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By T. E. Davidson, A. P. Lee

It is known from the early work of Bridgman that the two lowest-pressure transitions (I-II and II-III) are accompanied by substantial and abrupt changes in resistivity and Volume. However, unlike the temperature -induced allotropic transformations observed in such elements as lithium, cobalt, tin, and so forth, there is little actually known about many of the characteristics of the pressure-in&ced transitions. This current work involves an examination of the structural and transformation characteristics of the bismuth I-II and II-III transitions under hydrostatic pressures. The relationship of initial structure to the transformation pressure, rate, resistivity change, and resultant structure is discussed. It is shown that the transition pressure and transformation rate are independent of the presence of grain boundaries and associated anisotropy-induced deformation. An observed hysteresis in both the I-II and II-III transitions is shown. BISMUTH is one of the most interesting of the elements exhibiting pressure-induced polymorphs since it undergoes several allotropic transformations at pressures below 90,000 atm. It is known from the early work of bridman1,2 that the two lowest-pressure transitions (1-11 and 11-111) are accompanied by substantial and abrupt changes in resistance and volume. However, unlike the temperature-induced allotropic transformations observed in such elements as lithium, cobalt, tin, and so forth, there is little actually known about many of the characteristics of these pressure-induced transitions. It is the purpose of this work to examine some of the structural and transformation characteristics of the bismuth 1-11 and 11-111 transitions under hydrostatic pressures. Another interesting characteristic of bismuth is that, in its polycrystalline form, hydrostatic pressures of sufficient magnitude will induce severe progressive plastic deformation in the region of the grain boundaries.3 This deformation, which has also been observed in several other metals, is attributed to the high degree of anisotropy in the linear compressibility of bismuth, resulting in shear stresses in the grain boundaries when it is exposed to hydrostatic pressure. Most thermally induced allotropic transformations in metals, whether of the diffusionless ather-ma1 (martensitic) or isothermal nucleation and growth types, are dependent upon structure and prior history,4 viz., grain boundaries, deformation, and so forth. One logically wonders then whether the transformation characteristics of the pressure-induced polymorphs in bismuth might also depend upon initial structure, particularly with respect to the presence of grain boundaries and associated plastic deformation. In this investigation, the role of grain boundaries and plastic deformation on the characteristics of the bismuth I-II and 11-111 transitions will be established. The rather unique residual microstruc-tural changes associated with these transitions will be presented and discussed. The occurrence of a measurable hysteresis in both the I-II and 11-111 transitions will be demonstrated. The type of transformation mechanism based on the observed transformation rate will be discussed. EXPERIMENTAL PROCEDURE A) Apparatus. The hydrostatic pressure system utilized in this investigation is similar to that previously reported by Bridgman' and Birch and Robertson,5 and has been previously described.3 For the purpose of this work, the pressure medium utilized was a 1:l mixture of pentane and isopentane. Pressure measurement was by means of a manganin coil in conjunction with a Foxboro Recorder. The manganin coil was mounted in the bottom closure and inserted inside the pressure cavity. Based on calibration against a controlled clearance piston gage at approximately 10,000 atm, the estimated error in the pressure measurement was +2 pct. Assuming the nonlinearity in the pressure coefficient of resistivity between 10,000 and 28,000 atm to be not greater than 1 pct, then the estimated error in the range of the I-II and 11-111 transitions was +3 pct. B) specimen Material and Preparation. The bismuth utilized throughout this investigation was of

Jan 1, 1964

By T. A. Rickard

From time immemorial the fissure-vein has been held the simplest type of ore-deposit. The prominence given to it by Cotta and his disciples, from their study of the mines of the Erzgebirge, is impressed upon technical literature; and, in consequence, the ores which carry the valuable metals have been supposed to occur mainly in fissures, cleaving the rocks in diverse directions, and the noblest type of vein has been deemed that which cut across the country independent of its structure, whether evidenced as bedding, foliation or cleavage, and which was identified with rents produced in the rocky crust of the earth. As so conceived, the vein was a fissure filled with ore, extending through the country for a varying distance, and continued downward to a depth more or less proportionate to its longitudinal extent. The vein-material was bounded by an encasement of rock, and those immediate surfaces which limited it on either aide were called " walls." These primary conceptions have become modified by the experience of modern mining in widely separated regions. The study of lode-formations has led to the recognition of notable departures from the supposed normal structure of the veins of Saxony and Cornwall, the two classic homes of early economic geology. Typically the walls of a vein are conceived as parallel rockplanes enclosing the ore; the upper one being called the " hanging-," and the lower the "foot-wall."* Walls are rarely alike. Even where a vein traverses a homogeneons formation, such as a massive crystalline rock, it is usually found that the surface which bounds it underneath

