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By R. W. Parsons, P. R. Chaney

Oil recovery by the imbibition mechanism can be important in fractured carbonate reservoirs with a bottom water drive. Laboratory experiments were performed on water-wet carbonate rocks to model this process. The results are interpreted in light of the applicable scaling laws. The imbibition production behavior of a pillar of rock subjected to a slowly rising water table can be synthesized from data on total immersion experiments on small rock samples. If the rate of water table rise is slow enough and if the physical properties are such that the imbibition zone is of a small vertical extent, then only the final oil recovery on the small samples need be known. Applying laboratory imbibition data to a real reservoir should be done with caution because of possible wettability problems and the unknown behavior of two-phase flow in fractures. INTRODUCTION The spontaneous taking up of a preferential wetting fluid into a porous medium with the simultaneous expulsion of the contained fluid is termed imbibition. One of the many physical imbibition processes is the production of oil by the taking up of water into a water-wet reservoir rock. In certain types of heterogeneous reservoirs, e.g., fractured, it is realized that imbibition alone may be the dominant mechanism. Theoretical studies of imbibition oil recovery have followed several lines of attack. The behavior of certain mathematically tractable and conceptually simple models have been analyzed. Birks1 considered a bundle of vertical capillaries model, while Perotti et al.2 and Kelemen3 used a model of a series of vertically oriented fractures. If the oil production behavior from a block of reservoir rock is known, then the cumulative behavior of a vertical stack of these blocks subjected to a rising water table can be determined by a method outlined by Aronofsky et al. 4 Knowing the capillary pressure and relative permeability functions should uniquely set the imbibition behavior for a given sample. Solutions of the partial differential equations describing the process, however, present some formidable problems. Digital computer techniques have been applied to displacement processes in which the capillary pressure has been included.5"8 More recently, similar techniques have been used by Blair 9 to calculate countercurrent imbibition behavior. The fact that imbibition behavior is described by the usual fluid flow equations (Darcy's Law and continuity equation) implies that the derived scaling laws should apply equally to this situation. Use of model experiments to study imbibition has been employed by Graham and Richardson 10 and Mattax and Kyte,11 who actually tested the scaling law applicability. This study is concerned with scaled model imbibition experiments on water-wet carbonate rocks. Of particular interest is the slowly rising water table experiment. This simulates a highly fractured reservoir with the water table rising uniformly through the vertical fracture system. Experiments were performed on different sized samples and with different rates of rise of the water-oil interface surrounding the rock pillar. Total immersion imbibition experiments on smaller rock samples were performed to test the basic linear scaling laws and to see if these simpler tests could be used to synthesize the rising water table experimental results. THEORY IMBIBITION SCALING LAWS Scaling laws for the flow of two incompressible immiscible fluids in a porous medium have been presented by Rapoport.12 These are derived directly from Darcy's Law for the individual phases and the continuity equation. Results from a laboratory model experiment will duplicate those from some reservoir prototype if a constant proportion is maintained among the three forces acting on the fluids — the capillary pressure gradient, the gravitational gradient and the flowing pressure gradient. Operation of the model (i.e., fluid injection or withdrawal) must be conducted in accordance with specific equations. If the

Jan 1, 1967

By H. C. Brassfield, R. E. Fryxell, E. C. Duderstadt, E. A. Aitken, P. K. Conn

Permeation rates of hydrogen through are-cast tungsten were measured at temperatures from 1300" to 2600°C with hydrogen pressure differentials of 1 and 0.1 atm across isothermal membranes. Rates were nearly Proportional to square root of pressure, were inversely ProPortional to membrane thickness, and were temperature-dependent according to the equation: p = permeation coefficient in cu cm (stp)-mm per sq cm-min-atmlr2, R = gas constant in cal per mole-OK, T = absolute temperature in OK. Permeation rates of oxygen through tungsten were deternlined in the range 1965" to 2300°C and at calculated oxygen (02) pressures of 3.3 x 10-4 to 2.2 x at?n using sealed capsules containing Kmown quantities of tungsten oxide. Permeation coefficients obtained in this manner had a temperature dependency in the range of 40 to 45 kcal per mole of permeating species. Permeation coefficients for oxygen were higher than those for hydrogen in the temperature range studied. This is probably the result of oxygen solubility being much greater than hydrogen solubility at these temperatures at a gzven pressure. The purpose of this investigation was to determine experimentally the permeabilities of hydrogen and oxygen through polycrystalline tungsten at temperatures ranging from 1300° to 2600°C. Permeation rates of hydrogen through tungsten have been measured at temperatures up to 925°C,but no previous measurements have been reported for the temperature range covered in this investigation. Some diffusion measurements3&apos;&apos; and solubility measurements3 have been made for hydrogen at temperatures below 2200°C. No previous permeability studies of oxygen through tungsten are known to the authors; however, efforts have been made to determine diffusion rates5-&apos; and solubilities PERMEATION THEQRY Permeation has been defined by ortton" as the overall steady-state flow process from the gas phase on one side of a membrane or wall to the gas phase on the other side and includes the steps of adsorption, solution, diffusion, exsolution, and desorption; in a given temperature range, any of these processes may be rate-controlling. For diatomic gases, which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at a given temperature is directly proportional to the surface area of the membrane, the length of time of permeation, and the difference between the square roots of the pressures on each side of the membrane, and it is inversely proportional to the thickness of the membrane when diffusion-controlled, thus: q = total amount of gas permeating a membrane, p = temperature-de pendent permeation coefficient, A = area of membrane exposed, / = time, p i = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, d = thickness of membrane. When the surface reactions are not rate-controlling steps and the solution of the gas in the metal follows Henry&apos;s law, the permeation coefficient, P, is equal to the product of diffusivity and solubility. The permeation coefficient is also temperature-dependent according to the equation: Po = permeation constant, Q = activation energy, R = gas constant, T = absolute temperature. MATERIALS The tungsten materials used in this investigation were greater than 99.9 pct pure. The interstitial impurities ranged from < 1 to 50 pprn C, 7 to 35 ppm O, less than 15 pprn N, and undetectable quantities of hydrogen. Previous high-temperature studies of are-cast tungsten have shown that thermal treatment similar to that which the hydrogen permeation cells experienced reduces the carbon content from starting levels of 50 to 60 ppm to about 30 ppm. Metallic impurities were in the low (1 to 50) ppm range. The argon gas used in this investigation contained about 8 ppm N. None of the following gases were

