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By Paul C. Merritt

The story now unfolding on the Mesabi Range is more than just another chapter in the continuing history of iron mining. It is an epic of foresight, research and pioneering instinct just now culminating in the rapid growth of a new industry hardly more than ten years old. And that growth has been impressive. In the decade that has passed since Reserve Mining Co. blazed a trail as the first successful large- scale commercial taconite operation, the number of plants now existing or soon to be operating has grown to six. From Reserve's initial capacity of 3 million tons of pellets per year, total production capacity on the Range has surged to 31.5 million tons while capital investment has leaped from $300 million in 1955 to almost $1 billion today. During the past year alone, more than $500 million has been committed to these projects, an amount probably greater than that going into any other single mining area in the world. There is more yet to come.

Jan 10, 1965

By D. R. Bomberger, M. Deul

An automatic microscope has been developed to measure the size and populations of macerals and minerals in fine coal particles. Differentiations are made on the basis of reflectance. This study is concerned with the size distribution of pyrite inclusions. Most fine coal cleaning processes do not remove pyrite as completely as a straight density separation. Consideration of the pyrite size distribution is suggested as a more accurate method of predicting sulfur reduction by a cleaning process. Analyses of float-sink results and Deister Table operation in terms of pyrite particle sizes are made. Other potential applications of automatic microscopy are also discussed. In the study of coal cleaning by pseudo-gravity methods (tables, cyclones, hydrotators, etc.), it is customary to express the deficiency of the process relative to float-sink measurements in some form of "percent efficiency". These have been calculated in many different ways in order to provide a means of extrapolation of test data to untested coal feeds. This works quite well with coarse coal (here defined as larger than one-eighth in.). Large, heavy pieces of refuse are rejected rather thoroughly by many cleaning processes, and the efficiencies relative to float-sink results approach 100%. In coarse coals, the difference in the sizes of fine pyrite is masked by the averaging effect of the large coal envelopes. The existence and fate of fine pyrite is often hidden in the larger numbers representing coarse (and easily removed) pyrite. There are cases where it is desirable to subject fine coal (here defined as smaller than one-eighth in.) to cleaning processes. This is true of naturally occurring fie coal streams and in cases where comminution followed by cleaning is necessary to provide the quality desired. It is in this area that the use of process efficiency relative to float sink fails. Percent efficiencies decline to very low figures, and equivalent separation densities become a matter for conjecture. The net result is that an attempt to estimate product quality from float-sink data and a process efficiency figure often results in large errors. This work represents a new approach to the problem by observing the fate of pyrite particles, grouped by sizes, in a cleaning process. Examples are given which relate pyrite size measurements to float-sink washability and to a Deister Table operation. EXPERIMENTAL WORK The automatic microscope used here has been previously described.' Briefly, it is an instrument which measures the diam of particles (as defined by a range of reflectance) exposed on a polished specimen. The instrument scans a sample briquet, measures diam of exposed pyrite inclusions and records the data by size intervals. Preparation of the briquet is critical, due to the automatic nature of the process. The principal requirement is for an optically flat surface, so that focus will be maintained as the motorized stage moves the specimen under the lens. The various substances present must be polished to the same level in spite of the wide difference in hardness between coal substance and minerals. The polishing method must not pluck out small grains, which might be rather loosely held by surrounding coal. The procedure below was successful in producing all of these results. The coal sample (8 mesh or finer) was riffled (a micro vibrating riffle is essential) to obtain 15 g. One volume of Lucite powder (thermosetting plastic mounting medium) was mixed with three volumes of coal and mixed thoroughly. A briquet was formed using a cylindrical die (1 1/4 in. diam) at 3000 lb per in.* pressure and 150°C. Preparation of the optical surface was accomplished on automatic polishing equipment, according to the following schedule: 1) Grinding: 3 stages, using successively fine Carborundum grits of 180, 320 and 600 mesh. 2) Rough polishing: 2 stages, using 3µ alumina on cast iron, followed by 1µ alumina on lead. 3) Fine polishing: 2 stages, using 0.5µ alumina on napless broadcloth over bronze, followed by 0.1µ alumina on silk filament cloth over bronze. Raw data were corrected for the fact that the chords

