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By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7' has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers' requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant

By E. E. Underwood, L. L. Marsh

Aluminum single crystals, alloyed with 0.042 atomic pet Cu and 0.11 and 1.1 atomic pct Mg, were subjected to constant stress creep tests, tensile tests, and hot hardness measurements within a temperature range of 300° to 866OK. Calculations based on Dorn's temperature-compensated time parameter, 6, gave a value of DH, = 27,000 cal per mol for the activation energy of early creep in aluminum single crystals. Correlations have been obtained for aluminum alloy single crystals with the parameter E for solid solution strengthening, as well as with the parameter F for solid solution hardening, by using a valence of three for aluminum. Limited measurements on tensile specimens show that the slip band density tends to decrease with increasing temperature and with decreasing solute concentration. INCREASING interest is being shown in the mechanisms of plastic deformation in single crystals during tensile and creep testing. The complexity of deformational processes in polycrystalline materials has led to a search for simpler experimental conditions. Numerous creep and tensile investigations have been conducted with pure, metallic single crystals. To a lesser degree, the effects of alloying elements on the tensile properties of single crystals have been determined. However: the literature dealing with the effects of alloying additions in single crystals under creep conditions is vanishingly small. This paper represents an attempt to narrow this gap in the knowledge of the subject. Previous investigations of creep behavior at the Battelle Memorial Institute1-1 have been of great value in the analysis of the present single crystal data. It is equally desirable, however, to ascertain the extent of correspondence between the behavior of single crystal and polycrystalline materials. For this purpose, correlations, similar to those developed for polycrystalline aluminum alloys by Dorn and co-workers, have been made with the single crystal data. The results from this study have tended to confirm and extend those correlations to the case of alloyed single crystals. Materials and Procedures Three dilute binary aluminum alloys were prepared for this investigation from 99.99 + wt pct Al, 99.8 wt pct Mg, and 99.92 wt pct (electrolytic) Cu. The nominal compositions of the alloys were 0.042 atomic pct Cu, and 0.11 and 1.1 atomic pet Mg. Precautions were taken to avoid contamination of the stock during melting and casting of the alloys. After a heat treatment of 8 hr at 925°F the alloys were extruded, then machined into) threaded tensile specimens with a 3 in. reduced section and a 0.505 in. diam. Spectrographic examination showed less than 47 ppm metallic impurities in each alloy. The single crystals were grown by the strain-anneal method, with a critical strain of about 11/4 pet giving the optimum results. In general, 3 in. crystals were obtained with the Al-Cu alloy, but smaller crystals in the magnesium alloys necessitated the use of 2 in. and 1 in. gage lengths with the low and high magnesium alloy specimens, respectively. After an electrolytic polish, the orientation of that portion of the specimen containing the largest single crystal was determined from Laue back-reflection photographs. Tensile tests were conducted at a constant load rate of about 2 lb per min. Creep runs were made in a constant temperature room, under constant stress at the higher creep temperatures, and constant load at the lower temperatures. The eloneation was measured to within ±5 microin. by a specially designed capacitance extensometer. The ex-tensometer arms were attached to the 3 in. specimens at the shoulders of the test piece or, where the crystals were smaller than 3 in., by knife-edge grips.

Jan 1, 1957

By Peter Tegart

The discovery of gold in the Toodoggone River area is credited to Charles McClair who mined placer deposits in 1925, reportedly valued at $17,500. After he and his partner went missing in 1927, efforts to relocate their workings resulted in the formation of Two Brothers Valley Gold Mines Ltd. in 1933, in which the legendary Grant McConachie (first president of CP Air) played an active role. This was the age when the prospector first utilized the airplane to reconnoitre remote areas. What greeted the observer from the air was an area rich in orange and yellow colours characteristic of gossans formed by the oxidation of sulphides. However, Samuel Black, a Hudson Bay Company fur trader, had also noted in his diary as early as 1824, the unusual and many gossanous colours in the headwaters of the Finlay River. These gossans, coupled with white limestone bluffs and the presence of placer gold, attracted the first reconnaissance of the area by Cominco in 1929. Cominco was ever active in remote areas at this time. They staked and worked several base-metal showings hosted by limestone at the margins of intrusive stocks. These early workers also obtained erratic high gold assays from chalcedony float samples found in creeks draining into the Toodoggone River. However, because the samples gave inconsistent assays, no concerted effort was made to locate their source. Except for the occasional horse-supported prospecting party of the late 1940s and early 1950s, the area did not receive much attention until 1968. Work until this time focused on the base metal lead-zinc showings which contained attractive silver credits. Gold was not an attraction because of the set price established by the US government. The late 1960s saw the northward expansion of porphyry copper exploration into the Toodoggone. A program of gossan soil sampling (gossans which had attracted the early workers) was carried out by Kennco Explorations (Western) Ltd. in 1966-1967. They analysed for base metals in the field, using a cold extraction method. The Kemess copper- gold prospect was staked as a result of anomalous copper values from this early geochemical program. In 1968, Kennco continued the program of silt traversing and field geochemical testing. The samples were further subjected to multielement analysis consisting of copper, molybdenum, lead, zinc, cobalt, nickel, and silver at Kennco's North Vancouver laboratory. Several anomalous creeks, high in combinations of copper, molybdenum, and silver, were outlined. Some initial soil grids were also established. The fall of 1969 saw the return of Kennco prospector Gordon Davies and geologist Bob Stevenson to check out a well-defined molybdenum, scattered copper and silver anomaly in soils from a grid on the Chappelle claims. The subsequent analysis of several selected quartz felsenmeer floats yielded one assay which ran in the order of 0.25 kg/t (8 oz per st) gold and 2.2 kg/t (70 oz per st) silver. Subsequent trenching on the Chappelle claims exposed the source of float in a 4- m (134) wide vein of high grade gold-silver mineralization. These results led quickly to the realization that the district had precious metal potential. Subsequent exploration in the period 1969-1974 by Kennco resulted in the discovery of most of the gold and silver occurrences on the Chappelle and Lawyers properties. Several other gold and silver occurrences were found in this district by Cordilleran, Cominco, and Sumitomo, working the district during this period. Conwest optioned the Chappelle in 1973 and explored underground by adit entry as part of a one-year program. In 1974, Du Pont of Canada Exploration Ltd. optioned the Chappelle claims and in March 1980, using reserves developed on the A vein, placed the Baker mine into production at a rate of 90.7 Vd (100 stpd). The Amethyst zone on the Lawyers property, 8 km (5 miles) north of Chappelle, was found in 1973 by Kennco using continued, persistent followup prospecting of silver silt geochemical anomalies. A silt anomaly in the order of 3.4 ppm silver occurred in a stream flowing 300 m (984 ft)

