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By G. E. Archie

The usefulness of the electrical resistivity log in determining reservoir characteristics is governed largely by: (I) the accuracy with which the true resistivity of the formation can be determined; (2) the scope of detailed data concerning the relation of resistivity measurements to formation characteristics; (3) the available information concerning the conductivity of connate or formation waters; (4) the extent of geologic knowledge regarding probable changes in facies within given horizons, both vertically and laterally, particularly in relation to the resultant effect on the electrical properties of the reservoir. Simple examples are given in the following pages to illustrate the use of resistivity logs in the solution of some problems dealing with oil and gas reservoirs. From the available information, it is apparent that much care must be exercised in applying to more complicated cases the methods suggested. It should be remembered that the equations given are not precise and represent only approximate relationships. It is believed, however, that under favorable conditions their application falls within useful limits of accuracy. Introduction The electrical log has been used extensively in a qualitative way to correlate formations penetrated by the drill in the exploitation of oil and gas reservoirs and to provide some indication of reservoir content. However, its use in a quantitative way has been limited because of various factors that tend to obscure the significance of the electrical readings obtained. Some of these factors are the borehole size, . the resistivity of the mud in the borehole, the effect of invasion of the mud filtrate into the formation, the relation of the recorded thickness of beds to electrode spacing, the heterogeneity of geologic formations, the salinity or conductivity of connate water, and, perhaps of greatest importance, the lack of data indicating the relationship of the resistivity of a formation in situ to its character and fluid content. On the Gulf Coast it is found that the effects of the size of the borehole and the mud resistivity are generally of little importance, except when dealing with high formational resistivities or extremely low mud resistivities. Fortunately, little practical significance need be attached to the exact values of the higher resistivities recorded. Low mud resistivities are not common, but when this condition is encountered it may be corrected by replacing the mud column. With the present advanced knowledge of mud control, invasion of mud filtrate into sands can be minimized, thereby increasing the dependability of the electrical log. The effect of electrode spacing on the recorded thickness of a bed is often subject to compensation or can be sufficiently accounted for to provide an acceptable approximation of the true resistivity of the formation. As development of a field or area progressively enhances the knowledge of the lithologic section, the resistivity values of the electrical log take on greater significance, ultimately affording acceptable interpretations. The salinity, and

Jan 1, 1942

By K. O. Stamm, B. A. Rogers

Because it is the basis of the economically important operation of hardening steel by quenching, the A3 transformation in iron has been the subject of numerous investigations. Although the contributions to this subject are interesting, no general review will be given here. Readers who care to follow the matter further are referred to the comprehensive summary by Cleaves and Thompson,l which covers the literature to about 1935. Their references to 53 papers on the subject suggest that further investigation is hardly justifiable. However, considerable interest has devel oped recently concerning the reversibility of the transformation. From thermo-dynamic considerations, the transition ought to occur at the same point on heating or cooling, if the change of temperature is sufficiently slow. Yet all of the earlier investigators found a difference of several degrees. Burgess and Crowe,2 who used thermal methods, obtained average temperatures of 912" for Ac3 and 900°C. for Ar3 on electrolytic iron. Their data indicate a considerable range of temperature over which the change occurs, both on heating and on cooling. Terry3 measured the susceptibility in the critical range and estimated from the steepest parts of his curves that Ac3 came at 9I8° and Ar3 at 903°C. Ishiwara4 was one of the first investigators to report a shorter interval between the temperature of the change in the two directions. He measured the change of susceptibility of kaolin-coated samples of steel, in a hydrogen atmosphere, at rater of heating and cooling so low that about 3 or 4 hr. were required for the transformation to complete itself. His results show some variability between samples, but indicate that the difference between Ac3 and Ar3 is in the vicinity of 6°C. Roberts and Davey5 measured the space lattice in pure iron in the vicinity of 900°C. and concluded that a change occurs reversibly between 907' 3" and 910" 3°C., probably between 907" and 910°C. Wells, Ackley, and Meh16 made dilatometric determinations of the Ac3 and Ar3 points in samples of hydrogen-treated carbonyl iron maintained under a vacuum. They used three rates of heating and cooling: 2°, ½°, and .?°C. per min. and found the spread between the two points decreased with low rates. At the slowest rate, the Ac3 transition occurred at 909° to 909. 5°C. and the Ar3 change at 907°C. in three of the samples believed to contain the lowest percentages of alien elements. They concluded that if the rate of temperature change and the content of alien eiements were low enough, the A3 transformation would be completely reversible at 909.50 + 1°C. The question of reversibility is an interesting one and when some iron with especially small percentages of alien elements became available the opportunity to conduct an investigation was welcomed. This iron was prepared by the Division of

Jan 1, 1942

By B. A. Rogers, K. O. Stamm

Because it is the basis of the economically important operation of hardening steel by quenching, the A3 transformation in iron has been the subject of numerous investigations. Although the contributions to this subject are interesting, no general review will be given here. Readers who care to follow the matter further are referred to the comprehensive summary by Cleaves and Thompson,l which covers the literature to about 1935. Their references to 53 papers on the subject suggest that further investigation is hardly justifiable. However, considerable interest has devel oped recently concerning the reversibility of the transformation. From thermo-dynamic considerations, the transition ought to occur at the same point on heating or cooling, if the change of temperature is sufficiently slow. Yet all of the earlier investigators found a difference of several degrees. Burgess and Crowe,2 who used thermal methods, obtained average temperatures of 912" for Ac3 and 900°C. for Ar3 on electrolytic iron. Their data indicate a considerable range of temperature over which the change occurs, both on heating and on cooling. Terry3 measured the susceptibility in the critical range and estimated from the steepest parts of his curves that Ac3 came at 9I8° and Ar3 at 903°C. Ishiwara4 was one of the first investigators to report a shorter interval between the temperature of the change in the two directions. He measured the change of susceptibility of kaolin-coated samples of steel, in a hydrogen atmosphere, at rater of heating and cooling so low that about 3 or 4 hr. were required for the transformation to complete itself. His results show some variability between samples, but indicate that the difference between Ac3 and Ar3 is in the vicinity of 6°C. Roberts and Davey5 measured the space lattice in pure iron in the vicinity of 900°C. and concluded that a change occurs reversibly between 907' 3" and 910" 3°C., probably between 907" and 910°C. Wells, Ackley, and Meh16 made dilatometric determinations of the Ac3 and Ar3 points in samples of hydrogen-treated carbonyl iron maintained under a vacuum. They used three rates of heating and cooling: 2°, ½°, and .?°C. per min. and found the spread between the two points decreased with low rates. At the slowest rate, the Ac3 transition occurred at 909° to 909. 5°C. and the Ar3 change at 907°C. in three of the samples believed to contain the lowest percentages of alien elements. They concluded that if the rate of temperature change and the content of alien eiements were low enough, the A3 transformation would be completely reversible at 909.50 + 1°C. The question of reversibility is an interesting one and when some iron with especially small percentages of alien elements became available the opportunity to conduct an investigation was welcomed. This iron was prepared by the Division of

