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By Charles M. Packer, Oleg D. Sherby, Roy H. Johnson

Originally round tensile specimens of a eutectic Zn-A1 alloy develop elliptical cross sections during superplastic deformation. This observation, coupled with a detailed study of the microstructure and preferred orieniation, suggests that crystallographic slip and continuous grain boundary migration or re-crystallization are important processes during super-plastic deformation. In spite of the extensive activity in superplasticity1-15 and the numerous explanations proposed, no single model has had universal acceptance. It has been established, however, that the general requirements for superplastic extension of two-phase alloys include an extremely fine, stabilized grain size of the order of a few microns, a temperature about equal to or greater than one-half the melting point, a critical range of strain rate, and a similarity in the mechanical strength of the major phases. The proposed models can perhaps best be characterized in terms of the important phenomena associated with them. These phenomena include: phase instability,1 diffusional creep by volume diffusion3 or grain boundary diffusion4,5 slip and continuous grain boundary migration or recrystalliza-tion,= grain boundary Sliding,7-9,13,14 and dislocation glide.'5 In this paper, experimental observations will be reported which support a model involving slip and continuous grain boundary migration or recrystalliza-tion. Specifically, a correlation will be made between this model and the development of elliptical cross sections as originally round specimens are superplas-tically deformed. For the most part, superplasticity studies have been conducted with eutectic or eutectoid alloys. Probably the most thoroughly studied material has been the monotectoid Zn-A1 alloy.1,2,6,12,13,15 No attention to the eutectic Zn-A1 alloy has previously been reported, and the results discussed in this paper represent part of a general study of the superplastic properties of this alloy. MATERIALS The alloys used in this investigation were prepared by melting appropriate quantities of 99.99+ pct A1 and 99.999 pct Zn in air, mixing, and pouring into a water- cooled stainless-steel mold. Wet-chemical analysis was conducted with each heat of alloy prepared, using the procedure of Fish and smith.16 The composition of the eutectic alloy was 95.1 wt pct Zn. Ingots about 2 in. thick were rolled to 0.4-in. plate at about 300°C with a reduction of 5 to 10 pct per pass. Specimens were machined from the plate with the tensile axis parallel to the rolling direction. The specimens were round, with 0.150-in.-diam, 1.25-in.-long gage length, and 0.25-in.-diam threaded grip sections. EXPERIMENTAL PROCEDURE Specimens were mounted inside a uniform-temperature quartz tube which was surrounded by a double elliptical radiant furnace with a 12-in.-long uniform-temperature hot zone and a low thermal capacity. The tube extended through the top and bottom of the furnace and permitted rapid quenching of the loaded specimens when quickly filled with cold water at the conclusion of the test. The quench precluded any effects on specimen microstructure from a normal, slow cool. Constant stress was applied to test specimens by suspending a load on a constant stress cam of the type described by Hopkin.17 The design of this cam permitted application of a constant stress for elongations up to 200 pct. For greater elongation, approximately constant stress conditions were maintained by systematically reducing the load manually. RESULTS As part of an investigation of the superplastic properties of the eutectic Zn-A1 alloy, evidence was obtained for the development of elliptically shaped cross sections as originally round specimens were extended. For example, after an elongation of about 100 pct, a round specimen with an initial diameter of 0.150 in. became elliptical with major and minor axis of 0.128 and 0.88 in., respectively. Photographs are presented to illustrate the ellipticity developed during superplastic deformation, Fig. 1. The specimen shown was deformed at a stress of 500 psi, at a temperature of 285°C, and a strain rate of 2.28 x 10-2 min-1. The strain-rate sensitivity exponent* was measured at *The strain-rate sensitivity exponent, m, is defined as d In o/d In c where o is the steady-state flow stress and E is the strain rate. this temperature and in the strain rate range 10"3 to 10-1 min-1 was found to be about 0.5. This value is typical of those observed with superplastic materials. The material studied exhibited negligible strain hardening during superplastic deformation, the creep rate remaining constant under constant stress and temper-

Jan 1, 1969

By R. I. Garrod, R. A. Coyle

The shapes and positions of X-ray reflections from specimens of copper, steel, and aluminum alloy haue been examined in the elastic and plastic ranges both while the specimen was under stress and in the unloaded condition. For the aluminum alloy the shape was unaltered by the application of stress either within the elastic limit or in the plastic range provided that no additional plastic strain was induced. In copper the broadening accompanying plastic deformation was very slightly reduced when the specimen was unloaded. A similay but more marked elastic component of broadening was also found for steel, but in this case below the yield stress. Line profiles corrected for instrumental and particle-size broadening indicate very large internal stresses in local regions of the plastically deformed metals. The results are discussed in terms of a recent suggestion that the heterogeneous dislocation distribution between the cells and their boundary walls plays a major role in the peak shifts and broadening of the X-ray reflections. STUDIES of the X-ray line profiles from strained polycrystalline aggregates concentrate usually on one or the other of two main parameters: a) the displacement of the peak of the intensity contour from its position for a strain-free aggregate, or b) the shape of the profile. From peak shifts data can be obtained either on the relation in both the elastic and plastic ranges between applied external stress and average lattice strains in a given (hkl) direction, or, alternatively, on the residual lattice strains which are present after a plastically deformed specimen is unloaded.' On the other hand, the shapes of the broadened profiles from cold-worked metals can be analyzed to separate the broadening produced by small particle size and by heterogeneous lattice strains.' In this paper the terms "size broadening" and "strain broadening'' are used in the general sense adopted by warren.' In the past, apart from two early qualitative observation, it has been customary to examine only the movements of the peaks of the profiles while the specimen is actually under load, since the line broadening induced by plastic strain remains after removal of the external stress. Consideration of the implications of existing data of this type suggests, however, that fruitful additional information on a number of fundamental aspects might be gained by careful examination of whether the X-ray line profile is in fact different in the loaded and unloaded states of the specimen. By taking advantage of the sensitivity and convenience of modern diffractometer techniques it is possible to explore with relative ease the magnitude and importance of any elastic effects which may be superimposed upon the well-known permanent changes in profile. The main aim of the work to be described was thus to investigate this point for typical metals and alloys. For this purpose annealed specimens were extended first elastically and then plastically and the positions and shapes of X-ray reflections were recorded. Initially it was anticipated that prime interest would center on observations within the plastic range; it has been found, however, that small changes in profile sometimes occur both before and after the nominal elastic limit of the material is reached. It is shown that the results obtained have important implications in relation to the structural changes and processes associated with deformation. I) EXPERIMENTAL To enable the diffraction lines to be recorded while the specimen was under uniaxial-tensile stress, a small hydraulic testing machine was designed and constructed for direct attachment to the goniometer of a Philips diffractometer. The specimens, which were machined from 1/2-in.-diam rod and had a central rectangular section 3/8 by 1/16 in. over a gage length of 1 in., were held in the machine by split collets mounted in grooves in the cylindrical ends of each specimen. No special precautions were taken to ensure precise axiality of loading. Constant oil pressure was maintained by a lever and weights system and transmitted to the loading rig by flexible pipe. The actual load on the specimen was measured by a load cell in the machine to an accuracy of * 1 pct. To enable smooth X-ray profiles to be obtained the specimen and machine were oscillated continuously during recording through *7-1/2 deg about the normal half-angle position of the goniometer. The three materials chosen for the investigations were high-purity copper as representative of a ductile fcc metal, a low-carbon steel for a bcc metal, and an aluminum alloy as a material in which the proof stress/ultimate strength ratio is high. Details are as follows. a) Copper. 99.999 pct purity. After machining the specimen surface was polished mechanically and