Jan 1, 1964

By L. A. Rapport, J. R. McCord, W. P. Drews, K. H. Coats

Water movement about an oil or gas reservoir can be predicted provided an aquifer influence function is known. This function is generally determined from an electric analyzer study or by fitting an idealized mathematical model to field data. A prohlem arises in determining that influence function which best reproduces field data and satisfies certain smoothness requirements, without making any idealizations concerning aquifer geometry and heterogeneity. This study shows the problem to be solvable through the linear programming technique and presents applications to one oil reservoir and two gas storage reservoirs. In addition, a theorem is stated and proven which confirms influence junction smoothness requirements heretofore accepted on physical intuition and establishes additiotzal smoothness constraints formerly not recognized. INTRODUCTION The pressure decline accompanying production results in water encroachment into oil and gas reservoirs situated adjacent to aquifers. The importance of this water movement derives from the significant dependence of production rate upon reservoir pressure and of pressure, in turn, upon water encroachment. Pressure and rate of water movement are uniquely related through an "influence" function which may be in the form of reservoir pressure response to a unit water encroachment rate or of water movement caused by a unit reservoir pressure drop. This influence function reflects the heterogeneity and geometry of the aquifer and is therefore particular to each reservoir. If the influence function is known, then reservoir pressure may be predicted from a production rate schedule, or vice-versa, with the aid of the material balance equation which relates water influx to reservoir production and pressure. The problem of determining this influence function for a given reservoir has been approached in three different ways. Van Everdingen and Hurst calculated and tabulated certain influence functions pertinent to idealized mathematical models which satisfy simplifying assumptions such as aquifer homogeneity and elementary reservoir-aquifer geometries.' Other studies developed additional tables for a variety of elementary reservoir-aquifer geometrical con- figurations and demonstrated their validity and utility.:' Hicks, et al. described the use of an electrical network to determine an influence function giving "best" match of field history and allowing prediction of future performance.' Finally, Hutchinson and Sikora5 and Katz, Tek and Jones attempted to develop a calculation method for deriving the influence function directly from field data with no idealizing assumptions concerning aquifer geometry and homogeneity. They encountered difficulties with inaccuracies in field data and with satisfaction of well-known smoothness requirements of the influence function. This study is concerned with the determination of influence functions from field data and, more specifically, treats the following problem: given field pressure-production data of arbitrary accuracy, how does one determine the influence function which, subject to satisfaction of known smoothness requirements, gives best agreement with field history? A rigorous solution to this problem is ohtained through linear programming as described below. Example applications to one oil and two gas storage reservoirs are presented. In addition, a theorem is proved which confirms influence function smoothness requirements heretofore accepted on physical intuition and establishes additional smoothness requirements formerly not recognized.

Jan 1, 1965

By W. A. Backofen, D. Lee

Tlze condition of superplasticity or neck-resistanl flow that results front high strain-rate sensitivity has been observed in isothermal tension tests on several titanium alloys and one of zirconium hi general, il was associated with reasonably fine-grain micro-structures being stvained in the transformation range at rates below i - 10 -3 sec-&apos;. The metallographic mean-free path, L, was measured at room temperature after rapid cooling from the temperature of test-ing. The flow stress of Ti-GAL-4V at 950°C was proportional to La at different constanl <; the value of a decreased with increasing. E but at E< 1.5 x 10-4 sec-1 it varied only from 0.9 to 1.25. The findings were interpreted to mean that viscous boundary shear is the rate-controlling process of deformation at high levels of strain rate sensitivity in these materials. Elongation of over 1000 pet could be obtained, but a1 temperatures so high and rates so low that any practical application of the full effect would probably be difficult. As the transformation range was narrowed, by turning from Ti-6AL-4V to Ti-5Al-2.5sn to nomznally pure titanium, the allowable temperature varialion was correspondingly reduced. Superplasticily was not found in Armco iron, presumably because the transformation range was too narrow to allow the developtnenl of a reasonably stable microstructure for isolhermal lesting. THE work represented by this paper grew out of a recent study of texture hardening in a(hcp) titanium and zirconium-alloy sheet,&apos; of which part has now been published.2 It was found that, with heating, the tensile plastic-anisotropy index, R,* was decreased from well above 1 towards 1 as the temperature range for the a(hcp) -ß(bcc) phase change was entered. The clearest example of that trend is illustrated with previously unpublished data in Fig. 1. It might have been thought that such a development resulted simply from introduction of the cubic and therefore plastically less anisotropic phase. However, the accompanying change in the index of tensile strain-rate sensitivity, m = a log a/a log E, was rapidly upwards, to a high of 0.85 in some cases (also illustrated in Fig. 1). At the same time, the total tensile elongation rose to a maximum and the flow strength dropped away as R (and m) approached 1. Taken together, the observations cannot be understood as resulting from the presence of cubic phase, per se. It has been concluded instead that they reflect the largely noncrystallographic deformation which characterizes superplasticity. As demonstrated in other recent work? a necessary condition for super-plasticity is strain-rate sensitivity of flow stress sufficiently high that m is above a lower limit of -0.3. The origin of large m has been traced, in turn, to grain size so small that a substantial amount of viscous deformation is introduced by such processes as Nabarro-Herring diffusional flow4 and/or grain boundary shear.5,6 Because of problems in the processing of titanium and zirconium alloys—problems of high strength, limited ductility, and excessive springback, originating largely in slip resistance-it was natural to wonder if something useful might be done with superplasticity in those materials. Therefore experiments were made for more closely identifying and generally bounding the phenomenon with temperature and strain-rate limits, before attempting to decide about its exploitation. The results are being reported here. EXPERIMENTAL Materials. The two of primary interest were the titanium alloys of nominal composition (in wt pct) 5A1-2.5Sn and 6A1-4V. Others were a 4A1-1/4O2 titanium alloy, titanium of commercial purity (RC-70), Zircaloy-4. and Armco iron. All were received as annealed 3/16 in. thick sheet, except RC-70 which was & in. thick, and tested in that condition. Details of transformation temperature and grain size are given in Table I. The results of dilatometry for the measurement of transformation temperatures were unsatisfactory. Data were finally obtained by metallographic examination of each specimen after test, to determine from the amount of transformed 4 where the specimen had been heated in relation to the critical temperatures. Results were in reasonable agreement with information from the supplier. Strip tensile specimens were of full sheet thickness and taken along the rolling direction, except for those

