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By A. Heim, M. Gondouin

Invasion experiments were run on Berea sandstone cores to get laboratory measurements of resistivity and saturation profiles characteristic of water and oil sands invaded by mud filtrate. Injection rates were as low as 1.13 cm/D, and the cores were 30 to 36 in. long, cut parallel to the bedding planes. In the water-sand case, the resistivity profiles revealed the existence of an extensive transition zone between flushed and uncontaminated zones. In the linear geometry of the experiment, the width of the transition zone increased as the square root of the injected fluid volume. For the oil-sand case the core was prepared by displacing the formation water with kerosene to minimum water saturation. During the subsequent invasion experiment. oil saturation was measured directly by means of an oil-soluble radioactive tracer, and resistivity profiles along the core were taken at the same time. These data were interpreted in terms of an oil-water front, followed by a formation water bank, a zone of mixed waters, and finally, invaded mud filtrate near the borehole. Micro-fingering and capillarity seemed to affect considerably the resistivity profiles observed in the invaded oil-sand experiment. Beyond the regular conductive annulus or "low zone", it was found that a resistive "anti-annulus" could also be formed. As a result of these experiments, some simplified invasion profiles have been accepted and are being used in Grand Slam* interpretations. INTRODUCTION The importance of the mud filtrate-invaded zone in interpreting electrical logs has long been recognized.',* In trying to account for its effect, only very simple models of the resistivity profiles in the radial direction from the borehole have been used. In fact, most log interpretation charts have been based on resistivity models consisiting of two media of uniform resistivity (R, and R,) abruptly separated at the diameter of invasion. Such a clean separation of the media of different resistivities seems unrealistic, since flushing may not be perfect and may vary with radial distance into the formation.3** The nature of the transition zone, when it is within the radius of investigation of the surveying devices, may affect the log readings. Campbell and Martin' verified that a conductive annulus containing a high percentage of formation water may be formed when mud filtrate invades an oil-bearing sand. Interpretations which are to include the effect of such an annulus require the addition to the model of a conductive zone located at the outer rim of the invaded zone.' Using the Buckley-Leverett relations,6 aturation profiles may be derived, from which resistivity profiles can be calculated. Results of such computations by K. S. Kunz and J. H. Moran were given in a paper by Dumanoir. Tixier and Martin,7 and led to the construction of log interpretation charts which were based on a representation with three media of resistivities R, R0 and R1. Fig. 1 shows a schematic representation of a resistivity profile which includes an annulus. Campbell and Martin realized that, during the invasion of an oil sand, both capillarity and mixing would contribute to rounding of the profile shown in Fig. 1. Capillarity tends to draw some of the formation water from the annulus into the uncontaminated (Rt) zone, whereas mixing of the mud filtrate with formation water of the

Jan 1, 1965

By James E. Lawver, James L. Wright

This paper describes the design of a cell used to measure the electrical conductivity, or the reciprocal resistivity, of granular materials. It also establishes a quantitative relationship between the electrical conductivity and the electrical separation of selected mineral samples. It is estimated' that the free world produces about 13 million tons of mineral concentrates a year by electrostatic or electrodynamic methods. At least 95% of these concentrates are produced by corona discharge type machines that separate minerals by exploiting the differences in their electrical conductivity. But, what is meant by the electrical conductivity of a mineral? How large a difference in the electrical conductivity of two mineral species is necessary to effect a separation? Just what is the role of conductivity in electrical separations with regard to capacity and selectivity? There is a considerable amount of information in the literature on both the mechanisms of conduction and the values of the electrical conductivity of pure single-crystal mineral specimens. In addition, some insight into the role of mineral conductivity can be obtained by referring to a Bureau of Mines publication' in which 95 minerals have been grouped as conductors or insulators as a function of temperature. The classification was made on the basis of the percent of weight that reported as "conductors" in an electrical separator. But, as is often the case in the mineral industry, practical application leads theory — and there is little useful information in the literature giving any kind of quantitative relationship between electrical conductivity and electrical separations. The problem is a bit complex because electrical conductivity per se — which can be rather easily measured on large, single grains — is not sufficiently informative to permit quantitative predictions of the separability of the mineral system. Practical "high-tension"* separations are made at such feed rates that the band of minerals on the rotor is multilayered in thickness. Thus, the effective conductivities of minerals as seen by a high-tension machine include particle-to-particle contact resistance, which is often a controlling factor in making a separation. This is particularly true when the mineral grains are coated with slime or with a dielectric surface film. From a high-tension separation viewpoint, one is actually concerned with the time required for corona-charged grains to lose enough charge so that the centrifugal force acting on the particles exceeds the image force holding the grains to the rotor. This calculation requires a knowledge of the effective mineral conductivity s. (The conductivity of the metal rotor is sufficiently greater than that of the minerals so that it need not be considered in charge decay calculations.) The charge density at time t can be approximated by the relaxation equation.3 where t 5 charge density at time t r, - charge density when t = 0 cr e total electrical conductivity £ = permittivity The time required for the charge density to fall to l/e of its initial value is called the relaxation time and is numerically equal to €/n. AS defined here, u is the conductivity of an element of homogeneous grains making contact with each other and with a grounded rotor. This paper deals with the design of a conductivity cell used to measure a, or its reciprocal p, the electrical resistivity. CELL DESIGN Initial test work was performed with a cell recommended by ASTM.4 Since the reproducibility with the ASTM cell was not satisfactory, it was decided to