Jan 1, 1942

By M. A. Steinberg, J. Wulff, R. Kamm

In a previous paper1 from this laboratory, the development of a lead grid method for exploring the distribution of strain and density within metal powder compacts was described. In that work thin lead foil with rectangular holes cut at regular intervals was inserted with the powder fill, the arrangement pressed and then radiographed to permit measurement of the deformation of the lead grid. Densities at each grid element obtained in this manner were plotted as a function of the die dimensions. From such plots it was found that the densest part of a compact pressed from one side (the top) is at the top outer region and the least dense at the bottom outer region of the specimen. The axial density maximum occurs more often nearer the bottom than at the top. As a result of such exploratory measurements, it appeared reasonable to conclude that variations in density could be attributed in the main to die wall friction. Thus compacts of large diameter appeared relatively uniform in density except where the die fill had been uneven. Finally it was found that lubrication of the finely finished die cavity contributed more to magnitude and uniformity of density within the compact than interparticle lubrication. Since publication of the above results, it was found that circular-hole grids could be more accurately made and, when deformed within the powder, more readily measured and analyzed. Much of the former work was repeated and new results which include the effect of lubrication, compact height, pressure, speed of pressing and vacuum pressing are reported in the present paper. Circular-hole Grids and Analyses OF Radiographs Commercial lead sheet 0.008 in. in thickness was used in all the work reported. The 0.0938-in. diam holes were punched in the sheet on 1/8-in. centers to an accuracy of 0.001 in. The finished grid used contained eight or more holes in a row and from I to 24 rows. The lead sheet was clamped between two pairs of brass strips bolted to a small milling machine table which was itself bolted to a bench in correct position near a vise which held the punch. Travel of the lead grid in two dimensions was controlled by two steel lead screws calibrated in 0.001-in. divisions. A stripper plate was used on the punch to avoid distortion of the lead foil. A high carbon-high chromium (chrocar) one-piece steel die was used throughout the work. The die cavity was 1.125 in. in diam and the clearance between plungers and die wall was 0.001 in. The die was also used for pressing from both ends with two long plungers. Finally, lapping of die and plungers gave a surface whose rms value On an Abbot profilometer was 5 micro-in. The die walls and plungers were, except where otherwise noted, lubricated with a stearic acid suspension in benzene. This was put on in multiple layers and allowed to dry before filling the die.

Jan 1, 1949

By H. I. Najarian

This paper is a companion piece to the description of the electrothermic process that begins on page 141. It will be confined to a brief story of the development. of the Weaton-Najarian vacuum condenserf at this plant, together with up-to-date design and operating data. The Josephtown smelter was designed primarily for production of zinc oxide. However, the development of a method for production of zinc metal had always been under consideration, and accordingly one of the original eight units of the elcctro-thermic furnaces built in 1930 was set up to produce metal. The design of this furnace was identical with that of the oxide furnaces except that in place of oxide tewels opening into oxide manifolds, conventional conical clay condensers—similar to condensers used in horizontal retort smelting—were installed around the periphery of the furnace and in several tiers vertically for condensing the zinc vapors. The early experimental work in trying to condense zinc out of the mixtures of zinc vapor and carbon monoxide gas from the electrothermic furnaces indicated that, while the gases from electrothermic smelting would condense in surface-type condensers, the formation of blue powder was excessive and condenser efficiency low. Furthermore, operating a large unit of electric furnace with several hundred small condensers, with attendant high labor cost and unfavorable operating conditions, did not appeal to us. We also realized that a single unit of surface condenser capable of condensing 12 torg tons of metal per day would be of huge dimensions and possibly difficult of control. So we took as our aim the development of a method whereby a single condenser unit of reasonable dimensions would condense zinc, in one step, from the large volume of gases that the electric furnaces produced. We set about searching for knowledge on zinc metallurgy and design of zinc condensers in particular. Our study of the prior art focused our attention on the oft-repeated statement by earlier experimenters, that the most efficient way to condense metallic vapors, such as zinc vapors, was to bring the vapors into "intimate contact" with molten metal; but the methods offered for securing this "intimate contact" in any practical manner left much to the imagination. We were handicapped by not having some-one on the Josephtown smelter staff who could lay claim to being an expert zinc metallurgist and could give guidance from actual experience on the practicability of various schemes that haunted our imagination. Laboratory Experiments However, we had an expert ex-steam engineer in the person of George I?. Weaton, manager of the Josephtown smelter, who had had long experience with steam-jet condensers and would reiterate his belief at every opportunity that the logical and the most efficient way to condense zinc would be with a jet-type condenser. We became intrigued by the possibilities of a zinc con-

