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By M. S. Rashid, C. J. Altstetter

Allotropic transformations in cerium have been studied by dilatometric, resistometric, X-ray diffraction, and metallographic techniques. The dilatometric study indicated that, on cooling below O°C, the high-temperature fcc phase, y, transforms partly to the hexagonal phase, ß, and, on further cooling, to the collapsed fcc phase, a. The amount of $ phase present at room temperature is increased by repeated cycling through the a-y transformation. It has been shown metallograPhically that the y-ß transformation has many characteristics of a martensitic transformation. In contrast to the y-ß transformation the ?-a transformation does not give the manifestation of a shear transformation. Small cellular ? domains of random shape and size collapse to a in a short time with no apparent coordination with neighboring domains. The considerable confusion in the literature over the existence of more than one high-temperature fcc phase is discussed. Two such phases have been reported in the literature and an attempt is made in this study to clarify the situation. Twelve fcc and two hcp structures have been shown to be easily reproduced or eliminated. It is proposed that the two "additional" allotropes reported in the literature and fourteen of the phases detected here are not allotropes of cerium but are due to contamination. CERIUM exists in several allotropic forms, but there is some disagreement over what the forms are. Furthermore, the conditions favoring the presence of a particular allotrope and the nature of the transformations from one form to another are uncertain. The objectives of this research were 1) to ascertain the allotropic forms of cerium, 2) to establish the conditions under which the allotropes exist, 3) to study the effects of annealing and thermal cycling on the allotropic transformations, and 4) to study the transformation mechanisms. Dilatometric, resistometric, metallographic, and X-ray diffraction techniques were employed. The form of cerium commonly found at room temperature is fcc and is designated ?. A complex hexagonal phase, 8, forms when y is cooled to slightly below room temperature. At still lower temperatures the y fcc structure transforms to an fcc form with a much smaller lattice parameter, termed a cerium. A bcc form, 6, which exists just below the melting point (800°C), will not be considered further in this work. There is a substantial body of experimental evidence (reviewed by Gschneidnerl) which favors the acceptance of these four allotropes, though some investigators have tried unsuccessfully to observe the ß hexagonal form.'-' There is disagreement, however, over the phase-transformation temperatures, due, in part, to broad hysteresis and overlapping of the transformations between the a, ß, and ? forms. The transformations are also sensitive to prior thermal and mechanical treatment. The differing purity of cerium used by different investigators is undoubtedly a factor. Cerium is difficult to separate from other elements and is quite reactive, igniting spontaneously when it is filed in air. The highest purity of cerium to date is reported to contain several hundred parts per million by weight of impurities, and early investigations were carried out on cerium containing several percent of impurities. There have been reports of more than one fcc allotrope at room temperature. Gschneidner, Elliott, and McDonald5 obtained diffraction patterns of an fcc phase with a lattice parameter about 1 pct less than that of the ? phase, instead of the y phase, on slowly cooling cerium filings from 23° to -198°C and warming them back to room temperature. However, when the sample was heated to 447°C and cooled to room temperature it consisted of only the ? phase. They have designated this new fcc phase "a-? intermediate", and say it is quite sensitive to impurities. After prolonged high-temperature treatment of a powder specimen, Weiner and Raynor2 obtained a diffraction pattern of an fcc phase of lattice parameter about 1 pct less than the ? phase. This they called the y' phase. It could not be reconverted to the y phase and is claimed to be different from the a-? intermediate phase.5,6 Dialer and Rothe3 reported two fcc phases* after cycling their powder specimens between room temperature and -192°C. Gschneidner, Elliott, and McDonald5 suggested that one of the fcc structures obtained by Dialer and Rothe was equivalent to their "a-? intermediate" phase. Table I presents some pertinent data on the proposed allotropes. For the ?(fcc)-ß(hexagonal) transformation

Jan 1, 1967

By G. S. Tint, M. Herman, V. V. Damiano

Dislocation arrays and substructures were studied in cadmium doped zinc crystals using a newly devised etching technique. Cadmium precipitates delineating the dislocations were revealed by etching a surface closely parallel to the (0001) slip plane. Cinephotomicrography of the continuous etching process revealed the three-dimensional aspects of dislocations in the bulk crystal. Dislocation etch patterns were studied in both deformed and annealed crystals after suitable aging at room temperature. The effect of annealing was evidenced by a rearrangement of the dislocations into low-angle boundaries and hexagonal networks. ETCH pit techniques have been used extensively to study dislocations in both deformed and annealed bulk metal crystals. Ideally one hopes to obtain a one-to-one correspondence between the etch pits and the points of emergence of the dislocations at the surface. One then attempts to deduce the way in which dislocations are arranged in the bulk crystal from the arrangement of etch pits on the surface. It is clear that one can obtain only limited information of the dislocation configurations inside the crystal from etch pit studies of single surfaces. Considerably more information is obtained if one is able to follow the course of the dislocations through the crystal using progressive etching technique. Techniques of this sort were used by Gilmanl to study dislocations on the slip planes of NaCl crystals and by Damiano and Tint2 to study dislocation arrangement in zinc crystals grown from the melt. The present paper makes use of a technique first described by Tint and Damiano3 to observe and continuously record the dislocation structures which appear while a crystal surface was being progressively etched. Studies were made on cleaved (0001) surfaces to reveal the dislocations along their length on the surface closely parallel to the slip plane. The technique for revealing segments of dislocations along their length by etching is well known. Wilsdorf and Kuhlmann-wilsdorf4 revealed disloca- tions along their length in aluminum containing a few percent copper, when precipitates segregated along the dislocations. The technique was used by Low and Guard5 to study dislocation configurations on the slip plane in Fe-Si alloys containing carbon. In the present work the technique was applied to zinc containing cadmium since it was shown by Gil-man6 that a cadmium-rich phase could be made to precipitate from supersaturated solutions along dislocations in zinc. Segments of dislocations delineated by the precipitates were revealed by etching a surface prepared by cleaving the crystal. The three-dimensional nature of dislocations and substructures was thus studied from the cinephotomicro-graphic record of the continuous etching process. EXPERIMENTAL Single crystals of zinc containing the order of 0.1 pct Cd were prepared by slowly lowering a graphite crucible containing the melt through a temperature gradient of 15°C per cm at a rate of 1.5 X 10-3 cm per sec. "As grown" crystals were aged for periods of 1 month at room temperature, then cleaved in liquid nitrogen, and etched according to the procedure used by Gilman.' The etchant containing 32 g of CrO3, 6 g of hydrated Na2SO3 in 100 ml of water behaved as a chemical polish for zinc and etch pits were produced at the site of precipitates or inclusions. After the precipitates or inclusions were removed from the surface, the etch pits left behind were eventually polished smooth. This behavior enabled one to continuously observe the surface while the specimen was immersed in the etchant. Best results were obtained when the specimen surface was vertical and the reaction products of polishing were continuously removed by gravitational convection. Some crystals were heavily deformed in excess of 25 pct strain, others were lightly deformed the order of a few pct by compression such that the deformation occurred essentially by basal glide. Some crystals were etched immediately after deformation, others were allowed to age at room temperature for several weeks prior to etching. Heavily deformed crystals were annealed at various temperatures and etched on the cleavage plane immediately after annealing, others were allowed to age at room temperature for several weeks prior to etching. The etched structures of deformed and annealed structures were studied. Similar experiments were conducted on 99.9999 pct pure zone refined Tadanac zinc crystals which