Jan 1, 1897

By Charles Stuart

A PAPER on this subject can cover but a limited range. A thorough visualization of the subject would contemplate a comparative analysis of haulage machines and batteries of various types; the relationship of the storage-battery locomotive to other types of mine haulage should be considered and limiting factors in each case should be carefully developed. This paper will briefly deal with these factors. So far as the writer has been able to determine, the first storage-battery locomotives for mine haulage were manufactured in 1897 or 1898 and were tried out in the Pocahontas coal field, but they were not sufficiently satisfactory to justify their continued use. Battery explosions were frequent and caused serious damage to the wiring, electrical equipment, and the clothing and bodies of the motormen. Sulfuric acid was used as the electrolyte. Experiments were then conducted with locomotives bearing reels of flexible cable through which connection between the motors of the locomotive and the trolley wire was maintained. At first, these reels were turned by hand. Later, the reels were revolved by contact with the wheels of the locomotive, being raised out of contact with the wheels, by a lever, when necessary. About 1902, the plan of operating the reel, by chain and sprocket wheels, from one of the locomotive axles, as is still the practice, was devised. The popular floating motor-driven reel had its inception in the Pocahontas fields prior to 1906. The maximum radius of operation of the reel-type locomotive is about 500 ft. (150 m.) from point of connection with trolley wire. This is ample for room work and certain entry work, but the need for a machine that would operate entirely independently of the trolley wire was so great that, with the development of the storage battery, renewed efforts were made to manufacture a successful storage-battery locomotive. About 1908, the gasoline locomotive was introduced. In spite of many objections to this type of machine for such work, the fact that hun¬dreds of these machines were purchased was proof of the need for a machine operating independently of the trolley.

Jan 1, 1922

By Oscar Johnson

The industry has been canvassed for information on methods of handling grinding steel at milling plants, an important subject overlooked in most descriptive articles on milling plant arrangements. The data collected are offered in this paper as a guide to designers and planners who have loading and storage problems to solve. WITH capacities of milling plants expanding from a few hundred tons per day to many thousand, replenishment of grinding media is an important phase of mill operation. Information on this aspect of milling procedure, solicited from several mining companies, is summarized here. At International Nickel's Copper Cliff concentrator the normally strenuous job of changing rods is considerably simplified by the use of the Garrow rod charging machine, Fig. 1. The overhead crane, Fig. 2, brings a bundle of rods, weighing four to a ton, to the loading platform of the machine, positioned in front of the mill. The rods roll one by one down the slight incline of the platform onto a conveyor which sends them into the mill. A modified version of the Garrow machine, Fig. 3, is used at the Federal mill of St. Joseph Lead Co. An overhead crane places the portable steel structure in position in front of the discharge end of any one of the five 9x12-ft rod mills. It then raises a bundle of about twenty 3-in. rods to the discharge platform of the charging machine. The rods are 11 ft 7 in. long and weigh about 278 lb. By tripping a lever the operator allows one rod at a time to roll onto the inclined rollers. A slight push by the operator sends the rod smoothly into the mill. The Union Miniére du Haut Katanga rod charging machine, Fig. 4, is mounted on a pair of wheels at the forward end with swiveling castors at the back for steering it to position for use or storage. Wheels are equipped with locking brakes to maintain the machine in position while it delivers rods to the mill. The device is made in two parts. The first consists of the base, which carries the supporting wheels, grooved rollers, and drive. The other part serves as the rod deck, which can carry up to six 3-in. x 12-ft rods. A short boom built integral with the base reaches through the mill trunnion and delivers the rods into the mill barrel. Three grooved guide rollers ,are provided to receive the rods from the sloping charging deck. One rod at a time is fed to the rollers and thus delivered into the mill. Two of the rollers are driven by 11/2-hp motor through a V-belt drive. The third roller is driven off the first by a single V belt in a groove below the rod groove and on the same center line. Rods are delivered to the charger by an overhead crane in bundles of three to six as needed. The power is supplied by cables plugged into power outlets, suitably located near the rod mill discharge end. The Oliver Iron Mining Co. uses a rod charger, Fig. 5, suspended from a monorail by cables. It is constructed .of structural steel and has two decks, each capable of carrying five rods of 4-in. maximum diameter. The rods ride in grooved free-turning rollers. Legs extending down from the mill end of the mechanism act as supports when the unit is ex-