Jan 1, 1944

By J. E. Ostberg, G. Phragmen, A. Hultgren, S. Wohlfahrt

Detailed study was made of a number of rimming ingots, both low and high carbon, and especially upon effects of superimposed air pressure. Requirement to suppress core bubbles is between 10 and 15 atm; at 6.5 atm freezing was in semikilled manner and at 3 atm, steel was of rising type. Probable mechanism of freezing under various conditions is discussed. AN earlier paper' reported an investigation made by a committee for studying rimming steel ingots appointed by Jernkontorets in Stockholm. The present paper is the outcome of some further work done by the same committee. Since the characteristics of ordinary rimming steel are connected closely .with the amount of gas liberated during freezing and since this amount of gas is governed by the pressure, it was considered of interest to ascertain in what manner and to what extent definite pressures applied to the top of the liquid steel in the mold would affect the solidification process and the consequent structure of a rimming steel of ordinary composition. The experiments were made at the Domnarfvets Steel Works. The steel was made according to normal practice in a 4-ton Rennerfelt electric furnace. Ferromanganese was added in the furnace; no aluminum was added, with one exception. Analyses of the four heats are given in Table I. The top-poured ingots measured about 12 in. sq x 48 in. and weighed about 1300 lb. One or two ingots of each heat were allowed to solidify under pressure, using a special device for admitting compressed air to the upper closed part of the mold, as shown in Fig. 1. A heavy plate sealed with asbestos was bolted to the top of the mold. The plate had a tapered aperture for pouring. Immediately after pouring the hole was closed by a wedged plug, and compressed air was admitted through a hole in the plug. Because of some delay in applying the plug, full pressure was not reached immediately. The pressure was adjusted to the desired value as indicated by a manometer. In order that the interior of the ingot might have the benefit of the pressure, the freezing of the top crust was delayed by a refractory lining applied to the top part of the mold, Fig. 1. Ingots were also cast from each heat without applied pressure, and with and without refractory lining at the top. Axial sections of ingots were cut either of the whole ingot or of some part of it of special interest; sections were polished and usually etched.' To facilitate description of structures the following terms may be used for different types of ingots solidified under gas evolution: 1. Box-hat or boot-leg ingot: Abundant gas evolution during casting and during rimming; no rim holes. 2. Normal rimming ingot: Lively gas evolution during rimming; usually rim holes in lowest part of

Jan 1, 1952

By J. H. Frye, J. W. Caum

ONE of the most important methods of increasing the hardness of metals is alloying. In spite of the widespread use of alloys, the fundamental mechanism of alloy hardening is little understood. This is true even of the simplest form of alloy, the primary substitutional solid solution in which solute atoms substitute for solvent atoms at random in the crystal lattice of the latter. A fundamental understanding of the mechanism of solid-solution hardening would be important, both because of the widespread use of alloys of this type and because of the light that might be thrown on the mechanism of hardening in more complicated alloys. The present investigation covers the hardness of primary substitutional solid solutions of zinc, gallium,, germanium; and arsenic in copper. All of these are B subgroup elements from the third period of the periodic table. Cu, Zn, Ga, Ge, and As are in groups I, II, III, IV, and V, respectively and lie just to the right of the transition elements. Because of their cost, it is unlikely that Ga-Cu and Ge-Cu solutions will ever be of commercial importance, but the intent of this study has been to discover some of the fundamentals of solid-solution hardening and it has been demonstrated that such a study is far more likely to be fruitful if alloys are made up on the basis of position of the constituent elements in the periodic table than if commercially important alloys are used. Many investigations have. been made of the hardness of substitutional solid solutions, but lack of attention to purity of the metals, infrequent grain-size control, and the use of varying testing techniques have virtually invalidated any comparisons. The purpose of most investigations has been to solve immediate problems and not to solve the primary problem: Why do solid solutions usually have a greater hardness than pure metals? PREVIOUS WORK Theories have been advanced to account for the hardness of solid solutions,, but relatively little experimental work has been done. Perhaps the first experimental work of merit was that of Norbury1 on copper alloys. He showed that for several alloys there was a correspondence between the hardness of one atomic per cent solutions and atomic volume of the solutions. More recently Brick, Martin, and Angier2 have investigated the effect of various solute elements on the hardness of copper. They concluded that the hardening effect of these solutes depended "primarily on the difference in atomic volume of solute and solvent or, relatedly, upon the parameter, change of the solvent or the extent of solid solubility." They also observed the effect of these elements on hardness and texture developed by rolling and by annealing of rolled material. Austin3 examined the hardness and response to heat-treatment of various iron solid solutions. Frye and Hume-Rothery4 measured the hardness of a number of silver solid solutions containing approximately

Jan 1, 1943

By J. W. Halley, G. L. Plimpton

Because of the two distinct stages in the solidification of rimmed steel, segregation in the rimmed ingot is more complex than that in the killed or semikilled ingot. In the earlier stage, chemical reactions, resulting in evolution of gas and vigorous stirring of the metal, effect a degree of negative segregation unique to rimmed steel. The composition of this zone constitutes the principal quality advantage of this type of steel. In the later stage of solidification, after the evolution of gas has ceased, the segregation follows the general pattern of a more completely deoxidized steel. However, the composition of the liquid remaining after the first solidification stage varies markedly from that of the original melt, some constituents having been partially removed as reaction products while the concentration of others has been intensified by rejection from the metal solidifying in the first zone. The aim, from the standpoint of segregation, in rimmed steel of high quality is to effect a maximum negative segregation in the rim zone without excessive concentration of undesirable elements at the center of the ingot. To achieve this aim, the composition of the melt may be varied and the furnace and pouring practice may be adjusted within certain limits. It is the purpose of this study to discuss segregation in rimmed steel from the standpoint of the mechanisms that produce it and to survey the phases of open-hearth practice that influence those mechanisms. Mechanisms Producing Segregation The mechanisms that determine the degree of segregation in the rimmed ingot are closely interrelated, making it difficult to select the primary factors and to determine a satisfactory order for presenting them. For instance, the question of sulphur segregation is relatively simple, since sulphur is not directly involved in chemical reactions in the ingot; but its concentration in the rim zone is dependent not only on its original analysis in the melt, its segregation coefficient, and the freezing rate, but also on the rate of its removal from the impure film on the solidifying surface. This washing action involves all the factors (such as freezing rate, the carbon-oxygen product, pressure, etc.) that determine the rate of gas evolution and hence the efficiency of film removal. Sulphur distribution between the rim and core is affected by the volumetric ratio between the two zones, and its segregation in the core is a function not only of the freezing rate of the core but also of all the foregoing factors that determine its concentration in the metal when solidification of the core starts. To simplify the presentation, it is proposed to treat the mechanisms affecting segregation independently in this section, reserving a discussion of their over-all effects for the section in which actual segregation data are given. The factors affecting segregation will be treated in the following order: (I) differential solidification, (2) removal of constituents as