Jan 1, 1963

By R. W. Heckel, R. L. DeGregorio

The DeHoff method of determining the size distribution of ellipsoid-shaped, second-phase particles has been applied to the spheroidization of cementite in a eutectoid steel. The surface area of Precipitates determined from the various size fractions in the distribution was correlated with surface-area measurements based on the number of intersected interfaces on a random lest line. The precipitate particles were found to be oblate ellipsoids with an axial ratio of about 0.90. The size distributions were found to be log-normal. A method is proposed whereby the shrinkage of small particles and growth of large ones can be determined from the experimental data. The experimental data are compared to previously proposed mathematical models describing diffusion-controlled kinetics and various types of interface-controlled kinetics. The experimental growth and shrinkage rates are considerably slower than those predicted by diffusion-controlled kinetics. The best fit is obtained for a model describing interface-controlled kinetics limited by the rate of formation of cementite at the growing interfaces where the interfacial reaction rate is proportional to the solute thermodynamic activity gradient across the surface. THE subject of spheroidization of second-phase particles has been considered previously by other investigators. Livingston1 has studied the precipitation of the cobalt-rich phase from copper alloys containing 0.7 to 3.2 wt pet Co. His results indicate that the average particle size increases as the cube root of the heat treatment time in accord with diffusion-controlled kinetics.'-' Komatsu and rant' in their studies of the growth of SiO2 in a dispersion-strengthened copper-silica alloy found that the initial growth of SiO2 proceeded by diffusion-controlled growth and later stages were limited by interface-controlled growth. The values of the activation energy obtained for the interface- controlled process led them to the conclusion that the process was limited by the dissociation of SiO2 at the shrinking interface. The transition from diffusion-controlled growth to interface-controlled growth was characterized by a particle size which varied with the heat-treatment temperature. It is also interesting to note that the particle-size distribution as found by Komatsu and Grant exhibits log-normal behavior when replotted on log-probability coordinates. Dromsky, Lenel, and Ansell9 have observed the growth of Al2O3 particles having a mean free path of about 1.5 to 13 µ. Their photomicrographs indicate that the Al2O3 particle sizes were larger than those observed by Komatsu and Grant. Dromsky, Lenel, and Ansell concluded that the Al2O3 coarsened by an interface-controlled growth mechanism limited by the solution of A12O3 at the shrinking interfaces. Bannyh, Modin, and Modin10 have studied the spheroidization of a eutectoid steel (0.83 wt pet C). Their spheroidization (tempering) treatments were carried out in the range from 210o to 700°C for times between 1.5 sec and 20 hr. Measurements of mean particle size as a function of time indicated a cube root of time dependence of size at 700°C, in agreement with previous analyses of diffusion-controlled kinetics.2°7 At lower temperatures, the time dependence was less than the one-third power. It is important to note that, although mathematical models of growth* considering particle-size distribution have been available, measurements of only mean particle size have been carried out. DeHoff11 has presented a quantitative metallography technique which is applicable to the determination of the size distribution of ellipsoids of constant shape. This method is applicable to both oblate and prolate ellipsoids of all ratios of minor to major axis and is based upon an extension of Saltykov's analysis12 of the distribution of spheres of varying size. DeHoff's analysis is based upon measurements of the minor axis of the particles on a random plane of polish in a unit area. This method provides a measure of the number of ellipsoids in various size ranges per unit area. As pointed out by DeHoff, such measurements may be used to obtain surface area and total precipitate volume data. Thus, the accuracy of the distribution analysis may be checked by comparison of the surface and volume

Jan 1, 1965

By L. D. Mullins, E. B. Elfrink, W. L. Wahl

In the past few years several articles and papers presenting results of solution gas-drive depletion calculations have appeared in the lit-erature. Such calculations are of interest to the oil industry, for investment decisions must often be made before much is known about a reservoir. At other times, an estimate of the possible benefits to be realized from alternate production methods is desirable, and theoretical depletion calculations can serve as a floor or reference level from which to work. In any case, an estimate of ultimate oil recovery based upon engineering data is commonly required. An engineer confronted with the problem of obtaining, for a specific reservoir system, an estimate of ultimate oil recovery by solution gas-drive depletion usually will be forced to perform the calculations himself. This is despite the quantity of data in the literature. Rarely will either experience or the literature provide results from a reservoir system similar in all important respects to the one under consideration, and calculated results are not so plentiful that satisfactory interpolation procedures can be devised. Performing the calculations, however, is a tedious, time-consuming task unless an electronic computer is available, and, in practice, time and manpower are not always available for this purpose. A quick, simple, consistent method was needed for reducing the uncer- tainty in estimated oil recovery from solution gas-drive reservoirs when only minimum information about the reservoir system is available. PROCEDURE Method of Calculation The usual requisite assumptions were made so that the material balance equation could be used to calculate data for the charts. The following assumptions were made: (1) the reservoir is homogeneous and isotropic; (2) oil recovery is due entirely to solution gas drive and neither a gas cap nor a water drive nor gravity drainage is present; (3) the initial reservoir pressure is the bubble-point pressure of the reservoir fluid; (4) initial total liquid saturation is 100 per cent of pore space; (5) interstitial water saturation remains at the initial value as the reservoir pressure declines from the bubble-point pressure to atmospheric pressure; (6) equilibrium gas saturation is 5 per cent of pore space; and (7) oil and gas saturations are uniformly distributed throughout the reservoir at all times. There are no saturation gradients due to a wellbore, nor is the geometry of the reservoir system considered. The material balance equation was written in the form of a differential equation' which was integrated to determine the change in oil saturation for an assigned pressure drop. Formal integration was not possible, so recourse was made to the Runge-Kutta method' of numerical integration. All computations were performed on IBM equipment. Numerical integration yielded the change in oil saturation within the reservoir as the pressure. declined from the bubble-point pressure to atmospheric pressure. The initial oil saturation minus the change in oil saturation yielded the oil saturation at atmospheric pressure. The oil originally in place was obtained by dividing the initial oil saturation by the initial formation volume factor (differential liberation) while the oil in place at atmospheric pressure was obtained by dividing the final oil saturation by the formation volume factor at atmospheric pressure. U1timate oil recovery, expressed as a percentage of the initial oil in place, was obtained by dividing the difference between the oil initially in place and the oil in place at atmospheric pressure by the oil initially in place and multiplying by 100. PVT Data Charts were based upon 135 solutions to the material balance equation. PVT properties of the reservoir fluids were variables in this equation and had to be known as functions of pressure. The required PVT data might have been obtained from either actual reservoir fluid systems or correlated data. However, correlated PVT data were developed and employed in the calculations for the following reasons: (1) it is doubtful that 135 sets of PVT data could have been obtained for the values of variables investigated in this study, and (2) results of recovery calculations from randomly obtained PVT data could not be correlated as well as rssults from selected PVT data. The PVT data used to develop the

By J. D. Alexander, W. L. Martin, J. N. Dew

This paper presents data obtained using a flood-pot technique to determine the fuel available and the corresponding theoretical air requirements for in situ combustion of crude oils. Since the technique is relatively quick and easy, it is a practical and convenient tool for evaluating reservoirs as fireflood prospects. It is also a research tool which facilitates systematic study of the variables affecting fuel availability and corresponding air requirements. The understanding of these variables is of prime importance to those concerned with the technical and economic development of in situ combustion as an oil-recovery process. The experimental results show conclusively that the fuel available for in situ combustion is not a constant but, rather, varies with crude-oil characteristics, porous-medium type, oil saturation, air flux and time-temperature relationships. Thus, the fuel availability for specified field applications should be determined using actual reservoir crude and core material and the process conditions expected during in situ combustion in the reservoir. INTRODUCTION In situ combustion is a thermal process for recovering crude oil from reservoirs. The thermal energy released during the combustion of a small amount of the oil in place aids in the displacement of the remaining oil. Numerous articles have been published describing the in situ combustion process giving detailed results of laboratory and field experiments.10 In order to engineer an in situ combustion project, a number of important factors must be considered and determined. These factors include: (1) the amount of fuel consumed per unit of reservoir volume swept by the combustion zone, (2) the composition of the fuel consumed, (3) the amount of air required to consume this fuel, (4) the portion of the reservoir swept by the combustion zone, (5) the appropriate air-injection rates and pressures, (6) the amount of oil that will be recovered, (7) the rate of oil production and (8) the operating costs. Nelson and McNiell1 recently have described a procedure which utilizes laboratory combustion-tube data as a basis for the calculation of some of these design factors. Various authors have attempted to describe the in situ combustion process mathematically, and considerable progress has been made. Analytical solutions to the problem of heat transfer from a moving combustion front have been obtained for linear and radial systems."-' All of the published results involve the assumptions that: (1) fuel concentration is constant throughout the reservoir, or that fuel concentration is inversely proportional to the velocity of the front for a given rate of oxygen consumption; and (2) the fuel reacts instantaneously with injected oxygen, while liberating a constant amount of heat per unit weight of fuel at all temperatures. It seems both desirable and reasonable to test the validity of these assumptions experimentally. This paper presents laboratory data which were obtained by means of a "fire flood-pot" method for determining fuel availability and composition, and the corresponding theoretical air requirements for in situ combustion of crude oils under variable conditions. The mechanics of the method are similar to a conventional tube-run experiment.' The important differences involve the size of the reservoir model used and the method for providing the experimental environment. The new method subjects conventionally-sized core samples or unconsolidated sands to a programmed environmental sequence similar to that experienced by a similar volume of rock during the approach and passage of a combustion front in a long tube or in an oil reservoir undergoing in situ combustion. Restored-state samples can also be used. The small samples and relatively simple techniques involved allow an experiment to be set up, run and calculated in about three 8-hour days. This is a considerable improvement over long-combustion-tube techniques which can require several days to run and several more work days to set up and calculate. All the runs presented were run at 40-psig injection pressure. Pressure was not considered as a variable for these experiments, since we previously had found that it had only a small effect on fuel availability up to 600 psig.APPARATUS AND MATERIALS APPARATUS The fire flood-pot apparatus consists of a consolidated

