E phases. The principal new feature of electromotive-force results obtained for the liquid phase was an indication of anomalous fluctuations in the partial heats and entropies of solution of tin at certain compositions. However, since the values for these thermodynamic quantities were determined from the temperature coefficients of cell potentials, which are commonly subject to considerable error, confirmation by calorimetric measurements was considered desirable. A detailed investigation of the partial heats of solution of the components in the binary liquids was made using a liquid metal solution calorimeter. I) GALVANIC CELL STUDIES a) Experimental Details. Measurements were made, as a function of alloy composition and temperature, of the potentials of reversible galvanic cells of the form: ~n(liq)/~n++/~n-Ag (solid or liquid alloy) Details of the apparatus and experimental techniques have been given elsewhere.&apos; so that a brief account will suffice here. Molten salt, 58 mole pct LiC1-42 mole pct KC1, containing small amounts (1 to 2 mole pct) of stannous chloride was used as the electrolyte. The salts were dehydrated by pre-electrolysis and vacuum -drying techniques. Cells were established under an argon atmosphere by immersing tin and alloy electrodes in the molten salt contained in a large silica tube, heated in a vertical resistance furnace. The tube was sealed at the top by a head plate provided with openings permitting the simultaneous insertion of six electrodes, a central thermocouple sheath, and connections to vacuum and argon lines. Temperatures were controlled to *0.2"C over prolonged periods, with maximum variation over the electrodes at any time of 0.l°C. Temperatures were measured with a standardized Pt/13 pct Rh-Pt couple. The electromotive force of this and the cell potentials were measured on a Cambridge Vernier potentiometer and short-period galvanometer. Alloys were prepared from Pass "S" tin (99.999 pct) and Johnson-Matthey high-purity silver (99.999 pct) by melting in evacuated silica capsules and quenching in cold water. For liquid phase experiments, pieces of the resulting alloys were remelted into prepared silica electrode units, while solid electrodes were prepared by remelting into 3-mm bore tubing, inserting a cleaned molybdenum lead wire, and quenching to produce uniform rods about 3 cm in length, with soundly attached leads. In all cases remelting was done under an argon atmosphere. The solid electrodes were subsequently annealed in evacu ated silica tubes for 14 days at about 20°C below the solidus and quenched. Analyses showed that these techniques produced uniform electrodes with no significant change from weighed out compositions. b) Results and Discussion. Measurements were made on about forty alloys in the solid and liquid states, over varying ranges of temperature between 550" and 1050°K. Stable, mutually consistent, and reproducible electromotive-force data were obtained with most liquid alloys and these are shown in Fig. 1. Investigations were extended below the liquidus tem-