Jan 1, 1945

By V. R. Garfias

EVEN before the arrival of Cortes in 1519, the history of Mexico was closely linked to that of its mineral production; the mining activities of the Aztecs being thus described by Clavigero, one of the early historians: In the mountains of Anahuac there abound in veins all kinds of metals, and infinite variety of other fossiliferous products. The Aztecs obtained gold from the countries of the Cohuijques, of the Mixtecas, of the Zapotecas and from various other places. They gathered that precious metal usually in grain, from the sands of the rivers, keeping a certain portion for the crown. They obtained silver from the mines of Taxco, of Tzumpango and others; however, this metal was not as esteemed by them as by other neighboring nations. They had two kinds of copper; one hard, which they used instead of iron to make sickles, lances and all kinds of rural and military instruments and another, soft, with which they made kettles, goblets and other receptacles. This metal abounds mainly in the province of Zacatula and in that of Cohuijques, which at present is in the kingdom of Michoacan. They obtained tin from the mines of Taxco and lead from those of Izmiquilpan, located in the country of the Otomiea. From the tin they made money, and the lead, we know they sold in the market places, but we ignore the uses to which they applied it. They also had mines of iron in Tlaxcala, in Taxco and in other places; but they either had not discovered them, or did not know how to make use of the metal they contained. In Chilapa there were mines of mercury, and in other places there were mines of sulphur, alum, vitriol, cinnabar, cohre and of a white earth which they esteemed highly. As regards mercury and vitriol, we do not know of what use they were to them; the other metals they used in paintings and dyes. There were then great abundance of amber and asphalt-bitu- men of Judea--on the coast of the seas and many cities of that territory paid tribute of one and the other to the kingdom of Mexico. They mounted the amber in gold, and it was only used as ornament and display by them. With the asphalt they made certain perfumes. The following extracts dealing with pre-Colonial gold are taken from the famous "Cartas de Relación" to Charles V, in which Cortea described the progress of the Conquest: . . . here there came two chiefs who owned lands in the valley; one four leagues down the valley and the other two leagues up the valley and they gave me some gold necklaces of little value and seven or eight girls. . . . . . . that day I left the City of Churultecal and traveled four leagues to some villages of the City of Cuasucingo where the natives received me very well and gave me women and pieces of gold. . . .

Jan 1, 1937

By C. T. Cox

The title of this short paper necessarily implies that friction articles comprise a distinct and unique field and are different from the other metal-powder articles, such as bearings, electrical contacts, and magnets. However, this distinction is rather hard to define in that it is really one of degree and not Of kind. It would appear that the main distinction is that friction are are articles of rather large pressing area. In other words, they are articles in which the area Of the mold in which the metal powder is pressed is relatively large. Other articles made from meta1 powders are generally of rather small area, usually a few square inches, while in friction articles the area ranges up to several hundred square inches. The satisfactory production of meta1-powder friction articles involves many production problems and a large number Of these are accentuated by the large area' Since it is impossible in the short space of this Paper to describe adequately all the problems involved, I have thought it best to merely mention some Of them and to place particular emphasis upon a problem that is common to all metal-powder articles, although it is of greater importance in the making of friction articles. This problem has to do with the effect On the properties of a friction article of small variations in the composition. However, before discussing the problems, it is probably appropriate that some mention be made of the limitations on the use of friction articles. Most engineers are familiar with the general field that can be characterized as constituted by clutch facings and brake linings, and undoubtedly have heard many stories of how metal-powder friction articles have had a service life 10 times as long as nonmetallic friction materials, and of instances where metal-powder friction articles have operated satisfactorily where no other material could be used. These instances should not be regarded as criteria for the assumption that metal-powder friction articles are capable of universal use in the friction field and will always outperform other materials. On the contrary, metal-powder friction articles are unsuitable for numerous applications, either on a performance or on a cost basis. Metal-powder friction articles will not replace wooden block brakes for wagon wheels nor cast-iron brake shoes for railway car wheels, to mention just two obvious examples. Metallic friction articles cannot be used where they must act as heat insulatorsl for they have a relatively high thermal conductivity as compared with asbestos. This is a detriment in some uses, as in certain airplane brakes having hydraulic actuators provided with rubber seals. The metallic friction material readily transfers the heat developed at the braking surface back through the material to the rubber seal and destroys it. Within its limited field, metal-powder friction material has proved satisfactory, but many problems are involved in the Selection of the proper material to use in an application and in the commercial pro-