By F. D. Rosi

The plastic properties of extended silver and copper crystals of varying purity were studied as a function of crystal orientation in the early stages of flow. Variations in the gross shape of the shear stress-shear diagram and in the properties of critical Variationsshear stress and shear-hardening coefficient were correlated with changes in slip-band developments. The phenomenon of work hardening is discussed in terms of the existing dislocation theory. IT appears certain from the early studies on the deformation characteristics in metal crystals1-3 that plastic flow takes place in a preferred crystallo-graphic slip system which is determined by the geometry of the crystal (law of maximum shear stress), and that the value of shear stress for this system is independent of crystal orientation (law of critical shear stress). Experimentally, it has been demonstrated further that the law of critical shear stress can be extended to include extensive plastic flow.&apos; Thus, the shear-hardening coefficient, which is defined as the slope of the shear stress-shear curve, also is considered to be independent of orientation. It is noteworthy that deviations from this empirical shear-hardening law have been reported in cubic crystals whose initial orientation favors slip on more than two systems.&apos; Moreover, this law appears to have been derived from stress-strain data relating to relatively high values of shear strain (0.5 to 4), where widespread slip and complex distortions can be expected, regardless of crystal orientation. Since existing data indicate that the strain inhomogeneity in a crystal is manifested particularly in the early stages of flow, it would appear that a more exacting test as to the fundamental nature of the shear-hardening law would be to investigate systematically the shape of the stress-strain curve as a function of crystal orientation in the earlier stages of deformation. With regard to the general form of the shear stress-shear curve for cubic crystals, early studies show a parabolic hardening law, where the shear 1 stress is proportional to the square root of the shear-strain. Since this law was predicted theoretically by Taylor" in his original dislocation model for hard- ening, it has been accepted widely as a fundamental flow characteristic of cubic metals. However, it was recently pointed out by Masing6 hat the parabolic law is not the elementary form of hardening in cubic crystals, but instead is a consequence of complexities in the flow process (e. g., deformation bands and unpredicted secondary slip). Thus, in the very early stages of deformation (< 2 pct extension) where the occurrence of such complexities is unlikely, a different strain-hardening behavior might be anticipated. This view is supported by the recent work of Rosi and Mathewson7 on high purity aluminum where a linear law was obtained for extensions up to 2 pct. A linear hardening over a wider range of deformation also was reported by Rohm and Kochendorfer8 ho deformed aluminum crystals under conditions approximating pure shear. Even more pertinent is the recent evidence of Masing and Raffelsieper9 on high purity aluminum crystals. It was found that for crystals having initial orientations near a <l00> or <1ll> axis, a high hardening was obtained, whereas crystals with a <110> orientation exhibited a low and linear hardening curve followed by a region of more rapid hardening. Since much still remains obscure concerning the details of strain hardening as well as slip-band formation in face-centered-cubic crystals in the early stages of deformation, the present study was undertaken to evaluate the effect of crystal orientation on these two important manifestations of glide. It is important to note here that at the time of this study, Lucke and Lange11 presented information on the orientation-dependence of the shape of the strain-hardening curve in aluminum of various purities. Their work, which essentially represents an extension of that of Masing and Raffelsieper, in many respects is parallel to that of the present study. Experimental Procedure Production of Single Crystals: Single crystals of silver and copper of varying purity were used in

Jan 1, 1955

By Evans B. Mayo

This study examines the structural framework of the Southwest for evidence of the four principal trends of lineament tectonics. It attempts to classify their intersections and compares the positions of those trends that appear most favorable with the positions of the presently known mining districts. This is a controversial topic. The author, in presenting his analysis, is aware that the study of lineament tectonics and relation of ore districts to regional structure is complicated by insufficient data and, unavoidably, by personal bias. The development of lineament tectonics has been summarized by Umbgrove.&apos; Early attempts to fit ore districts into the Cordilleran framework were made by Billingsley and Locke, who do not refer to lineament tectonics, although their appoach is similar; they observe that heat and fluids, including the ore-depositing fluids, are most likely to rise at or near intersections of major structures where the crust is fractured, or weakened, to great depth. As a result of studies distributed over the earth-including ocean basins as well as continents— some tectonists recognize four dominant structural trends: 1) northwest; 2) northeast; 3) nearly east-west, or equatorial; and 4) nearly north-south, or meridional. Baker&apos; proposed a theory to account for these trends and Sonder" called their world-wide arrangement the regmatic shear pattern. Moody and Hill proposed a much more complicated shear network which, although fascinating and perhaps ultimately useful, will not be followed here. In a recent review of deformation within the Cordillera, Wisser mentioned the four fundamental directions. The fact that many geologists deny the existence of the regmatic shear pattern implies that the fundamental structures are far from obvious. It may mean, also, that some geologists are not accustomed to examine regional and world maps analytically. The maps require much study, and certain features should be isolated on overlays. Even so, with the present limited knowledge, uncertainties remain. The following analysis is a qualitative experiment, subject to change as information accumulates, and should be supplemented by the western sheet of the Tectonic Map of the United States.&apos; Many have probably gained the impression that the Cordillera of the West is oriented northwest-southeast and from this, unless experience rules otherwise, it is natural to assume that the structure likewise trends northwest-southeast. To an important extent this is true, yet anyone tracing off the western sheet of the Tectonic Map all the recorded north west-southeast structures may be surprised to see what a small part of the entire area they occupy. In southwestern U. S. (Fig. 1) the northwest-southeast structures are mostly restricted to the eastern, southern, and western parts. The eastern margin of the Cordillera from northern Colorado to the International Boundary near El Paso, Tex., is obviously determined by some structure other than northwesterly ones. In eastern Nevada and far southward toward the Gulf of California many mountain ranges, valleys, and faults are meridional. In the Rocky Mts. of Colorado, and at many places in southern Arizona, the crystalline Pre-Cambrian is foliated northeast-southwest. The Uinta Mts. of Utah trend approximately east-west, in much the same way as a broad belt of transverse, west-northwest structures—the Texas lineament of Hill",&apos; and Ransome10 in southern Arizona, southwestern New Mexico, and southern California. It seems, then that there are four regmatic shear directions in the Southwest, but at many places they are discontinuous, and their projections must be inferred. To clarify these trends the four sets have been isolated into two systems: 1) northwest-northeast and 2) east-west-north-south (Figs. 2 and 3). Northwest-Northeast System: A number of prominent northwest-trending zones of structure are easily recognized. They are designated by circled Roman numerals, the northeast-trending structures by circled capital letters. Perhaps no two geologists would agree completely on the positions of all these belts. Names given below are for convenience only, and may be discarded where other names have priority. (I) The Sierra Nevada-Lower California belt contains the Jurassic-Cretaceous granitic massifs of the Sierra Nevada and Lower California. These

Jan 1, 1959

By J. H. Henderson, L. A. Wilson, R. L. Gergins, R. J. Wygal, D. W. Reed

This paper presents a method of predicting the production history of an underground combustion recovery process. A rigorous solution of the thermodynamics and hydrodynamics involved is beyond the scope of this report. However, a practical scheme to appraise combustion recovery performance has been Worked out. By prudent assumptions, regarding the attainment of steady-state conditions, a trial-and-error solution, which satisfies both material balance and three-phase relative permeability requirements has been evolved and tested. As a combustion zone moves through a formation the interstitial water, the water of combustion and a portion of the oil wil1 be vaporized. These vapors will move downstream to a cooler region of the formation where they will condense. Part of the remaining oil will be displaced by the imposed gas drive and what remains behind will be consumed as fuel. The fluids will distribute themselves downstrean? in a manner which will satisfy the three-phase relative permeability characteristics of the formation. Three distinct zones will exist ahead of the combustion zone: (I) a zone termed a water bank which contains three mobile phases, oil, water and gas; (2) a region containing two mobile phases, oil and gas, called the oil bank; and (3) a zone having the fluid saturution distribution which existed prior to combustion. The mobile water will impose a water flood on the oil in the region containing three flowing phases. The process can be visualized as a simultaneous water .flood and combustion-supported gas drive. It is possible to estimate the saturation distributions in the water bank and oil bank as well as the production history for any combustion temperuture if the porosity, three-phase relative permeability characteristics, oil viscosity and initial saturations are known. This has been done for injection pressures ranging from I to 100 atm, oil viscosities of 10 to 1,000 cp and porosities from 20 to 40 per cent. Several of these calculations have been checked in the laboratory, with the result indicating rather good agreement between the predicted and observed production histories. The analytical and experimental techniques are described and the comparison of predicted and observed performance presented. INTRODUCTION Considerable research by the oil industry during the past 10 years has been directed toward the thermal recovery of crude oil. Of all schemes considered, the one receiving the most attention is in situ combustion. This is a process in which part of the oil is actually burned within the reservoir rock. The uniqueness of the process lies in its potential. Theoretically, this potential generates from the following: (1) it may open the door to vast reserves previously not economically producible, (2) it may induce increased production rates where low rates are now realized and (3) it may give high over-all recovery efficiency. The general idea of the process has received considerable attention in the literature &apos;-&apos; and the following brief description is intended for orientation only. In situ combustion can be visualized by considering a linear system, one end of which represents the injection well and the other the producing well. The formation at the inlet end is raised to ignition temperature by placing a gas or electric heater at the face of the formation or by the ignition of thermite, charcoal or similar material. While heating, the water and part of the oil in the heated region is vaporized and moved out into the reservoir by the injection of gas containing oxygen. In addition, part of the oil is displaced as liquid by the imposed gas drive. The oil not displaced is modified to an immobile, coke-like material (hereafter referred to as coke) by the high temperatures existing immediately ahead of the combustion zone. This coke is used as fuel, and the combustion front advances through the formation at a temperature which is probably in excess of 800°F. As the combustion front advancek it will drive ahead all interstitial oil not rendered immobile and all interstitial water plus the water formed by the combustion of hydrogen. As a result the sand behind the combustion zone is freed of all oil and water. Although the general description of the process has been outlined in the literature, there has been no consideration of the behavior of the fluids moving downstream from the combustion front. It is the purpose of this paper to present a technique