Jan 1, 1985

By I. M. Roberts

THE war emergency has affected every phase of industry. The gas and coke-oven companies have sought faithfully to discharge their responsibility in this critical period and have willingly modified their operations where possible to meet the ever increasing demands made upon them. Our company made commitments for blast-furnace coke for war purposes which necessitated a reduction in coking time in order to produce the amount required to. meet the new demands. At the same time there were certain customers of long standing, who had been supplied with foundry and egg-sized coke produced on fairly long coking periods, who also were engaged in war work and whose patronage we desired to retain. Coke produced on short coking rates from the coal mixture we were then using would not have been satisfactory for these customers. The average width of our ovens is 19 ¾ in., which is a little wider than the more modern ovens of the present day. They were originally designed to give somewhat cool tops in order to produce a rich gas. This necessitates carrying the heats a little on the warm side so that the tops will be fully carbonized. A reduction in coking time, as is generally known, is accompanied by a reduction in the average size of the coke produced. This is due to the greater shrinkage that takes place at the higher temperatures required to carbonize the charges in a shorter time. The net result is that the coke is more cross fractured and longitudinally fractured and breaks up into small sizes on handling. The cokes produced from the better coking coals seem to be more susceptible to fracture at high temperatures than those from poorer coking coals. A coal mixture that produces a beautiful foundry-sized coke at 30 to 36 hr. may yield a product at 18 hr. that would be so badly fractured as to be unsatisfactory for foundry practice. COKING CHARACTERISTICS OF COALS Our problem was to find some economical innovation and develop a method that would enable us to reduce the coking time and still produce a coke satisfactory to our foundry trade. However, before discussing the results of our present operations, it might be well to present a few observations on the coking characteristics of coals in general. Most coke-oven operators carbonize a blended mixture of coals. It may consist of a single high-volatile coal with a single low-volatile coal, or of a combination of several high-volatile and low-volatile coals. Medium-volatile coals of the Eagle seam are used for the production of high-grade foundry coke. Medium and high-volatile coals are often blended with one or more low-volatile coals. The possibilities are almost infinite, but the combinations are limited by such factors as cost and facilities for handling multicoal mixtures, and by other practical considerations. Every coal has characteristics that make it blend better with a particular coal or coals in preference to others. This property has

Jan 1, 1944

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' on lead, and Vandermeer and orddon' 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.' 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.'' 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 N. Brown, R. Kossowsky

