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By C. F. Jr. Tolman

IN February 1913, Prof. L. C. Graton and Dr. Joseph Murdoch1 presented to the American Institute of Mining Engineers a notable contribution to economic geology under the title The Sulphide Ores of Copper. The value of the work was recognized by mine operators, and Mr. Graton was assisted in his plan to extend his investigations,. by the organization of a commission to undertake a "secondary enrichment investigation." In this work lie secured the cooperation of the Geophysical Laboratory of the Carnegie Institution of Washington. Their report 2 on the chemical phases of the investigation has just been published. Incidental to investigations 3 carried on in my laboratory by advanced

Jan 2, 1916

By Henry Howe

1. Introduction.-This paper is based in large part on the examination of two rings, shown in section in Fig. 4 to 15, cut from an eroded 14-in. (35.56-cm.) gun, liner, and containing, according to Booth, Garrett, & Blair: Carbon, 0.380 per cent.; manganese, 0.655 per cent.; nickel, 2.810 per cent.; vanadium, 0; chromium, a few hundredths of 1 per cent.; tungsten, 0; molybdenum, 0. These rings were received from Admiral Joseph Strauss, then Chief of Ordnance, U. S. Navy, through the kindness of Mr. Hudson Maxim, Chairman of the Committee on Ordnance and Explosives,, of the U. S. Naval Consulting Board.

Jan 2, 1918

By C. F. Tolman

In February 1913, Prof. L. C. Graton and Dr. Joseph Murdochl presented to the American Institute of Mining Engineers a notable contribution to economic geology under the title The Sulphide Ores of Copper. The value of the work was recognized by mine operators, and Mr. Graton was assisted in his plan to extend his investigations, by the organization of a commission to undertake a "secondary enrichment investigation." In this work he secured the cooperation of the Geophysical Laboratory of the Carnegie Institution of Washington. The report2 on the chemical phascs of the investigation has just been published. Incidental to investigations3 carried on in our laboratory of Economic

Jan 1, 1916

A filled stope is one in which the support for walls and men and, at times, for the back of ore, is furnished by waste rock or sand tailings. The filling may be rock sorted out in the stope or from the walls, develop-ent, or the surface. The orebody is mined in sections, each practically an open or timbered stope, filled wholly or in part before adjacent ground is attacked. As a rule, the filled-stope method is limited to overhand flat-back, stepped-face, or rill stopes. The examples given are Copper Range, Iron Cap, Verde district, Zaruma district, Lucky Tiger, and Silver King Coalition.

Jan 1, 1925

By T. Cantwell, N. C. Rasmussen, H. E. Hawkes

Beryl is a mineral that may be difficult to distinguish from quartz by casual field inspection. The easily recognized green color and hexagonal crystal form of coarse-grained beryl are by no means universal, even in beryl from pegmatitic deposits. If it occurred as a fine-grained accessory mineral in an igneous rock, it would almost certainly escape detection unless samples were submitted for petrographic or chemical analysis. There may be substantial deposits of some beryllium mineral, other than beryl, that has been overlooked because that mineral also closely resembles the common rock-forming minerals. A reliable and simple method of identifying beryllium minerals and determining the beryllium content of a rock would be helpful in exploration. This article describes preliminary experiments in applying nuclear reaction to the qualitative identification of beryl and to the semiquantitative determination of the beryllium content of rock samples. Gaudin,1,2 the first to apply a nuclear reaction in detecting beryllium minerals, developed a method that irradiates the sample with gamma rays, which react with beryllium nuclei to produce neutrons. The neutrons are then measured with standard equipment. The cross section for this reaction is about 1 millibarn. The cross section is a measure of the probability that a reaction will take place, for example, between a beryllium nucleus and an incident gamma ray or alpha particles.3-5 At 1-millibarn cross section for the reaction, satisfactory performance required a source strength of the order of 1 curie (3.7 x 10"' disintegrations per sec, where each disintegration releases one or more gamma rays). The reactions will not take place if the gamma radiation is below a minimum energy, in this case 1.63 mev. The size of the source and the energy of the radiation made heavy shielding necessary for these experiments, both to reduce the background count of the neutron counter and to safeguard personnel. The original discovery of the neutron by Chad-wick in 1932 resulted from experiments with another nuclear reaction, induced by bombarding beryllium with alpha particles in which the products are carbon-12 and neutrons. The equation for this reaction is as follows:' " ,Be" + ,He'? 6C12 + 8,n' [1] re-particle neutron In the above nuclear equation (Eq. 1), the sub- script number indicates the number of protons in the nucleus (the atomic number) and the superscript the total number of neutrons and protons (approximately the atomic mass). For the alpha-neutron reaction the cross section is about 250 milli-barns, or 250 times that of the gamma-neutron reaction used by Gaudin. The positively charged alpha particle is repelled by the positive charge of the beryllium nucleus; it must, therefore, have a certain minimum energy in order to approach close enough to the beryllium nucleus to react. For reaction with the beryllium nucleus, the lower limit of the alpha-particle energy is 3.7 mev. The alpha-neutron reaction, with polonium-210 as an alpha source, was selected for the present experiments. Alpha particles are emitted by polonium-210 at 5.30 mev, which is adequate for the reaction with beryllium. Furthermore, this isotope of polonium emits alpha particles with negligible associated gamma radiation, thus eliminating the necessity of shielding. The half-life of polonium-210 is 138 days. Inasmuch as alpha particles carry a possible charge and are large compared with most nuclear particles, their energy is rapidly dissipated in passing through matter. Their range in standard air is 3.66 cm,3 and they penetrate only a few tens of microns into a mineral sample. The short range in air can be minimized by preparation of a flat sample surface that can be brought very close to the alpha source during analysis. On the other hand, short range of alpha particles in air lessens the radiological health hazard and makes it possible to use this method without shielding. It must be emphasized, however, that the alpha emitters are potentially very dangerous if they enter the human body. Polonium must be handled with extreme caution. The literature has reported experiments on the yield of neutrons from reaction of alpha particles with beryllium nuclei. Feld" reports that in intimate mixtures of polonium and beryllium, 3 x 106 eutrons per sec are produced per curie of polonium. Elsewhere in the same reference it is stated that a sandwich-type source yields about one third as many neutrons as an intimate mixture. A table of neutron yields for full energy polonium alpha-particles on thick targets as reported by Anderson7 is the basis of Table I. From Table I it can be deduced that the elements most likely to interfere, i.e., those that also produce neutrons when bombarded by alpha particles, are boron and fluorine. These data also show that it will probably not be possible to determine very small quantities of beryllium in rocks because of the masking effects of the major elements, sodium, magnesium, and aluminum. The neutrons emitted in the alpha reaction are detected by another nuclear reaction. Either of the