Jan 1, 1970

By Allen F. Agnew

Detailed stratigraphic studies in the Wisconsin-Illinois-Iowa district have made it possible to map the folds and faults that controlled the deposition of the zinc-lead ore. Prospecting on the basis of this mapping and prospecting in lower zones that are potentially ore-bearing have led to discoveries of ore. GEOLOGIC studies for the Federal and State governments in the Wisconsin-Illinois-Iowa zinc-lead district were begun in 1835, and subsequent surveys were made in the three states at intervals until 1916, see Table I. The current study of the district, Fig. 1, by the U. S. Geological Survey was begun in 1942 in the hope that a systematic investigation would help increase production of zinc and lead, then in extremely short supply. Major emphasis of the USGS program was on detailed mapping of the geologic structure and ore deposits. Preliminary maps and reports covering localities of intensive mining activity have been published during the course of this study, Fig. 2. By 1950 the objectives of the study by the USGS were revised; 71/2-min quadrangles of relatively unprospected localities as well as intensively mined localities are now being mapped in Wisconsin. Since 1945 the investigation in Wisconsin has been made in cooperation with the Wisconsin Geological and Natural History Survey, and since 1951 the geologic mapping of areas of particular interest in Iowa has been performed in cooperation with the Iowa Geological Survey. At intervals since 1943 the Illinois State Geological Survey has mapped the geologic structure and ore deposits of localities in the Illinois part of the mining district, see Fig. 2. Geology was applied by mining company personnel as early as 1853, but only sporadically, with periods of greater application between 1890 and 1925. Much of the so-called geologic work was in reality mining engineering. Since 1946 the major mining companies in the district have employed geologists who have successfully applied geologic techniques in the search for ore. History of Mining Occurrence of galena in the district was known as early as 1658 or 1659, when French explorers heard of lead mines that were apparently in the vicinity of Dubuque, Iowa. In 1690 a trading post was established near Dubuque to obtain galena. The first significant attempt at mining by white men took place in 1788 when the Indians granted to Julien Dubuque mining rights for 20 miles along the west side of the Mississippi River, including the vicinity of Dubuque, Iowa. By 1805 lead was being mined near Galena, Ill. In 1819 permanent settlement of the region was begun, and most of the important lead-producing areas had been found by 1830, see Fig. 3. Lead production in the Wisconsin-Illinois-Iowa district between 1830 and 1871 far exceeded that of any other district in the U. S.' Smithsonite was first mined in 1859, and sphalerite was mined as early as 1867. After 1873 the production of sphalerite exceeded that of smithsonite. In 1873 annual zinc production from the district first equaled lead production, and from then until 1893 production of zinc and lead was roughly the same. Since 1893 the ratio of zinc to lead mined has generally ranged between 5:l and 20:l. In 1942 the Wisconsin-Illinois-Iowa zinc-lead district ranked 14th among zinc-producing districts of the U. S. From 1946 until February 1953 the dis-

Jan 1, 1956

By R. H. Doremus, E. F. Koch

The first carbide phase that precipitates at 120°C from a iron containing about 0.02 wt pct, C was studied with the electron microscope. In both strained and unstrained material the carbide particles appeared to form on the dislocations in the iron, in agreement with the results of the kinetic study in part II. The structure of the carbide was tentatively identified as an expanded a-iron lattice (body-centered tetragonal) with about 0.7 wt pct C. This phase appeared to be metastable and apparently transformed into cementite or epsilon carbide when the iron was over-aged. WhEN a iron containing less than about 0.025 wt pct C is quenched from 700°C to room temperature the carbon is retained in solid solution and precipitates out slowly with time. The morphology and structure of the precipitating phase are still in doubt, two different carbide phases, epsilon carbide and cementite, have been identified, but there is considerable disagreement about the time and temperature at which they appear.1-4 Epsilon carbide seems to form at lower temperatures than cementite, although one group of investigators4 found only the latter phase over a wide range of aging temperatures. Usually these two phases have been identified after aging times much longer than needed to drain the carbon from supersaturated solution, at least for aging temperatures below 200oC. The precipitated carbides have been observed with the electron microscope,'-5 but again most results have come from samples aged much longer than necessary to reduce the carbon concentration in solution to a low value. In this study the carbide phases were observed in earlier stages of precipitation with the electron microscope, in order to learn more about the shape, size, and distribution of the carbide particles. Samples strained small amounts before aging, as well as unstrained samples, were studied, and the structure of the carbide phase was tentatively identified. EXPERIMENTAL "Ferrovac E" vacuum-melted iron, from which the wires for kinetic studies were also made (Refs. 6 and 7 and the following paper) was used for this work. An analysis of this material is given in Table I; it agrees well with the manufacturer's values. The number of inclusions in the iron was very small, as can be seen in the optical micrograph in the following paper. Pieces of iron about 1 mm thick and 5 to 10 mm in diam were used for all the studies except for those in which the sample was strained before aging; then the specimen was a rod 3 to 6 mm in diam and 20 cm long. The samples were held at about 700°C in wet hydrogen for at least an hour to remove residual carbon and nitrogen, after which they were heated to 950" (in the y region) and cooled to room temperature in the furnace. This treatment gave an average grain diam of more than 1 mm, so that the effect of grain boundaries on the precipitation process was negligible. The samples were carburized at 710°C for about 2 hr in hydrogen that had passed over toluene held at -30°C; then they were rapidly quenched into water. From chemical analysis this treatment gave a carbon concentration of from 0.012 to 0.016 wt pct, which is less than the solubility of carbon at this temperature. After quenching, the samples were aged at 120 "C in an oil bath for vari-

