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By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [I] where X is the thickness of the alloy layer, k the reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such. a plot has been con¬sidered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative, thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase .4 The reaction layers tend to have a

Jan 1, 1942

By M. A. Dayananda, R. E. Grace

Vapor-solid diffusion couples were employed in a study of ternary diffusion in the single-phase copper-rich corner of the Cu-Zn-Mn system Interdiffusion coefficients were measured at three different compositions corresponding to the intersections of diffusion paths determined at 850°C. Intrinsic diffusion coefficients were determined at two compositions by the Philibert-Guy method. New relations between the various intrinsic diffusion coefficients are also presented. MOST of the investigations of ternary diffusion have been made with "sandwich" couples formed by welding together two homogeneous solid solutions with or without markers placed at the interface. With such couples Kirkaldy and his coworkers1,2 have determined interdiffusion coefficients which describe ternary diffusion in the substitutional alloy systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy3 have reported intrinsic diffusion coefficients for Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.4 The use of semi-infinite diffusion couples, for example, vapor-solid couples, where the diffusing species are supplied from a vapor source in contact with a diffusion disk, has so far been confined to studies of binary diffusion. Balluffi et a1.5,6 have successfully determined the interdiffusion as well as the intrinsic diffusion coefficients in several binary metallic systems employing vapor-solid couples with markers initially placed at the vapor-solid interface. They have also discussed the general advantages and limitations of such couples. Vapor-solid diffusion couples can successfully be employed in ternary diffusion studies. The importance of such couples in ternary diffusion lies in the fact that inert markers lie close to the vapor-solid interface, and the composition of the marker plane is virtually known before experimentation begins. Another minor advantage is that the method of Philibert and Guy4 may be used with three alloys instead of four. Lastly, the diffusion paths need not be S-shaped, as pointed out by Meijering7 for "sandwich" couples. The Cu-Zn-Mn system is convenient for ternary diffusion studies because of the large single-phase field in the copper-rich corner. The vapor pressure of zinc above such alloys is known, and X-ray measurements indicate that the molar volume is nearly constant over a wide range of compositions.8,9 It is the purpose of this paper a) to extend the analysis of Balluffi and seigle5 to permit an evaluation of interdiffusion coefficients in ternary vapor-solid couples, b) to use the method of Philibert and Guy to determine intrinsic diffusion coefficients with such couples, and c) to present experimental data on both interdiffusion and intrinsic diffusion coefficients for the Cu-Zn-Mn system at 850°C. INTERDIFFUSION IN TERNARY VAPOR-SOLID COUPLES The analysis of Balluffi and seigle5 is extended in this section to a vapor-solid couple where two solutes diffuse from a vapor source into a ternary solid solution. To take into account the expansion of the diffusion disk caused by the absorption of mass from the vapor phase, the total fluxes are expressed on the basis of a coordinate system that moves with the velocity of the vapor-solid interface; thus. where D3ij are the intrinsic diffusion coefficients,4 v(x, t) is the local Kirkendall velocity of mass flow, and F(t) is the negative velocity of the vapor-solid interface (x = 0). Both these velocities are based on a fixed coordinate system far removed from the diffusion zone. Using the continuity relations and Darken's method1' for a ternary system in which components 1 and 2 diffuse from the vapor phase into a solid of negligible vapor pressure, one obtains

Jan 1, 1965

By J. T. Dewan

An experimental setup is described whereby the responses of Neutron logging instruments have been determined opposite formations of different porosities and under various borehole conditions. The results of these tests are presented in several charts which show how the Neutron log is affected by the following factors: hole diameter, casing, cement, salinity and weight of drilling mud, and position of logging tool with respect to the wall of the hole. The responses in the case of empty holes are also shown. A chart is furthermore presented which shows the shapes of the Neutron log, as a function of logging speed and time constant, at the boundaries between two formations with different porosities. These were derived mathematically using as a basis laboratory determination of the shape of the curve under static conditions, i.e. at very low logging speed. Corrections for the readings made opposite thin beds are given by these computations. The correction is found negligible under usual logging conditions for beds thicker than about 4 ft. INTRODUCTION The Neutron log is used in borehole surveys both for the delineation of porous formations and for the quantitative estimation of their porosities.1,2,3,4,5 It is common practice to calibrate the response of the Neutron log in terms of porosity values for each given geological unit by means of empirical comparisons between the deflections of the neutron curve and the porosity values given by the core analysis in a sufficient number of wells. Usually, the plots of the porosity values vs Neutron log deflections show a definite trend. It is therefore possible to trace an average line across the plotted points. This average line constitutes a calibration curve which can be used to evaluate the porosities from the Neutron logs in the other wells drilled in the same region. Futhermore, when the porosity values are plotted on a logarithmic scale and the Neutron log deflections on a linear scale, the calibration curve is practically a straight line. Accordingly the calibration curves are often determined by simply tracing a straight line between two points corresponding to two widely different porosities. Different choices are made for these two points, depending on local conditions. For example, one point will be defined by plotting the deflection of the Neutron curve opposite a formation known to be very tight, for which an average porosity value of 1 or 2 per cent is assumed. The other point may correspond to shale sections, to which a porosity of around 40 per cent is ascribed. The information provided by the eletrical logs — in particular the Laterolog, Limestone log or Micro-Latero-log — is also very often a help in the calibration of the Neutron logs. Empirical approaches such as these make possible the derivation of fairly reliable porosity values from the Neutron logs in many cases, at least in open holes and in essentially clean formations. There are, however, several causes of uncertainty which may sometimes entail appreciable errors. On the one hand, the Neutron log readings are influenced by the borehole conditions: hole diameter, presence or absence of casing and cement, presence or absence of drilling mud, characteristics of the mud, and position of the logging instrument with respect to the wall of the hole. The amplitudes of the curves opposite thin beds are furthermore atfected by the bed thickness,