Jan 1, 1968

By B. M. Larsen, T. E. Brower, J. W. Bain

A mass of circumstantial evidence is presented to indicate that the main source of alloy losses in open-hearth tapping is oxidation by air, with the steel apparently reacting with an amount of oxygen equivalent to about 30 times its own volume of air. The effect is erratic from heat to heat, depending largely on turbulence and distance of free fall of the stream of liquid metal. THIS paper reports another phase in a general study of oxidation in the open-hearth, various aspects of which have already been discussed in previous papers.1,2,3 It is based on experiments conducted on commercial, basic open-hearth furnaces at various times when opportunity offered, beginning about 1938, in an attempt to determine the mechanism and measure the amount of air oxidation during the flow of the tapping stream through the air into a ladle. This effect is closely connected, not only with alloy losses and control of chemical analysis, but possibly with various questions regarding inclusion content and steel quality and with a true picture of the deoxidation of steel in general. Thus it is believed that discussion of a large part of the results to date may be of assistance to others who are studying problems related to deoxidation or to steel cleanliness and quality. The literature reveals that strangely little attention has been devoted specifically to the effect of pouring steel through open air. Bardenheuer and Henke4 in 1939, in a paper devoted largely to overall losses of manganese in the basic open-hearth, reported that for a number of heats tapped into a tilted ladle held just beneath the runner so that the maximum distance of drop of the stream through the air was held to less than about 30 in., there was in most cases almost no loss of manganese from furnace to ladle. Hultgren,5 in 1945, showed that in high-carbon basic electric steel deoxidized in the furnace and containing no large inclusions as it left the furnace, large silicate inclusions, often rich in manganese oxide, were present in samples dipped from the pool in the ladle; also that the rise in content of large inclusions (above 0.01 mm dim) was greater when the metal stream was made to spray or flow in a turbulent manner. Our interest in this phase of oxidation in the open-hearth was first aroused by a study of alloy efficiencies on ladle additions. The frequency curves of manganese efficiency (net recovery of metal added in ladle) given in fig. 1 are of interest in this connection. Lowest, and also most variable (47 to 95 pct), recovery was in low-carbon heats having no coal additions to the ladle, progressing upward to a maximum average and least variable (82 to 97 pct) recovery in high-carbon heats killed with aluminum and silicon. Both coal additions and higher carbon contents in the tap stream, as well as additions of silicon and aluminum, help to lower the amount of manganese loss. But the most interesting point is the amount of manganese oxidized in many heats tapped at 0.50 to 1.06 pct carbon. It has been shown in a previous paper3 that the amount of oxygen in the tap stream in such heats is very small, usually below 0.01 pct, too small to oxidize any appreciable amount of manganese. Also, the fact that manganese should be oxidized at all in a metal solution containing such more stable oxide-forming elements as aluminum and silicon is an indication of some rather intense oxidizing effect such as could be caused by reaction with the air during ladle filling. Oxygen Balances from Tap Stream to Teeming Stream: Data in the form of alloy efficiencies, such as those shown in fig. 1, are not a proper measure of such a general oxidation effect. Having available

Jan 1, 1951

By S. K. Mitra

A refinement of the Seeger model for intersection process is investigated which is in better agreement with experimental observations than the original. It is shown that, in single crystals, the strain hardening in Stage II is mainly due to the short-mnge interactions when intersection is the rate-controlling process. It is also demonstrated that the creep curves, as predicted by this theory, are in good agreement with the experimental observations. MOTT: Cottrell? and Seeger have developed an approximate theory for plastic deformation of single crystals over the range of variables where the strain rate is controlled by the rate of intersection of dislocations. Although it is now generally agreed that the low temperature deformation of many pure metals is controlled by the intersection mechanism, various dictates of the over-simplified Seeger model are not in good agreement with all the experimental facts. It is the purpose of this paper to reveal that by appropriate extensions of the Seeger model, particularly those suggested by Basinski: a much more reliable theory results. The refined model to be presented here will be shown to account, in a satisfactory way, for the effect of stress, temperature, and strain on the creep rate under constant stress and for the effect of temperature and strain on the flow stress in constant strain-rate tests. EXPERIMENTAL METHOD To Check the theoretical deductions, both creep and tension tests were conducted on single crystals of high-purity Al (99.994 pct Al) so oriented that both the active slip plane and the Burger&apos;s vector of the operative dislocations on that plane made angles of about 45 deg to the tension axis. Single crystals of aluminum (5/8 in. by 1/10 in. by 8 in.) were grown in a graphite mold under an inert atmosphere using the Bridgman method. The chemical composition of the aluminum is given in Table I. A common seed was used for all crystals and their orientation is shown in Fig 3. The extensometry consisted of two differential transformers with matched outputs mounted so as to measure the extension in a 2 in. gage length. The amplified difference in output of the two transformers was recorded by a potentiometer. The amplification was calibrated before each run so that one chart division of the recording potentiometer indicated a 105 shear strain on the specimen. Stresses were measured to the nearest 1 x l04 dynes per sq cm. ACTIVATION VOLUME The concept of Basinski that the activation volume is not constant but is a function of the force that aids thermal fluctuation in effecting the cutting of dislocations will be adopted in this section. The force acting due to an applied shear stress on the dislocation being intersected is where L is the mean spacing between the forest dislocations, is the Burger&apos;s vector and T is the back stress. A detailed discussion about the origin of back stress will be taken up later in this report. As shown by Basinski, the activation energy, U, that must be supplied by a thermal fluctuation in order to effect intersection, is equal to where x is the distance through which the dislocation must be translated for complete intersection, and Fm is the maximum force encountered in intersection. When the applied stress is decreased abrupt ly F also decreases and the activation energy increases correspondingly as documented in Eqs. [ 1 ] and [2]. The Seeger equation for the strain rate when the deformation is controlled by rate of intersection of where the shear strain rate (per sec) N = the number of points per unit vol at which intersection can take place

Jan 1, 1962

By I. R. Kramer

The stress associated with the high-dislocation layer at the surface of deformed aluminum crystals was measured by progressively polishing the specimen and determining the change in the initial flow stress when the specimen was reloaded. This surface stress increased linearly with strain in the Stage II and Stage III region. The depth to which the high-dislocation layer extends was found to be 0.0025 in. The influence of the surface layer on Stage I is discussed and it is shown that Stage I ends when, on the secondary slip system, the difference between the applied stress and the opposing stress due to the surface layer is equal to the critical resolved shear stress. In previous papers&apos;-3 it was shown that the surface exerts a pronounced effect on the plastic-flow characteristics of metals. For fcc metals it was possible to increase the extent and decrease the slope of Stages I and II and decrease the work-hardening coefficient of Stage II by removing the surface of the specimen continuously during the deformation process.2,3 More recently,L it was shown that the activation energy for plastic deformation and the activated volume were also influenced by the surface. These changes were related to the existence of a high concentration of dislocations in the region near the surface of the deformed specimen and it was concluded&apos; that the effective stress, T, acting on a dislocation was T = Ta-Ti-Ts [1] where 7, is the applied shear stress, Tj is the internal stress, and TS is the stress associated with the surface region containing the high concentration of dislocations. From Eq. [I] it is seen that the effective stress, 7, acting on a dislocation is a function of 7,. Therefore 7, becomes important in any description of the work-hardened state. In this paper the value of 7, as a function of strain and its variation with depth are reported for aluminum single crystals. In particular, it will be shown that the end of Stage I occurs when the net stress, 7, on the secondary slip system is equal to the critical resolved shear stress. To measure Ts, single crystals of aluminum were deformed in tension to various strains, whereupon the load was removed and a known amount of metal was removed by electrolytic polishing. The differ- ence between the final flow stress before the specimen was unloaded and the initial flow stress upon reloading is designated as ?Tp and is the decrease in the stress due to the removal of the surface layer in whole or in part. The value for Tp is taken equal to -Ts. EXPERIMENT PROCEDURE The details of the tensile apparatus, method of electrolytic polishing, and crystal preparation were the same as those used previously,1"3 The single crystals were 1/8 by 1/8 in. in cross section with a 3-in. gage length. The initial purity of the aluminum was 99.997 pet. The specimens were held in vacuo at temperatures 50°C below their melting points for 16 hr and furnace-cooled. Just prior to the application of the tensile stress the specimens were electrolytically polished to remove 0.004 in. from the thickness. This latter operation was conducted after the specimen was placed in the tensile apparatus. The tensile tests were conducted at a strain rate, i, of 10"5 sec-&apos; and a temperature of 3°C. The aluminum crystals used for the determination of 7, are designated A1-3-12 and A1-116. The orientation of the various crystals used throughout the investigation is shown in Fig. 1. The ?Tp values for specimens A1-3-12 as a function of Ax were determined mainly at four strain levels, i.e., ? = 0.0217, 0.0381, 0.0593, and 0.075, where Ax is one half of the total reduction of the thickness after polishing and ? is the re-

