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By R. G. Davies, R. H. Richman

Several techniques, X-ray diffraction, transmission electron microscopy, conventional, metallography, and mechanical property measurements are combined to investigate decomposition in the suPersaturated solid solution Fe-27 at. pct Be. The following sequence of structures for aging temperatures below 400°C is established: massive short-range order, pseudo-FeBe (L2o) order, Fe3Be (DU3) order, sinusoidal modulation of composition, general or continuous precipitation, and discontinuous or cellular precipitation. In addition to this sequence itself, several features of the individual stages are noteworthy; for example, when coherent modulations occur, their development is parallel to (100) everywhere in the specimen apparently without incubation, and both the wavelength and the composition amplitude of the modulations increase with aging time. Two types of discontinuous reaction are observed, depending upon the aging temperature. At low temperatures (<550°C) the boundary-nucleated variety of discontinuous precipitate predominates; but at higher temperatures (>600°C) the crystallographic variety occurs instead. Hardness and flow-stress measurements clearly reflect the quoted structure sequence. Some qualitative aspects of the structure changes and of the relationship between mechanical properties and structure are discussed. BERYLLIUM in solid solution markedly strengthens iron.&apos;" A recent study demonstrated that not only were supersaturated single crystals of Fe-27 at. pct Be very strong, but they deformed primarily by mechanical twinning.3 Such behavior, coupled with the decrease in solid solubility of beryllium in a Fe from about 33 at. pct at 1165°C to about 10 at. pct at 500°C4 as shown in Fig. 1, leads naturally to questions about property changes with aging in this system. In 1929 roll,1 and later Seljesater and Rogers,5 reported that useful increases in strength could be obtained by aging quenched Fe-Be alloys, but it was not until quite recently that any of the details of precipitation in these alloys were studied. Richman6 observed that both an Fe3Be superlattice (with a DO3 crystal structure the same as Fe3A1, illustrated in Fig. 2) and a modulated structure preceded the appearance of a discrete second phase in the 20 at. pct Be composition. Here, a modulated structure refers to a periodic composition fluctuation within one crystal, while its lattice remains coherent. Subsequent work on a Fe-Be alloys by Heubner7 and von Heimendahl and Heubner8 confirmed the existence of the modulated structure, although only an FeBe (L20) ordered structure was detected (also shown in Fig. 2). Both Rich-man and Heubner corroborated the large increases in hardness during aging reported earlier, but other mechanical properties were not examined. Since modulated systems are encountered relatively infrequently, the influence of coherent modulation upon mechanical properties is not well-known. With the accumulation of information about age-hardening systems, it has become clear that many precipitation reactions cannot always be described by the concept of heterogeneous nucleation at some lattice discontinuity followed by diffusional growth. Rather, complex sequences involving prior "preparation" of the matrix are quite common; that is, a transition structure occurs in the parent phase, instead of in some "nucleus" form. Delineation of such subtle sequences appears to be a worthwhile step toward the understanding of solid-state precipitation. Since not many structural progressions of comparable nature have been reported, the objectives of the present survey are to identify and elucidate the various

Jan 1, 1967

By L. Yarborough, L. R. Smith

This paper presents results of a laboratory study of retrograde condensate recovery by revaporization into dry injection gas. Flow tests were performed in 10.6-ft long sand packs at 100F and 1,500 psi. In three runs methane revaporized the liquid from a n-pentane-methane mixture in the presence of immobile water. TWO of these tests were water-wet, and the third was totally oil-wet. In the three runs n-pentane recovery was complete after 2.5 hydrocarbon PV of injection. There was no significant performance difference between the two wettability extremes. In a fourth experiment, a methane-hydrogen sulfide mixture revaporized a synthetic light, sour condensate. No water saturation was present. Equilibrium compositions and volumetric data were obtained for the four-component condensate. The heavy component, n-beptane, was removed after 6 PV production. Comparison of the effluent fluid compositions with known equilibrium data shows that the flowing fluid was equilibrium vapor and that the mixing zone between equilibrium vapor and dry injection gas was short. Data indicated that complete recovery of retrograde liquid occurred after it was contacted by a sufficient quantity of dry gas. INTRODUCTION When pressure declines below the fluid dew point in a gas condensate reservoir, a liquid phase forms. In this process, referred to as retrograde condensation, the quantity of liquid formed is frequently small enough that the liquid is not a flowing phase. To prevent loss of valuable retrograde liquids, the process of dry gas cycling has been employed for several years as a more or less standard practice. In this procedure the reservoir pressure is maintained above the fluid dew point so that the liquid components may be produced as vapor and then separated at the surface. Although full pressure maintenance by gas cycling seems ideal in terms of preventing liquids loss, several factors can reduce the atuactiveness of such an operation. From a study of a condensate reservoir in Alberta, Canada, Havlena et a1.1 con-cluded that cycling under conditions of declining pressure leads to economic advantages and to a high recovery of hydrocarbon liquids. This study considered effects of volumetric sweep efficiency, retrograde behavior of the original wet gas and revaporization characteristics of the retrograde liquid when contacted by dry gas. The first major work concerning revaporization of liquid in a gas condensate system is that of Standing et a1.2 Calculations based upon the PVT behavior of a recombined gas condensate fluid indicated that all retrograde liquid can be recovered if it is contacted by a sufficient quantity of dry gas. The paper considered the effect of variable permeability upon the recovery of retrograde liquid. Standing et al. concluded that recovery of heavier components in the retrograde liquid is greatest if reservoir pressure is allowed to decline below the dew point prior to dry gas injection. Since the work of Standing et al., several laboratory studies have been reported which show that recovery of hydrocarbon liquids by vaporization into dry injected gas can contribute to increased recovery above that obtained by ordinary production practices. Vaporization from retrograde condensate,3 conventional oil4-7 and volatile oil8 reservoirs has been considered. There is little work that deals with revaporization recovery from condensate reservoirs. This study demonstrates that vapor-liquid equilibrium exists when a dry gas is injected into a porous medium containing retrograde condensate; investigates the effect of wettability on revaporization of retrograde condensate; and provides an indication of the amount of dry gas necessary to