Jan 1, 1945

By F. H. Deily, L. W. Ledgerwood, J. E. Eckel

A new method for drilling the earth's formations has undergone extensive laboratory and shallow earth drilling experimentation. This method, pellet impact drilling, uses the energy of a large mass of high velocity steel spheres to break and crush the rock. Pellets are confined to a region close to the hole bottom. Motive fluid for transporting and recycling the pellets is supplied by a modified jet pump. The pellet drilling method has inherent advantages over conventional rotary drilling. First, only a nominal amount of weight need be applied to the hole bottom. Second, only a very small amount of torque is required for bit rotation. Third, means are available for continual replacement of the cutter medium. The experimental laboratory work and analytical procedures necessary for the design of a pellet drill bit are described. In the laboratory program approximately half the effort was devoted to the development of a better understanding of the physical process, and half to the empirical testing of new bit configurations. Factors such as pellet size and velocity, jet pump characteristics and modifications, and power distribution are discussed. The design and construction of a pellet impact bit for drilling a 9 in. hole with 1 1/4 in. steel pellets are described. Drilling performance in representative rocks, hydraulic operating characteristics, and metallurgical problems are discussed. INTRODUCTION This paper discusses an attempt to reduce drilling costs through the development of a drilling method basically different from rotary drilling. Publications on drilling research indicate that the major effort on the part of manufacturers and operators has been confined to research in rotary, or rotary-percussion drilling. This applied drilling research has produced significant gains in drilling rates and bit life, but thus far it has failed to achieve any major decrease in general drilling costs. From recent statistics released by Drilling Contractors, it can be shown that the total cost of drilling an "average" well in 1953 was about 2 1/4 times the corresponding cost in 1935. Analysis of the costs will show that they are not due to inefficient field operations; they are due instead to both an inflated economy and greater "average" well depths. Diligent work by the industry has reduced the backlog of potential economic improvements in rotary drilling to a group of rather marginal prospects. Increasing depths and poorer quality reservoirs at these depths continue to make the drilling cost problem more acute. Hence, the aim of the work reported here was to develop a new drilling method not limited by the inherent characteristics of rotary drilling and thus capable of attaining further significant reductions in drilling costs. The effort devoted to research on this proposed new drilling method was of considerable magnitude and represented .in excess of 37 man-years of research. The affiliates of Standard Oil Co. (N. I.) sponsored this development program which was conducted by the Drilling Methods Section of the Carter Research Laboratory in Tulsa, Okla. The purpose of this paper is to

Jan 1, 1957

By Morris Muskat, J. M. McDowell

In both production and refining operations of the oil industry many processes are controlled by the gas-liquid phase relationships of the hydrocarbon mixtures of interest. The quantitative behavior of fractionating or distillation columns and stills depends on the changes in the equilibrium distributions of the hydrocarbon components between the gas and liquid phases as the pressure or temperature conditions may vary along the length of the column or as the gross operating parameters and compositions are varied. In oil producing operations the nature and amount of gas phase developed within an underground reservoir as it is being depleted and its pressure declines also involve the basic equilibrium gas-liquid phase interactions. The influence of surface conditions of temperature and pressure and various separation procedures on the nature and amount of stock tank oil and natural gas recovered from a given well stream is likewise determined by the same basic phase equilibrium characteristics of the hydrocarbon systems. Such equilibrium separation of the gas and liquid phases in a well stream is of importance both in establishing optimum separator conditions for obtaining maximum stock tank oil yields and in the general problem of crude stabilization. The phenomena involved in these problems and their quantitative aspects can, of course, be established in each individual instance by appropriate laboratory experimentation. It has been found, however, that by associating with the individual hydrocarbon components functional characteristics de- scribing their individual gas - liquid phase equilibrium behavior, the phase properties of the composite mixtures can be predicted by mathematical computation. These characteristics have been termed "equilibrium constants", or "equilibrium ratios"," and are defined by the general equation: where K, is the equilibrium ratio for the jth component, y, is the rnol fraction of that component in the gas phase, and xj is the corresponding mol fraction in the coexisting liquid phase. Considering the Kj as representing available and measurable properties of the individual components of a mixture, and as defined by Eq. (l), it is readily shown that in a coexisting gas-liquid system the rnol fraction concentrations of the individual components in the gas phase, y,, and those in the liquid phase, x,, are given by the expressions: where the nj are the corresponding rnol fraction concentrations in the composite system, and ng is the mol fraction of the whole which is in the gas phase. The basic unknown in Eq. (2) is n,: which gives the gross separation between the gas and liquid phases. This may be determined in principle by imposing the requirement that the sums of the mol fractions in both the gas and liquid phases are unity, i.e. by the equations: The solution of the equivalent Eqs. (3) lying between 0 and 1, when inserted into Eqs. (2), provides a complete description of the compositions of the coexisting gas and liquid phases. While the Eqs. (3) are essentially equivalent to polynomial equations, such transformations are of little value when dealing with multicomponent sys-

Jan 1, 1949

By J. M. McDowell, Morris Muskat

In both production and refining operations of the oil industry many processes are controlled by the gas-liquid phase relationships of the hydrocarbon mixtures of interest. The quantitative behavior of fractionating or distillation columns and stills depends on the changes in the equilibrium distributions of the hydrocarbon components between the gas and liquid phases as the pressure or temperature conditions may vary along the length of the column or as the gross operating parameters and compositions are varied. In oil producing operations the nature and amount of gas phase developed within an underground reservoir as it is being depleted and its pressure declines also involve the basic equilibrium gas-liquid phase interactions. The influence of surface conditions of temperature and pressure and various separation procedures on the nature and amount of stock tank oil and natural gas recovered from a given well stream is likewise determined by the same basic phase equilibrium characteristics of the hydrocarbon systems. Such equilibrium separation of the gas and liquid phases in a well stream is of importance both in establishing optimum separator conditions for obtaining maximum stock tank oil yields and in the general problem of crude stabilization. The phenomena involved in these problems and their quantitative aspects can, of course, be established in each individual instance by appropriate laboratory experimentation. It has been found, however, that by associating with the individual hydrocarbon components functional characteristics de- scribing their individual gas - liquid phase equilibrium behavior, the phase properties of the composite mixtures can be predicted by mathematical computation. These characteristics have been termed "equilibrium constants", or "equilibrium ratios"," and are defined by the general equation: where K, is the equilibrium ratio for the jth component, y, is the rnol fraction of that component in the gas phase, and xj is the corresponding mol fraction in the coexisting liquid phase. Considering the Kj as representing available and measurable properties of the individual components of a mixture, and as defined by Eq. (l), it is readily shown that in a coexisting gas-liquid system the rnol fraction concentrations of the individual components in the gas phase, y,, and those in the liquid phase, x,, are given by the expressions: where the nj are the corresponding rnol fraction concentrations in the composite system, and ng is the mol fraction of the whole which is in the gas phase. The basic unknown in Eq. (2) is n,: which gives the gross separation between the gas and liquid phases. This may be determined in principle by imposing the requirement that the sums of the mol fractions in both the gas and liquid phases are unity, i.e. by the equations: The solution of the equivalent Eqs. (3) lying between 0 and 1, when inserted into Eqs. (2), provides a complete description of the compositions of the coexisting gas and liquid phases. While the Eqs. (3) are essentially equivalent to polynomial equations, such transformations are of little value when dealing with multicomponent sys-