Jan 1, 1960

By O. Mellgren, A. M. Gaudin, P. L. De Bruyn

The adsorption density of ethyl xanthate on pyrite was determined as a function of xanthate concentration. Surface preparation of the mineral appears to have asafunctionsome effect on the subsequent adsorption process, A monolayer of xanthate on the surface is exceeded only in presence of oxygen. The effect of OH- , HS- (and x and CN- S=)and on the amount of xanthate adsorbed was investigated. Competition between OH- and X- (xanthate) ions for specific adsorption sites is indicated over a wide pH range. IN the flotation of sulfide ores, xanthates are most commonly used to prepare the surface of the mineral to be floated so that attachment to air takes place. The quantity of agent required to make the mineral hydrophobic is usually very small, of the order of 0.1 to 0.25 lb per ton of mineral. Details of the mechanism of pyrite collection are for the most part unsettled. Adsorption of collector has long been believed to involve an ion exchange mechanism as demonstrated for galena' and for chalcocite.2 In the work on chal-cocite it was also demonstrated that a film of xanthate radicals unleachable in solvents that dissolve alkali xanthates, copper xanthate, or dixanthogen was formed at the surface of the mineral. The unleachable product increased with increasing addition of xanthate up to a maximum corresponding to an oriented monolayer of xanthate radicals. Pyrite is extremely floatable with xanthate if its surface is fresh.9 ut the floatability decreases rapidly as oxide coatings increase in abundance. Pyrite shows zero contact angle when in contact with ethyl xanthate solution at pH higher than about 10.5;4 at neutrality, a contact angle of 60" is obtained at a reagent concentration of 25 mg per liter. Alkali sulfides and cyanides are pyrite depressants. In this study of pyrite collection the writers have sought to relate measured xanthate adsorption to the method used in preparing pyrite, to the presence or absence of oxygen, to concentration of hydroxyl, hydrosulfide, sulfide, and cyanide ions. The principal experimental tool has been radioanalysis," " using xanthatcx marked with sulfur 35. Experimental Materials Pyrite: Unlike most sulfides, pyrite is a poly-sulfide. The structure given by Bragg7 resembles that of sodium chloride, the iron atoms corresponding to the position of sodium and pairs of sulfur atoms corresponding to the position of chlorine. The edge of the unit cell in pyrite is 5.40 A and in halite 5.63 A. The S-S distance in pyrite is 2.10 A; the Fe-S distance, 3.50 A: and the Fe-Fe distance, 3.82 A. Natural pyrite from Park City, Utah, was used in this investigation. Pyrite 1 was obtained by hand picking pure crystals. Pyrite 2 and Pyrite 3 were obtained from finer textured crystalline material containing inclusions of silicates. The same cleaning technique was utilized for the preparation of Pyrite 2 and Pyrite 3, whereas a different cleaning technique was used for Pyrite 1. Pyrite 1 was prepared as follows: The crystals were ground in a porcelain ball mill and the 200/400 mesh fraction was separated by wet screening with distilled water, followed by washing for 1 hr with deoxygenated distilled water acidified with sulfuric acid to pH 1.5. The acid was removed by rinsing with deoxygenated distilled water on a filter until a pH of 6.0 was reached in the effluent. This filtration was carried out under nitrogen. The sample was then dried in a desiccator under nitrogen. The period of time for which this pyrite sample was in contact with water containing oxygen was about 4 hr. The specific surface as determined by the BET gas adsorption method was 582 cm2 per g. Final material assayed 53.12 pct sulfur and 46.5 pct iron (theoretical, for FeS,: S, 53.45 pct; Fe, 46.55 pct). After crushing, Pyrite 2 and Pyrite 3 were washed with 1 M HCl. rinsed, and fed to a laboratory shakinq table to remove the small amount of silicates. The concentrate obtained was ground in a laboratory steel ball mill. The 200/400 mesh fraction was separated by classification in a Richards hindered settling tube. This fraction was then given a final wash with 0.1 M HCl and deoxygenated water was filtered through the sample. The final effluent showed a conductivity equivalent to that of a solution having a salt concentration of 0.3 ppm. Aqueous hydrogen sulfide solution was then added to the sampln (about 100 ml saturated H,S solution to about 1000 g pyrite under a few hundred milliliters of water) which was stored wet under nitrogen. The sample stored in this manner showed no indication of formation of iron oxides, whereas iron oxides appeared

Jan 1, 1957

By Carrol M. Beeson

Reasons are given for using a Boyle's-law porosimeter in conducting core analysis for either routine or research purposes. Among other things, it is pointed out that such a porosimeter permits the measurement of all basic properties on the same sample, thereby eliminating the sources of error inherent in the use of adjacent samples. References are made to investigations of gas adsorption on various porous materials, to show that the use of helium in Boyle's-law porosimeters reduces to negligible proportions the error due to the adsorption or desorption of the operating gas. Two Boyle's-law instruments are described. which permit accurate and rapid measurements of porosity. Schematic sketches and explanation:; are included, along with derivations of equations required in performing precise determinations. Summaries of data obtained during calibration are tabulated and analyses of the data are resented as indications of the precision and accuracy of each device. Comparisons are also shown for measurements made with each of the instruments on the same test pieces and cores. INTRODUCTION An accurate porosimeter, operating on the principle of Boyle's law. is of considerable value in the analysis of cores for either routine or research purposes. This is due primarily to the fact that the measurement of porosity with such an instrument leaves the sample free of contamination by any liquid. When used in conjunction with an extraction apparatus' for determining oil and water saturations, a Boyle's-law porosimeter permits the measurement of all basic properties on the same sample. This eliminates the sources of error inherent in the use of adjacent samples, or the necessity of determining porosity after all other properties have been obtained. Large errors may result from combining measurements made on adjacent samples in order to obtain a single property. This type of error is definitely involved when oil and water are measured with one sample, and the pore vo1ume is measured with an adjacent one. Furthermore, the source of error would be present to some extent, even if the analyst could choose the samples so they were truly adjacent from a geological standpoint. The use of adjacent samples in routine core analysis also necessarily decreases the probability of correlating core properties. For example, the chance of correlating the "irreducible" interstitial-water saturation with permeability, is bound to be greatly reduced by measuring these properties on "adjacent" samples. For research purposes, amplification is scarcely required concerning the greater flexibility of a method for measuring porosity which leaves the core free of contamination by any liquid. Even under those circumstances which require that the core be saturated with a liquid, a previous measurement of porosity with a gas is useful in determining the degree of saturation that has been attained in the process. Furthermore, for comparable accuracy, porosity usually may be determined more rapidly with a gas than with a liquid. This advantage of the Boyle's-law instrument is most outstanding when the determination time is compared with that required in obtaining porosity by evacuation of the core followed by saturation with a liquid of known density. Several porosimeters which operate on the principle of Boyle's law have been described2,3,4,5,6,7 in the literature. No comparison will be attempted between those instruments and the ones described herein. Before helium gas became readily available, Boyle's-law porosimeters were subject to an appreciable error due to the adsorption of the operating gas on the surface of the core solids. There is considerable direct and indirect evidence in the literature to support the contention that the adsorption of helium on porous solids is negligible at room temperature. In discussing the use of Boyle's-law porosimeters, Washburn and Bunting2 stated that "for most ceramic bodies dry air is a satisfactory gas, but hydrogen will be required in some instances. Helium could, of course, be employed for all types of porous materials at room temperatures or above." Howard and Hulett8 obtained evidence that the adsorption of helium was negligible at room temperatures, even on activated carbon ; for the density measured with this gas was unaffected by changes in pressure or by changes in temperature from 25 °C to 75 °C. For oil-well cores, Taliaferro, Johnson, and Dewees" obtained lower porosities with helium than with air, but apparently did not study helium adsorption. From the work of these investigators, it follows that the use of helium in Boyle's-law porosimeters reduces the error due to gas adsorption to negligible proportions. This makes it possible to construct instruments which permit the determination of porosity with (1) a high degree of accuracy, (2) with great rapidity, and (3) without contamination. THE KOBE POROSIMETER The fundamental design of the Kobe Porosimeter was developed by Kobe, Inc., which firm built about 12 of the instruments during 1936 and 1937. Since that time, seven or eight more have been constructed with their permission, making a total of about 20 that have been put into operation.

