Search Documents

By V. A. Josendal, J. W. Wilson, B. B. Sandiford

Two radioactive tracers have been tested as a means of determining core saturation in multiphase flow studies. Cesium chloride was tried as a water-phase tracer, but complications in its use in low permeability cores resulted from sorption of cesium by the core or water-wet pads. IodoI3'ben-zene proved very satisfactory as an oil-phase tracer. The synthesis of iodobenzene from the sodium iodide as received from Oak Ridge is simple and direct. The tracer is insoluble in water and there was no evidence of sorption by any of the core materials used. use of the method to determine saturation profiles during capillary and dynamic desaturations and relative permeability measurements on oil-water and oil-gas systems is described. Comparisons of the dynamic and capillary methods of relative permeability determination were made using the tracer to check core saturation and saturation distribution. Other experiments are also described in which mobility of the oil phase at various saturations was measured by displacing labeled oil by flowing inactive oil. Similar experiments were made using water labeled with cesium 134. INTRODUCTION To be fundamentally sound. any laboratory method of determining relative permeability must meet, among others, the following requirements: (1) the core saturation between the pressure taps must be uniform, and (2) there must be uniform pressure difference between the phases in the region between the pressure taps. In practice it may eventually be shown that appreciable departure from either or both of these conditions may be permitted without introducing sensible error. but the magnitude of such error remains to be established. There is need then for methods of saturation determina- tion which will determine the saturation profile in a core as well as the overall average saturation given by the gravimetric or material balance methods usually employed. Methods which have received consideration include resistivity, X-ray absorption, gamma ray absorption, neutron diffraction, and radioactive tracers. The resistivity method has use in the determination of profile, but needs checking by independent means.' The X-ray method has been used successfully, but requires elaborate equipment and calibration.23 4 At present gamma ray absorption is practical only for very large cores. The neutron methodo does not appear adaptable to measurement of saturation variations in short cores since it is a scattering method. Russell, Morgan and Muskat' employed radiovanadium in a study of the mobility of interstitial water. Coomber and Tiratsook used radioiodine as an oil-phase tracer and measured profiles in unconsolidated sand packs. ADVANTAGES OF RADIOACTIVITY METHOD A thorough discussion of the theory of radioactive tracers and the technique of using them to study the movement of fluids in sands is given by Coomber and Tiratsoos and need not be detailed here. The method requires less equipment than the X-ray method; the counting problem is similar, but the generation and regulation of the radiation, which is a major problem in the X-ray method, is not required in the radioactivity method. In the X-ray method it is customary to add up to 20 per cent of absorber, usually an iodine compound, to the phase to be labeled. while in the radioactivity method a mere trace is sufficient. A possible disadvantage of the radioactivity method is that a disproportionate amount of the activity comes from the portion of the core nearest the counter, whereas the X-ray gives a true average saturation in the region traversed by the beam. 011 the other hand, this characteristic of the radioactivity method renders it peculiarly adaptable to study of certain types of radial variations in saturation. As with the X-ray method, a tracer may be added to either the oil or water-phase. An oil-phase tracer is more generally useful. however. since it permits work on oil and gas in the

Jan 1, 1952

By G. W. Preckshot, J. W. Gorman

MOLTEN metals offer an excellent medium for the study of molecular diffusion and interphase transfer. In the absence of intermetallic compound formation, solutions of molten metals are solutions of elements. Therefore, complicating factors such as molecular structure, dissociation, association, polarization, and so on, are generally absent. Further, metals remain in the liquid state over a wide range of temperature. Thus, the effect of temperature on transport processes can be studied in more detail. Although some data are available for the diffusion of metals in the molten state at high temperatures,"""".'!' the most useful and accurate data are those for the diffusion of various elements in mercury at room temperature. The effective radius of diffusion for the various elements in mercury may be calculated from the Stokes-Einstein relation.'-These calculated radii are compared with the atomic and ionic radii calculated from X-ray data on crystals." The effective radii of diffusion of the alkali and alkali-earth metals correspond to those of the neutral atom; those of cadmium, silver, lead, zinc, thallium, bismuth, and tin correspond to ionic radii; and those of copper and gold indicate larger radii due to association with mercury or more likely, faulty diffusion data. Independent evidence"' supports the notion that alkali metals are uncharged in amalgams. The concept of metals moving free of their conductance electrons in the liquid state has been discussed by Eyring, et al,'" in connection with studies on the viscosity of pure molten metals. Considering the approximate nature of the tabulated atomic and ionic radii and the variance in the diffusion measurements, the application of the Stokes-Einstein equation to the diffusion of metals in mercury gives gratifying results. It is noted that a number of these metals have article radii eaual to or less than those of the solvent mercury.".'*,"' Soba1,'" sing the inaccurate Roberts-Austin20 data, indicated that the effective radius of diffusion might well be a function of temperature. Additionally in studies of mass transfer between phases, many conflicting opinions have been expressed concerning the assumption of equilibrium at the interface." ,","," The results of the present work on the diffusion of solid copper in molten lead throws light on the tempera- ture variation of the diffusion radius as well as the extent of the interfacial resistance. The theoretical background and experimental procedure are presented here in detail. Results on other systems will be presented in subsequent papers. Nomenclature The following nomenclature is used in the paper: A—cross-sectional area of diffusion column, sq cm C, C,—concentration of solution and saturated solution respectively, g per cc D,D'—-diffusivity, sq cm per sec e—Naperian base h—ratio, k/D k—mass-transfer coefficient, cm per sec L—diffusion column length, cm n—series index q—flux, g per sq cm-sec r—radius, cm or A R—-gas constant t—time, sec T—temperature, K V—volume, cc w—weight of copper-lead alloy on copper cylinder WT—-total copper transferred to lead diffusion, column, g Z—distance from top of diffusion column, cm 2'—distance from copper-lead interface, cm (2' = L-2) u,,—roots of diffusion equation Mathematical Apparatus The model shown in Fig. 1 applies to the diffusion of solid copper into molten lead. Here Fick's first law may be written where all terms are defined in the nomenclature. It is assumed that the volume of the lead column is constant. This is justified since experimental densities compared favorably with calculated densities based on perfect interstitial mixing. Thus there is no counter diffusion of lead. It is clear that 2 in Equation [I] should be measured relative to the interface which moves relative to the diffusion cell but not to the liquid phase. Hence, the frame of reference is the plane of the copper-lead interface. The diffusivity calculated at constant volume, D", is that defined by Hartly and Crank" and is designated herein as D. No Interfacial Resistance—The two situations of the presence and absence of interfacial resistance will be treated. The simplest is the latter which re-