Jan 1, 1949

INTRODUCTION The preceding chapters have brought us to a point in the mineral appraisal process where the composited sample values can now be used to estimate the grade and tonnage of the total mineral deposit. There are many techniques whereby drill hole composites and/or other sample data are used to assign grade and estimates to the surrounding rock. Matheron and his students have properly called such techniques extension functions. Before embarking upon a detailed discussion of extension functions, it is necessary that we take time to consider the concept of geostatistics as advocated by George Matheron who developed the "Theory of Regionalized Variables," which he published in 1962 (Matheron, 1971). The concept of regionalized variables has important application in the techniques of mineral appraisal. The position or location of a mineral sample within a deposit can be almost as important as its value. Geostatistics, when defined as "the application of the theory of regionalized variables* to the study of mineralized volumes of rock," takes into consideration the position as well as the magnitude of the value of the sample. The principles of geostatistics, as outlined by Matheron, represent a major step forward in the mineral evaluation process, because they provide a sound theoretical and practical basis for quantifying the geological concepts of (1) area of influence of a sample, (2) the continuity or lack of continuity of mineralization within the ore body, and (3) the lateral changes in mineralization according to the trend direction of an ore body and its orthogonal components; or in other words, a measure of the anisotropy of the deposit. Royle (1971) has defined the objects of geostatistic as being: "1. To estimate the most likely value of blocks of ore, or the values of the whole deposit; and 2. to estimate the errors of such estimates. This latter is important as, in addition to providing a check on unwarranted optimism, it shows where more valuation work may be needed." Because of the great importance of these concepts in mineral evaluation, an introduction into the theory of regionalized variables, and the study of a practical approach to its application is outlined here. REGIONALIZED VARIABLES VS. RANDOM VARIABLES Classical statistics, as discussed in earlier chapters, grew out of the study and application of probability theory. Probability is concerned with the outcome of random events and therefore classical statistics is built upon the theory of random variables, i.e., the probability of independent events. The validity of most statistical inferences depends upon sample randomness being assured for unbiased results. Where independent events cannot be assumed the results of statistical inference becomes suspect. On the other hand, geostatistics is concerned with variables that have position in space as well as magnitude, hence the term regionalized variables. Mineral deposits are not the only field to which the theory of regionalized variables is applicable. Many natural phenomena that demonstrate a relationship between change in magnitude and position in space are amenable to application of geostatistical techniques. Mineral deposits vary greatly in their geosta-

Jan 1, 1980

By J. R. Thoenen, M. C. Malamphy, G. K. Dale

The beginning of the war and the events leading up to it precipitated a near crisis in the aluminum industry. Demands for the metal reached proportions far beyond the prewar production capacities and, in addition, the submarine menace seriously curtailed the importation of bauxite from South America, hitherto a chief source of high-grade ore. The situation required an intensive search for domestic ore to augment the reserves and in October 1941 Congress directed the Department of the Interior to investigate the extent, mode of occurrence, and quality of bauxite in the United States. In December of that year the Bureau of Mines and the Geological Survey began the search for bauxite in Arkansas, where more than go per cent of the domestic ore had been produced and where the greatest amount of bauxite was known to occur. The program involves the geophysical and geological investigation of the Arkansas bauxite region and the core drilling of areas considered favorable for the occurrence of bauxite deposits. Cores taken from the bauxite-kaolin zone are sampled and analyzed in the Bureau of Mines laboratory in Little Rock. The information from each of the deposits discovered is then assembled, the bauxite is graded with respect to its possible utility, tonnage estimates are made, and the whole is presented in the form of a war minerals report. Thirty-eight new bauxite deposits had been discovered and investigated at the end of the calendar year 1944, and the presence of several others had been indicated by the drilling. More than 5000 holes had been drilled throughout the bauxite region, and more than 60,000 chemical analyses had been made of samples taken from the bauxite-kaolin zone. A study of the chemical analyses led to certain general conclusions not only with regard to the chemical composition of Arkansas bauxite, but also with regard to its component minerals. Charts and diagrams based on these conclusions have been developed for practical use by the Bureau of Mines: (I) to serve as a check against laboratory analyses, (2) to present tonnage estimates of ore bodies based on mineral composition, (3) to illustrate the relationship of tonnages of bauxite to the alumina, silica, and iron content, and (4) to serve as a control for mining operations by providing a means for quick estimates of the value of the ore from a partial analysis of its chemical constituents. The use of charts and diagrams similar to those discussed in this paper-- is not new. The use of the trilinear diagram for studying the ultimate analyses of coals as of proposed by Ralston in Bureau of Mines Technical Paper 93 (1915) showed that the various ranks of coal fell in different areas on the diagram and that volatile matter, calorific value and other properties could also be plotted by the use of contours. A considerable subsequent literature, largely on classification of coals, has accurnulated since then, showing the utility