Jan 1, 1964

By P. A. Witherspoon, S. P. Neuman

Evaluating the permeability of a caprock overlying a potential gas storage reservoir is a very critical problem. Pumping water from the reservoir can be used as an evaluation tool in analyzing this problem. Fluid level changes that occur in the aquifer us well as in the caprock can be measured with appropriately placed wells. If the leakage of water from the caprock into the aquifer is considerable, the effects will be apparent in the aquifer. If the leakage is slight, however, it will not be possible to detect it with certainty from observations in the aquifer alone. Fluid level measurements in the caprock must be relied upon. and improved methods of analyzing such effects have been developed which are based on a theoretical analysis of fluid flow through a caprock of infinite thickness. An example applying these methods to field data is discussed. INTRODUCTION One of the most critical problems in evaluating an aquifer gas storage project is determining the tightness of the caprock overlying the formation to be used as the storage reservoir. A formation that has previously held oil or gas obviously has a suitable caprock, but an aquifer that contains only water gives no such assurance. A number of aquifer projects in the United States have been troubled by gas leaking out of the intended storage zone, and the ensuing difficulties have led to the development of new evaluation methods. One of these new methods is pump testing wherein water is removed from the aquifer at some controlled rate prior to injection of gas. This fluid withdrawal causes a pressure drop to move out through the aquifer for considerable distances in a matter of days or weeks. Depending on the properties of the caprock, a pressure transient can also pass upward (as well as downward) through the caprock layers adjacent to the aquifer. Thus, if the operator has placed observation wells at appropriate distances from the pumping well, the rapidity with which the pressure transients reach different points in the system can be used to investigate the fluid transport properties of both the aquifer and its caprock. The usefulness of pump testing has been recognized by groundwater hydrologists for many years as a means of determining the potential yield and properties of aquifers used in water supply They have introduced the term "leaky aquifer" for a system in which an aquifer is overlain (or underlain) by semipermeable caprock layers. The ease with which water leaks into the aquifer during pumping can, of course, be very beneficial in bringing additional water to the pumped well. Hydrologists have therefore devoted considerable attention to this prob-lem. From the gas storage standpoint, however, the tighter the caprock layers that overlie the intended storage reservoir, the better are the conditions for minimizing or eliminating any vertical migration of gas. Thus, after a suitable geologic structure has been found, the emphasis in aquifer storage projects is in determining that the caprock is tight. Attention has recently been focused on the use of pump testing as one approach to solving this problem.23,24 This paper presents a further development on evaluating the permeability of a slightly leaky caprock when the caprock is of infinite thickness. From the practical standpoint, this means that the caprock layers are thick enough that pressure transients do not reach the outer boundaries of the system during the pumping test. In a subsequent paper, an analysis of the case where the caprock is of finite thickness will be presented. PREVIOUS WORK ON LEAKY AQUIFERS Jacob" developed a partial differential equation describing the flow of water in an aquifer of permeability k that is overlain by a leaky caprock of permeability k'. Fig. 1 shows a schematic cross-section of the system under consideration. One of his principle assumptions was that if k > > k', the direction of flow is essentially vertical in the caprock and horizontal in the aquifer. Neuman19 confirmed the validity of Jacob's assumption using a mathematical model. Another assumption was that a permeable source layer overlies the caprock (Fig. 1) and is able to maintain a constant hydraulic head at the upper boundary of the caprock. By neglecting the effects of compressibility within the caprock, Jacob1* developed a solution for a bounded circular aquifer. Later, Hantush and Jacobx5 used the same assumptions to solve the case of an infinite radial aquifer that is pumped at a constant rate. Their solution may be expressed in di-mensionless parameters by

By G. V. Jere, C. C. Patel

Chlorination of the various constituents of ilmenite by different chlorinating agents in presence of various reducing agents, have been considered on the basis of the standard free energy and standard enthalpy changes as a function of temperature. The standard free energy change considerations show that it is beneficial to chlorinate ilmenite by chlorine in the presence of carbon and also that iron constituent of ilmenite can be preferentially chlorinated by clzlorine, titanium tetrachloride or their mixture. These findilzgs have been corroborated from the published work. METALLURGICAL processes involving the use of titanium tetrachloride have gained in importance because of the use of the latter in the manufacture of titanium metal. Since ilmenite is more abundant in nature than any other titanium mineral, the future of the metallurgical processes depends on the utilization of ilmenite for the production of titanium tetrachloride. In these laboratories, investigations have been carried out on the chlorination of ilmenite under a variety of conditions.1'2 During these studies, it was noticed that 1) preferential chlorination of iron was effected at low temperatures (400° to 600°C) and at low carbon content (6 to 7 pct), 2) carbonyl chloride retarded the chlorination of iron oxides and titania perceptibly, while 3) carbon-tetrachloride, compounds of sulphur and some other catalysts favored the chlorination. Moles3 has found that oxides of iron are chlorinated in preference to titania at high temperatures, while wilcox4 has claimed the preferential chlorination of titania between 1200" and 1500°C. It has been shown in this paper that preferential chlorination of titania claimed by Wilcox is not likely to occur. Daubenspeck and coworkers5,6 have claimed the preferential chlorination of iron by chlorine or by a mixture of titanium tetrachloride and chlorine between 700° and 1050°C in the absence of carbon. Even when plain titanium tetrachloride is employed as the chlorinating agent, pascaud7 noticed the preferential chlorination of iron and other oxides. The purpose of this paper is to explain from thermodynamical considerations, the various chlorination reactions studied so far. ILMENITE CONSTITUENTS AND THEIR CHLORINATION PRODUCTS Although the general composition of the ilmenite mineral is represented as FeTiO,, most of the ilmenites found in nature have variable quantities of TiO2 (44.6 to 64 pct), FeO (4.7 to 36 pct) and Fe2O3 (6.9 to 28 pct).8 The higher content of ferric iron in ilmenites was attributed by Millerg to the presence of arizonite (Fe2O3.3TiO2). But the X-ray studies by Overholt, Vaw, and odd" have shown that arizonite is a mixture of haematite, ilmenite, anatase, and rutile. Except for the anatase, similar views have been advanced by Lynd, Sigurdson, North, and Anderson8 from magnetic, X-ray, and optical and electron microscope studies. The ilmenite ores can, therefore, be assumed to consist of mineral aggregates of ilmenite, rutile and haematite. From the free energy of formation of ilmenite (FeTiO3), it has been shown by Kelley, Todd, and King11 that ilmenite is stable even up to its melting point (1367°C) and would not undergo decomposition into its constituent oxides. Schomate, Naylor, and Boericke12 have found that in the presence of a reducing agent the iron constituent of ilmenite is selectively reduced. The reaction of chlorine with ilmenite in presence of a reducing agent can, therefore, be synonymous with that of the reaction of chlorine with the constituents of ilmenite, viz., TiO2, FeO, and Fe2O3. Most of the reaction products of chlorination of ilmenite in the presence of reducing agents will be in equilibrium with their dissociation products, depending on the temperature. The titanium tetrachloride is, however, quite stable up to 1500°C due to its covalent nature. The equilibrium for the ferric chloride system has been investigated by Kangro and Bernstorff, 13, schafer14 and Kangro and petersen,15 and the results are summarized in Fig. 1, curves a, b, and c respectively. From these results, it is clear that the ferric chloride disociates as follows: 324° to 700°C FeaCl6(g) ?2FeCl2(c) + Cl2(g) [1] 324°to 900°C Fe2Cl6(g) =2 Fe Cl2 Reaction [I] (curve a) occurs in the forward direction to about 6 pct at 400°C but falls off very rapidly with increase in temperature and beyond 600°C, it is practically negligible, perhaps due to the formation of the stable monomer, FeC13(g). As the temperature is further increased, the amount of FeCl,(g) in-