Jan 1, 1961

By Robert T. MacMillan

Of all the mineral substances utilized by man, salt or sodium chloride has one of the longest and most varied histories. Because all animal life is descended from marine organisms, sodium and chlorine became necessary to life, and as sodium chloride meets requirements most readily, common salt has been essential to human and animal diets from earliest times. As civilization progressed, man learned to evaporate sea water and brines of saline lakes and springs to obtain salt, and gradually ceased to depend on the flesh of animals and the occasional salt outcrops or "salt licks" they frequented. He also learned that salt had a multitude of uses, particularly as a preservative of meat and other foods. The importance of salt in the minds of early men may be readily seen from many allusions in the Bible and other ancient writings. Expressions such as "not worth his salt," and "the salt of the earth" are deeply embedded in the English language. Salt has symbolized friendship, fidelity, purity, and hospitality. It has been used as currency; had religious significance; caused wars; and has been a favorite commodity for taxation. The English word "salary" stems from the Latin word for salt, in which Roman soldiers received part of their pay. Although salt today retains its dietary importance, it has thousands of other uses. Of each 100 pounds produced in the United States less than three pounds is for table use. The other 97 pounds goes for agricultural, industrial, and chemical uses. Fortunately, reserves of salt are enormous and reasonably well distributed on the face of the earth. The sea is an inexhaustible source of salt which may be had at prices which vary with climate and other factors. In addition, large underground salt deposits and many salt lakes, springs and playas are scattered throughout the world. Most countries have access to a salt supply, although some are more favored than others. Properties Crystallized sodium chloride or common salt is known as halite. Its molecular weight is 58.454 and it contains, by weight, 39.34 pct sodium and 60.66 pct chlorine. Alternate positions in the cubic lattice are occupied, respectively, by negative chloride and positive sodium ions; the crystal form is isometric. Crystallization from water produces concentric shells, and when broken, a crystal shows conchoidal fracture. Salt has a hardness of 2.5; its specific gravity ranges from 2.1 to 2.6 for rock salt and is 2.165 for the pure crystal. The refractive index is 1.554; it melts at 800.8 ± 0.5°C and boils at 1413°C. Its heat of fusion is 123.59 cal/ gram. Salt is transparent or translucent and highly diathermous. It is colorless when pure and has a vitreous luster. Salt containing traces of iron oxides has varying shades of yellow, orange, brown, pink, or red. The peculiar shade of red sometimes found in that produced by solar evaporation of sea water has been attributed to tiny organisms. Blue mottlings sometimes seen in halite crystals have been attributed to colloidal sodium. Salt is soluble in water to the extent of 35.7 parts per 100 parts of water at 0°C and 39.8 parts per 100 of water at 100°C. The small difference in solubility with increasing temperature is important in the economics of producing salt by evaporating brine. Salt has a negative heat of solution which is 1.281 kg-cal/ mole at 18°C in 200 moles of water.

Jan 1, 1960

By Frank C. Aplleyard

The two calcium sulfate minerals-gypsum and anhydrite-occur in many parts of the world, and gypsum has long been of economic importance in the family of industrial minerals. Gypsum, the dihydrate form of calcium sulfate (CaSO4•2H2O) and anhydrite, the anhydrous form (CaSO4) are frequently found in close association, and it is seldom that a calcium sulfate deposit will consist exclusively of one mineral or the other. Although known gypsum deposits are extensive, anhydrite makes up the largest part of total calcium sulfate reserves. However, it has very minor economic use, and most of the following discussion will be devoted to gypsum. Calcium sulfate is one of the principal constituents of evaporite deposits, and when pure, has the following composition: [Sulfur Combined Lime Trioxide Water (CaO) (SO,) (H2O) Gypsum 32.6% 46.5% 20.9% Anhydrite 41.2% 58.8% -] Deposits of pure gypsum or of pure anhydrite which are large enough to be considered commercial have never been found because of both the metastable relationship between the two minerals, and the presence of impurities such as calcium or magnesium carbonates, chlorides, other sulfate minerals, clay minerals, or silica. As a result most mine production of gypsum will range between 85 and 95% pure. Often it is used as mined, although in certain cases, one or more forms of mineral beneficiation are employed to upgrade the product. End Uses The largest use for gypsum is based upon the unique property which calcium sulfate has of readily giving up, or taking on, water of crystallization. With the application of a moderate amount of heat in a process known as calcining, gypsum is converted to plaster of paris (the hemihydrate of calcium sulfate, CaSO4 ½ H2O) which when mixed with water will set or harden as the calcium sulfate returns to the dihydrate form. This semifinished product, usually called stucco, is then manufactured into a large variety of plasters, wallboard, and block for construction use, or into plasters for industrial applications. About 75% of the gypsum used in the United States is calcined for these purposes. Uncalcined uses of gypsum are principally as a retarder for portland cement, as a soil conditioner, as a mineral filler, and other minor industrial applications. About 25% of the gypsum mined in the United States goes into these markets; however, in less developed countries where construction and other industrial uses may be quite limited, the use of uncalcined gypsum for portland cement retarder may well be the dominant-if not the only-market for the mineral. It has often been noted that calcium sulfate constitutes the world's largest reserve of sulfur, and minor use of both anhydrite and gypsum has been made to produce sulfuric acid or other sulfur compounds such as ammonium sulfate. However, because sulfur is readily available at lower cost from other sources, use of calcium sulfate has been limited to only a few locations where it could compete economically. No such use is reported in the United States at this time. Mineralogy Anhydrite, CaSO4 because of its geologically rapid conversion to gypsum, and relatively high solubility (about 0.2 g per 100 g H2O) is not often found outcropping in climates wet enough to support abundant vegetation except on steeply dipping slopes or other places where hydrated material is continuously removed. Anhydrite rock is most often light to bluish gray in color, and under the microscope, varies

