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By Robert Maes, Robert de Strycker

The Fe-Ni-As phase diagram has been established by the study of about a hundred alloys, by microscopic observation, and by thermal analysis, with arsenic contents up to 50 pct. The iron and nickel arsenides present extensive solid-solution fields, owing to the substitution of nickel by iron and vice versa; the extent of the solubility field of each compound has been determined with an accuracy of ±1 pct. In the investigated range of compositions, the solidification reactions were established, and the temperatures of the invariant reaclions detevmined with a preciston of iZ°C in the most favorable and ±5°C in the least favorable cases. The isothermal lines of the liquidus surface have also been drazum, with an accuracy estimated at i5°C. Reactions in the solid state, which take place for the formation or the decomposition of certain phases , were investigated in detail. ThE constitution diagram of the Fe-Ni-As system is fundamental for the understanding of the properties of nickel speiss; these by-products of the extraction of certain nonferrous metals indeed often contain the three elements iron, nickel, and arsenic as main constituents. The Fe-Ni-As system has already been the object of earlier investigations. In 1932, Guertler and Savels-berg' have presented some elements of the ternary phase diagram, for arsenic contents up to 55 pct (all percentages in this paper are given in weight percent), including the vertical section FezAs-Ni&s2. This investigation is, however, incomplete and certain anomalies suggested the necessity to verify the results published by these authors: the section Fe2As-Ni5AsZ, for example, is presented as quasi-binary, with a field of complete miscibility in the solid state, even though these compounds do not have the same structure. Recently, ~useck' established an isothermal section at 800°C in the Fe-Ni-As system by X-ray diffraction and microscopic examination of water-quenched alloys. These techniques are sometimes inaccurate for the determination of the fields where alloys are liquid at the investigated temperature, and they may lead to erroneous conclusions when a compound exists at the investigated temperature but is not stable at room temperature and cannot be maintained by quenching. LIMITING BINARY PHASE DIAGRAMS The Fe-As constitution diagram has been the object of several investigations which have been reviewed by Hansen and Anderko.3 For the Ni-As phase diagram, a recent study has been effected by Yund.4 In this system, Heyding and calvert5 have determined the existence of a compound of unidentified structure at arsenic contents slightly higher than those corresponding to Ni5As2 and at temperatures lower than about 200°C; by analogy with iron and cobalt arsenides, this compound could correspond to the formula Ni2As, as suggested by Kulle-rud; although this is not definitely established. In the region of arsenic contents from 35 to 55 pct, Fried-rich7 detected anomalies in the solidification reactions; an interpretation of these anomalies was given by Hansen ,8 which assumed that the solidification reactions in practice are not in equilibrium, but are meta-stable. The main features of the Fe-Ni constitution diagram are the existence of a complete miscibility field, at least at high temperatures, for the fcc phase (which will be designated by My in the remainder of this work) and of a limited solubility field for the bcc phase (designated by Ma). EXPERIMENTAL METHODS The fundamental technique used in this investigation was microscopic observation, which allowed the determination of the reactions occurring during solidification of the alloys, and possible reactions in the solid state.

Jan 1, 1968

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen's method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen's method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen's5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen's method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen's method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen's method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By Y. A. Chang

Phase relationships in the system Cr-Si have been established based on the melting point, X-ray, metallo-graphic, and DTA studies. The three intermediate phases, Cr3Si, Cr5Si,, and CrSi,, melt congruently at 177V ± I@,Cr3Si, 1680"i 20°, and 1490" *20°C, respectively, while the fourth intermediate phase CrSi, melts peritectically at 1413" i 5°C to Cr5Si3 and a melt containing 51 at. pct Si. The temperatures and compositions of the four eutectic isotherms occurring in this system are given below: DTA and metallographic evidences indicate that Cr5Si, undergoes a phase transformation at 1505" i20°C. The high-temperature form of this phase could not be retained by the quenching techniques used in this study. TECHNOLOGICAL interest in the developing of composite systems, consisting of Sic on the one hand as a fiber-reinforced material and metallic substances such as chromium, nickel, or Cr-Ni alloys as a binding agent on the other hand, stimulated the present investigation of phase relationships in the binary system Cr-Si. Earlier works concerning this system have been evaluated and summarized by ansen and Anderko.' Their phase diagram was based mainly on the works of Kieffer, Benesovsky, and schroth2 and Kurnakov.~ According to these authors, the three intermediate phases Cr3Si, CrSi, and CrSi, all melt congruently at approximately 1730°, 1600°, and 1550°C. However, they did not agree on the compositional stability of the fourth intermediate phase between Cr3Si and CrSi. Later Parthe, Nowotny, and schmid4 determined the structure of this phase to be tetragonal T-1 type using the single-crystal method, and concluded that this phase had a formula of Cr5Si3. Since the compilation of Hansen and Anderko,' a new phase diagram for the system Cr-Si has been proposed by Elliott5 based on the works of Goldschmidt and rand,' Guseva and ~vechkin,~ and Trusova, Kuzev, and Ormont8 and the earlier works quoted by Hansen and Anderko.' According to this proposed phase diagram, all four intermediate phases have large ranges of homogeneity and all melt congruently. More recently, Svechnikov, Kocherzhinskii, and yupkog studied the system Cr-Si by the DTA-method. According to their findings, the three intermediate phases, Cr3Si, Cr5Si3, and CrSi,, melt congruently at 1700°, 1720°, and 1475"C, respectively, while the fourth intermediate phase, CrSi, melts peritectically at 1475°C to Cr5Si3 and a melt containing 50 at. pct Si. The temperatures and compositions of the four eutectic isotherms were found to be: In view of the discrepancies existing in the literature concerning the system Cr-Si, it was decided to rein-vestigate the phase relationships in this system. EXPERIMENTAL a) Starting Materials. Chromium disilicide and chromium or silicon powders were used in the present study to prepare the melting point and DTA samples. CrSi, was obtained by directly reacting cold-pressed elemental powders in an atmosphere of Hz at a temperature of about 1250°C. Chromium powder, purchased from Stark Chemical Co., had the following impurities in ppm: Fe, 200; Mg, 1000; and 0, 250; while silicon powder, purchased from the Welded Carbide Co., had the following impurities in ppm: Ca, 700; and Fe, 3500. b) Melting-Point Determination and Differential Thermal Analysis. Cylindrical melting-point samples of approximately 13 mm in diam and 30 mm in length with a rectangular groove in the center were prepared by hot-pressing of well-mixed powder mixtures in graphite dies. Before the melting-point determination, the hot-pressed samples were ground on a sand paper to remove any minute surface contamination of graphite. A small hole of 1 mm in diam, drilled on the center portion of the samples, served as a blackbody cavity for the temperature measurements. DTA samples approximately 13 mm in diam and 15 mm in length were prepared in a manner similar to the melting-point samples. Melting points were determined using the Pirani technique under a helium atmosphere of 40 psi. The design, performance, and operation of this apparatus have been described in detail by Rudy and ~ro~ulski.'~ The temperature measurements were carried out with a calibrated disappearing-filament-type micro-pyrometer. The measured temperature was corrected for losses from the quartz window of the melting-point furnace and for deviations from blackbody conditions of the observation hole. The procedure for temperature correction has also been previously described." The DTA method of Heetderks, Rudy and Eckertl' was also used to check any phase transformations of selected alloys in the system Cr-Si. It was not possible to make remated runs on the same sample once melt-