Jan 1, 1955

By H. S. Bell

IT SEEMS unnecessary to dwell upon the advantages of the modern pipe still as compared with the older type of distillation equipment used by oil refiners. The relatively low installation cost, coupled with remarkable operating efficiencies of pipe stills, precludes the consideration of other types except in rare instances where some peculiarity of product or plant may have an influence. The question of the actual heat required to distil petroleum is quite involved. We have extensive data on the latent heats of the various hydrocarbons under different conditions of pressure. We also have information regarding the specific heats of various oils and the effect of temperature thereon. Because of the complexity of petroleum and of each fraction, it seems impossible to theoretically analyze the partial-pressure effect of the great number of hydrocarbons upon one another during distillation. If a distillation curve and percentage analysis of any crude or product are available, it is possible to construct a curve with ordinates representing per cent. distilled and B. t. u. per pound or per gallon, or other desired unit. To do so the crude is split into fractions, of 5 or 10 per cent. The boiling point and gravity of each fraction being determined, it is possible to evaluate the heat required. As each fraction is removed, the residue must be raised to a higher temperature and latent heat supplied for the successive fraction. As the calculations progress, the latent heats decrease while the specific heats increase. Such a curve is illustrated by Fig. 1 for a typical 39.9 B° North Texas crude.

Jan 1, 1928

By G. M. Ritcey, M. J. Slater, B. H. Lucas

The recovery of uranium from acid leach slurries by continuous ion exchange, or solvent extraction using sieve-plate pulse columns, is compared. Differences in processing costs are of prime concern and can be related to differences in the unit operations of the two methods, as well as the chemical and physical properties of the slurry. Parameters are defined for the operation of the solvent-in-pulp process and the design of the continuous ion exchange column. Pilot plant operating experience with both recovery systems is described, and an overall assessment of the relative costs is presented.

Jan 1, 1973

By George W. Healy, Ko Yamaguchi

In typical calorimetry the energy given off by a material under study is transferred to a water bath, whose temperature is sensed by a thermometer; for correct measurement the water bath must attain a uniform temperature to which the thermometer must respond. This introduces two sources of error, non-uniformity of the heat sink and a time lag until its temperature is registered. These errors may become important where a rapid process such as solidification of metals and alloys is being studied by means of Oelsen'sl quantitative thermal analysis. To overcome this difficulty, a calorimeter sink was conceived in which the water bath is replaced by a copper coil, which serves simultaneously as heat

Jan 1, 1967

THE refining period of an open-hearth heat blends imperceptibly into the finishing period, during which final adjustments are made in slag composition, in bath action and temperature, and in composition of the steel, in order to prepare it for casting into ingots. Operations must be governed by the consideration that alterations in the character of the heat during the finishing period must be held to a minimum. In a broad sense, the finishing and deoxidation period of a heat may be said to be- gin when the action of the last ore addition has ceased, and to end when the teeming of the ingots is completed. INGOT STRUCTLIRES A survey of the relative advantages and disadvantages of different types of ingot structure is required because deoxidation treatments during the finishing period control the amount of gas evolved during solidification and consequently determine the type of ingot structure. Four classes of ingots are recognized, de- pending upon the degree of deoxidation to which the steel has been subjected. These types are killed, semikilled, capped, and rimmed; typical examples of their structures are represented by ingots 1, 2, 5, and 7, respectively, of Fig 9-1. The actual ingots from which these cross sections were sketched were all poured to the same height (indicated by the dotted lines) in the same type and size of bottle-top molds. The eight drawings of the figure represent selected types of ingot structure in a continuous series from "dead killed" to "wild," resulting from variations in the total quantity of gas evolved, from none at all to copious amounts, during solidification of the steel in the mold. Killed and semikilled steels are adjacent at the "quiescent" end of the ingot structure series where only small amounts of gas are evolved. The term "quiescent" describes the action of the molten metal during and subsequent to the teeming of killed and semikilled steels. Capped and rimmed steels are adjacent at the