Jan 1, 1983

By A. W. Ruff

In the last ten years large gains have been made in the field of blasting. These gains have been both in the theoretical and in the practical application of explosives. One of the most publicized changes in the practical application of commercial explosives is the now-prevalent use of ammonium nitrate and fuel oil. The new water-compatible mixture of ammonium nitrate and TNT should also have a large field of application. Most of the theoretical gains have been concerned with the actual rock breakage obtained with explosives. In the last ten years, large gains have been made in the field of blasting. These gains have been both in the theoretical and in the practical application of explosives. One of the most publicized changes in the practical application of commercial explosives is the now prevalent use of ammonium nitrate and fuel oil. The new water-compatible mixture of ammonium nitrate and TNT should also have a large field of application. Most of the theoretical gains have been concerned with the actual rock breakage obtained with explosives. EXPANDING-GAS-BUBBLE THEORY There has been an outstanding change in the conception of how an explosive produces rock failure. The early theory which explained rock breakage was correct for some of the first force-producing agents such as quicklime. When a drillhole was filled with quicklime and water added, the material expanded and steam was generated. The expanding material and the steam exerted a slowly increasing pressure on the sides of the drillhole. The force broke the rock by splitting. Because a great quantity of gas was produced by the deflagration of gunpowder, the same process of the gas pressure splitting the rock was assumed to take place. Even after 80 years of use, the rock-breaking action of all high explosives was thought to be caused entirely by the expanding gas bubble which tore and split the rock. Fig. 1 shows a vertical section through an exploding spherical charge of high explosive. It illustrates the early theory which attributed the entire breakage to the expanding gas bubble. The basic idea of this theory is that the breakage started at the explosive charge and progressed toward the free face. REFLECTED-WAVE THEORY me expanding-gas- bubble theory has gradually been replaced by the reflected-wave theory. The reflected-wave theory explains rock failure by explosives in the following manner: The enormously high gas pressure in the drillhole produces fracturing of the rock on the sides of the drillhole. The fracturing around a 1 1/2-in. diam drillhole is usually confined to an area with about a 6-in. diam. In the fractured area, the pressure of the gas is reduced until the force on the walls is no longer capable of fracturing the rock. Although the gas pressure does not continue to fracture the rock, the pressure imposes a high impact stress on the wall rock. In addition, a pressure or seismic pulse is produced in the rock. The pulse is probably entirely a compression pulse when originally produced in the rock. But, with distance, part of the energy of the compression pulse is transformed into a tension pulse which follows the compression pulse. The explosive charges and burdens used in conventional mine blasting are such that the tension pulse of the original wave is probably too small to be considered in a practical evaluation of the theory. The compression pulse is transmitted through the rock with no associated fracturing.

Jan 1, 1961

By George D. Graffin.