Jan 1, 1968

By H. C. Theuerer

GeC14 may be purified by extraction with HCI and chlorine. The process is as effective for the removal of AsCI:, as the more cumbersome distillation methods usually used for this purpose. GERMANIUM for semiconductor use contains impurities at levels no higher than a few parts in ten million. Material of this quality is obtained from highly purified GeC1, by hydrolysis to the oxide and reduction of the oxide in hydrogen. When purifying GeCl,, AsC1, is the most difficult impurity to remove. This is usually accomplished by multiple distillation procedures.1-3 AsC1, may also be removed from GeC1, by extraction with HC1.1-4 Reducing the arsenic to low concentrations is not practicable, however, because of the large number of extractions needed. This paper discusses a new method for the removal of arsenic from GeC1, by extraction with HC1 and chlorine. The method is rapid, leads to little loss of germanium and is at least as efficient as the distillation procedures currently being used. Theory of Extraction Procedures In the simple extraction of GeC1, with HC1, the following reaction occurs ASCl8G8C1 D AsCl3rc1 at equilibrium CA/Cn= K, where K is the distribution coefficient, and C, and C,, are the molar concentrations of AsC13 in HC1 and GeCl,, respectively. The materials balance equation for this reaction is VACA + vncn = VnC,, where V, and Vn are the volumes of HC1 and GeCl4, respectively, and C, is the initial concentration of AsC13 in GeC1,. From this it can be shown that for multiple extractions where C,, is the concentration of AsC13 in GeC14 after n extractions, and r is the ratio of V, to V,,. It is assumed that r is maintained constant, that equilibrium is established during each extraction, and that K is independent of the AsCl3 concentration. By saturating the system with chlorine, the following reaction occurs in the aqueous phase AsCl3 + 4H2O + Cl2 D H5AsO4 + 5HC1 at equilibrium K&apos; = ------------ ai - a4 h2u - aet2 where a is the activity of the various components. The effect of this reaction is to reduce the concentration of the AsC1, in the aqueous layer and, therefore, to promote further extraction of this component from the GeC1, layer. If the arsenic acid remains entirely in the aqueous phase, the net effect of this reaction is to promote the removal of arsenic from the GeC11. The materials balance equation for extraction with HC1 and chlorine with the foregoing reaction is, then, VaCC + VACA + VACn = VnCo where C,. is the molar concentration of H3AsO, in the HC1. With the added assumptions that the activities of AsC13 and H8ASO4 in the aqueous phase are equal to their molar concentrations, it can be shown that for n extractions Cn/Cu = (1/rkK + rK + 1) n where k - K1 a4h2o - acl2/aoncl. It can be seen by comparing Eqs. 1 and 2 that if k is large, the removal of AsC1, by HC1 extraction will be greatly improved by the addition of chlorine. Dilution of the HCI used in the extraction with chlorine would also favor the separation. This, however, would increase the loss of GeCl,, which is undesirable. Experimental Procedure Germanium prepared from oxide of semiconductor purity is n-type with resistivities greater than one ohm-cm. The resistivity is controlled by the donor concentration, which is —lo-: mol pct. Germanium prepared from material with added arsenic will have lower resistivity commensurate with the arsenic concentration. With such material, at arsenic concentrations above 10-1 mol pct the resistivity is controlled by the added arsenic, and effects due to other impurities initially in the oxide are negligible. In this investigation GeO, of semiconductor purity was converted to GeCl,, and -0.01 mol pct As was added. This material was used for the extraction experiments and the purification attained determined by a comparison of the resistivity data for samples of germanium prepared from the initial and purified GeC1,. A method for calculating the arsenic concentration from the resistivity data is discussed later. The details of the experimental procedures used are as follows: Two hundred and thirty cu cm GeC1, were prepared by the solution of GeO, in HC1, followed by