Jan 1, 1969

By N. Tiner

THE mechanical properties of magnesium-alloy castings are greatly improved by grain refinement, and at present considerable attention is being paid to methods of obtaining fine-grained castings. One method of achieving this end is the use of proper melting and superheating techniques. These have been employed commercially to a great extent, but no comprehensive study of the subject appears to have been published at present. Numerous investigations found in the literature include some reference to superheating techniques, 1-4 and Achenbach, Nipper and Piwowarsky,5 based principally on thermal analysis, ascribe the grain-refining action of superheating to the influence of solid foreign particles or dissolved gases present in the melt upon the course of crystallization. The primary purpose of this paper is to present the principal facts concerning the effect of superheating on grain size of magnesium alloys. Attempts are also made to explain the experimental results in terms of a general hypothesis. The investigations are limited chiefly to common commercial casting alloys. In order to carry on this work, it was necessary to determine the factors influencing grain size and to develop a proper technique for the preparation of samples. The preliminary tests made by the author indicated that the grain size of magnesium alloys resulting from the solidification of a melt is determined by alloy composition, presence of impurities, rate of cooling during solidification, thermal history of the melt and to some extent the structure of the charge used. The rate of cooling is in turn dependent upon the mass of the melt, pouring temperature, and dimensions, properties and temperature of the mold into which the melt is poured. The final grain size of the alloys is still further modified by heat-treatment subsequent to casting. It is not within the scope of the present paper to discuss all of these factors, and it would suffice to note here that when equal amounts of magnesium alloys are prepared from the same alloying materials, melted in graphite crucibles under the same thermal conditions, then cast into graphite molds at a constant temperature, the .resultant solids have the same grain size. By maintaining all other factors constant, it is thus possible to vary thermal conditions of a melt and to examine the grain size of resultant castings. PREPARATION OF SAMPLES AND GRAIN-SIZE TESTING The alloys investigated in this paper were taken from ingots made by Permanente Metals Corporation or prepared by the author with pure carbothermic magnesium and necessary alloying elements. Melting was carried out under a flux in a graphite crucible heated uniformly by an

Jan 1, 1945

By E. W. Engle

For several years the Fansteel Products Co. has been engaged in e production and development of various of the rarer metals. It is at present engaged in the commercial production of tantalum, tungsten, and molybdenum in a very high state of purity. The information contained in this paper is partly a general compilation from various sources and partly information obtained as a result of recent years of work in the laboratory of this company. Tantalum, tungsten, and molybdenum form a group peculiar to themselves among the commercially available metals. Their very high melting points (tantalum 2770' C., tungsten 3350' C., and molybdenum 2550" C.) set them apart so far as the metallurgical processes for their production are concerned. Further, when properly prepared and treated they will stand a somewhat unusual degree of cold work, that is work below the temperature at which marked crystal growth takes place. Such cold-worked metal may show a high tensile strength; tantalum to 130,000 lb. per sq. in., tungsten to 490,000 lb., and molybdenum to 260,000 lb., in the form of fine wire. In physical appearance, these metals are not unlike some steels; they may be better described by saying that polished tantalum somewhat resembles lead; polished tungsten, iron; and polished molybdenum, nickel. The polished surfaces of all three remain untarnished in ordinary air. Air containing corrosion-producing impurities will, in general, show molybdenum the least resistant to corrosion and tantalum the most resistant. Molybdenum has, however, a high degree of resistance to corrosion by hydrochloric acid, a property that should render it of commercial interest. On the other hand, it is markedly attacked by some of the weaker organic acids. The three metals oxidize rapidly when heated at or above a dull red in air. This feature limits their use in many applications where their high melting point and strength make them appear usable. Tungsten and molybdenum, at red heat, are quite inert to hydrogen and nitrogen; while tantalum has a rather remarkable affinity for all the ordinary gases, which results in its becoming embrittled in their presence. This

Jan 1, 1925

By O. K. Miniato, L. Massé, K. Nobe, J. S. Aronofsky, W. F. 213-000-000-016 Seyer