Jan 1, 1961

By W. N. Lacey, B. H. Sage, J. S. Billheimer

A restricted ternary system made up of n-pentane, tetralin, and a purified bitumen was investigated at 70, 160, and 220 °F. Most of the experimental observations were at atmospheric pressure or at 200 psi." However, some experimental measurements were carried out at a pressure of approximately 8000 psi. It was found that the purified bitumen was precipitated from its solution or dispersion in tetralin by the addition of n-pentane and that the separation occurred at lower weight fractions of n-pentane at the lower temperatures. The bitumen-tetralin solutions show some colloidal characteristics at temperatures below 160 °F when near compositions at which the bitumen separates as a solid phase. At states remote from the phase boundaries and at temperatures above 160 °F these characteristics become less evident. Under these latter circumstances the mixtures tend to follow the behavior of true solutions, particularly in regard to the approach to heterogeneous equilibrium. An increase in pressure appears to increase the solubility of bitumen in tet-ralin-n-pentane solutions. This effect is more pronounced at temperatures above 160 °F than at lower temperatures. INTRODUCTION Asphaltic phases of plastic or solid nature have appeared in numerous instances during the recovery of petroleum from underground reservoirs. Such depositions occurring underground appear to have caused adverse production histories for particular wells or zones. Because of this field experience, it is desirable to understand the factors which influence the formation or separation of the asphaltic phases from petroleum. The problem is unusually complex because the number of true components involved is very large and the details of the phase behavior encountered are difficult to ascertain experimentally. The literature relating to asphalts, asphaltines, and bitumen is voluminous and widespread.' Only those references which are directly pertinent to the work at hand are cited. The separation of an asphaltic phase, hereinafter called bitumen? from naturally occurring hydrocarbon mixtures has been the subject of several investigations.2'3'4'5'6 It has been found that as many as four phases4 may be produced from a crude oil by the solution of a natural gas and propane at a pressure of 1500 psi and a temperature of 70 °F. The separation of bitumen from such naturally occurring mixtures results in at least one liquid phase which is substantially free of high molecular weight components.³ The influence of the solution of lighter hydrocarbons on the separation of bitumen from a Santa Fe Springs crude oil has been investigated. The results indicate that in the case of the methane-crude oil system, the quantity of plastic or solid phase separated reaches a maximum between 0.14 and 0.19 weight fraction methane and then decreases until negligible at higher weight fractions of methane. Similiar behavior was encountered in the case of mixtures of ethane and crude oil. The decrease in the quantity of the solid phase with an increase in the weight fraction of the lighter component appears to result from the formation of an additional liquid phase6 in which the bitumen is relatively soluble. The formation of this additional phase probably occurs at a weight fraction of methane close to that at which the quantity of separated solid reaches a maximum. A comparison of the deposition of bitumen in the field with the separation of asphalts from lubrication oil has been made' and apparently the phenomena are similar. The phase behavior of bitumen also appears to be comparable to that of coal tar."' The chemical and physical characteristics of asphalts and bitumen have been the subject of extended investigations which have been reviewed in some detail by Katz.¹º The conclusion was reached that the dispersion of bitumen in a number of organic liquids was not entirely colloidal since it was impossible to isolate individual dispersed particles even with the electron microscope. However, the evidence appeared to indicate that at states close to phase boundaries the extent of the dispersion of the phases influenced the equilibrium to a greater extent than is encountered in many simpler systems. From earlier study of field samples it became apparent that the phase behavior of bitumen-hydrocarbon systems was unusually complex. It was difficult to characterize in detail the phase behavior involved in naturally occurring hydrocarbon systems, even after a relatively extended investigation. For this reason, the study of a somewhat simpler system which still behaved in a similar manner became desirable. Three major constituents were necessary as-follows: a bituminous solid, a liquid constituent which was a reasonably good solvent, and a constituent in which bitumen was largely insoluble. A sam-

Jan 1, 1949

By J. B. Campbell, V. V. Valleroy, B. T. Willman, L. W. Powers

A steam drive of heavy oil was field tested in a shallow, low oil-saturation formation near Deerfield, Mo. The pilot was conducted in the Warner formation, a sandstone containing an 18' API oil having 1,000-cp viscosity at the 60F origind reservoir temperature. The formation war at a depth of 160 ft. Steam was injected into nine input wells arranged in an array of inverted five-spot patterns. In the completely confined center pattern, 14 temperature observation wells were installed to obtain thermal data and observe test progress. Late in the test, slugs of ammonia were injected to trace the flow paths of injected fluids. From the test area about 7,000 bbl of oil were produced. Data were obtained on areal and vertical temperature distribution, steam front advance, reservoir fluid movement and terminal saturations. This field test of a steam drive (I) demonstrated the feasibility of the method, (2) confirmed that the low residual oil saturations observed in the laboratory are obtained in the steam-swept region in the field and (3) provided recovery and conformance data for one set of field conditions. INTRODUCTION The Deerfield steam drive pilot test was conducted in a shallow sandstone containing 1,000-cp oil. The venture was undertaken cooperatively by the research and production departments of Carter Oil Co., which organizations have since been consolidated into Esso Production Research Co. and Humble Oil & Refining Co.. respectively. The production department was interested in steam injection at Deerfield because it appeared to be the most promising method of commercially producing this heavy oil deposit. The research department was interested in applying the new recovery method and in evaluating its performance in the field. At the time the test was begun, the initial oil saturation was not well known. Subsequent air coring and early pilot results confirmed that there was too little oil in place for profitable commercial exploitation by steam. Pilot termination at that time, however, would have been premature for evaluating field performance of the process, and the tert was continued to obtain additional data on steam injection as a recovery method. The test was located in Vernon County, Mo., about 10 miles north of the town of Deerfield and only a few miles from the Kansas border. The pilot site was selected as typical of the area. The location represented neither the highest nor the lowest oil saturation region in the acreage under lease in 1954. The steam drive was conducted in the Warner sandstone of Lower Pennsylvanian age. At the test site the top of the Warner occurs at about 160 ft subsurface and the formation is a fine- to medium-grained micaceous sandstone that dips gently to the northwest at the rate of 12 to 15 ft/ mile. A cross-section and permeability profile of the test location are shown in Fig. 1. At the pilot location the average total thickness of the Warner formation is about 43 ft, but the effective thickness for steam drive is 26 ft. Two distinct types of hydrocarbon saturation are apparent. The lower portion of the total sand, averaging about 17 ft thick, contains a very heavy asphaltic material that will not flow under the influence of a steam drive. This bottom interval, referred to as a dead oil residue, was not considered as part of the net sand undergoing steam exploitation. The initial formation and fluid properties of the upper 26 ft in the test area are summarized in Table 1, and variation of oil viscosity with temperature is shown in Fig. 2. Imbibition tests on preserved core samples taken at the end of the pilot test showed that the Warner sandstone was then neutral or slightly water-wet. Initially, the reservoir may have been strongly water-wet as indicated by low relative permeability to water during both water injection testing and early steam injection. PRIOR HISTORY Initial production tests of wells at the pilot site produced water with only a faint show of oil. No gas was produced except at Well 7-W in the pilot area and at another well about 1/3 mile northeast of the pilot. Prior to the start of the steam drive, a two-well water injection test and a two-well air injection test were conducted. No oil was produced by either. Water was pumped into Well I-W in the northeast corner of the pilot area with simultaneous production from Well 1 (Fig. 3). The air-injection tat was run at input Well 9-W and its offset, Well 2, in the southwest corner. Air and water injectivities were about the same when corrected for viscosity and pressure differences.