Jan 1, 1957

By John Chipman, Minu N. Dastur

This paper presents equilibrium data on the reaction of water vapor with vanadium dissolved in liquid iron at 1600°C. The thermo-dynamic behavior of vanadium and oxygen when present together in the melt is discussed. A deoxidation diagram is presented which shows the concentrations and activities of vanadium and oxygen in equilibrium with V209 or FeV2O4. STUDIES of the chemical behavior of oxygen dissolved in pure liquid iron1-3 have served to determine with a fair degree of accuracy the thermody-namic properties of this binary solution. The practical problems of steelmaking, however, involve not the simple binary but ternary and more complex solutions. Only a beginning has been made toward understanding the behavior of such systems. The silicon-manganese-oxygen relationship was studied long ago by Korber and Oelsen4 and more recently by Hilty and Crafts." The carbon-oxygen reaction was investigated by Vacher and Hamilton6 and by Marshall and Chipman.7 A number of deoxidizing reactions have been studied empirica1lys&apos;10 with the object of determining the appropriate "deoxidation constants." The work of Chen and Chipman" afforded a clear-cut view of the effect of the alloy element, chromium, on the thermodynamic activity of oxygen in liquid ternary solutions. These investigators determined the oxygen content of experimental melts which had been brought into equilibrium with a controlled atmosphere of hydrogen and water vapor and were able to show that the presence of chromium decreases the activity coefficient of oxygen. They determined also the conditions under which the two deoxidation products, Cr2O3 and FeCr2O4, were formed and showed that the activity of residual oxygen is considerably less than its percentage. It was the object of this investigation to apply a similar method to the study of molten alloys of iron, vanadium, and oxygen. Vanadium was once considered a moderately potent deoxidizer, but this is now known to be erroneous, in the light of its behavior in steelmaking practice. Its reaction with oxygen retains a certain amount of practical interest in that a high percentage of one element places a limit on the amount of the other that can be retained. As a deoxidizer it will be shown that vanadium lies between chromium and silicon. Experimental Method The apparatus was that used by the authors3 in their study of the equilibrium in the reaction: H2(g) +O = H2O(g);K,= [1] PII., ao Crucibles of Norton alundum or of pure alumina were used. The latter were made in this laboratory and were of high strength and low porosity. Under conditions of use they imparted no significant amount of aluminum (less than 0.01 pct) to the bath. Temperature measurements were made with the optical equipment and calibration chart of Dastur and Gokcen.= The charge was made up of calculated amounts of ferrovanadium (20 pct V) and clean electrolytic iron totaling approximately 70 g. The first few heats were made in alumina crucibles with an insufficient amount of vanadium so that no oxide of vanadium would be precipitated under the particular gas composition. All the heats were made at 1600 °C under a high preheat and with four parts of argon to one part of hydrogen in the gas mixture to prevent thermal diffusion. The rate of gas flow was maintained constant at 250 to 300 ml per min of hydrogen. The time for each heat was three quarters of an hour after the melt had melted and attained the required temperature (1600°C). The water-vapor content of the entrant gas mixture was gradually raised in succeeding heats, keeping the vanadium content of the melt constant. This was controlled by manipulation of saturator temperature. A point was reached when for a given H2O:H2 ratio some of the dissolved vanadium was oxidized and appeared as a thin, bright oxide film on top of the melt. By raising the temperature of the melt it was possible to dissolve the oxide film which reappeared as soon as it was cooled down to 1600°C. The temperature readings taken on the oxide film were consistently higher by 80" to 85 °C as observed by the optical pyrometer. The heat was allowed to come to equilibrium under a partial covering of this oxide film. At the end of the run the power and preheater were shut off and the crucible containing the melt was lowered down into the cooler region in the furnace. This method of quenching proved quite

Jan 1, 1952

By R. M. Waterstrat

The phases occurring in the V-Mn system were studied by means of X-yay diffraction and metallo-paphic techniques, using are-melted alloy specimens annealed in the temperature range 800° to 1150°C and quenched. The bcc solid solution extends at 1250°C all the way from vanadium to 6-manganese. Below 1050°C the a-phase is formed, and the terminal a-manganese phase is stabilized up to about 900°C by vanadium in solid solution. IN the only previous general survey of the V-Mn system Cornelius, Bungardt and Schiedtl reported the existence of three intermediate phases corresponding to the approximate compositions VMn,, VMn, and V5Mn. The phase VMn8 has recently been identified as a o phase2 but the alloy VMn was found to have a bcc structure2 corresponding apparently to the vanadium solid solution rather than to the large cubic unit cell reported by Cornelius et al. 1 Subsequent work by Rostoker and Yamamoto3 has shown that the vanadium-base bcc solid solution extends to at least 15 pct Mn at 900°C. An alloy corresponding to the composition VMn, was examined by Elliott,4 who reported that the as-cast sample as well as samples annealed at 1200o and 1300°C had bcc structures, but that annealing at 1000°, 800") and 600°C produced two phases. One of these phases was apparently the bcc solid solution and the other resembled the o phase structure. Hellawell and Hume-Rothery5 established the phase relationships in manganese-rich alloys above 1000°C, and showed that the o phase in this system is replaced by the 6 Mn (bcc) solid solution at temperatures above 1050°C. These results suggest that a continuous bcc solid solution may exist above 1050°C between vanadium and 6 Mn. The present investigation was undertaken in order to develop more complete information in regard to this system. EXPERIMENTAL METHODS The alloys used in the present work were prepared by arc-melting electrolytic manganese having a minimum purity of 99.9 pct and vanadium lumps with a purity of 99.7 pct. The major impurities present in these metals were carbon, nitrogen, and oxygen and this would account for the small percentage of nonmetallic inclusions observed metal-lographically. The arc-melting was at first performed under a helium atmosphere and it was necessary to keep the melting times as short as possible in order to minimize the loss of manganese by vaporization. It was later found that the evaporation of manganese was considerably reduced when the melting was done under argon atmosphere. The final composition of each alloy was calculated by assuming that the total weight loss during melting was due to evaporation of manganese. Compositions which were calculated in this manner agreed reasonably well with the results of chemical analysis, as shown in Table I. Spectrographic analysis revealed the presence of contamination by tungsten, but in no case was the percentage of tungsten greater then 0.4 at. pct. The specimens were in each case broken in half and the fractured section was examined visually and microscopically for evidence of inhomogeneity. Each specimen was homogenized at temperatures near l100°C, as shown in Table I. After this treatment most specimens consisted of large columnar grains of the bcc vanadium solid solution. The etchant used in most of the metallographic work consisted of 20 pct nitric acid, 20 pct hydro-flouric acid, and 60 pct glycerine. It was found that this etchant would clearly delineate the phases present in these alloys although it does not produce any striking contrast between the phases. For certain manganese-rich alloys, a 1 pct aqueous solution of nitric acid was used. This etchant gave a brown color to the a-manganese phase, whereas the o phase was virtually unattacked and appeared very light as shown in Fig. 1. The etchants used by Cornelius et a1.l were found to produce spurious effects in some of these alloys. In particular, the vanadium-rich alloys etched in hot sulfuric acid often appeared to consist of two phases when both X-ray diffraction and etching with the glycerine-acid mixture indicated the presence of single phase bcc solid solution. A few percent of what appears to be an oxide or nitride phase was found at the grain boundaries and in the interior of the grains, especially in the vanadium-rich alloys. All alloys were annealed in sealed silica tubes containing 1 atm of pure argon and these tubes were then quenched in cold water. Although some manganese loss occurred during annealing, the loss seemed to be confined to the surface of the speci-