Jan 1, 1969

By C. S. Samis, J. C. Mitchell

Sodion activity data have been obtained for the Na-A1 system for sodium concentrations in aluminum between NN, = 25 . 10-and 300 x 10&apos;. This concentration intert-a2 encompasses those sodium concentrations nor1)zally encountered in aluminum reduction cell operation. The sodium activity data were measured by a two-phase equilibration of sodium between a lead and an aluminam rich phase. The Na-Pb system was emplojed as a reference for the determination of the actiz7itj 0.f sodium. The activity of sodiin in aluminuwz exhibits large positi2.e deviations frorn ideality and a strong dependence, on concentration below NN, = 100 x 1K6. The inteated data indicate that the activity of aluminium is equal to its mole fraction over the range of miscibility of the Na-A1 sgstem. The data on the Na-A1 binary have been combined with experimental data on the cryolite-A1 system at 1025°C to obtain the activities of Na F and AlF, in liquid cryolite oz2er the cornposition 1-ange encountered in aluminum cell operation. The results are in agreement with activities calculated from the NaF-AlF, phase diagram. ALUMINUM is produced commercially by the electrolytic reduction of aluminum oxide dissolved in molten cryolite. There is considerable controversy over the actual mechanism of the discharge processes, but sodium potentials in the systems appear to play an important role in the reduction mechanism. The metal-salt reaction involving NaF and aluminum to produce A1F3 and sodium is responsible for the presence of sodium in the aluminum metal phase. Additional sodium may be produced from the simultaneous deposition of sodium and aluminum at the cathode as a result of a cathodic overvoltage. runert&apos; has suggested that sodium gas at atmospheric pressure would be the result of reaction between cryolite and aluminum at 1000°C. Subsequent investigations have shown that production of sodium at atmospheric pressure does not occur. These later investigations can be conveniently separated into two categories. The first involves sodium, aluminum, and cryolite, in which the sodium activity was measured. The second includes a lead phase for sodium activity measurement. Jander and errmann,&apos; studied the reaction: at 1090°C in alumina crucibles under an atmosphere of dry, oxygen-free nitrogen. The equilibrium constant for the reaction was expressed in terms of concentration. Their results in Fig. 1 show an increase in sodium content of the aluminum with increasing NaF/A1F3 weight ratio. Pearson and waddington3 performed similar experiments at 1000°C. Their results are included in Fig. 1. Dewing and ollinshead have measured the sodium content of aluminum as a function of the NF/AF, ratio at 1025"C, Fig. 1, and ewin&apos; measured the sodium content of the aluminum in a system involving the solid reactants NaF, cryolite, and liquid aluminum. This reaction is different from those discussed above. Two solid phases, NaF and Na3A1F6, and a liquid aluminum phase were present. The sodium concentration in the aluminum was determined by the temperature. Dewing&apos;s measurements covered the temperature range 679" to 896°C. Omo, Matsushima, and 1t02" investigated the equilibrium 6NaF ential thermal analysis. Stokes and Frank6 determined sodium activities by

Jan 1, 1970

By W. S. McCain, B. A. Wilcox, A. H. Clauer

The creep and creep-fracture behavior of a Ni-200-2Th0, alloy has been studied over the temperature range 816° to 1038°C and stress range 4000 to 19,000 psi Specimens having their axes either parallel or transverse to the final sheet-rolling direction were tested in air, and the apparent activation energy for creep was found to be 92 kcal per mole, regardless of specinien orientation. The stress dependence 01- the steady-state creep rate, was satisfied by where n depended on orientation; n = 9.7 for rrzaterial transverse to the rolling direction and n = 24.3 for material parallel to the rolling direction. In the latter case, the relation was also valid. The rupture strength of material parallel to the rolling direction was -1.5 times gveater than the transverse rupture strength. Several tests in vacuum revealed that here the creep rate was higher and rupture life lower than for comparable tests in air. THERE is an increased interest today in producing improved dispersion-hardened alloys for high-temperature structural applications. This had led various materials designers to modify existing alloys, such as thoriated nickel. One system that has received considerable attention is based on chromium additions to Ni-ThO2, with the obvious motive of improving the oxidation resistance. Another effect of chromium is that of lowering the stacking-fault energy, y, of nickel. For example, the addition of 30 wt pct Cr decreases y from -225 erg per sq cm for pure nickel1 to -70 erg per sq cm.&apos; This decrease in y could have several effects on the deformation behavior. There is some evidence that cross slip of dislocations around Tho2 particles is a mechanism of tensile3 and creep4 deformation in TD Nickel (Ni + 2 vol pct ThO2) at temperatures below 0.5 the absolute melting point of nickel, T,. A decrease in ? by chromium additions should increase the difficulty of cross slip. Also it has been suggested that the high-temperature (T > 0.5Tm) rate-controlling creep process in "recrystallized" Ni-Tho2 alloys is the climb of edge dislocations over Tho2 particles.5 According to weertman6 a decrease in the stacking-fault energy should decrease the dislocation climb velocity resulting in a decreased steady-state creep rate. Thus, chromium additions to recrystallized Ni-Tho2 alloys would be expected to decrease the creep rate, all other conditions being constant. However, a difficulty arises when the stacking-fault concept is applied to high-temperature creep of dispersion-strengthened metals which are produced on a commercial or semicommercial scale. This occurs because the materials are processed so that they have a high-stored energy of cold work, and the other substructural effects could obscure any influence of stacking-fault energy per se. An example of an alloy with a high stored energy of cold work is TD Nickel bar. This material has a fibrous grain structure (1 I diam by 10 to 15 p long), and the structure is stabilized by the ThO2 particles. Annealing at high temperatures, e.g., 3 hr at 1300°C, causes no recrystallization or grain growth.4 Previous work by the authors4 showed that the high -temperature creep behavior of TD Nickel could not be related to any simple dislocation theory of creep, and this probably was associated with the complex initial structure of the material.

Jan 1, 1968

By J. H. Reynolds

The possibility of using a semiconductor, metal, semiconductor structure as a light detector is discussed. A brief theoretical argument is presented which predicts that this structure should have pho-toresponse characteristics similur to those of a metal-semiconductor diode, but with the magnitude of the current increased by a transistor gain factor. Measurements made at low frequencies on a particulur S-M-S device agree u~th this prediction aizd shoul that significant gain factors are attainable. The current gain is substantially higher than that predicted for the metal base transistor. It is proposed that the operation of these units is more closely approxinzated by the metal-gate model which predicts higher current gains. A qualitative discussion of its high-frequency performance indicates that detection of light modulated at microwave frequencies by a S-M-S deuice is possible. ADVANCES in the technology of chemical vapor deposition&apos;-4 have made it possible to form a S-M-S structure consisting of a thin metallic layer sandwiched between layers of single-crystal semiconductor. It has been proposed5-7 that, if the metal layer is made sufficiently thin, this structure could be used in an amplifier having several advantages over presently available transistors including higher-frequency performance. Calculations8 predict that the maximum gain-bandwidth product is nearly an order of magnitude higher than that of a bipolar transistor having the same geometry. Maximum oscillating frequencies in the microwave range are predicted. Electrical measurements made on S-M-S devices have shown that, although the theoretical frequency characteristics are not presently attainable, current and power gain is obtained. Another possible application of the S-M-S structure is its use in a light detector. This structure is a three-layer relative of the metal-semiconductor diode. Light detection using M-S diodes is the subject of considerable present interest. They are known to have a short response time and the ability to detect light having a photon energy below the semiconductor bandgap. In this paper, the mechanism by which S-M-S photocurrent is generated is discussed. An expression is derived which shows that the response characteristics are similar to those of a M-S diode, but that the magnitude of the current is increased due to the transistorlike behavior of the device. The results of low-frequency response measurements on a particular S-M-S structure are presented. These agree with the theoretical predictions and show that significant gain factors are attainable. A qualitative discussion of the high-frequency characteristics is presented which predicts that detection of light at microwave frequencies by a S-M-S device is possible. THEORY In this discussion, the photocurrent, iT, measured across terminals attached to the semiconductor emitter and collector layers is related to the current pho-toemitted from the metal base layer. The latter will be referred to as the primary photocurrent. The behavior of the primary photocurrent is determined by the characteristics of the two metal-semiconductor diodes. The diode photoemission is illustrated in Fig. 1, which shows the emitter and collector potential barriers. The metal thickness has been greatly exaggerated. As will be discussed later, the actual barrier shape can be much more complex, but this diagram illustrates the essential features of the photoemission process. An absorbed photon having an energy greater than the barrier height can emit an electron into the emitter or collector. Since this process is discussed