Jan 1, 1967

By J. N. Ong

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

Jan 1, 1962

By J. G. Patchett, R. W. Rausch

Fresh waters and the presence of clay in many Rocky Mountain and West Coast sands require special methods of log analysis. Archie&apos;s saturation equation requires addition of a shale correction term, and the SP equation must also be modified to account for clays. Suitable equations were developed several years ago, but have not been widely used due to the algebraic complexity. A computer-oriented method has now been developed to overcome this problem. The basic shaly sand equations are rearranged in four different ways to permit solution for various sets of available input data. Essential to application of the method is the correction of observed SP values to those that would be observed if the resistivity of the formation waters were exactly interchangeable with the activity. A graphic method for doing this is given. Where conditions require consideration of the effect of clay in the sands, the method presented has been found to improve the accuracy of water-saturation determinations. INTRODUCTION Log interpretation in many Rocky Mountain and West Coast basins is complicated by rapid vertical and lateral changes in water resistivity. Calculation of formation water resistivity from the SP curve becomes difficult in zones that contain clay, since changes in SP deflection may be due to changes in either clay content or water salinity. In hydrocarbon-producing reservoirs, the problem is further complicated because hydrocarbon saturation also reduces the SP.1 A log interpretation system using computers has been developed to provide a solution to this problem, based on equations proposed by de Witte.2 Four different simultaneous solutions of de Witte&apos;s equations have been made. Each solution method uses a different set of input data as independent variables. Thus, a choice of solution method is possible, depending upon the logs run and the availability of other data. Two of the solutions do not require a knowledge of water resistivity. This system is intended to be used primarily in multiple sandstone-shale sequences of low and moderate resistivities where the principal contaminant in the sandstones is clay. However, where sufficient regional data are available, interpretation in single-zone sandstone reservoirs can also be improved by using the method. THEORY AND HISTORY OF SHALY SAND ANALYSIS The log interpretation formula originally proposed by Archie3 in 1941 is applicable only to rock-fluid systems wherein the rock has negligible electrical conductivity. In 1949, Patnode and Wyllie4 showed that if the rock itself can be considered conductive due to the presence of clay, a different calculation approach is necessary. During the following years, this problem was investigated at great length, as was the related problem of the effect of rock conductivity on the SP.5-11 These investigations established functional relationships between SP, resistivity, water saturation and water resistivity for such a formation. Refs. 2 and 12 provide summaries of these studies. Unfortunately, practical use of these relationships required that water resistivity be known independently from the SP. Although log interpretation methods for rock systems containing clay were proposed at that time,&apos; they were not generally accepted for routine use. There are three principal reasons for this. First, in many field situations involving high-salinity water, rock conductivity may be neglected (even if present) without introducing appreciable error. This may be seen by considering the following expression for waier-saturated rock.&apos; 1/R2=1/R1+1/FRn....(1) where 1/R, is conductivity due to clay. As Rw becomes small, I/FRw becomes much greater than 1/R, which may be neglected. Where 1/R, may be neglected, the sandstone is called clean. If the term may not be neglected, the sandstone is termed dirty or shaly. For resistivity purposes, the classification between clean and shaly sands then depends not only upon the conductivity due to shale in the sand, but also upon the resistivity of the associated water (shale is used here to mean surface condition due to disseminated clay). A sand of given conductivity might safely be treated as clean in association with high-salinity water, but would require shaly sand methods if associated with fresher waters. Shaly sand methods are not required in many areas having saline waters; but in Rocky Mountain and West Coast sands having relatively fresh waters (often more than 0.3 ohm-m resistivity at formation conditions), the shaly sand methods are needed. Errors Rw calculations from the SP due to the presence of shale are likewise related to water salinity. In saline water formations drilled with fresh mud, the ratio of mud filtrate resistivity to water resistivity is high, the SP is large and the presence of shale can introduce large errors in water resistivity calculated by the conventional method. When the resistivity ratio is low, the errors are smaller. At zero SP, no error would result from shale. Thus, from the SP viewpoint, a given rock could be shaly if associated with a saline water, and clean in association with a fresh water, which is the opposite of the resistivity-oriented definition above.