MUCH work has been done dealing with the effect of mechanical stress on electrode potential in an electrochemical system. The contradictory nature of the experimental results indicates the complexity of the problem although thermodynamic considerations show that a simple relationshir, should exist. In those systems where a gas was the electromotive active substance satisfactory agreement between theory and practice has been found. Des Coudres' found this to be so even when the active substance of the electrode, in this case mercury, was in the liquid state. In contrast, attempts to correlate theory and experiment for the solid state have met with a very limited success. The early workers in this field, Andrews,2 Walker and Dill3 used iron, certainly one of the most reactive of metals. Others have made use of less active metals such as copper and nickel. Recently Fryxell and Nachtrieb4 investigated the electrochemical behavior of gold and silver under both tensile and compressive stresses and concluded that it was doubtful whether true stress potentials could ever be measured. Much of the lack of success to measure the thermodynamic stress potential can be ascribed to the presence or formation of a complex film on the metal surface in contact with the electrolyte. Further, the theoretical stress potential is very small and therefore difficult to measure directly. Thus the calculated emf between a 24 B & S gage cold-drawn copper wire stressed with a weight of 1 kg and an unstressed portion of the same wire is only 2.60 X 10"7 volts. This is very small compared to that which can be produced by chemical reactions at the metal electrolyte interface which in turn can be so large as to mask completely the stress potential. Hence in this type of measurement all chemical side effects must be eliminated or reduced as much as possible. It was for this reason that the system copper-sodium chloride solution was selected for study. INSTRUMENTATION In the many preliminary experiments conducted, two major difficulties were encountered. The first was to measure the small electro-potentials to be expected and the second to obtain a suitable electrode surface. The conventional potentiometric method was found to be unsatisfactory for measuring the small emf expected. However, by using an L & N No. 2290 galvanometer having a resistance of 915 ohms consistent measurements were possible. The reference electrode was always the unstressed one made from the same sample of wire. The steady current flow was approximately 10-8 amp. Lewis and Randell5 have stated that for currents of the order of 10-8, if there is no sensible polarization, the measured emf may be taken as a reversible one. To check the galvanomenter readings an alternative method was devised to measure the potential difference between the wires. This involved a Liston-Falb d-c breaker amplifier model 10, an L & N k-2 potentiometer and a moving-coil galvanometer having a sensitivity greater than 0.1 µv (microvolt) per mm. To increase further the output voltage of the amplifier a d-c amplifier, model B. L.-932 was introduced into the circuit. This amplifier was in turn connected to a Brush recorder which had been calibrated previously by the test signals from the Liston-Falb instrument. These test voltages employed took into account the impedance of the input current. Unfortunately, this method had too low a sensitivity for measurement below 10 µv. Above this value the voltage agreed reasonably well with those obtained directly by the simple galvanometer method. The main advantage of the amplifier setup was that one did not have to wait until no deflection occurred on the galvanometer in the circuit when first exposing the wires to the solu-

Jan 1, 1959

By Attilio Ligasacchi

The production of magnetite in copper smelting has been the subject of wide investigation in the past.1-9 It is accepted that most of the magnetite is produced in the converters and returned to the re-verberatory furnace with the converter slag. Part of this magnetite is circulated back to the converters in the matte. As a result, if proper fluxing practice is not followed, and temperatures in the converting process are not strictly controlled, an undesirable circulating load of magnetite may occur. This might ultimately lead to saturation in the reverberatory bath with consequent settling of the magnetite at the furnace bottom. This paper contains the cumulative results of a series of investigations on the formation and control of magnetite presently being conducted by the metallurgical department of the Chino Mines Division of Kennecott Copper Corp. THE METHOD USED FOR THE DETERMINATION OF MAGNETITE AND OTHER MAGNETIC MATERIALS Conventional wet chemical magnetite analyses are neither reproducible nor theoretically sound. These analyses are sensitive to time, temperature, and heating rate-all factors which tend to decrease their accuracy and reproducibility. To overcome the unreliability of the above method, H. W. Mossman1 developed an inductance bridge magnetite "meter" which completely replaces the wet chemical analysis with the advantage of quicker and reproducible results. Fig. 1 is a schematic diagram of the meter in use in the Chino metallurgical laboratory. When a pulverized specimen with magnetic properties is placed in coil A of the inductance bridge circuit, the permeability of the core is increased, causing a voltage drop across the coil. The unbalance is amplified to operate the balancing motor which adjusts the movable iron core in coils C and D to bring the bridge back to balance. An indicator arm connected to the movable iron core indicates directly the percent, or weight, of the magnetic material in the specimen. Coil B acts as a reference coil and a zero adjustment. The meter is standardized with a set of various amounts of -100 mesh pure magnetite crystals (99.8 pet Fe3O4) thoroughly mixed in a test tube with -100 mesh quartz sand. These mixtures are combined with inert transoptic powder and heated to 140° to 160°C (melting point of the powder) and subsequently cooled to room temperature, solidifying the whole mixture, in this manner eliminating any possible preferential orientation of the magnetite grains. In order to determine the effect of the particle size" of the magnetite and other magnetic materials on the meter determinations, five size fractions were obtained by wet screening of the 99.8 pet pure magnetite and several reverberatory matte and slag samples. The following size fractions were investigated: -80 + 100; -100 + 150; -150 + 180; -200 + 250; -250 + 300 and -100 mesh. The deviation of the meter readings for the various sizes of each sample never exceeded ±0.3 pet. This deviation is considered well within the accuracy needed for common smelter operation procedures. Further investigation proved also that grinding slag and matte samples in our laboratory disc grinder normally produced a powder constituted of 95 pet -200 + 300 mesh. For practical purposes a - 100 mesh size was used as standard for our studies. It was also found that for rapid determinations tamping of the sample in the test tube was sufficient and gave comparable results with those samples solidified with transoptic powder. For the purpose of this study we define the magnetite content in copper smelter slags and matte as the equilibrium amount of crystalline Fe3O4 existent in the specimen at a given reference temperature, excluding any secondary magnetite precipitated in the specimen during nonequilibrium conditions. MAGNETITE DETERMINATION IN SLAGS Since it is impossible to ascertain the status of equilibrium of a conventional slag sample, due to