Jan 1, 1968

By F. H. Bunge, W. H. Jr. Dailey

This paper covers an investigation of the magnetic roasting characteristics of several iron ores when treated in the form of small pebbles (1/8" to 1/2" in size), and in the form of balled fines. The roasting treatment was carried out with apparatus capable of very close control of time, temperature, face velocity, and per cent combustible in the reaction gas. The effect of rapid initial heating was not studied although it is believed that this has a major effect on the results when processing solid pebbles. The test equipment is a fixed bed type, with such a wide range of gas velocities, temperature, combustible content and etc., that the results obtained can be made to approximate those from various commercial roasting processes. The data presented in this report covers reaction rates, effect of processing variables on silica in the concentrate, flow resistance of beds, and to a limited extent, the effect of particle size. The work is far from complete and raises many more problems than it gives answers for. We believe, however, that much of the information will be useful to those engaged in investigation of magnetic roasting processes. We measured the time required for various degrees of completion of the reaction of hematite to magnetite, for finely pound material in balled form and for carefully sized crushed ore. Measurements were made for a variety of Minnesota and Labrador ores. This report covers an ore requiring fine ginding (-325 M) for liberation (Lower Kevin) and an ore requiring coarser grinding (-100 M) for liberation (Upper Olson). These ores represent approximately the range of characteristics for a group in the west end of the Mesabi Range. Our data shows that the reaction rate is very fast for the finely ground material and that tests are readily reproducible. The reaction rate of the larger size material, in the range of 1/8" to 1/2", is much slower and the results more erratic. We found that for the ores tested, the percentage of silica in the Davis tube magnetic concentrate was a function of iron recovery. Normally the concentrate had a low and relatively uniform percentage of silica up to a critical value of recovery. Above this critical recovery value the percentage of silica increased very rapidly. For example, for one particular ore roasted in the form of 3/8" diameter balls made from -28 mesh fines, the silica remained at about 7% to 8% until the recovery exceeded about 93%. Increasing the recovery beyond 93% resulted in over 25% silica with the additional recovery. The degree of conversion of hematite to magnetite (% completion of roast) required to obtain 93% recovery for balled material, varied inversely with the gas flow rate. Percentage silica in the concentrate resulting from roasting 3/16" and 1/2" solid material was relatively erratic. However, for varying degrees of iron recovery the lowest silica percentages corresponded to those obtainable when roasting fines. It is thought the probable reason for the erratic values was the variation in shattering or cracking of the pebbles during initial heating and roasting. There is some indication that very fast initial heating will greatly increase the permeability of the individual particles of ore to gas flow so that the reaction rate for coarse sizes will approach that obtainable with balled fine material.

Jan 1, 1961

By Ashok K. Sinha

The quasi-binary systems "VFe3"—VCo,—VNi,— "VCu3"and "TiFe3"—TiCo3,—TiNi3-"TiCu3"have been studied by a combination of microscopic and X-ray methods. Of the Phases encountered, eleven had close-packed ordered layer structures. Within each system, there is an approximately linear variation of the degree of hexagonality of the stacking arrangement with electron concentration, e/a. A study of eighty -four known examples of AB3 structures in transition metal alloys indicates that at e/a = 8.65 the ordered structure of the close -packed layers changes from "triangular" (AuCu3 type) to "rectangular" (SbCu3 type). At e/a < 8.65, the slope of hexagonality us e/a line increases with the group number of the A component. An interesting series of close-packed ordered structures is known to exist at the composition AB3; however, their alloy chemistry has not yet been fully understood. Dwight and Beck1 observed a correlation between position of the components in the periodic table and the type of crystal structure of the binary AB2 structures formed by transition metals. No consistent effect due to atomic size was noted and they proposed that electron concentration* predominates in In the present paper, the AB3 structures are characterized by a symbol describing the stacking and a symbol specifying the ordered layer. The stacking symbol used was introduced by Zhdanov,7 and later used in the International Tables,8 and by Beck9 in his survey of possible layer stacking structures. Alternating positive and negative integers are used to represent the number of positive (e.g., in abcabc...) and negative (e.g., in cbacba...) stacking sequences. T denotes the triangular ordering found in close-packed planes of the AuCu3 structure and R the rectangular ordering found in close-packed planes of the SbCu3 structure, Figs. 3(a) and (b). The present structure symbols are listed in Table I alongside the prototypes, where known, and other structural characteristics of AB3 phases found in the present investigation. EXPERIMENTAL The starting materials were metals of 99.9+ purity. The alloys were prepared by arc melting under argon atmosphere using a nonconsumable tungsten electrode and water-cooled copper hearth. The total weight loss upon melting and subsequent annealing was always less than 0.5 pct and hence the alloys will be referred to by their intended (unanalyzed) compositions. The alloys were homogenized and annealed at suitable temperatures in the range 750" to 1200°C, the annealing periods varying from 3 days at 1200°C to 10 days at 750°C. The heat treatments were carried out in sealed silica capsules under argon atmosphere and with a molybdenum foil cover between the alloy and the walls of the capsule. The quenched alloys were microscopically examined and reduced to powder by crushing or filing. The powders were, whenever necessary, given a stress-relieving anneal at the original annealing temperature. X-ray powder patterns were obtained with an asymmetrical focusing camera, a Guinier-deWolff focusing camera, or a Debye-Scherrer camera. Cr, Co, or Cu radiations were used. In some cases, to ensure the minimum degree of contamination, the deeply etched specimens were mounted in the asymmetrical focusing camera to obtain an X-ray pattern. Internal silicon standards were employed for lattice parameter determinations. The intensity calculations were made by using a Fortran IV program

Jan 1, 1970

By B. H. Caudle, A. R. Khan

The oil production performance of thin-oil-column type reservoirs producing entirely by natural water drive are discussed in this paper. The dimensionless production histories were obtained in a series of scaled porous-medium laboratory-model tests under varying effects of rate of production, mobility ratio across moving boundary, ratio of oil- and water-sand thickness and mobility ratio across fixed boundary including the effects of different residual oil saturations in the water-invaded regions. This scaled-model study of thin oil columns indicated that greater recovery of oil results for lower values of the following: rate of production, mobility ratio across the moving boundary, water-sand thickness relative to the oil-sand thickness, and mobility ratio across the fixed boundary or residual oil saturation in the water-invaded region of oil sand The results of the study are given as dimensionless production history plots which may be used to predict the performance of the field they represent. INTRODUCTION Oil fields producing under natural water drive can be classified into two major groups: (1) an "edge-water drive" reservoir group in which the water is encroaching from the reservoir periphery, and (2) the group of reservoirs in which the oil-sand is entirely underlain by an aquifer. Reservoirs in the second group are further subclassified as "bottom-water drive" reservoirs and "thin-oil-column" reservoirs. The latter reservoirs are characterized by their relatively equal oil- and water-sand thicknesses and by having both the oil and water zone relatively thin. When oil is produced from a water-drive reservoir by a partially penetrating well, water breaks through sooner or later before all of the displace-able oil is recovered. Many analyses of this general situation have been made with varying degrees of realism in their approaches, both theoretical and experimental5.6 in nature. Pertaining to the scaled laboratory model studies of natural water drives using porous media, detailed investigations have been made by Henley, et al.7 on bottom-water drive and by Caudle8 on edge-water drive reservoirs. No laboratory model studies, however, have been made to investigate the performance characteristics of thin-oil-column reservoirs. This paper presents the results of a study on scaled models of thin-oil-column reservoirs, operated under varying conditions corresponding to the actual field practices. SCALING PARAMETERS The object of scaling is to produce a one-to-one relationship between physical and dynamic parameters of the model -and prototype. The most comprehensive treatment of scaling techniques for oil reservoirs is given by Geertsma, et a1.,9 which covers two methods for arriving at dimensionless groups for scaling. Table 1 lists the scaling parameters suitable for creating kinematic and dynamic similarities between the model and the prototype in the variables considered for the thin-oil-column reservoirs. In order to achieve similarity it is essential that the dimensionless groups listed in Table 1 have equal values in the model and the protorype simulated. Since it has been established that the role of interfacial forces is neglible in gross fluid movement in a reservoir no attempt was made to scale capillary forces- Although there are reports describing Scaling criteria for these forces,10,ll consideration of the necessary but restrictive conditions for