Jan 1, 1964

By Carl Pierce

THE writer of this article has not attempted to write a technical paper; on the contrary, he has tried to express in "steel-plant English," for steel men, a viewpoint drawn from his practice and experience. It is not his thought that it shall be taken as the "last word" in the making of this class of steel, or that good rimming steel cannot be made by any other practice. The paper was written to serve as the basis of a discussion from which it is hoped much benefit may be derived. The paper deals only with rimming steel made by the open-hearth process, and with the lower carbon steels, such as sheet and tin bar, rivet stock, skelp, etc., although good rimming steel as high as 40 to 50 carbon can be made by having good open slags and giving proper attention to working and tapping temperatures.

Jan 2, 1926

By J. O. Betterton, W. M. Spicer

The solubilities of antimony in the a and ß-forms of zirconium were determined between 750" and 1300°C. The a-phase forms by a peritectoid reaction, and the a/(a + ß) and ß/(a + ß) phase boundaries rise in temperature with in- ' creasing antimony. Impurities in the 99.95 pct zirconium were sufficient to influence the phase boundaries and the variation reported is approximate. The restricted solid solubility of the terminal zirconium phases, which is especially characteristic of this system, is thought to result from the low free energy of the Zr2Sb phase. ZIRCONIUM-antimony alloys are important in zirconium alloying studies since antimony is one of the highest valent elements which can be used to make zirconium alloys. The dilute alloys are of further interest as they have somewhat better corrosion resistance' than pure zirconium. The first investigation of the phase diagram was made by Russi and wilhelm2 who found a eutectic reaction, liquid (- 17.5 at. pct Sb) = ß zirconium (- 11 at. pct Sb) + Zr2Sb, at 1430°C'. The Zr2Sb phase was of complicated hexagonal structure, and by thermal analyses of the relatively impure alloys then available, Russi and Wilhelm found evidence for the peritectoid formation of the a-phase. EXPERIMENTAL In the present work, the phase diagram was re-investigated in the region 0 to 5 at. pct Sb and 750" to 1300°C using iodide-zirconium alloys. Details of the procedure have been described earlier. Essentially the alloys were prepared by arc casting and were then examined by the annealing and quenching method. The times of annealing varied from 1 hr at 1300°C to 30 days at 760°C. As in other zirconium phase-diagram studies1"5 the impurities in the zirconium were still sufficient to affect the results, and the experiments will therefore be described in 3 parts. The results from the first 2 parts of the work are shown in Fig. 1. Here the ß/(ß + Zr2Sb) and a/(a + ZrzSb) phase boundaries were determined with alloys made from 99.9 pct zirconium,* and cast under such conditions that the Vickers hardness of a alloys extrapolated to 95 to 110 VPN at 0 at. pct Sb. Such alloys were not suitable for investigations of the (a + ß) region, and the results shown in Fig. 1 near the (a+ ß) and (a +ß + Zr2Sb) regions were determined with purer alloys. These alloys had an extrapolated hardness range of 75 to 85 VPN and were made from 99.95 pct zirconium. A deviation from binary equilibrium occurs in Fig. 1 as indicated by the (a + ß) region of pure