The first use of graphite is lost in the mists of time. It was used by primitive man to make drawings on the walls of caves and by the Egyptians to decorate pottery. As early as 1400 A.D. graphite crucibles were being made in the Haffnerzell district of Bavaria. Through the Middle Ages graphite was confused with other minerals, especially galena and molybdenite. Two common names that are still used for the mineral are "Plumbago," meaning leadlike, and "Black Lead." The latter name implied that graphite is either composed of lead or at least contains a large percentage of it. Gessner is credited with having recognized it as a separate mineral in 1565, but its composition was not determined until 1779, when Scheele demonstrated that graphite oxidized to carbon dioxide, thus proving its carbon constitution. In 1789, Werner named it "graphite" from the Greek word "graphein," meaning to write. The United States has long relied on foreign countries for its graphite supplies. This reliance has been due more to the lack of suitable domestic graphites than to any particular preference for buying minerals overseas. Ceylon (now Sri Lanka) graphites were imported as early as 1820, and Madagascar graphites have been imported since the properties on that island were opened up about a hundred years later. Mexico has long supplied the United States with most of its requirements for amorphous graphite. Physical Properties and Classification Graphite is found in laminated, flaky aggregates disseminated in schistose rocks. It also occurs in veins and exhibits a foliated or fibrous structure. Graphite is a black lustrous mineral that crystallizes in the hexagonal system, with rhombohedral symmetry. The crystals have tabular form and are six-sided; the faces are commonly striated. The flakes have perfect basal cleavage and are opaque. When well crystallized, the flakes have a black metallic luster while the amorphous material is black and earthy, with a microcrystalline compactness. The flakes feel greasy. Graphite is an excellent conductor of heat and electricity. It melts at approximately 3550°C at a triple point under 1250 psi. It sublimes between 3300-3500°C at 14.7 psi. At 3726°C a second triple point occurs at approximately 100,000 atmospheres. Thermal oxidation in the presence of oxygen begins at 300°C and the rate increases with temperature. The three forms of carbon (charcoal, graphite, and diamond) are distinguished by chemical and physical tests. The specific gravity of charcoal is 1.3 to 1.9, of graphite 2.266 g/ cm3 (crystal density), and of diamond 3.5. Graphite has a hardness of 1 to 2 (Mohs' scale). Natural graphite can be divided into three classes: disseminated flake, crystalline vein (fibrous or columnar), and amorphous. Flake graphite is a lamellar form found in metamorphic rocks, such as marble, gneiss, and schist. Each flake is separate, having crystallized as such in the rock. Crystalline vein graphite is found in the form of well defined veins or as pocket accumulations along the intrusive contacts of pegmatites with limestones. The graphite of such deposits is of two types, foliated and columnar. The important Sri Lanka (Ceylon) deposits are vein type. Amorphous graphite is commonly found as minute microcrystalline particles more or less uniformly distributed in feebly metamorphic rocks, such as slates and shales, or in beds consisting practically entirely of graphite. The latter usually are metamorphosed coal seams and carry as much as 80-85% graphitic carbon, while the former, being altered carbonaceous sediments, commonly range from 25 to 60%

Jan 1, 1983

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By B. B. Rath, Hsun Hu

Rates of migration of large-angle boundaries have been studied in zone-refined aluminum crystals, defonned 80 pct by rolling in the (110)[112] orientation at -78°C followed by a recovery anneal at 80°C. Artificially nucleated grains show a marked variation. by an order of magnitude, in their growth rates in different directions. The average activation energy for the migration of all boundaries was found to be about 16,000 cal per mole. The anisotropy of the boundary migration is rationalized on the basis of the boundary structure. It has been observed by Beck and HU,1 Kohara el al,2,3 and Czjzek and Haessner4 that recrystallized grains formed upon annealing Of deformed sing1e crystals of aluminum show anisotropic growth characteristics. Kohara et al. found that single crystals rolled in the (110)[112] orientation, when random nuclei were provided on one side of the crystal by rubbing with emery paper and annealing, developed a sharp recrys-tallization texture on the other side of the crystal upon further annealing. This sharp recrystallization texture consisted of four components, which were related to the deformation texture of the crystal, i.e. (110)[112], by rotations of ±40 deg around each of the two common [ 111] axes' They also noted that recrystallized grains were elongated in directions perpendicular to either of these two common [1111 axes. They attributed this anisotropic growth to the difference in the rate of self-diffusion or diffusion of impurity atoms along the tilt and the twist boundaries. A somewhat similar investigation was conducted by Czjzek and Haessner4 On strained single-crystal sheets Of alum- inum. These authors claimed that the matrix structure of the deformed crystal had a greater effect on the growth anisotropy of the recrystallized grains than did the boundary orientation itself. In the present investigation quantitative measurements of the rate of grain boundary migration in anisotropic growth have been made in zone-refined aluminum (99.9999+pct pure) crystals deformed 80 pct by rolling in the (110) 112] orientation. Crystals of this particular orientation were chosen because of the following desirable features: 1) the crystal does not change its orientation during rolling; 2) the rolling plane contains all the significant crystallographic directions; and 3) when annealed, following deformation, the crystal does not re-crystallize spontaneously but polygonizes to a stable and homogeneous structure. Hence, the initial orientation of the crystal and a constant strain energy in the matrix can be maintained during subsequent grain boundary migration studies. It is essential to keep the driving force constant for the study of boundary mobility.5 EXPERIMENTAL PROCEDURE A cylindrical single crystal of 1 in. diam was grown by the Bridgman method in a high-purity graphite mold. The resistance ratio, R(4.2°K) /R(298°K) , of the grown crystal was approximately 2.0 x 10-4. A number of slices, 1/4 in. thick, were cut from the crystal along the (110) plane and were mechanically and electrolyti-cally polished to remove the strained surface layer. The crystals were then rolled along the [112] direction to 80 pct reduction in thickness at -78°C. To minimize surface friction, the crystals were rolled between two layers of 0.005-in. teflon sheet. Rolling was interrupted, prior to completion, to remove the surface layers and the edges by electropolishing. These and similar precautions in handling the rolled crystals