By G. R. Pickett

Examples are presented which show that the velocity~ amplitude, attenuation and apparent frequency of several acoustic waves can be recorded in the borehole. Examination of such recordings, termed "character" logs, indicates that the wave types observed include a refracted compressional wave and a wave which travels with formation shear velocity. Laboratory data are used to show that compressional and shear wave velocities are dependent on porosity, effective stress and lithology; but that the change in reciprocal velocity per unit change in porosity is larger for shear waves than for compressional waves. We, therefore, conclude that. the accuracy of porosity determinations can sometimes be improved by use of shear wave velocities, provided that the shear wave amplitudes are large enough to delineate the shear arrival from the preceding compressional arrival on the character log. Borehole data are presented which show that the difference between shear wave and compressional wave reciprocal velocities can be used to predict porosities. This is a refinement which may allow the prediction of porosities from single-receiver acoustic logs without introduction of errors from borehole fluid traveltimes. Laboratory and field data are presented to show that the relationship between compressional and shear wave velocities can be used to indicate lithology. An example is presented to show that fractures usually cause a greater reduction in borehole shear wave amplitudes than in compressional wave amplitudes, an effect which may offer a more reliable means of detecting fractures. The complexity of the borehole acoustic wave train can rake presently available cement bond logs highly sensitive to the gate and bias settings used. The character log offers a means to circumvent possible misinterpretations by recording all amplitudes, from which the interpreter can select the appropriate data for evaluating the cement bond. Character logs may also be used as a quality control for open-hole transit-time logs when existence of small compressional wave amplitudes interferes with the proper functioning of bias-controlled timing devices. Evaluation of the potential uses of character log data is not complete; but a character log presented in a form convenient for routine use would be a desirable addition to currently available logs. To summarize, possible applications for such a log in formation evaluation include the following (1) quality control of transit-time logs, (2) refinement of porosity predictions, (3) determination of lithology, (4) improvement of fracture detection and (5) improvement of cement bond evaluation. Suggestions are made regarding the requirements for a suficient but practical character log for routine use. INTRODUCTION Acoustic logs have become a widely used porosity tool in formation evaluation. In addition, there is a growing application of acoustic logs in cement bond evaluation and fracture detection. These applications have mainly involved the use of logs of first-arrival transit times and amplitudes and have not included detailed studies of the complete signal. The purpose of this paper is to show that significant benefits in formation evaluation can be gained by a more complete use of the acoustic wave train generated in the borehole by an acoustic logging tool. We hope that this discussion will also stimulate further development of logs suitable for routine use so that these benefits may be realized. Examples of acoustic wave train logs, termed "character" logs, are presented to show that several identifiable acoustic waves are present in the borehole. The measurable characteristics of these acoustic waves and some of their relations to formation properties of interest are also discussed. The more obvious potential uses of character logs are listed, and some suggestions are made regarding the requirements for a sufficient but practical character log for routine use. CHARACTER LOGS Some 10 years ago, Vogel' and Summers and Broding' noted that the signals received uphole from an acoustic logging tool located in a borehole had a number of interesting characteristics. The logging tool consisted of two or more pressure transducers spaced on an acoustically insulated body (Fig. la). One of the pressure transducers was used as a transmitter to generate pressure waves in the borehole fluid. The other transducer served as a receiver to detect any pressure waves reaching it in the borehole. The receiver then converted these pressure waves to electrical signals which were transmitted to the surface and displayed on an oscilloscope as a record of time vs receiver-signal amplitude. Fig. lb is a schematic representation of a typical record. The interesting characteristics seen in the earlier' and subsequent experiments were (1)

By J. M. Eldridge, P. Balk

Phosphosilicate glass films were formed, by reacting gaseous P2O5 with SiO2, over a large range of temperature (800° to 1200°C) and gas phase composition (nearly two orders of magnitude of effective P2Ospressure). The film compositions generally corresponded with the liquidus curve, delineating the maximum solubility of the tridymite Phase of SiO 2 in phosphosilicate liquid solution at the temperature of film formation. It is shown that the P2O5 concentration of the phosphosilicate liquid film tends to decrease by reaction with the underlying SiO 2 layer until the liquidus curve is reached. The validity of the thermodynamic argument used in this explanation is supported by the results of a determination of the composition of borosili-cute films, prepared by reacting gaseous B2O3 with SiO2 at different temperatures. The kinetics of phosphosilicate film formation were described by a model predicated on a steady-state diffusion of P2O5 through the film. UNDERSTANDING of the processes leading to formation of phosphosilicate and borosilicate glasses is of great importance for producing passivating layers on FET devices. Passivating films with optimum characteristics are preferably formed in a separate step, independent of the doping of the semiconductor.' The results of an investigation carried out to gain improved insight into the mechanism of glass formation are presented in this paper. It would be expected that application of the known Pz05-Si02 and B 2 O 3-SiO2 phase diagrams should be useful in extending understanding of the glass-forming processes. However, the question of the propriety of treating thermally grown SiO2 in these binary oxide systems by the methods of equilibrium thermodynamics must be considered when this application is attempted. Although Sah et a1.' and Allen et al. 3 investigated the kinetics of formation of phosphosilicate glass (PSG), they failed to adequately relate their diffusion models to the occurrence of experimentally observed phases in the PSG/SiO 2/Si system. Horuichi and yamaguchi4 investigated the diffusion of boron through an oxide layer and described their results in terms of a model similar to that of Sah and coworkers. More recently, Kooi 5 and Snow and Deal6 reported the compositions of PSG films formed by depositing P2 O 5 onto SiO2. These compositions apparently coincide with those at the liquidus curve delineating the maximum solubility of crystalline SiO2 in phosphosilicate liquid solutions. These authors did not discuss the thermodynamic implications of their results on the structure of thermally grown SiO2 films. The structure of thermally grown Sio2 films and that of vitreous silica are generally thought to be quite similar. Since the solubility of a substance depends on its structure, it is relevant that the solubility of vitreous silica in water7 is highly reproducible, like the solubility of thermally grown SiOz in phosphosilicate liquid. Furthermore, the vitreous silica-water system appears to be in true thermodynamic equilibrium (viz., the same solubility value can be approached from both supersaturated and under-saturated solutions). Sosman7 suggested that a type of two-dimensional lattice may form at the silica/solution interface, resulting in the observed solubility behavior that is characteristic of a crystalline solid. An alternative explanation may be that vitreous silica has a microcrystalline grain structure. Other investigators have suggested that vitreous silica has essentially the structure of B cristobalite,' or is composed of microcrystals of p tridymite or cristobalite, or a mixture of both. Presumably the grain size would be sufficiently large to minimize any appreciable contribution of the grain boundaries to the solubility of the crystalline matrix. The present investigation was carried out to clarify the significance of the boundaries in the Pa,-SiO, and B2O3-SiO2 Systems in determining PSG and BSG (borosilicate) film compositions. Furthermore, the kinetic data for PSG film formation were extended, using a wider range of formation parameters than were previously reported. One model describing the kinetics of film formation will be presented that is compatible with the thermodynamics of the Pa5-Si02 system. EXPERIMENTAL PROCEDURE Glass Film Preparation. SiO2 films (1000 to 8000A thick) were obtained by oxidation of silicon substrates in dry O2 at 1100°C. PSG and BSG films were prepared by exposing these layers to gaseous oxides obtained by reacting high-purity POC13 and BBr3, respectively, with O2. A double-columned saturator was used to ensure complete saturation of the N 2 carrier