Jan 1, 1962

By J. D. Verhoeven

In the past 15 years a considerable amount of experimental and theoretical work has been done concerning the onset of convection in liquids as a result of interm1 density gradients. This work, which has been doue in many different fields, is reviewed here and extended slightly to give a rrlore quantitative understanding to the probletrz of conzection in liquid metal dlffusion experinletzts. In liquid metal systems the capillary reservoir technique is currently used, almost exclusively, to measure diffusion coefficients. In this technique it is necessary that the liquid be stagnant in order to avoid mixing by means of convection currents. Convective mixing may result from: 1) convection produced as a result of the initial immersion of the capillary; 2) convection produced in the region of the capillary mouth as the result of the stirring frequency used to avoid solute buildup in the reservoir near the capillary mouth; 3) convection produced during solidification as a result of the volume change; and 4) convection produced as a result of local density differences within the liquid in the capillary. The first three types of convection have been discussed elsewhere1-a and are only mentioned for completeness here. This work is concerned only with the fourth type of convection. Local density differences will arise within the liquid as a result of either a temperature gradient or a concentration gradient. It is usually, but not always, recognized by those employing the capillary reservoir technique that the top of the capillary should be kept slightly hotter than the bottom and that the light element should be made to migrate downward in order to avoid convection. In the past 15 years a considerable amount of work, both theoretical and experimental, has been done in a number of different fields which bear on this problem. This work is reviewed here and extended slightly in an effort to give a more quantitative understanding of the convective motion produced in vertical capillaries by local density differences. The Stokes-Navier equations for an incompressible fluid of constant viscosity in a gravitational field may be written as: %L + (v?)v = - ?£ + Wv - g£ [1] where F is the velocity, t the time, P the pressure, p the density, v the kinematic viscosity, g the gravitational acceleration, and k a unit vector in the vertical direction. A successful diffusion experiment requires the liquid to be motionless, and under this condition Eq. [I] becomes: where a is the thermal expansion coefficient [a =-(l/po)(dp/d)], a&apos; is a solute expansion coefficient [a&apos; = -(l/po)(dp/d)], and the solute is taken as that component which makes a&apos; a positive number. Combining with Eq. [3] the following restriction is obtained: Since there is no fixed relation between VT and VC in a binary diffusion experiment, Eq. [5] shows that the condition of fluid motionlessness requires both the temperature gradient and the concentration gradient to be vertically directed. Given this condition of a density gradient in the vertical direction only, it is obvious that, as this vertical density gradient increases from negative to positive values, the motionless liquid will eventually become unstable and convective movement will begin. The classical treatment of this type of instability problem was given by aleih&apos; in 1916 for the case of a thin fluid film of infinite horizontal extent; and a very comprehensive text has recently been written on the subject by handrasekhar.&apos; It is found that convective motion does not begin until a dimensionless number involving the density gradient exceeds a certain critical value. This dimensionless number is generally referred to as the Rayleigh number, R, and it is equal to the product of the Prandtl and Grashof numbers. For the sake of clarity a distinction will be made between two types of free convection produced by internal density gradients. In the first case a density gradient is present in the vertical direction only, and, since the convection begins only after a critical gradient is attained, this case will be called threshold convection. In the second case a horizontal density gradient is present and in this case a finite convection velocity is produced by a finite density gradient so that it will be termed thresholdless convection. Some experimentalists have performed diffusion experiments using capillaries which were placed in a horizontal or inclined position in order to avoid convection. These positions do put the small capillary dimension in the vertical direction and, consequently, they would be less prone to threshold convection than the vertical position. However, if the diffusion process produced a density variation, as it usually does, it would not be theoretically possible to avoid thresh-