Jan 1, 1959

By G. L. F. Powell, L. M. Hogan

Samples of silver and Ag-O alloy, 0.12 wl pet, have been undercooled to a maximum of 250°C by melting in a slag of commercial soda-lime glass. Grain refinement occurred in undercooled silver samples whet the degree of undercooling exceeded a critical value which varied from 153° to 175°C, depending on the melting conditions. In under cooled Ag-0 samples, the grain structure was fine and equiaxed at degrees of undercooling larger than 50oC. The grain refinement in both silver and Ag-0 alloy samples was the result of recrystallization during or immediately following freezing. When the oxygen content was increased, the degree of undercooling at which recrys-tallization occurred decreased. INVESTIGATIONS of the grain structure of strongly undercooled melts of nickel and cobalt1-4 have revealed a change in room-temperature grain size as a function of undercooling. At large degrees of undercooling the grain size was fine, but samples undercooled by smaller amounts exhibited a much coarser grain structure. The reported undercooling at which this grain size transition occurred in nickel varied between 140° and 175'C undercooling. Walker1 attributed this grain size change to an enhanced nuclea-tion rate. Cavitation at a melt-solid interface was con sidered to generate a high-pressure wave. This, in turn, produced nucleation in the liquid as a result of an elevated freezing point increasing the undercooling in the melt. A similar grain size transition was observed in undercooled silver between 133° and 153°C undercooling.5 The grain size transition in undercooled silver was found to be dependent on oxygen con tent. More recently, the authors5 showed that a simila transition occurred in an undercooled Cu-O alloy, =0.08 pet, but not in oxygen-free copper undercooled more than 200°C. The transition was attributed to recrystallization of the solidified grains after freezing; the greater the degree of undercooling, the more complete the recrystallization. In view of this effect of oxygen content on grain size transition, additional undercooling experiments were carried out with silver. This paper reports the results of these studies on silver and Ag-O alloys undercooled more than 50°C EXPERIMENTAL 1) Materials. The silver was supplied by Matthey Garrett Pty., Ltd., as fine granulate, silver mini' mum 99.9 pet, and contained the trace impurities shown in Table I. The silver originated from two different refineries resulting in the difference in impurity content shown in Table I. However, the variation in composition had no discernible effect on the undercooling behavior. Samples of the silver were melted in an open-ended, vertical, cylindrical resistance furnace, wound with Kantha] wire, the temperature of which was adjusted by means of a variable transformer, 2) Melting and Undercooling. Bulk samples of silver were undercooled by preoxidation and removal of oxidized impurities in a glass slag, as previously described,5 but special precautions were necessary to allow comparison between oxygen-free silver and a Ag-O alloy. Samples free of oxygen were prepared by first melting weights of granulate varying from 200 to 400 g in clean vitreous silica crucibles in air for approximately 15 min. A sample was frozen and a complete glass cover formed over the top surface by adding granulated glass rod. The sample was then melted and frozen several times until no oxygen bubbles appeared in the glass slag. Subsequent thermal analysis indicated that the oxygen content was negligible. The glass acted as an efficient barrier to absorption of oxygen from the air. Ag-O alloys were prepared by melting silver in silica crucibles with only a partial cover of glass, so that the top surface of the melt was in contact with air. The silver was held molten in air for several hours at 1000° to 1050°C, in the expectation that the oxygen in solution would reach equilibrium with atmospheric oxygen. At T - 1000°C the equilibrium oxygen content was calculated as 0.12 wt pet O, using Sieverts law and Eq, [l], derived by Mizikar et a!.7 from the data of Sieverts and Hagenacker8 for 1 atm of oxygen:

Jan 1, 1970

By B. H. Caudle, W. J. Bernard

Factors which influence the success or failure of a waterflood can seldom be determined in the laboratory. For this reason pilot waterfloods are initiated in a repreventative portion of the oil reservoir in question. For a pilot flood to predict quantitatively the recovery to be expected in a field-wide waterflood operation, the pilot area must behave as though it were confined (surrounded by similar areas). In this study, laboratory fluid-flow models were used to determine the simplest pilot pattern, for particular conditions of mobility ratio and initial gas saturation, that would behave as though it were confined. Pilot patterns studied ranged in complexity from a single inverted five-spot to a grouping of nine regular five-spots. Only the innermost producing well in each pattern was studied. Model results showed that the optimum number of wells in the pattern depends upon the oil-water mobility ratio and the expected oil-bank size. Unfavorable mobility ratios will, in general, require more wells in the pilot pattern than will favorable mobility ratios. Pilot patterns in reservoirs which contain a dispersed, flowable, free gas saturation will require fewer wells than for the under-saturated case. The single inverted five-spot pattern was found to be unsatisfactory for predicting behavior of fully developed waterfloods. In particular, it is possible that, in reservoirs which contain a flowable, dispersed gas phase, the oil bank will never be observed at the producers due to the large amounts of free gas which continue to be produced with the oil. INTRODUCTION One method which has been used to predict the performance of a waterflood is the pilot flood. The pilot waterflood is a flood which involves only a small cluster of the reservoir wells and is located in a small, representative portion of the reservoir. The object is that oil produced from the pilot can, in some way, be related to the oil recovery to be expected from a field-wide expansion of the waterflood. However, these field pilot waterfloods have often been unreliable in the prediction of oil recovery in a fully developed waterflood. This unreliability has also been demonstrated in several laboratory studies of pilot floods. Some of the investigators have shown that there are situations in which the pilot flood oil production is far too optimistic with respect to the oil recovery in the fully de- veloped flood. Others4-G have shown that the pilot results can also be pessimistic, especially if the pilot waterflood is initiated in an oil reservoir which has been depleted by primary recovery and is at very low pressure. The major reason for this unreliability of pilot water-floods is the migration of fluids into or out of the pilot area. By the well-known method of images, if straight lines can be drawn to represent vertical planes of symmetry in a porous medium which contains pressure sources and sinks (injectors and producers), then these lines are invariant streamlines, or lines across which there is no potential gradient, and therefore no flow. In an actual reservoir, these lines of symmetry can never be established exactly because of reservoir inhomogeneities and irregular reservoir boundaries. However, if the reservoir is relatively large and contains wells in repetitive patterns, these lines of symmetry are commonly assumed to exist for the pattern units sufficiently far removed from the reservoir boundary. Lines of symmetry for the five-spot injection pattern are shown in Fig. 1. Each five-spot unit in this figure can be considered confined with respect to flow across its boundary. In pilot floods this is not the case. The lines of symmetry for the pilot patterns investigated in this study are shown in Fig. 2. It is obvious that the fluid within these pilots is not confined and is therefore able to migrate into or out of the pilot area. Intuitively, one can see that, if more wells are added to the pilot, the innermost unit tends to behave more and more like the confined pattern. However, there is a practical limit to the number of wells which should be placed in the pilot. This limit is usually determined by economic factors. It was the purpose of this study to use laboratory fluid-flow models to determine which of the previously mentioned pilot patterns will force the innermost producing well to behave as it would in a fully developed waterflood. Since fluid migration is influenced by initial saturation conditions and the mobility ratio, these factors were included in the study. The ultimate objective of this study was to develop data which would allow the operator to choose a pilot pattern and operating conditions that will yield a production history which can be applied directly as an estimate of the performance of each production well of the fully developed waterflood. BASIS FOR THE STUDY The basic problem of field pilot floods is the migration of the reservoir fluids into or out of the pilot area. This problem has been the subject of previously reported model studies on pilot floods. These studies have been concerned mainly with the development of arbitrary "correction factors" to be applied to the simple, unconfined pilot systems such as the single five-spot. The correction factors were intended to adjust the production history of the un-