Jan 1, 1970

By Clark L. Corey, Bogdan Lisowsky

Electrical resistivity, X-ray line positions, degree of order, and microstructures have been investigated for Ni-A1 alloys near the Ni3Al composition. The results indicate that Ni3Al undergoes disordering between 1250oC and the mp; also supersaturated y, produced in y + y&apos; alloys by gas quenching, is extensively ordered prior to y&apos; (Ni3Al) phase separation. The latter reaction, if not both, must follow the cooperative phenomena model. Shifts in line position as a function of quench-indulced super satulration are shown. Lattice pavarneters of equilibriunz and nonequilibrium phases are given. THE objective of this investigation was to determine the mechanism and kinetics of the reactions which occur in Ni3A1 and hypostoichiometric Ni3A1 alloys. The results are of particular significance relative to pre-precipitation phenomena. Early work on Ni-A1 binary compositions near the Ni3A1 composition (13.6 wt pct Al) has been adequately reviewed by Hanssen,1 whose phase diagram is presented in Fig. 1. williams2 verified the suggestion made by Taylor and Floyd3 and others4 that y&apos;, Ni3A1, may precipitate coherently on (100) planes of the y phase (see Fig. 1 for phase nomenclature); he further suggested a two-step precipitation mechanism consisting initially of probably short-range ordering followed by actual precipitation of y&apos;. The precipitation stage in low-aluminum hypo-eutectic compositions has been studied by a number of investigators;*"7 short-range order or "zone" formation have been suggested as explanations for various diffuse X-ray scattering effects. The ordering reaction in Ni3A1 alloys is characterized by a) a very rapid rate of ordering in nonstoi-chiometric compositions, b) absence of a disordered phase region for the stoichiometric compound, y&apos;, or Ni3A1, c) precipitation phenomena as a dominant aspect in hypoeutectic alloys, and d) an increase in elec-trical resistivity on ordering.&apos; The latter two factors were found by Newkirk to characterize ordering in Co-Pt, for which an extensive and detailed analysis was made.&apos; An electrical-resistivity increase on ordering has also been reported for cuAu3.10 PROCEDURE Ni-A1 alloys in the form of 1300-g chill-cast ingots were prepared by vacuum melting electrolytic nickel and high-purity (99.99 pct) aluminum. Very small heats prepared from high-purity carbonyl nickel, supplied through the courtesy of Dr. Goff of the Naval Research Laboratory, were used for comparison with the larger ingots and no differences were noted. The cast material was homogenized in purified argon for a minimum of 72 hr at 1200°C and water-quenched from 1350°C. Compositions studied are given in Table I. The 10 pct A1 alloy was both hot- and cold-rolled. X-ray superlattice line intensities and peak positions were obtained from -270 mesh filings, using CuK, radiation with a LiF crystal monochromat adjusted to receive both 01 and a2. One-degree slits and a 1/8 deg per min scan rate were used to record line traces. A standard tungsten powder, obtained through the courtesy of G.E. Research Laboratory, was used to calibrate line positions.

Jan 1, 1968

By B. K. Larkin, H. R. Bailey

One of the most complicated and potentially one of the most promising secondary recovery methods is that of underground combustion. A number of field tests1,2,3 have been performed recently, apparently indicating that the underground combustion process is technically feasible. Relatively little has been published concerning laboratory or theoretical investigations of the underground combustion process. A few results of laboratory tube runs have been published4,5 and these data are valuable in understanding the process. The tube run data also emphasize the complexity of the thermal recovery process. Under various conditions, problems in heat transfer, multiphase fluid flow and combustion rates arise. For example, at low temperatures the combustion process proceeds so slowly that the front cannot be propagated. It is a problem in heat transfer to predict what injection rate of air is necessary to sustain combustion in a particular reservoir. Certain fluid flow aspects of underground combustion have been studied by Wilson, et a13. In the development of some of the flow equations, assumptions of adiabatic combustion were made. Vogel and Krueger1 have devised an analog model of the heat conduction process for a constant temperature cylindrical source moving radially outward in a homogeneous conducting medium. Jenkins and Ramey7, in a discussion of the Vogel and Krueger paper, present an analytical solution of a heat conduction problem related to problems considered by Vogel and Krueger. In the present paper an idealized model of the heat conduction problem is considered, which is more general than the model of Vogel and Krueger or Jenkins and Ramey. In particular, initial well heating, vertical heat losses and arbitrary frontal velocities are included. Equations for the temperature are obtained in terms of integrals. These integrals have been evaluated numerically for the case of frontal movement corresponding to a constant air injection rate and the case of constant frontal velocity. These results are presented graphically. From these graphs one may estimate conditions under which nearly adiabatic temperatures are obtained. The application of these results requires some knowledge of reservoir thermal properties, combustion rates and residual fuel content. Assuming no vertical losses it is possible to obtain explicit evaluations of these integrals in the linear con- stant velocity case and in the radial case corresponding to a constant air injection rate. PRESENTATION OF RESULTS The geometry of the radial system is illustrated in Fig. 1 where the reservoir is represented as a slab of thickness h. By making an energy balance for an infinitesimal volume, one obtains the following equation. T= x T+F(z.r).........(1) where F (z,r) =HWv1/pc (r-r1), if z h/2 = 0, if z >h/2 . In Eq. 1, V- represents the Laplacian operator and 8 is the Dirac delta function. Eq. 1 is the well-known diff-sion equation with a source term and may be applied to a linear system. For example, if the source is moving in the direction of the x axis, then the argument of the delta function is x - 1,. In deriving Eq. 1 the following approximations were made concerning the actual combustion process: (1) all heat transfer is by conduction in a homogeneous medium, (2) the formations bounding the reservoir have the same thermal properties as the reservoir, (3) the combustion fuel is consumed instantaneously as the front arrives, (4) there is a constant fuel concentration