Jan 1, 1957

By J. H. Swisher

The solubility of sulfur and rate of solution of sulfur in pure Lron were measured in H2S + H2 and H2S + H2 H2O gas mixtures. The solubility and diffusivity of sulfur at 1410°Care 0.13 pet S and 1.0 x 10-5 sq cm per sec, respectively. The solubility iS the same, but the rate of sulfurization is slower in the presence of H2O in the reacting gas. Under these conditions, the over-all rate is controlled jointly by a slow surface reaction and by solid-state diffusion; the mechanism for the surface reaction has not been identified. KNOWLEDGE of the behavior of sulfur in solid iron is desirable for the metallurgy of such products as free machining steel, where a high sulfur level is required, and inclusion-free high-strength steels, where the sulfur specifications are very low. The present investigation was undertaken to check previously reported values for sulfur solubility and diffusivity in 6 iron, and to study the poisoning effect of chemisorbed oxygen on sulfurization kinetics in H2-H2S-H2O gas mixtures. All of the experiments were performed at 1410°C. The thermodynamic behavior of sulfur in 6 iron was the subject of a paper by Rosenqvist and Dunicz.' The sulfur solubility at 1400" and 1500°C was determined by equilibrating pure iron specimens with H2-H2S gas mixtures. The maximum solubility of sulfur in 6 iron was alsc determined by Barloga, Bock, and parlee2 by reacting iron wires with sulfur in sealed capsules. In another investigation, the diffusion coefficient of sulfur in 6 iron at temperatures up to 1450°C was measured by Seibel.3 The method used was to measure sulfur concentration profiles in diffusion couples containing radioactive sulfur EXPERIMENTAL Apparatus. A vertical resistance furnace wound with molybdenum wire and containing a recrystallized alumina reaction rube was used for the experiments. The hot zone in the furnace was approximately 2 in. long with a temperature variation of ±3oC. The hot zone temperature was automatically controlled to within ±2°C, and the test temperature was measured with a pt/Pt-10 pet Rh thermocouple before and after each experiment. Flow rates of the reacting gases were obtained using capillary flow meters. Materials. The source of H2S in the gas train was a premixed cylinder containing 5 pet H2S in H2. This mixture then was diluted with additional hydrogen and argon. In some experiments, water vapor was introduced by passing hydrogen and argon through a column containing 10 pet anhydrous oxalic acid and 90 pet oxalic acid dihydrate. The vapor pressure of water above this mixture is well-known.4 Argon was used as a diluent to minimize thermal segregation of H2S in the furnace5 and to reach higher H2O:H2 ratios than could be obtained in mixtures of H2 and H2S alone. Argon was purified by passage over copper chips at 350°C and subsequently over anhydrone. Hydrogen was purified by passage over platinized asbestos at 450°C and then over anhydrone. The H2-H2S mixture was purified by passage over platinized asbestos and then over P2O5. The specimen stock was made by melting and vacuum-carbon deoxidizing electrolytic "Plastiron" in a zirconia crucible. The principal impurities are listed in Table I. In some of the equilibrium experiments, six-pass zone-refined iron was used to minimize impurity side effects. This zone-refined iron had a total impurity level of about 25 ppm. Procedure. Specimens were annealed in hydrogen for a period of at least 2 hr at the beginning of each experiment. The specimens were held in the reacting gas for times varying between 10 min and 17 hr, and cooled to room temperature in a water-cooled stainless-steel block at the bottom of the furnace. The pH2S/pH2 ratios reported are those for gas equilibrium at 1410°C. Calculations based on available thermodynamic data8 showed that the only other gaseous8 species that formed in significant amounts in the furnace were S2 and S. Even when water vapor was introduced into the gas mixture, the concentrations of SO2, SO, and so forth, were negligible. The initial partial pressure of H2S was therefore corrected for its partial dissociation to S2 and S in determining the equi-

Jan 1, 1968

By R. W. Fountain, J. Chipman

THE solubility of nitrogen in iron and steel has been of considerable interest due to the role of nitrogen in strain-aging and in quench-aging. It is generally considered that quench-aging is the result of precipitation of carbide and nitride particles from supersaturated solid solution, while strain-aging results from the segregation of carbon and nitrogen atoms to dislocations.1-9 The rate of strain-aging is controlled primarily by the amount of carbon and nitrogen in solution and the temperature. In experiments on strain-aging of pure iron with only carbon or nitrogen as impurities, Fast" has shown that even after 40 hr at 50°C carbon did not give any strain-aging while

Jan 1, 1959

By S. J. Matas, R. F. Hehemann

The existence of two distinct forms of bainite—upper and lower bainite—in hypoeutectoid steels is confirmed by a systematic study of the structure of the product resulting from this mode of austenite decomposition. The transition between these two forms occurs at about 650° F regardless of the alloy content of the steel and their structural differences can be interpreted in terms of the kinetics of carbide precipitation from supersaturated ferrite. In the past few years, a renewed interest has been displayed in the kinetics and mechanism of the bainite reaction in steels. Several rather divergent models for the transformation mechanism have evolved from these studies,'-' however, it is difficult to evaluate these models critically on the basis of the existing experimental data. In particular, a more detailed knowledge of the structure of bainite should be helpful in providing a framework for the construction of an appropriate model. Metallographic studies7-l4 have led to a recognition of at least two distinct forms of bainite—frequently termed upper and lower bainite. Although the morphology of bainite changes with reaction tem- perature, there appears to be a relatively sharp transition between the two forms. This occurs in a narrow temperature range near 650° F. Transformation at temperatures below about 650° F results in the presence within the bainite of small plates of carbides oriented at an angle of 60 deg with respect to the direction of growth of the plate, while at higher temperatures carbides are oriented parallel to the growth direction. There is no generally accepted view regarding the significance of this structural transition. Some authors feel that carbides precipitate from austenite at all reaction temperatures1' while others claim, at least for low-temperature bainite, that carbides precipitate from supersaturated ferrite.14.15 It was recognized many years ago that the nature of the carbide in bainite depends on the reaction temperature. The carbide hase in upper bainite is unmistakenly cementite.16-19 The exact nature of the carbide in low-temperature bainite is less certain. Magnetic measurements of lower bainite reveal no cementite Curie point21'22 and dilatometric studiesz0 produce total expansions which are larger than those predicted on the basis of a ferrite-plus cementite structure. These effects have been attributed to the