Jan 1, 1969

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970

By J. P. Zannaras

Referring to the article by R. J. Charles and P. L. de Bruyn, let us assume that W = weight of glass bar; P = weight of hammer; e = total deformation; K = unit of deformation; K = potential stress energy; E = modulus of elasticity; L = length of the bar; 7 = coefficient of inertia; h = height, ft; V = velocity, fps; and a = cross section area. The portion of kinetic energy which is effective in producing stress energy in a fixed bar struck horizontally is given by the formula" 1 + 1/3 W/P K =1+1/3w/p/(1+1/2w/p)2 P.V2/2g = Ph where 1 + 1/3 W/P ? (1 + 3W/P/(1=1/2w/p)2 [8] Putting e e = W/P =------------ From the above equation it can be seen that the maximum transfer of kinetic energy to stress energy is when e = 0 or W/P = 0 which indicates that the weight of the hammer must be very large as compared with the weight of the impacted rod. Eq. 8 diametrically opposes the conclusions reached by the authors of this article. In fact, if their suggestions were followed to the extreme when e = co when P = 0, there would be no transfer of kinetic energy to stress energy at all, as 7, becomes zero. Eq. 8 presumes that the velocity with which the stress is propagated through the bar is infinite, whereas the authors claim that the compression waves reflected are reaching the struck end of the bar prior to the complete transfer of the kinetic energy to cause such modification of the conditions there as to make them reach the reverse conclusions demonstrated by the above formula. That such interference exists is unquestionably demonstrated by the authors and others. However, if my observations are correct, such interference for this specific experiment and also for practical comminu- tion is insignificant, and the conclusions of the authors are in error and must be reversed to comply with Eq. 8. Eq. 5, w. = AE 2/2, given by the authors on page 51, is derived from the following equation (Eq. 9): K = 1/2Pe, where P = Sa, S = ?E, e = EL, and L = 1. The above formula, Eq. 9, cannot be applied in this case. This formula is applicable for static loads where the load increases from zero up to its final value, P, in such a way that the deformation at different instants is proportional to the loads acting at those instants and actually represents the area of a right triangle in the strain load diagram of base e and height P. The typical photographs shown in Figs. 3 and 4 represent the familiar strain load diagrams, and since the line of the wave marks the existence and intensity of the strain with the unquestionable conclusion that such strain has been caused by the action of a load acting continuously all along the wave until it reached the horizontal axis, the work stored at this point is represented by the area under the wave line and the horizontal axis and not by the area of the fictitious triangle given by the authors. Then if this is correct, even visual estimation of these areas at gage stations given in the typical photographs of Figs. 3 and 4 suffice to contradict the authors&apos; calculation given in Figs. 6a and 6b and Figs. 7a and 7b. The typical photographs presented by Charles and de Bruyn show a considerable variation of the intensity of the strain at different stations but very small variation of areas which actually represent the stress energy at the corresponding stations. And, apparently, by squaring the small quantities, the authors magnified their error tenfold. J. M. Frankland&apos;s paperV iscusses the relative strain intensity and not the total energy for different types of impact loading. He states in his paper, "The reader is explicitly warned not to confuse the results in this report with those obtained when the load is applied by a blow as from a hammer. In this case the peak load rises to very large but mostly unknown values. The accompanying large deflections and stresses are the result of high values of P, not of the dynamic load factor n. According to Frankland "the dynamic load factor" is the numerical maximum of the response factor. It therefore appears that the authors followed the same procedure in obtaining the relative strain energy ab-

Jan 1, 1957

By J. U. Messenger

A technique is described whereby the resistance of an emudian to breaking can be quantitatively determined. Produced ailfield emulsions are usually the water-in-oil type and, accordingly, do not conduct an electrical current. However, there is a threshold of A-C voltage pressure above which an emulsion will break and current will flow. The more stable an emulsion, the higher the required voltage. A Fann Emulsion Tester, modified so that low voltages (0 to 10 v) can be accurately measured, is suitable. This technique has application in evaluating the effect of a demuksifier on the stability of an emulsion. Emulsions can, in essence, be titrated with demulsifiers by adding a quuntity of demulsifier, stirring, and measuring the voltage required to cause current to flow. Any synergistic effect of two or more materials added simultaneously can be followed accurately. A demulsifier that significantly lowers the threshold voltage (from 100 to 400 v to 0 to 10 v for the emulsions in this study) is effective and can cause the enlulsion to break. A demulsifier that will bring about this drop in the threshold voltage at low concentration ir very desirable. The technique is also well adapted for rapidly screening demulsifiers. INTRODUCTION Stable emulsions in produced reservoir fluids resulting from certain well stimulation and completion procedures are common problems. The use of suitable demulsifiers can often mitigate these difficulties. At the present time, a rapid and efficient method for selecting satisfactory demulsifiers is not available. It is badly needed. Reliance is now placed primarily on trial-and-error procedures. A new test method has been developed which permits a more rapid and precise selection of demulsifiers. It involves measuring the electrical stability potential of an emulsion before and after a demulsifier has been added. This paper describes this method and shows where it should have application in field emulsion problems. NATURE OF OILFIELD EMULSIONS Two immiscible components must be present for an emuhion to form; we are concerned here with crude oil and water. An emulsifier must be present for tin emulsion to be stable. J Emulsifiers can be substances which are soluble in oil and /or mter and which lower interfacial tension. They can be colloidal solids such as bentonite, carbon, graphite, or asphalt which collect at the interface and are preferentially wet by one of these phases. Unrefined crude oils can contain both types of emulsifiers, A popular theory is that, of the two phases in an emulsion, the dispersed phase will be the one contributing most to the interfacial tension.&apos; Usually this phase contains the least amount of emulsifier. The stability of a water-in-oil emulsion is affected by the fol1owing: l) viscosity; (2) particle or droplet size; (3) interfacial tension between the phases; (4) phase-volume ratios; and (5) the difference in density between the phases. A stable emulsion is usually characterized by high-viscosity, small droplets, low interfacial tensions, small differences in density between its phases, and slow separatian of the phases. It also has low conductivity (high electrical stability potential). Water-in-oil and oil-in-water emulsions"&apos; are both common; however, oil field emulsions are predominantly water-in-oil emulsions. The emulsions which commonly occur during oompletion and stimulation operations contain a combination of several of the following: acids, fracturing fluids (oil, water, acid), and formation water and oil. Produced emulsions usually contain formation water and oil. Emulsions form in oil wells because oil and water are mixed together at a high rate of shear in the presence of a naturally occurring or unavoidably produced emulsifier. During the completion and stimulation of productive zones, and while formation fluids are being produced, oil and water are very often commingled. These mixtures are formed into emulsions by agitation which occurs when the fluids are pumped from the surface into the matrix of the formation or produced through the formation to the surface. Restrictions to flow (such as perforations, pumps, and chokes)".&apos;" increase the level of agitation; tight emulsions are more likely to form under these conditions. Often an emulsified droplet is an emulsion itself.&apos;" Therefore, emulsion-breaking problems can be quite complex. The complexity can be even greater if a third phase (gas) is included. Demulsifiers operate by tending to reverse the form of the emulsion. During this process, droplets of water become bigger, viscosity is lowered, color becomes darker, separation of the phases faster and electrical stability potential approaches zero. Any of these effects could be followed as a means of determining emulsion stability. However, electrical stability potential is the most reproducible and most easily measured parameter for following the stability of a water-in-oil emulsion.