By D. M. Boulin, E. S. Greiner

Single crystals of vanadium were bent at 293" and 77°K to a maximum fiber strain of about 1 pct. Analysis of slip line and etch markings of- crystals deformed at either temperature show the slip planes are {112}. The slip directions at 298° and 77°K, deterwined from the asterism axes of rotation of crystals compressed in a {110} direclion, were (111). Etch pits, associated with dislocations, were observed in the plastically deformed vanadium. There was no evidence of mechanical twinning. THIS paper presents results on single crystals of vanadium plastically deformed by bending and compressing at 298° and 77°K. Bcc metals have been observed to slip on {110}, (1121, and (123) planes while the slip direction has invariably been found to be ( 111) 1 Lindley and smallman2 have studied the deformation intension of polycrystalline vanadium between 298° and 20°K and reported that at and above 77°K the deformation is predominantly by slip, but at 20°K the deformation is associated with twinning. Later, Edington and smallman3 found that single crystals of vanadium compressed in a (111) direction at 77°K deformed by twinning on { 112}( 111) systems. Clough and pavlovic4 have reported that mechanical twins were observed in vanadium loaded by impact at 77°, 173°, and 195°K, respectively. PREPARATION OF SINGLE CRYSTALS The vanadium single crystals were made from commercial vanadium reported to contain 0.03 pct C, 0.03 pct 0, 0.02 pct N, 0.0X* pct Ca, 0.0X pct Si, proximately 0.8 cm diam, 4 cm long and were grown in (100) and (110) directions. A crystal for studies of etch pits was gound to have a face parallel to a {l00} plane by the Bond crystal-orienting technique.7 In order to avoid straining, the crystals were placed on the steel mount with a low-melting organic compound (glycol phthalate) before grinding. Crystals for the bending experiments were ground to have the four side faces parallel to ( 100) planes. The crystals were electropolished8 in 10 pct H2So4 using a current density of about 3 amp per sq cm to remove the strained surface material. The crystals were bent slowly by three-point loading in a stainless-steel jig designed by Sylwestrowicz.9 The end rollers of the jig were 3.8 cm apart. DEFORMATION AT 298°K The bent vanadium crystal, after removal from the jig, had a radius of curvature of 20.4 cm over the 2-cm length close to the center loading roller, where the maximum bending moment occurred. This radius of curvature corresponded to a maximum fiber strain of 0.9 pet. The side faces contained slip bands as shown in Fig. 1. These bands are straight where the strain is high, top and bottom of micrograph, but are curved on either side of the neutral axis in the center. This curvature of the slip bands in the low-stress area may be due to cross slip. The plastically deformed crystal was subsequently electropolished and then electroetched in 10 pct H2SO4 solution, using a current density of 0.25 amp per sq cm. The structure is shown in Fig. 2. The directions of the traces on two adjoining faces were plotted stereo graphically, Fig. 3.* Since there were two sets of

Jan 1, 1968

By F. I. Stalkup

Vapor-liquid phase equilibrium experiments have been conducted in a static equilibrium cell on mixtures of a light, 45 API stock- tank gravity reservoir fluid and a rich hydrocarbon gas containing approximately 55 mole per cent of intermediate hydrocarbons. Both apressure-vs-composition study of the gas and a simulated reservoir fluid, and a multiple-batch contact simulation of the condensing-gas-drive oil recovery process were performed. In the latter experiments equilibrium gas and liquid compositions were analyzed. Also, conventional, "condensing-gas-drive", long-tube displacement experiments of the reservoir fluid and gases of various richness were performed. The results of these experiments could not be satisfactorily interpreted by the conventional pseudo-ternary-diagram representation of multicom-ponent phase behavior. The results seem to be explained better by considering a bubble-point surface and a dew - point surface joined in a plait-point locus. Portions of the plait-point locus cannot be "seen" directly by the rich hydrocarbon gas because of curvature of the dew-point surface. In such a system, continuous injection of the rich gas over stationary reservoir fluid might form a zone of contiguously miscible compositions from pure rich gas to pure reservoir fluid by: (1) saturating the reservoir fluid with injected gas to the bubble-point surface; (2) creating by mass transfer with fresh injected gas a path of contiguously miscible compositions along the bubble - point surface to the plait-point locus; and (3) creating by mass transfer with additional injected gas a path of gas compositions along the dew-point surface up to the point where direct miscibility results between dew-point fluid and the injected rich gas. INTRODUCTION The use of the pseudo-ternary-phase diagram to illustrate miscible displacement phase behavior has been discussed by several authors.5,7 Such a representation of phase behavior is not rigorous, but the ternary diagram nevertheless gives a qualitative picture of what actually occurs in a miscible displacement process. Fig. 1 is a typical illustration of miscible displacement phase behavior by a ternary diagram. The multicomponent hydrocarbon system is divided into three pseudo-components: a light fraction containing methane and nitrogen, an intermediate fraction containing ethane through hexanes plus carbon dioxide, and a heavy fraction containing heptane and heavier components. A two-phase region is bounded by a dew-point curve and a bubble-point curve, which are joined at the critical point. The concept deduced from such a representation for miscible displacement by a condensing-gas-drive process is as follows: a rich gas G, which lies to the right of the limiting tie line through the critical point C, is injected into the reservoir and contacts reservoir fluid L, saturating the reservoir fluid to give bubble-point fluid L1 and equilibrium dew-point gas GI. Continued injection of rich gas changes the composition of the saturated liquid L1 through a series of liquid compositions lying along the bubble-point curve, until the critical composition C is reached, at which point direct miscibility with the rich gas is achieved. Some equilibrium gas with compositions lying along the dew-point curve from G1 to C is also formed in this process. Thus, continuous injection of rich gas forms a

Jan 1, 1966

By R. R. Goddard

By use of the frequency response method with a radioactive tracer, it was possible to determine fluid dispersion and distribution in a natural consolidated and an unconsolidated medium. Measurements were made in a linear flow system at oleic saturations of 69 per cent in the consolidated medium, and 100 per cent in both media. Dispersion and distribution were obtained by measuring the amplitude attenuation and the phase velocity of sinusoidal waves with a dual monitor apparatus. The gamma ray emissions permitted in situ measurements at any distance along the porous samples. One result of importance was that the effective diffusivity increased as the wave length increased. As a consequence, a dispersion coefficient appropriate for the injection of large slugs might exceed the value measured by use of small slugs. Since flow models based solely on fluid velocity and an effective diffusivity coefficient imply that the diffusivity should be independent of frequency, such representations were not adequate for the data of this study. A comparison was made with a capacitance model of porous media with deadend PVs, but even this model was not completely adequate. By using attenuation and phase velocity data, fluid dispersion can be predicted without postulating a differential equation satisfied by the tracer concentration, thereby eliminating the need of a complicated model to represent dispersion. INTRODUCTION The flow of similar miscible fluids through a porous medium can be fairly adequately described by two parameters: the average fluid velocity and the effective diffusivity.1-3 It has been pointed out recently, however, that significant discrepancies exist between this representation and the experimental data.4-7 An improved agreement can be obtained by introducing additional parameters based on the concept of dead-end pores. The purpose of the present investigation was to find out whether the frequency response method could be used to measure the relevant parameters. The method was used in the following form. A stream of fluid was flowed at a constant rate through a sample of porous material and the concentration of a radioactive tracer in the fluid was varied sinusoidally at a fixed frequency. The effects of flow through a porous medium are a decrease in the amplitude of the concentration wave and an increase in the velocity of the peaks of the waves above the average velocity. Attenuation and phase veIocity of the waves were measured as a function of frequency and fluid velocity. The simple two-parameter model implies that the diffusivity should be independent of frequency. Data reported in this paper show that the diffusivity decreases as the frequency increases. Hence, as shown also by many others, the two-parameter model is not completely adequate. Coats and Smith 5 used two additional parameters in their model: the volume of the dead-end pores and the rate of mass transfer between dead-end pores and the flowing stream. Their capacitance model of a porous medium containing some stagnant fluid, to which transfer occurs by molecular diffusion, did not explain the dispersion results of either the present study or of theirs. Instead, the capacitance effect can be better described as the result of extreme velocity variations within the pores of the medium, with transfer between the velocity zones by convection. EXPERIMENTAL PREPARATION OF POROUS MEDIA Data reported here were obtained with a natural Berea sandstone, and with two packings of 20/25 mesh sand. Pertinent information about these media is listed in Table 1. The sandstone core was first sealed with a non-