Jan 1, 1965

By D. H. Yardley

GEOCHEMICAL investigation of trace elements in surface materials was begun near Ely, Minn., in 1953 along the basal contact of Duluth gabbro with Giants Range granite (Fig. 1). This article presents data on the distribution of copper and nickel in till and in stream sediments in the area and proposes an explanation for the types of distribution found. The Duluth gabbro, one of the world's largest basic intrusives, intrudes rocks which range in age from Keewatin to middle Keweenawan. Within the test area the gabbro is in contact with granite except for short sections where it is in contact with remnants of iron formation. Sulfide mineralization occurs within the gabbro, near and parallel to the basal contact for a distance of several miles. Schwartz and Davidson' have described the geologic setting of the mineralization. The sulfides, believed to be syngenetic, include chalcopyrite, cubanite, pentlandite, pyrrhotite, and minor amounts of bornite. They occur disseminated in the silicates and as small interstitial masses. The ratio of copper to nickel is about 3.8:1, based on 66 chemical analyses of rock samples from various outcrops (Ref. 1, p. 702, and Ref. 2). Test Procedures: With specified exceptions, all nickel and copper tests were made by the chromo-graph method,:' which measures the intensity of a colored spot formed by a reaction between the metal being determined and special reagent paper. The intensity is then compared to the intensity of spots prepared from samples of known metal content. Details of the test procedure are outlined in another article (Ref. 4, pp. 77,78). All soil samples tested in this investigation to date have been weighed on an analytical balance. However, a volumetric scoop designed to provide about 0.1 g of soil adds to the speed and ease of testing and has been found to give satisfactory results (Ref. 5, p. 531, and Ref. 19). The size of the samples used for the tests was 0.1 g. Whenever such small samples are used there is some question as to whether they are representative of the several grams in the field sample. Many repeat tests of the samples used in this investigation demonstrated that results can be reproduced within the limits of accuracy of the method without formal mixing beyond that inherent in screening the soil fractions. Furthermore, the 0.1 g is probably as representative of the field sample as the field sample is of its area of influence. Hawkes and Lakin (Ref. 6, p. 291), who considered the general problem, compared ground and quartered bulk samples of 500 g with 5-g grab samples. They concluded that "there is no significant loss in accuracy of data by substituting grab samples for bulk samples." The term soil implies somewhat different things to the geologist, engineer, and soil scientist.' For convenience the term as used in this article refers to unconsolidated material (the mantle) overlying bed rock. Sampling Procedure: Samples were taken at 100-ft intervals along north-south traverse lines across the gabbro-granite contact. The soil (till) samples were taken at an average depth of 1 ft, which was below the high-humus surface layer and into clean till. Samples taken at 1-ft intervals down to ledge showed as high a metal content at 1 ft below the air-surface as at greater depths and in two instances were slightly higher. The till at 1-ft depth did not appear to differ from material at greater depths. Total depth to bedrock has been tested at only a few points and where measured varied from 1 to 10 ft. Aerial Distribution Contours and Profiles: Plotting of copper, nickel, and cobalt content in contour form (Fig. 2) shows that anomalous amounts of these metal ions occur in till over and closely adjacent to mineralized areas of the gabbro. Contouring nickel content alone, or the copper content, outlines the same target area. Contours of the copper content provide a more distinct anomaly than nickel because of the higher copper concentration. The traverses are rather widely spread for interpolation; however, drilling has confirmed the target area essentially as shown.

Jan 1, 1959

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By J. E. Walstrom

While intensive research continues to promote a more complete understanding of the potential and resistivity measurements that comprise the electric log, it is believed that consideration should also be given to translating these numerous and often widely separated findings into a coordinated and readable body of fundamental facts designed specifically for the petroleum engineer and geologist. Although provision is made through publication for a ready exchange of new theoretical concepts. it is also desirable to provide reviews and appraisals of the more established techniques and methods from the operating standpoint so that an economic and practical application may be realized concurrently with the theoretical progress. With these basic premises as a guide the author reviews the presnt state of electric log interpretation. The paper is directed not so much to the logging or research specialist as to the petroleum engineer and geologist to whom the electric log is only one of the many tools which he employs. Frequently, these persons do not have the time to follow in detail the many specialized contributions that appear and, as a consequence. are not in a position to place these contributions in proper relation to each other, or to the art as a whole. The paper reviews the basic steps in making quantitative determinations from the electric log of the amount of oil or gas present in subsurface formations and also discusses the degree of reliability of these determinations under various conditions. The paper also indicates the trend of future developments in electric logging systems and methods of interpretation. INTRODUCTION The electric log has been used about 20 years as a means for studying the formations penetrated by a well bore. The first half of this period is characterized by the development of suitable logging techniques and equipment. Although progress in this direction is continuing at a satisfactory rate, the last ten years are characterized more by an increasing interest in methods of electric log interpretation. During this period, a large number of fundamental papers have been published, expounding various logging techniques and particular phases of the interpretation problem. Many of these papers represent important contributions, and a few are classic. This paper is an effort to outline as concisely as possible and in simple terms the main course of progress in electric log interpretation. More specifically, it is the purpose of the paper to review the necessary elements and basic steps used in making quantitative determinations of water saturation from the electric log; and to point out the degree of reliability of these determinations under different conditions. It is strongly advised that the operating staffs of the drilling and exploration departments of oil companies cooperate wholeheartedly with both the electric logging service companies and research organizations in the testing and development of new logging systems and interpretation methods. One purpose of the paper is. however, to indicate the degree of caution which must be exercised in placing confidence in new techniques and interpretation methods that have not been thoroughly tested in the field. It is entirely possible to be cooperative in trying new methods and yet reluctant to believe in the results until the methods are firmly established. It is important to define the meaning of quantitative electric log interpretation. In the most general sense, an interpretation of the log has been made when the electrical characteristics of the formations, as portrayed on the log, have been translated into terms describing the formation geometry, rock type, or any other physical characteristics of the formations. The determination that the top of a sand is at a certain depth is an interpretation of the log. Structural determinations made by correlating electric logs from a given area are also interpretations of the logs. The term quantitative interpretation, however, will be used in this paper in the restricted sense to indicate the determination of the water saturation of a formation. This determination defines the fluid content of an oil and gas productive formation only if the porosity is known, and it assumes that the remainder of the pore space contains hydrocarbons. This assumption is believed to be true for most oil and gas productive formations. The quantitative electric log interpretation may he said to be a determination of the fluid content only to the extent which the water saturation, under the conditions given above. defines it. THE BASIC STEPS The fundamental steps in calculating water saturation from the electric log are: 1. Determination of the true resistivity of the formations from the apparent resistivities as recorded on the electric log.