Jan 1, 1965

By O. D. Gonzalez, R. A. Oriani

The migration of hydrogen and of deuterium dissolved in a iron and in nickel induced by an applied electrical potential has been measured over a range of temperature. In all cases the intevstitial solute migrates to the cathode. The deduced charges of transport are positive, independent of or slightly dependent on temperature, and markedly larger for the beavier mass. These results are interpreted as showing predominating momenlum transfer between electron holes and the acticated complex of the elementary diffusion act. THE migration of components of a metallic system under the action of an applied electrical potential is called electromigration or electratransport. This phenomenon has been known since 1861 and is becoming of increasing interest to metal scientists because of the opportunity it offers to explore the connections between mass transport and electron transport. Until recently, reliable data have been very scarce because of the difficulties inherent in the measurements. In addition, theoretical understanding has been either nonexistent or rudimentary and at present this situation is only moderately improved. Whereas the prevalent notion had been (and is still widely held) that electromigration directly reflects the state of ionization of a component in its equilibrium state in the metal, it is now becoming clear that the major, if not the sole, factor is the momentum transfer between the charge carriers, themselves in motion because of the applied field, and the metallic components in their activated state. It becomes important therefore to obtain reliable data over a range of temperature on electrornigration in systems where only one component moves, that is, either in pure metals (vacancy motion) or in interstitial solid solutions. Our choice of systems was dictated by our measurements&apos; of the Soret effect in solid solutions of hydrogen and deuterium in iron and nickel. Indeed, the main reason for making measurements on electromigration at all is that we suspected a mechanistic connection between thermal diffusion and electromigration. In our former paper&apos; we proposed that what is common to both phenomena is the momentum transfer between the charge carriers in the metal and the atom as it jumps from one equilibrium position to another. In Soret diffusion, however, there is in addition the dissipation of the energy of the jumping atom via pho-nons. We have since found that similar ideas for this interconnection have been developed by Fiks.2 In the present paper we will discuss in more detail our understanding of the mechanism of electromigration itself, but we turn first to a presentation of the experiments and results. EXPERIMENTS AND RESULTS Let us consider a metallic system in which only one component, m , can diffuse at the temperature in question, and to which are applied simultaneously an electrical potential gradient, grad cp, and a chemical potential gradient, grad p,. One may write3 for the material flux Jm and the electronic charge flux Je by applying the condition, grad = 0, to Eq. [I] and evaluating grad(um/T) for the isothermal case and for activity coefficient independent of composition over the relevant composition range. ere, c is the concentration and D the diffusivity of the mobile component. The experimental technique that we have used to measure Z* for the isotopes of hydrogen individually dissolved in each of two transition metals has been developed from a method used by Wagner and Heller.4 (A somewhat similar method was also used by Herold.5) A wire or thin rod of the metal under study connects two volumes of gaseous hydrogen at identical pressures; hence grad um = 0. A direct current is made to pass through the specimen, serving to maintain the specimen at the desired temperature and also to produce the electromigration of the hydrogen dissolved in the metal in equilibrium with the gaseous hydrogen. Under these conditions, the flux of hydrogen from one volume to the other is given, from Eq. [I] for grad( um/T) =0by

Jan 1, 1968

By R. L. Schmidt, J. D. Verhoeven

The diffusion coefficients and electrotralzsport mobilities of aluminum, gallium, and arsenic have been determined in molten germanium with the capillary reservoir technique. The diffusion coefficients are slightly higher than those determined by the solidification technique of Brirton et a1.1 It was found that aluminium and gallium migrate to the cathode in molten germanium) whereas arsenic migrates to the anode under an electric field. A possible technique for producing p-n junctions by means of electric field freezing is discussed in view of the experimental data. In the past decade or so the literature has abounded with articles concerning the solid-state properties of the semiconducting elements germanium and silicon. It is surprising by comparison how little has been published concerning the liquid-state properties of these materials. In the production of doped germanium or silicon the diffusion coefficient of the dopant in liquid germanium or silicon is an important quantity. Yet, to the best of our knowledge, no one has ever made a direct measurement of the diffusion coefficient of solutes in either molten germanium or silicon. A number of authors&apos;-4 have determined some diffusion coefficients by the indirect technique developed by Burton et al.1 This technique appears to give numbers of the correct order of magnitude but it does depend upon a number of assumptions in the analysis and also requires prior knowledge of the viscosity of the melt. In the present work a more direct measure of the diffusion coefficients of arsenic, gallium: and aluminum in molten germanium has been made. It has been shown independently by two groups of authors5, 6 that, when an electric current is passed through the interface of a solidifying metal containing an impurity, the resulting electrotransport in the liquid boundary layer at the interface offers a mechanism for control over the redistribution of the impurity accompanying the solidification. These authors show that the degree of control is proportional to the mobility, U of the impurity atoms in the liquid boundary layer, where the mobility is defined as the drift velocity relative to the solvent per unit electric field. In principle the results apply to the solidification of a doped semiconductor and offer an interesting technique for control of the doping of a semiconductor. In the present work the mobilities of aluminum, gallium, and arsenic were determined in molten germanium in order to evaluate the potential usefulness of electro-transport as a technique for solute control when applied to the solidification of doped germanium. EXPERIMENTAL PROCEDURE Both the diffusion coefficients and the mobilities were measured using high-purity alumina capillaries and a resistivity technique for analysis. A schematic diagram of the electrotransport apparatus is shown in Fig. 1 and the details of the cell design are shown in Fig. 2. For the mobility experiments electrical contact with the bottom of the capillary was made with graphite, as shown in Fig. 2. In order to prevent electrical contact with the melt the graphite was coated with a thin layer of alumina using a plasma spray torch. The cell assembly, a graphite electrode, and another assembly containing two blank capillaries were fastened to the lavite disk shown in Fig. 1. To make a run the system was evacuated and the doped germanium was outgassed at the operating temperature of 1030°C. The cell and blank capillaries were then submerged beneath the melt and a slightly positive pressure of helium was introduced to fill them. After passing current through the cell for a given time the cell and blank capillaries were raised from the melt and the furnace was shut off. The temperature of the cells dropped below the freezing point of germanium within 1 to 2 min after the furnace was shut off.