Jan 1, 1967

By E. Hein, R. A. Dodd

The fatigue softening of prior strain-hardened poly crystalline copper has been determined by measuring changes inflow stress resulting from fatigue treatments. Tensile fatigue does not soften the metal, while the softening due to reversed stress fatigue depends on the extent to which fully reversed stressing is approached. True tensile fatigue is shown to be possible only in the case of long wire specimens. Annealing following fatiguing of strain-hardened metal shows that tensile fatigue is very effective in modifying normal recovery and recrys-tallization. OBSERVATIONS by Ludwik and Scheu,&apos; Kenyon,&apos; Polakowski and Palchoudhuri, Kemsley, and Broom and Ham,596 have shown beyond doubt that strain-hardened metals are softened by reversed-stress fatigue. To some extent the softening might be associated with a rearrangement of dislocations, but the results of Broom and Ham5 on the temperature dependency of the fatigue hardening of annealed copper, and those of McCammon and Rosenberg7 on the partial recovery at 100&apos;C of fatigue-hardened copper suggest that point defects may be involved. Since lattice vacancies are the only species of point defect present in appreciable quantities in thermody-namic equilibrium, most attention has been accorded them in the various theories advanced to explain hardening and softening effects resulting from fatigue. Precise mechanisms remain uncertain, and while some effects may be due to single vacancies, defects arising from vacancy clusters may also contribute to the changes in properties. All types of plastic deformation result in point-defect formation, one frequently invoked formation mechanism involving the nonconservative motion of jogs formed by the intersection of, for example, mixed dislocations. But since fatigue deformation is thought to be a particularly effective way of forming point defects, additional mechanisms peculiar to fatigue must be sought. One possibility is that jogged loops contract during the unloading cycle to give rows of vacancies. A local high-vacancy concentration could conceivably promote polygonization and recovery by climb, and, therefore, could explain the fatigue softening of strain-hardened metals under appropriate conditions of temperature. Conversely, the experiments by Broom and Ham6 on the fatigue hardening of copper single crystals involving subsequent tensile testing of previously fatigued specimens, resulted in the observation of distinctly lowered yield points. This could be due to vacancy atmospheres associated with dislocations, possibly augmented by jogs on dislocations. In addition to the yield-point phenomenon, a post-yield hardening was observed, with a temperature-dependence resembling the friction-hardening of irradiated metals,9 this again suggesting a point-defect mechanism. An important development in this field has been the observation,10 by transmission electron microscopy, of high concentrations of prismatic loops in fatigued aluminum. By analogy with quenched aluminum filmso11 it seems certain that these loops originate in the collapse of vacancy clusters formed during deformation. Metals, such as copper, having a relatively low-stacking fault energy would tend to produce Frank sessile loops (in practice tetrahedral defects with stacking faults on all (111) planes) rather than the glissile prismatic loops observed in aluminum. The manner in which these various defects affect the different aspects of fatigue behavior has not yet been fully investigated. The present work was designed principally to indicate whether tensile fatigue gives rise to hardening and softening effects similar to those associated with reversed stress fatigue, and with the hope of providing additional information on the contribution of point defects to fatigue deformation. Despite the uncertain ty often associated with the interpretation of resistivity data, i.e., the relative contribution of stacking faults and other defects, such measurements are conveniently employed to study point defect pheno-

Jan 1, 1962

By C. G. Dunn, W. W. Martin

Various X ray diffraction techniques have been developed for determining orientations of crystals. Transmission and back-reflection Laue methods1,2,3 in particular have been found to be very useful. In many applications, however, a need still exists for a simplification of the details of analysis so that orientations can be determined more rapidly, and operators with little or no training in crystallography can be easily instructed in the necessary procedures. Filling this need in part is a system of analysis that has been in use for several years in the Metals Section of the Laboratory, General Electric Co., Pittsfield, Mass. This method is an extension of the one of Majima and Togino,4 which uses fifty-five indexed standard transmission Lauemams to cover the entire range of crystal orientations. Greater rapidity in determining the orientation of a crystal is achieved by using a slightly larger set of standard Lauegrams and by systematizing the steps followed. This system of analysis in its present form constitutes the subject matter of the present paper. Although the method uses transmission X ray Laue patterns, many of the operations are applicable to the analysis of back-reflection Lauegrams. Very briefly the method is based on the fact that Bragg and azimuthal angles for two or more identified Laue diffraction spots completely determine the orientation of a crystal, and standard Laue photographs of the Majima and Togino type provide a ready means for identifying Laue spots. After a preliminary analysis, which consists of identifying the pattern in terms of one of the standard patterns, a correctly marked Lauegram is selected to carry out the final analysis. From measured Bragg and azimuthal angles, the normals (poles) of the reflecting planes for the selected Laue spots are located on a stereographic projection and the orient.at.ion of the crystal determined (in terms of the positions of cube poles for example) by a few additional operations on a \I1ulff net. The actual procedure followed will be illustrated in detail after a brief treatment or X ray problems connected with orientation determinations and a discussion of useful principles and techniques. X Ray and Plotting Problems RELATIVE ADVANTAGES OF BACK-REFLECTION AND TRANSMISSION LAUE DIFFRACTION METHODS In the back-reflection Laue method it is easy to make a direct measurement of the tilt of a zone of Laue spots. Specimen thickness also is generally no problem. In the case of thin specimens, however, the time of exposure is less for the transmission Laue method. For example, with silicon ferrite this advantage holds up to a thickness of 0.6 mm if tungsten radiation at 40 kv peak voltage is used. Furthermore, the transmission photograph represents the entire thickness of the crystal whereas the back-reflection picture represents only a surface layer (a thickness of less than 0.05 mm for silicon ferrite), the deeper layers supplying a negligible amount to the diffraction pattern. If a crystal is distorted, the transmission Laue pattern gives more information particularly with regard to the orientation of the crystal and the overall amount of spread in orientation. Finally a 3 1/4 X 4 in. film suffices for transmission photograms; a 4 X 5 in. or 5 X 7 in. film with a central hole is needed for back-reflection patterns Not only is the manipulation of film easier because of the size of film, but