Jan 1, 1969

By J. E. Powell, F. H. Spedding

WHILE rare earths are reported to be widely distributed in nature and are not really rare," in practice, there are only a few minerals which are sufficiently rich in rare earths to serve as practical sources. Perhaps the best known of these is monazite which is a phosphate mineral containing rare earths and thorium. This mineral occurs as a dense brown sand in gravel beds and is particularly rich in the light rare earths of the cerium subgroup. This mineral is processed commercially for its thorium, cerium, and lanthanum content, and, consequently, furnishes rich concentrates from which neodymium, praseodymium, samarium, europium, and gadolinium may be obtained. Unfortunately, monazite is rather lean in rare earths heavier than gadolinium. A second mineral which is rich in the light rare earths is bastnasite, a fluoro-carbonate. Extensive deposits of this ore have been discovered in the western United States and have received considerable newspaper publicity in recent years. While bastnasite is very rich with respect to cerium, lanthanum, and neodymium, it contains even less heavy rare earths than does monazite. One of the better sources of heavy rare earths of the yttrium subgroup is gadolinite, a black silicate rock from which the rare-earth content can be extracted readily by acid leaching. It is obtained chiefly from Norway at the present time, although there are known deposits in the United States. Other sources of heavy rare earths include fergu-sonite, euxenite, and samarskite which are refractory tantalo-columbate ores. These minerals require caustic fusion or reduction to carbides with carbon before the rare-earth content can be extracted. All of the minerals which are rich in the heavy rare earths contain yttrium as a major constituent. After the rare earths have been extracted as a group from an ore by chemical means, it is generally convenient to precipitate them from acid media with oxalic acid in order to eliminate certain non-rare-earth impurities such as iron, beryllium, etc., which are usually present. The oxalate can then be readily ignited to R2O3. The oxide can be dissolved in acid and is the starting point for subsequent separation into the pure components. Perhaps the principal reason why the rare earths have not been studied as extensively as other elements of the periodic table, whose natural abundances are comparable, is that they are extremely difficult to separate from each other by the usual chemical means. Prior to 1945, the separation of one trivalent rare earth from another was a laborious process. All separations were based on repeated fractionation processes, i.e., fractional precipitation, fractional decomposition, fractional crystallization, etc. These processes were repeated from a few hundred to many thousands of times in order to obtain individual rare-earth salts of reasonable purity. Of course, mention should be made that, in the few cases where a rare earth could be oxidized or reduced to a valence state other than three, more conventional chemical means could be utilized to separate the oxidized or reduced ion from the other normally trivalent rare earths. The ionic states which deserve special mention are CeIV, SmII, Eu11, and Yb11. When it is possible to remove an element of the series efficiently, due to an optional valence state, its immediate neighbors also become easier to isolate. For example, binary mixtures of lanthanum and cerium, and praseodymium and cerium can be obtained by a relatively small number of fractional operations. The tetravalent state of cerium then allows the complete resolution of the binary mixtures by ordinary chemical means. Although the tetravalent state of cerium has been known for a long time, the divalent states of samarium, europium, and ytterbium were not used extensively in separations prior to 1930 because they are relatively unstable in aqueous media.'-" No attempt will be made to give a comprehensive review of the extensive literature dealing with the separation of rare earths. Rather, this paper will be confined to a review of those methods which have been developed at Iowa State College during recent years, and which have proved extraordinarily successful for the isolation of highly pure rare earths in quantity. It was obvious that, if pure rare earths were to become generally available, methods would have to be developed wherein the thousands of fractional operations made necessary by the similarity of rare-earth properties could be performed automatically. The development of chromatographic techniques and ion-exchange resins appeared to offer a mechanism by which this objective could be accomplished. A number of early attempts were made to separate rare earths by these means; for example, Russell and Pearce12 passed a mixture of rare earths through a cation-exchange column and reported

Jan 1, 1955

By R. M. Hudson, P. E. Perry

Weight-gain data obtained by nitriding low-carbon sheet steel in an amrnonia CNH,) atmosphere indicated that the process obeyed a parabolic rate law. The calculated actization energy for nitriding in the range 964" to 1268°F agreed reasonably well with published data. At 1358"F, rate data indicated that the activation energy decreased. Weight-gain data obtained by uszng mixtures of NH3 -Nz at 1268°F containzng jrom 10 to 100 zol pct NH3 also obeyed a parabolic rate law. The rate of 'nitriding increased with an increase in the NH3 content of the gas Mixture. It is well-known that steel heated in gas mixtures containing ammonia (NH3) takes up much larger quantities of nitrogen than steel heated in nitrogen, both gases having a total pressure of 1 atm;' this phenomenon can presumably be attributed to the catalytic decomposition of NH3 on the steel surface to furnish nascent (monatomic) nitrogen. This process was studied bv Brunauer. Jefferson, Emmett, and Hend-ricks at furnace temperatures of 752" and 831°F2 using mixtures of NH3 in Hz. Englehardt and wagner3 reported that, at a furnace temperature of 914°F and under their experimental conditions, both nitriding and denitriding were controlled by the rate of gas-metal reactions at a steel surface rather than by the rate of diffusion of nitrogen in iron. The present study was undertaken to obtain information on the kinetics of nitriding low-carbon steel strip at higher temperatures so that practical rates for short-time strip-annealing treatments could be estimated. Variables studied included time: temperature, and NH, content in the annealing atmosphere. Mechanical and chemical characteristics of steel nitrided in this manner will not be considered in the present article. MATERIALS AND EXPERIMENTAL WORK The samples used were from a commercial low-carbon steel, 0.0244 cm thick, in the cold-reduced condition. The chemical composition of this steel is given in Table I. Panels were cut to 5.1 by 17.8 cm, degreased in toluene, and weighed just before treatment. Four specimens were nitrided under each of the experimental conditions. A study was made of the nitriding rate of steel in a 100 vol pct ammonia atmosphere, 740 mm pressure, at five specific temperatures within the range 964" to 1358°F. The nitriding rates of steel in ammonia-nitrogen gas mixtures containing 10, 18, 26, 50, and 100 vol pct ammonia, 740 mm total pressure, at 1268°F were also determined. All atmospheres used were dried by successively passing them through drying towers packed with soda lime and with Linde Molecular sieve Type 4A. Quoted gas compositions refer to those entering the furnace. Specimens were held in the constant-temperature zone of a vertical annealing tube furnace for times of 14, 3, 5, 10, or 15 min. Gas flow rates were maintained at 3.8 cu ft per hr, which was nineteen volume changes per hour for the system used. The rate of flow was selected to provide a high level of free NH3 for cracking on the steel surface where the ammonia gas is most effectively used as a nitriding agent. The vertical annealing tube furnace consisted of a Hevi-Duty tube furnace with a 2 1/2-in.-ID mullite ceramic high-temperature tube. The constant-temperature zone (controlled within 10°F) was about 10 in. long. After each specimen was degreased, a hole was punched in one end, for attaching the specimen by hook to a chain so that it could be lowered into or raised from the high-temperature portion of the tube by means of a power-driven winch. A stainless-steel access port with O-ring seals was connected by suitable glass-to-metal seals to the cool upper portion of the furnace tube. After the weighed specimen was placed in the access port, the furnace tube was evacuated to approximately 10"3 torr, and then the system was flushed thoroughly with the atmosphere under study. When the gas flow rate and constant-temperature zone of the furnace were established, the specimen was lowered into the constant-temperature zone. The atmosphere flowed from the top to the bottom of the vertical furnace tube and was then vented. For all these runs, during the first 3 min of the time the specimen was in the constant-temperature zone of the furnace the specimen was heating up to the tempera-

Jan 1, 1970

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.' Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.'.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949

