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By L. W. Holm

Laboratory flooding experiments on linear flow systerns indicated that high oil displacement, approaching that obtained from completely miscible solvents, can be attained by injecting a small slug of carbon dioxide into a reservoir and driving it with plain or carbonated water. Data are presented in this paper which show the results of laboratory work designed to evaluate this oil recovery process, particularly at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi. Under these conditions CO2 exists as a dense single-phase fluid. It was found that a bank, rich in light hydrocarbons, was formed at the leading edge of the CO? slug during floods on long cores. Formation of this bank is probably due to a selective extraction by the C02 and, it is believed, partially accounts for the attractively high oil recoveries. In crddition to the efficient displacernerlt of oil from the pores of the rock by this process, the favorable rnobility ratio related to a C0 2-water flood also contributes to high oil recovery. A further advantage of this process is noted on limestone and dolomite rock, in that the CO1 reacts with the porous medium increasing its permeability. Flooding experiments were conducted on sandstone and vugular dolomite models. The results of this experimental work show the effect on oil recovery of type of porous medium, pore geometry, flooding length, and flooding pressure. The porosity of the cores and rilodels varied from 16 to 21 per cent and their pern~eabilities ranged from 100 to 200 md. A reconstituted West Texas reservoir oil, a West Texas stock tank oil, an East Texas stock tank oil and Soltrol were used to represent reservoir oils in this study. Oil recoveries ranging from 60 to 80 per cent of the original oil in place in these cores were obtained by CO2,-carbonated water floods at pressures between 900 and 1,800 psi, compared with conventional solution gas drive and water-flood recoveries of 30 to 45 per cent on the same cores. Oil recoveries greater than 80 per cent resulted frorn f1oods at pressures above about 1.800 psi. There high recoveries were noted from both the sandstone and the irregular Porosity carbonate cores. In all floods, additional oil was recovered by a solutiorr gas drive resulting from blowdown following the flood. Oil recoveries of 6 to 15 per cent of the original oil in place were obtained during this blowdown period. This additional recovery was found to be a function of oil remaining after the flood, decreasing with decreasing oil saturation. It was also noted that highest oil recoveries by blowdown were obtained when carborlated water rather than plain water followed the CO, slug. INTRODUCTION Miscible phase or solvent flooding processes, which are designed to increase oil recovery -from petroleum reservoirs, involve the injection of small quantities of a petroleum solvent into the reservoir, followed by an inexpensive scavenging fluid which is miscible with the solvent. Essentially complete displacement of oil from the pores of reservoir rock has been obtained by this technique. CO,, although not completely miscible with most reservoir oils at moderate pressures, is highly soluble in these oils at pressures above about 700 psi; there is appreciable swelling and reduction in the viscosity of oil when CO, is dissolved in it. Therefore, CO, could be expected to perform similarly to other oil solvents as a displacing agent. CO, is also highly soluble in water at elevated pressures, so water should be a satisfactory material to drive a slug of CO, through an oil-bearing reservoir. A favorable mobility ratio would be obtained through the reduction in viscosity of the oil and the use of water as a final displacing agent. A number of investigations of the use of CO, to improve oil recovery have been reported in the literature.2,3,4,5,6 These studies, however, have been conducted on uniform porosity sandstone at relatively low temperatures and pressures. The behavior of CO1 as a flooding agent at temperatures above its critical temperature could not be predicted adequately from these studies, particularly for the case of non-homogeneous rock. The purpose of this work was to evaluate the oil recovery efficiency of a process involving the injection of a CO2 slug followed by carbonated water, at reservoir temperatures above 100°F and in the pressure range of 600 to 2,600 psi, and to compare this process with conventional water flooding. The investigations were primarily designed to provide information on the efficiency of the process in irregular porosity carbonate rock. The effects of flooding path length, the presence of free gas, the type of oil to be recovered, and the amount of solvent required were also determined. The essential results of static phase behavior studies and experimen-

By William C. Sleppy

The nmgnetic susceptibility of heat-treatable aluminuin alloys is sensitive to chanyes such as solution or dissolution of solute and the precipitation of mew phases. By measuring the change in the magnetic susceptibility of aluminum alloys caused by various heat treatments, an empirical relation was found from which atomic arrangements in dilute binary alloys of copper, zinc, and magnesiutn in aluminum have been delineated. The relation predicts the ultimate formation of C1LA12 when copper is precipitated from solid solution in aluminum. Euidexce joy silovt- range order is found for copper in solid solution in aluminum in the sense that copper atoms avoid being nearest neighbors to an extent greater than would result from a purely random arrangertzeizt. Hume-Rothery has predicted such short-range order joy solid solution of copper in aluminum The Al-Zn system agrees with evidence obtained from X-ray scattering at small angles and predicts a tendency for zinc atoms to cluster in solid solution in aluminum. In the Al-mg system, the empirical relation indicates an approach to randor distribution of magnesium in solid solution in aluminum with a tendency for magnesium segvegation which increases with incveasing temperature. ThE magnetic properties of metals are complicated by the fact that contributions are made to them both by electrons of a "metallic" type which belong to the crystal as a whole, and by electrons in states localized on particular atoms. An expression1'2 for the bulk magnetic susceptibility of aluminum may be written as the sum of three contributions: where XA1 is the bulk susceptibility of aluminum per gram of material (in the cgs system, the units are those of reciprocal density); Xa1+3 is the diamagnetic contribution of the electrons localized in ion cores; Xa1 is. the paramagnetic spin contribution of conduction electrons often called Pauli paramag-netism: Xa1 is the diamagnetic contribution of the conduction electrons often called Landau diamag-netism. Ion core diamagnetism arises from the precession of the electron orbits which occurs when a magnetic field is applied to a system of electrons moving about a nucleus. Its contribution to the magnetic suscepti- bility is small, temperature-independent, and unaffected by alloying. The conduction electron diamagnetism is also temperature-independent and arises from the translatory motion of the electrons. For perfectly free electrons this contribution should be exactly one-third of the Pauli spin paramagnetism, but this relation is seldom even approximately true. Blythe2 determined the conduction electron diamagnetism in pure aluminum and found it to be extremely small. Any change in the conduction electron diamagnetism caused by alloying is neglected in this work. The Pauli paramagnetic contribution3 to the magnetic susceptibility of aluminum depends upon the number of electrons that occupy excited states and whose spins can be turned parallel to an applied magnetic field. The number of electrons free to turn in the field is proportional to the temperature and each spin contribution to the susceptibility is inversely proportional to the temperature. A slight temperature dependence of Pauli paramagnetism occurs when the number of electrons occupying excited states cannot increase sufficiently to balance the inverse dependence on temperature of each spin contribution. The decrease of the magnetic susceptibility of aluminum with increasing temperature is attributed to a temperature dependence of the Pauli paramagnetism. Estimates of the Pauli paramagnetism of aluminum have been made by several workers.2,4,5 All of the values are in reasonably good agreement with each other. In this work Xal at 17°C is taken as 0.761 X 10-8 cu cm per g. An expression similar to [I] can be written for the magnetic susceptibility of an aluminum base alloy containing a fractional weight percent x of solute:' Xa = (1 -x)XAl+3 +xXsoluteion * XaPauli +Xadia) [2] where X, is the magnetic susceptibility per gram of alloy, Xal'3and Xsolute ion are the ion core diamag-netic contributions, and xpauli and xdia are the Pauli and diamagnetic contributions of conduction electrons in the alloy. If the components of a mixture are not alloyed but simply mixed together in their pure states without producing a new phase, then the magnetic susceptibility of the mixture is given by the Wiedemann additivity law: Xm =x1X1 +x2x2 + ..xnxp [3] where X, is the susceptibility per gram of mixture and xnXp are the weight fractions and susceptibilities, respectively,-. for the pure components. The additivity law is not applicable to alloys because the outer electronic structures of the components are changed by alloying.' Both the Pauli paramagnetism and Landau diamagnetism are affected; hence the magnetic susceptibilitv of an alloy is usually different from that calculated using the additivity law. In this work the difference, X, -X,, is taken as a measure of the change caused by alloying.

Jan 1, 1968

By J. D. Defilippi, E. M. Gilbert, K. G. Brickner

FCC chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Transformation to martensite is considered to be responsible for this behavior in some metastable Cr-Mn-N steels. However, very stable Cr-Mn-N steels also exhibit a ductile-to-brittle transition. The results of this study indicate that deformation faulting is the probable cause of the brittle behavior of stable Cr-Mn-N steels. Deformation faulting accounts for the ductile behavior of these steels in a tension test at -320°F and brittle behavior in an impact test at -320°F. Deformation faulting also accounts for the toPological features observed on the fracture surfaces of impact specimens of these steels. FACE- centered- cubic chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Many Cr-Mn-N steels transform to martensite during deformation,l-5 and several investigatorsl-3 have suggested that the brittle behavior of these steels is caused by martensite formation. However, very stable Cr-Mn-N steels also exhibit brittle behavior. Schaller and Zackeyl reported that a very stable Cr-Mn-N steel (less than 3 pct martensite formed at -320°F) exhibited a transition temperature higher than that for steels in which large volume fractions of martensite formed during testing. The explanation given by Schaller and Zackey for this observation was that in the very stable steel the martensite, because of its higher interstitial content, was more brittle than that formed in their other steels. This explanation was questioned by Tisinai and samans4 and Baldwin.6 Moreover, because the toughness of stainless martensite at cryogenic temperatures is generally very low, this explanation does not account for Thompson's7 observation that small additions of nickel (1 to 3 pct) greatly improve the toughness of high nitrogen (0.35 pct) Cr-Mn-N steels. The present paper summarizes the results of an investigation of the low-temperature brittleness in very stable Cr-Mn-N steels. The importance of the mode of deformation on the toughness of these steels is discussed. Table I. Compositions of the Steels Invertigated, Pet Steel C Mn P S Si Ni Cr N - A 0.09 14.70 0.018 0.011 0.47 0.22 18.40 0.54 B 0.12 14.90 0.001 0.008 0.48 0.14 17.80 0.38 C 0.12 14.95 0.004 0.005 0.62 3.95 18.43 0.38 MATERIALS AND EXPERIMENTAL WORK The compositions of the steels investigated are shown in Table I. Steels A and B had compositions within the limits of a proprietary Cr-Mn-N stainless steel,* whereas Steel C was similar in composition to the proprietary steel except for its 3.95 pct Ni content. All steels were hot-rolled to 1/2-in. thick plate. The plates were subsequently annealed for 1 hr at 2000°F and water-quenched. Standard longitudinal and transverse Charpy V-notch impact specimens were machined from the annealed plates. Duplicate longitudinal and transverse impact specimens were tested at 212", 80°, 32", 0°, -100°,-160°,-200°,-256", and -320°F. Longitudinal tension-test specimens were also machined from the plates and tested at a crosshead speed of 0.05 in. per min at the aforementioned temperatures. The fractured impact and tension-test specimens of all three steels were examined to determine whether martensite had formed during testing. Magnetic, X-ray, electron-diffraction, and electron-microscopy techniques were used to detect the presence of martensite in the highly deformed areas of these specimens. Metallographic examination of highly deformed areas of impact and tension-test specimens revealed the presence of dark-etching bands, such as those shown in Fig. 1. These bands were observed only in deformed samples and were thought to be associated with the low-temperature brittleness of the Cr-Mn-N steels. Accordingly, a sample 1 in. wide by 3 in. long was cut from the 1/2-in.-thick plate of Steel C. This sample was surface-ground to a in. and then cold-rolled 60 pct at -320°F. Thin foils were prepared from the cold-rolled sample and examined in a JEM electron microscope. Brightfield, dark-field, and selected-area diffraction techniques were used to determine the cause of the dark-etching bands. Fractographic experiments were also performed. Impact specimens Of Steels A, B, and C were broken at -320oF, and the fracture surfaces of these specimens were immediately shadowed with carbon. The carbon replicas were examined in a Siemens electron microscope, and attempts were made to correlate the topological features of the fracture surfaces with the deformation mechanisms that could be occurring during an impact test of these steels.