Jan 1, 1967

By A. G. Worthing

Black: Bodies.-In the ordinary conception, a black object is an opaque object that reflects but little of the light that is incident on it. This means naturally that such an object is a good absorber of luminous radiation. The black body; which is so closely connected with high-temperature measurements, represents the limit in blackness of all black objects. It is a body that not only absorbs all visible radiations but also all other radiations in the infra-red and the ultra-violet regions of the spectrum which are incident on it. No substance is known that is completely black; platinum black, one of the nearest if not the nearest representative of the ideal, reflects 1 per cent. or so of ordinary visible radiation. The closest approach to the ideal is a small opening in the wall of a relatively large opaque cavity. Any radiation incident on this black body will be almost completely absorbed if the relative dimensions are properly chosen no matter what the material may be. The great difference between the blackness of such a cavity and of lampblack, for instance, will be apparent to one who makes the simple test. Non-black Bodies.-The field of non-black bodies covers all real bodies. Their characteristics are extremely varied. So far as absorption of radiation-is concerned, these bodies range practically from the almost completely black, platinum-black, and lampblack, which absorb all but a fractional part of 1 per cent. or so of the incident radiation, by an infinite variety of steps to freshly polished silver, which ordinarily absorbs only a few per cent. The exact percentage absorbed depends not only on the nature of the incident radiation, but also on the temperature of the body, the condition of its surface, the angle of incidence, the nature of the surrounding medium, and on certain other less important conditions. As consequences of these varied characteristics, we have not only the differences of color of ordinary objects, but also the changes of color that any one object undergoes on heating or when lighted front various directions. This complexity of the phenomena, in a way, is responsible for the meagerness of knowledge, regarding materials at elevated temperatures. Measurement of High Temperatures.-Excepting in cases where the thermocouple or the gas thermometer are applicable, in which case the temperatures obtained are true temperatures regardless of-the material" studied, high, temperatures are almost always, if not always, determined from measurements of radiation. In fact, determinations of temperature from this latter point of view are often so much more convenient than the thermocouple and especially the gas-thermometer determinations that, in the region where all of these types of measurements may be made, the radiation measurements are often preferred. This is true even though the temperatures usually thus directly determined are not the actual temperatures, a consequence of the sources of the radiation being non-black bodies; in other words, a consequence of being concerned with iron, or glass, or tungsten instead of small openings leading to relatively large-cavities uniformly heated. Coordination of Experimental Results.-In order that data on iron, glass, tungsten, or other non-black bodies obtained in one laboratory, may be, correlated with similar data obtained elsewhere, temperatures must be expressed on a common scale. The true temperature scale is the natural scale for this purpose it is ordinarily the scale to which all other temperatures can be most directly reduced. When the measurements depend on the radiation, a knowledge of emissive powers repre-

Jan 9, 1919

By J. W. Spretnak, H. R. Ogden, A. G. Imgram

The effect of working reduction, stress-relief annealing, and recrystallized grain size on the tensile and notch-tensile properties of molybdenum and Mo-0.5 Ti was studied. It was found that increasing the amount of working reduction increased the strength and reduced the tendencies toward brittle behavior. Stress -relief annealing did not alter the strength but lowered the transition temperature. Increasing the recrystallized grain size lowered the strength and raised the transition temperature. The notch -unnotch strength ratio began to decrease with decreasing temperature at temperatures below those at which the notched ductility fell to zero for all of the micro structural conditions investigated. BEING bcc metals, the refractory metals in Groups Va and VIa (V, Cb, Ta, and Cr, Mo, W) undergo a ductile-to-brittle transition and exhibit brittle fractures at low temperatures. Previous research has shown that molybdenum and tungsten not only have higher transition temperatures than columbium and tantalum but show a marked sensitivity of transition temperature to structure as well.' Recrystallized materials become brittle at considerably higher temperatures than is the case with material having a worked or fibered micro-structure. Evidence of structure sensitivity has also been detected in columbium- and tantalum-base alloys containing appreciable amounts of molybdenum or tungsten such as F-48 (Cb-15W-5Mo-1Zr) and Ta-10w.2 This paper describes the results of research conducted to further evaluate the effects of metal. lurgical structure on the low-temperature tensile and notch-tensile properties of molybdenum and Mo-0.5Ti. The effects of rolling reduction, stress-relief annealing temperature, and recrystallized grain size were studied. Considerable progress has been made in explaining the fundamental mechanisms of the flow and fracture characteristics of bcc metals. Several of these concepts are helpful in interpreting the data obtained in this study. Brittle fractures occur when the highly temperature-sensitive yield strength equals, or exceeds, the temperature-insensitive brittle cleavage fracture stress.3 The rapid increase in yield strength with decreasing temperature, characteristic of all bcc metals, is therefore of primary concern. petch4 has described the yield strength, ay, (stress required to initiate plastic flow) of bcc metals by the expression where ai is the frictional resistance to slip, Ky is a constant numerically equal to the slope of a a vs curve, and 2d is the average grain diamefer. The oi term itself is thought to be composed of a temperature-insensitive component dependent on impurity content and second-phase particles and a temperature-sensitive component dependent on the Pierls-Nabarro force.5 This equation has also been demonstrated to hold for the flow stress (stress required to maintain continued plastic flow).' Brittle-crack nucleation is thought to occur by the coalescence of dislocations piled up in slip planes at sessile dislocations or twin and grain boundaries.7,8 These proposed mechanisms require that a large number of dislocations be released into the active slip planes so that sufficiently large stress concentrations are produced at the dislocation pile-ups to enable coalescence into a micro-crack. Therefore, at least a microscopic amount of slip must occur in some grains to facilitate initial crack formation. Cottrell 7 has predicted that brittle fracture, nucleated by slip, should occur when where ty is the shear yield strength, ß = 1 in un- notched xension, u is the shear modulus, and y is the effective surface energy. This equation incorporates the Griffith concept of fracture that a crack will propagate if the decrease in strain energy equals or exceeds the increase in surface energy.