Jan 1, 1959

By M. A. Orehoski, J. M. Hodge

It is now generally conceded that if a steel is to develop optimum physical properties in the conventionally quenched and tempered condition, the microstruc- ture after quenching should consist wholly of martensite; and that transformation of austenite to intermediate-temperature products during quenching will have a deleterious effect upon the physical properties, particularly the toughness, of the tempered material. This implies that, in order to obtain the optimum physical properties from a given steel, its "harden-ability " should be high enough to suppress all transformation except that to martensite under the heating and quenching conditions to which it will be subjected, and this premise is probably the most important reason for hardenability control. However, the criterion of hardenability that at present is most widely accepted and used is based on a microstructure of 50 per cent martensite. This criterion, which was suggested by Grossmann,' does have considerable justification. It may be readily measured by a fracture or etch test and, since it represents the point at which the hardness is changing most rapidly with variations in cooling rate, it may be determined empirically from a hardness-depth curve by determining the point of steepest slope (the inflection point). Furthermore, in plain carbon steels or in steels of low hardenability, the difference in hardenability expressed in

Jan 1, 1947

By J. M. Hodge, M. A. Orehoski

It is now generally conceded that if a steel is to develop optimum physical properties in the conventionally quenched and tempered condition, the microstruc- ture after quenching should consist wholly of martensite; and that transformation of austenite to intermediate-temperature products during quenching will have a deleterious effect upon the physical properties, particularly the toughness, of the tempered material. This implies that, in order to obtain the optimum physical properties from a given steel, its "harden-ability " should be high enough to suppress all transformation except that to martensite under the heating and quenching conditions to which it will be subjected, and this premise is probably the most important reason for hardenability control. However, the criterion of hardenability that at present is most widely accepted and used is based on a microstructure of 50 per cent martensite. This criterion, which was suggested by Grossmann,' does have considerable justification. It may be readily measured by a fracture or etch test and, since it represents the point at which the hardness is changing most rapidly with variations in cooling rate, it may be determined empirically from a hardness-depth curve by determining the point of steepest slope (the inflection point). Furthermore, in plain carbon steels or in steels of low hardenability, the difference in hardenability expressed in

Jan 1, 1947

By R. J. Wasilewski

OBSERVATIONS have been made that the substitution of antimony for bismuth in Bi2Te3 leads to anomalies in some of the electrical and magnetic properties of the Bi2Te3-5S2TeS alloy system at the composition ratios 2 Bi2Te3 : 1 Sb2Tes and 1 Bi2Te3 : 2 Sb2Te3. Airapetiants and Efimova1 have reported the peaking of the nondegenerate hole mobilities, at these compositions for sintered materials and ascribe the peaking to the formation of ordered alloys. From a study of these materials produced by the Bridgeman

Jan 1, 1962

By Louis A. Panek

Ground movements in the zone adjoining an active cave were measured at four sites in the San Manuel Mine. Measurements were made to detect extension and inclination, basic components of displacement, which can readily be duplicated by mine personnel using relatively simple equipment. The displacements demonstrated the development of a zone of strain relief surrounding the active cave, within which the ground tends to migrate toward the cave, and extension cracks develop tangential to the cave. This expansion of the ground surrounding an active cave can be exploited to promote future caving; it also creates special problems with respect to the design of an effective ground support system for mine openings in the production area.