By D. L. Feucht, R. L. Longini

The semiconductor heterojunction is considered in terms of simple models which may lead to an understanding of move complex heterojunctions. Metallurgical and electrical properties of hetero-junctions aye discussed including the interface structure, energy -band diagram, and carrier transbovt across the interface. It is found that in a heterojunction all mechanisms such as injection, tunneling, and junction recombination found in simple junctions play modified voles. INTERFACES between materials (grain boundaries, the electrical junction between two differently doped materials in a single crystal, the oxide-metal interface, or metal-metal junctions) are of considerable importance in many situations. These various interfaces all have one very fundamental thing in common. Quantum mechanically speaking, the wave functions of the electrons in one material may penetrate the other material but, in general, only to the extent of angstroms. From an electrical point of view the conduction mechanism changes as a current passes through such junctions. In some cases the change is tremendous, in others almost negligible. The interface, then, is the locus of a change of conduction mechanisms. Some of these, particularly in semiconductors, are well-understood. The ordinary p-n junction in a single crystal can be the locus of an injection mechanism or a tunneling process, depending on conditions. The mechanisms are probably best understood in semiconductors because of the possible simplified view of particlelike conduction. The bands are either nearly filled or nearly empty and band overlap is seldom involved. The same fundamentals are probably important in other situations too but they are very difficult to look at naively. Although the simple look at the semiconductor case only gives us a relatively rough picture which must then be refined, the other systems, which involve a more complex situation, immediately are in many ways too difficult. There are too many initial choices of complex systems and therefore it is not possible to be even reasonably certain of any one model. Because of the relative simplicity of semiconductors, their good and controllable structure, and because of the ability to make many measurements on them not normally available to either metals or insulators! they are probably the best understood materials. It is therefore desirable to use them as a tool to further the understanding of interfaces in general. Semiconductor-heterojunction concepts were first proposed by kroemer1 in 1957. This was followed several years later by reports on the fabrication and experimental characteristics of heterojunction structures by Anderson2 and Diedrich and jotten.3 I) THE HETEROJUNCTION STRUCTURE To get down to hardware, when we refer to a semiconductor heterojunction we imply that there exists an intimate contact between different semiconductor materials. We could put two pieces of material together, complete with oxide layers, we could remove the oxides, or we could even melt the interface and hopefully get wetting and a good "bond" on solidifying. In fact we could by some means grow a crystal of one material using the other as a seed. Essentially we are interested only in the last two because they are the simplest to look at analytically. The degree of perfection of fit varies greatly and is reflected somewhat in the arc welder's joint strength. The lattice match of the two materials, their orientation, and so forth. is obviously necessary for a good bond but so is the continuity of any polar bonds which are involved such as in the III-V semiconductors. The mechanical misfit between two similar lattices can be described in terms of edge dislocations. The edge-type dislocations must be very close together for the usual misfit and there must be dislocations for each of several different Burger's vectors in order to produce a lattice match. The .'dangling bonds'' resulting will be involved in producing interface charge. Order of magnitude estimates of the charge density extrapolated from low densities of dislocations in homogeneous materials give 5 x 1013 cm-2 Ge-Si and 1 X 1012 cm-2 Ge-GaAs electronic charges. Edge dislocations also act as very active recombination centers between holes and electrons. One lattice "matching" difficulty usually exists even if two structures have essentially the same lattice constants as they will have different coefficients of therma1 expansion. Thus, on cooling from the usually high temperature of fabrication to room temperature, dislocations are produced, a good fit not existing at both temperatures. In brittle materials this shrinkage may even result in cracking. For the Ge-Si interface the mismatch is about 2 x 10 -6 per degree whereas it is less than 10"7 per degree between germanium and GaAs. The exact effect of the misfit is dependent on the thickness of the materials involved. For a very

Jan 1, 1965

By N. J. Grant, C. C. Wang

The Ti-Cr-O ternary system has been studied in detail near the titanium-rich corner within the limits of 10 wt pct 0, and 20 wt pct Cr. Studies were extended, but not in detail, to the region beyond 25 wt pct 0, (50 atomic pct) and 62 wt pct Cr (60 atomic pct). Four isothermal sections at 1400°, 1200°, 1000°, and 800°C are presented as well as two vertical sections at 1 and 2 wt pct 02. DURING the last decade much interest has been shown in the development of high strength titanium alloys for high temperature and corrosion resistant applications. Extensive research is being carried out at present, as the current literature indicates, in order to study the properties of titanium and to develop improved alloys. Two of the important alloying elements in commercial titanium alloys are chromium and oxygen and it would be desirable to know their combined influence upon titanium. For this purpose the present work was carried out to investigate the titanium-rich corner of the ternary system TiICr-0. The binary systems Ti-Cr and Ti-0 have been published recently. The Ti-Cr system was studied by several investigators " and their results are in close agreement. The eutectoid decomposition of the B phase has been shown to be extremely sluggish. TiCr, was the only intermetallic compound found in this binary system and was formed at 1350°C by a transformation from the p phase. TiCr? was established as the cubic C 15 (MgCu,) type of structure with 24 atoms per unit cell and was designated as the y phase. This terminology will be adopted in the present work. There was disagreement about the actual composition of this compound among the several investigators, although it is evident from their data that the compound probably has a solubility range of about 2 to 3 pct and is in the vicinity of 65 pct Cr. It has been indicated recently that a high temperature modification of this y phase (TiCr,) existed at a temperature above 1300°C." ' This high temperature modification was identified as a hexagonal C 14 (MgZn,) type of structure with 12 atoms per unit cell. The exact transformation temperature from the high temperature phase to the low temperature phase has not been established. A considerable hysteresis was observed and, due to the sluggishness of this transformation, the high temperature phase often co-existed with the low temperature phase at temperatures below 1300°C. A preliminary study of several Ti-0 compounds and the Ti-0 system had been carried out by Ehr-1ich."-"' The most complete binary Ti-0 system was the one reported recently by Bumps, Kessler, and Hansen." The first intermediate phase found in the system was the 8 phase which formed by a peritec-toid reaction of the phases a and Ti0 at temperatures below 925 °C. This reaction is extremely sluggish. The structure of this 8 phase was tentatively identified by these authors as being tetragonal and the lattice constants were found as c,, - 6.645A, a,, = 5.333A and c/a = 1.246A. Experimental Procedure The raw materials used for this investigation were TiO,, electrolytic chromium, iodide titanium, and sponge titanium. The TiO, was in the form of powder of chemically pure grade (99.8 pct pure). The chemical analysis of the electrolytic chromium was: 0, 0.50 pct; Fe, 0.07; Cu, N, and C, 0.01; and Pb, 0.001. The oxygen in the chromium was calculated as part of the final oxygen content of the alloys. The alloys were prepared by the cold crucible method using a tungsten arc. The entire system was evacuated and flushed with purified helium three times and then filled with helium. Each alloy was melted, turned over, and remelted at least four times to insure homogeneity. The total melting time was generally from 6 to 10 min. A master alloy of 25 pct 0,-75 pct Ti was prepared to facilitate alloying by melting compacts of TiOl powder with either iodide or sponge titanium, yielding the compound TiO. It was found necessary to bake the TiO, powder compact at about 150°C to remove adsorbed moisture. This was done to prevent the disintegration and spattering of the compact when the arc was struck. TiO, powder dissolved quite readily into the melt and no other trouble was encountered.

Jan 1, 1955

By J. S. Levine, M. Prats

A homogeneous and uniform cylindrical reservoir containing oil and gas is fractured vertically on completion and is produced at a constant bottom-hole pressure. The fracture has an infinite flow capacity, is of limited lateral extent and is bounded above and below by the impermeable strata defining the vertical extent of the reservoir. Results show that such a fractured reservoir can be represented by a reservoir of circular symmetry having very nearly the same production history. The well radius of this circular reservoir is about 1/4 the fracture length and is essentially the same as that obtained previously for a single fluid of constant compressibility. At the same value of cumulative oil production, gas-oil ratios of fractured reservoirs producing at constant terzinal pressure are larger than those of reservoirs having no fractures. This leads to more inefficient use of the reservoir energy in fractured wells and results in lower reservoir pressures for the same cumulative oil production. The reduction in operating life due to fracturing a reservoir is not as great as that for a slightly compressible fluid. This diflerence can be accounted for by the lower reservoir pressure in the fractured reservoir and its adverse effect on the average mobility and compressibility of the oil. As anticipated, the reduction in operating life increases czs the reservoir permeability decreases. The type of results presented in this report can be used to determine the economic attractiveness of fracture treatments per se, to setect the initial spacing to be used in developing a field, and to compare the relative merits of fracturing available wells and infill drilling. INTRODUCTION The effect of vertical fractures on a reservoir producing either an incompressible or a compressible liquid has already been discussed in the 1iterature.l,2 Those results indicate that the production history of such a reservoir is essentially the same as that of a circular reservoir having an effective well radius of approximately one-fourth the fracture length. The present work reports on the effect of a vertical fracture on a reservoir producing two compressible fluids —oil and gas—by solution gas drive. Because of the empirical nature of the PVT and relative permeability data used to obtain the performance of such reservoirs, results can only be obtained numerically and with the aid of high-speed computers. Since reservoirs lose their radial symmetry when fractured vertically, pressure and saturation can no longer be given only in terms of distance from the well. Two coordinates (such as x and y) must now be used to describe the pressure and saturation within the reservoir, and, since we are dealing with compressible fluids, time is also a variable. Thus the solution of a vertically fractured reservoir requires finding two unknowns (pressure and saturation) in two space variables (say x and y) and in time (t). Since no means are readily and generally available for solving such problems at the present time, we have used the results of previous work1,2 to approximate the effect of a vertical fracture on a reservoir producing both oil and gas by depletion. The purpose of the present wmk, then, is to investigate the possibility of using available numerical techniques (limited at the moment to one space variable) to study the two-space-variable flow behavior resulting from a vertical fracture. Results obtained in the course of this investigation are also reported and discussed. Input and output data of the numerical methods used are given in practical units: BOPD, feet, psi, cp, and md. Results are discussed fist in terms of specific reservoir and crude properties and geometries. Later, dimensionless parameters are introduced in order to extend results to different values of some of the reservoir and fracture properties. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable, circular, cylindrical outer boundary of radius r,. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below' the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. 1 indicates the general three-dimensional geometry of the fractured reservoir. Gravity effects and the effects of differential depletion resulting from variations in hydrostatic head (pressure) will be neglected. Thus, the flow behavior in the fractured reservoir is described by the