Jan 1, 1970

By Jerome J. English, Gordon W. Powell

An experimental investigation and mathematical analysis of the thermal-dilation behavior of the titanium alloy Ti-7Al-3Cb have shown that the linear dimensional changes associated with the polymorphic transformation need not be isotropic. The absolute magnitude of the linear dimensional change, which may be either positiue or negative, associated with the cr-p transformation is dependent upon the relutzve volumes of different orientations of the transformation product. It is hypothesized that the dilation irregulati-ties that have been observed during the polymorphic transformation of pure, coarse-grained titanium and other titanium-base alloys can be explained in the same manner. When titanium is heated above about 165O°F, the hcp a structure transforms to bcc 0. Thermal-dilatioh measurements have shown that the transformation is accompanied by a decrease in length of 0.16 pct.' Such dilation behavior would be expected because the volume of the hcp unit cell is about 0.3 to 0.4 pct greater than that of the bcc unit cell. A recent investigation2 of the thermal-dilation behavior of an experimental a-p* titanium alloy, Ti- 7A1-3Cb, containing 0.06 wt pct 0 showed that its dilation behavior during the polymorphic transformation differed substantially from that reported for unalloyed titanium. The first time the alloy was cycled through the transformation, the dilation curve closely duplicated that of unalloyed titanium. However, upon repeated cycling through the transformation temperature range, both the magnitude and the sign of the dimensional change associated with the transformation were observed to vary with each cycle. This investigation was undertaken to obtain additional data on the dimensional changes associated with the polymorphic transformation in the Ti-7A1-3Cb alloy and to determine the cause of the dimensional irregularities. After testing, the specimens were examined metallo-graphically. In addition, Laue back-reflection patterns were obtained from selected sections taken perpendicular to the specimen axes to determine the a orientations present in these sections. White radiation from a tungsten target and a 0.1-mm-diam collimator were used to produce the diffraction patterns. RESULTS Dilation Curves. Three types of thermal-dilation curves were obtained when the a-8 titanium alloy was heated and cooled through the transformation temperature range. These three types of curves are illustrated in Fig. 1. The type I curve represents what is considered normal behavior, because the dilation change is what would be expected on the basis of the volumes of the unit cells of a and p. The Type I1 curve is the inverse of Type I. Normal behavior is characterized by an expansion on cooling through the transformation, whereas a contraction takes place in the Type 11 curve. With Type ni behavior, no clearly distinguishable length change occurs during the transformation. No other anomalies that might be indicative of other phase transformations were observed in the dilation curves at lower temperatures. Apparently, the cooling rate was low enough for equilibrium to be reached during the 0 to a transformation. Table I lists the types of dilation curves observed during the polymorphic transformation as a function of the direction of measurement and cycle number. The A1 value was determined by extrapolating the low-temperature (a + 5 pct p) and high-temperature (100 pct p) segments of the dilation curves to a common temperature and measuring the difference in the or-dinates at that temperature, see Fig. 1. The transformation occurs over a temperature range in this alloy, so the magnitude of A1 is not an absolute value but depends on the choice of temperature. A mean temperature, T,, within the transformation temperature range was selected for the measurement. T, on cooling occurred about 100°C lower than T, on heating. The first time each of the three dilation specimens was heated to above the temperature, that is, Cycle 2, normal Type I behavior was observed. In Cycle 3, two deviations from normal behavior occurred. First, during cooling of the longitudinal specimen, a substantially larger expansion, +0.21 pct, was measured as 0 transformed to a compared with +0.03 pct in Cycle 2. Second, the thickness specimen was observed to undergo a contraction instead of the anticipated expansion on cooling. Continued cycling of the three specimens from room temperature to 2500°F produced additional changes in the dilation behavior. These changes did not seem to be related to the fabrication direction of the alloy because the values of a1 for the longitudinal, transverse, and thickness specimens varied unpredictably in magnitude and sign. Furthermore, both the longitudinal and transverse specimens showed all three types of dilation curves at least once during the six cycles that they received. Fig. 2 is a sketch of the transverse specimen after

Jan 1, 1967

By R. H. Richman, F. Borik

A 0.3 pct C-12 pct Cr-6 pct Ni steel was rolled to 93 pct reduclion in area as austenite at 510°C, and then partially transformed as desired to ~rlartensite by qnenching to - 196°C. Pole figures for the austenitic matrix and for the martensitic product were separately determined by an X-ray transmission method. The deforitration texture of' the warm-worked austenite is characlerized by (110)(225) components, and is thus closely similar to those produced in a brasses. The pole jigure of the martensite in partially transformed material agrees well with that which can be constructed by transfortnation of the {110)(225) orientations according to either the Kuvdjuniov- Sacks or the Nishi-yatuu relatiotship. Howeuer, an important result of this construction is that me-third of the predicted orientations are missing. A graphical analysis can then be used to show that in deformed austenite certain crystallographic variants of martensite (related to the most probable austenite slip systems) are suppressed, resulting in this preferred transformation. The evidence for preferred transformation is corroborated by the measured elastic anisotropy of warm-rolled and fully transformed H-11 steel. EXTENSIVE plastic deformation of a polycrystal-line aggregate in a manner that causes flow predominantly in one direction results in a preferred orientation of the constituent crystallites. The particular orientations that are produced depend upon the crystal structure and composition of the material, as well as upon the temperature, mode, and degree of deformation; in any case, the preferred crystallo-graphic orientations, or textures, are reflected in directionality of mechanical properties. Although such anisotropy may be exploited in certain specialized applications, it is more commonly diminished or eliminated by heat treatment lest it interfere undesirably in subsequent forming operations or in structural design. In the recently developed thermomechanical treatments that significantly enhance the strength of some steels,1,2 considerable deformation of the metastable austenite prior to the martensite transformation is essential to the strengthening process. If the austenite is textured by the deformation, and if the transformation to martensite proceeds according to one of the relationships established for transformation in annealed austenite, then it must be expected that the martensite will also possess a preferred orientation even though the multiplicity of martensite orientations possible in a given austen- ite crystal will tend to restore some degree of randomness. The existence of a residual anisotropy, both mechanical 3-6 and crystallographic,' has been substantiated. In the latter crystallographic investigation, preferred orientations were determined for the martensitic structure of an SAE 4340 steel rolled 72 pct as austenite at 833°C and then quenched. However, the choice of a composition that transformed almost completely to martensite during the quench to room temperature did not permit direct measurement of the prior austenitic texture. In fact, when the "ideal orientations'' associated with well-known fcc rolling textures were converted, alone or in combination, to martensite according to the Kur-djumov-Sachs (K-s)' or Nishiyama8 relations, the agreement obtained with the observed martensite texture was only fair at best. Recently a pertinent aspect of the austenite to martensite transformation was reported by Bokros and parker,10 who found that certain habit-plane variants of martensite were suppressed by tensile deformation of Fe-31.7 Ni single crystals prior to the necessary subzero cooling. It might be anticipated that the consequences of such preferred transformation are sustained during the formation of martensite in warm-worked austenite that has a well-developed deformation texture. The present investigation was undertaken first to establish more firmly the relation between preferred orientations in plastically deformed austenite and in the resulting martensite, and second to examine the textures for evidence of deformation-induced preferred transformation. EXPERIMENTAL PROCEDURES An alloy containing 0.3 pct C, 12 pct Cr, 6 pct Ni, and the balance iron, was selected because the mar-tensite-start temperature (M,) of about -100°C allowed convenient experimental manipulation of either austenite or martensite at room temperature. Furthermore, this composition can be readily deformed as metastable austenite at moderately elevated temperatures without intervention of appreciable isothermal or athermal decomposition products. The alloy was austenitized at 1150°C, aircooled to 510°C, rolled unidirectionally at this temperature to 93 pct reduction of cross-sectional area, and finally oil-quenched to room temperature. Partial transformation to martensite was accomplished by quenching to -196°C as needed. The rolled stock was reduced in thickness from 0.067 to 0.010 in. by etching in a solution of 5 pct HC1, 45 pct HNO3, and 50 pct water, and further thinned by careful mechanical polishing to maintain the two sides of the sheet parallel within 0.0003 in. After mechanical polishing to 0.005 in., electropolishing in 1:9 perchloric-acetic acid solution produced a final thickness of 0.002 in. The preferred orientations were determined from