Jan 1, 1968

By J. H. O’Dette

BLISTER formation on wrought aluminum products has been a matter of concern to aluminum fabricators for many years. The fact that blisters make their appearance during the final stages of fabrication means that much time and effort have been expended before it is evident that the material must be scrapped. This and the loss of production are ample reasons for embarking on a research program to find out more about blistering and possible methods of control. Many excellent papers on this subject have appeared in the technical literature in the last few years. In one of the more recent papers, Kostronl gives a fairly complete review of the problem of gas in aluminum and blistering in general. From the work of the various investigators, a general mechanism for the formation of blisters has evolved and may be summarized briefly as follows: Hydrogen gas is usually present in the cast ingot, in the atomic or ionic state, in excess of the solid solubility. At room temperature the gas atoms are relatively immobile, but at elevated temperatures they become mobile and diffuse to free surfaces where they associate to form molecules. If these free surfaces are discontinuities within the ingot then the associated gas molecules collect and build up considerable pressure until equilibrium is reached with the dissolved gas around the discontinuity. Since the solubility of the gas is proportional to the square root of the partial pressure it is evident that large pressures may be built up at the discontinuities. When the metal is rolled to sheet the pressure of the gas in these, discontinuities is sufficient to deform the surface of the sheet and form a blister, particularly when the strength of the material is reduced during the annealing. Although the mechanism of the formation of blisters was fairly well known, the actual impor- tance of the individual roles played by the gas and the discontinuities was not so well established that positive methods for control of blistering were at hand. It was the object of the investigation to learn more about the nature of the discontinuities giving rise to blistering and to develop methods of control. The investigation was carried out in three stages as follows: a) A study of the more commonly used methods of removing hydrogen from aluminum, such as fluxing and holding, and their effects on blistering. b) Location of the discontinuities giving rise to blistering. c) A study, by indirect methods, of the movement of gas in the metal and its effect on blistering, and the development of methods of blister control during fabrication. Removing Gas and Reducing Blistering by Fluxing or Holding-—The work of removing gas and reducing blistering by fluxing or holding was carried out on metal of Alcan 2s (1100) composition with an artificially high gas content. The high gas content was obtained by introducing water into the melt prior to casting; the water reacted with the aluminum forming A12O3 and hydrogen. The procedure was to raise the gas content by introducing water into an aluminum melt and using half the melt to cast one ingot immediately. The remaining metal was treated again with water to make up for the reduction in gas content during holding, while the first ingot was being cast, and then given a fluxing or holding treatment and cast into an ingot. Samples for gas determination were cast from the molten metal before and after the gassing operation; before, after, and during fluxing, and while casting. Samples were also cut from sections of the ingots. Gas determinations were made on these samples using the well known vacuum fusion technique. All ingots were hot rolled at 500°C to 0.250-in. slab which, in turn, was cold rolled to 0.040 in. sheet. The sheet was coiled and annealed for 2 hr at 500 °C and then cut into 5-in. squares which were inspected for

Jan 1, 1958

By I. S. Levy, J. L. Brimhall, B. Mastel

Specimens of&apos; Hastelloy X-280, a low-cobalt version of the solid-solution- hardened nickel-base alloy Hastelloy X, were given a series of thermomechanical treatttzents. They were then Lensile-tested at room temperature and 1350°F. The Microstructures of the specimens tested at 1350°F were studied by electron Microscopy. Microscopy showed that dislocation tangling, caused by the cold working, mas still in evidence after aging-for 24 hr to temperatures as high as 1550oF. (Cr, Mo)23 C6, (Fe, Mo)6 C&apos;. as well us an unidentifiable phase precipitale due to the combination of the thermomechanical treatments and subsequent tensile strain. The room -temperature and 1350°F tensile properties show a general increase ill strength and decreccse in ductility with increusing cold-work level. This is due to the dislocation taangling-. PerLurbatiot~s to this general trend occur- due to solid-solution weakening at the higher cold-work levels as a direct result of the preciplitation reactions. THE requirements for corrosion resistance and high-temperature strength place nickel-base alloys among the more promising materials for advanced nuclear reactor applications. However, when these alloys are irradiated at service temperatures, they generally suffer severe embrittlement&apos;" and reduction in rupture life.3 Certain experimental treatments resulted in improvements in the tensile and stress-rupture properties of Hastelloy X-280, a solution-hardened nickel-base alloy.&apos; To provide a basis for understanding these improvements, unirradiated tensile specimens were examined by electron microscopy. The results are reported in this paper. EXPERIMENTAL DETAILS Material. Hastelloy X-280, a low-cobalt version of Hastelloy X, is a member of the solution-hardened class of nickel-base alloys. The Hastelloy X-280 was obtained from 4- and 1-in: thick plates in the mill -annealed condition. Table I gives the chemical composition of the material as reported by the National Spectrographic Laboratories. ~x~erimental Treatments. Plates of suitable size, 12 by 3 by 1 in., or by + in., were cut under a water jet from the stock material and examined ultrasonic -ally for homogeneity of grain size and absence of voids. The acceptable plates were solution-treated at 2150°Ffor 1 hr and air-cooled. These plates were then reduced in thickness by cold rolling 0, 10, 15: or 20 pct along the original rolling direction. The plates were machined into buttonhead tensile specimens with a gage diameter of 0.125 in., with a gage length of 1.125 in., and with their tensile axes parallel to the rolling direction. The specimens were examined for quality of finish with a penetrant dye, ultra son ically checked for voids, and finally given a dimensional tolerance check with an optical comparator. The acceptable specimens were aged for 24 hr at either 1000" or 1500 F and air-cooled. These specimens were then held at 540°F in a water loop for approximately 18 days to qualify as controls for similar specimens irradiated under the same conditions of time, temperature, water chemistry, and flow rate. Table U summarizes the treatments. These treatments were investigated to establish whether prior precipitation and stabilization of carbide phases at strain sites within the matrix could reduce the amount of carbides available for precipitation at grain boundaries during service. Tensile-Test Conditions. Specimens were tested to fracture at room temperature or 1350 F in air on an Instron tensile-testing machine at a crosshead speed of 0.05 in. per min. The time for the furnace to reach equilibrium at 1350°F was approximately 30 min; soak time prior to testing was 15 min; and test duration was approximately 5 min.

Jan 1, 1968

By Franklin J. Hill, Theodore D. Tiemann

Sized fractions of Wisconsin Gogebic taconite were reduced with hydrogen over the temperature range from 600° to 1000°C. In general, the degree and rate of reduction increase with temperature. Particle size has no observable effect except in the smaller fractions at 900°C and above, where reduction is impeded, possibly due to the siliceous nature of the ore. Gaseous diffusion appears to be significant as a rate controlling factor at certain stages. THE depletion of high grade iron ore reserves in the United States has established the need to utilize all available iron ore deposits, both in long range planning and from the viewpoint of national emergency. This has led to extensive research and development in this field. The beneficiation of Wisconsin Gogebic taconite ore has been previously studied by investigators at the University of Wiscconsin, 1 the United States Bureau of Mines,, Battelle Memorial Institute, 3 and others. Methods investigated have included concentration by flotation processes, magnetic and gravity separation, magnetic roasting and various combinations of them. The foregoing studies have been concerned with the production of an enriched ore suitable for blast furnace use. If the ore could first be reduced to metallic iron and then beneficiated, the product could be used directly in the open hearth or electric steel-making furnace. The by-passing of the blast furnace should enhance the economic feasibility of the beneficiating process. The work reported here,4 was undertaken to establish data on the hydrogen reduction of Wisconsin taconite that would eventually lead to the development of an economic direct reduction process for this and perhaps other low grade siliceous ores. The volume of work on direct reduction can be judged by the fact that 240 direct reduction processes were patented in the United States alone up to 1951, 5 and numerous additional processes have since been developed. Some of the factors contributing to direct reduction development are: 1) The increasing capital cost of the blast furnace and its accessory equipment. 2) The decreasing availability of high grade domestic ore. 3) The high cost of steel scrap for use in the open hearth and electric furnaces. In general, direct reduction processes can be divided into two types; those using a solid reductant (coal, peat, lignite) usually carried out in a kiln, and those using a gaseous reductant (H2, CO) in a shaft furnace or a fluidized bed retort. As there is no low cost coal readily available in northern Wisconsin but natural gas could be quite easily obtained, it is believed a gaseous reductant process would offer the greater feasibility for use on Wisconsin taconite. It is hoped that this preliminary work will beof interest to other investigators in this increasingly important field. TACONITE ORE The ore used in the investigation was obtained originally from the U. S. Bureau of Mines, and consisted of a representative composite made up from trench samples of the Norrie, Pabst, Plymouth, Pence, and Yale members of the Wisconsin Gogebic range iron formation. Chemically, the ore contains approximately 52 pct SiO, and 30 pct Fe. X-ray diffraction and other studies indicate the principal minerals to be quartz (SiO2), hematite (Fe2O3), and goethite (Fe2O3. H2O). Minor amounts of iron containing silicates, siderite (FecO3), and magnetite (FeO-Fe2O3) are present. The iron minerals and quartz are so finely disseminated that the ore requires grinding to less than 200 mesh (74 µ) for essential liberation.l,2 The iron content of each of the several size fractions studied is shown in Table I. EXPERIMENTAL METHOD The method used throughout the investigation was based on that developed by the U. S. Bureau of Mines in Minneaopolis6,7 in which the course of reduction is followed by the loss in weight of the ore sample. More specifically, a 100-g sample of the size frac-