Plain carbon steels with 0.48 and 0.95 pct C were quenched and tempered at 705°C to produce carbide dispersions with spacings on the order of 1 p. The morphology of the structure consisted of a carbide-dislocation network. The strengthening due to the dispersion was found to vary linearly with M-½ where M is the mean free-ferrite path determined by the entire network. No preyield microstrain preceded the upper yield point. After prestraining, the lowest stress at which dislocation movement could be detected was 104 psi; this frictional stress was independent of the dispersion and prestrains up to 6.5 pct. The Cottrell-Petch equation for grain-size strengthening was used to discuss the dispersion strengthening in this investigation. The results support an impurity mechanism for the upper yield point rather than one based on the Johns ton- Gilman theory. IT was pointed out by Gensamerl that the mean free path in the matrix is the important variable which controls the degree of dispersion strengthening. Gensamer's data on steels showed a linear relationship between the yield point and the logarithm of the mean free-ferrite path. The first theory was by Orowan,2 who suggested the mechanism of dislocations bowing between particles, with the resulting relationship that where a is the yield point, P is the distance between particles, and G is the shear modulus. The Orowan equation applies to that range of dispersion where P is large compared to the particle size and the particles are not coherent, so that the matrix is essentially free of internal stresses. As was pointed out by Orowan, there are different degrees of dispersion which, in turn, will influence the strength-controlling mechanism. However, in this investigation, we wish to confine ourselves to the region of coarse dispersion, where the Orowan mechanism should, intuitively, be applicable. It was soon evident that the data, which existed at about the time that the Orowan theory was proposed, did not agree with the Orowan equation in that the actual strengthening was always greater than the theoretical predictions. Thus, Fisher, Hart, and pry3 modified the Orowan theory by suggesting that the Orowan process took place in the microstrain region preceding macroscopic yielding and the subsequent, rapid work hardening in the form of residual dislocation loops around the particles largely determined the observed macroscopic yield point. The F-H-P theory stated that the increment of strengthening due to the work-hardening mechanism was proportional to f3/2 where f is the volume fraction of the precipitate. F-H-P used data by Shaw, Shepard, Starr, and Dorn4 on A1 3-5 pct Cu to support their theory. Roberts, Carruthers, and Averbach5 were the first to make a microstrain study of dispersion strengthening, and they found that for steel the Gensamer relationship was obeyed. Hayman and Nutting6 suggested that in the case of tempered steel 1) the ferrite grain boundary was the primary obstacle and 2) the carbide particles simply formed part of the grain boundary obstacles. They found that the strength varied as G"" where G is the ferrite grain size. Turkalo and LOW' determined the structure of quenched and tempered plain carbon steel using a replica technique; they concluded that the carbide particles did not necessarily lie in the ferrite grain boundaries. When they defined the mean free-ferrite path as being determined by both particles and the ferrite path boundaries, their data obeyed the Gensamer relationship. Meiklejohn and skoda8 showed that the strengthening from iron particles in mercury was a function of the particle size and the distance between particles. Dew-Hughes9 explained the Meiklejohn and Skoda results by the following theory: 1) grown-in dislocations which surrounded the particles were produced by the thermal stresses during the time the material was cooled to the testing temperature, and 2) the observed strengthening was associated with the cutting of the grown-in dislocations by the glide dislocations. Ansell and Lenel10 proposed a theory in which the glide dislocations pile-up or surround the particle until the number of dislocations in the pile-up is sufficient to yield or fracture the particle. The resulting theory says that the yield point varies as p-1/2, where P is the distance between particles. The Ansell-Lenel theory is almost identical to the

Jan 1, 1965

By A. S. Yue, A. G. Guy

A study was made of the effects of a prolonged flux of zinc atoms through the a solid solution of zinc in copper. The experimental arrangement consisted essentially of a copper disk about 0.01 in. thick, at one of whose surfaces a gaseous atmosphere containing zinc atoms was maintained, and at the other surface a gaseous atmosphere with a minimum of zinc atoms was maintained. During prolonged theothersurfaceexposure at high temperatures the zinc content of the copper disk gradually built up to the steady-state concentration distribution and then remained at this value. The concentration-distribution curves for various conditions were determined by chemical analyses. The results showed that the condition of steady-state diffusion was achieved. The diffusion coefficients calculated from the experimental data, although not of high precision, agreed with the values obtained by other workers using unsteady-state methods. Relatively slight porosity developed in the specimens in the course of diffusion. A LTHOUGH most diffusion studies have been made under unsteady-state conditions, it is known' that the steady-state method is often superior with respect to the directness and accuracy of interpretation of the data. Steady-state diffusion of gases through metal diaphragms is well known. Also, Harris' and Smith" have used the steady-state method in studying the diffusion of carbon in aus-tenite. The accepted mechanism in this system involves the motion of the interstitial carbon atoms in the rigid framework of the lattice of iron atoms. Thus, there is little difficulty in visualizing the steady flow of the small carbon atoms through the austenite. The situation in substitutional diffusion is quite different. Here the atoms are comparable in size, and it is not evident how a steady flow of one of the atoms through the solid solution might be achieved. At the time the present research was started, it was known that a previous exploratory attempt to produce steady-state diffusion in a substitutional alloy, the Au-Ag system,' had been unsuccessful and had indicated that perhaps there were basic difficulties that could not be ovei-come. Therefore, the present research began as a study of the effect of a prolonged flux of metal atoms through a substitutional solid solution. Eventua.lly, it was possible to produce actual steady-state diffusion in the system chosen for study, the a Cu-Zn alloys. Experimental Procedure The aim in the experiments was to maintain a high zinc content, about 30 pet, at one surface of a copper sheet, and to maintain a low zinc content, near 0 pet, at the opposite surface. The zinc would then diffuse into and through the copper, first building up to the steady-state concentration distribution and then maintaining this distribution. The three types of specimens that were used are shown in Fig. 1. In type A specimens the copper disk through which diffusion occurred was welded to the top of a cylindrical molybdenum tube, the bottom of which also was sealed by welding. At the diffusion temperature the brass chips in the molybdenum container were the source of the zinc vapor which maintained the lower surface of the copper disk at 30 pet Zn. The upper surface was maintained at 0 pet Zn by the vacuum in which type A, and also type B, specimens were diffused. Since the molybdenum container was impervious to zinc vapor, it was intended that the only path of escape for the vapor from the brass chips would be through the thin copper diffusion disk. However, it was found that small leaks often developed at the welded joints during the diffusion treatment, and in most specimens some of the zinc was lost in this manner. Although even small losses of this kind were a serious handicap in attempting to determine the flux through the disk, they did not prevent the maintenance of satisfactory boundary conditions for the attainment of the steady-state condition. Type B specimens differed from type A in having a weight of about 300 g supported on the copper disk by 15 to 20 short quartz rods. This change was made when it was observed that the copper disk was being bowed upward by the difference in the pressures acting on its two surfaces. Since the grain-boundary cracking which occurred in the bowed specimens could be attributed largely to the accompanying creep,3 it was desirable to minimize this effect. The counterweight was effective in significantly decreasing both bowing of the disk and cracking at grain boundaries. Type C specimens differed considerably from the others in that the low-zinc atmosphere at one sur-