Jan 1, 1968

By O. D. Gaither

This paper is an analytical study of the flow of fluids through small vertical conduits. Small conduits are defined as 11/4-in. nominal diameter tubing size and smaller, and approximately twice this area for annular conduits (i.e., 1- X 21/2-in. annulus and smaller). Experimental data are presented for the 1-X2-in. and 11/4- X 2%-in. annuli, and the I-in. and 11/4-in. tubing, since these represent the small conduit sizes and configurations generally encountered in oilfield applications. Data have been gathered for these conduits for single-phase water, single-phase gas and two-phase water-gas mixtures, with particular emphasis on high gas-liquid ratios. Water rates in excess of 2,000 BID and gas rates in excess of 2.5 MMcf/D, and two-phase flow ratios in between these two, represent the scope of the data gathered. Existing equations have been applied to predict flowing pressures and compared with experimental data. New correlations have been developed. INTRODUCTION The increased economic pressure on the domestic oil industry in the United States has constantly required the use of new techniques and equipment designed to reduce the cost of finding and producing oil and gas. Since tangible items are most readily apparent in economic analysis, the advent of lower-cost well completions was inevitable. One of the methods used to reduce costs which has received widespread attention is the slim-hole completion technique where tubing is used as the well casing and in which small conduits are used for tubing if necessary. Small conduits, defined by Kirkpatrick1 as "11/4-in. diameter nominal tubing and smaller for tubing flow and less than twice the 11/4-in. diameter nominal tubing internal flow area for annulus flow", have also found widespread usage as siphon strings for de-watering gas wells and as "kill" strings in deep high-pressure oil and gas wells. The growing use of small-diameter tubing has resulted in an increased need for development of improved methods to measure or predict flowing bottom-hole pressures since the physical dimensions generally preclude the use of subsurface-recording pressure gauges. Even in the cases where small bombs are available, the relatively high velocities encountered at nominal flow rates make it necessary to use excessive weight bars or special hold-down devices. Attempts to use recognized correlations to accurately predict flowing or gas-lift performance in wells equipped with small conduits have been generally unsuccessful. Insufficient field data were available to allow the development of a correlation on this basis, and an experimental approach was applied in an attempt to obtain a workable relation. The experimental approach used to obtain the data presented in this paper was actually a compromise between a field installation and a laboratory study. A test well 1,000 ft in length was used to obtain flow data on single-phase liquid, single-phase gas and two-phase water-gas flowing mixtures. Liquid rates up to 2,200 B/D and gas rates up to 3 MMcf/D were used in the single-phase flow studies. Two-phase flow rates from 100 to 600 B/D with gas-liquid ratios from 500 to 8,000 cu ft/bbl were recorded. Experimental data were obtained for single- and two-phase flow through 1-in and 11/4-in. nominal tubing, and through the annuli between 1- and 2-in. and 11/4- and 2%-in. nominal tubing strings. Experimental results for the two-phase flow are compared to the Poettmann-Carpenter correlation2 which is widely used as a comparative standard for development of multiphase flow predictions in flowing and gas-lift wells. Correlations developed by Tek,3 Baxendell and Thomas" were also investigated. The experimental data recorded herein fell in between the two flow regimes as defined by Ros," and this correlation also failed to yield satisfactory results. The fact that existing correlations failed to confirm the experimental data led to the need for development of a new correlation. Although a two-phase flow study was the primary objective of this investigation, data were also recorded for single-phase flow of water and gas, and constants were developed relating to pipe roughness and equivalent diameters for annular flow. These single-phase studies assisted materially in the development of certain of the two-phase flow results. Considerable previous work has been published which presented relationship of surface measurements to bottom-hole condition. The works of Buthod and Whiteley,6 Jones,' Poettmannb and the Texas Railroad Commission" are classic examples of the successful use of mathematical relationships which allow acceptable predictions of subsurface pressures, when gas is the flowing fluid. Darcy and others have derived relationships which may be used with minor modifications to predict subsurface flowing conditions in injection and water-supply wells. As previously stated, the application of the single-phase flow relationships

By J. G. Patchett, R. W. Rausch

Fresh waters and the presence of clay in many Rocky Mountain and West Coast sands require special methods of log analysis. Archie's saturation equation requires addition of a shale correction term, and the SP equation must also be modified to account for clays. Suitable equations were developed several years ago, but have not been widely used due to the algebraic complexity. A computer-oriented method has now been developed to overcome this problem. The basic shaly sand equations are rearranged in four different ways to permit solution for various sets of available input data. Essential to application of the method is the correction of observed SP values to those that would be observed if the resistivity of the formation waters were exactly interchangeable with the activity. A graphic method for doing this is given. Where conditions require consideration of the effect of clay in the sands, the method presented has been found to improve the accuracy of water-saturation determinations. INTRODUCTION Log interpretation in many Rocky Mountain and West Coast basins is complicated by rapid vertical and lateral changes in water resistivity. Calculation of formation water resistivity from the SP curve becomes difficult in zones that contain clay, since changes in SP deflection may be due to changes in either clay content or water salinity. In hydrocarbon-producing reservoirs, the problem is further complicated because hydrocarbon saturation also reduces the SP.1 A log interpretation system using computers has been developed to provide a solution to this problem, based on equations proposed by de Witte.2 Four different simultaneous solutions of de Witte's equations have been made. Each solution method uses a different set of input data as independent variables. Thus, a choice of solution method is possible, depending upon the logs run and the availability of other data. Two of the solutions do not require a knowledge of water resistivity. This system is intended to be used primarily in multiple sandstone-shale sequences of low and moderate resistivities where the principal contaminant in the sandstones is clay. However, where sufficient regional data are available, interpretation in single-zone sandstone reservoirs can also be improved by using the method. THEORY AND HISTORY OF SHALY SAND ANALYSIS The log interpretation formula originally proposed by Archie3 in 1941 is applicable only to rock-fluid systems wherein the rock has negligible electrical conductivity. In 1949, Patnode and Wyllie4 showed that if the rock itself can be considered conductive due to the presence of clay, a different calculation approach is necessary. During the following years, this problem was investigated at great length, as was the related problem of the effect of rock conductivity on the SP.5-11 These investigations established functional relationships between SP, resistivity, water saturation and water resistivity for such a formation. Refs. 2 and 12 provide summaries of these studies. Unfortunately, practical use of these relationships required that water resistivity be known independently from the SP. Although log interpretation methods for rock systems containing clay were proposed at that time,' they were not generally accepted for routine use. There are three principal reasons for this. First, in many field situations involving high-salinity water, rock conductivity may be neglected (even if present) without introducing appreciable error. This may be seen by considering the following expression for waier-saturated rock.' 1/R2=1/R1+1/FRn....(1) where 1/R, is conductivity due to clay. As Rw becomes small, I/FRw becomes much greater than 1/R, which may be neglected. Where 1/R, may be neglected, the sandstone is called clean. If the term may not be neglected, the sandstone is termed dirty or shaly. For resistivity purposes, the classification between clean and shaly sands then depends not only upon the conductivity due to shale in the sand, but also upon the resistivity of the associated water (shale is used here to mean surface condition due to disseminated clay). A sand of given conductivity might safely be treated as clean in association with high-salinity water, but would require shaly sand methods if associated with fresher waters. Shaly sand methods are not required in many areas having saline waters; but in Rocky Mountain and West Coast sands having relatively fresh waters (often more than 0.3 ohm-m resistivity at formation conditions), the shaly sand methods are needed. Errors Rw calculations from the SP due to the presence of shale are likewise related to water salinity. In saline water formations drilled with fresh mud, the ratio of mud filtrate resistivity to water resistivity is high, the SP is large and the presence of shale can introduce large errors in water resistivity calculated by the conventional method. When the resistivity ratio is low, the errors are smaller. At zero SP, no error would result from shale. Thus, from the SP viewpoint, a given rock could be shaly if associated with a saline water, and clean in association with a fresh water, which is the opposite of the resistivity-oriented definition above.

By R. A. Burmeister, G. P. Pighini, P. E. Greene

An open tube vapor phase epitaxial growth system has been used for large area (multiple substrate) growth of GaAs1-xPx on GaAs substrates. The GaCl-GaCl transport reaction is used with either a GaAs or Ga (nonsaturated) source. Selenium and tellurium have been used for donor impurities, and zinc as an acceptor. The useable substrate area in this system is approximately 20 sq cm. The uniformity of thick-ness of the epitaxial layers are typically better than ±5 pct across a given wafer. Electrical and optical measurerments indicute comparable uniformity in electrical and luminescent properties within a wufer. The application of this system to the large scale pro-duction of GaAs1-x Px for display devices, both discrete and arrays, is discussed. Typical electrical and luminescent properties of light emitting diodes fabricated front material produced by this technique are presented. THE most promising materials currently being utilized for visible injection electroluminescence are GaAs1-xPx, Ga1-xAlxAs, and Gap. All have reasonably efficient emissions in the red portion of the visible spectrum at room temperature; Gap also has an efficient green emission.' At present, GaAs1-xPx has a technological advantage over Ga1-xAlxAs and Gap for display applications, since relatively large (several sq cm) areas of GaAs1-xPx suitable for use in electroluminescent devices may be readily grown by vapor phase growth techniques. In contrast, the preparation of Gap and Ga1-xAlxAs for electroluminescent device applications generally employs solution growth techniques which are at present not well suited for the growth of large areas of uniform thickness and doping level. The capability of uniform growth over large substrate areas and the use of multiple substrates is necessary for the practical utilization of electroluminescent devices. This is particularly important when quantity production or monolithic devices are required. Furthermore, in many display applications arrays of light emitting devices are used, the individual elements of which are of a size resolvable by the unaided eye. Thus the overall dimensions of display are substantially larger than those of most semiconductor devices. It is also necessary to achieve a high degree of control over the growth parameters to attain the required degree of reproducibility of materials properties for electroluminescent devices. In the case of GaAs1-xPx it is necessary to accurately and precisely control the phosphorus content of the alloy, both on a macroscopic and microscopic scale, in addition to the parameters generally associated with epitaxial growth such as thickness and doping level. This value is critical, as it has a major effect on the performance of electroluminescent devices. This paper describes the epitaxial growth of GaAsl-xPx suitable for electroluminescent display devices using a system developed specifically for this purpose, and which contains several novel features. The results of studies of selected physical properties of the epitaxial layers are also discussed. Finally, a brief summary is given of the characteristics of display devices fabricated from GaAsl-xPx grown in this system. EXPERIMENTAL A) Reactants. A number of techniques suitable for the vapor phase epitaxial growth of GaAs1-xPx have been reported in the literature.'-' The method selected for this investigation is that in which the Ga is transported by the GaC1-GaCI3 reaction in an open tube process. The results reported here were obtained using either the combination of GaAs, AsC13, and pH3, or Ga, AsH3, pH3, and HC1 as the initial re-actants.* The ASH3 and pH3 were obtained as dilute *Several different sources of supply were used for these reactants, y~elding comparable results._____________________________________________________ mixtures in HZ; the HC1 was obtained from the reduction of AsC13 by Hz at elevated temperatures. Both selenium and tellurium were employed as donor impurities, and zinc as an acceptor impurity. Selenium was introduced in the form of H2Se, tellurium in the form of tellurium-doped GaAs, and zinc in the form of diethy1 zinc. B) Apparatus. The prinicipal difference between the apparatus used in the present study and that of Tietjen and Amick,8 in addition to size and other related design features, is that RE induction heating is utilized in place of resistance heated furnaces. Induction heating was selected for this application because it appears to have several advantages, including: 1) It is possible to keep all fused silica portions of the apparatus at temperatures well below those of the reaction zone, thus minimizing a possible source of contamination. 2) The thermal mass of an induction heated system can be made small, thus reducing the total time required for the growth process. 3) Sharp temperature profiles (desirable for high deposition efficiency) are easily achieved. 4) The volume of the system for a given substrate area can generally be made smaller than a comparable resistance heated unit. This results in shorter time