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 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

Jan 6, 1976

By H. I. Aaronson, C. Laird

The kinetics of thickening and of lengthening of ?' plates in an Al-3.93 pct Cu alloy in the temperature range 203" to 300" C were determined by means of transmission electron microscopy. The rate of thickening was found to be less than that allowed by volume diffusion control at all temperatures, by amounts which increased with decreasing temperature, in agreement with the predictions of a general theory of precipitate morphology.1 Thickening was treated on the basis of the ledge mechanism. Ledges were deduced to spread across the broad faces of ?' plates at volume dzjrfusion-controlled rates, as anticipated from the disordered structure of their edges. Lengthening of 8' plates, on the other hand, took Place more rapidly than allowed by volume dzjrfusion. This occurred despite clear morPhological evidence of a bmrier to growth at the edges of these plates. It was concluded that the misfit dislocation structure comprising the barrier requires that lengthening take place by a jog mechanism. The tnisfit dislocations, however, also serve as diffusion short circuits, and allow high overall lengthening rates to be achieved. In Part I' it was shown that, within the range of aging temperatures and times studied, the broad faces of 8' plates formed in Al-4 pct Cu are fully coherent with the a, matrix. Virtually .all of the dislocations present in these faces were found to have developed as a result of plastic deformation in the a phase. Such dislocations are thus "intruders", rather than the more usual misfit-compensating variety. The edges of 8' plates were confirmed, by extension of the earlier studies of Mat-suura and Koda,3 to be made up of edge-type misfit dislocations, in sessile orientation with respect to lengthening of the plates. These interfacial structures should cause 8' plates to thicken and to lengthen at rates less than those allowed under the condition of volume diffusion control, such as would be expected if the interphase boundaries had disordered structures.' The narrow width of 8' plates, the reproducible crystallography of their broad faces, and the appearance of these plates in cross section as octagons rather than as circular discs2 provide qualitative support for these deductions. The present study of the rate of thickening and the rate of lengthening of 8' plates was undertaken in order to examine them on a quantitative basis. I) THICKENING KINETICS OF THE BROAD FACES OF?' PLATES A) Literature Review. The measurements now available on the thickening kinetics of single-phase precipitate plates consist of one plot of the thickening of a proeutectoid ferrite plate in an Fe-C alloy,' showing (as predicted) thickening rates less than those allowed by volume diffusion control. B) Experimental Procedure. Details of the preparation of the 4-3.93 pct Cu alloy used in this study have been previously reported.4 As in Part 1,' transmission electron microscopy was the observational tool employed. A general description of the apparatus and procedures of the electron microscopy studies is given in Section I of Part I. In thin foils, 0' plates tend to form at and parallel to the foil surface.' A direct investigation of the thickening process by means of hot-stage transmission electron microscopy was therefore not feasible. It was thus necessary to use the conventional method of aging individual bulk specimens for a wide range of different times at the various temperatures studied. In each specimen, the thicknesses of a number of plates were measured. Since thin foils prepared from "bulk-aged" material contain a large proportion of grains with orientations near (001) , it was relatively easy to find, near the edges of the foils, the characteristic multifold patterns of intersecting extinction contours which indicate regions where the foil is exactly at an (001) orientation. The thicknesses of large numbers of plates were measured along the (200) branches of the "stars" so that the 8' plates were precisely parallel to the optical axis of the microscope. Wherever possible, intersecting extinction contours were adjusted with the parameter s > 0 to improve the visibility of the plates in bright-field illumination. These precautions, in combination with taking the measurements at the thinnest parts of the foils, minimized the errors in the measurement of the thickness of the plates resulting from inexact parallelism to the electron beam. Since the plates were very thin, it was not easy to measure their thickness on the photographs. The techniques of enlargement and of microdensitometry were employed to minimize errors from this part of the measurement. A further source of possible error, that the plates can appear thicker because of contrast associated with mismatch normal to the plane of the plate, was also considered. The images of the plates were usually thinner than those of dislocations, however, and no anomalous changes in apparent plate thickness were observed when regions of foil containing plates were tilted through various diffracting conditions. Any error from this cause must therefore be small. Other sources contributing errors were: a) the microdensitometer traces per se and the subjective estimates of their peak limits, and b) slight fluctuations in magnification associated with small changes in the current of the objective lens of the electron microscope. The overall error probably amounted to no more than 5 to 10 pct. In order to obtain readily interpretable data on thickening kinetics, it is essential that the diffusion fields of adjacent ?' plates not be allowed to overlap. Calculations'-' showed that this condition is definitely not ful-