Jan 1, 1962

By Morris Cohen, Robert C. Ruhl

Fe-Ni-B alloys were inresligated by X-ray diffraclion after splat quenching. Although this rapid cooling did not produce a measurable supersaturation of dissol1ed boron in either binary Fe-B or Ni-B alloys, a marked increase in dissolved boron was achieved by the splal quenching of lernary Fe-Ni-B alloys. Boron additions up to 2.0 wl pcl to Fe-13Ni and Fe-24Ni alloys cause an increase in retained austenite from 0 to 59 pet and to 92 pet, respectively. The martensitic phase in the Fe-13Ni-9 at. pct B alloy is .found to conlain about 0.6 at. pet interstitial boron, as evidenced by the tetragonality of this phase, and about 3.6 at. pct substilutional boron, us deduced from the lattice paratrieler decrease, the balance of the boron being precipitated as (Fe,Ni)aR. The austenitic Fe-Ni-B plznses also contain both interstitial and substitutional boron. Iron-Boron System. The phase diagram and related information about the solid solutions and intermediate phases in the Fe-B system are given by ansen,&apos; Elliott.2 and Pearson.1 The equilibrium solid solubility of boron in both ferrite and austenite is quite small: the maximum solid solubility of 0.02 wt pct B (0.11 at. pct B) occurs in iron at the eutectic temperature of 1150°C. while the maximum solubility in a iron is less than 0.01 wt pct.l There is disagreement in the literature as to whether these solid solutions are substitutional or interstitial. Based on the measured activation energy of boron diffusion in iron, it appears likely that boron moves interstitially in austenite. 4 However, this observation does not rule out the possibility that some of the dissolved boron may also occupy substitutional sites in this phase. Investigations of internal friction of boron in iron have suggested that boron is interstitial there.&apos; Shevelev, 5 on the other hand, reports a decrease in the ferrite lattice parameter with dissolved boron content, thus indicating a substitutional solution. Unfortunately. Shevelev&apos;s methods and analysis are unclear. Goldhoff and spretnak6 have measured the lattice parameters of pure iron and an Fe-0.005 wt pct B (0.027 at. pct) alloy at both room temperature (ferrite) and from 920° to 1200°C (austenite). They reporte: a lattice contraction in the ferrite of 0.0003 ± 0.0002 due to boron, thus indicating a predominately substitutional solution. Appreciable (0.0010 to 0.0060) lattice contractions were found in boron-containing austenites, but these effects were much larger than could be accounted for by the substitutional solution of all the boron present. Nickel-Boron System. Elliott 2 gives a summary of thephase diagram and recent work on this system. The solubility of boron in nickel reaches a maximum of 0.03 wt pct at the eutectic temperature of 1080°C. Iron-Nickel System. ansen&apos; presents the equilibrium diagram for this system and also discusses the metastable austenitic and martensitic phases along with the a=? transformations. The lattice parameters of Fe-Ni ferrites have been recently redetermined by Abrahamson and Lopata.7 Their data, Fig. 1, show an unusual change in slope at about 1.7 at. pct Ni. Very few measurements of the lattice parameters of Fe-Ni martensites are available in the literature. The values of Roberts and Owen8 are considerably higher than those measured in the course of the present work: they find that a, is constant at 2.874? from 8 to 30 at. pct Ni. Both the slope change in the ferrite parameters and the occurrence of a maximum plateau in the marten-sitic lattice parameters vs composition denote the

Jan 1, 1970

By L. O. Storey

The McDermitt mine was found as a separate mercury ore-bearing occurrence approximately 305 m (1000 ft) northeasterly and in a different geologic setting from the old Cordero mine, which had been the district&apos;s major producer. The following briefly describes the discovery of the new deposit and the Placer Amex lnc. involvement. The Cordero mining property was under lease by Sierra Mineral Management from the owner Fred H. Lenway in February 1971, when the property was brought to the attention of Placer Amex Inc. (known at that time as American Exploration and Mining Co.) by Richard F. Hewlett of Sierra Mineral Management. The property was first examined by Amex geologists in the spring of 1971, who reported favorably on the project. During that year, Sierra Minerals Management had retained Dr. Larry Walters as a consultant. He proceeded to drill test mercury soils anomalies which he had found northeast of the old Cordero mine in an area overlain by recent alluvium and gravel. An area known as the D area was subsequently blocked out and ascribed a tonnage of about 18 1 kt (200,000 st) which occurs in the vicinity of the eastern edge of the currently defined McDermitt ore body. This mineralization was found in flat lying mercury-bearing lakebeds, unlike the steep structurally controlled ore which was mined in the old Cordero mine. It became apparent to Placer Amex that since the chances of much more extensive ore were good in such a geologic environment, additional exploration was warranted. A joint venture was formed in October 1972 by American Exploration and Mining Co. and Sierra Mineral Management to further explore the Cordero property. The project exploration was fully funded and managed by Amex. Sampling began by Placer Amex in the D area where an open trench had exposed the lakebed ore. Visible cinnabar could not account for the high-grade mercury assays taken from the trench, and an unknown mercury mineral was suspected. Subsequent work established the presence of a chlorine-bearing mercury sulfide which may have enriched the lakebeds as a secondary supergene mineral. Early identification of the mercury-bearing mineral corderoite (Hg3Cl2S,) aided in the geologic concepts for the ore occurrence and was helpful in exploring for the expansion of the D area. Corderoite was found occurring with cinnabar in the lakebeds, and in places it is a major contributor. Specimens of the unique ore were given to Dr. Eugene E. Foord and Dr. Pieter Berendsen at Stanford University, who subsequently identified the chemical and crystallographic makeup of the new mineral and described it for the first time as a naturally occurring substance. Metallurgical work on mercury recovery from the newly described mineral was carried out by the Placer Development Ltd. laboratories in Vancouver, and an acceptable recovery system was worked out together with a planned mill design. Step out drilling from the D area by Placer Amex Inc. encountered extensive flat lying lakebed ore. The McDermitt ore body, as subsequently defined by drilling, was found to contain 2.7 Mt (3 million st) of open pittable ore, containing approximately 5 kg/t (10 lb per st) Hg. The ore body gently dips to the north and is found lying mainly in claybeds just above an opalite breccia blanket which overlies the earlier volcanics. Some ore is also found in the opalite breccia. The mine and mill were constructed under an operating joint venture with Placer Amex Inc. and Sterling Mineral Ventures, and production began in June 1975 at the rate of 20,000 flasks per year. The mine is currently in progress.