Jan 1, 1981

By E. T. Turkdogan

In this theoretical paper, a transport-reaction mechanism is suggested for the enhancement of the rate of vaporization of metals, or other materials, brought about by the process of convection and condensation. Based on theoretical reasoning it is predicted that, when there is a temperature gradient surrounding the heated object, a slight increase in the rate of vaporization brought about by natural convection is enhanced further as a result of condensation of the vapor close to the surface of the object. In order to derive the effective vapor-concentration profile, consideration is given to the super saturation of the vapor necessary for the homogeneous nucleation of the condensed phase from the vapor. For the formulation of the rate equation based on this mechanism, adequate information should be available on the transport properties of gases and vapors at elevated temperatures and the method of calculating nucleation pressures of the vapor. The methods of deriving such data are discussed in the paper and a rate equation is calculated for the vaporization of iron in helium for various temperature gradients in the boundary layer. Considerations are also given to the effect of oxygen on rates of vaporization of metals under isother ma1 and nonisotherma1 conditions. THE study of the methods of enhancement or retardation of basically transport-controlled vaporization reactions is of theoretical interest with possible practical implications. There are several ways of bringing about such effects. For example, Turk-dogan, Grieveson, and Darken1 demonstrated that the rates of vaporization of metals under isothermal conditions were increased by several orders of magnitude, up to the maximum rate attainable in vacuo, by introducing some reacting gas into the inert atmosphere surrounding the metal. Such an effect is brought about by the interaction of the counter-diffusing reacting gas and metal vapor in close proximity of the metal-gas interface. Another case which is often experienced in practice is that of vaporization affected by natural convection. Although several theoretical and experimental studies of this problem have already been made, no detailed consideration has been given to the possible effects of condensation of the vapor in the boundary layer on vaporization rates, which constitutes the subject matter of this paper. BASIC CONCEPT OF ENHANCED DIFFUSION-LIMITED VAPORIZATION When a heated object, for example a metal sphere, is submerged in a fluid medium, heat is transferred from the surface of the object to its surroundings by four simultaneously occurring transfer processes: i) free-molecular conduction at the gas-solid interface over the distance equal to the mean free path of the gas, ii) conduction and convection through the fluid-dynamic boundary layer, iii) latent heat of mass transferred, and it!) radiation. The free-molecular conduction becomes pronounced only when the total pressure in the system is very low, e.g., below 1 mm Hg. Therefore, this term may be neglected for ordinary pressures. At low mass-transfer rates, due to vaporization of the object, the contribution of process iii) to the heat transfer can also be neglected. Finally, since the temperature profile is not affected by radiation, the latter need not be considered. The natural convection is brought about by gravitational body forces arising from a decrease in the

Jan 1, 1964

By Harrison R. Cooper

Measurement of process material composition with on-line instrumentation has commanded attention of metallurgical plant management as a logical extension of the sampling operation, making possible immediate determination of essential data needed to maintain efficiencies at the highest possible level. The current status of methods employed for online composition analysis of slurries and solid materials is reviewed.

Jan 1, 1984

By N. B. Aughenbaugh, W. C. Patrick

The availability of a thorough, simple-to-use roof fall classification system is desirable for several reasons. First, such a system would expedite the reporting of falls for the purposes of estimating material removal costs, analyzing damage levels, and complying with federal regulations to report falls in certain areas of the mine. Second, the classification system would allow the mining engineer to record falls routinely with little time and effort expended. This would encourage him to make observations concerning what type of roof support would work best in a given situation. Third, and probably most important, an

Jan 3, 1979

By William Hurst

This is a presentation of the diffusivity theory for the calculation of the water drive on an oil reservoir in which the history of reservoir pressure with time are the essential parameters for the determination of the rate and cumulative water encroachment into a field. The main body of the paper is essentially the application of the principles underlined here to actual field data. It consists of the work plots of the radial-flow case, and includes a discussion of an illustrated problem for which the water-drive calculations are treated in conjunction with the volumetric-balance equation. The appendix is a mathematical treatment of the linear, radial, and spherical cases of water influx into a reservoir. Introduction The evaluation of oil reserves and the prediction of pressure behavior with different rates of production are related to the volumetric balance of the fluids entering and leaving the space occupied by the oil and gas originally present in the formation; that is to say, important information can be gleaned from a volumetric study of the oil, gas, and water produced from a formation as it affects the extent of change in volume of oil zone, the gas cap, and the amount of water influx from the adjoining water sands. It is not the purpose of this paper to enter into a discussion of the equation of volumetric balance, in which such pertinent information as subsurface sampling and the measurement of reservoir pressures play a predominant part, as this has been discussed in detail by others.1,2 However, there is an inherent difficulty that has limited the general application of this equation to a study of oil reservoirs; that is, the insufficient knowledge of the analytics for expressing the water drive on a field as a function of reservoir pressure. This to a large degree has been overcome and it is the purpose of this paper to present this theory in such form as to be applicable for reservoir calculations. Water Drive If the amount of oil originally in place and the gas space are known, it is a relatively simple matter to determine, by the volumetric equation, the cumulative water influx into a reservoir from the adjoining water sands. Often, however, the oil reserve as well as water influx must be 'determined, and in order to be able to make this calculation it is essential to assign a mathematical relationship for the varying water term that is compatible with conditions known to exist in the formation and gives an accuracy acceptable for engineering calculations. Various equations have been employed empirically by different investigators in making reservoir studies of water drive. One form used by Schilthuis2 expresses the rate of water influx into a reservoir at any time as proportional to the pressure