Jan 1, 1962

By F. B. Foley

IT is with an unusual degree of personal satisfaction that I find myself in a position to pay tribute to the memory of Henry Marion Howe. One could not have spent any length of time in the presence of Dr. Howe without profiting intellectually. I do not hesitate to say that my years of association with him were the most stimulating of all my years of metallurgical study. He always impressed one with his own eager search for knowledge. Never dependent on the written word alone he sought information from anyone whose opinion he valued. His ability to piece together bits of apparently conflicting data from various sources so as to build up a logical hypothesis was unique. A small slight man with the intellect of genius he would have gone to the top in any endeavor he undertook and it was fortunate for metallurgy that its study attracted him as it did. Howe was a modest man. I like to recall an incident which left a lasting impression with me. The lab- oratory in his home, "Green Peace," was in the basement and access was by way of stairs leading down from his secretary's room. In using these stairs my attention was attracted many times to an ordinary cardboard shoe box which reposed on the shelf above the landing. It was crudely labeled on its side in black ink "Vanity Box." My curiosity was aroused to the point that I finally asked his secretary what it was. With some amusement she took the box from its shelf on the stairway, opened it and showed me its contents—numerous letters, from the foremost men of science of every civilized country throughout the world, commending his "Metallography of Steel and Cast Iron." I recall that in reply to one who thought there was not enough of Howe's own researches in his book he wrote, "Primarily I am a writer, secondarily an investigator." Howe wrote to make his readers think. No one ever strove harder than he to be right but above all, whether his viewpoint proved ultimately to be right or wrong, he was always content if by his stand, he provoked a reader to take the next step along the path to greater knowledge. I doubt that he was ever afraid to be wrong for he was always secure in the thought that his effort was guided by a sincere search for the truth. One continually searching for truth is entitled to occasional excursions up the wrong alley. A glance backward to the metallurgical confusion of some thirty to forty years ago, or need one go back so far, provides convincing proof of what a host of companions one may have in a common acceptance of ideas which the future will prove to be wholly untenable. Well over a hundred years have passed since investigators have interested themselves in the effect of increasing the temperature of iron and steel on their mechanical properties. We are told by Charles Walrandl in "Industrial Annals" for June 11, 1822, that bend tests, conducted in a Russian steel works of Prince Demidoff, on steel bars "highly heated" and bent during cooling became brittle when bent at an iris blue color. He concluded, "That when steel is heated to a temperature between 473°F and 662°F the mettle was more brittle between these limits than at a much lower or at a much higher temperature." It was a curious bit of information recognized as true to this day and still not explained satisfactorily. In 1878 Charles Houston in Annales de Mines associated this brittleness with an increase in tensile strength at 572°F. When this relatively low temperature is exceeded it is recognized that steel becomes weaker as temperature is increased up to the melting point, where no strength of practical importance remains. It is easy to believe, in fact it goes without saying, that this weakening as the temperature of a metal is increased is the result of the motion of the atoms making up the metal, a motion which itself is evidence of the temperature increase. However, if we are considering iron or steel we find that this decrease in strength is not a steady one, for, besides the increase in strength just referred to, one comes to a temperature, the critical temperature, where results of tests indicate the metal to be extremely weak and then as temperature increases to become sensibly stronger again. This apparent anomaly was made the subject of the first Howe Memorial Lecture, delivered by Albert Sauveur in 1924. It may be of interest to review these findings of Sauveur. He used two methods of investigation. One involved the twisting of bars. The bars were heated in an

Jan 1, 1951

By J. A. Elias, A. J. Heckler

A simplified method is described for the prepauatior~ of comnposite samples for determination of one quadrant of an X-ray pole figure of a sheet material by the Schulz reflection method. Other special conzposite sampling methods were used to investigate specific areas of the pole figures. Plotting nets for these sampling plans were drawn by a computer. Step-scanning techniques were used to obtain detailed information about specific regions of a pole figure. Satisfactory pole figures were obtained for large-grained (0.5 to 1 in. diam) sheet materials. COMPOSITE sampling techniques for preparing one quadrant of an X-ray pole figure have been reported by a number of authors.'-5 All of these methods are similar in that they use a composite sample prepared by stacking and holding together coupons cut from a sheet material. The schulze reflection technique is applicable to the composite sample so that only minor corrections are needed for defocusing and absorption effects. Also, a relatively large area of a sheet is sampled through the use of multiple cross sectional pieces. In general, sampling methods necessary to obtain a composite-type specimen have been formidable enough to discourage their use in routine pole figure determinations. This paper presents a versatile sampling technique which is simpler than those previously described along with an accurate method for obtaining stereographic plotting nets for any orientation of a composite specimen surface. A step-scanning technique is used to obtain more quantitative determinations of specific regions in pole figures, and the composite technique is satisfactorily applied to determine pole figures of very large grained sheet materials. REVIEW OF PREVIOUS TECHNIQUES Mueller and ~nott' first proposed a technique for obtaining one complete quadrant of an X-ray pole figure by using a sheet sample and six different composite samples in which the individual coupons were aligned and held together by two types of jigs. Data from the seven different samples were overlapped to obtain a single quadrant. ~eieran~ and Lopata and ~ula~ obtained a complete quadrant of a pole figure from a single sample prepared by forming a cube from coupons cut from a sheet. These coupons were bonded together using an epoxy cement, and a cut was made at 54.7 deg to the normal, transverse, and rolling directions of the sheet, Fig. I. The normal direction of the cut face projects into one quadrant of a stereographic projection at equal angles to the three principal orthogonal reference directions mentioned above. X-ray reflection data obtained along a spiral path in physical space could then be plotted on a stereographic net offset 54.7 deg from the normal, as shown in Fig. 2. A rotation about an axis representing the surface normal is designated as a, and a rotation about an axis lying in the plane of the surface is 4. From Fig. 2 it is apparent that a tilting angle of no more than 55 deg @ is necessary to obtain the complete quadrant. ~eber~ devised an improved sampling technique by cutting coupons 45 deg to the rolling direction of a sheet, stacking and bonding these with an epoxy cement at an angle of 54.7 deg to a reference plane, and finally grinding and lapping a flat specimen surface parallel to this plane. An important consideration of this technique and that of Lopata and ~ula~ is variation in the diffracting power of the specimen surface due to the bonding medium. While any composite-type sample will have some such variation due to boundaries between coupons, the problem can be minimized by elimination of the bonding medium and by avoiding prolonged etching times which could lead to significant inter lame llar attack of the coupon faces. EXPERIMENTAL TECHNIQUE We were working concurrently though independently on a technique similar to ~eber's,' but which does not