Jan 1, 1952

By E. H. Jr. Dix

OF all the alloying elements used in commercial aluminum alloys, copper stands out as by far the most important, and it is perhaps for this reason that the constitution of the aluminum-copper system has received the attention of a number of experimenters covering a period of approximately 20 years. It would be expected that during this time the equilibrium relations had been thoroughly and exactly worked out. In a general way this is true, but there is a surprising lack of agreement in the details of the high aluminum end of the diagram, particularly in regard to the solid solubility of copper in aluminum, which has been given variously as 2 per cent. to 5 per cent. at the eutectic temperature. The importance of this is much greater than might at first appear to one unfamiliar with modern commercial aluminum alloys. This is true because, with one exception, the susceptibility of the strong alloys to heat treatment depends, in part at least, upon the solid solubility relations of copper in aluminum. In 1919, Merica, Waltenberg, and Freeman1 published the first detailed information on these solubility relations. They found that the solubility of copper decreases with falling temperature from about 4 per cent. at 5.25° C. to about 1 per cent. at 300° C. and is apparently still diminishing at lower temperatures. In 1921 there was published a brief account of the results obtained in the National Physical Laboratory, Teddington, England.2 This laboratory, however, reported that 5 per cent. of copper is soluble in aluminum at 540° C., and that this amount decreases to about 3 per cent. at 20° C.

Jan 2, 1926

By P. Douglas, G. M. Leak, B. Mills

The sinusoidal surface relaxation technique has been used to measure the surface self-diffusion coefficient of spectroscopically pure nickel over a wide temperature range under a hydrogen atmosphere. A kink in the Arrhenius plot has been observed. In the temperature range T/T 0.98 to 0.80 (T in O K and T, is the melting temperature) the average self diffusion coefficient is given by Below the temperature T/T,- 0.80a decrease in the slope of the log Ds us 1/T plot is observed. This is associated with a diffusion process characterized by a lower activation energy (-20,000 cal mole'') and smaller preexponential term (-10- sq cm sec"). A series of experiments were carried out at T/Tm = 0.61 under a hydrogen atmosphere of higher oxygen partial pressure than for the rest of the experiments. It was found that Ds was significantly depressed due to oxygen adsorption. This evidence supports the opinion that the low temperature process (activation energy -20,000 cal mole-') is unlikely to be due to oxygen adsorption. An interesting feature of the present data is that the transition temperature (T/Tm - 0.80) is a function of orientation. For a small number of crystals of measured orientation the transition temperature was observed to be higher towards the low index (100) pole. Theories of surface diffusion are briefly reviewed and it is concluded that the present reszuts are best explained by invoking a surface roughening process. GJOSTEIN has recently analyzed available surface diffusion data for a wide range of metals. He suggested that two mechanisms were operative for fcc metals, an adatom process at high temperatures and a vacancy process at low temperatures. Results for nickel can be summarized as follows. At low temperatures (T/T, - 0.3 to 0.44) under ultra high vacuum conditions, Melmed2 measured an activation energy Q of 21 kcal mole-' using field electron emission microscopy. At higher temperatures (T/T - 0.7 to 0.9) under a vacuum of 10- ' torr, Maiya and lakel measured y as 39 kcal mole-' using the multiple scratch smoothing technique. The present work was undertaken to try to find out if two distinct processes could be observed. High temperature results give Q about 47 kcal mole-': there is evidence also for a low temperature value of about 20 kcal mole-'. These measurements were all made under a hydrogen atmosphere, in the temperature range 860" to 1412°C. Concurrent with the present study Bonze1 and jostein> have also observed a break in the Arrhenius plot for the (110) surface of nickel. These measure- ments under ultrahigh vacuum conditions using the laser diffraction technique are in excellent agreement with the work reported here under hydrogen annealing conditions. THEORY The available surface relaxation techniques include single and multiple scratch smoothing and grain boundary grooving. The processes have been compared in detail by Gjostein for conditions where surface diffusion dominates6 and Mills et al? where volume diffusion dominates. In summary the relevant points are as follows. Grain boundary grooving gives an average Ds for the two surfaces adjacent to the boundary and this can, to some extent, be simplified by using symmetrical bicrystals. This technique has been used to study the effect of environment on Ds for silver and copper.'-'' Scratch techniques yield Ds values for the small orientation range exposed by the scratches (-2 deg). The multiple scratch process is preferable because the profile rapidly becomes sinusoidal and can then be interpreted theoretically in a relatively simple way. Also corrections for mass transport processes other than surface diffusion can be introduced easily. Mullins" considered a sinusoidal profile described the wavelength of the profile. After time t the profile can be described by the equation The terms A, A', C, and B which account, respectively, for contributions due to evaporation-condensation, diffusion through the gas phase, volume diffusion through the lattice, and surface diffusion are defined as: where Ds = the surface self diffusion coefficient ys = the surface energy per unit area p = the equilibrium vapor pressure over a flat surface pa = the equilibrium vapor density over a flat surface DG= the diffusion coefficient of vapor molecules in the inert gas DM = the mass transfer diffusion coefficient which for a pure cubic metal is Dv/f where Dv is the radiotracer diffusion coefficient and f is the correlation factor H = the molecular volume V = the surface density of atoms, il2'3 M = mass of an evaporating molecule