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,'. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal's stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950

By Shiou-Chuan Sun

THIS paper presents the design and operation of a frothmeter capable of measuring the frothing characteristics of pine oils and other frothing reagents. The experimental data show that the frothability of pine oil is governed by: 1-rate of aeration, 2-time of aeration, 3-height of liquid column, 4-chemical composition of pine oil, 5-pH value of solution, 6-temperature of, solution, and 7-concentration of pine oil in solution. The effect of mineral particles on the behavior of froth also was studied, and the results can be found in a separate paper.1 The results also show that the relative frothabilities of pine oils in the frothmeter generally correlate with those in actual flotation, provided that other factors are kept constant. In addition to pine oils, the other well-established flotation frothers were tested, and the results are included. In this paper, compressed air frothing is the frothing process performed by means of purified compressed air, whereas sucked air frothing is the frothing process accomplished by purified air sucked into the glass cylinder by a vacuum system. The term vacuum frothing denotes that froth was formed by degassing of the air-saturated liquid under a closed vacuum system. Apparatus The frothmeter, shown in Fig. 1, is capable of reproducibly measuring the volume and persistence of froth as well as the volume of air bubbles entrapped in the liquid and is capable of being used for compressed air frothing, sucked air frothing, and vacuum frothing. Fig. la shows that for compressed air frothing, the apparatus consists of an airflow regulating system, 1-3; a purifying and drying system, 4-8; a standardized flowmeter to measure the rate of airflow from zero to 500 cc per sec, 9; and a graduated glass cylinder, 13; equipped with an air regulating stopcock, 10; an air chamber, 11; and a fritted glass disk to produce froth, 12. The fritted glass disk, 5 cm in diam and 0.3 cm thick, has an average pore diameter of 85 to 145 microns. The pyrex glass cylinder has a uniform ID of 5.588 cm and an effective height of 63 cm. The inside cross-sectional area of the glass cylinder was calculated to be 24.53 sq cm, or 3.8 sq in. For sucked air frothing, Fig. lb shows that the apparatus for compressed air frothing is used again, with the following modifications: 1-compressed air and its regulating system, 1-3, are eliminated; and 2-a vacuum system, 16, equipped with a vapor trap, 15, and a vacuum manometer, 17, is added. The vacuum system can be .either a water aspirator or a laboratory vacuum pump. Any desired rate of airflow can be drawn into the glass cylinder, 13, by adjusting the opening of the air regulating stopcock, 10. The sucked air stream is cleaned by the purifing and drying system, 4-8, before entering the glass cylinder, 13. When this setup is used for vacuum frothing, the air regulating stopcock is closed. The frothmeter has been used for almost 3 years and has proved to give reproducible results, as illustrated in Table I. With a magnifying glass and suitable illumination, the frothmeter also can be used to study the attachment of air bubbles to coarse mineral particles.2 Experimental Procedures Except where otherwise stated, the data presented were established by means of the compressed air method. The volume and persistence of froth were recorded respectively at the end of 4 and 6 min of aeration at a constant rate of airflow of 29.3 cc per sec which is equivalent to 71.6 cc per sq cm per min, or 462.6 cc per sq in. per min. The aqueous solution for each test, containing 1000 cc of distilled water and 19.2 ± 0.5 mg frothing reagent, was adjusted to a pH of 6.9 ± 0.2. The volume of froth is expressed as cubic centimeter per square centimeter and is equivalent to the height of the froth column (the distance between the bottom and the meniscus of the froth). The volume of froth was obtained by multiplying the height of froth by the cross-sectional area of the glass cylinder, 24.53 sq cm. Before each test, the glass cylinder, 13, was cleaned thoroughly with jets of tap water, ethyl alcohol, tap water, cleaning solution, tap water, and finally distilled water. The cylinder with stopcock,

Jan 1, 1952

By A. M. Johnson, M. M. Singh

The mechanism of failure under a drill bit is still improperly understood in spite of several investigations of the subject. Generally, the cratering process under static loading conditions is considered to be similar to that achieved dynamically by impact. This paper attempts to indicate that, although the sequence of fracturing in the two cases appear to be identical, at least some dissimilarities exist. For example, the width-to-depth ratios of the craters vary to some extent, and the amount of energy consumed per unit of volume of craters is unequal for the two different loading conditions. Prevalent rock penetration processes are dominated by methods utilizing mechanical attack on rock. It is, therefore, generally accepted that a better comprehension of the mechanism of rock failure under a wedge would prove beneficial towards improving present drilling techniques. Several attempts have been made in recent years to explain how craters are formed under a drill bit, but the mechanism of failure beneath a bit is still improperly understood. 1-11 Most investigators, to date, have inferred the sequence of events occurring during crater formation from analyses of force-time diagrams,1"6 from theoretical considerations,7 or from a study of the configurations of final craters.8-l0 These analyses have led to the presentation of widely divergent models for rock failure beneath a drill bit, ranging from brittle to viscoelastic. The cratering process under dynamic loading commonly is regarded as being similar to that obtained under gradually applied, or 'static', loads. But the effect of rate of loading on the action of a bit is still disputed. Some investigators11-12 maintain that there should be no such effects, whereas others have demonstrated experimentally that these exist.13-17' The purpose of the investigation reported in this paper was to examine petrographically the damage done to rock under the action of a chisel-shaped wedge, both with 'static' and dynamic loading, and to determine if rate-of-loading effects could be detected. Significant quantitative differences in crater volumes and depths were found to exist for a given consumption of energy. On the basis of this data, an attempt was made to indicate some of the rheological properties that a proposed model should possess. All the work reported herein was conducted at atmospheric pressures. EXPERIMENTAL APPARATUS AND PROCEDURE Two types of rocks were employed for most of the experiments reported in this paper, viz. Bedford (Indiana) limestone and Vermont marble. The mechanical properties of these rocks are given in Appendix A. Actually two types of Vermont marble were used, but since no marked difference could be discerned between the two varieties (as seen in Fig. 10) the data was used collectively for the analysis. Stronger rocks were not employed owing to difficulty in generation of observable craters without damage to the equipment. Six-in. diam cores were drilled from the rock samples and embedded in 8-in, diam steel pipe with 3/8-in. wall thickness, using hydrostone to fill the annulus between the core and the pipe. This procedure was adopted to confine the rock specimen so that fractures would not propagate to the edges of the cores. This goal was achieved satisfactorily for these tests because no cracks were observed to extend into the medium surrounding the rock, even when craters were formed only 1 in. from the rock core periphery. Three to four craters were formed on a core face, because the rock damage from any one crater generally did not appear to extend into the others. Whenever, interference between damaged areas around adjacent craters was suspected, the data was rejected for purposes of the analysis. The limestone and marble samples were tested with a 60-degree, wedge-shaped bit, 1 5/8-in. in length, made of tool steel. The bit shank had two SR-4 type electrical resistance strain gages, mounted axially, to record the force-time history during the loading operation. The static indentation tests were conducted using a 50-ton capacity press fitted with an adapter for drill bit attachment. See Fig. 1. The force exerted by the bit at any instant was measured with strain gages affixed to the bit shank. An aluminum cantilever, with two SR-4 strain gages mounted near its clamped end, was employed to measure bit displacement. Both sets of gages were included in Wheatstone bridge circuits,