Jan 1, 1968

By J. H. Reynolds

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

Jan 1, 1968

By K. Takahashi, I. Iwasaki

The methyl stretching vibrations for a series of normal xanthates, isoxanthates and normal amines were determined with the aid of an infrared spectro-photometer, and the results were compared with published information on the corresponding alcohols. The frequency shifts of methyl stretching vibrations may be attributed to the inductive effect of polar groups. The hydrogens in the shorter chain alkyl groups are somewhat polar and can be expected to interact with water molecules by hydrogen bonding. Contact angle, surface tension lowering, solubility, and critical micelle concentration appear to be related to the induced polarity of the alkyl groups. Traube's rule states that in homologous series of compounds solubility decreases and surface activity increases regularly with the size of the hydrocarbon group. Analyzing the work of transfer of a solute from solution to surface, Langmuir' interpreted this rule to mean that each CH2 group added to a molecule produced its effect independently of the others. It is also well known2 that the maximum equilibrium contact angle with sulfhydryl collectors is independent of the polar groups and of the sulfide minerals, and that it increases to a certain limit with the number of carbon atoms in the alkyl group. This observation is thought to demonstrate the orientation of the collector molecules at the sulfide surfaces. The dependence on the hydrocarbon chain length is usually explained as due to the screening of the force field of polar mineral surfaces.3-5 Here again, Langmuir's principle of independent surface action appears to be implied. Heteropolar compounds consist of nonpolar and polar groups, the former being the hydrocarbon group and the latter containing such electronegative atoms as O, N, S, P, or halogens. According to Palit6 the hydrogens in the alkyl groups are more electroposi- tive than in the paraffins owing to the negative inductive effect of the polar groups and a possibility that a hydrogen bond with water molecules ensues. Goto and Takenaka7 provided direct evidence of the inductive effect by measuring the shift of the C-H stretching vibrations of alcohols, acids, and alkyl bromides with an infrared spectrophotometer. Their approach appeared to be directly applicable to the studies of surface activity both at air-water and water-mineral interfaces encountered in flotation systems. The present article attempts to relate the C-H stretching vibrations of alkyl xanthates, alcohols, and amines with such flotation chemistry parameters as contact angle, surface tension lowering, solubility, and critical micelle concentration. MATERIALS AND METHODS Normal xanthates from methyl to octyl inclusive and the isopropyl, isobutyl, and isoamyl xanthates used in this investigation were prepared in the usual manner.8 Normal amine hydrochlorides with carbon chain lengths of 1, 2, 4, and 6 were from Distillation Products Industries, of 8 from Archer-Daniels-Midland Co., and of 10, 12, 14 and 16 from Armour and Co. Normal propylamines, pentylamines and heptylamines from Distillation Products Industries were used both as received and as hydrochloride formed by converting the amines according to the procedure described by Li9 Perkin-Elmer Model 521 and 621 infrared spectro-photometers were used to investigate the spectra in the frequency region of 3050 to 2800 cm-' with frequency scale expansion. The accuracy of the frequency readings was within + 1 cm-1. The KBr micropellet technique was used to prepare the xan-thate samples for measurements, and the halocarbon mull technique was used for amines and amine hydrochlorides. EXPERIMENTAL RESULTS Fig. 1 shows the CH3 asymmetric stretching vibrations as a function of the number of carbons in the alkyl group for normal xanthates, isoxanthates and amines. Also included in the figure are data for normal alcohols and isoalcohols taken from the article