Jan 1, 1950

By Francis Collins, E. R. Brownscombe

A study has been made of the material balance-fluid flow method of estimating reserves and degree of water drive from pressure and production history data. By considering the effect of random pressure errors it is shown that in a particular example a standard deviation of three and one-half pounds in each of ten pressure survey? permits the determination of the reserves with a standard deviation of 8 per cent and the water drive with a standard deviation of 15 per cent, assuming that certain basic geologic data are correct. It is believed that this method of estimating reserves and water drive is useful and reliable in a number of cases. The method is particularly valuable when reservoir pressure data are accurate within a very few pounds, but may also be applied with less accurate pressure data if a relatively large reservoir pressure decline occurs early in the life of the field, as for example in an under-saturated oil field. INTRODUCTION A knowledge of the magnitude of reserves and degree of water drive present in any newly discovered petroleum reservoir is necessary to early application of proper production practices. A number of investigators have contributed to methods of relating reserves, degree of water drive, and production and pressure history. 1-8 Three types of problems of increasing complexity may be mentioned. If a reservoir is known to have no water drive. and if the ratio of the volume of the reservoir occupied by gas to the volume of the reservoir occupied by oil (which ratio permits fixing the overall compressibility of the reservoir) is known, then only one further extensive reservoir property remains to be determined, namely the magnitude of the reserves. A straightforward application of material balance considerations will permit this determination. The problem becomes very much more difficult if we wish to determine not only the magnitude of the reserves but also the magnitude of water drive, if any, which is present. In principle, a combination of material balance and fluid flow considerations will permit this evaluation. Finally, if neither the magnitude of reserves, the degree of water drive, nor the ratio of oil to gas present in the reservoir is known and it is desired to determine all three of these variables, the problem could in principle be solved by a fluid flow-material balance analysis which determines the overall compressibility of the reservoir at various points in its history. The change in compressibility with pressure would provide a means of determining the ratio of gas to liquid present, since the compressibilities of gas and liquid vary differently with pressure variation. However, in practice this problem is probably so difficult as to defy solution in terms of basic data precision apt to be available.' It is the purpose of this discussion to illustrate the second case, which involves the determination of two unknown variables, single phase reserves and degree of water drive, from pressure and production history and fluid property data, and to study the precision with which these unknowns can be determined in this manner in a particular case. Although an electric analyzer developed by Bruce as used in making the calculations to be described, numerical methods necessary in carrying out the process have been devised and have been applied for this purpose. Schilthuis,' for example, developed a comprehensive equation for the material balance in a reservoir. He combined this with a simplified water drive equation, assuming that the ratio of free gas to oil was fixed by geological data and that a period of constant pressure operation at constant rate of production was available to determine the constant for his water drive equation. On this basis he was able to compute the reserves and predict the future pressure history of the reservoir. Hurst developed a generalized equation permitting the calculation of the water drive by unsteady state expansion from a finite aquifer. He showed in a specific case how the water influx calculated by his equation, using basic geologic and reservoir data to fix the constants, matched the water influx required by material balance considerations. Old3 illustrated the simultaneous use of Schilthuis' material balance equation and Hurst's fluid flow equation for the determination of the magnitude of reserves and a water drive parameter from pressure and production history. He used this method to calculate the future pressure history of the reservoir under assumed operating conditions. As a basis for determining reserves, Old assumed a value for his water drive parameter and calculated a set of values for the reserves, using the initial reservoir pressure and each successive measured pressure. The sum of the absolute values of the deviations of the resulting reserve numbers from their mean value was taken as a criterion of the closeness of fit to the experimental data possible with the water drive parameter assumed. New values of the water drive parameter were then assumed and new sets of the reserves calculated until a set of reserves numbers having a minimum deviation from the average was established. The average value of- the re-

Jan 1, 1949

By Eugene F. Broome, Hugh A. Walls

A diffusion measurement technique based on a shear cell comprised of only two segments is described. The diffusion boundary value problem for the finite capillary geometry is solved in general for any arbitrary initial concentration profile and is subsequently specialized for the modified shear cell problem. Effects of convection and mixing at the shear interface were found to be negligible. Mercury self-diffusion coefficients were determined from -25° to 252°C. These data are in good agreement with those found by Meyer. ALTHOUGH diffusion in liquid metals has been of interest for over two centuries, the need for measurement techniques of improved accuracy and precision has become increasingly apparent as additional data have been obtained and theory has become more refined. These conditions reflect the experimental difficulties inherent in liquid diffusion measurements, in which transport by other processes, such as convection, tends to mask the diffusive transport. Frequently the disagreement between several theoretical predictions is less than that found between different sets of data obtained for a system. Moreover, as has been shown by Nachtrieb,1 diffusion data are needed over much larger temperature ranges if the functional dependence on temperature is to be known. Thus, improved techniques must be devised if experimental data are to augment fundamental understanding of the liquid state and to meet technological needs. The available techniques have been discussed elsewhere.' Of these, only the capillary-reservoir, long capillary, and shear cell techniques will be discussed briefly in terms of experimental advantages and disadvantages. These methods served to establish design criteria for the modified shear cell described here. The capillary-reservoir technique of Anderson and saddington3 has been the most widely used method in recent years. The method offers experimental simplicity relative to other methods and has been employed for high-temperature measurements. Moreover, the mathematical relationship between the measured concentration ratio and the diffusion coefficient is such that smaller values of the ratio are achieved for a specified diffusion time relative to other methods. The amplified errors between the concentration ratio and the calculated diffusion coefficient are diminished at lower values of the ratio.' The method also permits multiple determination by the simultaneous use of several capillaries. Disadvantages of the capillary-reservoir method are primarily associated with the hydrodynamic ef- fects of convection and of placing the capillary in the reservoir. These effects are most pronounced in the region near the open end of the capillary and produce an ill-defined boundary condition between the capillary and the reservoir. Such effects are not amenable to experimental or mathematical correction2 (although this has been suggested4). The long-capillary method of Careri, Paoletti, et al.5-10 involves filling one half of a small capillary tube of 150 to 200 mm total length with material of one composition or radioactivity and the other half with the second part of the diffusion couple. This arrangement eliminates the adverse hydrodynamic effects associated with the capillary-reservoir technique; however, certain other experimental difficulties are encountered in this method. The more significant of these difficulties involve the melting, expansion, contraction, and solidification of the diffusion system. The dependence in some cases of the diffusion coefficient on the capillary diameter noted by Careri et a1.7 (termed the "wall effect") has been alternatively explained by Nachtriebl as a convection effect during solidification. In mutual diffusion measurements, the convection problems associated with melting and solidification are increased because of the differences in melting points and in expansion coefficients between the halves of the diffusion couple. However, the errors caused by convection effects within this method are usually less than those in the capillary-reservoir method. Furthermore, the concentration profile needed to determine concentration-dependent diffusion coefficients by the Boltzmann-Matano analysis can be obtained from this method. Of the previous attempts to use shear cells, only the cell used by Nachtrieb and Petit11,12 appears to have yielded good data. They reduced the mechanical complexity of the conventional shear cell by using a cell comprised of only four segments. Three of these segments were filled with ordinary mercury and the fourth with radioisotopic mercury in their determination of mercury self-diffusion coefficients. The average concentration (radioactivity) was determined in each segment following a period of isothermal diffusion. These concentration values were fitted to concentration profiles obtained from the Stefan-Kawalki tables, and the diffusion coefficients were evaluated. Thus, although the number of cell segments is reduced in their method, some information about the concentration profile can be obtained in terms of the Stefan-Kawalki analysis. Moreover, their cell is suitable for measurement of diffusion coefficients at elevated pressure, as they successfully demonstrated with mercury. Consideration of the design and experimental features of the methods discussed above suggested several criteria for the new cell: 1) a ''total" capillary system, as opposed to a capillary-reservoir system, should reduce adverse convection effects; 2) such a capillary system should avoid the problems en-