By A. Satter, J. M. Campbell

Reported herein are the results of a careful and detailed study of the non-ideal behavior of pure gases and their mixtures. Included are: (1) new data on five ternary systems composed of methane, ethane and H2 S; (2) a simple compressibility factor correlation that is inherently superior to present correlations, particularly for gases containing H2S and CO2; and(3) a detailed study of combination rules and the effect of system composition on the choice thereof. This study makes use of the rather large mass of data already available in the literature. A complete re-examination of the data and ideas presented in the last 25 years was considered desirable as a prelude to our basic concern — the effect of diluents on gas behavior. A consideration of both the macroscopic and microscopic properties of gases provides a better insight which, in turn, gives a firmer basis for improved correlation techniques. Such a study has shown that expressing the compressibility factor Z as a function of acentric factor w, as well as reduced temperature and pressure, yields a correlation that is broader in scope. The study of various combination rules has shown that better results are obtained by "tailoring" the rule used to the system composition. To do so improves the basic reality of results by overcoming some of the anomalies often found when using Kay&apos;s rule alone. Tentative recommendations are made regarding the most reliable combination rule for use with a given class of gas. The data presented are useful for estimating the direction and magnitude of the expected deviation when using a given rule. Although more work is needed, particularly around the critical region and with CO2 mixtures, the advantage of the classification scheme proposed is apparent. INTRODUCTION When one attempts to write a PVT equation to fit the data for actual gases, greater precision is obtained by the use of a multiple number of empirical constants. This has lead to multiple-constant equations such as Benedict-Webb-Rubin, Beattie-Bridgman, Keyes, etc., which are capable of yielding very precise results for pure gases in a range for which data to get the constants are available. As a matter of practicality, though, the use of such equations for gas mixtures is limited. Because of the infinite number of gas analyses available, any attempt to compile the constants needed requires a prohibitive amount of experimental data. This could be overcome by the use of a combination rule, but there is no real advantage in doing so because the end result offers no practical impovement over the Z factor correlation. The most widely used method of predicting the volumetric properties of pure gases is based upon the "theorem of corresponding states". According to this theorem, "all pure substances have corresponding molal volume at corresponding temperature and pressure if the reference point of correspondence is the critical point". Generalized compressibility charts for gases were prepared first by Cope and associates1 in 1931 and later by Brown and co-workers2 in 1932. However, the most commonly used charts are those of Dodge,3 Nelson and Obert,4 Hougen and atsson: and Standing and Katz.6 The work of Katz and co-workers has provided us with basic data for the hydrocarbons most widely used today. Their original chart6 was compared with a relatively large amount of multi-component data for gases consisting almost entirely of normal paraffin hydrocarbons. A deviation of only + 1.2 per cent was obtained.39 In the 20 years following publication of this work it has been found that the behavior of most mixtures of paraffin hydrocarbons could be predicted by this correlation within at least 5 per cent. Where difficulty has been encountered it has largely involved one or more of the following circumstances: pressures above 4,000 psig, mixtures containing large amounts of heavy ends and/or aromatics, systems in the critical region and mixtures containing polar compounds and/or CO2. The abnormal error sometimes found with such gases, not too unexpected for this method, is

By R. R. Vandervoort, W. L. Barmore

Tensile creep experiments were conducted on high-purity, poly cvystalline rhenium from 1500" to 2300°C at stresses from 1500 to I0,OOO psi in a vacuum of 10-a torr. The apparent activation energy for creep was 60 kcal per mole, and the steady-state creep rate varied directly with stress to the 3.4 power. Dislocation substructure that developed during creep was studied by transmission electron microscopy. Possible rate-controlling deformation mechanisms are discussed. The creep behavior of most metals at elevated temperature can be represented by the following equation:&apos;&apos;&apos; t = Cf(s)(^)(s/E)nD [1] where i = steady-state creep rate, C = constant, f(s) = a function involving microstructure, s = applied stress, E = the average elastic modulus at test temperature, n = constant, D = diffusion coefficient According to this well-established relationship, metals with higher elastic moduli and lower diffusion coefficients should have greater creep resistance at the same stress and temperature and equivalent mi-crostructures. While no diffusion data are available, the diffusivity of rhenium should be less than that for most other refractory metals because of its high melting point and hcp crystal structure. The Sherby-Simnad relation for calculating atomic mobility in metallic systems3 predicts that the diffusion coefficient for rhenium is less than that experimentally determined for tungsten4 in the temperature region 1500. to 2200°C. At these temperatures the elastic modulus for tungsten5 is only slightly larger than the extrapolated modulus for rhenium.6 Thus, rhenium is a good possibility for a a high-temperature structural material, but few data on the creep of rhenium have been reported. This investigation was undertaken to study the high-tempera-ture deformation behavior of rhenium in detail. EXPERIMENTAL TECHNIQUES The material used in this study was consolidated from high-purity powder. After cold pressing the powder to a plate a in. thick, the billet was sintered in hydrogen at 2250°C for 24 hr. The plate was reduced to 0.100 in. by cold cross rolling with intermediate anneals at 1650°C for 20 min between passes. The plate was further reduced to 0.060 in. by unidirectional cold rolling with similar heat treatments between passes, and then finally stress-relieved in hydrogen at 1650°C for 30 min. Specimens tested at 1900°C and below were pretest-annealed at 1900°C for 2 50 hr. Specimens tested above 1900°C were pretest-annealed at 2400°C for 5 hr. The impurity content in the "as-received" plate was quite low, table I. Essentially no change in impurity levels was detected in specimens after creep testing. All creep tests and annealing treatments were conducted in a vacuum of 10-8 torr in a test furnace heated by a tungsten mesh element. The load was applied to the specimens through a bellows, and stresses were maintained to ±1 pct of the selected value by periodic corrections for changes in specimen cross-sectional area during creep and for changes in the bellows spring force due to load column extension. One-inch-diameter tungsten force rods were used in the hot zone of the furnace. Deformation at temperature was measured by optically tracking gage marks on the specimen. Temperature was measured by a calibrated optical pyrometer and was determined to ±5"C. Grain sizes were determined by the linear intercept method and specimens were examined in the "as-polished" condition, using polarized light. Specimens annealed at 1900°C had a grain size of 52 ± 5µ , and those annealed at 2400°C had a grain size of 148 * 11 µ. Pieces were cut from the gage section of creep-tested specimens and planed to a thickness of about 0.010 in. by spark discharge machining. Thin foils for viewing by transmission electron microscopy were obtained by electropolishing in a solution of 6:3:1 ethyl alcohol, perchloric acid, and butoxy ethanol, respectively, using the window technique. Bath temperature was —4OoC, and the cell potential was 35 v. The foils were examined in Siemens Elmiskop I, operating at 100 kv. RESULTS AND DISCUSSION In order to analyze the results from creep experiments, Eq. [I] is rewritten in the following form: <=Kf(s)ne-/RT [2] where K = constant, ?// = apparent activation energy for creep,