Jan 1, 1964

By A. O. P. Casbarian

An analytical method is developed to determine the variation of the ultimate lateral resistance of a plate in a cohesionless soil with depth. This analysis is based on a modification of Rankine's classical earth pressure theory and the theory of plasticity as applied to soils. The ultimate resistance is defined as the product of the effective stress at the midpoint of the plate, the area of the plate and a dimensionless variable termed the ultimate resistance factor. This variable has been plotted us the depth ratio: i.e., the ratio of of the depth of embedment us the height of the plate. The resistance of a plate may then be calculated using the values af the ultimate resistance factor from the chart provided or the equation may be programmed for use in an analysis of anchor systems in cohesionless soils. It is emphasized that the analysis is semitheoretical. The theory has been compared with experimental results reported in the literature and results indicate general agreement. Actual field tests are necessary to further verify this theory. INTRODUCTION With the exploration for oil offshore in waters all over the world, it is of importance to determine the behavior of the various soils in relation to their ultimate resistance to deformation. Examples of such problems are the holding capacity of anchors and the lateral resistance of piles. Very little information is available in the published literature on the design and performance of anchors, in either cohesive or cohesionless soils. The analysis developed in this report is the first step in obtaining a solution for the determination of anchor holding capacity in a cohesionless material. DISCUSSION The theory used in the analysis is based on the ultimate strength of the soil and is the maximum resistance developed by the plate against further movement. In such a state the elastic deformations are disregarded in comparison with the plastic deformations. Hence, the plate can be considered as completely rigid. The theory of plasticity determines the three unknown stresses at any point by means of two equilibrium conditions for a small earth element in combination with the failure condition. However, the exact solutions can only be carried out in a few simple cases such as, for example, when the rupture or failure lines are straight (Rankine theory) or with spiral and straight rupture lines (Prandtl theory).l Kiitter 2 derived a single equation expressing the variation of the stress in any given rupture line. To utilize this equation, it is necessary to know the stress in the rupture line at a certain point. Unfortunately, this is difficult to obtain unless the rupture line intersects the free surface at a certain angle or when the earth is cohesion-less and unloaded. A method to overcome this is to consider only the boundary conditions at both ends of a rupture line without investigating the equilibrium of the earth above the rupture line. This assumes that the rupture lines meet the surface at statically correct angles, so that boundary stresses may be determined. As Kiitter's equation furnished a relation between these stresses, the unit earth pressure may be calculated at the point where the rupture line meets the wall. Another way in which Kotter's equation may be applied is in investigating the equilibrium of a soil mass above a rupture line. This method assumes that the failure or rupture line is known and that the boundary stresses in the rupture line at the ground surface can be determined. In this case it is possible to determine the earth pressure from the equations of equilibrium.

Jan 1, 1967

By F. O. Shuck, F. E. Butler

A diaphragm diffusion cell suitable for use with liquid metals was designed and tested by measuring the diffusion coefficients for a Hg-10 pct In alloy at 25°C. The binary diffusion coefficient and the coefficients for In and Hg tracers were measured at this composition. The measured coefficients for both tracers were less than the binary diffusion coefficient. When these coefficients were combined with the activity correction term of Darken, the predicted binary coefficient was somewhat higher than the experimental value. In recent years a number of investigators have been studying diffusion of liquid metals in order to gain a better understanding of the liquid state and to examine possible applications to liquid metal processing. The bulk of this work has involved either self-diffusion or diffusion of low concentrations of solute metals in an essentially pure solvent metal. The most common experimental technique employed has been the capillary-reservoir method of Anderson and saddington1 since it is well-suited to measurements involving low concentrations of solutes. As an expansion of previous studies, an investigation of the variation of diffusion coefficient over large composition ranges has been undertaken in this laboratory. Although it is possible to modify the capillary-reservoir method for such measurements, the technique loses its principal advantage of requiring only small quantities of solutes. Therefore, it was felt desirable to investigate other possible experimental techniques applicable to measurements over large composition ranges. A technique which has been used widely in measurements of other liquid systems and seemed potentially applicable to studies of liquid metals was the diaphragm cell. This method has been found to combine relative simplicity of operation with accurate and reproducible results. In use with normal liquids, the tyiical diaphragm cell utilizes a porous glass disk. However, because of the high surface tension, it is not possible to use a diaphragm of such fine pore structure with liquid metals. Furthermore. projected use at high temperatures makes the use of glass undesirable. Consequently, the first problem was the search for an appropriate cell design. EXPERLMENTAL Diaphragm Cell. A number of possible cell designs were examined. Prototypes of several were constructed and tested. The final design is shown in an exploded view in Fig. 1. The cell consists of two identical chambers, one on either side of a 0.20-in.-thick partition. The chambers are 0.15 in. deep and have a volume of 3.45 cu cm. Each chamber is provided with two small threaded holes for filling and emptying. The filling holes may be sealed with stainless-steel screws. Drilled lengthwise through the center partition is a 0.250-in.-diam hole. Inserted into this hole is a rod having seven 0.059-in.-diam holes drilled radially through it. The total "hole" volume is 0.078 cu cm. When the rod is properly aligned, the holes in it constitute the "diaphragm" through which diffusion occurs. The center section was of Teflon and the rod and face plates were of Plexiglas. Four such cells were constructed and used in this study. Subsequent to this investigation, a similar cell constructed entirely of iron was fabricated and tested at higher temperatures. Several considerations led to this final design. It is desirable to minimize the volume of the cell chambers to decrease the time required for a measurement. However, the total volume of metal in the diaphragm must be small in comparison with that in the chambers. To facilitate filling and emptying it is desirable to have a diaphragm which may be closed.