By H. I. Aaronson, H. A. Domian, G. M. Pound

The thernodyna,nics of I the Proeutectoid ferrite re-action ha1.e been investigated on the bases of three diifevent descviptions of the statistical thernzodynamics of interstitzal solid solutions. Especially at low ternperatures, substantial dijeretzces are found in the valltes of the extrapolated y/y + a and cr/a + y equilibriurn curls, and in the To- co7nposilion metastable eqliilibriunz curl-es thus co,npited. Although neither actiztity nor phase-diagram date are able to distingrish udeqiutely among the various descviptions, the statustics of Lacher, Fouller, and Guggenheinz provide the ?nost conplete epresentation az3ailable of the single carbon-ctrbon interaction energy (w) nzodel of an intevstitiril solid solution, and the relationships deduced frojrl then2 are accordingly pre.ferred. The findings tlzut w in austenite &apos;aries significu?ztly uith tenpevntrue and that phase-diagawr data arc not accurately con?palible usith eqcrctions deduced on the basis of actility infoation indicate, hou&apos;e13er, that a wzore cornplex nlodel of the uustenite , und pvobably of the .feyrite, solirl solutions will have to forn the basis of f4tuve statistical t1.eat1nents. Some suggestions for such a ruodel arc advanced. Althoug11 w represents a vepltlsio energy in austozite, it was found to corvcsporzd in ferrite to a binding energy, in qualitatit.e accord zc,itlz the internal-friclion results of Keefer and wert. ThE transformation of austenite to proeutectoid fer-rite is becoming recognized as an exceptionally useful vehicle for quantitative studies of the kinetics of phase transformations.&apos;" Reasons for this popularity include well-characterized microstructures which develop on a convenient scale with acceptable kinetics within a considerable temperature-composition region, the absence of great sensitivity to common impurities, and, especially. the availability of a unique wealth of the ancillary information indispensable for the quantitative interpretation of kinetic measurements, including phase diagram,3 crystallographies diffusivity,5 inter-facial energy,=17 elastiit," specific vlume, &apos;&apos;&apos; and ativity&apos;-&apos; data. Development of considerable amounts of additional thermodynamic information from activity data is of particular importance with respect to kinetic studies, since much of this information is needed in temperature-composition regions not directly accessible to presently available techniques for the measurement of equilibrium properties. A generally useful approach to the thermodynamics of solid solutions, which is of especial value in this situation, is based upon the formulation of the free energy of such solutions as a function of temperature and composition. The free energy of solid solutions has been resolved into many components. Particularly in the case of interstitial solutions, with which we shall be concerned in the present study, however, only the positional entropy component has been intensively studied. The other components are conventionally taken into account by fitting equations for the activity of the interstitial species or the temperature-composition path of phase boundaries, derived principally from positional entropy considerations, to experimental information on these quantities through adjustment of one or more constants in the equations. A number of studies of the thermodynamics of interstitial solid solutions have been made primarily on this basis,&apos;"25 but only Kaufman, Radcliffe, and cohenZ2 (hereafter KRC) and ener&apos;&apos;% ave applied the results of such studies to develop relationships for the thermodynamic quantities of interest in the austenite —- proeutectoid ferrite transformation. KRC made use of a model developed by cheil&apos;&apos; (on the basis of a previous study by ohansson&apos;), and subsequently rede-rived correctly by Speiser and retnak,&apos; in which a carbon atom is considered to inhibit occupancy of a certain number of its nearest-neighboring interstitial sites. schei120 determined the number of sites in austenite thus excluded by matching calculated and experimentally measured curves for the variation of carbon activity with the mole fraction of carbon. zener17 used a different approach. He assumed that the positional entropy of carbon is ideal both in austenite and in ferrite (i.e., no excluded interstitial sites), and included all other contributions of carbon in a temperature-independent "free-energy change" accompanying the transfer of 1 mole of carbon between the two phases. This quantity was determined by "pinning" an equation derived for the boundaries of the a + y region to experimental data on the compositions of these boundaries at a single temperature. In the present investigation, three different approaches to the thermodynamics of the proeutectoid ferrite reaction are examined comparatively: I) the method of Zener; 2) the model employed by KRC and predecessors; and 3) the more detailed statistical thermodynamic treatment of the same model developed by acher and Fowler and uenheim, &apos; in which the problem of overlapping regions of influence of individual interstitial atoms is resolved. In order to make these comparisons, it is necessary to undertake an extension of one aspect of Zener&apos;s method; since the Lacher- Fowler -Guggenheim (LFG) treatment has not been previously used in the present context, the necessary thermodynamic "superstructure" for this treatment will be developed in parallel

Jan 1, 1967

By ALBERT P. J. BORDEAUX

THIS paper briefly describes the general outline of cyaniding silver-ores in Mexico, with special reference to personal experiments made in the Temascaltepec district. The most important papers on the subject deal with cyaniding gold-silver-ores, the gold predominating in value, so that the treatment is nearly the same as for gold-ores, the losses of silver being considered of little importance. I describe here the treatment of silver-gold-ores containing very little gold, which is more general in Mexico than elsewhere. The cyanide treatment, which was so successfully applied to gold-ores, did not succeed immediately with silver-ores on account of their varying composition. Gold occurs in nature usually in the native state, while silver occurs generally in combination with sulphur (argentite), and various combinations of sulphur, antimony, and arsenic. In former times there was a complete difference in the treatment of gold-ores and silver-ores. Amalgamation, which was successful with gold-ores, was generally inadequate with silver-ores. The usual treatment in Mexico for silver was the patio process, the theory of which was satisfactorily explained only quite recently by Mr. Ortega and others. GENERAL OUTLINE OP THE CYANIDE TREATMENT. The general tendency of the present practice is to slime the silver-ore as much as possible, and in order to obtain a higher efficiency, with less loss of cyanide, and greater speed, the following lines are observed 1. Crushing by stamps with 30- or 40-mesh screens, then crushing by Huntington or Chilean mills, through 60- or 80-mesh screens. 2. Concentration upon vanners.