Jan 1, 1959

By R. H. Jacoby, V. J. Berry

When dry gas is injected into a reservoir containing a volatile crude oil, a significant amount of the reservoir liquid phase may become vaporized. The resultant rich gas phase, when subsequently produced, con-tributes to tank oil production. This contribution assumes greater importance, the more volatile the oil in-olved. Oil recovery may be sub-stantially greater than that predicted by conventional frontal-drive methods, which do not consider the vaporization equilibrium between the reservoir oil phase and the injected gas. A calculation method has been (developed to account for vaporiza-. tion of the reservoir liquid phase during gas-injectiorz operations, and for the tank oil production which results from this factor. Recovery performance calculations are presented for a reservoir containing a highly volatile oil. Tank oil recovery is calculated to be about twice that predicted by the use of the conven-rional frontal-drive equations. In contrastto usual pressure maintenance performance results, in which the gas-oil ratio rises at an increasing rate after gas breakthrough, the pre-dicated gas-oil ratio rises rapidly to about 12,000 scf/bhl and then rises much less rapidly. During gas inje-tion, most of the reservoir liquid phase contacted is evaporated by the dry injection gar. The gas-oil ratio during this period is dependent upon reservoir pressure. The higher the operating pressure, the lower the gas-oil ratio. The predicted behavior i., in accordance with laboratory PVT tests made to .simulate the vaporization behavior. In addition to recovery performance predictions, results of the calculation procedure include complete wellstrearn composition data of value in the design of gasoline plant facilities often used in con-rrction with gas-injection operations. INTRODUCTION In the cycling of gas-condensate reservoirs, dry gas is injected to maintain reservoir pressure during wet gas production and to thereby eliminate or reduce ultimate loss of liquids due to retrograde condensation within the reservoir. Gas injected into crude oil reservoirs has a dual function. It displaces oil to the producing wells and at the same time serves to partially or fully maintain reservoir pressure. Oil shrinkage which would occur upon pressure reduction is thereby minimized or eliminated. Accepted calculation methods are available'= for predicting recovery performance of either gas-condensate reservoirs or crude oil reservoirs which are being subjected to gas injection. In gas-condensate reservoirs, any retrograde liquid formed does not flow, and it is necessary to account only for the vaporization equilibrium between this liquid and the injected gas. Conversely, in normal crude oil reservoirs, both the oil and gas phases flow, but it has not been considered necessary to account for any vaporization of the reservoir liquid which might occur upon contact with the dry injection gas. Recently, high shrinkage reservoir fluids known as "volatile oils" have been found in increasing amounts. These oils are characterized by tank oil gravities above 4.5" API, solution gas-oil ratios above 1,000 scf/bbl, and reservoir volume factors above two. Special techniques have been devised for predicting depletion performance of reservoirs containing such oils.74.5.1; One of the characteristics of reservoirs producing volatile oils is that the reservoir gas phase carries a significant amount of oil which is recoverable as stock-tank liquid. This unusual vaporization be-havior implies that an appreciable amount of reservoir liquid would be vaporized upon contact of the oil with dry injection gas. In a gas-injection operation, tank oil recovery would he obtained not only through frontal displacement of the reservoir liquid by the injected gas, but also through production of the rich gas phase. This means that not only are improved methods needed to predict recovery of such oils from reservoirs undergoing gas injection, but it would also be expected that high oil recoveries might be obtained by such operations. When relatively dry gas is injected in to a volatile oil reservoir, phase equilibrium between the injected gas and the reservoir oil will tend to bc established. Initially the most volatile components, such as propane, the butanes and the pentanes, will account for most of the material transferred from the oil phase to the gas phase. As the partially stripped oil phase is contacted with additional dry injection gas, the heavier intermediate components, such as the hexanes, the heptanes and the octanes, will gradually transfer to the gas phase in increasing amounts. This is because the supply of lighter components in the oil phase dwindles due to the stripping action of the injected gas. This stripping action will usually continue to be effective down

By C. O. Burgess, W. D. Forgeng

The results of an investigation of the ternary system iron-chromium-silicon were reported in 1936 by the present authors.l Partly for the sake of theoretical interest, and partly because of the possible commercial importance of these alloys, the present investigation was undertaken to determine the effect of some of the commoner elements likely to occur, deliberately or otherwise, in such alloys if made on a commercial scale. The elements thus added were carbon, nickel or manganese. The alloys studied were, therefore, parts of quaternary systems. This investigation was concerned primarily with the effect of these additional elements on the alpha-iron phase and the boundary between this phase region and the alpha plus sigma two-phase region. The sigma phase is a ternary solid solution based upon the compound FeCr. The work was performed mainly by X-ray methods, but a number of microscopic examinations were also made and are reported. While isolated alloys in the composition ranges studied may have been discussed in metallurgical publications, no systematic investigation of any assistance to us was found. Of the earlier work, the investigations on the iron-chromium-carbon system and on the chromium carbides by Westgren and his coworkers2'3 enabled us to identify the carbide phase. Several articles appeared after the present experimental work had been completed. Lucas and Wintrup4 determined the solubility of carbon in molten iron-chromium-silicon alloys. Tofaute and his coworkers5'6 have made detailed studies of the iron-chromium-carbon system, which will be referred to later. Materials and Methods Materials.—The iron, chromium and silicon used were essentially the same as those used in the investigation of the ternary system.l The