Jan 1, 1966

ABOUT 2 lb. of alumina (aluminum oxide) of high purity is required to produce a pound of metallic aluminum. Projected production of metallic aluminum in the United States is now seven to ten times the peacetime rate a few years ago. In the past, all the alumina for aluminum production in the United States has been obtained from bauxite. Part of the bauxite was mined in the United States--chiefly in Arkansas-and part was imported from Surinam. All of it was chemically treated in the United States to separate the greater part of the aluminum oxide from the bauxite, alkaline solutions being used, in a method known as the Bayer process. The ingredients of the bauxite other than alumina, such as the compounds of iron titanium, and silicon, constitute the tailings from the Bayer-process operation. This product contains sufficient iron to give it a red color and hence it is called "red mud." Lime and soda used in the processing, are also present. Varying amounts of alumina remain in the red mud, depending upon the characteristics of the bauxite, the effectiveness of the treatment, and in particular upon the amount of silica originally present in the bauxite. High-silica bauxites result in high alumina loss in the red mud.

Jan 1, 1942

By Franklin H. Sharp, Kenneth L. Clifford

During the last few years the New Lead Belt of Southeastern Missouri has become the main source of lead in the United States. It also produces significant amounts of zinc, copper and silver. The mines are located on a narrow, mineralized trend extending southward from Viburnum, MG. for about 35 miles. The ore occurs as replacement deposits in the Bonneterre lime- stone formation which is about 1000 ft below the surface. In most of the mines, enough water is produced to supply the milling requirements without any reuse. There are dry areas, however, and at least two mills must rely on water reclaimed from their tailings lake to augment the mine water. These mills have no choice but to utilize recycled mill water.

Jan 7, 1973

By A. M. Skov, L. F. Elkins

Inclusion of anisotropic permeability in mathematical analysis of pressure transients observed during development of the huge Spraberry field indicates a major fracture trend which is in good agreement with that observed by fluid-injection tests spread over a 12- by 17-mile area. Delineation of this trend is important in selecting a pattern of injection for the pending large-scale water flooding in this field. Determination of reservoir parameters yielding best agreement between calculated pressures and observed reservoir pressures in newly completed wells was made using an IBM 650 computer. INTRODUCTION The Spraberry field covering 400,000 acres is a tight sand of less than 1-md permeability cut by an extensive system of vertical fractures. Primary recovery dominated by capillary retention of oil in the fractured sand matrix blocks is less than 10 per cent of oil in place. Strong forces of capillary imbibition of water into the sand, coupled with water flow under dynamic pressure gradient, indicate considerable increase in oil recovery can be achieved through water flooding. Best results will occur if the pattern of water injection is selected to force the water flow across the grain of the major fracture system. Existence of an oriented vertical fracture system in the Spraberry, observed first in cores, was highlighted more recently by the 144-fold contrast in permeability along and at right angles to the major fracture trend required to match relative water breakthrough times in Humble Oil & Refining Co.&apos;s waterflood test there. Spraberry operators since have conducted two gas-injection tracer tests for further areal confirmation of the fracture trend. Re-analysis of early reservoir pressure transients for evidence of anisotropic permeability has permitted many more local determinations of major fracture trend without resort to further field tests. This paper is limited to updating analysis of reservoir pressure transients to include anisotropic permeability as a test for orientation of the major fracture trend in the Spraberry. The reader is referred to Refs. 1 and 2 for information about general Spraberry reservoir performance and to Refs. 3 and 4 for information about significance of fracture orientation in selection of the injection-well pattern for water flooding the Spraberry. RESERVOIR PRESSURE DATA—DRIVER AREA During early development of the Spraberry Driver area, Sohio Petroleum Co. made the extra effort to measure the initial pressure in each of the 71 wells in a 5-mile-long area immediately after completion. Progressively greater reductions in pressure ranging up to 400 psi were observed throughout the six-month development period. Detailed data are presented in Ref. 1. Since the reservoir oil was undersaturated some 300 psi initially, early reservoir performance involving 55 new well pressures is subject to analysis as flow of a single compressible fluid in a porous media. Assumption of uniform permeability in all directions yielded good agreement between calculated pressures and observed pressures of these wells in the earlier study,&apos; but subsequent, additional, mathematical development to include anisotropic permeability in the transient pressure considerations and present availability of electronic computers to perform the much more extensive arithmetical calculations now yield even better agreement. The previous analysis, assuming uniform permeability, consisted essentially of calculating pressure reduction expanding circularly around each producing well and summing these effects at the time and location of each newly completed well for comparison with the measured pressure reduction. Permeability, effective fluid and rock compressibility, and permeability X thickness were varied until the best match with measured pressures was obtained. The present analysis, assuming anisotropic