Jan 1, 1970

By J. D. Livingston, H. E. Cline

Cu-Pb alloys in the vicinity of the monotectic composition have been directionally solidified under a high temperature gradient at rates up to 2 X l0-' cm per sec. Over a wide range of compositions, high growth rates yield a composite structure consisting of continuous rods of lead in a copper matrix. This range of compositions increases with increasing growth rate, in agreement with arguments based on the relative velocities of composite growth and the growth of copper dendrites or lead drops. The breakdown of the composite structure at slow growth rates is explained in terms of the relative interphase surface energies. The observed interrod spacings of the composite structure are large compared with the predictions of the Jackson-Hunt equations of eutectic growth. ThE directional solidification of many eutectic alloys produces fine composite structures of parallel lamellae or rods. There has been considerable interest not only in the fundamentals of this two-phase solidification process,'-3 but also in the interesting physical properties produced by such regular and aniso-tropic microstructures. Composite structures can be grown only over a limited range of composition, beyond which coarse primary dendrites of one phase appear. In organic eutec-tics, this composition range of composite structures has been shown to increase with increasing growth rate.7"10 These results were explained in terms of the relative velocities of composite (coupled) growth and dendritic growth. Although similar arguments should apply to metallic eutectics,11-13 suitable experimental results are lacking. In contrast to the work on eutectics, the directional solidification of monotectic alloys has received little attention. (The monotectic reaction is similar to the eutectic reaction, except that one of the resulting phases is a liquid, which subsequently solidifies in a separate reaction at a lower temperature.) Directional solidification of some monotectic alloys'4715 yields regular rodlike microstructures, whereas in other cases macroscopic separation of solid and liquid phases occurs.16 chadwick17 rationalized these results in terms of the probable relative magnitudes of the various interphase surface energies. A recent study of chill-cast Cu-Pb alloys18 revealed a fine rodlike microstructure in alloys near the monotectic composition. It was decided to investigate the directional solidification of such alloys, and to determine the range of composition and growth conditions yielding composite structures. The Cu-Pb system is convenient for such a study, both because it is simple metallurgically, with no compound formation and negligible solid solubilities, and because its basic properties are well-documented. Recent literature on the Cu-Pb system includes studies of bulk thermo-dynamic properties,'g surface energies,20"21 densi-ties,25 and diffusion constants.a6 A similar study of the directional solidification of Cu-Pb alloys was recently undertaken, independently, by Kamio and Oya." EXPERIMENTAL Alloys were prepared by melting 99.999 pct Cu and 99.999 pct Pb in a graphite crucible, stirring well, and pouring into a cold graphite mold. Rods 0.175 in. in diam were machined from the ingots. Alloy compositions studied ranged from 25 to 55 wt pct Pb. Samples were placed in graphite crucibles 5 in. long with 4 in. OD and 0.035-in. walls. They were melted under flowing argon in a vertical, two-zone. platinum -wound furnace. A voltage stabilizer was used to minimize fluctuations in input power. The narrow specimen diameter minimized convection. Directional solidification was achieved by driving the crucible downward into a +-in. hole in a water-cooled copper toroid. The toroid was located immediately below the narrow end zone of the furnace. The end zone was separately powered to maintain high local temperature. Therefore a high temperature gradient (approximately 300 deg per cm) was maintained in the specimen throughout the run. The crucible motion was screw-driven. and a wide range of drive speeds were available. The limited rate of heat removal caused a thermal lag in the specimens at high drive rates. However. temperature-time curves from thermocouples imbedded in a representative sample indicated that the average growth rate still approximately equaled the drive rate. Although the specimens were initially homogeneous, melting and re solidification redistributed the lead. producing composition variations of several percent along the specimen length. (During melting. lead melted first and ran down the sample surface. Rapid freezing tended to reproduce the resulting composition gr~dient, but slow freezing did not because a slow-moving interface tended to reject lead. as discussed later.) To determine local composition. ;-g samples were cut from regions exhibiting various microstructures and were chemically analyzed for lead content. Micrographs were taken on as-polished or lightly etched surfaces. Three-dimensional structure of the lead network was viewed with a scanning electron microscope after removal of some of the copper matrix with nitric acid. RESULTS Several different microstructures are observed, depending on composition and drive rate. Because melting and resolidification produced composition gradients, results are best presented in t&ms of final local composition, rather than initial or average composition. The ranges of local compositions and drive

Jan 1, 1970

By R. D. Taylor, Jim Douglas Jr., H. H. Rachford Jr., P. M. Dyke

A major obstacle to the use of wetting agents in .secondary recovery by water flooding is the adsorption of the agents on the sand. As a result of adsorption, the surfactant always lags behind the floodwater front. Consideration of the chromatographic theory of adsorption indicates that the detergents will not lag as much if used in very high concentrations. An investigation was made of the possibility of using high concentrations economically by flowing slugs of wetting agents followed by normal flood water. The experiments consisted of adsorption studies on Alundum powder and Berea sandstone. Flow rests on a 12-in. Alundum core and 22-in. Berea core were used to determine rate of detergent movement. The results of the flow experiments indicate that the relative rate of surfactant advance is, indeed, sensitive to the concentration of the agent. A 10 per cent slug moved with a rate that war 78 to 95 per cent as fast as the rate of advance of the flood water. By contrast, one with 25 ppm (the number of parts of commercial detergent in a million parts of water on a weight basis) concentration moved less than one-fourth as fast as the flood water, and calculations indicate that in very long porous systems the rate of movement of the lower concentrations will be a small fraction of the rate of advance of the flood front. The results. of the adsorption studies were utilized to calculate the rate of advance of the detergent when only the initial concentration was known. The calculated rates showed substantial agreement with the experimental flow tests in the high concentration ranges. The adsorption results were also used to estimate the cost of the materials for a slug-type surfactant flood in the field. In addition to the faster rates of movement, the concentrated detergent slugs removed much more oil than the dilute solutions. However, the effectiveness of the slug process depends on many variables. The quantity of oil removed is increased markedly by increasing the flooding rate. The efficiency is also influenced by the type of crude, type of reservoir rock and initial water saturation. Therefore, a careful analysis of each reservoir system is required before the economic value of the process can be determined. INTRODUCTION It is well known that the displacement of oil by invading water during water flooding is far from complete. It is generally agreed that the unrecovered oil is retained in the porous medium by the capillary forces which may be relatively large compared to the forces generated by the flowing water. Therefore, it was logical that some early workers should turn to surface-active materials to reduce the capillary forces to facilitate the release of oil. As early as 1927,' a patent was granted for the use of surface-active materials in water flooding. In 1932, when soap solutions were passed through Bradford and Venango sands, it was reported that the results were inconclusive, erratic and that "further investigation is needed to determine exactly the function of the solution and to obtain a clearer insight into the phenomena involved."' Some of the modern scientific reports conclude with a similar statement,' showing that the lack of agreement on the mechanism of oil removal by wetting agents is still very widespread even though several comprehensive studies have been reported.'." Although there is a lack of agreement as to the general effectiveness of the detergents for water flooding, most investigators do agree that all of the common detergents are strongly adsorbed onto the solid surfaces of the reservoir. In the early calculations it appeared that all additives would be lost before reaching much of the formation area which contained the additional oil to be removed. Experiments indicated that if the usual small waterflood concentrations of wetting agents were used, the rate of advance of detergent through the formation would be only a small fraction of the rate of advance of the flood front. Indeed, some investigators4 felt that the use of wetting agents would never be economically feasible because of their adsorption. For example, DunningG estimated that the wetting agent in concentrations of 25 ppm, would advance only 0.05 times as fast as the flood front. Ojeda, et al,' found that a surfactant in a concentration of 10 ppm moved less than 0.01 times as fast as the flood front. It is significant, however, that both investigators found that increased concentrations of wetting agents moved faster, relative to the flood front, than solutions at the lower concentrations. Ojeda showed that an extrapolation of his data indicated a relative rate of 0.5 at 1 per cent concentration, while Dunning6 estimated a relative rate of 0.46 for a 1 per cent concentration. It was obvious that these concentrations could not be used for continuous injection because the cost of the injected detergent would far exceed the value of additional oil produced. Traditionally, detergents are used in very low concentrations for they show good