Jan 1, 1948

By J. R. Thoenen, M. C. Malamphy, G. K. Dale

The beginning of the war and the events leading up to it precipitated a near crisis in the aluminum industry. Demands for the metal reached proportions far beyond the prewar production capacities and, in addition, the submarine menace seriously curtailed the importation of bauxite from South America, hitherto a chief source of high-grade ore. The situation required an intensive search for domestic ore to augment the reserves and in October 1941 Congress directed the Department of the Interior to investigate the extent, mode of occurrence, and quality of bauxite in the United States. In December of that year the Bureau of Mines and the Geological Survey began the search for bauxite in Arkansas, where more than go per cent of the domestic ore had been produced and where the greatest amount of bauxite was known to occur. The program involves the geophysical and geological investigation of the Arkansas bauxite region and the core drilling of areas considered favorable for the occurrence of bauxite deposits. Cores taken from the bauxite-kaolin zone are sampled and analyzed in the Bureau of Mines laboratory in Little Rock. The information from each of the deposits discovered is then assembled, the bauxite is graded with respect to its possible utility, tonnage estimates are made, and the whole is presented in the form of a war minerals report. Thirty-eight new bauxite deposits had been discovered and investigated at the end of the calendar year 1944, and the presence of several others had been indicated by the drilling. More than 5000 holes had been drilled throughout the bauxite region, and more than 60,000 chemical analyses had been made of samples taken from the bauxite-kaolin zone. A study of the chemical analyses led to certain general conclusions not only with regard to the chemical composition of Arkansas bauxite, but also with regard to its component minerals. Charts and diagrams based on these conclusions have been developed for practical use by the Bureau of Mines: (I) to serve as a check against laboratory analyses, (2) to present tonnage estimates of ore bodies based on mineral composition, (3) to illustrate the relationship of tonnages of bauxite to the alumina, silica, and iron content, and (4) to serve as a control for mining operations by providing a means for quick estimates of the value of the ore from a partial analysis of its chemical constituents. The use of charts and diagrams similar to those discussed in this paper-- is not new. The use of the trilinear diagram for studying the ultimate analyses of coals as of proposed by Ralston in Bureau of Mines Technical Paper 93 (1915) showed that the various ranks of coal fell in different areas on the diagram and that volatile matter, calorific value and other properties could also be plotted by the use of contours. A considerable subsequent literature, largely on classification of coals, has accurnulated since then, showing the utility

Jan 1, 1948

By Rex W. Woods, Morris Muskat

A leastmsquare analysis procedure has been developed and applied for the study of the deviations in estimations of oil in place as given by the material-balance equations. The data used were those obtained from field observations on the Jones sand in the Schuler pool, Arkansas, and the Monroe dolomite in the Reed City pool, Michigan. Possible effects of water intrusion were taken into account by expressing the cumulative water influx in terms of various functions previously proposed in the literature. Formulas were developed and values calculated for the minimum deviations and minimal percentage deviations in the calculated volumes of oil in place from the average values, as could be obtained by suitable choice of the water encroachment and initial gas-cap volume parameters. The results show that the fluctuations in these calculated volumes are very insensitive to the values chosen for the rate of water intrusion and initial gas-cap volume, and hence cannot be safely used in discriminating between spurious values for these parameters and such as actually pertain to the producing reservoirs. Moreover, the exact form of the water-intrusion function seems to have but little effect on the fluctuations in the computed oil in place. Accordingly, it is concluded that the material-balance method does not of itself provide a satisfactory criterion for determining the basic physical unknowns of producing reservoirs or in making conclusive decisions regarding the production mechanism, unless independently established geological control data are available for eliminating unreasonable values for the reservoir parameters, even though they may still satisfy the material-balance formulas. If, however, from core or logging data the initial oil in place and the gas-cap volume can be established in advance, the material-balance formulas can be inverted to find the water intrusion. Moreover, by determining by such calculations the water-intrusion coefficient, the iuture production performance can then be predicted by the aid of the materiaI-balance formulas for specified operating conditions. This type of application may be of particular value in predicting the results of Pressure-maintenance operations. Introduction The evaluation of the forces acting upon an oil reservoir is a problem of considerable interest to the operator as an aid in determining the proper method of operation for the reservoir to obtain an optimum recovery of oil. In many pools, the nature and magnitude of the forces acting upon the reservoir remain unknown until an appreciable amount of ultimate recovery is obtained. To be of value to the operator, a reliable interpretation of reservoir performance should be available in the early life of the pool to permit an optimum plan of operation. Progress has been made in an understanding of reservoir behavior and the importance of the different factors involved. The material-balance method of estimating oil in place has been proposed as a tool in analyzing reservoir-performance problems.l The solution of such problems by this method ordinarily involves two or more unknown values relating to the nature of the reservoir, and the results

Jan 1, 1945

By Paul J. Sirkegian

The problem of properly controlling the movements of underground trains in the Emma Nevada and Morris Brooks workings of the Consolidated Coppermines Corporation of Kimberly, Nev., became more complex as the rate of production increased. Ore from these mines, which are connected through a 7000-ft. single-track haulageway (Fig. I), is hoisted through the Emma Nevada shalt. All production to date has been from one level. Because of heavy ground, even on the main haulage horizon, experience has shown that it is necessary to have a minimum cross section in the drifts, thus making it impractical to have a double track system. In 1937, production was 3000 tons per day; in 1938 it was increased to 6000 tons per day and in 1940 to 9000 tons per day. Each increase necessitated a revision in the method of controlling the underground traffic. In 1937 the tramming signal system consisted of a few signal lights in the main haulage drift. These lights were two 100-watt bulbs in a metal box that had one green and one red lens on each side. The box was mounted on the underside of a drift cap timber and could be seen For a considerable distance. The lights were so arranged that all boxes showed either red or green at the same time and all were controlled by a magnetic contactor at the entrance to each lateral drift. When the lights showed green, the main haulage was clear of traffic and a train could enter it. As the motor entered the main haulage drift, the motorman pulled the cord of the magnetic contactor switch, thus changing all the main haulage lights to red, which indicated that no other train could use the main haulage until the first train had turned into a lateral drift. When a train left the main line, its motorman pulled the cord connected with the magnetic contactors, causing the haulage lights to show green again. This arrangement permitted only one train at a time to use the main haulage and thus limited the number of train trips per shift, but it was satisfactory when the ore handled was only 3000 tons per day. Second SystEM Installed With a gradual increase in production it became necessary to place a train dispatcher in charge of all trains. He controlled their movements orally, giving his orders direct or by mine phone, instructing them where to load, when to leave for the station and when to return. His objective was to group several trains traveling in the same direction. Because of the human element involved, some mistakes were made. The danger of a serious collision was always possible. There was a 90° turn and curve in the underground haulageway, therefore travel in this section was always dangerous if mistakes were made in directing traffic. To protect the train crew, particularly the rear switchman who rode the last car or caboose, a two-way push button and flash-signal system was installed on the