Jan 1, 1938

By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS' calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c', in certain bee metals and alloys are the result of large negative contributions to c' = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.' On this basis, and following Zener,2 the association between high c/c' ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

By Harry C. Gatos, Frank J. Bachner

It was shown through high-pressure experiments that tin loss by volatilizatim is necessary for the degrada-tion of the superconducting transition temperature of Nb,Sn associated with high-temperature annealing. Crystallochemical analysis of the degraded Nb3Sn showed that it constitutes a new phase with ordered niobium-site vacancies, created by the migration of niobium atoms to vaccnt tin sites. This new phase was found to form when 4 pct Nb-site vacancies were present. It has a transition temperature of 6'K and a lattice parameter of 5.283A. A similar degradation effect was observed in Nb,Al. Its superconducting transition temperature dropped from 16.5" to 8" K following a high-temperature annealing. The superconducting temperature degradation in these 0-tungsten structure compounds is attributed to the disruption of the interchain d bonding by the periodic interruption of the niobium atom chains. By annealing the degraded Nb, Sn at 1000 C in nitrogen its normal superconducting behavior is restored most likely due to the incorporation of nitrogen atoms causing the elimination of the ordered vacancies. HANAK et al.' have observed low superconducting transition-temperature values (T, - 9"K) in some NbsSn samples deposited from the vapor phase. They attributed such low T, values to disorder in the 0-tung-sten structure. Much lower T values (down to 5.6"K) were reported by Reed et al.zC for NbsSn samples annealed at high temperatures. These authors also attributed this degradation effect to disorder (random occupation of the A and B sites by niobium and tin) but pointed out that such disorder could be brought about (by high-temperature treatment) only in samples containing niobium in excess of the stoichiometric composition NbsSn. Both groups reported that the normal superconductivity behavior could be rever-sibly restored by appropriate heat treatment. Courtney et al., also found that degradation in NbsSn requires excess niobium brought about by the loss of tin during the treatment. However, these investigators proposed that the degradation is due to niobium-site vacancies resulting from the migration of the niobium atoms to the vacated tin atom sites. They did not consider the reversibility of the effect. The present study attempts to establish the nature of the above degradation phenomenon. EXPERIMENTAL PROCEDURES All compounds prepared for this investigation were made from the powders or filings of the elements which were intimately mixed, cold-pressed into a cylindrical pellet at approximately 50,000 lb per sq in., and then submitted to the desired heat treatment. The samples annealed under high pressure were placed in a MgO sample container which was mounted in a pyrophyllite tetrahedron designed for a tetra-hedral-anvil press. Details of the experimental arrangement are given elsewhere. This setup allowed heating at 1800°C or above under pressures in excess of 30kbars for 3 hr. The samples annealed in a vacuum were prepared in a high-temperature vacuum furnace which could reach temperatures up to 2400°C under a pressure of 2 x lo-' Torr. For annealing in a reactive atmosphere, a quartz tube was placed in a clamshell furnace and the desired gas ambient passed through the tube. Lattice parameters were determined using a Debye-Scherer 114.6-mm camera. Cohen's method, programmed for the IBM 7094 computer, was used to calculate the lattice parameter from the measured d spacings. X-ray integrated intensity measurements were made on several samples. These samples were ground to -400 mesh and the powder mixed with a solution of collodion in amyl acetate. The mixture was poured into a depression milled in a bakelite disc. When the mixture dried, the surface of the disc was ground flat leaving a diffraction surface defined by the face of the disc. The disc was mounted in a Philips rotating specimen holder which allowed the rotation of the sample in the plane of the diffraction surface and the integrated intensity measured using a scintillation counter and a pulse-height analysis sys-tem. The superconducting transition temperatures were determined by means of self-inductance techniques.' EXPERIMENTAL RESULTS AND DISCUSSION The Role of Tin Loss in the Degradation of Super-conductivity. The loss of tin during high-temperature annealing can be effectively suppressed by annealing under high hydrostatic pressures. Accordingly, a series of experiments were performed under pressures of approximately 30kbars. This pressure was the minimum under which high-temperature experiments could be safely performed in the particular pressure apparatus employed. Experiments were also designed to test high-pressure effects on the superconductivity behavior of NbJSn. The results of the high-pressure annealing experi-ments are summarized in Table I. All samples were prepared as described earlier. They were reacted and homogenized at 1000°C for 24 hr under argon at-