By K. G. Wikle, W. W. Beaver

The factors which control the rate of dissolution of pure gold in cyanide solution were studied both directly and through measurement of solution the current-potential curves for the anodic and cathodic portions of the reaction. The mechanism of dissolution is probably electrochemical the reaction in nature, and the rate is determined by the rate of diffusion of dissolved oxygen or cyanide to the gold surface, depending on their relative concentrations. The significance of the results and the effects of impurities are considered. ALTHOUGH the dissolution of gold in aerated cyanide solutions has been used as an industrial process for treatment of gold ores since the late nineteenth century, the factors which determine the rate of the reaction have never been identified unambiguously. Studies of the rate of dissolution by Maclaurin,1 White,2 Christy,3 Beyers,4 Thompson,6 and others are contradictory in their conclusions; some claiming that diffusion of the reactants to the gold. surface controls the rate, and others that the chemical reaction is inherently slow and related to high activation energy for the reaction. Christy3 and 'Thompson" both suggest that the reaction is electrochemical in nature and that the dissolution of gold proceeds at local anodic regions while the oxygen is reduced at cathodic regions on the gold surface. Although their studies are ingenious and do indicate an electrochemical reaction under the conditions of study, their experiments were of limited nature and failed to identify the rate-controlling process in the system. The importance from an industrial viewpoint of a knowledge of the mechanism and rate-controlling factors in gold dissolution can be illustrated as follows: If the rate is controlled by a slow chemical reaction rather than by diffusion of the reactants, then an increased temperature should have a marked accelerating effect; agitation of the slurry should have no effect on rate: and increased concentration of reactants should cause acceleration of the rate. If the rate is controlled by the diffusion of one or the other of the reactants to the gold surface, then increased agitation should increase the rate; increased temperature will increase the rate, but not as much as for the case of a slow chemical reaction; increased concentration of the reactant which is diffusion limited will increase the rate; and the concentration of other reactants should be without effect on the rate. It may be concluded that for design of a commercial process for gold leaching, the rate-controlling factors of the reaction should be understood so that an intelligent choice of the conditions of agitation, temperature, and reactant concentration may be made. The experiments described here lead to the unambiguous conclusion that in a system of pure gold and a pure aerated cyanide solution the rate of dissolution is controlled either by the rate of diffusion of dissolved oxygen or cyanide to the gold surface, depending on the relative concentrations of each. There is also ample, but not conclusive, evidence that the mechanism of the reaction is identical to that of electrochemical corrosion. The practical significance of these conclusions will be discussed later in the paper. Experimental The experimental method used in this work was to employ an electrolytic cell which performed the overall gold-dissolution reaction, and to study the anodic and cathodic reactions of this cell as to their nature and the rate-controlling factors. Simple experiments on the rate of dissolution and the potential of the dissolving specimen also were performed under conditions of agitation, temperature, and concentration identical to those used in the electrode studies. Analysis of the electrode studies by well established theories of electrochemical corrosion were made, and the results were found to bear a one-to-one relation with actual rate and potential measurements. Electrode Studies: The Anodic Reaction: The gold specimen used for all of the electrode studies and the rate determination consisted of a sheet of 99.99 + pct Au wrapped around a lucite rod and sealed at the edges with plastic cement, thus forming a cylinder of gold of known and constant area (8.0 sq cm). The lucite rod was threaded into a brass spindle which could be rotated at speeds of 100, 300, and 500 rpm. For the electrode studies electrical contact between the gold cylinder and the brass spindle was made by means of a gold strip covered with plastic. The anodic dissolution of gold was studied by immersing the electrode in a solution containing known concentrations of KCN and KAu(CN)2 but free of oxygen, and by passing an anodic current through the gold electrode. The pH of the solution was maintained between 10.5 to 11.0 in these and all other tests by addition of KOH. The pH was measured before and after each test by means of a glass-elec-

Jan 1, 1955

By W. W. Whitaker, C. W. Manry, R. H. McLean

In an eccentric annulus, cement may favor the widest side and bypass slower-moving mud in the narrowest side. Tendency of the cement to bypass mud is a function of the geometry of the annulus, the density and flow properties of the mud and cement and the rate of flow. Bypassing can be prevented if the pressure gradient protluced from circulation of the cement and buoyant forces exceeds the pressure gradient necessary to drive the mud through the narrowest side of the annulus at the same velocity as the cement. In the absence of buoyant forces, one requirement for this balance is maintenance of the yield strength of the cement greater than the yield strength of the mud multiplied by the maximum distance from the casing to the wall of the borehole and divided by the minimum distance. If the yield strength of the cement is below this value, bypassing of mud cannot be prevented unless buoyant forces or motion of the casing significantly aid the displacement. INTRODUCTION Successful primary cementing leaves no continuous channels of mud capable of flow during well treatment and production. Prevention of channels requires care. Tep-litz and Hassebroek provide evidence of channels of mud after primary cementing in the field.' Channeling of cement through mud in laboratory experiments has also been reported.'-' Recommendations for improving the displacement of mud include (1) centralizing the casing in the borehole,'-" 2) attaching centralizers and scratchers to the casing and moving it during displacement,18 "3) thinning the isolating the cement by plugs while it is circulated down the casing,%( (5 establishing turbulence in the cement," and (6) holding the cement slurry at least 2 lb/gal heavier than the mud and circulating the cement slurry at a very low rate of flow.' Although much has been written about the above parameters, the relative importance of each has not been well defined. In this investigation, the mechanics of mud displacement are described through results from analytical models and experiments. The model chosen — a single string of casing eccentric in a round, smooth-walled, impermeable borehole — is analagous to casing centralized in a borehole which is not round and to placing more than one string of casing in a borehole. In each, some paths for flow are more restricted than others. A fluid flowing in the borehole may seek the least restricted, or most open, path. This tendency for uneven flow can lead to channeling of cement through mud unless preventive measures are taken. The analytical models describe channeling and give means of balancing the flow. Experimental data test the analytical models and illustrate effects of motion of the casing, differences in density and mud's tendency to gel. Results are encouraging. Piston-like displacement of mud by an equal density cement slurry is possible through proper balance of the flow properties of the mud and cement slurries to the eccentricity of the annulus. The more eccentric the annulus, the thicker must be the cement relative to the mud. If proper balance is not achieved. bypassing of mud by cement cannot be prevented without assistance from motion of the casing or buoyant forces. Increasing the rate of flow can help to start all mud flowing but cannot prevent channeling of cement through slower moving mud in an eccentric annulus. Thinning the cement slurry tends to increase channeling although the extent of turbulence in the annulus may be increased. Description of flow in an eccentric annulus begins in the next section. It is assumed that (1) the casing is eccentric and is stationary, (2) the mud and cement slurries have the same density and (3) the gel structure of the mud has been broken and the mud and cement follow the Bingham flow model. Effects related to these restrictions will be discussed. FLOW PATTERNS SlNGLE FLUID IN ANNULUS Flow of a single fluid through an eccentric annulus is illustrated in Fig. 1. Part A shows laminar flow of a Newtonian fluid. This distribution of flow was calculated by Piercy, Hooper and Winney.' In fully developed turbulent flow, the velocity distribution around the annulus is less distorted, but the flow still favors the widest part of the annulus Parts B, C and D of Fig. 1 are a qualitative representation of the flow of a Bingham fluid. The yield strength of the fluid increases the severity of bypassing compared to Newtonian flow. At a very low rate of flow, all flow is confined to that portion of the annulus which has the minimum perimeter-to-area ratio. The fluid shears on the perimeter of that area when the pressure gradient multiplied by the area just exceeds the yield stress of the fluid multiplied by the perimeter. Whether or not the minimum perimeter-to-area region encompasses all of the annulus or only a part (as shown in Part B) depends on the geometry of the annulus. If only a part begins to flow, increasing the rate of flow increases the area flowing until finally there is flow throughout the annulus.

By A. E. Jenkins, O. C. Roberts, D. G. C. Robertson

Using an inverted-cone coil at 450 kHz, it has been possible to levitate iron (FeS), cobalt (CoS), and nickel (NiS) sulfides. Important nontransition metal sulfides such as ZnS, PbS, and Cu2S have proven impossible to levitate although Cu-Fe-S ternary alloys containing 30 wt pct S and up to 10 wt pct Cu, and Cu-Co-S and Cu-Ni-S ternary alloys containing 30 wt pct Cu have been levitated. The levitation technique has been used in preliminary experiments on the vaporization from liquid sulfides and the reaction of liquid metal-sulfur alloys with oxidizing atmospheres. The course of the reactions with pure oxygen were followed using highspeed photography and two-color pyrometry. ELECTROMAGNETIC levitation is now established as a basic laboratory technique in high-temperature research but its application has been restricted mainly to metals and alloys. Applications have included alloy preparation,' metal purification,2'3 determination of liquid metal densities and emissivities,4,5 and studies of metal supercooling,4 alloy thermodynamics,6 and vaporization phenomena.7-9 The application of the technique to compounds has not been considered previously. The successful investigation of the reactions between dilute iron alloys and oxidizing atmospheres10'1 has prompted the current physico-chemical studies involving levitated metal sulfide drops and flowing inert or oxidizing atmospheres. This paper presents the results of such a study and provides a basis for future studies involving a wide range of other compounds of metallurgical interest. The successful levitation of many metal sulfides and mattes provides a method of studying the oxidation reactions fundamental to flash-smelting and similar pyrometallurgi-cal operations under closely controlled laboratory conditions. In addition the system allows the use of a controlled atmosphere (e.g., a gas stream of a certain H2/H2S ratio) with a particular chemical potential to study the relevant thermodynamic equilibria or the mass transfer processes between the atmosphere and the levitated drop under conditions where the hydrodynamics of the system can be closely defined. The optimum frequency for the levitation melting of metals in an inverted-cone coil type inductor is within the radio frequency range 400 to 500 kHz. At frequencies lower than 10 kHz the rate of heat generation is usually insufficient to melt the levitated charge' or where melting is achieved, "dripping" from the charge is encountered.'' At frequencies above 2 mHz the levitation force decreases. Metals, alloys and preheated elemental semiconductors such as germanium and silicon, have been levitated but the levitation of only a few metal compounds has been reported. Jostsons13 and the authors have levitated liquid titanium-oxygen alloys containing 50 at. pct 0 while clark14 has reported the levitation of mixtures of FeS and MnS for short periods. With a "cold crucible" inductor sterling15 has melted ferrites by preheating them by induction in a 4 mHz field and melting at a lower frequency. However this second type of inductor has been designed purely for the melting of materials without contamination; there is only a small gas film between the charge and the inductor and the electromagnetic levitation effect is of secondary importance. For this reason further discussion will be restricted to the use of the coil type inductor. The assessment of the suitability of a particular metal compound for levitation is based upon the following two criteria: i) thermal stability, and ii) physical "levitability". In this paper these two criteria will be considered separately. The thermal stability of a solid or liquid metal compound with respect to a gaseous environment depends upon its chemical reactivity with that environment or, in the case of an inert atmosphere considered here, its volatility. The physical criterion as to whether or not a particular compound can be levitated is based upon a comparison between those physical properties of the compound determining "levitability" which are defined by the fundamental equations of levitation theory as developed by Okress et a1.,16 and the properties of the metals. Since it is not practical to cover the vast field of metal compounds, further discussion will concentrate on the metal sulfides but the treatment would be applicable to any metal compound. THE THERMAL STABILITY OF METAL SULFIDES The temperatures usually encountered during levitation in inert atmospheres cover the range 1400" to 2000°C. The stabilities of the condensed states of the sulfides under these conditions are considered in relation to the periodic classification by reference to Table I. Two general classes of sulfides emerge. The solid sulfides of elements of group IIB and of groups further to the right are volatile while those sulfides of group IB and of groups further to the left are nonvolatile solids. The sulfides described as volatile may be dismissed as unsuitable for levitation. The stabilities of the more favorable nonvolatile sulfides under the anticipated conditions must be studied more closely From Table I it is seen that the alkali metal sulfides exist as liquids in the temperature range of in-