Jan 1, 1969

By P. E. Baker

An experimental study of heat flow in steam flooding was carried out with steam displacing water in a plane-radial fluid-flow model. Temperature distributions in the model reservoir, overburden, and substratum were measured at frequent intervals during flooding by means of a fixed array of thermocouples. Heat losses to overburden and substratum and the division of heat between the steam and hot-water zones in the reservoir were calculated from the temperature data by performing numerical integrations over the appropriate volumes. Temperature profiles and heat distribution results are presented. Some results were (1) the fraction of injected heat that is lost to overburden and substratum, when expressed as a function of time, did not depend on injection rate; (2) a significant portion of the injected heat was contained in the hot-water zone ahead of and underlying the steam front in the reservoir. The division of heat between the steam and hot-water zones did depend on injection rate; and (3) considerable gravity override was observed. The experimental results are compared with those of several published theoretical studies of heat transfer in hot-fluid injection; approximate agreement on heat losses is found with some of the most idealized theories. A valid comparison cannot be made in regard to steam us hot-water zone; basic interpretation of the hot-water zone, in terms of a vertical steam front, is clouded by gravity override in the experiments. INTRODUCTION The experimental study reported here primarily concerns two problems of heat transfer in steam flooding that have economic and engineering importance. These are (1) the fraction of injected heat lost to the overburden and substratum, and (2) the division of the remaining heat between a zone containing steam and a zone of hot water at lower-than-boiling temperature. The volume of the steamed region, which has a direct effect on oil recovery, can be calculated readily from these results. Several valuable theoretical studies have been published on this problem, but no experimental tests of the theories have previously appeared. Tests were needed because the effects of the necessary simplifications in the theories could not be determined otherwise. The basic, untested theoretical problem is the effect of "decoupling" heat and mass transfer, and the resulting inability to include the effects of heat transfer and condensation on fluid flow. The theoretical problem solved so far has been a heat transfer problem in which fluid is present as a heat carrier and flows in a stipulated manner, either linear or plane-radial. The simplifications that have sometimes been made in regard to thermal conductivity by, for example, Marx and Langenheim,l Lauwerier2 and Thomas3 apparently do not have an important effect on heat loss calculations, although the results of the different methods disagree to a certain extent, as shown by Spillette4 and by Ramey.5 A recent paper by the author6 compared the results of experiments in hot-water flooding with several theoretical results and showed a rather poor agreement. It will be seen that the experimental heat loss results for steam flooding, however, show acceptable agreement. These comparisons are discussed in a later section. EXPERIMENTAL APPARATUS AND PROCEDURE The system studied was one in which a sand pack, initially water saturated and at a uniform temperature, was flooded with steam at a constant rate and temperature. The temperature distribution in the "reservoir" and adjacent "strata" was measured with an array of thermocouples, and heat losses were determined from these measurements. The sand pack contained no oil because the only concern of the experiments was heat flow, and it was important to have the flow pattern as simple

Jan 1, 1970

By W. A. Klikoff, I. Fatt

The concept of fractional wet wattability is examined. Fractional water wettability of a reservoir rock is defined as the fraction of the internal surface urea that is in contact with water. Capillary pressure and relalive permeability of unconsolidated sand are shown to be functions of fractional wettability. INTRODUCTION The petroleum industry has long recognized that wettability of reservoir rock has an important effect on multiphase flow of oil, water and gas through reservoirs. As early as 1928 the American Petroleum Institute sponsored a study of wettability as part of API Project 27 at the U. of Michigan.' Despite 30 years of research, there is still little exact knowledge of the wettability of reservoir rocks. There are two parts to the wettability problem. After agreeing to a uniform nomenclature in regard to wettability,' the first question to be answered is, "What is the in situ wettability of a given reservoir rock?" If this can he answered the next question is, "What part does wettability play in determining the characteristics of multiphase fluid flow through the rock?" This paper represents an oblique attack on the problem of wettability. No attempt is made here to answer the basic question of wettability in situ. instead the consequences of the concept of fractional wettability are examined. Multiphase flow in sandpacks is shown to he highly influenced by fractional wettability. Jennings' has given 3 definition of wettability and the other terms used in discussing wettability. These terms must be applied to the physical situation existing In reservoir rock. A survey of the pertinent literature from 1928 to 1956 indicates that the concept of a contact angle was applied to reservoir rock in the same way it would be applied to a flat, homogeneous surface. Attempts were made to state quantitatively the wettability of a reservoir rock in terms of a contact angle which was presumably constant at all points on the very rough and heterogeneous interior surface of a porous rock. Calhoun, et al,3-6 prepared synthetic consolidated and un-consolidated porous media in which they claimed there was a known uniform contact angle. They then showed the effects on the capillary pressure and relative permeability characteristics of varying this angle. The API Project 47 at the U. of Texas' and others' have made extensive studies of an indirect approach to the contact angle through the use of heat of wetting data. Even if successful. however, this approach also states the wettability of porous rock in terms of a contact angle which is uniform over the entirc surface. If the angle varies from one part to another on the internal surface, there is no way of determining from the measurements the area distribution of contact angles. In 1956 Brown and Fatt5 suggested that the concept of a contact angle, as applied to reservoir rock, be abandoned. This suggestion was made because it is known that the internal surface of most reservoir rocks is composed of many different minerals, cach with a different surface chemistry and a different capacity to adsorh surface active materials from reservoir fluids. Furthermore, the operation of a contact angle in determining the form of a fluid-fluid interface is difficult to picture in the very complex geometry of a pore. Brown and Fatt proposed that the wettability of reservoir rock be stated in terms of the fractional internal surface area that is in contact with water or oil. All surfaces on which there is water are called water-wet; surfaces on which there is oil are called oil-wet. The fractional water wettability is then stated as a number which represents the fraction of the internal surface that is in contact with water. A symmetrical statement can be made for the fractional oil wettability. The concept of a fractional wettability as previously stated has in its favor the recognition of the heterogeneous mineral composition of most reservoir rocks. Another point in its favor is that fractional wettability can be measured quantitatively with relative ease. Hol-brook and Bernard10 se a simple dye adsorption test to obtain fractional wettability of reservoir rocks. Amott11 uses a combination of imbibition and displacement to arrive at a wettability index of reservoir rocks which seems related to fractional wettability in the range 0.25 to 0.75 fractional water wettability. Jennings" has shown the changes in relative permeability that take place when a porous material is changed from unity to zero fractional water wettability. He also shows that reservoir rocks in their natural state, but at room temperature and atmospheric pressure, have relative permeability characteristics which would indi-