Jan 1, 1969

By E. R. Brownscombe, Francis Collins

A study has been made of the material balance-fluid flow method of estimating reserves and degree of water drive from pressure and production history data. By considering the effect of random pressure errors it is shown that in a particular example a standard deviation of three and one-half pounds in each of ten pressure survey? permits the determination of the reserves with a standard deviation of 8 per cent and the water drive with a standard deviation of 15 per cent, assuming that certain basic geologic data are correct. It is believed that this method of estimating reserves and water drive is useful and reliable in a number of cases. The method is particularly valuable when reservoir pressure data are accurate within a very few pounds, but may also be applied with less accurate pressure data if a relatively large reservoir pressure decline occurs early in the life of the field, as for example in an under-saturated oil field. INTRODUCTION A knowledge of the magnitude of reserves and degree of water drive present in any newly discovered petroleum reservoir is necessary to early application of proper production practices. A number of investigators have contributed to methods of relating reserves, degree of water drive, and production and pressure history. 1-8 Three types of problems of increasing complexity may be mentioned. If a reservoir is known to have no water drive. and if the ratio of the volume of the reservoir occupied by gas to the volume of the reservoir occupied by oil (which ratio permits fixing the overall compressibility of the reservoir) is known, then only one further extensive reservoir property remains to be determined, namely the magnitude of the reserves. A straightforward application of material balance considerations will permit this determination. The problem becomes very much more difficult if we wish to determine not only the magnitude of the reserves but also the magnitude of water drive, if any, which is present. In principle, a combination of material balance and fluid flow considerations will permit this evaluation. Finally, if neither the magnitude of reserves, the degree of water drive, nor the ratio of oil to gas present in the reservoir is known and it is desired to determine all three of these variables, the problem could in principle be solved by a fluid flow-material balance analysis which determines the overall compressibility of the reservoir at various points in its history. The change in compressibility with pressure would provide a means of determining the ratio of gas to liquid present, since the compressibilities of gas and liquid vary differently with pressure variation. However, in practice this problem is probably so difficult as to defy solution in terms of basic data precision apt to be available.' It is the purpose of this discussion to illustrate the second case, which involves the determination of two unknown variables, single phase reserves and degree of water drive, from pressure and production history and fluid property data, and to study the precision with which these unknowns can be determined in this manner in a particular case. Although an electric analyzer developed by Bruce as used in making the calculations to be described, numerical methods necessary in carrying out the process have been devised and have been applied for this purpose. Schilthuis,' for example, developed a comprehensive equation for the material balance in a reservoir. He combined this with a simplified water drive equation, assuming that the ratio of free gas to oil was fixed by geological data and that a period of constant pressure operation at constant rate of production was available to determine the constant for his water drive equation. On this basis he was able to compute the reserves and predict the future pressure history of the reservoir. Hurst developed a generalized equation permitting the calculation of the water drive by unsteady state expansion from a finite aquifer. He showed in a specific case how the water influx calculated by his equation, using basic geologic and reservoir data to fix the constants, matched the water influx required by material balance considerations. Old3 illustrated the simultaneous use of Schilthuis' material balance equation and Hurst's fluid flow equation for the determination of the magnitude of reserves and a water drive parameter from pressure and production history. He used this method to calculate the future pressure history of the reservoir under assumed operating conditions. As a basis for determining reserves, Old assumed a value for his water drive parameter and calculated a set of values for the reserves, using the initial reservoir pressure and each successive measured pressure. The sum of the absolute values of the deviations of the resulting reserve numbers from their mean value was taken as a criterion of the closeness of fit to the experimental data possible with the water drive parameter assumed. New values of the water drive parameter were then assumed and new sets of the reserves calculated until a set of reserves numbers having a minimum deviation from the average was established. The average value of- the re-

Jan 1, 1949

By J. J. Tietien, R. O. Clough

A technique previously used to prepare alloys of InAs1-xPx and GaAsl-x Px, miry: the gaseous hydrides arsine and phosphine, has been extended to grow single -crystalline GaAs 1-x Sb x by replacing the phos-phine with stibine. Procedures were developed for handling and storing stibine which now make this chemical useful for vapor phase growth. This represents the first time that this series of alloys has been grown from the vapor phase. Layers of P -type GaSb and GaSb-rich alloys have been grown with the carrier concentrations comparable to the lowest ever reported. In addition, a p-type alloy containing 4 pct GaSb exhibited a mobility of 400 sq cm per v-sec which is equivalent to the highest reported for GaAs. RECENTLY, interest has been shown in the preparation and properties of GaAs1-xSbx alloys, since it was predicted1 that for compositions in the range of 0.1 < x < 0.5, they might provide improved Gunn devices. However, preparation of these alloys presents fundamental difficulties. In the case of liquid phase growth, the large concentration difference between the liquidus and solidus in the phase diagram, at any given temperature, introduces constitutional supercooling problems. It is likely that, for this reason, virtually no description of the preparation of GaAs1-xSbx by this technique has been reported. In the case of vapor phase growth, problems are presented by the low vapor pressure of antimony, and the low melting point of GaSb and many of these alloys. In previous attempts1 at the vapor phase growth of these materials, using antimony pentachloride as the source of antimony vapor, alloy compositions were limited to those containing less than about 2 pct GaSb. This was in part due to the difficulty of avoiding condensation of antimony on introducing it to the growth zone. A growth technique has recently been described2 for the preparation of III-V compounds in which the hydrides of arsenic and phosphorous (AsH3 and pH3) are used as the source of the group V element. With this method, GaAs1-xPx and InAs1-xPx have been prepared2&apos;3 across both alloy series with very good electrical properties. Since the use of stibine (SbH3) affords the potential for effective introduction of antimony to the growth apparatus, in analogy with the other group V hydrides, this growth method has been explored for the preparation of GaAs1-xSbx alloys. In addition to GaSb, these alloys have now been prepared with values of x as high as 0.8. In the case of GaSb, undoped p-type layers were grown with carrier concentrations equivalent to the lowest reported in the literature. Thus it has been demonstrated that, with this growth technique, all of the alloys in this series can be prepared. EXPERIMENTAL PROCEDURE A) Growth Technique. The growth apparatus, shown schematically in Fig. 1, and procedure are virtually identical to that described2 for the growth of GaAs1-xPx alloys, with the exception that phosphine is replaced by stibine.* HCl is introduced over the gallium boat to *Purchased from Matheson Co., E. Rutherford,N+J. transport the gallium predominantly via its subchlo-ride to the reaction zone, where it reacts with arsenic and antimony on the substrate surface to form an alloy layer. The fundamental limiting factors to the growth of GaAs1-xSbx alloys from the vapor phase, especially GaSb-rich alloys, are the low melting point of GaSb (712°C) and the low vapor pressure of antimony at this temperature (<l mm). Thus, relatively low antimony pressures must be employed, which, however, imply low growth rates. To provide low antimony pressures, very dilute concentrations of arsine and stibine in a hydrogen carrier gas were used. Typical flow rates (referred to stp) were about 4 cm3 per min of HC1 (0.06 mole pct)+ from 0.1 to 1 cm3 per min of ASH, (0.002 to 0.02 mole pct), and from 1 to 10 cn13 per min of SbH3 (0.02 to 0.2 mole pct), with a total hydrogen carrier gas flow rate of about 6000 cm3 per min. Although no precise data on decomposition. kinetics exist, it is known4 that stibine decomposes extremely rapidly at elevated temperatures. However, the high linear velocities attendent with the high total flow rate (about 2000 cm per sec) delays cracking of the stibine until it reaches the reaction zone and prevents condensation of antimony in the system. To improve the growth rates of the GaSb-rich alloys, growth temperatures just below the alloy solidus are main-