Jan 1, 1967

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968

By J. Clair, H. Mirabel

The determination of the temperature and electrical potential distributicms in the cathodes of aluminum electrolytic cells is difficult. The reascms come from the various nature and the intricate three-dimensional geometry of the materials; besides thermal and electrical phenomena react upon each other. A method of calculation using a computer program applied to a mathematical model, figuring the cathode, is developed. Both of the thermal and electrical phenomena are simultaneously considered. Temperature and electrical potential distributions are finally obtained by successive iterations. Results are compared with measurements on industrial cells. Theoretical and practical applications of these studies are given. Up to the present time the study of the distribution of the temperatures and electric potentials in the electrodes, anode and cathode, of the electrolytic cells used for the production of aluminum was limited to one of the two aspects of the phenomena because of lack of a simultaneous method of calculation. For example, the anode or cathode drop was studied assuming that the temperatures in the iron and carbon are known, a method that obviously is very approximate since iron resistivity, in particular, greatly varies with temperature, which in turn depends on current density. Consequently we tried to find a method of calculation simultaneously taking into account both thermal and electrical phenomena. We proceeded to the study of the cathodes as an initial approach to the problem. Although the cathode and surrounding materials may have varied forms and particularly very heterogeneous characteristics, their structures are simpler than that of the Sijderberg anode and boundary conditions are more easily represented than in the case of anodes even though they are prebaked. The study was in two parts: a) development of a model schematizing the true geometry of a cathode and defining the thermal and electrical boundary conditions, and b) working out a method of calculation of the temperatures and potentials by means of an electronic computer. To facilitate solution of the problem, a model was used initially much simplified in comparison with an actual cathode. This model permitted development of the method of calculation. In a second phase, this model was adjusted to the study of actual cathodes and applied to different types of cells: low- or high-intensity cells, cells set up at ground level or above ground level, cells with cathodes more or less heat-insulated. Simultaneously measurements were made with cells equipped with cathodes of the types studied to compare the values resulting from calculation. The initial model was also used for general studies, in particular for studying the effects of current density in the carbon and iron. The results were confirmed or made precise by the model of the true cathodes. This report successively describes: a) the manner in which the model representing a cathode was worked out, with the simplifications and/or the hypotheses used, b) the method of solution of the problem by means of the electronic computer, and c) an example, stating the extent to which the results obtained may be realistic. Further the possibilities offered by such a study are examined. 1) CATHODE REPRESENTATION The purpose of this phase is to represent the cathode in the form of a so-called "mathematical model", that is with a simplified geometrical configuration, in order to meet the subsequent calculation requirements, while keeping to the true facts as closely as possible. This model further includes the thermal and electric conductivities with regard to temperature for the varied materials composing the cathode, as well as the thermal and electrical conditions at the model boundaries. 1.1) Guiding Principles. For calculating the temperatures and potentials the model is divided by trior-thogonal planes into a network of small elementary parallelepipeds. At the summit of these parallelepipeds' so-called mesh points, the temperatures and potentials are computed. The number of mesh points is of course limited by the capabilities of the computer, since 1) the number of equations to be solved depends on the number of mesh points selected, and 2) the amount of time spent by the computer considerably increases with increasing this number. These conditions call for the following requirements as concerns the model: a) Dimensional requirements: the calculation will be all the more accurate as the network is more closely meshed. Since the number of mesh points is limited in practice, it is necessary to restrict the dimensions of the model. b) Geometrical requirements: so as to make things easier in working out the network, the model must be given a simple geometry. In particular, it will be convenient to have the cathode so constituted that the surfaces limiting the cathode and the surfaces within the cathodes separating the different materials consist of triorthogonal planes. 1.2) Schematization of the Cathodes. After the tech-

Jan 1, 1968

By H. K. Birnbaum

The effect of 1ow-temperature stabilization anneals on the structure of the 0 phase Au-Cd alloys and on the diffusionless transformations observed in these alloys was examined by X-yay diffraction techniques. A phase separation in the ß-phase region was proposed to account for the experimenta1 results. The effects of quenching from elevated temperatures on the transformation behavior of these alloys were shown to be consistent with the proposed mechanism. IT has been shown that the high-temperature ß phase (CsCl structure) of the Au-Cd alloy system transforms to a phase having an orthorhombic (D2) ß&apos; structurel1-3 for compositions near 47.5 at. pct Cd and a tetragonal (4/m, m, m) ß" structure* in the vicinity of 50.0 at. pct Cd. Both transformations are diffusionless, crystallographically reversible, and occur on cooling at about 60° and 30°C respectively. The temperature interval from the beginning to the end of the transformation is of the order of 5°C in each case. Although the transformations are normally athermal, some of them have been reported to occur isothermally.= wechsler6,7 has shown that the effects of quenching a 49.0 at. pct Cd alloy from elevated temperatures are consistent with the retention of a nonequilibrium number of lattice vacancies. Annealing of these quench effects results in a broadening of the X-ray reflections.8 After a suitable quench, the 47.5 at. pct Cd alloy transforms to a phase having not the p&apos; orthorhombic structure but another structure which has properties similar to that of the ß" tetragonal structure.5.9 This change in the type of transformation has also been obtained after long anneals in the ß-phase region at about 70oC10 The present investigation was primarily concerned with the structural changes accompanying the above transformation phenomena. The change in transformation product and accompanying physical changes during an anneal in the ß phase have been termed stabilization effects. Experimental Procedure —The results reported in this investigation were obtained with the use of a Norelco diffractometer fitted with a temperature-controlled cryostat. The specimen temperature was controlled to better than ± 0.l°C during the measurements. CrKa radiation monochromated electronically with the use of a scintillation counter and pulse height analyzer was utilized. Specimens containing 47.5 and 50.0 at. pct Cd were prepared by sintering filings obtained from homogenized ingots of the proper alloy composition. (Gold of 99.999 pct purity and cadmium of 99.98 pct purity were used). All heat treatments were carried out with the specimens capsulated in vacuum ( < 10 % mm Hg) or in a He-H gas mixture. The quenching technique used in these experiments was to drop the pyrex capsule which contained the specimen from the annealing furnace into water, the temperature of which was controlled. The pyrex capsule shattered on contacting the water resulting in a relatively rapid quench. After the heat treatment, the specimens were mounted in the diffractometer and were left undisturbed in the diffractometer specimen holder during each sequence of measurements. EXPERIMENTAL RESULTS A) Low-Temperature Annealing—The transformations which were considered "normal" for these alloys were those obtained athermally during furnace cooling at approximately 50°C per hr after an elevated temperature anneal. Under these experimental conditions, the specimens were observed to transform to phases having structures whose diffraction patterns could be indexed as the ß&apos; orthorhombic structure for the 47.5 at. pct Cd and as the 0" tetragonal structure for the 50.0 at. pct Cd alloys. The transformation temperatures on cooling were approximately 60" and 30°C, respectively. Under the "normal" conditions both transformations were observed to go to completion, i.e., the entire volume of the ß phase was transformed to the product phase. In some specimens an extremely weak ß 110 reflection was observed at 20°C indicating that a small amount of retained ß was present. The effect of low-temperature annealing on the nature of the diffusionless transformations was examined for the 47.5 and 50.0 at, pct Cd alloy. The specimens were annealed in evacuated capsules at temperatures in the vicinity of 600°C (as specified in Table I) for 24 hr and were then cooled to 100°C at a rate of 50°C per hr. The specimens were then removed from the capsules and mounted in the diffractometer without allowing the specimen temperature to drop below 80°C. Annealing at the low temperatures was accomplished in the diffractometer by means of the cryostat which was mounted around the specimen. During the low-temperature anneals the lattice parameter, integral breadth of the reflections, and ratios of the integrated intensities of the fundamental and super lattice reflections for the 0 cubic phase were periodically determined. After annealing for the required time, the specimens were slowly cooled in the diffractometer and the diffraction patterns were recorded as a function of temperature. The specimens were cooled until the phase transformations were completed, following which the specimens were heated and diffraction