Jan 1, 1943

By William Hurst

This is a presentation of the diffusivity theory for the calculation of the water drive on an oil reservoir in which the history of reservoir pressure with time are the essential parameters for the determination of the rate and cumulative water encroachment into a field. The main body of the paper is essentially the application of the principles underlined here to actual field data. It consists of the work plots of the radial-flow case, and includes a discussion of an illustrated problem for which the water-drive calculations are treated in conjunction with the volumetric-balance equation. The appendix is a mathematical treatment of the linear, radial, and spherical cases of water influx into a reservoir. Introduction The evaluation of oil reserves and the prediction of pressure behavior with different rates of production are related to the volumetric balance of the fluids entering and leaving the space occupied by the oil and gas originally present in the formation; that is to say, important information can be gleaned from a volumetric study of the oil, gas, and water produced from a formation as it affects the extent of change in volume of oil zone, the gas cap, and the amount of water influx from the adjoining water sands. It is not the purpose of this paper to enter into a discussion of the equation of volumetric balance, in which such pertinent information as subsurface sampling and the measurement of reservoir pressures play a predominant part, as this has been discussed in detail by others.1,2 However, there is an inherent difficulty that has limited the general application of this equation to a study of oil reservoirs; that is, the insufficient knowledge of the analytics for expressing the water drive on a field as a function of reservoir pressure. This to a large degree has been overcome and it is the purpose of this paper to present this theory in such form as to be applicable for reservoir calculations. Water Drive If the amount of oil originally in place and the gas space are known, it is a relatively simple matter to determine, by the volumetric equation, the cumulative water influx into a reservoir from the adjoining water sands. Often, however, the oil reserve as well as water influx must be 'determined, and in order to be able to make this calculation it is essential to assign a mathematical relationship for the varying water term that is compatible with conditions known to exist in the formation and gives an accuracy acceptable for engineering calculations. Various equations have been employed empirically by different investigators in making reservoir studies of water drive. One form used by Schilthuis2 expresses the rate of water influx into a reservoir at any time as proportional to the pressure

Jan 1, 1943

By Albert Sauveur

Some writers believe that when austenite transforms completely into pearlite on slow cooling through the thermal critical range, such transformation does not imply the formation of any of the so-called transition constituents: martensite, troostite and sorbite. Might it not be claimed with as much justification that when water freezes it does so suddenly, solid ice being obtained without passing through the intermediate stages of ice and water? Obviously, regardless of the speed of solidification, this would be erroneous. Before reaching the completed solid condition, this must of necessity pass through an unbroken series of stages when the system consists of mixtures of water and of ice, the former decreasing and the latter increasing in amount. Are not these "transitionV stages in the freezing of water similar to the transition stages occurring in the transformation of austenite into pearlite? To clarify, let us consider in Fig. 1 the mechanism of the transformation of eutectoid steel from its austenitic to its pearlitic condition as it cools slowly through its thermal critical range. It is generally admitted that this transformation is the result of two distinct phenomena: (1) the allotropic change of gamma iron into alpha iron and (2) the crystallizing out of solution of the carbide Fe3C. Whether this crystallizing of Fe3C implies also its formation is immaterial for our purpose. In other words, whether it is the carbon in atomic dispersion which is present in gamma iron or molecules of Fe3C has no bearing upon the matter to be discussed. The transformation of gamma iron into alpha iron cannot take place suddenly. It must of necessity be progressive, regardless of the speed with which it may take place. At A, for instance, there would be present AB gamma iron and BC alpha iron. The distance MN does not refer to falling temperature, but to the passage of time. It may be assumed that the transformation takes place at a constant temperature (the Ar321 point). In a similar way, the crystallization of Fe3C out of the austenite solid solution must be progressive as depicted between M and N. At A there would be present AB gamma iron, BC alpha iron, CD carbon dissolved in gamma and in alpha iron and DE Fe3C. This condition may be described according to individual preference as martensite or troostite. To sum up, can the metal pass from condition

Jan 1, 1931