Jan 1, 1970

By Brian F. Dyson

The surface tensions at 1550°C of some Fe-S alloys (in the range 0.008 to 0.052 wt pct S), Fe-Sn alloys (0.31 to 48.4 wt pct Sn), Fe-P alloys (0.038 to 2.38 wt pct P), Fe-Cu alloys (2.15 to 22.8 wt pct Cu), and Fe-1 pct C-S alloys (0.005 to 0.076 wt pct S) along with the surface tension of the base iron have been measured by the sessile-drop method. A mean value of 1754 dynes per cm was found for the surface tension of the base iron. Sulfur was found to be highly surface-active, the surface-tension results being in quantitative agreement with existing data. Tin and copper were found to be less surface-active than sulfur while phosphoms was completely nonsurface-active. The surface tensions of Fe-1 pct C-S alloys were found to be lower than those of the Fe-S alloys containing the same sulfur content. This was shown to be a mmzifestation of the increase in the thermodynamic activity of suZfur by carbon. It is only in recent years that attempts have been made to measure the surface tension of liquid iron of known high purity.1-3 Earlier measurements4-7 were made on liquid iron containing variable amounts of what are now known to be surface -active solutes. The exact value of the surface tension of liquid iron is still, however, open to some doubt. Halden and Kingery&apos; reported a value of 1720k 34 dynes per cm at 1570°C, Kozakevitch and Urbain8 gave 1790k 25 dynes per cm at 1550°C, while Van-Tszin-Tan et al. obtained a value of 1865k 37 dynes per cm at 1550°C. The first systematic investigation into the effect of controlled solute additions on the surface tension of iron was made by Halden and Kingery.&apos; They showed that sulfur and oxygen were highly surface-active, whereas nitrogen was only slightly active, and carbon inactive. A subsequent investigation by Kingery indicated that two other group-6B elements, selenium and tellurium, were also surface-active. This highly surface-active nature of sulfur and oxygen has recently been substantiated by Kozakevitch and Urbainla and Van-Tszin-Tan et al. l1 Kozakevitch and Urbainl2 have also conducted an experimental survey of the effects of a number of metals on the surface tension of liquid iron. Their surface-active nature was, in all cases, less than that of the group 6B elements. The present investigation was undertaken to study in more detail the surface tensions of dilute Fe-S alloys and to measure the surface tensions of binary alloys of iron containing phosphorus, copper, and tin. The effect of sulfur additions on the surface tension of Fe-1 pct C alloys was also determined. EXPERIMENTAL PROCEDURE The sessile-drop method was employed in the present investigation. An apparatus was built similar in principle to that described by Humenik and Kingery.lS It consisted of a horizontal silica tube, which could be evacuated to pressures less than 10-5 torr, with its central portion surrounded by a water jacket within which was a high-frequency coil. This generated heat in a tantalum susceptor placed inside the silica tube, which in turn radiated heat to the specimen mounted on a recrystallized alumina plaque. Temperatures were measured by an optical pyrometer and photographs of the molten drop were taken on a fixed-focus plate camera giving a magnification of X2. Surface-tension values were determined from the resultant drop using the method described by Baes and Kellogg.l4 The high vapor pressure of molten iron made it necessary to conduct all the experiments under a 1/4 atm of argon (greater than 99.995 pct purity). The analysis of the base iron used in the investigation is given in Table I. Each sample was approximately 3 g in weight and had a hemispherical base to ensure a uniform advancing contact angle on melting. The iron alloys were prepared individually in the sessile-drop apparatus by drilling a hole in the top of each sample and adding the required amount of solute, the drops being analyzed after the experiment. This method of preparation had the advantage of ensuring a consistent minimal contamination by oxygen due to refractory attack and also allowed surface tension to be measured at the same time. Every precaution was taken to ensure that the specimen was not contaminated by grease when it was introduced into the apparatus, the samples being cleaned in acid, dried in alcohol, and rinsed in petroleum ether. All handling was done with tweezers. Once the specimen had been placed inside the susceptor, the furnace was evacuated and the Sample leveled. The furnace was then degassed at approximately 1000"C before the argon was introduced. In every case the surface tension was determined at 1550" C.

Jan 1, 1963

By J. E. Ryan

TRONA, Calif., is a miniature urban community of some 3500 people, located on the northwest shore of dry Searles Lake in the extreme northwest corner of San Bernardino County, approximately 186 miles north and east of Los Angeles. Since it is situated on the Mojave Desert, a typically desert climate prevails with wide variations in temperature between day and night, extreme daytime summer heat, and cool to cold winters. Rainfall averages somewhat less than 4 in. per year, and dust storms are common. The rate of evaporation, .however, is great, amounting to 6 to 9 ft of water per year. The extremely low humidity makes the summer heat of 110°F tolerable with only a mild, temporary discomfort. Nature of Deposit During the periods when Searles Basin was flooded, the waters that passed through Indian Wells Valley spread out to form a broad, shallow lake providing, in effect, a settling basin for suspended sediment. The drainage into the deeper and more isolated Searles Basin thus was clarified to a great degree before concentration began. Today, the elevation of the dry surface of Searles Lake is 1618 ft, and the salt deposit measures 5x7 miles. At the eastern and northeastern margins of the main playa zone and just at the foot of the alluvial slope of sand and coarser wash from the Slate Range mountains, a rim of crusted salts rises a few feet above the level of the flat. The deposit is a saline efflorescence composed of salts that were presumably brought up with rising ground waters to be deposited at the surface by solar evaporation. This deposit consists chiefly of trona, and it is after this Trona Reef that the town Trona was named. Strip mining operations have been conducted in the past at infrequent intervals for the recovery of crude trona salts. The main focal point of interest in Searles Lake from a commercial standpoint is the main salt body located almost centrally in the basin. The exposed portion of this porous saline deposit covers approximately 12 sq miles and averages 71 ft deep. Its interstitial voids, which constitute 50 pct of the total volume, are permeated with a brine, which is in equilibrium with the soluble salt deposits. The brine is the raw material for the operations of the American Potash and Chemical Corp. plant at Trona, shown in Fig. 1. The soluble salt deposits are of interest for their potential values in future technologic development. The brine, which is stratified according to slight differences in density, stands usually within 6 in. of the surface of this exposed, firm, salt body. The surface is usually dry and will support the weight of heavy mobile units and drilling equipment. Occasionally, however, surface waters from the higher watersheds encroach upon the main salt body during infrequent periods of precipitation on the surrounding mountains. This water dissolves surface salt, becomes a dilute brine, and has been observed to stand as high as 18 in. above the salt surface when undisturbed. Windstorms will shift the water back and forth across the lake surface. The exposed salt body is surrounded by additional submerged areas of commercial soluble salt deposits covering some 20 sq miles, hidden from view by marginal playa mud. These vary in depth up to as much as 30 ft. Thus, the outline of exposed and submerged salt deposits of commercial value is estimated to cover a total area of 32 sq miles, which is roughly circular but slightly elongated from northwest to southeast. It has been estimated that each square mile contains about 100 million tons% f alkali salts. The results of drill borings in the past 15 years have brought to light the interesting fact that the main salt body lies superimposed on an impervious mud deposit from 10 to 15 ft thick containing relatively little soluble salt. Under this deposit lies a second soluble salt body 35 ft deep. The lower salt body is interspersed with numerous insoluble mud lenses and its composition is considerably different from that of the primary, or main salt deposit. Recent drill borings have not penetrated beyond 300 ft. They have, however, revealed that underlying the lower salt body, the mud sediments carry deposited minerals of trona, nahcolite, mirabilite and much less soluble carbonates or sulphates of calcium and/ or magnesium. This structure is shown in Fig. 2. Current Lake Survey Program Several hundred holes have been drilled in the deposit. However, to carry out a thorough and carefully correlated study of the composition of the soluble salts and other minerals in the dry lake basin, a drilling program was inaugurated recently and is now nearing completion. In this survey, pattern drill holes are sunk at regular lh-mile intervals to a depth of approximately 150 ft. Drilling equipment consists of a No. 51 C. P.