Jan 1, 1970

By D. Weinstein

The high temperature mechanical properties of stainless steels after fast neutron irradiation are discussed in the light of effects caused by lattice dattmage and effects caused by helium generated from n,a transmutations. Embrittlement at high temperatures is due to helium accumulation at grain boundaries and to cavity formation and proPagation along grain boundaries. Following from the embrittlement mechanism, it is suggested that when deformation occurs by mechanisms associated with super plasticity, helium ac-curnulation at boundaries should be attenuated and cavities, if formed, should be nonpropagating. As the mean free Path between interphase boundaries of a two-phase Fe-Cr-Ni alloy was decreased, the degree of superplastic deforrnation at 870°C increased, as vneaszired by total elongation and by the expottent m = a log 'a/a log 'i. This alloy and type 304 stainless steel were cyclotron irradiated in an a-particle beam to a helium concentration of -1 x 10 atom He per atom. The stainless steel specimen was embrittled, but the ductility of irradiated two-phase Fe-Cr-Ni alloys correlated with the values of. m during 'defor-malion. The .finest grained, helium-injected specimens that deforrned with highest m values exhibited the largest elongations to ,fracture. These results could be correlated with metallographic observations of cavity behavior: the propensity for intergranular propagation was lessened as the m value increased. It is concluded that superplastic deformation is ef-fectizle in attenuating helium embrittlement at elevated temperatures. One of the principal problems associated with development of fast breeder reactors is application of alloys such that suitable fuel cladding results. Stainless steels and other Fe-Cr-Ni alloys, because of highly acceptable nuclear characteristics, represent the primary materials for this component, and an exhaustive research and development effort is being conducted. The main deficiency of these materials has been a severe loss of ductility at high temperatures after fast neutron irradiation. An extensive body of mechanical property data and microstructural observations has provided an adequate phenomenological description of embrittlement; in conjunction with transmission electron microscopy studies, a reasonably acceptable embrittlement mechanism has been obtained. Following from this mechanism, it is suggested in the present work that ductility would be enhanced if deformation could occur by mechanisms associated with the phenomenon of superplasticity. Experiments to test this hypothesis have been conducted, and the results are presented and discussed in this paper. IRRADIATION EMBRITTLEMENT AT HIGH TEMPERATURE Austenitic stainless steels have been irradiated to accumulated fast neutron fluences of 1020 to 1022 nvt at temperatures between 60" and 600°C. Specimens that have been exposed to these conditions and subsequently tensile tested at temperatures between 600" and about 900°C exhibit approximately 5 pct total elongation to fracture.'-3 For unirradiated specimens receiving a nearly identical thermal exposure, total elongation at these test temperatures is about 45 pct. Examination of irradiated specimens has shown that fracture propagation is entirely intergranular. These phenomenological aspects of irradiation embrittle-ment at elevated temperatures are well known and are not generally disputed. Although the explanation of this phenomenon has been controversial, a mechanism for ernbrittlement has emerged that accounts reasonably well for the observed mechanical behavior. The controversy resulted primarily from an indeterminate role of neutron-in-duced lattice damage, if any, and a presumed, but experimentally unverified, contribution to embrittle-ment from helium generated by n,a transmutations. Recently, Holmes and coworkers4 have conducted experiments that separate these effects, and the results are instructive in formulation of the ernbrittlement mechanism. Holmes el al.4 irradiated type 304 stainless steel in EBR-I1 to a fluence of 1.4 x 1022 nvt (E > 0.18 mev); the irradiation temperature was 538" * 48°C or, in terms of absolute melting point, 0.49 * 0.03 T,. After irradiation, tensile tests were conducted at temperatures of 21" to 870.C, the specimens first being annealed for 30 min at each test temperature. In addition, thin sections of irradiated specimens were annealed for 1 hr at identical temperatures, electro and examined by transmission electron microscopy. Thus, for a given temperature, it was possible to correlate mechanical properties with the defect structure. At room temperature, the yield stress of irradiated specimens was a factor of 2.5 higher than unirradi-ated specimens exposed to an equivalent thermal history. Electron microscopic examination of the irradiated specimen revealed a high density of lattice damage in the form of Frank sessile dislocation loops and polyhedral voids. Holmes et al.4 concluded that the presence of this defect substructure caused the increase in yield stress and that after irradiation in a fast neutron flux at 0.49 Tm, substantial lattice dam-age persists. Annealing at progressively higher tem-

Jan 1, 1970

By E. Martinez

Samples of chrysocolla, a hydrated copper silicate, from several sources were submitted to differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). Pure samples of chrysocolla are difficult to obtain, but comparison of the thermograms revealed that certain reactions occurred in all the samples and it is believed that these are due to chrysocolla. Endothermic reactions occurred at 50' to 175°C, 350° to 650°C, and 980° to 1100°C each of which caused a weight loss. The first was due to loss of absorbed water, the second to a dehydroxyla-tion, and the last to conversion of cupric oxide to cuprous oxide. In addition, two exotherms were detected at 685° to 695°C and 935° to 950°C. Infrared spectra of heated samples indicated the exotherms were due to changes in the Si-O bonds leading to the formation of cristobalite. The results suggest that thermoanalysis may be a more sensitive and reliable method for detection and identification of chrysocolla than X-ray diffraction, infrared spectroscopy, or optical techniques. The recovery of copper from oxide ores has been the subject of much research in recent years. One of the principal oxide copper minerals is chrysocolla, a hydrated copper silicate. The information available indicates that it has widely varying properties depending on the origin of the sample. Chrysocolla usually is found associated with cuprite, malachite, azurite, and native copper. Most of these other minerals are recoverable by present day flotation practice, but chrysocolla is lost in the tailings.1,2 Reagent combinations that are successful in laboratory chrysocolla flotation with ore from one source have been found to be ineffective with another. 3 The copper segregation process offers an altemative to beneficiation of oxide copper ores.4'5 The process is of particular interest in processing ores that cannot be treated by conventional hydrometal-lurgical methods because of high acid consumption.6 Fuller understanding of the properties of chryso- colla may prove of value in the search for improvements in both the flotation and segregation processes. Chrysocolla samples from Arizona, Nevada, Chile, Australia, and South Africa were studied by differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). In addition, a sample from Miami, Ariz., was submitted to X-ray diffraction, infrared spectrophotometry, and surface area determination. EQUlPMENT Differential thermal analysis (DTA) detects, amplifies, and records exothermic-endothermic reactions occurring in a sample as its temperature is raised at a constant rate, usually 10°C per minute. A unit made by the Robert L. Stone Co. was used in this study. The tests can be run if desired with a gas streaming through the sample. A thermobalance records weight losses or gains in a sample as its temperature is raised at a uniform rate. The gravimetric analyses (TGA) were run on a Chevenard thermobalance converted electronically for graphic recording. A heating rate of 5°C per minute up to 1100°C was used in these tests. A Perkin Elmer Infrared Spectrophotometer, Model 221, was used with sodium chloride optics obtaining IR spectra in the 2 to 15 region. A pressed pellet technique with potassium bromide was used in preparing the samples. DESCRIPTION OF SAMPLES Chrysocolla is found in the oxidation zones of copper deposits commonly associated with malachite, azurite, and limonite. It is described as varying in composition and in color from bluish green to brown or black. Inclusions of other minerals are usual so chemical analysis of chrysocolla samples may be suspect. However, it is considered by many to be a solid solution of CuO, SiO2 and H2O with a general formula of CuO.SiO2.2H2O or 2CuO.2SiO2. 3H20. Chukhrov7 has described a sample from the Urals as CU3,5(OH)2 (A1Si3) O10.nH2O and stated that chrysocolla is a montmorillonite-type mineral. On the basis of X-ray analyses, DTA, and infrared spectra of chrysocolla from the Inspiration Mine, Ariz., Sun8 concluded that there was no substantial evidence to classify it as a montmorillonite mineral. Chrysocolla samples from many sources throughout the world were used in this investigation. The following is a brief description of each:

Jan 1, 1963

By R. E. Reed, C. J. McHargue

Single crystals of aluminurn were reduced 90 pct in diameter by extrusion at 296" and 77°K. The resultant double fiber texture had a strong (111) component with a weak (001) component. The relative anzounts of these components varied with starting orientation. Decreasing the Lemperatuve of defovtnation increased the amount of (001) texture component in crystals with inilia1 orientations near (111). The starting orientation and temperature of deformation strongly affected the morphology of the (001) component. The effects of orientation and Lemperatuve upon the distribution of the (001 ) texture component in extruded aluminum single crystals were rationalized on the basis of deformation band formation and interaction. MANY papers since the early 1920s have discussed the occurrence of the double fiber texture (111) + (001) in wires and rods of deformed fcc metals. Aside from the reporting of experimental results for the various metals under a variety of fabrication conditions, emphasis has been placed on two related problems. One problem deals with the prediction of ideal end orientations based on the glide systems and flow directions. The other problem seeks the reason why different amounts of each component may be produced by the same fabrication schedule for metals apparently having the same deformation systems. Some of the difficulties in developing a satisfactory explanation have their origin in the experiments themselves. One mistake has often been the assumption of an initially randomly oriented specimen or complete ignorance of effects of starting orientation. Recent studies by Grewen and Wassermann,1 Cullity and co-workers,2' and McHargue4 have shown that the initial orientation may be the most important factor in determining the final orientation. Hence only limited comparisons of data from different studies can be made unless all conditions of the initial material are specified. Another question has been the nature of the (001) component. Hibbards suggested that any (001) present was the result of re crystallization during fabrication. Although Fleischer6 found no (001) texture in aluminum swaged at room temperature, and Dayal 7 found that component to disappear at very high reductions, a double fiber texture has usually been reported for aluminum. Vandermeer and McHargue showed that, while some (001) in aluminum may be the result of recrystallization, much of this component has its origin in the deformation process. Ahlborn and Wassermanng found the (001) component in silver deformed at low temperature not to be the product of recrystallization.

Jan 1, 1968

By W. N. Poundstone

The mining and ventilating system used in development work in the Pittsburgh Seam in northern West Virginia is discussed. The seam conditions and the nature of the accompanying methane gas are described. The type of equipment and the mining cycle will be discussed, showing how they are well suited for very gaseous development work. Face ventilation in development work is possibly the fastest growing problem of the industry. The coal mines of the future will be faced with the prospect of mining from under increasing depths of cover. Consequently, larger and larger amounts of methane gas probably will be found. The Pittsburgh Seam, in northern West Virginia, is an example of an area already faced with this problem. At the present time, most of the development work being done in this seam lies beneath 500 to 1200 ft of cover. The Pittsburgh Seam in this area has always been very gassy—even near the outcrop—and the recent development work has been accompanied with extremely large volumes of gas. In many cases, a single development section has liberated in excess of 1,000,000 cfm in 24 hr. This problem of heavy gas liberation was the chief concern, several years ago, when continuous mining equipment was first considered at Christopher Coal Co. All of us were apprehensive about the liberation that would accompany rapid extraction in a single working place. However, the experience during the past few years has shown that this ability to mine only one place at a time, is actually the key to working this type of coal. With all of the mining or advancement concentrated in one place, the ventilation can also be concentrated. By this it is meant that continuous mining permits the active working place to be ventilated with a maximum amount of fresh air, taken directly from the intake source without first passing another working place. Continuous mining (and a good ventilating system) also permits a much greater concentration of attention or vigilance to the actual working place. There are two things that are very important to the mining of coal having high rates of liberation. First, adequate volumes of air are necessary. Second, and perhaps more important, a mining and ventilating system must be used that will provide an uninterrupted flow of air to every portion of the working section. Liberations of this magnitude take only a few seconds of interruption for a dangerous accumulation of gas to occur. With adequate volumes of air available, the ability to concentrate ventilation more than offsets the concentration of gas emission that is inherent with continuous mining. The mining system used with continuous mining equipment at Humphrey Mine is similar to the system used at many mines in the area for development work. This system is designed to favor ventilation, realizing that other efficiencies are meaningless if the equipment must stop because of ventilation difficulties. This plan is especially well suited to minimizing ventilation interruptions. Basically, the overall plan of mining is to develop headings into virgin coal and encircle or block out large areas. These blocks are generally at least 2000 ft sq. The purpose of this blocking out is to bleed gas from the area before pillaring. Experience has shown this method to be quite effective, even in the most gassy areas. The gas in this field seems to migrate or flow readily from the solid coal into the outside return headings of the development work. The numerous clay veins and slips that are found in the area are extremely good avenues for gas flow. A block of coal, surrounded with development headings, usually bleeds off readily; and since it is cut off from the virgin coal, it is not subject to gas migration, through the seam, from this source. However, the outside return of the encircling development work, adjacent to the virgin coal, may liberate gas for years. This liberation from the outside ribs in the virgin coal is the reason split ventilation is used in development work. If split ventilation were not used, there would, in many cases, be a serious build-up of gas in the intake before it could reach the working face. Fig. 1 shows a typical development section having seven headings. The two outside places on each side are returns, and the three center headings serve as intakes. This section is equipped with a ripper-type continuous mining machine. An off-track loading machine is used to load from a surge pile on the