By G. S. Ansell, J. Weertman

The creep behavior of an aluminum alloy hardened with a finely dispersed phase of aluminum oxide was investigated. The as-extruded alloy shows an approximate steady-state creep in which the creed rate depends exponentially on the applied stress. The activation energy of creeb is abbroximately 150,000 cal per mole. The recrystallized alloy shows no steady-state creep. ONE method of improving the creep resistance of a metal is to introduce a finely dispersed second phase into the metal matrix. The improvement of the creep resistance has been qualitatively explained by assuming that the dispersed second-phase particles act as obstacles to dislocation motion. If the main effect of second-phase particles is simply to hinder dislocation motion then it is possible to derive a high-temperature creep equation for a dispersion-hardened alloy in a straightforward manner. In the Appendix of this paper such an equation is derived from a creep model which works very well for pure metals. Recently, F. V. Lenel has fabricated, for the first time, powder extrusions of aluminum-aluminum oxide in a large-grained recrystallized form. This alloy, designated as MD 2100, consists of a fine dispersion of aluminum oxide plates in a matrix of commercial purity aluminum. A considerable amount of investigation has been carried out concerning the microstructure and physical properties of this alloy.&apos; ) The aluminum oxide is present in the form of flakes 130A units thick and 0.3 u on edge. They are dispersed in the aluminum matrix with an average spacing of approximately 0.5 jx. The spacing varies in the range of 0.05 to 1.5 µ. The alloy structure is extremely stable at high temperatures. For this reason the alloy offers a unique opportunity for a fundamental study of creep of a very finely dispersed two-phase alloy. Lenel supplied specimens in both the unrecrystallized and recrystallized condition. This paper reports high-temperature creep experiments carried out on these specimens. The results obtained were rather unexpected. No steady-state creep was observed in the recrys-tallized material. In fact, after some transient creep which takes place upon loading, the creep rate is essentially zero ( < 10-8per min). If the second-phase particles acted solely as obstacles to the motion of dislocations, measurable steady-state creep would be expected. Since none is observed it appears that the main effect of the fine dispersion in the recrystallized material is to inactivate the dislocation sources themselves, rather than hinder the motion of dislocation loops created at these sources. EXPERIMENTAL DETAILS Specimens were tested in wire form, 0.087 in. in diam for the as-extruded alloy, and 0.035 in. in diam for the recrystallized alloy. These samples were held in friction-type wire grips; a gage length of 2.5 cm was used for all the creep tests. The specimens were held at 600°C in the test apparatus for at least 15 hr prior to each test. The tests were run under the condition of constant loading and, since the creep strains were small, can be considered as constant stress tests. The temperature of testing was held constant within 3°C. Elongations were measured with an optical cathetometer which was capable of measuring strains as smaIl as 0.00012. This allowed the measurement of strain rates as low as l0-8&apos;per rnin. In addition to the creep tests optical micrographs were made in order to determine both the grain size and microstructure of these materials. RESULTS Fig. 1 shows a few typical creep curves obtained from the as-extruded material. The elongations were somewhat erratic, but each curve shows a region of quasi-steady-state creep from which an approximate steady-state creep rate can be obtained. In general the higher the stress at a given temperature, the greater the total elongation before fracture. The lower the applied stress, the longer is the region where the creep rate is almost constant. Summary data from the creep tests of the as-extruded material are listed in Table I. The steady-state creep data of the as-extruded material for a range of stresses at a constant temperature follow a creep equation of the type creep rate = K&apos; = A exp (&) [11 where A and B are constants, k is Boltzmann&apos;s constant, T is the absolute temperature, and a the stress. The standard error of estimate of the data received is less than one order of magnitude. As shown in Fig. 2, if one compensates the creep-rate data for the effect of temperature over the range of test temperature, the steady-state creep data roughly follow a creep equation of the type Temperature compensated creep rate = K* = A exp

Jan 1, 1960

By L. Seigle, R. Resnick

An inert-marker movement experiment indicates that the ratio of the intrinsic diffusion coefficients DC:DTa = 80:l in TaC at 2500°C. Measurements of the diffmion coefficient of carbon in nonstoichiometric TaC at temperatures from 1700° to 2700°C reveal that Dc increases with decreasing carbon content, but much less than expected from the probable change in vacancy concentration with carbon content. A diffusion process involving two simultaneously operating mechanisms is postulated, and shown to be theoretically feasible. The average value of the carbon diffusion coefficient is given by DC = 0.18 exp[(-85,000 ± 3000)/RT] sq cm per sec over the composition range 46 to 49.5 at. pct C. BECAUSE of their high melting points and hardness, the carbides of the IV, V, and VI group transition metals, along with those of uranium, have attracted considerable interest for applications at high temperatures. In these applications the reactivity of the materials is important, and, since rates of diffusion within the compounds influence reactivity, a knowledge of diffusion kinetics and mechanisms is desirable. While many investigations of the mechanical and electrical properties of these compounds have been made, only two fundamental investigations of diffusion in the carbides are known. Chubb, Getz, and Townleyl measured the diffusivity of carbon and uranium in UC, and Gel&apos;d and Liubimov2 measured the diffusivity of carbon and niobium in NbC. This paper describes an investigation of the diffusion of carbon in tantalum monocarbide and, in particular, the influence of carbon deficiency on this process. Tantalum carbide melts at approximately 3800°C, which makes it one of the highest melting materials known. The compound exists over a rather wide range of carbon Content.3-7 At the peritectic temperature, 3240°C, the phase extends from about 36 to 50 at. pct C. Although the compound can exist with a substantial carbon deficiency, the high carbon phase boundary remains near the stoichiometric composition over the entire temperature range; i.e., no carbon excess is observed. The structure of TaC is the NaCl type wherein carbon atoms normally occupy the octahedral sites in a somewhat expanded fcc lattice of tantalum. Decrease of the lattice parameter with decreasing carbon suggests that the removal of carbon introduces octahedral vacancies into the lattice. I) EXPERIMENTAL DETAILS AND RESULTS Inert-Marker Experiments. In a compound such as TaC the interstitial element would be expected to diffuse more rapidly than the metal. This was confirmed by an inert-marker experiment, following Srnigelskas and irkeendall.8 Ideally, the markers should be placed at the interface between a slab of low-carbon TaC and graphite, and their movement during subsequent inter-diffusion measured. Unfortunately, no solid could be found which is unreactive in contact with carbon at the high temperatures employed in these experiments. In order to circumvent this problem, a specimen was designed in which the markers consisted of several small canals running just below the surface of a tantalum slab. This specimen was prepared by machining grooves on the surface of the tantalum slab and then diffusion-bonding a thin plate of tantalum to the slab over the grooves. The surface of the plate was then ground down until the distance between the canals and surface was as small as possible (about 0.01 cm). Thus, the canals would lie entirely within the TaC phase after a short period of diffusion. The diffusion anneal consisted of immersing the metal sample in high-purity graphite powder and heating for approximately 10 hr at 2500°C under vacuum. At this temperature, the vapor pressure is sufficiently high and the transfer of carbon from graphite sufficiently rapid to allow the surface of the diffusion sample to attain the stoichiometric carbon concentration very quickly. Conclusions regarding the relative diffusion rates of carbon and tantalum in the compound layers (TaC and Ta2C) can be drawn from the location of the canals after the diffusion anneals. If the growth of the layers is governed mainly by the diffusion of carbon, as expected, the canals should remain close to the sample surface. If the diffusion of tantalum contributes appreciably to formation of the compound layers, the distance from the markers (canals) to the surface should increase. Fig. 1 shows, diagrammatically, the appearance of the specimens after diffusion, and Table I presents the depth below the surface at which the