Jan 1, 1910

By Herman Poole

WHEN finely divided ferrous sulphide, FeS, is roasted at a moderate, carefully regulated temperature, the iron and sulphur are oxidized, the first products being probably ferrous oxide and sulphurous acid. In the presence of oxygen of the air the ferrous oxide soon becomes ferric oxide and in the presence of oxygen and the ferric oxide the sulphurous acid oxidizes to sulphuric acid. These facts are well known, having been established by Plattner many years ago. As a further reaction, some of the sulphuric acid parts with a portion of its oxygen to oxidize more ferrous oxide to ferric oxide, and a portion of it escapes uncombined or else unites with the iron oxides to form sulphates. Ferrous sulphate is usually soon oxidized to ferric sulphate and if the heat becomes sufficient this is then decomposed into sulphuric acid and ferric oxide. As a result of these reactions a mass of more or less pure ferric oxide is formed which is generally made porous by the escaping gases and, if rabbled properly, practically all the sulphur is expelled. If ferric sulphide or ordinary pyrites, FeS2, is roasted, a portion of the sulphur sublimes and usually burns to form sulphurous or sulphuric acid, although at times and under favorable conditions some of the sulphur is driven off uncombined and can be collected as such. Under ordinary methods of roasting, however, only a small portion escapes combustion. By the combustion of the sulphur an increase of heat is de¬veloped and, as a consequence, the reactions mentioned take place more rapidly and actively-more sulphuric acid is formed and the oxidation is more complete-nearly all the iron being left as ferric oxide with practically no sulphate or ferrous oxide. When the iron sulphide is in lumps the roasting proceeds generally as with fines, but with some changes due to mass. The

Sep 1, 1905

By Galen Clevenger

THE losses of gold and silver occurring during the conversion of the precipitate, resulting from the cyanide process, into bullion may occur in two ways: first, there may be mechanical losses during the handling of the precipitate up to the time that it is charged into the melting furnace; and second, there may be losses after the precipitate reaches the melting furnace. Much of the loss during the handling of the pre-cipitate can be eliminated, and in fact, in modern plants this loss is known to be very small; particularly since preliminary acid treatment of the precipitate with the attendant extra operations has been abandoned in all but certain plants where gold predominates and this extra step is still deemed necessary. The losses in the melting furnace are from dusting and volatilization; losses in the furnace bottom and linings; floor sweepings; and slag and matte. The gold and silver in the: products which do not: go out of the flue are readily recoverable by standard methods, and while there may be considerable gold and silver tied up at times, the ultimate loss with careful "work should be small. The losses resulting from volatilization and dusting in connection with the melting of the silver slime from copper refineries have been determined by standard methods, and the possible recovery: definitely estab-lished through the installation and operation of electro-static precipitation units. This subject has not been thoroughly investigated in connection with the melting of`. cyanide precipitate; at least, there are no published accounts of such tests. Experiments have been made in the past to determine melting losses by weighing and assaying the precipitate, but this method gives results which are uncertain on account of the difficulty of accurately sampling and assaying cyanide precipitate. Attempts to ascertain these losses by bubbling a measured sample of the gas through cyanide solution or, other absorbent have likewise failed to give depend-able results.

Jan 1, 1922

By Joseph W. Richards

THIS method of briquetting flue-dust, or flue-dust mixed with fine ores, or, in a few exceptional cases, coke-dust, has come into large commercial use in Europe, and a small plant is already in operation in the United States. It promises to become of such great importance to the iron industry of the United States that the following description will certainly interest the majority of our pig-iron producers. Discovered in 1908, the process rests upon the observation of Dr. Schumacher that blast-furnace flue-dust, while possessing of itself no binding or cementing properties, acquires strong cementing properties if mixed with a very small amount of certain salt solutions, the amount of which is so small that the resulting cementation appears to be rather by catalytic action of the salts added than by the mass-action of such chemicals. To be more specific, fresh blast-furnace flue-dust mixed with from 5 to 10 per cent. of its weight of magnesium chloride or calcium chloride solution-that is to say, with from 0.25 to 2 per cent. of its weight of magnesium chloride or calcium chloride-acquires the property of setting within a short time, from 15 to 60 min., and forming a hard cemented briquette. Alkaline solutions appear to have no action such as described, and they even interfere, if present, with the action of the magnesium and calcium solutions. When treated in this way the flue-dust briquette sets very hard, apparently from pure excess of cementing- and setting-power. It is, therefore, possible to . mix with the flue-dust a considerable proportion of inert ore or like material, which has no setting-power by this process, and thus to make a compound briquette containing large quantities of ore mixed with flue-dust, but in which the flue-dust may be regarded as the cement or binding-material. A particularly strongly cementing flue-

May 1, 1912