Jan 1, 1985

By H. J. Ramey

A general solution is presented for the transient temperature distribution caused by radial movement of a cylindrical heat source through a homogeneous medium of infinite extent. This problem represents a highly simplified model of the movement of a combustion front during the thermal recovery of oil. Numerical solutions are presented for a heat source moving at a constant velocity, and a velocity inversely proportional to the radial location of the heat source. Numerical solutions are presented for both finite and infinite vertical thickness of the heat source, i.e., with and without vertical heat losses. The numerical solutions are used to estimate the fuel concentration needed to maintain a combustion front during the thermal recovery of oil. The sensible heat carried to the combustion front by the injected gas stream is discussed in regard to the fuel concentration. Numerical solutions for a heat source (combustion front) of finite vertical thickness indicate the field conditions that may be necessary to sustain the temperature of a combustion front above the ignition temperature of the fuel over considerable distances from an injection well. The results also have implications in regard to the quantity of heat required during ignition. The results of this computation apply to a highly idealized model of a thermal recovery process. But the results may be used as a guide in engineering consideration of the thermal recovery process. INTRODUCTIO N The thermal recovery of crude oil has received considerable attention since the publication by Kuhn and Kochl of laboratory and field tests of this method of oil recovery. Other publications2,3,4,5,6, since that time have dealt with various features of the thermal recovery of oil and have illustrated the extremely complex nature of this process. Vogel and Krueger7 described an electric analog computer designed to solve a moving heat source problem which was analogous to movement of a combustion front during the thermal recovery of oil. The heat source was maintained at constant temperature and was a cylindrical source of infinite height (no vertical heat loss) moving radially at either constant velocity, or at a velocity inversely proportional to the radial location of the heat source. Jenkins and Ramey2 presented analytical solutions to a similar heat conduction problem and pointed out the possible importance of vertical heat losses. The following presents a general solution to the transient heat conduction problem introduced by Jenkins and Ramey4 as well as numerical solutions for a wide range of conditions possibly similar to those that might exist during field operation of the analogous thermal recovery process. DESCRIPTION OF PROBLEM The problem considered in this paper is determination of transient temperature distribution caused by a cylindrical heat source of infinite or finite vertical height, moving radially through an isotropic medium of infinite extent. It is further assumed that the heat flux generated at the surface of the moving heat source may be a function of time such that the fuel concentration required may be constant, or permitted to vary, and that heat is generated at the surface of the heat source only. In regard to the thermal recovery of oil the assumption that heat is generated at the surface of the front is equivalent to assuming that the thickness of the combustion zone is infinitely small, or that the reaction rate between fuel and oxidant gas is infinite. The last assumption does not appear stringent. See laboratory information published by Martin, et al3 Under these assumptions the temperature distribution throughout an infinite medium caused by a heat source moving radially with an arbitrary velocity may be described by The heat generation function or heat flux at the surface of the source, +(t), is Note that the fuel concentration may be defined as a function of time. Eq. 1 is derived in the Appendix.

By J. E. Berry

AII evaluation is made of the acoustic velocity log for measurement of formation porosity. Plots of field-observer1 velocities vs core-measured porosities of sandstones and limestotnes with inter intergranular porosity show that the velocity log gives a useful measure of porotity, in agreement with published data. A new method of plotting electrical and velocity log data makes it easier to recognize hydrocarbon-water coritnct~ from log darn and to make serni-quantitative estinlates of hydrocarbon saturation. Two examples of this interpretation technique are given. This paper also discusses the various factors that affect acoustic velocity and shows how corrections can be made for some of these factors. INTRODUCTION Although the continuous velocity log was developed primarily as an aid to seismic interpretation, it is finding widespread use for measurement of porosity. The purpose of this paper is to evaluate this use of the log. Results are presented for the velocity-porosity relationship in many sandstones and one limestone. Practical applications of porosity values derived from the velocity log to improve interpretation of electrical surveys are presented. Various parameters which affect velocity in porous media are considered. Porosity, composition, cementa-tion, pressure difference (overburden pressure minus fluid pressure), fluid saturation, and wellability are discussed. Some of the ideas are opinions based on general considerations of well logging problems while others are supported by published data and our own observations. Major conclusions from these studies arc given in the body of the paper and detailed discussions of some of the various factors affecting porosity are given in the Appendix. POROSITY Sandstones The primary factor affecting the velocity of sound in porous media is porosity. Wyllie, et al,1 have reported a time average equation for the relationship between velocity and porosity.* This has found considerable acceptance in the industry. Other relationships between velocity and porosity have been proposed, none of which are entirely satisfactory. It is doubtful that any one relationship will completely describe all situations. We have tried an empirical relationship based on correlating log velocities with core-measured porosities. Measured porosities were averaged over a depth interval equal to the spacing used in recording the velocity logs. The depth range for the information used was from 2,000 to 12,000 ft. Velocity measurements were normalized for the effects of depth and overburden pressure. A detailed discussion of the basis for this normalization is given in the Appendix. The change is usually insignificant and when working with individual formations it can be neglected. All velocity measurements were normalized to a depth of 10,000 ft. The velocity-porosity data for sandstones in Fig. 1 came from 20 wells scattered throughout the Mid-Continent and Gulf Coast areas. The scatter of the data points is attributed to three causes: 1. There is no theoretical basis for expecting an exact velocity vs porosity relationship and it is not possible to correct precisely for the effects of such factors as impurities, grain shape, manner of cementation, etc. Some of these factors are discussed in the Appendix. 2. Porosities measured by core analysis are not necessarily representative of what the velocity log "sees". 3. Inaccuracies appear in the velocity log reading. This is particularly true of velocities from one-receiver logging tools.*" A linear-time curve (time-average equation) is plotted in Fig. 1 along with the best straight line through the points. Velocities used for the linear-time curves were 19,500 ft/sec for the matrix velocity (zero porosity) and 5,500 ft/sec for fluid velocity. For clean sandstones with velocities greater than 10,000 ft/sec, there is little difference between the velocity-porosity and the time-porosity curves. Both curves are well within the scatter of data points. The data points in Fig. 1 were restricted primarily to clean sandstones, using the SP and/or gamma-ray logs as clues to the lithology. Where a lithologic de-