Jan 1, 1952

By S. W. Nabbs, W. D. Bachman, A. W. Last

A study has been made of wet, autogenous grinding of disseminated copper ores, including testing of a large number of samples from. Kennecott Copper Corp.&apos;s Chino mine. The grindability of the various samples was found to vary over an extremely wide range, even among samples taken from diflerent locations within the same ore body. These variations in grindability can be qualitatively correlated with the composition of the rock and the fracturing and alteration that had occurred. Because of the large-scale nonhomogeneity of disseminated copper ore bodies, extensive and careful testing of autogenous grinding is needed. An accurate correlation of the grinding data from various samples with the geology of the ore body and with mining plans will indicate if variations in grinding mill throughput can be avoided in practice by mixing or blending of mill feed and if, therefore, autogenous grinding can be applied successfully. In the past 15 years, comminution by primary autogenous grinding has been investigated and applied economically in the minerals industry, particularly in iron-ore processing. Successful application of primary grinding is described by A. A. Dor,l.&apos; P. B. Dettmer,334 R. R. Turner, and W. F. McDermott." other authors describing the advantages of primary grinding include H. Hardinge,&apos; R. T. Hukki,&apos; D. S. Coyle" and F. C. Bond,"," to mention only a few. For the past several years, Kennecott Copper Corp.&apos;s Metal Mining Div. Research Center has been investigating primary grinding of disseminated copper ores. Both fully autogenous and semi-autogenous grinding has been explored. Ores from three of Kennecott&apos;s western operating properties and from several development properties have been tested. Host rocks include diabase, schist, silicated and argillaceous limestones, shale, granite porphyry, quartzite, and granodiorite. The object of this paper is to supplement the general knowledge in the field of primary grinding by presenting information gained from the studies with the various disseminated copper ores. Data are presented which show that carefully considered test programs are required to determine the practicality of applying autogenous grinding to a specific mining-beneficiation operation. Particularly this is so if more than one rock type occurs within an ore body or if there are wide variations in the degree of rock alteration within a deposit. Extensive sampling and subsequent testing of the ores within a mine are required if serious pitfalls are to be avoided and good engineering data acquired. We hope that this presentation will stimulate studies to increase the understanding of the fracturing process applicable to large pieces of rock, a factor which is important in autogenous grinding. Test Facilities and Procedures Both pilot-scale and full-scale test facilities were used to investigate primary grinding characteristics of the disseminated copper ores. A 6-ft Hardinge Cascade mill, a 24-ft Hardinge Cascade mill, and a 5-ft Aerofall mill were used in the studies. The Cascade mills were operated wet, while the Aerofall mill was operated both wet and dry. The Cascade mills were operated both for fully autogenous and for semi-autogenous grinding; the Aerofall mill was operated only semi-autogenously. Fully autogenous grinding, as the term is used in this presentation, is defined as the direct grinding of coarsely crushed rock by the action of the rock mass. Semi-autogenous grinding is defined as the grinding of coarsely crushed rock with the rock mass supplemented by a steel ball charge. Most of the test work was done using the 6-ft Cascade mill, operated under fully autogenous grinding conditions. Only limited testing was conducted with the 5-ft Aerofall mill and only one ore was tested using the 24-ft Cascade mill. This presentation is concerned, therefore, primarily with fully autogenous, pilot-scale grinding in the Cascade mill. Fig. 1 presents a diagram of the test facilities used with the 6-ft Cascade mill. Principal test equipment consists of a 6-ft Cascade mill, an 18-in. spiral classifier, an elevator, a 2 x 9-ft belt feeder, a conventional integrating kilowatt-hour meter, and a recording wattmeter. In testing, feed charges, adjusted as to weight, were deposited as evenly as possible on the belt feeder every 15 min. The weight of each charge was adjusted to maintain a mill charge of 27 to 30% of mill volume. The classifier was adjusted to obtain the desired size-consist of the final product, generally at 20% + 100 mesh. After equilibrium was established in the circuit, the feed, mill discharge, classifier sand, and classifier overflow were sampled and their size distributions determined. During the sampling periods, the power drawn by the mill was measured to determine the energy consumed in the reduction of the size consist of the ore solids. Fully Autogenous Pilot Grinding Tests on Various Kennecott Ores Typical test results obtained in the 6-ft Cascade mill with samples from Kennecott&apos;s Ray Mines Div., Chino Mines Div., Utah Copper Div., and a development property designated as Mine A are presented in Table 1. As shown, the ores that were ground most easily in the pilot-scale mill were composite mine samples obtained

Jan 1, 1971

By M. E. Wadsworth, K. C. Bowles, H. E. Flanders, R. M. Nadkarni, C. E. Jelden

The kinetics of precipitation of copper on iron of various purity were carried out under controlled conditions. The rate of reduction has been correlated with such parameters as copper and hydrogen ion concentration, geometric factors, flow rate, and temperature. The character of the precipitated copper as a function of flow conditions and rate of PreciPitation has been observed under a variety of conditions. ThE precipitation of copper in solution by cementation on a more electropositive metal has been known for many years. Basile valentine&apos; who wrote Currus Triumphalis Antimonii about 1500, refers to this method for extraction of copper. Paracelsus the Great2 who was born about 1493 cites the use of iron to prepare Venus (copper) by the "rustics of Hungary" in the "Book Concerning the Tincture of the Philosophers". Agricola3 in his work on minerals (1546) tells of a peculiar water which is drawn from a shaft near Schmölnitz in Hungary, that erodes iron and turns it into copper. In 1670, a concession is recorded4 as having been granted for the recovery of copper from the mine waters at Rio Tinto in Spain, presumably by precipitation with iron. Much has been published in recent literature on the recovery of copper by cementation, the majority of the articles being on plant practice.5-24 The rest include articles on investigation of the variables involved25-28 and a review of hydrometallurgical copper extraction methods." This literature has established: a) The three principal reactions in the cementation of copper are Cu + Fe — Fe+4 +Cu [ 11 One pound of copper is precipitated by 0.88 lb of iron stoichiometrically. In actual practice about 1.5 to 2.5 lb of iron are consumed. 2Fe+3 + Fe — 3Fe+2 [21 Fe +2H&apos;-Fe+2 + H2 [3] Reactions [2] and [3] are responsible for the consumption of excess iron. Wartman and Roberson&apos;28 have established that Reactions [ I] and [2] are concurrent and much faster than Reaction [3]. b) Acidity control is important in the control of hydrolysis and the excessive consumption of iron. he commercial workable range is approximately from pH = 1.8 to 3." c) Iron consumption is closely related to the amount of ferric iron in solution. Jacobi" reports that, by leaving the pregnant mine waters in contact wi th lump pyrrhotite (Fe7S8) for 3 hr, all the iron was reduced to the bivalent condition and scrap iron consumption was cut to 1.25 lb scrap per pound of copper precipitated. He also reported that SO2 has been used successfully to reduce ferric iron to the ferrous state. d) The ideal precipitant is one that offers a large exposed area and is relatively free of rust. e) High velocities and agitation show a beneficial effect upon the rate of precipitation, as it tends to displace the layer of barren solution adjacent to the iron and also dislodges hydrogen bubbles and precipitated copper to expose new surfaces. Little work, however, has been published on the reaction kinetics of copper precipitation on iron. Cent-nerszwer and Heller20 investigated the precipitation of metallic cations in solutions on zinc plates. They found the cementation reaction to be a first-order reaction. The rate constant was independent of stirring for high stirring rates and they concluded that the rate is governed by a diffusional process at low stirring speeds and by a "chemical" process at higher stirring speeds where the rate reaches a constant value. This conclusion has been challenged by King and Burger30 who could not find any region where the rate was independent of the stirring speed, although the rate constant they had obtained for high stirring speed was greater than the maximum value of the rate constant reported by Centnerszwer and Heller (by a factor of six). King and Burger, therefore, concluded that the rate of displacement of copper was controlled only by diffusion. Cementation of various cations on zinc has been summarized by Engfelder.31 APPARATUS A three-necked distillation flask of 2 000-mm capacity was used as a reaction vessel. A pipet of 10-mm capacity was introduced through one of- the side necks, the sample of sheet iron, mounted in a rigid sample holder, through the other, the stirrer being in the middle as shown in Fig. 1. The whole assembly was immersed in a constant-temperature bath. The stirrer was always placed at the same depth in the solution. EXPERIMENTAL PROCEDURE Reagent-grade cupric sulfate (J. T. Baker Chemical Co., N.J.) was used to make up a stock solution containing 10 g of copper per liter which was then diluted to various concentrations as required. Experimental data were obtained by measuring the amount of copper and iron ions in solution at successive time intervals. The initial volume of the solution was always 2000 ml, 10-ml aliquots being removed each time for chemical analysis. Because the total volume change of the solution was less than 10 pct, no correction was used for solution volume change. Nitrogen was bubbled through the solution before and