Jan 1, 1960

By C. O. Burgess, W. D. Forgeng

The results of an investigation of the ternary system iron-chromium-silicon were reported in 1936 by the present authors.l Partly for the sake of theoretical interest, and partly because of the possible commercial importance of these alloys, the present investigation was undertaken to determine the effect of some of the commoner elements likely to occur, deliberately or otherwise, in such alloys if made on a commercial scale. The elements thus added were carbon, nickel or manganese. The alloys studied were, therefore, parts of quaternary systems. This investigation was concerned primarily with the effect of these additional elements on the alpha-iron phase and the boundary between this phase region and the alpha plus sigma two-phase region. The sigma phase is a ternary solid solution based upon the compound FeCr. The work was performed mainly by X-ray methods, but a number of microscopic examinations were also made and are reported. While isolated alloys in the composition ranges studied may have been discussed in metallurgical publications, no systematic investigation of any assistance to us was found. Of the earlier work, the investigations on the iron-chromium-carbon system and on the chromium carbides by Westgren and his coworkers2&apos;3 enabled us to identify the carbide phase. Several articles appeared after the present experimental work had been completed. Lucas and Wintrup4 determined the solubility of carbon in molten iron-chromium-silicon alloys. Tofaute and his coworkers5&apos;6 have made detailed studies of the iron-chromium-carbon system, which will be referred to later. Materials and Methods Materials.—The iron, chromium and silicon used were essentially the same as those used in the investigation of the ternary system.l The

Jan 1, 1938

By H. C. Brassfield, R. E. Fryxell, E. C. Duderstadt, E. A. Aitken, P. K. Conn

Permeation rates of hydrogen through are-cast tungsten were measured at temperatures from 1300" to 2600°C with hydrogen pressure differentials of 1 and 0.1 atm across isothermal membranes. Rates were nearly Proportional to square root of pressure, were inversely ProPortional to membrane thickness, and were temperature-dependent according to the equation: p = permeation coefficient in cu cm (stp)-mm per sq cm-min-atmlr2, R = gas constant in cal per mole-OK, T = absolute temperature in OK. Permeation rates of oxygen through tungsten were deternlined in the range 1965" to 2300°C and at calculated oxygen (02) pressures of 3.3 x 10-4 to 2.2 x at?n using sealed capsules containing Kmown quantities of tungsten oxide. Permeation coefficients obtained in this manner had a temperature dependency in the range of 40 to 45 kcal per mole of permeating species. Permeation coefficients for oxygen were higher than those for hydrogen in the temperature range studied. This is probably the result of oxygen solubility being much greater than hydrogen solubility at these temperatures at a gzven pressure. The purpose of this investigation was to determine experimentally the permeabilities of hydrogen and oxygen through polycrystalline tungsten at temperatures ranging from 1300° to 2600°C. Permeation rates of hydrogen through tungsten have been measured at temperatures up to 925°C,but no previous measurements have been reported for the temperature range covered in this investigation. Some diffusion measurements3&apos;&apos; and solubility measurements3 have been made for hydrogen at temperatures below 2200°C. No previous permeability studies of oxygen through tungsten are known to the authors; however, efforts have been made to determine diffusion rates5-&apos; and solubilities PERMEATION THEQRY Permeation has been defined by ortton" as the overall steady-state flow process from the gas phase on one side of a membrane or wall to the gas phase on the other side and includes the steps of adsorption, solution, diffusion, exsolution, and desorption; in a given temperature range, any of these processes may be rate-controlling. For diatomic gases, which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at a given temperature is directly proportional to the surface area of the membrane, the length of time of permeation, and the difference between the square roots of the pressures on each side of the membrane, and it is inversely proportional to the thickness of the membrane when diffusion-controlled, thus: q = total amount of gas permeating a membrane, p = temperature-de pendent permeation coefficient, A = area of membrane exposed, / = time, p i = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, d = thickness of membrane. When the surface reactions are not rate-controlling steps and the solution of the gas in the metal follows Henry&apos;s law, the permeation coefficient, P, is equal to the product of diffusivity and solubility. The permeation coefficient is also temperature-dependent according to the equation: Po = permeation constant, Q = activation energy, R = gas constant, T = absolute temperature. MATERIALS The tungsten materials used in this investigation were greater than 99.9 pct pure. The interstitial impurities ranged from < 1 to 50 pprn C, 7 to 35 ppm O, less than 15 pprn N, and undetectable quantities of hydrogen. Previous high-temperature studies of are-cast tungsten have shown that thermal treatment similar to that which the hydrogen permeation cells experienced reduces the carbon content from starting levels of 50 to 60 ppm to about 30 ppm. Metallic impurities were in the low (1 to 50) ppm range. The argon gas used in this investigation contained about 8 ppm N. None of the following gases were