Jan 1, 1946

By Morris Muskat

The detailed analogy between flow systems in porous media and the corresponding poten-tiometric model systems is developed under conditions where it may be desirable to take into account variable pay thickness, variable porosity, and permeability, and also the dependence of the fluid density on pressure. It is shown that in such models it is only necessary that the electrolyte thickness be made everywhere proportional to the millidarcy-feet of the formation. In contrast to the iso-vol type model, previously suggested as a basis for the analogy, the porosity does not enter directly in the construction of the model. It is introduced only in translating the electrical voltage gradient measurements into the equivalent fluid travel times. A discussion of this procedure is given. I NTRODUCTION It is now some 50 years since it was pointed out' that on the basis of Darcy's law Laplace's equation must govern the steady state flow of homogeneous fluids through porous media. It is 16 years since the obvious implication of this fact, namely, that such steady state homogeneous flow systems in porous media could be simulated by electrical analogies, was first applied2 to problems of practical interest with respect to oil production. In these initial studies major emphasis was placed on the use of electrolytic models, made of blotting paper, to give a direct and graphic history of the fluid particle motion in regular and infinite well networks. However, it was also noted there that the basic requirement of the model was that it give a potential distribution similar to the pressure distribution in the flow system, and that from the electrical measurement of the potential distribution the fluid particle motion could be graphically or numerically determined. This was demonstrated by application to the five-spot infinite network, for which a conducting metallic sheet was used to establish the equipotential contours. As anticipated, the fluid particle motion computed from these contours agreed well with that given directly by the blotting paper model. For irregular well distributions it was found more convenient to use electrolytic bath analogs rather than metallic sheets. Several investigations,3'4 as applied specifically to cycling well patterns, have been reported with these models, which have become known as "potentiometric models." However, the extremely laborious nature of both the electrical measurements by direct probing and the associated interprctive computations retarded the widespread use of these procedures. The electrical measurements can be accelerated by using a four-probe electrodc,5,6 which provides a means for simultaneously determining the streamline paths along which the fluid particles must move and the voltage gradients along these paths which are proportional to the fluid velocitics. With the increasing frequency of discovery of condensate pools, as drilling depths are becoming greater, the applicability of the potentiometric model to production problems, and especially to the study of well patterns for cycling, has been given a fresh impetus. Although the formal theory for determining the motion of fluid particles in porous

Jan 1, 1949

By William R. Patterson

ACCORDING to the phase diagram for the Mn-Ni system,' the high-temperature, fcc y-manganese solid solution is stabilized to below room temperature, in the range approximately 22 to 28 wt pct Ni. However, pearson2 cites evidence in the literature showing that for manganese contents greater than about 75 wt pct the quenched phase in Mn-Ni alloys is fct. This is in keeping with zener's3 suggestion that in manganese-rich alloys the fcc high-temperature phase undergoes a diffusionless or martensitic transformation to a fct structure upon quenching. Work by Basinski and christian4 on manganese-rich compositions in the similar alloy system Mn-Cu established that in alloys of greater than about 82 wt pct Mn the y-manganese phase underwent a fee fct martensitic transformation upon quenching to room temperature. Striking evidence for this martensitic transformation was the highly twinned or banded microstructure, an example of which is shown in Fig. 1. Similar microstructures have also been found in quenched Mn-Cr5 and Mn-Au6 alloys. In the present investigation, we attempted to obtain similar evidence of a fcc — fct martensitic transformation in manganese-rich Mn-Ni alloys. Manganese alloys in the range 10 to 30 wt pct Ni were prepared by arc-melting, under argon, at atmospheric pressure. The alloys all were 50 g in size, and negligible weight loss occurred during melting. The starting materials were electrolytic manganese and nickel, both of 99.9+ pct purity. The alloys were subsequently homogenized 48 hr at 1750°F, hot-rolled 50 pct at 1700°F, annealed 2 hr at 1700°F, and water-quenched to room temperature. All heat treatment was done in purified argon. Both X-ray and metallographic techniques were used to examine the structures of the quenched alloys. X-ray diffractometer studies were conducted on powder specimens obtained from filings rean-nealed 2 hr at 1700°F in argon and water-quenched. Identification of the intensity peaks from the diffractometer counter traces showed that below about 10 to 12 pct Ni the y phase decomposed partially upon quenching to give an a- + ?-manganese structure. In the range approximately 12 to 25 pct Ni, the structure was found to be fct ? manganese with a c/a ratio approaching 1.0 at 25 pct Ni. Beyond approximately 25 pct Ni, the structure remained fcc. These results, including lattice-parameter determinations, are given in Table I. Metallographic examination. was carried out on specimens polished and etched after quenching, and also on polished specimens reannealed and quenched. In the first case, the distinctive twinning or banding so prevalent in Mn-Cu alloys was sought, while in the second, the surface relief effect generally regarded as being truly characteristic of a martensitic transformation was sought. The microstructure of representative alloys in the range 12 to 25 pct Ni is shown in Fig. 2. The structure of the Mn-15 pct Ni

Jan 1, 1965