By W. A. Young

Polynomial functions of temperature were obtained for the specific heats, thermal diffusivities, and thermal conductivities of zirconium hydrides containing 4 at. pct U. Three hydrides (H/Zr atom ratios of 1.58, 1.65, and 1.70) were studied over the range a" to 900°C and a fourth (H/Zr = 1.81) was studied over the range 0° to 760°C. The specific heats were determined from enthalpy measurements which were obtained using a unique drop calorimeter specifically designed for use with materials in which high temperature phase transitions and/or high dissociation pressures occur. Thermal diffusivities were measured by the flash method using a pulsed laser. The thermal conductiuities were obtained as the product of specific heat, thermal diffusivity, and density. The specific heats agree, within 10 pct, with values derived using a theoretical model in which the hydrogen and zirconium atoms are treated as Einstein and Debye oscillators, respectively. RELIABLE values of the thermophysical properties of the fuel are required to predict the operating temperatures and temperature response of SNAP nuclear reactors. Among the most important of these properties are the thermal conductivity, specific heat, and thermal diffusivity. A considerable number of investigations1-4 have been made of these properties for the Zr-H and Zr-H-U systems.* However, little of the drides, however, this direct method cannot yield meaningful results, since the hydrogen will redistribute under the influence of the thermal gradient, thus forming a concentration gradient; hence, one has a spectrum of compositions, rather than a homogenous alloy. Although the "average" composition of the material may be identical to the initial uniform concentration, the directly measured value of conductivity will be dependent on the thickness of the specimen, due to the highly sensitive dependence of transport properties on hydrogen content. This dependence is strikingly illustrated by the work of Bickel,5 who found that the electrical conduction of zirconium hydrides ranges from primarily hole conduction to primarily electronic conduction, depending upon the hydrogen content. Fortunately, the direct measurement of thermal conductivity is unnecessary, since it can be expressed as the product of the specific heat, thermal diffusivity, and density, all of which can be directly measured with considerable accuracy. EXPERIMENTAL Specimen Preparation. The combined fuel-moderator material used in SNAP reactors is a hydrided zirconium-uranium alloy containing -10 wt pct U. The alloy used in this work was representative of that used in nuclear reactors except that normal uranium was substituted for the enriched uranium required for reactor usage. It was produced by a triple-arc-melt and double-extrusion process. All specimens were prepared from a single cylindrical extrusion which contained 10.30 pet U, 89,35 pct Zr, and 0.35 pct impurities, The specimens for each composition were hydrided simultaneously with ultrapure hydrogen (10 ppm total impurities) using standard fuel production techniques which routinely yield homogeneous, crack-free fuel with negligible increases in the impurity levels. The hydrogen content of each specimen was determined from its weight gain and the density was measured by liquid displacement, Chemical analyses yielded hydrogen concentrations which agreed with the weight gain data within ±0.02 in H/Zr atom ratio) the concentrations of all other elements agreed almost exactly with the initial values after adjustment for the added hydrogen. The specimens used for the determination of specific heat were centerless ground to 2.00 cm diam after hydriding. A thin slice was carefully removed From each end for metallographic examination. In every case, this examination revealed a uniform structure as evidenced by the appearance and distribution of the two phases present in the fuel at the hydrogen concentrations used. TWO specimens (H/Zr = 1.600 and 1.632) appeared to be entirely 6 phase with equi-axed grains; the specimen with H/Zr = 1.756 showed

Jan 1, 1970

By H. I. Kaplan, C. Laird

Pulsating contpresslon experiments have been carried out on coppev single crystals in order to test the adequacy of mechanisms which have been suggested for stage I cvack grouth when tension-compression loading is the mode of- applying stress. Although dejorrrzation continues slowly for many millions 01 cycles under Pulsating compression stresses both within slip bands formed in the first cycle and by the creation of new bands, the morphology of these bands is not typical of fatigue slip bands in general and neither initiation of cracks nor propagation of artificially induced cracks was observed. It is therefore concluded that 1) initiation and growth of cvacks in fatigue is a consequence of repeatedly reviersed, microplastic deformation rather than intermittent, unidirectional deforma-tion, 2) gvowth of- cracks in polycrystalline specimens FAILURE of a plain specimen subjected to cyclic tension-compression stresses is known to take place by two stages of cracking.1,2 The first stage is characterized by propagation along slip planes roughly at 45 deg to the stress axis, in the outermost layers of the specimen, and at a rate of the order of angstroms per cycle. The average macro orientation of a stage I crack is normally at right angles to the stress axis,3 however, except in a few cases, e.g., single crystals in suitable orientation, when both the micro and macro directions of propagation are at 45 deg to the axis. After a stage I crack has penetrated to such a depth that the stress on the remaining section of metal is significantly increased, stage II crack propagation succeeds stage I, at right angles to the stress axis both micro and macroscopically. Direct evidence of the processes occurring during a subjected to pulsating compression stresses is caused by the setting-up of local tensile stresses due to interactions between grains, and 3) both unslipping mechanisms and operation of the "plastic blunting process " within a single slip band are adequate descriptions 01- stage I growth, being fundamentally similar. The slip mode of a material, however, is considered to control whether unslipping or the plastic blunting process takes place. Thus materials of planar slip mode fauor unslipping while those hacing a wavy mode, and capable of cross slip, can fail in stage I by the plastic blunting process. Similarly, and perhaps more importantly, reversed torsion and tension-compression modes of applying stress may be expected to cause the unslipping mechanism and the plastic blunting process, respectively. single stress cycle4,5 shows that stage II crack propagation takes place by a repetitive plastic rounding and closing of the crack tip. This mechanism has come to be called the "plastic blunting process".6 On the other hand, the extreme smallness of the phenomena occurring in stage I growth prevents elucidation of its mechanism by direct observation. Many suggestions have been proposed for this mechanism,&apos;"-" most of them involving some kind of random or systematic unslipping process. It is possible, however, that the mechanism of stage I growth is essentially the same as that of stage 11, but occurring on a much smaller scale.6 In this situation, it has been observed that cracks propagate along slip bands comprising dislocation cell structures and bounded on either side by regions of different dislocation density and distribution." Since there is evidence that such bands are softer than their matrix, * it may be expected that the plastic blunting process occurs within a single slip band during stage I growth, rather than on two gross bands as in stage 11, when the acting stress is greater.= The blunting of the crack tip allowed by coordinated

Jan 1, 1968

By Giovanni Barla, Stefan H. Boshkov

This paper examines the application of gelatin mixture models to the study of factors such as gravity effects, tectonic and residual stresses, anisotropy, physical nonlinearity, time-dependent behavior of the rock mass and connectedness of the geologic space. The technique of calibrating gelatin mixtures proposed by Richards and Mark in 1966 is applied to the particular problem considered. Similitude relationships between model and prototype are discussed with reference to the constitutive equations describing the physical behavior of the rock mass. The interaction between two openings in a linearly elastic medium, under conditions of plane strain, is used as an illustrative example with the view to describing the history of stress and deformation changes on the rock medium and lining around a slusher drift while undercuts are made in block caving. The prediction of the displacement, stress field and mode of fracture associated with a given rock structure, its initial stress field, and its physical properties is essential to rock mechanics and ground control. The basic approach is to assume the rock mass to behave as a continuous, homogeneous, and isotropic medium. The classical theory of elasticity is the simplest theory based on such a concept. Specification of the elastic constants, the initial state of stress in the ground, and the boundary conditions on stress and displacement allows one to predict stress and displacement within the body. Subsequently, provided that a criterion which governs rock fracture under various stress conditions has been established, a stability analysis of the rock structure can be performed. A natural extension of the present knowledge consists of removing some of the simplifying assumptions which characterize the analytical solutions based on the classical theory of elasticity. Complex geometry, the significance of tectonic and residual stresses, anisotropy, physical nonlinearity, time-dependent behavior of the rock mass and connectedness of the geologic space are some of the important factors which are neglected in the classical approach. A better insight into the real problem can be attained with either the finite element method of stress analysis or an experimental technique. The former has already been applied with success on several occasion 1-4 and is destined to render great service in the field of rock mechanics and ground control. The latter, which will be considered in this paper, has been used extensively in applications too numerous to be enumerated. Experimental technique involves either prototype testing, if the area to be studied is accessible, or model testing. Two- and three-dimensional photo-elastic analyses are very convenient means of obtaining the stress distribution in models of complex geometry. In general, such analyses are confined to studies of stress fields around openings which are sufficiently far removed from the surface boundary so that the stresses in their neighborhood are practically equal to those produced by an initial uniform stress field; i.e., so that gravitational effects are negligible. There are, however, many rock structures where these effects must be taken into account to attain a more realistic representation of the problem. Surface and near surface rock structures, systems of openings interacting with one another, and structural components loaded only by their own weight are some of the obvious examples. This paper was written to show how factors neglected in the usual analysis based on the classical theory of elasticity, can be taken into account when gelatin mixture models are used inconjunction with photoelastic methods. The interaction between two openings in a linearly elastic medium, under conditions of plane strain, is used as an illustrative example, with a view to describing the history of stress and deformation changes on the rock medium and lining around a slusher drift while undercuts are made in block caving. The birefringence of gelatin mixtures has been known for some time. A series of experiments were carried out by Rossi in 1910,5 but after that very