Jan 1, 1961

By S. Vela, R. M. McKinley, L. A. Carlton

Johnson et al. have described a new well-testing technique that measures formation flow properties between wells.' The technique, called pulse-testing, requires a sequence of rate changes in the flow at one well and measzcrement of the re.rulting pressure changes at an adjacent well with a very sensitive differential pressure gauge. This paper describes an extensive application of the technique in a producing oil field. Pulse-tests on 28 of 45 possible well pairs in the field provided a picture of the areal distribution of reservoir hydraulic diffusivity, trans-missibility and storage. The primary objective in presenting these data is to demonstrate the potential of the methcid for reservoir description. A second objective is to show in three ways the qualitative and quantitative accuracy of reservoir parameters determined from pulse-tests: (I) pulse-test data show a nonuniformity in the field, closely correlating with the oil-water distribution as given by production data: (2) pulse-test values for permeability are comparable with core va1ue.s; and (3) perhaps most important, the field responds to a conventional interference test in the manner in which pulse-test data predict it should. The pulse-testing technique by Johnson et al.' is an ideal source of data for purposes of reservoir description, for it provides a measurement of formation storage S = +ch, hydraulic diffusivity 91 = k/+cp and transmissibility T — This paper describes an application of this method in a producing oil field. Results were analyzed to give numerical values for the parameters 7, T and S. These values were compared with oil-water production data (for the effect of fluid saturation), with core data and with data from an interference test. The reservoir in which the pulse-test survey was run is the result of a structural trap formed by a fault along the east side of a north-south trending anticline. A down-structure aquifer providcs a natural flank water drive for the pool. The producing formation is a dolomitic lime- stone having mainly vugular permeability; the formation oil has a gravity of 29" API with negligible dissolved gas. The field contains 19 wells, all on pump, arranged on 40-acre spacing along the top of the anticline. Fig. 1 shows the location of all these wells except two at the south end of the field. The dashed line on the right-hand side of the figure represents the approximate location of the fault with respect to well positions. Pulse-Test Survey and Analysis of Data A pulse-test requires a pulsing well and a responding well. In the field, changes were made in the rate of flow at the pulsing well by stopping and starting the pump periodically and measuring the corresponding pressure

Jan 1, 1969

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

By R. F. Domagala, D. J. McPherson

Iodide zirconium was combined with calculated amounts of ZrO2 or master alloys and arc-melted. Annealing treatments were carried out at 21 temperature levels. Metallographic examination of the heat treated specimens permitted construction of the binary phase diagram from zirconium to ZrO2. Oxygen additions to zirconium raise the transformation temperature as well as the melting point. Features of the diagram include the peritectic formation of beta, the formation of alpha directly from the melt, an intermediate phase ZrOB with a' range of homogeneity, and a eutectic between alpha and Zr02. PHASE relationships in the Zr-0 system were determined in the range 0 to 66. 7 atomic pct 0 (ZrO,). Arc-melted alloys were annealed at temperature levels between 600" and 2000°C. Determination of the phase boundaries was accomplished by metallographic evaluation of specimens quenched from the various temperatures. Incipient melting techniques were used to determine solidus curves, and X-ray diffraction work was employed to study the lattice parameters of the a solid solution and the phase ZrO,. Experimental Procedures Westinghouse "Grade 1" iodide zirconium crystal bar (approximately 99.8 pct pure) was employed for the investigation. This material is substantially free of the impurity inclusions characteristic of most zirconium metal. Previous work has shown it to be the most satisfactory grade for phase diagram studies. The zirconium crystal bar, as-received, was coated with corrosion product from autoclave tests by which its grade designation is determined. The bars were sand blasted lightly, pickled for 1 min in a 20 pct HN0,-5 pct HF aqueous solution, rinsed in water and acetone, and dried. The bars were rolled to about 1/32 in. strip, cut into 10 in. lengths, and pickled again. The material was sheared to approximately Y4 in. squares, cleaned with acetone, and stored for use. Two pounds of specially prepared "chemically pure," and 100 grams of spectrographic grade ZrO, were obtained for the preparation of alloys. The "Specpure" ZrO, was obtained from Johnson, Mat-they Co.. Ltd.. and Titanium Alloy Manufacturing Div. of National Lead Co. supplied the other grade of oxide. The "chemically pure" material (henceforth referred to as C.P. ZrO,) was used for the preparation of all alloys employed in the determination of phase relationships. A limited number of alloys were prepared with the "Specpure" oxide to recheck certain phase boundaries. Analyses of the two grades of oxide are given in Table I. The C.P. ZrOI was received in powder form, not suitable for arc melting. Therefore, this material was compressed to wafers 1 in. in diameter and about Vn in. thick. These were segmented and stored for use. The "Specpure" material, in the form of small granules, was suitable for use in the as-received condition. A nonconsumable electrode arc-melting furnace was used to prepare alloys. A water-cooled copper crucible and tungsten-tipped electrode were employed. The material was placed in the crucible and rapidly melted under a protective atmosphere of helium gas by striking the arc on a tungsten stud and directing it upon the charge material. Details of operation, including drawings of this type furnace, have been published.'