Jan 1, 1950

By S. A. Spachner

An analysis of the powder patterns of the omega transition phase in three binary titanium alloys containing 8 pct Cr, 13 pet Mo, and 15 pet V, respectively, showed that all could be indexed on an orthorhombic unit cell. The unit-cell dimensions were all quite similar. There is evidence for the occurrence of more than one transition phase in Ti-Cr and Ti-V alloys. FOLLOWING the discovery of a new brittle phase in certain titanium-chromium alloys by Frost, Parris, Hirsch, Doig, and Schwartz,&apos; named ? by these investigators, much interest has developed concerning the identification of alloy systems in which this phase exists, kinetics of the transformation in such systems, and the crystal structure of the ? phases appearing. Omega has been found in alloys of titanium-manganese, titanium-molybdenum, titanium-iron,&apos; and titanium-vanadium.&apos; In the present work, a study was made of the powder patterns of the ? phase occurring in alloys of Ti-8Cr, Ti-13Mo and Ti-15V in an effort to obtain a basis of comparison for ? phases appearing in these different alloys. Comparison of Alloys for ?-Phases Two hundred mesh powders of Ti-8Cr, Ti-13Mo and Ti-15V were prepared. A portion of powder sufficient for three x-ray powder specimens was placed in a Vycor tube, evacuated to less than 0.1 µ pressure, filled with argon, and sealed. The tubes were then heated to 900°C, held at this temperature for 30 min, and water-quenched. Following this transformation to the ß phase, the specimens were quenched in lead or solder pots, held at the desired temperature for varying lengths of time and water-quenched. The heat-treatments used and the phases identified are listed in Table I. The intermediate water quench was used in lieu of direct downquenching from 900°C to the bath temperature desired to circumvent the possibility of transformation of the powder specimen from ß to (ß + a) while it was being moved from the homog-enization furnace to the lead bath. To check the possibility that upquenching to the bath temperature might bring into play a different mechanism than downquenching to this temperature, resistivity measurements were compared on Ti-8Cr rod specimens which were transformed isothermally at 400°C by downquenching from the solution-treatment temperature and those which were transformed at 400" C by upquenching ß specimens from room temperature. The results are shown in Fig. 1. No difference in transformation mechanism was noted. It soon became apparent that sufficiently detailed Debye-Scherrer photograms of the ? phase in the alloys which were to be used could not be obtained by the use of copper radiation. Although satisfactory photograms of ß and ß + a phases were obtained with this radiation, the ? phase appeared to exhibit mild fluorescence, making interplanar spacing computation virtually impossible. Molybdenum radiation appeared to offer promise in cutting down this fluorescent effect, the mass absorption of titanium for molybdenum radiation being 23.7 in contrast to 204 for copper radiation. The reduction in the accuracy in determining the location of the photo-gram lines caused by the shorter wave length of molybdenum characteristic radiation did not appear to be a significant factor. Utilizing a camera of 57.3 mm radius, best results were obtained for exposure times ranging between 30 and 40 hr. Tube potential

Jan 1, 1959

By S. Kado, G. Derge, L. Yang

Self-diffusion coefficients of silver in molten silver have been measured by means of the capillary-reservoir method in the temperature range 1002" to 1105°C. The results can be .represented by the equation D = (7.10 i 0.06) X 10-4 exp [(—8150 ± 1130)/RT]. The heat of activation agrees within the limit of experimental uncertainty with that for the viscous flow. The validity of the Eyring and the Stokes-Einstein equations are examined on the basis of the self-diffusion coefficients obtained and the known viscosity data of molten silver. MEASUREMENT of the self-diffusion coefficient of silver in molten silver was made in the temperature range 1275° to 1378°K, using the capillary-reservoir method and &"&apos; as the radioactive tracer. The experimental arrangement is shown in Fig. 1. Silver of 99.99 pct purity (fine silver), was melted and degassed in vacuum in a graphite crucible situated inside a McDanel vacuum jacket. The crucible (4 in. tall and 1 in. ID) was protected both at the top and at the bottom with graphite shields and contained about 220 g of silver. The sample holder was a piece of graphite rod (1 in. long and 1/2 in. diam) with 4 capillaries drilled longitudinally into it. The holder was screwed onto a long graphite rod (12 in. long and 74 in. diam) which was connected to a steel disk hanging on a nylon string through a glass pulley. The steel disk kept the sample holder at the center of the McDanel tube and was heavy enough to overcome the buoyancy when the holder was lowered into the molten silver. By turning a handle connected to the pulley through a tapered glass joint, it was possible to raise or lower the sample holder without breaking the vacuum. Two such arrangements were constructed, sitting side by side in 2 Kanthal furnaces. One with non-radioactive silver in its crucible was used for the diffusion run and the other with radioactive silver in its crucible was used for filling the capillaries. To fill the capillaries with radioactive silver, the sample holder was degassed first and then lowered into the radioactive molten silver in vacuum. Purified argon gas was then admitted into the system to push the liquid silver into the capillaries. After cooling in argon, the filled capillaries were polished on emery paper to expose the top of the rod and used immediately as samples for the diffusion run which was carried out at the same temperature as that used for filling the capillaries. During the diffusion run, the samples were degassed in vacuum and lowered slowly into the nonradioactive molten silver before purified argon was admitted into the system. After a predetermined period of time, the samples were raised out of the melt and cooled in argon. The temperature of the melt was measured before and after the run with a chromel-alumel thermocouple inside a McDanel protection tube. Another chromel-alumel thermocouple attached to the outside wall of the McDanel vacuum jacket was used to indicate any fluctuation in the temperature of the furnace during the run, which was found to be less than ± 2°C for the longest run made (93 min). The temperature gradient inside the molten silver was found to be negligible. No significant difference was observed in the results obtained whether the melt was stagnant during the run or was stirred by raising and lowering the sample holder slowly a few times a minute for a distance of about 1/4 in. inside the melt.