Jan 1, 1968

By Harry A. Wahl

Precent fracture design procedures are bared on the total fracture area created. A method to distinguish beI,,.ecn total area and [he propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The difierences between effective fracture area and torn] area are demonstrared in example calculations. This work is hayed on experimentally determined transport efficiencier of solids in sand-liquid slurries. Newtonian and non-Ne~vtoninn systems are considered. INTRODUCTION Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected, they developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin4 hows that partial monolayers of sand have large flow capacities compared to thick* dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the deired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al.&apos; They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan&apos;gin&apos; using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltow studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However. the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections. EXPERIMENTAL RESULTS The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid sturries. A 10%-ft long transparent

Jan 1, 1966

By C. D. Stahl, S. M. Farouq Ali

This investigation attempts to describe and simulate the alcohol displacement process by means of a cell model, as employed in chemical engineering practice. The proposed model is more simple than previously proposed models. and utilizes parameters chosen on a theoretical basis. The model successfully reproduced the formation of the stabilized bank and the breakthrough of alcohol, the latter depending on one of the model parameters, which may be correlated with the length of the porous medium. Moreover, the effects of the phase behavior of the liquid system involved, as observed in experimental studies, were reproduced. Several variations of the basic model were devised and tested on a digital computer. These included the cases in which: (1) the actual value of fractional flow was used in cell-to-cell computations; (2) the number of cells was varied within the same run; and (3) incomplete rather than complete phase equilibrium was assumed within each cell. The proposed cell model clarifies the basic mechanism of the process. Detailed concentration profiles obtained for each cell, for instance, showed the mechanism of bank formation in relation to the phase behavior characteristics. The results obtained indicated a varying degree of phase equilibrium concommitant with changes in the velocities of the phases in an actual alcohol displacement. This condition was approximated by changing the number of cells during the simulation. Interesting information was obtained on the influence of path length on the efficiency of alcohol displacement, which has been the subject of some controversy. Certain limitations preclude the use of the proposed model as a substitute for experimental studies. The results obtained were, nevertheless, of value in interpreting the experimental results. INTRODUCTION During recent years considerable effort has been directed toward an understanding of alcohol displacement, the process whereby oil and water are recovered from a porous medium by the continuous injection of a solvent. The complex nature of the physical process involved has so far defied a complete mathematical treatment. Other methods of approach, amounting to an overall material balance, have been proposed, yielding useful information on certain aspects of the process.1-3 Taber et al, in particular, defined the displacement mechanism in terms of the phase behavior of the alcohol-oil-brine system invoIved.2 Wachmann reported a mathematical treatment of alcohol displacement subject to certain simplifying assumptions? Donohue proposed the use of a "cell model" for simulating alcohol disPlacement.5 The nature of the assumptions involved limited the utility of the model. The present work attempts to examine the variables involved in the simulation of alcohol displacement and discusses several possible versions of the basic cell model. Under certain conditions the model results are similar to the experimental results. In particular, the spontaneous formation of of the stabilized bank and the effects of the system phase behavior were successfully reproduced. PREVIOUS WORK ON CELL MODELS Cell models and the theoretical plate concept are often used in solving chemical engineering problems in which an explicit mathematical solution may be difficult or impossible to obtain. Examples of such applications occur in distillation, gas-liquid chroma tography,6 reactor technology, absorption, etc. In petroleum engineering, such a model was used by Attra7 to describe non-equilibrium gas drive, and by Higgins and Leigh ton8 to calculate sweep efficiency in water flooding. Aris and Amundsen pointed out the equivalence between the diffusion model and perfectly mixed cells connected in series.9 Deans proposed a three-parameter cell model to simulate two-component

Jan 1, 1966

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute&apos;s influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger&apos;s argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.&apos; Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute&apos;s influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute&apos;s influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968