Jan 1, 1967

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

Schedule of Events

Jan 1, 1977

By I. R. Kramer

A delay time for yielding in cold-worked face-centered-cubic metals was found. Slip on (123) planes was observed. Glide on these planes occurred during the delay-time period before slip starts on the (111) planes. AN important approach to the study of the anchoring and blocking of dislocations is available through the delayed-yield phenomenon which has been observed in body-centered and hexagonal close-packed metal by several investigators. Clark and his associate1-5 showed that a delay time for yielding is present in mild steels and fine-grain molybdenum. Type 302 stainless, SAE 4130 normalized, SAE 4130 quenched and tempered, and 24s-T aluminum aid not have a delay time. Kramer and Maddin6 studied the delay-yield effect. in metal single crystals. While they found a delay time in body-centered-cubic metals none could be found in the face-centered-cubic metals. Later7 a delay time was found in hexagonal close-packed metals. cottrell8 has proposed an explanation for the difference in the yield phenomena of b.c.c. and f.c.c. metals based upon the anchoring of edge dislocations by the proper types of impurity atoms (C and N). In the body-centered-cubic lattice the interstitial atoms are near a cube edge and can interact with an edge dislocation, while in a face-centered-cubic lattice the distortion around an interstitial atom is of spherical symmetry and cannot anchor a screw dislocation which has practically no hydrostatic component. Cottrell&apos;s theory seems to account rather well for the behavior of body-centered-cubic . metals. EXPERIMENTAL PROCEDURE The apparatus used in these experiments is essentially of the same design as described previously.&apos; Single crystals 1 in. long and having a diameter of % in. were placed in a pendulum which consisted of a bar 8 ft long designed with a crystal holder to accommodate the specimen at low temperatures. This portion of the apparatus was supported on fine molybdenum wires. A bar of the same diameter and length comprised the other portion of the apparatus. This bar was supported on a set of roller bearings arranged around the periphery of the bar to allow accurate alignment. This bar was propelled by means of a spring-loaded gun and allowed to strike the lead bar in front of the single-crystal specimen. SR-4 type A-8 resistance strain gages were cemented to the specimen and the strain measurements were obtained by amplifying the strain-gage output by means of a high-gain preamplifier. A tektronix 545 oscilloscope was used together with a polaroid camera to record the strain and time sweep. An Ellis Associate Bridge was used to calibrate the strain gages and calibration readings were obtained before each test. The sweep of the time signal was initiated by means of a miniature thyraton which was fired when the two bars came into contact. The single-crystal specimens were cut from single-crystal bars about 12 in. long, grown by a modified Bridgman technique. The aluminum crystals were made with material of 99.99 pct purity while the purity of the copper was 99.999 pct. A cut-off wheel was used to prepare the specimens which were then machined to the desired length. The two opposite faces of the specimen were parallel to each other and perpendicular to the axis of the specimen. The specimens were compressed 1 pct. No machining followed thereafter. In some cases prestraining was carried out in liquid nitrogen by impacting the specimens directly in the apparatus so that subsequent observations could be made without allowing the specimen to warm up to room temperature. The single crystals were compressed 1 pct at room temperature in a hand press without much control of the rate of deformation. In some cases specimens were recompressed to obtain the desired length change. As far as could be determined in these experiments this factor did not seem to influence the results. The SR-4 strain gages were glued with a cellulose type cement onto the specimen surface and baked at 45°C for 12 hr. As a check on the baking treatment gages were allowed to dry at room temperature. All delay time tests in this paper were conducted in a liquid nitrogen bath at -195°C. A schematic delay time oscilloscope trace is shown in Fig. 1. At point B the elastic stress wave caused by the impact reaches the strain gage on the specimen. The portion BC is the elastic strain. In this investigation the strain at point C was used to calculate the critical resolved shear stress by multiplying by the proper modulus depending upon the orientation of the single-crystal specimen. The time between C and D is the delay time portion of the curve. This portion of the curve is fairly flat but does have a definite microstrain associated with it. After the point D is reached the specimen deforms rapidly and the strain reaches a maximum at E. Following this, depending upon the length of the bar behind the specimen, the strain remains constant for a period and then decreases when the reflected elastic wave returns from the end of the pendulum bar. A permanent plastic strain is recorded on the oscilloscope trace and also measured by a strain-measuring bridge. The strain, E p,

Jan 1, 1960

By R. W. Kraft

A back- reflection precession-type X-yay camera for determining the crystallographic orientation of the crystallites of both phases in small areas of thick specimens of polyphase alloys is described ad the geometry, advantages, and limitations of the apparatus are discussed. Metallographic obseg-vations of interfacial angles (or habit planes or growth direction are made on the same specimen so that the crystallographic and metallographzc orientation data call be directly correlated. An example of the application of tile technique to a unidi-~~ectionally solidified CuA12-A1 eutectic specimen is presented. The interfacial planes ad growth directions of each phase were established, and the orientation relationship between the phases was observed and found to be approximately intermediate between two previously reported relationships. The crystallographic interfacial relationship between two solid phases is an important parameter in a variety of metallurgical phenomena because of the energy associated with the interface and because this energy is at least partly associated with the way in which the two space lattices are in contact along the interface. In order to describe the interfacial planes in the crystallites of both phases it is necessary to determine the crystallographic orientation of each phase in a specimen relative to each other, and to directly correlate these data with met-allographic measurements from which the interfacial planes can be determined on the same specimen. The back-reflection Laue technique is the easiest way to determine the orientation of thick single crystals or large grains and the method can be combined with metallographic techniques to provide the necessary data, provided the reflections from each phase can be distinguished from one another. However, if the crystallites are small or of varying orientation or if one or both phases has a unit cell with less than the maximum symmetry, many overlapping and complex Laue patterns are recorded simultaneously and it becomes impractical if not impossible to interpret the photographs. All of these complexities were present in a unidirectionally so- lidified A1-CuA12 eutectic alloy1 for which a crystallographic analysis was desired. Consequently the method described here was developed since no known X-ray or electron diffraction technique had all of the following attributes which were required. 1) Method should yield data from which the crys-tallographic orientation of every crystallite or diffracting unit in the irradiated area can be determined. 2) Method should be adaptable to the study of small areas. Depending upon the degree of preferred orientation in the specimens, it should be possible to obtain reliable data in a reasonable length of time on irradiated areas as small as 1.0 or even 0.1 mm in diam. 3) Method should permit direct correlation of crystallographic data with microscopic orientation data pertaining to crystallite axes, habit, morphology, and growth directions as determined by optical microscopy. 4) method should be such that selected areas of large specimens can be easily studied. Trepanning of a small specimen (such as an electron microscope specimen) from larger specimens was undesirable since it would greatly increase the problem of correlating the crystallographic and microscopic directional data. Requirements 3 and 4 dictated that an X-ray back-reflection pinhole technique should be used on large samples, such as metallographic specimens which had previously been examined and analyzed for their microscopic characteristics. Similarly, requirement 2 could be satisfied by choosing a collimator of appropriately small diameter. Exposure times would not be excessive provided the detector were close enough to the specimen. Because of space limitations film was chosen in preference to a Geiger counter. Requirement 1 was fulfilled by using monochromatic radiation and providing enough additional degrees of freedom in specimen rotation to compensate for Bragg law restrictions on diffracted beams. DESCRIPTION OF APPARATUS The apparatus shown in Fig. 1 consists of a pin-hole collimator, (a), projecting through a rotatable circular film in a holder, (b), which records X-ray reflections in the back-reflection region. The specimen, (c), is mounted on the end of a shaft, (d), which is provided with an adjustment, (e), so that the specimen surface can be placed accurately on