Jan 1, 1970

By L. Cichowicz, K. K. Millheim

The constant-rate drawdown test performance for a low-permeability, verticany fractured gas well was investigated. A series of gar wells were tested by flowing each well at constant rate until the data could be analyzed using con-ventional radial flow theory. Each well was then shut in to build up. After a sufficient buildup was obtained, another flow Iest commenced but at a higher flow rate than Ihe first test. Again, the well was shut in when radial fiow was obtained. his procedure was repeated for three to four different flow rates. Two wells in the San Juan basin were tested using this procedure. Both wellere fractured after completion, cleaned up and then shut in until flow testing commenced. Test designs of both wells permitted investigation of the most realistic values of egective permeability, wellbore radius and turbulence factor. Also, being able to determine the eflective fracture flow area and vertical fraclure efficiency was inherent with this testing approach. It was observed that fractures in both wells influenced the Pressure behavior for approximately Is to 40 hours (depending on the flow rate) before radial flow was evident. After this time, drawdown data were analyzed using radial pow theory. When a low-permeability gas well has vertitally oriented, induced fractures, the early flow geometry ic. essentially linear. It will be shown how to determine when a flow test has been conducted long enough so lha' the most representative values of effective permeahiiity. wellbore radius and turbulence factw can be calculated. From the linear pressure data, valuable information about The fracture treatment, such as the effective flow area and vertical fracture efficiency, can be determined for vertically froctured wells. Introduction During tests on gas wells in the Sari Juan basin7 initial transient behavior lasted for many days because of the low permeability of some porous media. As a result, stabilized flow performance could not be obtained. If these wells received some type of stimulation treatment, early pressure behavior deviated from conventional theoretical radial Row. When conventional radial flow theory was used to analyze these low-permeability fractured gas wells, larger values of flow capacity and absolute open flow potentials (AOF) sometimes resulted. Wells were assigned open flow poten- tials that proved to be 3 to 10 times higher than the well would sustain over a longer period of production. In some cases where the wells had flowed for longer periods of time during a constant-rate drawdown test, it was noticed that the effective flow capacity appeared to be decreasing with time until a certain value was reached. The early nonradial pressure behavior can be explained If linear flow is assumed. Rusell and Truitt mathematic. ally investigated the vertically fractured well in a bounded area. They showed that early flow behavior was essentially linear and, for x,/x. approximately less than 0.10 radial flow was obtained after short periods of time. Then realistic values of effective permeability and skin could be determined. Scotta experimentaliy studied the vertically fractured well with a heat flow analog. He showed that earb flow was linear, Both studies indicate that, for small values of x,/x,, linear flow approaches radial flow if the well is tested long enough, To help prove this concept of early linear flow caused by induced vertical fractures, two low-permeability gas wells were tested. Both wells received large fracture treatments prior to testing. A vertical fracture was indicated from the analysis of fracture treatments, As anticipated, tests of both wells indicated early linear flow that was later followed by a period of radial flow, Data collected from each well were analyzed. From the well tests, plus other information on each well, the effective permeability, wellbore radius and turbulence factor were calculated. Effective fracture flow areas calculated from test analyses for each well proved to be approximately one-fourth the created area calculated from classic hydraulic fracturing theory: other fractured wells that were tested but not presented in this paper also indicated that the effective fracture flow area was one-fourth to one-third the created area predicted from hydraulic fracturing theory. The vertical fracturing efficiency was estimated from the calculated values of effective wellbore radius and fracture flow area. For the two wells tested, calculated fracture lengths x, were 112 and 105 ft, and the vertical fracturing efficiencies E, were 122 and 183 percent. Development of Flow Model Agnew' showed that most induced fractures below 1,500 ft are vertical. Anderson and Stah15 indicated that most of the fractures they studied were vertical. Thc model proposed for early flow in most vertically fractured gas wells is shown by Fig. 1. This model should approximate early flow behavior until radial flow is reached, at which time a radial model with an effective wellbore radius of 0.5 they will

Jan 1, 1969

By C. van Dijk

In Sept., 1960, a steam-drive project was started in the solution-gas drive area of the Schoonebeek field. A part(ern of three five-spots and one four-spot was selected covering an area of 65 acres. The pay in the project area has good lateral continuity and dips slightly to the northeut; it is about SO ft thick and permeability increases from 1,000 and at the bottom to approximately 10,000 md at the top. The oil originally in place was 12.6 X 10' bbl. The oil has an in situ viscosity of about 180 cp. At the start of the steam drive the cumulative primary production due to. solution-ga.7 drive amounted id 4 Percent of the oil originally in place. Reservoir pressure had dropped about 120 psi and no significant primary re-.serves remained. Some 11.3 million bbl of steam (all steam quantities are expressed in barrels of water vaporized) have been injected, resulting in production of an additional 4.1 X I0 9bl of oil, or 33 percent of the oil originally in place. This corresponds to a cumulative oil-stearn rario of 0.37 bbllbbl. It appears that the steam preferentially moves r updip while liquids are produced mainly from downdip wells observations indicate that tile steam flows through only the upper part of the formation. The lateral steam distribution in the pattern is satisfacrory since several prodriction wells hardly reacted and, hence, cori tributcd little to the oil production. Production performance and results from material balance calcutlations agree satisfactorily with the results of large-,scale laboratory experiments. On the basis of these experirmental results the .steam drive, together with a cold water follow-up. is expected to bring ultimate recovery to a value of crt leas: 50 percent of the oil originally in place. No serious production problems have been encountered. However, due to mechanical fuilure, two old prodriction wells and one injection well had to be replaced. An extension of the. steam drive in this area is under connstruction. Introduction The Schoonebeek oil field, discovered in 1943 and developed after World War 11, is situated in the eastern part of the Netherlands. The main oil reservoir in this field is the Valanginian sand. A completely sealing fault divides this reservoir into two areas (Fig. 1): the southwestern part of the sand body where primary production is ob- tained by means of a solution-gas drive, and the remain. der where edge-water drive is the production mechanism. In the greater part of the field the reservoir consists of a single, unconsolidated sand body. The net thickness ranges from 30 to 100 ft and the top is between 2,400 and 2,800 ft below sea level. Formation permeability varies from approximately 10,000 md at the top to values of the order of 1,000 md at the bottom, and porosity is about 30 percent. The reservoir contains a paraffinic oil of 25" API gravity with an in situ viscosity of 160 to 180 cp. Initial oil saturation was high (85 to 90 percent). The relatively large quantity of oil in place (more than 10' bbl), and the low ultimate primary recoveries expected from this field — approximately 15 percent stock-tank oil initially in place (STOIIP) for the water-drive area and 5 percent STOIIP for the solution-gas drive area — clearly indicate ample scope for secondary recovery. Because ies-ervoir and crude characteristics made this field suitable for thermal secondary recovery, a hot-water drive project was started in the water-drive area about 10 years ago. A few years later a steam drive and an in situ combustion project were started in the solution-gas drive area. This paper deals with the performance of the steam-drive project, which was started in Sept., 1960, and which is still in operation. Design of Steam-Drive Project, An experimental investigation of the steam-drive process carried out by schenk in 19561 indicated that under schoonebeek conditions steam injection could be an attractive secondary recovery method. the findings and encouraging results of a pilot test in the Mene Grande field in venezuela,i led to the design of a steam-drive project in the schoonebeek field, Pruject Site and Pattern In 1958 the reservoir pressure in the solution-gas drive area had decreased to about 120 psi, and oil production rates of wells in this area had dropped to 7 to 10 B/D. The cumulative primary production was about 4 percent STOIIP, leaving an oil saturation of approximately 85 percent. In view of the large amount of oil left behind in the reservoir, the solution-gas drive area was selected for the planned steam-drive project. The area in the vicinity of Well S1 3 (Fig. 2) was considered to be suitable since it is at least partly isolated from the rest of the field by faults and the sand is relatively thick (about 80 ft).