Jan 1, 1970

By P. S. Kotva

Dislocation substructures in superalloy matrices of varyzng co)npositions have been studied. In general, it has been found that the alloys can be classified into &apos;&apos;high", &apos;&apos;medium", and "low" stacking fault energy classes based on the type of dislocation substructure observed in the matrix and that the substructure can be correlated to the stacking fault energy. The effect of different types of dislocation substructure and dislocation reactions on the intragranulur precipitation of carbide phases has been studied. In a Ni-Cv-Mo-Fe matrix, precipitation of MC carbides in association with stacking faults has been observed. In most superalloys, solid-solution strengthening and precipitation hardening are the chief mechanisms employed to achieve strength. The latter contribution to strength is usually achieved by the precipitation of / in certain wrought alloys. Insufficient attention has been given to the problem of obtaining strength in su-peralloys by controlling precipitation of carbides on imperfections within the matrix. The present work was undertaken to investigate the dislocation substructure in various superalloy matrices, to study the effect of such substructure on subsequent precipitation of carbides in the matrix, and to investigate whether certain modes of precipitation of carbide phases found in austenitic stainless steels2"4&apos;6 would occur in nickel-base alloy matrices with dislocation substructures of the same type as those found in austenitic steels. 1) EXPERIMENTAL TECHNIQUES Five-pound heats of the various alloy compositions reported here were vacuum-cast. The ingots were given light deformation by rolling to break up the as-cast structure and then homogenized for 24 hr. HASTELLOY alloy X (nominal composition: Ni-2OCr-17Fe-8Mo-0.05C) was homogenized at 2150°F and In-cone1 625 (nominal composition: Ni-20Cr-5Fe-8Mo-3.5Cb-0.05C) was homogenized at 2280°F. Fabrication of 0.004-in. sheet was achieved by cold rolling with intermediate annealing treatments being carried out at the same temperature as those used for homogeniza-tion. Each solution anneal was followed by quenching. The aim of this procedure was to redissolve as much of the primary carbide phase as possible. Samples of the 0.004-in. sheet were cut and encapsulated in quartz capsules and then heat-treated in the tube furnaces. Thin foils were prepared using an ethanol-10 pct perchloric acid bath at 32°F and at a voltage of 22 v. A "window" technique was employed. Observations were made on a JEM-7 electron microscope operating at 100 kv. 2) EXPERIMENTAL RESULTS a) Types of Dislocation Substructure. Fig. 1 shows a schematic correlation between stacking fault energy, SFE, and the type of dislocation substructure observed in various matrices of nickel- and cobalt-base alloys. A precise quantitative determination of stacking fault energy is not implied in the figure but the correlation between stacking fault energy and the type of dislocation substructure obtained allows alloys to be divided into three classes in analogy with the classification employed by Swann and ~uttin~&apos; for binary alloys of copper. Class I alloys are associated with a "high" SFE and show a cellular substructure of dislocations as typified by the micrograph of a thin foil of pure nickel deformed 4 pct at room temperature in Fig. 2. With decreasing SFE the tendency toward cell formation is lessened and dislocations tend to be arranged in coplanar groupings. Examples of this class of alloys with "medium" SFE are provided by the mi-crostructure of solution-heat-treated, quenched, and deformed thin foils of HASTELLOY alloy X, "Waspaloy" (prior to any aging), and Inconel 625. Fig. 3 shows a thin-foil micrograph of an alloy of Inconel 625 composition, solution-heat-treated, quenched, and deformed 5 pct at room temperatures. No evidence of any cell structure can be obtained in materials of "medium" stacking fault energy, Fig. 3, even after severe deformation. The stacking fault energy of the alloy shown in Fig. 3 is, however, not low enough to make the dissociation of dislocations visually obvious. As stacking fault energy decreases further, with successive addition of solute in the matrix, there is an increased tendency toward dissociation of dislocations and cross slip becomes progressively more difficult. Eventually, when the stacking fault energy is "low" enough, complete dissociation of dislocations is seen to occur as shown in Figs.

Jan 1, 1969

By W. F. Hower, W. Brown

Large-scale sand consolidation tests were conducted in an effort to determine the reasons for the successes and failures of this method of sand control. Several different consolidating materials were used in treating both clean and bentonitic sands that were packed in a chamber having a capacity of 3.3 cu ft. The results were essentially the same for all of the different consolidating materials, The data show that low-viscosity consolidating materials pumped at a relatively slow rate gave the best results. Where the formation has produced sand, the treating fluids can compress the formation, thus permitting the channeling of fluids to another horizon. Pressure-packing these zones before attempting to consolidate is recommended. Sands containing more than 4 per cent of water-swelling clays are not good candidates for consolidation. It is indicated that loose sand, particularly when it is bentonitic, can be fractured during the placement of the treating fluids. INTRODUCTION Sand production in oil and gas wells has plagued the industry for many years, and numerous cures for this problem have been suggested. Most methods have been successful to a certain degree, but the great variety of well conditions that exist in the different areas has magni- fied the problem and limited the successful use of the various systems. Four review papers1-4 present a wealth of information concerning the degrees of success that have been obtained by the different sand-control methods. The bridging of sand grains by the use of gravel packs and screens has been quite successful. However, these methods do not leave the casing clear for all types of multiple completions, and the cure does not last for the production life of the well in some instance:;. The control of loose sands by sand consolidation with resins has never been as successful as desired. It has always been hoped that such a treatment would eliminate all sand problems for the life of the well, but. initial applications, starting in the middle 1940&apos;s, were only moderately successful. Lott, et a1,3 reported a success ratio of approximately 50 per cent and made the following conclusions. The highest percentage of successes were obtained where: a. Consolidation of a zone was made at the time of initial completion or prior to the production of sand. b. The interval treated was less than 12 ft in length. c. Between 30 and 50 gill plastic/ft of producing interval was displaced through the perforations. REASONS FOR SAND CONSOLIDATION FAILURES Our own experiences in the field of sand consolidation point toward the following conditions as the major reasons for the failure of sand consolidation attempts. 1. Mud-plugged perforations and mud invasion of the formation. 2. Sand in the casing covering all or part of the perforations. This sand could be either formation sand or one of the coarser sands used as propping agents in hydraulic fracturing. 3. Holes in the casing. 4. Channels behind the casing. 5. Attempting to treat too long a perforated section. 6. Too high a percentage of water-swelling clays in the formation. 7. Formations that have produced sand. Recent attempts were made to treat perforated sections ranging from 10 to 30 ft, in wells that have produced sand, by using a straddle packer that was raised and lowered through the perforations as the consolidating material was being pumped. In most instances, the pressure required to pump fluid into the formation varied considerably as the tool was raised and lowered. This suggested the possibility that significant differences in permeability were present or that only part of the formation had produced sand. There were times when a sudden break in pressure indicated that a fracture was being formed. Research conducted several years ago concerning the problem of the control of water in air and gas drilling indicated that shale sections could be fractured quite easily. In addition, it was determined that it was easier to pump fluids into shale bodies by fracturing the shale itself, or the interface between the shale and sand, than to pump into a fluid-saturated formation. Formations that produce sand are usually adjacent to shale bodies and frequently have shale streaks of various thicknesses inter-bedded in the sand. Therefore, where shale is exposed to fluid pressure it

By A. K. Mukherjee, John E. Dorn

The effects of strain rate and temperature on the critical resolved shear stress for (321)[111] slip were determined for the silver-rich CsCl type of intermetallic compound AgMg. The flow stress increased only slightly as the test temperature was first decreased below room temperature; a rapid increase in the flow stress was obtained with yet further decrease in temperature from about 250&apos; to 4OK. The effect of both the temperature and strain rate on the flow stress over the low-temperature range could be rationalized satisfactorily in terms of the Peiwls mechanism when the deformation was controlled by rate of nucleation of pairs of kinks. IN spite of the well-documented interest of metallurgists and engineers concerning the mechanical behavior of intermediate phases and intermetallic compounds, very little definitive information is available on this important subject. As recently summarized by westbrook,1 only limited and modest progress has been made thus far in elucidating the details of the mechanism of plastic deformation for the intermetallic compounds; the available information largely concerns phenom-enological descriptions of empirical observations and experimental facts, principally with reference to poly crystalline aggregates. The present report on the elucidation of the rate-controlling mechanism for slip in the bcc structure of AgMg is part of the comprehensive program of a systematic investigation on the mechanical behavior of intermetallic compounds. The intermetallic compound AgMg has a CsCl type of lattice structureZ and is completely ordered up to its melting point of 820c3 This material was selected for our present investigation because of its simple crystal structure, moderate and congruent melting point, ordered structure persisting up to the melting point, and some solubilities of the constituent elements, which could be expected to help in the growing of single-crystal specimens. Whereas previous investigations on the properties of AgMg include hardness,*"6 slip systems,7 tensile flow stress of polycrystalline specimens,&apos; and electrical resistivity,4 the current investigation will be directed principally at elucidating the rate-controlling dislocation mechanism responsible for slip in single crystals at low temperatures. It will be shown that the strain rate is consistent with a model involving the rate of nucleation of pairs of kinks by the Peierls mechanism for plastic deformation. EXPERIMENTAL TECHNIQUES Single-crystal specimens of the AgMg intermetallic compound were prepared and tested as follows: 1) A master alloy ingot of AgMg was produced by melting and chill casting the high-purity silver (99.995 wt pct) and high-purity magnesium (99.997 wt pct) in an induction furnace under a helium atmosphere. 2) Sections of the above-mentioned ingot were placed in a graphite mold containing a spherical cavity in which a single-crystal sphere of 1 in. diam was grown under helium by the Bridgman technique. 3) The operative slip systems were investigated at room temperature on a singlecrystal of AgMg, from measurements of the angles made by the slip traces on the two surfaces of the specimen, which were at 90 deg to each other. The investigation confirmed that the AgMg compound undergoes slip primarily in the (321) plane and in the [Ill] direction, but a small amount of secondary slip was also noticed in the (112) (111) system. No slip was observed in the (110) planes. 4) The single-crystal sphere, mentioned earlier, was oriented in a graphite mold containing a cylindrical cavity of 3/8 in. diam above the spherical receptable to give the angle xo = 45 deg between the axis of the cylindrical bar and the normal to the slip plane (321), and the angle AO = 45 deg between the slip direction [Ill] and the axis of the bar. Oriented single-crystal bar seeds were produced by melting, under a helium atmosphere, a polycrystalline bar in the cylindrical cavity above the oriented spherical seed and by growing an oriented single-crystal bar from the seed. 5) Finally, oriented single-crystal specimens were grown from these cylindrical seeds. 6) The cylindrical specimens were machined in a High-Tension Spark Cutting unit to give a 2-in. gage length. The spark-machined gage section was elec-tropolished in a bath containing 200 ml of H3PO4,