Jan 1, 1970

By S. R. B. Cooke, H. S. Choi, D. H. Harraway, I. Iwasaki

The mineralogy of natural iron ore samples and their slimes have been investigated and the nature of slime interference in iron ore flotation has been studied. The results have been correlated with the flotation behavior of a natural ore sample. Various conclusions have been reached as a result of these studies. In the flotation of iron oxide ores, desliming is generally considered to be an essential step to successful separation, irrespective of whether the iron oxide or siliceous gangue minerals are to be floated, although some workers have found empirically that certain collectors and reagent combinations are less sensitive to the presence of slime than others. The detrimental effect of slime is considered to be twofold. First, the presence of slime presupposes a high reagent consumption because of high specific surface. When clays are present and when cationic collectors are used abstraction by ionic exchange may augment this condition. Attempts to compensate by the addition of large amounts of reagent result in only partial correction. Second, slime coatings on granular particles tend to interfere with the bubble-mineral contact. The nature of slime coatings in flotation is quite complex and has been the subject of considerable study; an attempt was recently made by Fuerstenau et al.&apos; to relate the slime-coating density with flotation recovery and with the properties of the electrical double layer at the mineral surfaces. Although major constituent minerals in the oxidized iron ores of the Mesabi and Cuyuna ranges are hematite and goethite (limonite) as the iron oxides, and quartz and chert as the siliceous gangue, very little is known of the mineralogy and of the chemical and physical characteristics of the slimes, and still less of the interaction between slimes, collector, and the mineral surfaces. For pragmatic reasons iron ore slimes are defined as — 20p material, based upon the calculated settling velocity of a quartz sphere of the stated diameter, and of all other equal-settling mineral particles. Active slime interference with flotation is usually attributed to particles 5p in size or finer, the extent of such interference appearing to depend not only on the mineralogy but also on the size distribution of each mineral in the slime fraction. The objective of this work was to acquire a more specific knowledge of the constitution of iron ore slimes and of their role in flotation. The mineralogi-cal composition of natural slimes was obtained by differential thernal analysis (hereinafter referred to as DTA), electron microscopy, and chemical and X-ray analyses. Some flotation tests were made on natural ore samples. The surface properties of several constituent minerals were investigated by electrophoretic measurements and by determination of the adsorption of some typical flotation collectors. Finally, simplified flotation tests were made on granular goethite and quartz in the presence of various artifically prepared slimes; the results were compared with laboratory flotation tests made on natural ores. MATERIAL AND METHODS Mineralogy of Some Iron Ore Slimes: Samples of two wash-ore tailing::, hereinafter identified as A* and B, *Sample A of the present investigation 18 the same am ore A in ref. 3. of a wash ore C, and of a paint rock D, all from the Mesabi range, were selected for investigation on the basis of prior information concerning their flotation behavior. The two wash-ore tailings, when deslimed, were known to respond well to flotation, whereas the wash ore was high in goethite, tended to be slimy, and responded poorly to flotation. The paint rock also exhibited sliming tendencies, and was suspected to contain relatively large quantities of clay minerals because of its high A1203 content. Gruner states that the paint rock of the Mesabi frequently contains kaolinite. To ascertain the relative sliming tendencies of each sample a standardized desliming method was employed. All samples were ground through 65 mesh using jaw and rolls crushers. A 500-g sample of each

Jan 1, 1962

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas&apos;-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller&apos;s results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By H. G. Doll

A new electrical logging method called Laterolog is described which provides for better recording of formation resistivity. In this method a current, preferably of constant intensity, is forced into the formation perpendicularly to the wall of the hole as a sheet of predetermined thickness by means of a special electrode arrangement and of an autonlatic control system. The essential advantages of the Laterolog over the regular resistivity logs are explained. With the Laterolog, the mud column has much less influence than with conventional methods. The Laterolog is, therefore. particularly useful in wells drilled with highly conductive mud. Moreover. when the electrode system is located opposite a bed of moderate or small thickness, the disturbing effect of the adjacent formations becomes practically eliminated, provided the bed is thicker than the sheet of current. which itself is usually a few inches to a few feet thick. The sequences of beds are. therefore, much more sharply differentiated, and, in many cases, it is possible to read directly from the logs values close to the true resistivities of the formations without further corrections. Field examples are shown to illustrate the results of the method in various types of formations. INTRODUCTION As soon as it was introduced into the petroleum industry, electrical logging roved to be a powerful instrument for the delineation of the strata traversed by bore holes and for correlation of such strata." Research and engineering efforts were mostly devoted at this early time to the design of the techniqurs which could provide the best data for these purpoes. Later, attention was directed toward the quantitative analy5i.s of electrical logs, in order to obtain information on. reservoir characteristics, and, in particular, on oil and water saturation.3,4 Efforts have been made, accordingly, with a view to improving the already existing methods, or to finding new methods which could satisfy these new requirements." Quantitative analysis implies a determination as accurate as possible of the true resistivity of the formations. In fact, however; the "apparent resistivity" recorded in front of a given bed by a conventional electrical logging method is frequently quite different from the true resistivity of this bed. This is due to the combined influence of the mud column, of the adjacent formations both above and below the bed, and of the invaded zone, in which the original fluid has been more or less replaced by mud filtrate. When the beds are thick enough, and, as is frequently the case in sand and shale formations, when their resistivity is not much greater than that of the mud, it is generally possible to obtain their true resistivity directly on the electric log, or at least to obtain an approximate value which can be corrected without undue difficulty by means of recently published charts known as "departure curves."" When the beds are thin, and particularly when, in addition. their resistivity is substantially greater than that of the mud column, the apparent resistivities recorded on conventional logs are seriously affected, and it is generally very difficult, if at all possible, to estimate their true resistivity with a good enough accuracy. In the most severe cases, such as are encountered in holes drilled through hard formations with muds of high salinity, the conventional logs are so distorted and rounded that they do not even show clearly the houndaries of the different beds. In order to overcome the effect of the mud column and of the adjacent formations, it is possible to make use of appro. priate systems whereby the measurements involve a comp3ratjvelv thin slice of space at the level of the measuring device. A mention is due, in this respect, to a measuring system. called the "guarded electrode;" invented by C. Schlumberger over 20 years ago. The system, schematically represented in

Jan 1, 1951