Jan 1, 1969

By Andrew Cosgarea, William R. Upthegrove, Morteza Mirshamsi

The capillary-reservoir technique was used with lead-210 and cadmium-115m to determine the self-diffiLsion coefficients of both cadmium and lead in the liquid binary Cd-Pb system. The self-diffusion coefficients of pure cadmium and pure lead were obtained and were compared with the theoretical predictions. Good to excellent agrement between the experimental and predicted values was obtained. The self-diffusion coefficients of cadmium were tneasuved in alloys containing 2.50, 9.13, 17.40, 31.00, 45.00, 69.00, and 97.00 lot pct Cd by determining- the amount of cadniiutn-115m which diffused out of a small-bore capillavy into an infinite reservoir during- a given time peviod. Sinzila7-measurements were made with lead-210 to determine the self-diffusion coefficients of lead in these identical alloys. Diffusivities were determined from measurenzents performed in the temperature interval of 290" to 480°C. The results were correlated with the Ar-vhenius equation, and the maximum variation of the equation parameters (Q and Do) was also inrestigated . THE theory of diffusion in liquids, particularly liquid metals, is relatively undeveloped in contrast to that for the gaseous and solid states. Although the practical application of liquid metals as heat-transfer media has become increasingly important, few liquid-metals systems have been investigated. Experimental data of fundamental significance in this field are not readily obtained, which may explain but not justify the present lack of knowledge. What work has been completed is primarily restricted to liquid diffusion of pure metals; little work has been done in liquid-metal diffusion of binary mixtures. A review of liquid-metal diffusion theory and research is available elsewhere.1-4 In an effort to add to the knowledge of liquid-metal systems and to increase the basic understanding of the diffusion process in liquids, a study of diffusion in the binary-liquid system, Cd-Pb, was undertaken. The capillary-reservoir technique5 was employed to measure the self-diffusion coefficients of cadmium and lead in molten binary alloys. Measurements were made with seven selected compositions and over a temperature range from 290° to 480°C. The experimental apparatus consisted essentially of the following items: constant-temperature bath, diffusion cells, capillaries, capillary-filling device, and a radioactive tracer counting system. EXPERIMENTAL APPARATUS Constant-Temperature Bath. A cylindrical steel vessel, 8 in. in diam and 15 in. deep, surrounded by an insulated heating coil was used with a sodium-potassium nitrate salt mixture heating medium. The bath was maintained slightly below the desired control temperature by the furnace-heating element; and a 250-w heater, actuated by a Bayley proportional temperature controller, was utilized for the final control of the temperature. A constant-speed mixer stirred the salt to insure a uniform temperature within the bath. Four calibrated Chromel-Alumel thermocouples were placed at various positions in the salt bath to verify the absence of temperature gradients. The observed temperature variation during any diffusion run was less than 0.l°C. The entire furnace assembly was mounted on four shock absorbers to exclude building vibrations and the stirrer propeller blades were adjusted so not to induce vibrations within the reservoir. A schematic diagram of the furnace and the constant-temperature bath is shown in Fig. 1. Diffusion Cell. The diffusion cells and associated parts were the same, except for slight modification, as the one used by walls1 in this laboratory, and are shown in detail elsewhere.' A graphite crucible, 4 in. long and 40 mm (1-1/2 in.) ID, enclosed in a 60-mm (2-1/4 in.) Pyrex tube cell about 18 in. long, was used as a container for the melt. The reservoir (molten alloy in the graphite crucible) was usually about 2 to 2-1/2 in. deep. Graphite was used because of its satisfactory nature as a refractory material and the low solubility of carbon in molten Cd-Pb alloy.677 The Pyrex cell was closed at the bottom and fitted at the top (open end) with a 2-in. Dresser coupling. A brass flange was welded to the top of the coupling. The upper part of the diffusion assembly was bolted to this flange with an O-ring seal. The lower part of the diffusion cell was supported in a 3-in. brass cylinder which was open to allow for circulation of salt around the cell. The top assembly consisted of two synchronous motors, a drive shaft, a thermocouple well, and controlled-atmosphere inlets and outlets. One motor was used for rotation of the capillaries at a rate of 1/2 rpm in the reservoir during the diffusion run. The other motor was used for the vertical positioning of the capillaries and the capillary holder by means of a simple screw drive. The capillary holder and drive assembly were lowered into the reservoir for the run and raised after the desired diffusion time at a rate of approximately 0.4 in. per min. Capillary holders were made of graphite. These

Jan 1, 1967

By M. I. Jacobson, A. S. Yue, A. E. Vidoz, F. W. Crossman

An equation governing the concept of constitutional supercooling under the combined effect of concentration and temperature gradients was used to produce platelike Al-CuAl2 eutectic composites for mechanical properties studies. Compression specimens were prepared from a single-colony Al-CuA12 eutectic composite ingot, 2 in. in diam and 12 in. long. The specirrzens were cut such that the platelets were oriented parallel, 45 deg, and perpendicular to the compression direction. Since the ingot was of eutectic composition, The aluminum-rich matrix could dissolve 5. 7 wt pct Cu in solid solution, and therefore could be strengthened by precipitation hardening. Specimens were tested at room temperature and elevated temperatures in the unidirectionally solidified, solution-treated, and solution-treated plus aged conditions. The results were compared with those for the conventionally cast and extruded specimens. For the controlled material, the highest strengths were obtained with platelets oriented parallel to the compression axis. In the unidirectionally solidified condition, 0.2 pct offset yield strength was 32,000 psi; however, this was increased to 59,000 psi by solution treatment, and further increased to 90,500 psi by solution treatment and aging. The attainment of high compressive strengths in the Al-CuAl2 eutectic composites was interpreted in terms of the buckling of elastic CuAl2 platelets in the plastically deformed a aluminum matrix. SINCE the discovery of high-strength whiskers,' scientists and engineers have made significant progress toward incorporating these whiskers into metallic matrices, forming composites for basic studies and structural application. The general procedure is to produce the whiskers first and then to bind them together with a ductile matrix. The production of whisker-reinforced composites requires tedious handling techniques,, particularly when it is desired to align the whiskers unidirectionally. Furthermore, the interfacial bond between the whisker and the matrix is frequently poor3 so that the resulting composite has strengths lower than expected. These disadvantages are generally true for any metallic composite produced by physically mixing the components. It is possible to eliminate these shortcomings by growing whiskers directly in the matrix material by eutectic solidification.4-8 In eutectic solidification, the matrix phase and a whisker phase are grown approximately simultaneously from a liquid of the same overall composition at the eutectic temperature. If the solidification process is controlled by varying the freezing rate, the temperature gradient, and the impurity content, platelike or filamentlike whiskers are produced parallel to the growth direction. The morphology of the grown-in reinforcement, i.e.. plates or rods, generally depends on the volume fraction9 of the dispersed phase present in the eutectic mixture. Since the unidirectional eutectic solidification is a one-step process, i.e., the liquid-solid transformation process, an excellent interfacial bond between the matrix and whisker is obtained. An additional advantage is that no special handling technique for whiskers is needed. In recent years, many investigators10-13 have studied the effects of growth variables on the micromorpholo-gies of binary eutectic alloys produced by controlled solidification. The study of their mechanical properties was initiated by Kraft and coworkers14-16 who found that the strength of cast A1-CuA12 eutectic alloy can be increased threefold by unidirectional solidification. In the A1-AL3Ni system, a strength of 50,000 lb per sq in, was reported for the unidirectionally solidified eutectic alloy, a value five times higher than for conventionally cast material. Thus, the unidirectionally solidified eutectics can be used as fiber-reinforced composite materials. In this paper, we shall first use an equation17 as a guide for the production of eutectic composites in general and the Al-33 wt pct Cu eutectic in particular. Experimental data supporting the theoretical prediction are given. Second, the compressive properties of the grown A1-33 wt pct Cu eutectic were thoroughly investigated in terms of platelet orientations, thermo-mechanical treatment, and temperature. The experimental data are interpreted in terms of a buckling model of fibers in elastic fiber-plastic matrix metallic composites. EXPERIMENTAL PROCEDURE Crystal Growth. The following experimental procedure was adopted for the production of controlled microstructures in the A1-33 wt pct Cu eutectic alloy. The controlled solidification was accomplished with a movable resistance-wound radiation furnace. Fig. 1 is a schematic drawing of the solidification apparatus. A water-cooled chiller was placed into a degassed high-purity graphite crucible containing the charge. Rubber stoppers wrapped with aluminum foil were used to seal both ends of the quartz tube through which a dried argon atmosphere was passed under a slight positive pressure. At both ends of the quartz tube, radiation shields were used to minimize heat loss. The quartz tube was held in place by two steel clamps and the furnace was drawn vertically by means of a steel cable against the steel truss which permits the furnace to move without touching the tube. The drive mechanism consisted of two pulleys, a counter weight.

Jan 1, 1969

By J. D. Miller, J. E. Sepulveda

Tar sand deposits in the state of Utah contain more than 25 billion bbl of in-place bitumen. Although 30 times smaller than the well-known Athabasca tar sands, Utah tar sands do represent a significant domestic energy resource comparable to the national crude oil reserves (31.3 billion bbl). Based upon a detailed analysis of the physical and chemical properties of both the bitumen and the sand, a hot-water separation process for Utah tar sands is currently being developed in our laboratories at the University of Utah. This process involves intense agitation of the tar sand in a hot caustic solution and subsequent separation of the bitumen by a modified froth flotation technique. Experimental results with an Asphalt Ridge, Utah, tar sand sample indicated that percent solids and caustic concentration were the two most important variables controlling the performance of the digestion stage. These variables were identified by means of an experimental factorial design, in which coefficients of separation greater than 0.90 were realized. Although preliminary in nature, the experimental evidence' gathered in this investigation seems to indicate that a hot-water separation process for Utah tar sands would allow for the efficient utilization of this important energy resource. The projected increase in the ever-widening gap between the domestic energy demand and the domestic energy supply for the next few years has motivated renewed interest in energy sources other than petroleum, such as tar sands, oil shale and coal. Although a number of research programs on the exploitation of national coal and oil shale resources have already been completed, very few programs have been initiated on the processing of tar sand resources in the United States. In recognition of their significance as a domestic energy resource, investigators at the University of Utah have designed an extensive research program on Utah tar sands. An important phase of this program, and the main subject of this publication, is the development of a hot-water process for the recovery of bitumen from Utah tar sands, as a preliminary step toward the production of synthetic fuels and petrochemicals. The term "tar sand" refers to a consolidated mixture of bitumen (tar) and sand. The sand in tar sand is mostly a-quartz as determined from X-ray diffraction patterns. Alternate names for "tar sands" are "oil sands" and "bituminous sands." The latter is technically correct and in that sense provides an adequate description. Tar sand deposits occur throughout the world, often in the same geographical areas as petroleum deposits. Significantly large tar sand deposits have been identified and mapped in Canada, Venezuela and, the United States. By far, the largest deposit is the Athabasca tar sands in the Province of Alberta, Canada. According to the Alberta Energy Resources Conservation Board (AERCB),2,3 proved reserves of crude in-place bitumen in the Athabasca region amount to almost 900 billion bbl. To date, this is the only tar sand deposit in the world being mined and processed for the recovery of petroleum products. Great Canadian Oil Sands, Ltd. (GCOS) produces 20 million bbl of synthetic crude oil per year. Another plant being constructed by Syncrude Canada, Ltd. is expected to produce in excess of 40 million bbl of synthetic crude oil per year. According to the Utah Geological and Mineral Survey (UGMS), tar sand deposits in the state of Utah contain more than 25 billion bbl of bitumen in place, which represent almost 95% of the total mapped resources in the United States.4 The extent of Utah tar sand reserves seems small compared to the enormous potential of Canadian tar sands. Nevertheless, Utah tar sand reserves do represent a significant energy resource comparable to the United States crude oil proved reserves of 31.3 billion bbl in 1976.5 Tar sands in Utah occur in 51 deposits along the eastern side of the state.4 However, only six out of these 51 deposits are worthy of any practical consideration (Fig. 1). As indicated in Table 1, Tar Sand Triangle is the largest deposit in the state and contains about half of the total mapped resources. Information regarding the grade or bitumen content of Utah deposits is still very limited. The bitumen content varies significantly from deposit to deposit, as well as within a given deposit. In any event, the information available6-8 seems to indicate that Utah deposits are not as rich in bitumen as the vast Canadian deposits which average 12 to 13% by weight.9 Although many occurrences of bitumen saturation up to 17% by weight have been detected in the northeastern part of the state (Asphalt Ridge and P. R. Spring), the average for reserves in Utah may well be less than 10% by weight. Separation Technology As in any other mining problem, there are two basic approaches to the recovery of bitumen from tar sands. In one