Jan 1, 1968

By D. Kuhlmann-Wilsdorf

A new theory of work hardening is developed which rests on only a few simple principles and is applicable to a wide variety of materials and dislocation structures. It explains, qualitatively, the general characteristics of the three-stage shear stress-shear strain curve of fcc metals, as well as the most important features connected with easy glide. The value of, the work-hardening coefficient in stage 11, is derived quantitatively, from first principles, and is shown to be insensitive to many changes in detailed dislocation behavior. The low rate at which energy is stored during mechanical working in stage 11, the dependence of slip line length on stress, and the so-called Cottrell-Stokes law are explained. Although the theory is primarily developed for fcc metals and alloys, it is largely applicable also to some other materiuls, and in particular apparently to poly crystalline simple steels in theh linear range of hardening. FOR pure fcc metals and alloys, after many different pretreatments and under a great variety of testing conditions, the well-known three-stage work-hardening curve is commonly observed. Moreover, the work-hardening coefficient in stage 11, 011, bears an almost constant relationship to G, the modulus of rigidity, such that K = G/Brr" = 300, within a factor of about 2 either way. The very fact that the three-stage curve and the value of K are so very persistent, can hardly be understood except on the assumption that some quite simple phenomena are responsible. In this light all available theories of work hardening must be judged unsatisfactory: Each of them is based on some quite specific dislocation model, while it is known that metals with similar values of K may have widely different dislocation structures, for example, dislocation tangles in the case of pure fcc metals, and piled-up groups of dislocations in a-brasstype alloys. Thus, while a particular theory might conceivably represent a special case with a reasonable degree of accuracy, it cannot possibly have illuminated the underlying principle. Another severe criticism applying to the presently most widely discussed theories is that they employ empirical or even quite unexplained parameters in order to arrive at a numerical value of K. This indicates that some vital aspect of the work-hardening process has remained unexplained. In the present paper, a new theory of work-hardening is developed which does not suffer from the above shortcomings. It is derived from first principles, and is founded on the realization that the underlying causes for the three-stage work-harden- ing curve and for the persistence of the numerical value of O,, must be few and simple. As a first step it is shown herein that the experimental oklservations on "easy glide" can be explained on the assumption that in this stage dislocations multiply, beginning in a number of restricted area:;, and from there penetrate into crystal regions still substantially free of glide dislocations until a quasi-uniform dislocation distribution has been established. During "easy glide", the resistance to the movement of the foremost dislocations, advancing into still largely a dislocation-free regions, is believed to control the flow stress. This resistance is determined by various factors, among them the reaction of the dislocations against bowing-out into loops, which is due to their line tension. Without such bowing-out no dislocation multiplication would occur, but the corresponding contribution to the flow stress stays practically constant all through stage I. According to the present theory, stage TI begins as soon as there are no more areas left into which newly formed dislocations have not yet penetrated, i.e., as soon :is a quasi-uniform dislocation density has been attaned. Regardless of how, in detail, the dislocations should happen to be arranged at the end of "easy glide", whether in pileups or tangles, on one glide system or on several, the stress necessary to overcome the line tension of the segments must now increase, because the dislocation density increiises while the average free dislocation length decreases. It is argued that all other contributions to the flow stress stay at about the same level as in stage I, and that the said increase in the stress necessary to bow out dislocation segments into loops is responsible for the major part of work hardening in stage 11. Stage TII of the stress-strain curve is explained by largely follouing the ideas of Seeger and his co-workers; however, it is pointed out that the start of stage m may on occasion indicate the onset of "conservative climb" instead of cross slip. Indirect evidence indicates that linear work hardening persists even under the profuse action of cross slip, but at a lower rate. Only when, in addition to cross slip, climb operates extensively, does the work-hardening rat,. drop sharply, ultimately down to zero. BRIEF SURVEY OF EXPERIMENTAL EVIDENCE The stress-strain curve of crystals of many different substances are qualitatively similar. No significant permanent plastic deformation takes place below the so-called "critical resolved shear stress". As the applied stress is raised beyond this level. yielding occurs with little or no work hardening and

Jan 1, 1962

By S. K. Tarby, W. O. Philbrook

The rate of FeO and MnO reduction from silicate and aluminate slags by carbon-saturated iron is dependent on both slag composition and temperature. Owing to variable stirring rules during- the course of reaction, the reduction processes occur in two stages in stationary graphite crucibles. In the first stage the slirring caused by CO evolution results in forced convection conditions in the slag. As the boiling action subsides during reduction, the flow conditions within the system become those defined by natural convection. Analysis of the data by an unsteady-state penetration model indicates that the rate of reduction is controlled by the rate of cocur-rent flow of&apos; cations and anions from the bulk slag to the interface during both stages of reduction. The hearth reactions of the blast furnace have been extensively investigated from the viewpoint of equilibrium by deductions from controlled laboratory experiments. However, the literature contains relatively few studies that have been directed toward the area of slag-metal reaction kinetics, and the majority of these have been concerned with the rate and mechanism of sulfur transfer between iron and slag. More recently, attention has turned to the kinetic factors in the reduction of oxides from liquid slags. One of the first investigations in this field was conducted by Dancy1 on the reduction of pure liquid FeO and pure liquid Fe3O4 by carbon-saturated iron. The integrated form of the rate equation indicated that the reduction of FeO was of the first order up to 80 pct reduction. Over the initial 30 pct of reduction, the magnetite reaction was also interpreted as a first-order process. The rates of reaction were extremely rapid as indicated by a 30 pct reduction of the liquid magnetite in a time interval of about 1 to 2 sec. Phil-brook and irkbbride&apos; studied the reduction of FeO from a lime-alumina-silica slag by carbon-saturated iron and solid graphite in stationary crucible assemblies. With the use of the differential form of the rate equation, the rate of the reduction reaction was found to be proportional to the second power of the concentration of the reactant FeO for both the slag-metal and slag-graphite reactions. These authors presented a number of comments in an effort to explain the difference between the molecularity of the above reaction and the observed second-order relation. One such argument, recently extended by Wagner,3 was that the rate-limiting step may well be one of transport control. A complete discussion of the proposed mass-transport control mechanism of this reduction reaction will be presented in a later section of this paper. Kinetic studies of the reduction of other oxide species, namely chromous oxide, titania, and silica, have also been reported. McCoy and philbrook4 used rotating crucible assemblies to investigate chromium reduction from Ca0-SiO2-A12O3 slags. First-order kinetic law was obeyed for the slag-metal reduction reaction as determined by the integration method of data analysis. Due to scatter of the data, any dependence of the rate constant on temperature or slag composition was obscured. Concentration-time data for the reduction of titania from blast-furnace type slags under reducing conditions were obtained by Delve, Meyer, and Lander.&apos; The data were too few, however, for a formal kinetic interpretation. Kinetic data for the very slow reaction of silica reduction have been observed by McCoy and Philbrook6 and Fulton and chipman.7 The former experimenters found the reaction-rate constant for silica reduction by carbon-saturated iron to be 20 to 60 times less than the rate constant for chromium reduction. In their work on the reduction of SiO2 in mechanically stirred systems, Fulton and Chipman also found small values for the specific reaction rate and derived a high value for the energy of activation for the reaction. In both of these investigations, the reduction process was assumed to follow first-order behavior. schuhmann8 proposed that the rate-limiting step in this reaction is the diffusion of oxygen from the interface through a boundary-layer film to the bulk metal phase, and Rawling and Elliott9 have reported experimental confirmation of this hypothesis for temperatures below 1600°C. Turkdogan et a1.10 have also concluded that the rate of reduction of silica is a slow process and controlled by the diffusion of oxygen in the metal, but only in the absence of carbon monoxide bubbles at the slag-metal interface. In the presence of bubbles, achieved either by injecting carbon monoxide at the slag-metal interface or by blowing it through the metal and slag, these investigators found a rather rapid reduction of silica which appeared to be controlled by an interfacial reaction involving the de-sorption of silicate ions from the slag-metal interface to the metal phase as silicon and oxygen atoms. In view of the unresolved nature of the kinetics of FeO reduction and the lack of kinetic data for the manganese reaction,