By P. Duwez, C. B. Jordan

The phenomenon of the change of volume of pressed powder compacts upon sintering is well known in the field of powder metallurgy. Depending upon the metal or metals involved and the pressure used in forming, a compact may, in the course of time of sintering at a given temperature, expand mono-tonically, contract monotonically, or first show a volume change of one sign followed by a change of the opposite sign. It is clearly desirable to have accurate knowledge of the magnitude and sign of the change in dimensions to be expected in any given case, both from the point of view of direct usefulness in the fabrication of parts by powder metallurgy, and from the longer range viewpoint of elucidating the fundamental mechanism of metallic sintering. The present study was therefore undertaken as a first step in acquiring systematic and reasonably quantitative knowledge of the change in density of metal powder compacts during sintering. For practical reasons, copper was selected as the material to be studied first, and its densification followed as a function of temperature and time of sintering in hydrogen and in vacuum. Experimental Procedure The copper powder used was that designated by the manufacturer (Metals Disintegrating Co., Elizabeth, N. J.) as MD-151. This powder was sifted through Tyler standard screens to separate the fraction having particle size range between 200 mesh and 325 mesh, and this fraction was used in all the subsequent work. Compacts weighing about 10 g were then pressed in a 1 in. diam round die, using a pressure of 20,000 psi throughout. Sintering was carried out in commercially built electric furnaces in which the resistance windings are so disposed as to produce a nearly uniform temperature along the axis of the furnace for a length of about 18 in. centrally located. In order to be able to sinter in a controlled atmosphere, a 2 in. stainless steel tubing was inserted in the furnace. Each end of the tube was cooled by a water jacket about 7 in. long, and closed with a rubber stopper. The hydrogen used for one series of specimens was purified as described in Ref. 1. For the other set, a pressure of about 0.5 mm Hg was maintained during sintering by a Welch Duo-Seal Pump. The specimens were heated on square trays made of stainless steel. In placing specimens in the trays, a thin even layer of powdered aluminum oxide was first sprinkled on the bottom of the tray. A copper guard disk about half the thickness of the specimen was then placed in the tray and covered with a second layer of alumina. The actual specimen was then set on the guard disk, and a final coat of alumina sprinkled over the specimen. This technique was evolved for sintering the specimens in such a way as to reduce the influence of unknown extraneous factors to a minimum. If the specimen is placed directly on the tray and sintered, it is found that the resulting shape is that of a frustum of a cone, rather than a section of a right circular cylinder, since friction with the tray prevents the bottom of the specimen from contracting at the same rate as the top. In the arrangement used in these experiments, the guard disk provided a support which shrank at the same rate as the specimen, and the alumina powder reduced to a minimum friction between guard disk and tray, and between specimen and guard disk. The procedure followed in sintering consisted of bringing the furnace to the required temperature, and then inserting the specimen into the central heated portion of the furnace tube in one of the two atmospheres used. At the end of the heating period, the specimen was cooled by bringing it into a portion of the furnace surrounded by a water jacket. These manipulations were carried out without opening the furnace, by means of rods which were attached to the trays and operated through a sliding seal in the rubber stopper. The progress of densification of the copper compacts was studied at 1300, 1400, 1500, 1600, 1700, and 1800°F. At each of these temperatures, a specimen was allowed to sinter for each of the following time intervals: M, 1, 2, 4, 8, 16, 32, and 64 hr. The thickness and diameter of each specimen were measured with micrometers before and after sintering, and each was weighed on an analytical balance after sintering. Results The techniques described in the preceding section were found to give satisfactory results. The specimens were not detectibly warped after sintering, and were usually of uniform diameter (that is, truly round) to within 0.001 in., a very few showing a variation in diameter of ±0.002 in. All specimens were found to have the same diameter

Jan 1, 1950

By F. B. Plummer

GEOLOGICAL engineering as applied to oil fields, or production geology as some prefer to designate the profession, is designed to fill in the border line between pure geology and pure petroleum engineering. Therefore the production geologist may, and frequently does, reach out to grasp much in both professions. Where once the oil geologist was content to pick samples out of a mud ditch and try to identify oil formations from the color or appearance of flakes of rock bailed out of a well, now he has to deal with graphic electrical logs obtained by intricate and highly technical electrical apparatus and to make exact determinations to the fraction of an inch of the depth and thickness of an oil sand 2 miles below the surface.

Jan 1, 1944

By C. A. Stetefeldt

Jan 1, 1892

By Cleveland Meeting

Jan 1, 1945

Jan 1, 1934

By S. A., Taylor

IT is very difficult to arrive at exact figures for the cost of maintaining excess capacity of coal mines, but we can approximate the various items. To do this, I will take the Pittsburgh district of Pennsylvania and the other districts can be compared to this one. I believe we can take the depreciation item of plant ac- count as a whole and discount it over a period of 20 years; while this is high for some items it is low for others and I believe it is not far from a safe basis. This equals 5 per cent per year, and this depreciation will take place about as rapidly when not in use as when in operation. A fair value in the Pittsburgh district to- day for plant and houses is close to $4 per ton per annum. At 5 per cent this will equal 20 cents per ton per year. The item of keeping the mine in condition, free from water, etc., will be close to an average of 2y2 cents per ton per annum.

Jan 1, 1928