Jan 1, 1964

By F. Bonaccorso, G. Venturello, C. Antonione

A study of the effect of small amounts of interstitial impurities on recovery and re crystallization in high-purity iron (99.995 pct) has been undertaken. This paper gives results on the effect of carbon, introduced in small-dosed amounts @om 0.0005 to 0.0086 wt pct) by heating iron specimens of high purity m a static atmosphere of CO + ,. The materials prepared in this way, cold-worked 80 pct and subjected to a series of isochronal and isothermal annealings, were submitted to examinations by X-rays, micrographs, and hardness tests. It was observed that effect of carbon is remarkable in the sense of blocking recovery of mechanical properties up to the temperature at which re crystallization begins. On the contrary, carbon has a negligible effect on primary re crystallization temperature, when compared with the known effect of substitutional impurities. This is in agreement with the high mobility of interstitials. In effect, only a slight decrease, -20 pct, of the grain-boundary motion rate was noted, due to the interaction between the grain boundary and the carbon atoms. On the other hand, in the samples in which the carbon content is above the solubility limit at the temperature at which re crystallization occurs, a slight increase of nucleation frequency is noted due to the presence of precipitated carbides. ThE effect of purity on recovery and recrystalli-zation phenomena has been known for a long time; however, recently, new attention has been given to the problem since new methods for obtaining metals with extremely low impurity contents have become available. Most of this research work essentially concerns the effects of impurities which cause precipitates or give rise to substitutional solid solutions. The works of Bolling and winegard1 and Aust and utter&apos; on lead, and Vandermeer and orddon&apos; on aluminum, 01sen4 on nickel, and Abrahamson and Blakeney on iron should in particular be referred to. On the effect of this type of impurities a quantitative theory has been formulated by Detert and Lucke6 and has lately been discussed critically by Cahn7 and Gordon and vandermeer.&apos; Interstitial solid solutions in iron have not as yet been studied. As the study of the effect of interstitials is of great interest both from a theoretical and practical standpoint, it was deemed useful to examine the effects of carbon, nitrogen, and boron on recovery and primary recrystallization of iron. There already is some work by Chaudron et al.,1-" on the effect of interstitials on iron; their work, however, mainly concerns secondary recrystallization. The present paper refers in particular to the effect of carbon. EXPERIMENTAL PART Preparation of Materials. The pure iron used for this research was obtained from FeCIS recrystal-lized and purified by extraction with isopropylic ether. From the ferric chloride purified in this manner, hydroxide was precipitated with a solution of very pure ammonia, and, by calcination in pure sintered alumina crucibles, oxide was obtained. Reduction of the oxide to iron sponge was performed in sintered alumina tubes with very pure hydrogen at 650°C; at the end of the operation temperature was increased to 900°C. Specimens for the experiments were obtained by sintering the sponge at 1480°C in pure Hz after a pre sinter ing treatment at 900° C. It is important to note that the treatment at 1480°C in Ha produces a further purification from more volatile elements such as zinc, cadmium, arsenic, lead, and tin. Details on the preparation and characteristics of this type of very pure iron are given in a previous work.&apos;&apos; Only the complete analysis performed by neutron-activation methodsz3 is given here, Table I. Some of the specimens prepared in this way were carburized in the 0 region with very low amounts of carbon by treating them at 700°C in a static atmosphere of Ha containing a definite amount of CO. The set-up used is described in Fig. 1. A gas-tight quartz tube containing the specimen to be carburized and an internal friction control specimen, after being evacuated, was filled with Hz

Jan 1, 1963

By Linda Lee, R. E. Reed-Hill, C. R. Smeal

Four fcc metal surfaces, etched to make them responsive to polarized light, have been studied with an electron microscope. Jones&apos;prediction that these surfaces are grooved has been verified. Optical-goniometer measurements made on commercially pure nickel indicate that the groove walls are poorly defined (100) facets. Surface mientations close to either 4001 or {ill).- show no extinctions on the polam&apos;zid-light microscope. An explanation is offered for this orientation dependence. It has also been deduced that polarized-light extinctions on a grooved cubic-metal surface should not be used directly in crystallographic-orientation determinations. The nature of the etching solutions that produce these surfaces is considered. A cubic-metal surface may be made responsive to polarized light in two basic ways."&apos; In one, an anodic film, believed anisotropic, is formed on the surface. A plane-polarized-light beam, at normal incidence, should be reflected from this type of film with an ellipticity that varies with grain orientation. Under crossed polarizers of a polarized-light microscope, each grain may be distinguished from its neighbors by a difference in reflected-light intensity. An alternate treatment,&apos; more generally applicable to cubic metals and of principal concern here, involves etching of grain surfaces. The characteristic features of this surface were first deduced by Jones3 from light-microscope observations. She concluded that, in general, grain surfaces were furrowed so that light was reflected from two parallel sets of etched facets. A grooved surface produces elliptical polarization of a plane-polarized beam because the beam does not strike groove walls at normal incidence. Jones also observed that the furrows must have faces inclined to each other by approximately 90 deg, since the light returns along the incident path, and that a grooved surface should show four maxima and minima of reflected-light intensity during a 360-deg stage rotation of the polarizing microscope. Positions of maximum extinction were predicted to occur when groove axes were parallel to either polarizer or analyzer vibration directions. Because of the limited resolving power of Jones&apos; optical microscope, her deductions were primarily indirect. Proof of the correctness of her conclu-sions, as demonstrated by the electron microscope, will be given as well as evidence concerning the crystallographic nature of the etch furrows and the types of etching solutions that produce them. EXPERIMENTAL PROCEDURE During a comprehensive study of hot plastic deformation in nickel and nickel alloys, an etch was evolved that produced a surface with an excellent polarized-light response on Nickel 200 ("A" Nickel). The etching solution and associated metal-lographic procedures are given in Table I. In evaluating this etch, a study was made of the topological features of the etched surface and their relation to the underlying crystalline structure. As part of this investigation, large crystals (2 mm average diameter) were grown in a 1-cm-sq Nickel 200 specimen. After the surface was etched, the crystallographic orientations of ten grains were determined by the standard back-reflection Laue technique of Gren-inger.4 Maximum extinction positions during a microscope stage rotation were also measured for the ten grains. Groove-wall positions on the surfaces of the ten grains were measured with a two-circle optical goniometer. The technique was essentially that of Barrett and Levenson.5 Several grain surfaces were photographed with a Philips Model 100A electron microscope. All specimens were replicated with collodion, or collodion backed with formvar and chromium shadowed at 18 to 20 deg. The basic material was Nickel 200. However, an electron-micrographic study was also made of surfaces developed by polarized-light etches on other fcc metals (90-10 a brass, Monel 400, and lead). All etching procedures are given in Tables I and 11. EXPERIMENTAL RESULTS Fig. 1 shows typical electron micrographs of three different fcc metal specimens and an optical micrograph of a fourth. All photographs show a grooved structure corresponding closely to Jones&apos;3 predictions. Also, as noted by Jones, extinctions were always observed when groove axes were either parallel or perpendicular to the microscopes&apos; vertical cross hair. The symmetry of the grooves, with respect to the twin boundaries in Fig. 1, implies that furrows have a crystallographic basis. The coarse-grained Nickel 200 specimen was used to study this basis. Facet Orientation. The poles of the ten Nickel 200