Jan 1, 1979

By E. Klar, A. B. Michael

Differences in the electrical conductivities of copper powder sintered under reducing, selectively oxidizing, and neutral atmospheres are related to impurities in solution or as precipitated oxides. The precipitation of impurities as oxides during sintering in nitrogen is proposed for maximizing the conductivity of sintered copper. Conductivity equations for two-phase systems are summarized. Selected equations are applied to porous sintered copper and composite structures. A recent review of the influence of impurities on the electrical conductivity of copper by Gregory et al.1 emphasized that an impurity in solid solution has a much more pronounced effect on reducing the electrical conductivity than when present partly or wholly as a second phase. When impurities in solid solution can be precipitated as oxides, the copper is purified with respect to these elements and the conductivity is increased. Cast and wrought copper, therefore, frequently contain an intentional residual oxygen concentration to oxidize and precipitate impurities less noble than copper. Copper powders generally also contain impurities which can contribute to a reduction in the electrical conductivity of the sintered material. The most deleterious impurities commonly found in commercial copper powders which markedly decrease the electrical conductivity when in solid solution but which can be precipitated as oxides include iron, tin, antimony, arsenic, cobalt, and nickel. In addition to impurities, porosity in sintered copper also contributes to a reduction in the electrical conductivity. The work reported herein discusses the influence of impurities, sintering atmospheres, and porosity on the electrical conductivity of sintered copper. These are important factors for controlling the electrical conductivity of materials such as sintered copper electrical contacts. Several publications on the electrical conductivity of sintered copper and composite materials with random pores or obstacles have incorrectly considered the conductivity to be proportional to the volume fraction of conducting material. However, analyses and equations have been proposed, the earliest of which is perhaps Lord Raleigh's of 1892,' which more accurately describe the conductivity of two-phase systems. These equations which in many cases allow one to closely estimate the electrical conductivity of porous sintered materials and two-phase composites will be reviewed and related to the measured electrical conductivity of sintered copper, copper-graphite. and Ag-W composites. INFLUENCE OF IMPURITIES AND OXIDIZING, REDUCING, AND NEUTRAL ATMOSPHERES Zone-Melted and Leveled Copper. The electrical conductivities of an electrolytic copper and a lower-purity compacting grade of copper powder after consecutive treatments in reducing or selectively oxidizing atmospheres are compared in Fig. 1. The powder and drillings from the electrolytic copper ingot were melted and solidified in a graphite crucible under hydrogen. The vertical zone leveling technique of multiple passes in opposite directions was used to obtain a uniform distribution of impurities. The electrical conductivity was measured on machined specimens 3 by 0.10 in. diam of the zone-leveled material and after the same specimens were consecutively treated as follows: 1) heating in hydrogen at 1600°F for 3 hr; 2) heating in air in a sealed tube so that 0.04 pct 0 was introduced; heating was started at 1000°F for 1 hr and continued at 1800°F for 8 hr; the stepwise diffusion treatment was used to avoid loss of copper due to evaporation of copper oxide at higher temperatures; and 3) final heating in hydrogen at 1600°F for 3 hr. A L&N Kelvin Bridge, type 4306, and a test fixture with knife edges 2 in. apart were used to measure the room-temperature conductivity with an estimated accuracy of ±0.5 pct. In all cases the conductivity of the electrolytic copper was approximately 100 pct of IACS. The conductivity of the impure copper was 80 pct of IACS both in the cast state and after heating in hydrogen. However, after the heating in air, the conductivity of the impure material was 100 pct IACS. After again heating in hydrogen, the electrical conductivity decreased to 60 pct of IACS. This decrease is attributed both to the dissolution of impurities and observed intergranular cracks due to the phenomenon of hydrogen embrittle-ment in copper. These data show that the electrical conductivity of commercial copper as represented by a compacting type powder can be increased significantly by the precipitation of impurities as oxides through heat treatment in an oxidizing atmosphere. Sintered Copper Powder. A commercial compacting type of copper powder pressed to various densities was sintered either in nitrogen, dissociated ammonia, or dissociated ammonia followed by a selectively oxidizing atmosphere of air in sealed Vycor tubes so that 0.06 pct O was added to the material. The electrical conductivity was measured perpendicular to the pressing direction on as-sintered specimens of approximately 3 by 0.25 by 0.15 in. The fully dense material was obtained by zone melting and leveling

Jan 1, 1969

By J. W. Spretnak, D. A. Chatfield, G. W. Powell, J. R. Eifert

In nzost cases, the driving force for a lattice transformation is produced by supercooling below the equilibriunz transformation temperature. The interfnce reaction in isothermally annealed, multiphase diffusion couples may involve a luttice transformation which also requires a driving force. Direct experinzental evidence has been obtained for the existence of the driring force in the form of a supersaturated phase at the aocc)-0@cc) interface in Cu:Cu-12.5 ult pct A1 couples; the super saturation is equivalent to an excess free energy of approximately 3 cal per mol at 905. A tentatiue interpretation of the dynanzic situation a1 the interface based on the free energy-composition diagram is proposed. THE presently accepted theory of diffusion in multiphase couples1 states that there will be a phase layer in the diffusion zone for every region which has three degrees of freedom and which is crossed by the diffusion path in the equilibrium phase diagram. For binary systems, this restriction excludes all but single-phase fields and, for ternary systems, only one- and two-phase fields are included. In addition, Rhines"~ as well as other investigators3 6 have reported that the compositions of the various phases adjacent to the interfaces are, for all practical purposes, the compositions given by the intersections of the diffusion path with the solubility limits of the single-phase fields of the equilibrium phase diagram. Some studies of the rate of thickening of these intermediate diffusion layers indicate that the thickness of the layer changes para-bolically with time, or: where x is the position of the interface relative to an origin xo, t is the diffusion time, and k is a temperature-dependent factor. crank7 shows mathematically that, if the compositions at an interface are independent of time and the motion of the interface is controlled by the diffusion of the elements to and from the interface, then the segments of the concentration penetration curve for a semi-infinite step-function couple will be described by an equation of the form: hence, Eq. [l] follows from Eq. (21 if the interface compositions are fixed and if the motion of the interface is diffusion-controlled. Although the concept of local equilibrium being attained at interfaces has assumed a prominent role in the theory of diffusion in multiphase couples, experimental evidence and theoretical discussions which challenge the general validity of this concept have been reported in the literature. arkeen' has stated that strict obedience to the conditions set by the equilibrium phase diagram cannot be expected in any system in which diffusion is occurring because diffusion takes place only in the presence of an activity gradient. Darken also noted that it is usually assumed that equilibrium is attained locally at the interface although the system as a whole is not at equilibrium, the implication being that the transformation at the interface is rapid in comparison with the rate of supply of the elements by diffusion. ISirkaldy3 indicates agreement with Darken in that he believes the concept of local equilibrium is at best an approximation because the motion of the phase boundary requires that there be a free-energy difference and, hence, a departure from the equilibrium composition at the interface. Seebold and Birks9 have stated that diffusion couples cannot be in true equilibrium, but the results obtained are often in good agreement with the phase diagram. The initial deviation from equilibrium in a diffusion couple will be quite large because alloys of significantly different compositions are usually joined together. Kirkaldy feels that the transition time for the attainment of constant interface compositions (essentially the equilibrium values) will be small, although in some cases finite. Castleman and sieglelo observed such transition times in multiphase A1-Ni couples, but at low annealing temperatures these times were quite long. Similarly, ~asing" found departures, which persisted for more than 20 hr, at phase interfaces in Au-Ni and Fe-Mo diffusion couples. Braun and Powell's12 measurements of the solubility limits of the intermediate phases in the Au-In system as determined by microprobe analysis of diffusion couples do not agree with the limits reported by Hiscocks and Hume-Rothery13 who used equilibrated samples. Finally, Borovskii and ~archukova'~ have stated that the determination of the solubility limits of phase diagrams using high-resolution micro-analyzer measurements at the interfaces of multiphase couples is not an accurate technique because of deviations from the equilibrium compositions at a moving interface; diffusion couples may be used to map out the phase boundaries in the equilibrium diagram, but the final determination of the solubility iimits should be made with equilibrated samples. The purpose of this work was to investigate the conditions prevailing at an interface in a multiphase diffusion couple and to compare the interface compositions with those associated with true thermodynamic equilibrium between the two phases. Microanalyzer techniques were used to measure interface compositions in two-phase Cu-A1 diffusion couples annealed at 80@, 905", and 1000°C for various times.

Jan 1, 1969