Jan 1, 1962

By A. G. Spillette, R. L. Nielsen

The purpose of this paper is to further the understanding of reservoir response to hot-water injection by desuribing a two-dimensional, mathematical model of the process. Key assumptions are that no gas phase is present, and that the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. The resulting system of three partial differential equations is solved simultaneously through the use of a "leap-frog" application of standard alternating direction implicit methods for the solution of the mass-balance equations and the method of characteristics for solution of the energy-balance equation. The utility of the mathematical model is demonstrated by comparing numerical and analytic temperature distributions for hot-water bank injection and by comparing calculated with observed field behavior. Additional calculations show that hot waterfioding can recover significantly more oil than cold waterflooding, and that a hot-water bank recovers, with less energy input, nearly as much oil us continuous injection. Introduction Consistent field success with hot fluid injection processes requires good reservoir description and a thorough understanding of recovery mechanisms. The latter is fostered by a combination of well designed experimental studies and physically sound mathematical modeling. The purpose of this paper is to further the understanding of reservoir response to hot-water injection by describing a two-dimensional mathematical technique, indicating its validity, and demonstrating its utility for studying the effects of reservoir and operating parameters. Published experimental studies of hot fluid injection processes are few." Even if extensive data were available, two considerations discourage exclusive reliance on laboratory or field work. First, because of the severity of scaling requirements," laboratory results must be interpreted with care. Second, because of the one-shot nature of field experiments — injectivity/productivity tests and pilot floods—results seldom are available over the desired range of operating conditions. These factors emphasize the need for devoting attention to mathematical modeling to complement laboratory and field work. Through the use of mathematical models, scaling uncertainties can be bridged and response can be predicted for unique combinations of reservoir and operating conditions. Numerous mathematical models developed during recent years enable us to calculate temperature distributions, thermal efficiency (or conversely, fraction of heat lost), and oil recovery behavior for hot fluid injection. Ramey" and Spillette&apos; recently have provided reviews of these methods. Most models have concentrated on predicting temperature distributions and thermal efficiency; few have been directed at predicting oil recovery.&apos;."1° Although these techniques are useful for estimating effects of reservoir parameters and operating conditions on process performance, results are limited by the assumptions made and by the methods of coupling independently solved fluid-flow and energy-balance equations. A computer-based method is presented for predicting total reservoir response to hot-water injection that obviates most simplifying assumptions. The model simulates fluid flow and heat transfer in two dimensions within a vertical cross-section spanning the oil sand and adjacent unproductive strata. Known numerical procedures are used to solve the governing partial differential equations. The mathematical model handles the effects of reservoir heterogeneity, gravity, capillarity, relative permeability and temperature-dependent fluid properties. In addition, a wide range of operating conditions can be modeled, including hot-water followed by cold-water injection. Mathematical Description of Hot-Water Injection Key assumptions in the mathematical model for hot-water injection are that (1) no gas phase is present and (2) the injected fluid reaches thermal equilibrium instantaneously with the reservoir fluids and sand. Relative permeability and capillary pressure are assumed independent of temperature. Darcy&apos;s law for multiphase fluid flow relates the velocities of the oil and water phases to the phase pressure gradients by the following relations:

Jan 1, 1969

CONTENTS PAGE HESSE, A. W,-Safeguarding Coal-mining Operations against Danger from Oil and Gas Wells. Discussed by A. W. Hesse, T. G. Fear, George H. Ashley, George S. Rice, W. E. Fohl, R. V. Norris, S. A. Taylor, F. B. Tough, C. W. Gibbs, A. Hurlburt, S. W. Meals 1 DAWSON, THOS. W.-Belt Conveying of Coal at H. C. Frick Coke Company Mines. Discussed by F. F. Jorgensen, Thos. W. Dawson, Graham Bright, A. W. Hesse 13 OTTO, HENRY H.-Ultimate Recovery from Anthracite Coal Beds. Discussed by R. V. Norris, S. A. Taylor, Henry H. Otto, Douglas Bunting, Graham Bright, Howard N. Eavenson, J. B. Warriner 15 HOSLER, Rush N.-Schedule Rating Coal Mines in Pennsylvania for Compensation Insurance Rates. Discussed by E. A. Holbrook, W. W. Adams 17 ARCHBALD, HUGH.-Application of Gaussian Curve to Mining Industry. Discussed by Donald A. Laird, T. T. Read 19 ASH, SIMON H.-System of Coal Mining in Western Washington. Discussed by Eli T. Conner, Simon H. Ash 21 MILLER, J. S.-Method of Mining a Steeply Pitching Anthracite Vein by Successive Skips. Discussed by Eli T. Conner, J. S. Miller, J. B. Warriner 22 HARRINGTON, GEORGE B.-New Orient, an Unusual Coal Mine. Discussed" by George S. Rice, Eli T. Conner, John A. Garcia, George B. Harrington, F. F. Jorgensen, Graham Bright, W. M. Hoen, George N. Simpson, W. C. Adams, R. W. McNeill, Chas. C. Whaley, Carl Scholz, E. T. Gott, Andrews Allen 23 PERROTT, G. ST. J.-Properties of Liquid-oxygen Explosives. Discussed by George S. Rice 48 Safeguarding Coal-mining Operations against Danger from Oil and Gas Wells Discussion of the paper of A. W. HESSE, presented at the New York Meeting, Feb-ruary, 1925, and issued, as Paper No. 1412-F, with MINING AND METALLURGY, February, 1925. A. W. HESSE.-The well under investigation, No. 101, Fig. 2, was started about Sept. 5, 1921, and drilled-in in November. The first hole was started with a 13-in. bit and reached the Pittsburgh coal at a depth of 563 ft.; at 602 ft. the 10-in. casing was run in and the well was continued with a 10-in. bit and 1400 ft. of 8-in. casing was put in. It was then continued to a depth of 1770 ft. and 6-in. casing put in; then continued to a depth of 2555 ft. where the gas was struck. As the well produced only about 100,000 cu. ft. per day. 2-in. tubing was used to conduct the