Jan 1, 1970

By K. H. Kilgren

At high formation pressures the distillate produced from a gas-condensate reservoir may be black in color. In this event the dense gas phase existing above the dew point is correspondingly dark. Volumetric phase data and an analysis of a reservoir fluid exhibiting these characteristics, together with a description of the visual equilibrium cell in which these observations were made, are presented in this paper. INTRODUCTION Previously the author, like many others in the oil and gas industry perhaps, tacitly assumed that the expressions black or dark oil system, crude oil system and bubble-point system were synonymous. Crude oil reservoir fluids are bubble-point systems and yield a black or dark stock-tank oil of relatively low API gravity. Conversely, a clear or amber colored trap distillate of high API gravity is assumed indicative of a dew point system or a gas-condensate reservoir fluid. This broad classification appears satisfactory for shallow reservoirs, but as the following study demonstrates, may be misleading when applied to deep reservoirs. Theoretically, there is no reason to exclude the possibility of producing a dark, low-gravity distillate from a gas-condensate reservoir. At sufficiently high values of pressure and temperature, heavy, dark-colored hydrocarbons may exist in the vapor state of a multi-component system. If enough dark-colored components are present in the reservoir vapor phase, the resulting condensate will be dark. The reservoir fluid investigated in the present study supports this contention. Stock-tank production was black in color and measured 29" APT gravity. From outward appearances, the liquid closely resembled a medium gravity crude oil. Experimental measurements proved the reservoir fluid was in reality a gas-condensate system. Volumetric phase data for this high-pressure system and a description of the visual cell in which the study was conducted successfully are presented in this paper. THEORY Phase behavior of a reservoir fluid can be predicted accurately with reference to a pressure-temperature phase diagram. If the reservoir temperature is lower than the critical temperature of the hydrocarbon fluid in place, bubble-point behavior will be observed. If the reservoir temperature lies between the critical and cricondentherm temperature, dew point behavior and retrograde condensation will occur. For reservoir temperatures above the cri- condentherm, only a single gas phase can exist in the reservoir regardless of pressure. Providing the composition of the reservoir fluid were known, it would be possible to predict the critical temperature and estimate the phase behavior from equilibrium relationships. However, the usual practice is to obtain a sample of reservoir fluid, subject it to varying pressures at the reservoir temperature and observe the phase behavior experimentally. The latter method was used to obtain the data reported here. WELL AND TRAPPING INFORMATION A summary of pertinent data for the well from which the reservoir fluid was sampled is presented in Table 1. This well is located offshore Louisiana. Except for the pressure which substantially exceeds hydrostatic pressure, the information does not appear unusual. Prior to the sampling program, the well was produced for 22 hours at a stock tank oil rate of 139 B/D. Average trapping conditions and gauging data for the six-hour test period that followed are summarized in Table 2. Samples of the first-stage trap gas and liquid were obtained during the latter portion of the test period. Ambient temperature remained 5 to 10F below trap temperature and presented no problem for sampling. Surface wind and moderate foaming of stock-tank oil presented some difficulty in obtaining accurate stock-tank gauges. SAMPLE ANALYSIS Compositions of the gas and liquid samples are shown in Table 3. The trap gas was analyzed by isothermal chromatography which revealed only a trace of heptane in the stream. The trap liquid was initially analyzed by low-temperature fractional distillation, yielding a bottom product of heptane and heavier components. Specific gravity of this fraction was measured and the mol weight was determined by freezing point depression. The hexane and lighter overhead gas collected during distillation was

Jan 1, 1967

By E. C. W. Perryman

The recovery and recrystallization characteristics of superpurity aluminum have been investigated using electrical resistivity, X-ray line breadth, and hardness measurements for the former and the micrographic method for the latter. The three different properties recover at different rates and have different activation energies. The recrystallization results agree well with Avrami&apos;s theory and furthermore indicate that the perfect subgrains formed during recovery are not the nuclei for re-crystallization. WHEN a metal is plastically deformed, its physical and mechanical properties generally undergo considerable changes and by subsequent annealing these changes are partly or wholly annihilated. Thus, a recovery process can be discussed, taking this term in its general sense. In practice, however, there is reason to discriminate between two apparently different processes, one most easily followed at low temperatures, in which the properties return to an almost constant value between that of the cold worked and fully annealed material, and a second process in which the properties return to their original values before cold working and which is accompanied by the formation and growth of new grains having an orientation different from that of the matrix. In this paper the word recovery will be taken to mean the changes in some property as a function of annealing time which occur either without the appearance of new grains or under conditions such that the new re-crystallized grains are very small (= 2 microns), are very few in number, and substantially do not affect the property being measured. This definition is rather abitrary, for it will depend upon the sensitivity of the technique used for the observation of new recrystallized grains, which in the present work was about 1 to 2 microns. However, it is helpful to use the term recovery in this sense and to reserve the term recrystallization for the processes of nucle-ation and growth of new grains in the cold worked matrix. Although considerable work has been done on recovery and recrystallization, most workers have based their study on the measurement of one or perhaps two parameters. Since very small amounts of impurities have such a profound effect on the recrystallization characteristics of a pure metal, it becomes extremely difficult to correlate one piece of work with another. With this in mind, the present work on recovery and recrystallization was done on the same material. Experimental Procedure Material Used and Fabrication: The composition of the superpurity aluminum used throughout this investigation was 0.002 pct Cu, 0.003 pct Fe, 0.003 pct Si, and <0.001 pct Mg. The ingot was hot rolled to 0.250 in., annealed, and cold rolled to 0.034 in. A large number of reductions and intermediate anneals were carried out so as to produce material with a minimum of preferred orientation and maximum homogeneity. For the recovery part of the investigation, the final cold reduction was 20 and 80 pct and for the recrystallization part, 20 pct. After each pass in the cold rolling process, the material was quenched in cold water in order to keep the rolling temperature as near room temperature as possible. Annealing Procedure: For the recrystallization work, specimens 1x1 in. were cut from the 0.034 in. cold rolled sheet and a hole was drilled in each through which a wire was threaded to support it in the salt bath. The temperature of the salt bath was controlled to +2°C and the time taken for a specimen to reach temperature was approximately 5 sec. These 1 in. squares were then divided into three groups, one of which was given 5 min at 318°C and another 2 hr at 244°C. These treatments were such that recovery was almost complete and a well defined subgrain structure produced. Separate specimens of each group were annealed for different times at 301°, 318°, 355°, and 373°C, i.e., three specimens for each annealing time. The delay between finish of cold working and start of annealing was about 1 hr. For the recovery work, strips 0.062 in. thick were cut from the cold worked sheet, annealed, and then given the last cold rolling operation. This was done for each annealing temperature. By this means it was possible to minimize the delay between cold working and annealing. In general, all measurements were carried out within 1 hr of the last cold rolling operation. Annealing at low temperatures was done in an oil bath the temperature of which was maintained constant to +1°C. Electrical Resistivity Measurements: Strips 20x0.5x0.05 in. were machined and the electrical resistance measured using a Kelvin double bridge. Measurements were made in an oil bath maintained at 20rt0.1°C. The same specimen was used for the complete isothermal annealing curve.