Jan 1, 1964

By R. J. Lutton

Empirical data from 91 rock excavations have been used to construct a family of slope curves on a chart relating excavation height and inclination. The highest and steepest slopes from each excavation are plotted and connected by a line. The 31 1ines appear to establish one or two geometrical slope fields through which the curves are projected. The curves apparently represent a lumped eflect of many factors too complex to be considered individually. Important factors such as geological structure or ground-water conditions can dominate the picture, but where these factors do not overshadow others, the slope chart should be useful for estimating or checking optimum inclination. The U.S. Army Corps of Engineers (USAE) has been engaged since 1962 with the U.S. Atomic Energy Commission in a joint research program to develop nuclear excavation technology. The Corps is responsible for collecting the requisite data on engineering and construction problems associated with nuclear excavation. The ultimate objective is to develop a capability to use nuclear explosives as a construction tool on public works projects such as harbors and canals. The present study on empirical inclination-height curves for conventionally excavated slopes is an outgrowth of an investigation&apos; sponsored by the USAE Nuclear Cratering Group on applicability of data from existing excavations in establishing guides for engineering judgment in crater excavation. Data were generously contributed by over 50 mining companies among other organizations. Inasmuch as several companies preferred that their contribution be anonymous, all data are treated so here. Some Factors Affecting Stability Many factors affect or are suspected of affecting the stability of excavated slopes, e.g., adverse structural orientation, degree of structural ordering, ground water, climatic conditions, mechanics of excavation, and plan-profile configuration. Such factors are lumped together in developing a slope chart. Obviously geological structure and ground water can overshadow all other factors. Where such is the case, the simplification of slope charts may give an erroneous picture (not conservative enough). A further complication results from the fact that the concept of stability may vary according to the use of the excavations. For example, slope adjustments that would be regarded as failure in a powerhouse excavation, might be tolerable in a mining operation. Mine slopes are continually being modified by further excavation, and instability that would develop in a similar permanent excavation slope over a period of years might not have time to develop in a mine. Inclination vs. Height Charts Charts of inclination vs. height for particular formations or conditions have been used in the past as an aid for designing excavation slopes. Some of these have been based upon empirical analyses of collections of data and experience. MacDonald" and Lane have presented slope tables and charts for excavated and natural slopes in relatively weak sandstone and shale. Coates&apos; has shown an inclination-height chart for slopes in incompetent rock. Most organizations have developed slope design criteria which relate bench widths, heights, and inclinations to use in various rocks. Slope data collected in present studies can be similarly used to develop inclination-height charts; however, a plot of all slopes on such a chart shows very little because of the wide spread of the data. Reasons for the dispersion of points are: (1) many slopes are not carried at optimum inclination, particularly in mines where maintaining roadways and following irregularities of ore bodies are more important than achieving steep inclinations; (2) many engineers and geologists with varied backgrounds and viewpoints have been involved in designing these slopes; and (3) each slope is characterized by a unique combination of factors affecting stability and in turn optimum inclination. Significant curves can sometimes be constructed where the points can be grouped into related clusters from the same excavation. The essence of this approach appears when only two slopes from each excavation are considered—the highest slope and the steepest slope, connected by a line segment (Fig. 1). This reduces considerably the usable data because in many cases only one of these two slopes is available. Nevertheless, the concession seems justified. Construction of Slope Curves Ninety-one pairs of points and connecting line segments were assembled in this study. The line segments were assumed to approximate a geometrical slope field (Fig. 2), and a family of curves has been visually projected through to represent the slope field. It should be

Jan 1, 1971

By D. F. Stein

In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Because of this limited success, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. As a result of these calculations, it was concluded that autoradiograPhy is a rather insensitive technique to measure grain boundary segregation. The range (energies) of the emitted particles (ß and a) must be low, and the concentration of the radioactive speczes at the grain boundary must be (in general) two or three orders of magnitude greater than the concentration within the grain. Because of these very restricted conditions , the limited success of the technzque is not surprising. In spite of the apparent usefulness of autoradiography in demonstrating segregation, it has had very limited success in demonstrating grain boundary segregation. Sulfur segregation in iron1 and possibly polonium segregation in Pb-5 pct B1 2 alloys are the only autoradi-ography experiments that have demonstrated segregation to grain boundaries in metals without the formation of a second phase. Segregation to a boundary without the formation of a second phase is often called Gibbs&apos; absorption and is discussed by McLean in Chapter 5 of Ref. 10. There are several394 experiments showing grain boundary diffusion of a radioisotope, but this type experiment is not representative of equilibrium between the concentration of an element at a grain boundary and that in bulk, so it will not be discussed in this paper. In an attempt to determine if temper embrittle ment of low-alloy steels was associated with segregation of antimony to grain boundaries, a program to use auto-radiography (using Sb-125) was initiated. Even though other measurements strongly suggest that segregation is occurring during embrittlement, no evidence of grain boundary segregation was observed in the auto-radiography experiments. An attempt was also made to detect segregation of carbon (using C-14) to grain boundaries in iron during slow cooling. There is again strong indirect evidence7 that segregation occurs during such a treatment, but the autoradiography experiment gave no evidence of such segregation. Because of the failure of these experiments and the general lack of success by our metallographic unit in measuring grain boundary segregation using autoradi-ography, a model system amenable to mathematical analysis was devised to determine which variables in the experiment are most important. MODEL SYSTEM The model system is illustrated in Figs. 1 and 2. It is a semi-infinite bicrystal with a single grain boundary perpendicular to the top face. The width of the grain boundary, W, is defined as the region to which segregation has occurred and it is assumed that this region is of constant composition. The assumption of an infinite dimension is for mathematical reasons but the results of such an analysis (as will be demonstrated later) are valid for even very small specimens. It also is assumed that the measurement is not limited by means of detecting the radiation (photographic emulsions, counters, and so forth) but that the means of detecting radiation is linearly sensitive to the radiation and has infinite resolving power. The distance y is the perpendicular distance from the center of the grain boundary to the point at which the background radiation is measured and x is the integration variable. CALCULATION FOR BETA PARTICLES Two values of the intensity of radiation will be calculated, the intensity at the center of the grain boundary and the intensity far from the grain boundary. The radiation at the center of the grain boundary can be calculated in the following way. Assume a grain boundary of width W having a uniform concentration equal to Cgb + Cb where CGb is the excess concentration of the element under consideration at the grain boundary and Cb is the bulk concentration. The intensity of radiation, IgB, at the center of the grain boundary, is a consequence of the amount of radioactive material, decay rate, absorption, and geometrical factors which can be represented mathematically by the following expression:

Jan 1, 1968

By K. K. Clark

Excessive injection pressures in water injection wells may create deeply penetrating fractures, or may open up existing reservoir fractures. If these fractures are oriented toward offset producing wells, oil recovery at injected water breakthrough and ultimate recovery will be impaired. A method of calculating fracture lengths from pressure fall-off test data is presented. The method is based on a linear flow model that simulates conditions present during the early-time period after shutting in an injection well. Fracture lengths can be calculated directly if formation permeability is known. A graphical technique is presented that provides fracture lengths based on permeabilities calculated from normal fall-off tests, where those permeabilities are adjusted for flow geometry. Test data from four injection wells and results obtained from applying the method to these wells are discussed. Introduction Rates of water injection into nonstimulated wells in low permeability reservoirs frequently fall below economically desirable levels. Therefore, some form of stimulation such as hydraulic fracturing often is performed on these wells. Usually these fractures penetrate a short distance from the well — short as compared with interwell spacing — and therefore should not create problems of water channeling to offset producing wells. In the past, some operators have been tempted to increase injection pressures continually to maintain a specified injection rate. But pressures cannot be increased indefinitely. Field data indicate that continued injection above fracture opening pressure can cause excessively long fractures to approach between well distances. If these long fractures intersect or closely approach offset producing wells, premature water breakthrough can result. It is difficult to seal effectively these fractures by various workover procedures after premature water breakthrough has occurred. This paper describes testing procedures that are potentially capable of detecting premature water breakthrough before it occurs. Knowledge of fracture lengths and fracture opening pressures can assist field engineers in selecting optimum operating conditions for water injection wells. Fracture lengths should be calculated from pressure fall-off tests on injection wells, and maximum permissible iniection pressures should be determined from step-rate injectivity tests. Equipped with this information, the field engineer is in a better position to recommend for a particular injection well the optimum operating conditions that will lessen the chances of channeling to offset producers. Historically, pressure transient tests have been conducted primarily on producing wells and analysis procedures have been based on radial flow concepts. Several authors have suggested that these same procedures be applied to tests conducted on water injection wells. This application is justified for wells that are not connected to extensive fracture systems. However, if the formation is severely fractured, the interpretation methods must be modified. Several authors have presented the pressure response of various systems that are intended to simulate reservoir conditions. A paper by Russell and Truitt* on vertically fractured svstems is probablv the most useful from the standpoint bf the fieid engineer. Russell and Truitt presented the pressure-vs-time behavior of a well connected to vertical fractures with various fixed lengths. Their permeability adjustment technique is used in this paper to refine methods of calculating fracture length and interwell permeability. Theory and Definitions Three flow-system geometries are considered in analyzing injection well test data. These various geometries are applicable during specific time intervals of transient pressure tests. Schematic drawings of the flow models, and the time intervals over which they are applicable, are shown in Fig. 1 in the chronological order that they are applied to the pressure response of water injection wells in fractured formations. The very early response is simulated by an infinite linear system as shown in Fig. 1A. This representation permits the calculation of matrix surface area exposed to the fracture. The model shown in Fig. 1B is identical with the one studied by Russell and Truitt. They evaluated the transient pressure response of this vertically fractured system by finite difference techniques. The results were presented as tabulations of dimensionless pressure drop functions for a range of fracture lengths. A semilog plot of these data shows that the apparent matrix permeability can be related to the true matrix permeability by a simple exponential function. Their adjustment factor is used in this paper to improve the accuracy of matrix-permeability and fracture-length calculations.