Jan 1, 1968

By E. S. Davenport, R. J. Hafsten, R. A. Grange

The influence of austenite grain size upon the hardenability of steel is now fairly well understood; for a given austenite, increasing the grain size increases the depth of hardening, and, since the latter is related to the fundamental transformation behavior of austenite, it follows that austenite decomposition must, in general, be retarded by increasing grain size. To date, very little quantitative information bearing directly on the effect of austenite grain size upon the progress and result of isothermal transformation has been published. Davenport and Bain,' and Zimmerman, Aborn and Bain2 have shown that the transformation is definitely relarded in hypereutectoid plain carbon steels at temperatures near and above the upper region of rapid transformation (Ar') when the austenite grains are increased in size. More recently, Griffiths. Pfeil and Allen3 investigated the effect of a series of different heating (austenitizing) temperatures upon the progress of isothermal transformation at 1245°F. (675°C.) and 745ºF. (395°C.) in a medium carbon, low-alloy steel; while they reported no measurements of the austenite grain size, their results suggest that increase in grain size retards austenite transformation at 1245ºF. (675°C), but has no appreciable effect at 745°F (395°C.). The present paper deals with the results of a study of the isothermal transformation of austenite in a single commercial alloy steel in which a fine-grained or a coarsegrained state was induced by appropriate selection of austenitizing temperature. The data are presented in the form of isothermal transformation diagrams, which clearly show that coarsening the grains lessens the rate of transformation of austenite to proeutectoid ferrite and pearlite—that is, at temperature levels above about 1000°F. (540°C.)—but is without significant effect at lower temperatures where the transformation product is bainite or martensite. It is to he presumed that the foregoing statement would be valid, at least in principle, for many other grades of steel; it confirms again that the mechanism of transformation to a pearlitic structure is fundamentally different from that to an acicular structure. A number of related observations were made, which seem to throw some light on the transformation process as it takes place in alloy steels, particularly at temperature levels in the vicinity of 1000ºF. (540°C.), where the transition from lamellar to acicular structures occurs. These data are discussed briefly in the belief that they may lead to a clearer understanding of this aspect of the subject. Material and Experimental Procedure The material investigated was a cornmercial grade of S.A.E. 4140 steel, the composition of which was as follows: 0.37 per cent C, 0.77 per cent Mn, 0.98 per cent Cr and 0.21 per cent Mo. It was hot-rolled to a 1 1/8-in. round bar and normalized by air-cooling from 1800°F. (980°C.).

Jan 1, 1941

By Walter C. Lawson

The primary objective in laying track in panel sections is to reduce the number of track laborers required. This is possible because the work is mechanized. Moreover, because the work is mechanized and each of the operations needs only a few men, and each is self-contained, the work can be carried on at night as well as in daylight; therefore, the method provides a means of preparing tracks on more than one shift. The laying of tracks in open pits and quarries in panel sections is not new but new methods have been made possible by the introduction of new types of equipment. The purpose of this paper is to describe the methods that are followed in the Morenci open pit. General Mining Operations Full-scale ore production at Morenci is about 50,000 tons daily. The normal yearly output of ore and waste is 32,000,000 tons, of which 30,000,000 tons is handled by rail haulage. This requires the building of approximately 47 miles of loading and other temporary tracks during a 12 months' period (Fig I). Broken ore and waste is loaded into 90-ton capacity dump cars with 5-cu-yd full-revolving electric shovels. Shovel banks are uniformly 50 ft high. They are blasted with churn drill holes and the broken material from a blast is loaded out with two shovel cuts, the first one being called (locally) the "splatter" cut and the second one the "clean-up" or "face-up" cut. When a shovel is making its clean-up cut, the loading track is about 70 ft from the toe of the bank and, under normal conditions, a bank is blasted against it without removing the track. It is thus evident that each track is used for two shovel cuts before relocation is necessary, inasmuch as a single position serves for both the clean-up cut prior to blasting and for the splatter cut following the blast. The normal advance of a solid bench by a single blast is 40 ft (Fig 2). Preparation OF Panel Grade In preparation of panel grades bulldozers and rooters are used for the bulk of the work and an auto-patrol road grader for the final stage. At Morenci, bulldozers have always been used for track-grade preparation, but before the introduction of the other two types of equipment grades were uneven and irregular at best, and always necessitated a big gang of track laborers to hand-block under the ties with rocks after a track was laid into place. High blocking also made poor track because of instability and caused frequent derailments. Under these conditions derailments were generally bad as re-railing became difficult. Much track was torn up and many tics broken in the process. The inadequacy of the hand-blocked track, together with the inefficiency of hand blocking, constantly pointed, to the desirability of reducing the amount of labor required, so various means were tried to improve conditions, such as wood

Jan 1, 1949

By R. J. Hafsten, E. S. Davenport, R. A. Grange

The influence of austenite grain size upon the hardenability of steel is now fairly well understood; for a given austenite, increasing the grain size increases the depth of hardening, and, since the latter is related to the fundamental transformation behavior of austenite, it follows that austenite decomposition must, in general, be retarded by increasing grain size. To date, very little quantitative information bearing directly on the effect of austenite grain size upon the progress and result of isothermal transformation has been published. Davenport and Bain,' and Zimmerman, Aborn and Bain2 have shown that the transformation is definitely relarded in hypereutectoid plain carbon steels at temperatures near and above the upper region of rapid transformation (Ar') when the austenite grains are increased in size. More recently, Griffiths. Pfeil and Allen3 investigated the effect of a series of different heating (austenitizing) temperatures upon the progress of isothermal transformation at 1245°F. (675°C.) and 745ºF. (395°C.) in a medium carbon, low-alloy steel; while they reported no measurements of the austenite grain size, their results suggest that increase in grain size retards austenite transformation at 1245ºF. (675°C), but has no appreciable effect at 745°F (395°C.). The present paper deals with the results of a study of the isothermal transformation of austenite in a single commercial alloy steel in which a fine-grained or a coarsegrained state was induced by appropriate selection of austenitizing temperature. The data are presented in the form of isothermal transformation diagrams, which clearly show that coarsening the grains lessens the rate of transformation of austenite to proeutectoid ferrite and pearlite—that is, at temperature levels above about 1000°F. (540°C.)—but is without significant effect at lower temperatures where the transformation product is bainite or martensite. It is to he presumed that the foregoing statement would be valid, at least in principle, for many other grades of steel; it confirms again that the mechanism of transformation to a pearlitic structure is fundamentally different from that to an acicular structure. A number of related observations were made, which seem to throw some light on the transformation process as it takes place in alloy steels, particularly at temperature levels in the vicinity of 1000ºF. (540°C.), where the transition from lamellar to acicular structures occurs. These data are discussed briefly in the belief that they may lead to a clearer understanding of this aspect of the subject. Material and Experimental Procedure The material investigated was a cornmercial grade of S.A.E. 4140 steel, the composition of which was as follows: 0.37 per cent C, 0.77 per cent Mn, 0.98 per cent Cr and 0.21 per cent Mo. It was hot-rolled to a 1 1/8-in. round bar and normalized by air-cooling from 1800°F. (980°C.).

Jan 1, 1941