Jan 1, 1956

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study&apos; that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,&apos; flow in packed columns,&apos; fracture flow capacity&apos; and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

By John D. Verhoeven, Edward E. Hucke

An experimental technique has been developed for the measurement of the rate of electrotransport to a precision of 1 pct in the molten Bi-Sn system. Results are presented across the phase diagram from 30°C above the liquidus to 520°C. A phenomenological description is presented and the data on Bi-Sn are thereby converted to the effective charge, Analysis of the data indicates the true charge of the migrating tin species in bismuth to be +1.8 at 500°C. The data agree well with the recent work of Belashchmko. fieldintensity. The resistivity of the molten Bi-Sn system is also presented. WHEN an electric field is applied to a metal, a relatively large current is produced due to the ease with which electrons move within the metal. The electric field also produces a force on the ions which might cause them to migrate. Such a migration of metallic ions has been detected under certain conditions. This electromigration of the metallic ions will be referred to herein as electrotransport. The study of electrotransport in metallic systems has a rather long history dating back to the initial work of Gerardin1 in 1861. General reviews of electrotransport in liquid and solid metals have been published by Schwarz,2 Jost,3 Seith,4 and Heumann.5 In reviewing the literature it is apparent that the theoretical developments are not yet complete. The difficulty arises in describing the momentum transfer between the migrating ions and the electrons. In addition, there is a lack of good quantitative electrotransport data at high temperatures, especially in liquid metal systems. This work was undertaken to establish quantitative electrotransport data in a liquid metal system which might serve as a critical test of the theoretical developments. The Bi-Sn system was chosen for analysis, and the rate of electrotransport was determined as a function of temperature and composition. THEORETICAL CONSIDERATIONS If all of the atoms of a metal are considered to be positively charged due to the loss of electrons to the

Jan 1, 1963

By Henry Phelps Howland

During the last decade no topic has created more interest or received more thought among blast-furnace men than coke. One reason for this is, undoubtedly, the remarkable increase in the use of byproduct coke. Formerly our coke was made at a distance from the furnaces and by a distinct organization. There was little cooperation or development possible under these conditions. Today the situation is greatly changed. Much of our coke is made by the organization operating the furnaces and the coke oven is operated with the primary object of obtaining the best results in the blast furnace. The effect of changing the method of coke manufacture, even in some minor detail, is often felt almost immediately at the blast furnace. There naturally results one of the most valuable assets of the byproduct coke oven, i.e., the possibility of increased blast-furnace efficiency due to close observance and correct operation of the ovens. The results are evident, but often it is difficult correctly to account for them. In attacking the solution of a problem of as much importance as why one coke is better than another, there are facts which should be kept clearly in mind. The author hopes, in this paper, to bring out some points relative to the use of carbon in the blast furnace which will be of value in solving this question. GeÜner&apos;s Ideal Working Years ago GrÜner made a statement regarding the use of carbon in the blast furnace, which has been very generally accepted by metallurgical and blast-furnace men. I quote this theory as given by Prof. Richards on p. 248 of Metallurgical Calculations: "From the standpoint of the generation of the maximum quantity of heat in the furnace, GrÜner was right in formulating his dietum of the ideal working of a blast furnace, vie.: All the carbon burnt in the furnaee should be first oxidized at the tuyères to CO and all reduction of oxides above the tuyères should be caused by CO, which thus beeomes Co2."

Jan 1, 1917

INCREASING realization that pouring and ingot-mold practices involve many factors of fundamental importance to ingot quality and general steel-mill operations has caused these phases of steelmaking to become major concerns of operators and metallurgists engaged in control of quality and costs. Methods of pouring steel from the ladle into the ingot molds have some direct effects on ingot quality. The mold itself governs solidification and dimensions of the ingot and in so doing exerts some very tangible influences not only on ingot quality but also on product yields and general steel-mill processing. In addition, practices are employed&apos; in the handling of molds during daily open-hearth operations that are important to quality and production costs. Therefore, pouring and mold practices must be considered highly specialized and important steps in steel-mill operations. MOLD DESIGN Mold design is difficult to discuss in a precise manner because it varies greatly throughout the industry, both in theoretical concepts and practical application, and few well developed data are available. Most ingot molds are designed to meet conditions peculiar to a given plant wherein quality standards are dictated by end-use requirements, which may differ considerably, even for the same grade of steel. The mold designer must also consider the equipment available to process ingots and the product obtained from them. Such equipment, used for stripping, heating, blooming and finishing operations, is seldom, if ever, exactly the same in any two steel plants. Thus, pronounced contrasts in mold designs can be expected to continue, even among plants making strictly comparable types of product, particularly because some producers are just beginning to realize the benefits possible from specialized designs. Certain fundamentals are used in mold design but even these