Jan 1, 1969

By F. Weinberg

Measurements have been made of solute segregation during dendrilic growth by using radioactive solute elements and ,measuring the activity of den(12-ites cut from decanted specimens. This has been done for both lead awl tin based binary alloys contaitzing the following solute additions: Ag, T1204, was dependet on ko, the equilibrium distribution coefficient in the following way Fay k &apos;c 0.1, C/C 0.6; for k0 >0.1. 0.6 <c,/c,< I. Qualitative obse?-vations were madc of dendritic segregation, by using autoradiographic techniques, for the Sn + Ag110 and Sn + Tlo4 systems. The observation were found to he in general agreement with the measurements ofCA/Co. Autoradiographic were also obtained of scctiolccl delzr11-iie stalks. These indicated that the stalks had a substructure, dclileated by solute corzetlt?atio?zs nlolg the substructure walls. A new dendrite growth direction <JI2> is reported for tila. SOLUTE segregation in dilute binary alloys has been investigated by Pfann,&apos; Smith, Tiller, and Rut-ter,&apos; and others. They considered the case of a slowly advancing plane solid interface, and derived expressions for the distribution of solute in both solid and liquid during solidification. To determine these expressions, they assumed no diffusion in the solid and either complete mixing in the liquid:&apos; or diffusion controlled solute movements in the liquid without any convective mixing.&apos; The present investigation considers solute segregation during dendritic growth, in which case the solid-liquid interface is not plane, and the growth rates are rapid. Segregation under these growth conditions has not been treated mathematically, because of the relative complexity of the system. It has been suggested by Chalmer, on the basis of preliminary results, that an alternative to the diffusion and heat flow controlled conditions during growth is &apos;diffusionless" dendritic growth in which solid is formed with the same composition as the liquid. He suggests this type of growth may depend upon a solvent-solute relationship that permits some solid solubility without excessive increase in internal energy, as is the case for solutions of tin in lead. On the other hand, Montariol,4 and others, have shown experimentally that some segregation does occur during dendritic growth in metals using etching and radioactive tracer techniques to indicate the concentrations of the solute. The present investigation was undertaken to determine, both qualitatively and quantitatively, the extent of solute segregation associated with dendritic growth in a series of binary alloys, as a function of solute concentration. PROCEDURE The solvent materials used were Vulcan Electrolytic tin (99.997 pct purity) and Tadanac lead (99.998 pct purity). The solute materials were Zn, Sn, and Sb (better than 99.998 pct purity), Ag and Co (99.5 pct purity), and T1 (Fisher "purified" metal sticks). Activation of the solute metals was carried out in the reactor at Chalk River, Canada. Master alloys were prepared by induction heating from the radioactive solute metal and the pure solvent, under argon, in graphite crucibles. Pieces of these alloys were then added to the solvent to give the required solute concentration. Dendrites were grown in essentially the same manner as that described by Weinberg and Chalmer, , in which controlled orientation single crystals were grown dendritically in horizontal graphite boats, and the liquid decanted. The crystals were grown and decanted in an atmosphere of tank argon. Before decanting, a sample of the liquid was drawn up in a glass tube and allowed to solidify rapidly. The orientations of the single crystals were such that <loo> was parallel to the growth direction, and (100) in the horizontal plane for lead, and [1101 and (110) respectively for tin. With these orientations long dendrite stalks formed along the bottom of the boat in the dendrite direction (<100> for lead and [I101 for tin) from which secondary branches grew. Only these secondary branches, which grew freely in the liquid from the dendrite stalk to the liquid surface, were used in the measurements. Accordingly, effects due to substrates and oxides on the surface of the liquid need not be considered. In order to measure the solute concentration C, of the dendrites, individual dendrite stalks were cut from the decanted specimens, remelted, and formed

Jan 1, 1962

By C. S. Matthews, M. J. F. Rosenbaum

The purpose of thir work wax to lcarn it~lzut infori~lation could he obtained from various typs of pilot water floods and to attempt to find the optunum pilot patter11, for a revervoir which had previously been depleted by a solution gas drive. The study was made in the laboratory with mathemetical methods a dynamic analog and a potentiotnetric analog. Results werp tested against the field llistorics of a nrrnlber of pilot water floods. At a reasonable valrre of currzulative injection, the total production rate for the one-injector five-spot should reach about 6.5 per cent of injection rate, and for a four-injector five-spot, about 9 per cent. Accurate estimates of ultimate recovery cannot be made on the basis of such snzall prorluction rates. However, with a pilot composed of nine ir1jector.s and 16 producers the production rate is approximately 50 pcr cent of injection rate at a reasonable value of camulative injection. Sonle inforn~ation for extended performance predictions might he obtained from such a large pilot. These conclusions were drawn on the basis of results obtained for unit mobility ratio, and a sturly using tlre potentiometric analog was made of the effect of other mobility ratios to determine the range of applicability of these predictions. For the four-injector, five-spot pilot with the ratio of production to injection rate (before water breakthrough) is about twice that for with it is about two-thirds; and with M0= 10, it is about one-third For high mobility ratios, it was found that the production rate increased considerably as water-cut increased. These result can be used to modify, qualitatively, the inter.pretntions based on curves for the unit rnobilit\. ratio CaSeS. It was found that the maximum ratio of production rate to injection rate obseriled in field pilot floods was of rhe scime order as that prerdicted by these methods. The time required to reach thisr maximum did not generally agree with the time predicted for a homogeti~orir reservoir. The differcrlce between predicted and observed time of response gives an indication of the permeability profile and of the condition of the producin,g wells. Pilot water floods of the pattern type are generally carried out in reservoirs which have been depleted by solution gas drive and are at low pressure. Under these conditions, oil and water can be considered incompressible. It is assumed that, as the water is injected, an oil bank forms ahead of it and that there is a distinct interface between the water zone (or bank) and the oil zone (or bank) and between the oil zone and the region ahead of the oil zone. It is further assumed that only gas is mobile in the unflooded (gas) region, only oil is mobile in the oil bank and only water is mobile in the water bank. The saturations and the mobilities associated with each zone are assumed uniform. We idealize our reservoir to be homogeneous, horizontal and of constant thickness. Effects of gravity within the producing layer are assumed negligible. If the actual time-dcpendent flow problem is approximated by a acries of steady-state problems. the potential and stream function in the oil bank and water hank satisfy Laplace&apos;s equation in two dimensions. We can therefore use a poteiitiometric analog of this system. Potentiometric models have yielded uscful results in this laboratory&apos; and clsewhere in the study of a variety of secondary recovery problems. For the case where M = I, we generally prefer to use theoretical mcthods as well as a simpler dynamic analog. Except where otherwise noted, the ratio, side of five-spot/wellbore radius. is taken to be 3,600. a figure which corrcsponds to a normal-size wellbore in a 10-acre well spacing. THEORETICAL EVALUATION OF VARIOUS PILOT PATTERNS, Mw0 = 1 <&apos;he theoretical models which we used to examine the performance of various pilots are shown in Fig. 1. Image theory was used to determine the ratio of production rate to injection rate as a function of the volumc of the flood. The ratio of production rate to injection rate was chosen because this is an easily measurable quantity which is characteristic of a pilot