Jan 1, 1968

By W. F. Kieschnick, and W. J. McGuire&apos, Eugene Harrison

This paper concerns the induction and extension of fractures into rock formations as involved in drilling, completing, and production stimulating operations on wells. Conclusions concerning formation breakdown are derived from (I) a review and extension of published analyses relating to mechanical theories of rock stress and the state of stress in the earth&apos;s crust and (2) a correlation of field data from fracturing operations. Conclusions concerning the mechanics of fracture extension, which indicate the relationship between fracture dimensions and rock properties, depth, and volume of injected fluid, are tentative and largely establish limits of relationships. These conclusions are derived from stress calculations, limited field data, and laboratory experimental studies. The experimental work involves the study of the stresses at the fracture boundaries and the geometry of pressurized fractures by means of photo-elastic modeling methods. Results of this investigation indicate that a large majority of pressure induced wellbore fractures are vertical, particularly in deeper wells; and variations in the pressures necessary to create and extend fractures can be explained largely on a basis of established rock properties. It is also shown that variations due to tectonic forces should usually be expected to be slight. Other results indicate that during that extension of fractures rather large fracture volumes are temporarily created by the parting of the formation. The purpose of this paper is to present the results of calculations and laboratory experiments concerning the mechanics of fracture induction and extension with a view to broadening existing knowledge relating to these phenomena. It is believed that continued progress in developing knowledge of this type is important to the further development of techniques for drilling and completing wells. When a wellbore is subjected to sufficiently high pressure, fracturing of the formation surrounding the well occurs. This phenomenon is a common cause of lost circulation during drilling operations, is a deliberately planned factor in most squeeze cementing operations, and is the controlling factor in many productivity stimulation operations. The exploitation of formation fracturing in recent years has been particularly impressive in sand-viscous fluid well stimulation treatments which were first introduced to the industry by the Stanolind research group1,2,3 several years ago. The borehole fracturing phenomenon has been analyzed mathematically by application of the principles defining the elastic and inelastic behavior of thick-walled cylinders of homogeneous, isotropic, and impermeable material.1,5,6 This basic argument is re-presented in this paper along with new considerations which strengthen it. In addition to these arguments relating to fracture induction some calculations and experimental results relating to the mechanics of fracture extension are presented. Since the nature of the pressure induced fracture at distances from the well is of great importance in considerations of well stimulation procedures there appears to be a need for an integrated approach which deals with the mechanics of fracture extension as well as with wellbore rupture.

Jan 1, 1955

By Yves Dardel

The literature concerning the remelting of alunlinum and its alloys is very rich. Unfortunately the majority of the papers on this subject have no scientific value, for the theories or explanations are too often in opposition to the laws of physical chemistry. Furthermore only a few of the methods of purification are considered in the literature. Hence it has seemed necessary to the author to sketch a general theory of the purification of secondary aluminum. The purpose of the purification is to eliminate the impurities that the charges, and the atmosphere of the furnaces bring into the bath during the successive remelt-ings. Indeed scrap as well as metal can be used when soiled with oil, greases, water, or others, if it has been sufficiently dried and contains oxides. At the melting point of the metal, the oils and greases are decomposed into their constituent elements H², O2, H²O, co², CO, CH,, and others. These gases are added to the corresponding gases in the atmosphere of the furnace. The impurities introduced into the metal during the remelting will accordingly be the products resulting from the action of these gases on the liquid bath. The quantity of hydrogen that is soluble in aluminum and its alloys is given by the relation of sieverts3 as a function of its partial pressure PH2 in the atmosphere m = K vPH² [I] where K is a constant, which depends only upon the temperature and increases with it. The experiments of Rijntgen and Braun4, RÖntgen and M611er5, Bircum-shaw6 and Winterhagerl have rendered it possible to determine the value of K, when the temperature is less than 1.000°C. One obtains: log K = - 4,702.5T + o 238 [2] Besides its usual significance, the term Ph~ represents also the internal pressure of dissolved hydrogen, since in the equilibrium, that is1 when no gas exchange Occurs between the two phases, the Pressures of hydrogen in the metal and in the atmosphere must be equal. Eq I shows that when the partial pressure of H2 increases the amount of dissolved hydrogen in equilibrium increases, and that, if the contrary Occurs, the quantity of H² should diminish. However, if for any reason the diffusion of hydrogen is hindered and the total amount of dissolved gas remains constant while the temperature decreases, the internal pressure of H² increases until it reaches the value of the hydrostatic pressure. At this point, bubbles of hydrogen appear in the bath and escape out of it. The amount of hydrogen in the metal is then limited by a a depending On the hydro- static pressure, which is practically equal to one atmosphere. Indeed hydrogen does not accumulate in the form of a hydride appearing as a separate solid phase. However1 even the mechanism of the solubility is not yet elucidated. One does not know exactly as yet, whether the

Jan 1, 1949

By George A. Roberts, Arthur H. Grobe

H. H. Hausner (Sylvania Electric Products Inc., Bayside, N. Y.)—I tested the 18-8 stainless steel powder described by Grobe and Roberts and the results were excellent. The powder was compacted and sintered in purified hydrogen to a very low density (approximately 20 pct and more porosity). Where the other powders show very little ductility when sintered to such a low density, the described stainless steel was surprisingly high in ductility. I would appreciate it if the authors could give us some data on a similar powder but without silicon and also data on 430 stainless steel powder. H. S. Kalish (Sylvania Electric Products lnc., Bay-side, N. Y.)—I should like to verify the excellent results obtained by Grobe and Roberts with their pre-alloyed stainless steel powder. It seems to me, however, that their data are conservative and that even better densities and higher tensile strength can be obtained with these powders by the selection of proper particle size fractions. The accompanying data were obtained by sintering compacts pressed from the powder made by Vanadium-Alloys Steel Co. to 0.8 in. in diam about % in. high in a cylindrical double action die without the use of lubricant. The compacts were sintered for 1 hr at 2370°F in hydrogen purified by passing it through a Deoxo unit (palladium catalyst) and a Lectrodryer. Even the density obtained using the as-received (—100 mesh) compacted at 40 tsi was quite high as was the hardness. This indicates that by increasing the sintering temperature slightly above 2350°F the coining and subsequent secondary sintering operation can be avoided. With the — 325 mesh fraction, however, very much higher density can be obtained and a high hardness. I have no tensile data to present, but I feel that it is not too optimistic to expect. that unusually high tensile strengths and good ductility can be obtained in this sintered material on the basis of the density and hardness data. The sintered stainless steel made by the above-described methods came out of the furnace very bright and clean. The purified hydrogen atmosphere is important in sintering stainless steel to reduce the oxide present in the powder. The result of such a sintering is good densification and good ductility of the sintered product. G. A. Roberts (authors&apos; reply)—We are greatly indebted to Messrs. Hausner and Kalish for their discussions of our paper. Their encouraging remarks are greatly appreciated and their confirmatory data will do much to add to the value of the paper. At the present time it is impossible to provide complete data on a similar stainless steel powder without silicon, but we do know that, in general, the properties are slightly inferior. Data on such a powder and on other stainless steel types are to be published in the near future.

Jan 1, 1952