Jan 1, 1951

By K. K. Clark

Excessive injection pressures in water injection wells may create deeply penetrating fractures, or may open up existing reservoir fractures. If these fractures are oriented toward offset producing wells, oil recovery at injected water breakthrough and ultimate recovery will be impaired. A method of calculating fracture lengths from pressure fall-off test data is presented. The method is based on a linear flow model that simulates conditions present during the early-time period after shutting in an injection well. Fracture lengths can be calculated directly if formation permeability is known. A graphical technique is presented that provides fracture lengths based on permeabilities calculated from normal fall-off tests, where those permeabilities are adjusted for flow geometry. Test data from four injection wells and results obtained from applying the method to these wells are discussed. Introduction Rates of water injection into nonstimulated wells in low permeability reservoirs frequently fall below economically desirable levels. Therefore, some form of stimulation such as hydraulic fracturing often is performed on these wells. Usually these fractures penetrate a short distance from the well — short as compared with interwell spacing — and therefore should not create problems of water channeling to offset producing wells. In the past, some operators have been tempted to increase injection pressures continually to maintain a specified injection rate. But pressures cannot be increased indefinitely. Field data indicate that continued injection above fracture opening pressure can cause excessively long fractures to approach between well distances. If these long fractures intersect or closely approach offset producing wells, premature water breakthrough can result. It is difficult to seal effectively these fractures by various workover procedures after premature water breakthrough has occurred. This paper describes testing procedures that are potentially capable of detecting premature water breakthrough before it occurs. Knowledge of fracture lengths and fracture opening pressures can assist field engineers in selecting optimum operating conditions for water injection wells. Fracture lengths should be calculated from pressure fall-off tests on injection wells, and maximum permissible iniection pressures should be determined from step-rate injectivity tests. Equipped with this information, the field engineer is in a better position to recommend for a particular injection well the optimum operating conditions that will lessen the chances of channeling to offset producers. Historically, pressure transient tests have been conducted primarily on producing wells and analysis procedures have been based on radial flow concepts. Several authors have suggested that these same procedures be applied to tests conducted on water injection wells. This application is justified for wells that are not connected to extensive fracture systems. However, if the formation is severely fractured, the interpretation methods must be modified. Several authors have presented the pressure response of various systems that are intended to simulate reservoir conditions. A paper by Russell and Truitt* on vertically fractured svstems is probablv the most useful from the standpoint bf the fieid engineer. Russell and Truitt presented the pressure-vs-time behavior of a well connected to vertical fractures with various fixed lengths. Their permeability adjustment technique is used in this paper to refine methods of calculating fracture length and interwell permeability. Theory and Definitions Three flow-system geometries are considered in analyzing injection well test data. These various geometries are applicable during specific time intervals of transient pressure tests. Schematic drawings of the flow models, and the time intervals over which they are applicable, are shown in Fig. 1 in the chronological order that they are applied to the pressure response of water injection wells in fractured formations. The very early response is simulated by an infinite linear system as shown in Fig. 1A. This representation permits the calculation of matrix surface area exposed to the fracture. The model shown in Fig. 1B is identical with the one studied by Russell and Truitt. They evaluated the transient pressure response of this vertically fractured system by finite difference techniques. The results were presented as tabulations of dimensionless pressure drop functions for a range of fracture lengths. A semilog plot of these data shows that the apparent matrix permeability can be related to the true matrix permeability by a simple exponential function. Their adjustment factor is used in this paper to improve the accuracy of matrix-permeability and fracture-length calculations.

Jan 1, 1969

APPROXIMATELY 3500 people thronged the Hotel Statler from February 18 to 24 for the 173rd general meeting of AIME. It was a technical extravaganza in that 82 technical sessions were held, at which 500 authors presented some 350 papers. Fortunately, Jerry Peirce, outgoing President, didn&apos;t have, to preside at all the events although after his year&apos;s stint as President, he has more than a nodding acquaintance with some of the latest problems in the mining, metals, and petroleum industries. Although the Welcoming Luncheon on Monday noon was the official opening of the meeting, Local Section Delegates and the Board of Directors convened on Saturday and Sunday, respectively. The large attendance and business like demeanor of these two groups was in accord with the energetic and competent service they have rendered the Institute through the year. To the applause of engineers and their wives who thronged the grand ballroom of the Statler for the Welcoming Luncheon, President Peirce introduced Oliver B. Hopkins, president of the Canadian Institute of Mining and Metallurgy and C. Gerow, secretary of CIM. Dr. Hopkins brought greetings from the CIM and expressed his satisfaction in the splendid spirit of cooperation that exists between the two Institutes. Dr. Hopkins is president, Interprovincial Pipe Line Co., Toronto, and counts as a close personal friend M. L. Haider, who is the 1952 President of AIME and lately of Toronto where he was a director and general manager of Imperial Oil Ltd. Mr. Haider will be known shortly as Mike to thousands of AIME members as he makes his Local Sections presidential tour. There was a pause in luncheon proceedings when Judge Harold R. Medina arrived amid the applause of the audience and somewhat breathless from his trip via motorcade from an antitrust trial against investment bankers at the courthouse downtown. With the Judge at his elbow, President Peirce took the opportunity in his introduction to good humoredly chide the Judge for the vixenish habits of public servants in their treatment of astute businessmen. The successful inventor who patents his inventions is a monopoly; the copper manufacturer who buys his competitors a drink is in collusion; but the business failure need only look to the government for a subsidy, Mr. Peirce pointed out. Judge Medina, quickly captured the admiration of his listeners. He spoke about justice, deploring partisan deals on nominations for judge-

Jan 1, 1952