Jan 1, 1959

By C. R. Clark, G. Swift, D. S. Roberts

The purpose of this investigation was to measure PVT behavior of various types and combinations of heavy hydrocarbon components from the paraffinic, naphthenic and aromatic classes where the relative proportions Of the various components were selected to approximate those of natural gas or gas condensate systems. Synthetic mixtures were used so that the compositions Of the various components could be measured accurately. n-Heptane, methylcyclohexane and methylbenzene were used to represent the paraffinic, naphthenic and aromatic components of the heavy fraction. In the mixtures studied, the heavy fraction composition was held constant at O. O5-mole lraction, the balance being methane except for one mixture where 0.10-mo1e fraction of an intermediate component, propane, was added. The PVT data for the mixtures were determined in a variable-volume, constant-mass apparatus at psuedo-reducedtemperatures from 1.84 to 2.00, over a pseudo-reduced pressure range from 2.3 to 12.0. The experimental results showed that, regardless of the type of heavy material (paraffinic, naphthenic, aromatic, or combinations thereof) mixed with methane or methane and propane, the compressibility factors at equal values of pseudo-reduced temperature and pressure varied by less than 2.2 percent. INTRODUCTION PVT data is used for natural gas and gas condensate fluids in determining reserves of reservoirs and performance of wells, in metering produced fluids, and in recombining samples for laboratory studies. While there are vast amounts of PVT data reported for natural gas and gas condensate systems from which useful correlations have been developed, &apos; the compositional analyses for these systems and the resultant correlations typically were made with components analyzed through some arbitrary carbon number, usually C6, with the residue reported as a lumped "heavy" fraction. The heavy fraction was stoichiometrically recombined on the basis of an apparent molecular weight to give the final compositional analysis. It is virtually impossible to make a systematic analysis of the effect that variation of the relative amounts of paraffinic, naphthenic and aromatic constituents of the heavy fraction of natural systems might have on PVT behavior. Because there is considerable latitude in the relative amounts of these constituents, one speaks of crudes or condensate liquids as being "paraffin base", etc. It is of interest to determine if changes in the relative amounts of these three types of hydrocarbons in the heavy fraction cause significant changes in PVT behavior. If so, steps should be taken to describe better the nature of the heavy fraction in PVT correlations. If not, more confidence can be placed in the correlations presently employed. DESIGN OF THE EXPERIMENTAL INVESTIGATION We attempted to determine if changes in the base of the heavy fraction would cause significant changes in the PVT behavior of gas or gas condensate fluids. Synthetic mixtures were used to enable us to systematically vary the base of the heavy fraction and to analyze accurately the fluids. We found that the heavy fraction of naturally occurring condensate systems seldom exceeds 0.05-mole fraction. Thus, the mole fraction of the heavy fraction in the synthetic systems studied was set arbitrarily at 0.05, to maximize whatever deviations in PVT behavior that might occur. Further, we judged that since the C7 hydrocarbons normally are present in greater quantities than higher carbon number hydrocarbons in naturally occurring systems, the use of n-heptane, methyl cyclohexane, and methylbenzene to represent the paraffinic, naphthenic, and aromatic species in the heavy fraction would be most appropriate. Finally, to enable us to compare our

Jan 1, 1970

By M. King Hubbert, David G. Willis

A theoretical examination of the fracturing of rocks by means of pressure applied in boreholes leads to the conclusion that, regardless of whether the fracturing fluid be of the penetrating or non-penetrating type, the fractures produced should be approximately perpendicular to the axis of least stress. The general state of stress underground is that in which the three principal stresses are unequal. For tectonically relaxed areas characterized by normal faulting, the least stress should be horizontal; the fractures produced should be vertical with the injection pressure less than that of the overburden. In areas of active tectonic compression, the least stress should be vertical and equal to the pressure of the overburden; the fractures should be horizontal with injection pressures equal to or greater than the pressure of the overburden. Horizontal fractures cannot be produced by hydraulic pressures less than the total pressure of the overburden. These conclusions are compatible with field experience in fracturing and with the results of laboratory experimentation. INTRODUCTION The hydraulic-fracturing technique of well stimulation is one of the major developments in petroleum engineering of the last decade. The technique was introduced to the petroleum industry in a paper by J. B. Clark,&apos; of the Stanolind Oil and Gas Co. in 1948, and since then its use has progressively expanded so that by the end of 1955 more than 100,000 individual treatments had been performed. The technique itself is mechanically related to three other phenomena concerning which ah extensive literature had previously developed. These are: (1) pressure parting in water injection wells in secondary-recovery operations, (2) lost circulation during drilling, and (3) the breakdown of formations during squeeze-cementing operations, all of which appear to involve the formation of open fractures by pressure applied in a wellbore. The most popular interpretation of this mechanism has been that the pressure had parted the formation along a bedding plane and lifted the overburden, notwithstanding the fact that in the great majority of cases where pressures were known they were significantly less than those due to the total weight of the overburden as determined from its density. Prior to 1948, this prevalent opinion had already been queried by Dickey and Andresen,2 in a study of pressure parting; and by Walker,"&apos; who, in studies of squeeze cementing, pointed out that the pressures required were mostly less than those of the overburden, and inferred that the fractures should be vertical. J. B. Clark,&apos; in his paper introducing hydraulic fracturing, and later Howard and Fast," and Scott, Bearden, and Howard," also of Stanolind, postulated that the entire weight of the overburden need not be lifted in producing horizontal fractures, but that it was only necessary to- lift an "effective overburden," requiring a correspondingly lower pressure. Hubbert,7 in discussing the paper by Scott and associates, pointed out that the normal state of stress underground is one of unequal principal stresses; and in tectonically relaxed areas, characterized by normal faults, the least stress should be horizontal. Therefore, in most cases, fracturing should be possible with pressure less than that of the overburden and, moreover, such fractures should be vertical. Harrison, Kieschnick, and McGuire,8 also on the expectation that the least principal stress should be horizontal, argued strongly in favor of vertical fracturing. Scott, Bearden, and Howard6 observed that, when

Jan 1, 1958

By B. A. Eaton, R. H. Jacoby

This paper presents the depletion-performance correlations developed using data from PVT studies and well-completion tests of 27 rich gas-condensate and volatile-oil reservoir fluids. The PVT behavior for each fluid war determined experimentally in the laboratory, and the depletion performance of each fluid was then calculated. Well-completion test data consisting of reservoir pressure and temperature, initial total gas-oil ratio, and stock-tank oil gravity were used with the depletion-performance data to develop general performance correlations. Three correlations are presented. The first equation shows the empirical relation of gas in place per barrel of hydrocarbon pore space with reservoir pressure and temperature, and initial total gas-oil ratio. The second equation is the correlation of stock-tank oil in place per barrel of hydrocarbon pore space. The third equation relates stock-tank oil production (to 500-psia depletion pressure) with pressure, temperature and oil gravity. All three correlations are also presented in convenient graphical form. Gas production to 500-psia depletion pressure is approximately 92.6 per cent of the gas in place for each fluid, so no correlation was developed for gas production. INTRODUCTION The rate of discovery of shallow, low-pressure and low-temperature oil reservoirs in the United States has been declining in recent years. For this reason, the search for oil has gone to greater depths where high pressures and temperatures are encountered. A high-pressure and high-temperature reservoir is the environment in which many rich gas condensates and highly volatile oils are found. Because of this trend, the performance prediction of such reservoirs has become an important task of the reservoir engineer. The need and usefulness of a performance correlation based on field data that are available from the usual well-completion tests have previously been established. These earlier attempts have shown that the phase behavior of rich gas-condensate systems and volatile-oil systems can be correlated with fluid properties, pressure and temperature. However, very little information on gas-condensate depletion performance5 was available at the time of these earlier attempts. The availability of more recent data has made possible the development of an improved correlation. The data, as listed in Tables I and 2, are for 25 gas-condensate and two volatile-oil systems that were studied. The problem was to correlate the data for in-place fluids and the production data with the initial total gas-oil ratio, initial reservoir pressure and temperature, and stock-tank oil gravity. These correlations were obtained by multiple regression analysis, whereby the data were fitted to an equation by the method of least squared error. BASIS OF THE CORRELATIONS 1. The data used in the development of these correlations were obtained from depletion-performance calculations6 and well-test or production measurements. 2. All of the independent variables used in the correlations are available from the usual well-test completion data. 3. The reservoir volume considered is 1 bbl of hydrocarbon pore space (HCPS). 4. The gas-oil ratio used is the total standard cubic feet of gas (at 14.7 psia, 60F) coming off the entire separator train per barrel of stock-tank oil. This minimizes the effect of separator conditions which might vary from system to system. 5. The correlated pressures are the actual reservoir pressures which might or might not be the saturation pressure of the reservoir fluid.

Jan 1, 1966