Jan 1, 1955

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By Michael P. Robinson

It has been suggested that streaming potentials are not nomlally logged because the streaming potentials known to be generated across mud filter cakes are substantially cancelled by streaming potentials generated in contiguous shale beds. Laboratory measuments of streaming poterztials acrons hand specirnens of shale have been adduced as evidence to support the suggestion. The experiments show that streanzing potential depends on the resistivity of the equilibrating solution and on pressure drop. Meizsurenlents were made perpendicular to the bedding planes of the shales. The mechanism of streaming potential generation in shale which the suggested cancellation theory iniplies has been critically examined. Conclusions reached are tested by comparing self potentials logged before and immediately after changing the resistil~ity (but not the weight) of mud in a borehole. The resultant SP change is found to equal the theoretical electrochetnical potential change, i.e., cancellation of .strearning potential is independent of mud resistivity. Since streaming po/entials generateal across mud filter cakes depend critically upon mud reistivity, shale .strearlling potential in situ must he equally sensitive. Using plausible values for the pemleahility, porosiy arzd compressibility of shale, the van Ererdingerl-Hurst approach shows that the pressure drop between horehole pressure and formation pressure in a radially honzogeneous shale is unlikely to coincide with the zone of filtrate invasion. If, perchance. this coincidence occurs with one mud a chatzge 10 a second must result in non-coincidence, i.e., a .YP logged in the second mud should show a streaming potenlial. The dilernrna may he overcome by postrrlating: (I) perrneabilities of shale7 parallel to their beddine planes greatly exceed their cross-bedding permeabilities; (2) a resistivity-sensitive mud cake of low permeability forms either on the face of, or probnhly in the lanlinations of, many shales. These postulates are examined with reference to the pres.sure and SP histories of the McClosky and Aux Vases zones in the Illinois Basin and some srcpport for them found. It is concluded that a definitive solultion to the streaming potential problem does not exist. INTRODUCTION Recently Gondouin and Scala' published a contribution to the streaming potential problem which is notable particularly for the elegance of its experimental techniques. The conclusions drawn by Gondouin and Scala from their studies amplified those previously suggested by Schehck'. In essence they suggested that the streaming potentials known to develop across mud filter cakes" are not normally observed on SP logs because they are largely cancelled by streaming potentials generated in adjacent shales. This suggestion appears so reasonable that many workers in the logging field will be prone to accept it. We incline strongly to the view that the suggestion is basically correct. Nevertheless, it is important to realize that the cancellation hypothesis in the form put forward by Gondouin and Scala does not appear to meet all the known experimental facts. It is the principal intention of this note to call attention to what appears to be a flaw in the relevancy of the experimental evidence adduced by Gondouin and Scala and to suggest an alternative hypothesis to remove it. The consequences of the new hypothesis are compared with field data which, we believe, are unique. A second but not less important purpose of this note is to emphasize that even the new hypothesis does not fully explain all field observations. Hence we conclude that further study of the streaming potential problem is required before it can be said that a definitive solution to it has been attained. The bare experimental bones of laboratory data on streaming potentials appear to be as follows. 1. A streaming potential is developed across a mud filter cake. This streaming potential is virtually independent of cake thickness but depends on the mud resistivity. The relationship is of the form, 2. A streaming potential is developed across a shale. This potential is independent of shale thickness but depends on the resistivity of the permeating solution if the shale has been first equilibrated in this solution. The relationship is of the form, The relationship in (1) was determined first by Wyllie3, confirmed by Gondouin and Scala and qualita-

By N. Mungan, J. L. Thompson

Laboratory displacement tests were performed to study oil recovery elficiency by gravity drainage in fractured systems under miscible conditions. The porous media used were cylindrical Berea and Blue Jacket sandstone cores containing a number of well-defined, artificially formed, vertical and subvertical fractures. Butane and Soltrol 130 were the two miscible fluids used. The purpose of the study was to examine the influences of the displacement rate, fracture density, fracture orientation, fracture permeability, matrix permeability, crossflow, core length and connate water on the oil recovery. It was found that displacement rate, matrix permeability and the subvertical fractures affected oil recovery most. The critical flow rate, based on the matrix permeability, was found to be a significant factor in the process. For displacement rates below the critical flow rate, the oil recovery efficiency appeared to be unaffected by the density of the subvertical fractures. At the high displacement rates, the fracture density becomes important, with the recovery being the most efficient in the core having the greatest number of the subvertical fractures. The magnitude of the fracture permeability, the fracture orientation, the core length and the connate water have little effect on the oil recovery efficiency. INTRODUCTION Gravity drainage under miscible conditions from relatively thick reservoirs can be a very efficient recovery process, especially at low flow rates where the gravity forces are dominant and, consequently, the adverse viscous fingers associated with the unfavorable viscosity ratio are minimized or eliminated. Such a process might involve injection of an LPG or some solvent bank at the crest and then driving the bank with dry gas. For some favorable combination of reservoir temperature, pressure and oil composition, there may be no need to inject any solvent bank, since enrichment of the dry gas by the light ends of the crude creates an in-situ solvent bank. Slobod and Howlett2 have studied the effects of gravity segregation in vertical unconsolidated porous media under miscible conditions in the laboratory. The main variables in their study were the viscosity ratio, the density differences and the rate of flow. In this study, the objective was to find the influence of fractures on gravity drainage under miscible conditions. A greater number of related variables were also studied. LABORATORY STUDY CORE DESCRIPTION Displacement tests were performed mostly in cylindrical Berea sandstone cores. In a few cases in which a much lower matrix permeability was desired, Blue Jacket sandstone cores were used. The vertical fractures were formed by cutting the cores with a thin circular blade or by parting them along a bedding plane. The vertical fracture plane always contained the axis of the cylindrical core. The subvertical fractures, cut with a saw, were inclined 45' from the horizontal. The line of intersection between the planes of the vertical and subvertical fractures was parallel to the circular faces of the cores in all cases except one, as depicted by VF3HF-2 in Fig. 1. Fracture geometry of the other cores is also given in Fig. 1. Tables 1 and 2 give the physical properties of the solid and fractured cores, respectively. The suffixes and prefixes shown for each core have been used throughout the paper so that the reader may discern the fracture geometry from the core numbers.

Jan 1, 1970