Jan 6, 1925

By A. H. Grobe, F. N. Rhines

AT elevated temperatures the oxide of silver is unstable in the air at atmospheric pressure, consequently no external oxide scale forms upon pure silver under conditions of high-temperature annealing When small quantities of certain alloying elements are present in the silver, the formation of a thin external scale is possible&apos; and in addition there may form a subscale composed of the oxide of the solute element precipitated within the body of the silver Norbury2 and Leroux and Raub3 have reported internal oxidation (subscale formation) in alloys of silver with 2, 7 5, and 30 per cent of copper The presence of the subscale is believed to be responsible, at least in part, for the objectionable "fire mark" in Sterling silver&apos; Several other alloys of silver, after oxidizing heat-treatments, are known to exhibit undesirable polishing characteristics that may be the result of internal oxidation Except for the absence of an external scale of silver oxide, it is to be anticipated that silver alloys will prove to be very similar in their oxidation behavior to the alloys of copper, the oxidation characteristics of which have been studied in some detail 5,6 The present research confirms this anticipation The oxidation of a series of 20 dilute alloys of silver has been studied metallographically, some types of subscale not encountered among the copper alloys have been found Instances of internal oxidation in alloys of most of the metals of the I-b and VIII groups of the periodic system are on record, but evidence of this type of oxidation in alloys of the metals of the intermediate groups is lacking A number of the metals of the intermediate group, among them cadmium, lead, tin, and zinc, appear to provide the conditions essential to subscale formation, i e , they form oxides with a relatively low negative free energy of formation, they dissolve other metals that form more stable oxides, and, presumably, oxygen will diffuse through them In a study of 4o alloys of these white metals only a few cases of internal oxidation have been found The probable reasons for this difference in behavior will be discussed presently EXPERIMENTAL PROCEDURE Silver -The silver alloys employed in the oxidation studies were prepared in heats of 30 grams each from high-purity silver (99 993 per cent Ag)* and the purest avail-

Jan 1, 1942

By N. S. Stoloff, M. Gensamer

The effects of temperature, grain size, and magnesium content on the strength and ductility of cadmium were studied in the range -269° to 23 °C. A sharp drop in ductility between -140° and -190°C marked a transition in fracture mode from ductile shear to inter gvanular fracture. The addition of up to 15.35 wt pct Mg in solid solution raised the transition temperature, and for two compositions produced basal cleavages. The relatively high ductility of unalloyed cadmium at cryogenic temperatures is attributed to temperature independence of the yield stress and the absence of dislocation locking. ALTHOUGH numerous studies have been made of the mechanical properties of cadmium single crystals,1-5 no comprehensive investigation of deformation and fracture in polycrystalline cadmium has been carried out. This investigation was initiated to determine the mechanisms of deformation and fracture in polycrystalline cadmium, and to attempt to correlate these mechanisms with the behavior of other metals of hexagonal close-packed structure. A second objective of this work was to determine whether the slip systems and mode of fracture of polycrystalline cadmium could be altered by reduction of the axial ratio, which is 1.886, through alloying. Dorn and co-workers&apos; have been able to induce prismatic slip in magnesium through alloying to reduce the axial ratio. Single crystals of cadmium are so highly ductile that glide strains of 400 pct are observed at room temperature, and 80 pct at -269°c.l Failure in every reported case is by necking down and shearing off of the crystal. Cleavage in cadmium single crystals has never been observed. Magnusson and aldwin reported a ductile to brittle transition for polycrystalline cadmium at about —160 C for specimens tested at a strain rate of 0.05 in. per in. per min in tension. However, even at -196° substantial ductility was retained. The transition temperature was strain rate dependent, impact loading at 19,000 in. per in. per min raising the transition temperature to about -85°C while leaving the low temperature ductility unchanged. No information was given on microstructures or fracture mode, nor were stress-strain characteristics reported. In the present investigation, tensile tests were carried out on polycrystalline cadmium and solid solution Cd-Mg alloys to determine flow stresses, work-hardening behavior, fracture strength, and fracture ductility. Variables employed included temperature, alloy content (and c/a ratio), and grain size.Some compression data also have been obtained for comparison purposes. I) EXPERIMENTAL PROCEDURES A) Polycrystalline Cadmium. Two purities of cadmium were employed in this investigation. Cadmium of 99.95 pct purity was supplied by Belmont Smelting and Refining Co. Cadmium of 99.99+ pct purity was supplied by American Smelting and Refining Co. Threaded cylindrical tensile specimens were machined to give approximately a 1/2 in. long straight gage section with a reduced diameter of about 0.110 in. Specimens were heat treated in evacuated pyrex capsules in the range 140" to 290°C to produce desired grain sizes. All specimens were polished in a solution containing 320 g Cr03 and 20 g NaS04 in 1000 cc of H20. Occasionally this solution caused staining of the specimen, in which case a further polish with a solution of one part HN03 and two parts H202 in two parts ethyl alcohol was employed.&apos; Tensile testing was carried out on a screw-driven Instron machine, at a constant rate of crosshead movement, which for most tests was 0.01 in. per in. per min. Load vs time, and therefore load vs total strain, were recorded. Temperatures from -196" to -40°C were obtained by passing nitrogen gas through a copper coil immersed in liquid nitrogen, and then feeding the gas into a jacket around the specimen. Tests at -269°C were carried out in a helium cryostat, at a crosshead rate of 0.1 in. per in. per min, with specimens of 1 in. gage length. Compression specimens were tested in a jig similar to one designed by ilman. The jig was mounted on the under side of the Instron crosshead. Load was transmitted by means of a rod connected to a movable part of the jig at one end, and the load cell at the other end. A downward movement of the crosshead applied a compressive load to the specimen.

Jan 1, 1963