Jan 1, 1970

By H. H. Waller, D. L. Monroe, D. P. R. Smyth

ORIGINALLY slusher drift development was conventional, advancing the drift full 10x13-ft size at 6 ft per round. This proved dangerous and costly because the weak fractured rock of the orebody cannot be left raw for any length of time without its reacting with air to cause spalling. With this method of drift development ground conditions were worsened by many blasts and the length of time it was necessary for the drift to remain open. The problem was practically solved by driving 5x7-ft pilot drifts, then enlarging to 10x13-ft raw size by slashing with 50 to 60-ft diamond drill holes. Calculated explosive charges are used to avoid wall and roof shattering. Still more recently jacklegs and sectional steel replaced the diamond drills, resulting in the same work for less than half the cost, see Figs. 1 and 2. Crosscuts at right angles to the main haulage drifts, which cross through the center of the ore-body, divide the ore into 200-ft blocks. Eight slusher drifts on 50-ft centers draw from one block. The slusher floor is 11 ft above the rail, inclined at 1 pct grade, and the top is 18 ft below the undercut. The finished slusher drift is 102.5 or 120 ft long, depending on whether it is north or south of the crosscut. Drawpoints are staggered on each side at 17.5-ft centers. The completed drift is concreted and has an inclined ramp and a vent at the back. When crosscuts and gangways have been excavated and concreted and slusher stations installed, slusher drift development is carried out in 10 clear-cut stages: 1—Pilot drift is driven full length, 5x7 ft. 2—Station is excavated at half-way point in pilot drift. 3—Pilot drift is enlarged to slusher drift size by drilling. 4—Lower part of slash is blasted and mucked for floor concrete. 5—Floor is poured. 6—Inside upper half of slusher drift is blasted, mucked, and concreted. 7—Outside upper half of slusher drift is blasted, mucked, and concreted. 8—Drawpoints are excavated. 9—Drawpoints are concreted. 10—Concrete ramp and sheave protection recess are constructed at back end of slusher drift. A 5x7-ft pilot drift is driven full length on the center line of the proposed slusher drift using a jackleg and detachable bits on 7/8-in. hexagon steel. A 10-hp air-driven slusher and 36-in. scraper pull muck directly into cars in the main haulage crosscut, see Fig. 2. Operations are on a three-shift basis. One man mucks the previous round, drills, and blasts his round in a shift. Average advance is 5 ft per shift. When the pilot drift is completed, 7 ft of drift in the center section is enlarged to full raw slusher drift size of 10x13 ft, for the set-up to drill long slash holes. The pilot drift is slashed to full raw size from this station with jacklegs and tungsten carbide chisel bits on 7/8-in. sectional steel. Crews line the holes without trouble, working from controls established by the engineers, and the pattern of holes for the slash is arranged to give the least shattering effect

Jan 1, 1955

By C. S. Matthews, G. L. Stegemeier

In one field in South Texas, approximately 72 per cent of the pressure build-up results show a characteris-i.rtic "hump" (i.e., the pressure builds up and then falls off) which makes interpretation by. standard methods impossible Correlation of size and time of hump with formation permeability. well productivitv index, and method of completion led to the tentativc, conclusion that the humps were caused by segregation of gas and oil in the wellbore after closing-in"'. This conclusion was confirmed by performance of simple laboratory bubble-rise experiments, by theoretical bubble-rise time calculations, and by a detailed calculation of PVT behavior in the well of a particular well Oil which accurate Surface and bottom-hole pressure measure-ments were untile. The hump behavior has since been found to occur in many other fields. The cause, however, is not the mine in all cases. In some of these the hump is trace-ahie to leaks in the tnbing which allow influx from the annulus after closing-in. In other cases the hump is traceable to leaks in the device separating pay horizons in dually completed wells. It is concluded that the recording of both surface and bottom-hole pressures is desirable in wells which show an anomalous build-up behavior. A number of field examples is discussed where use of both sets of measurements enables the cause for anomalous behavior to he found, (and a reasonable interpreation of bottom-hole pressure to be made. INTRODUCTION Theoretically the pressure build-up in an infinite reser-voir should be a linear function of In [(t + at)/nere t is the production time and At a the closed-in time. Some of the variations from this behavior arc well known, such as the curved portion immediately after shut-in which results from after-production and skin effect, and the flattened end portion which results from boundary effects in a limited reservoir. The effect of stratified producing zones and irregular geometrical drainage patterns may also contribute unusual characteristics to build-ups. However, the effect of still another phenomenon—that of movement of fluids within the wellbore—has been neglected in most build-up studies to date. Fluid movements within the wellbore after shut-in occur as a result of after-production, packer failures, leaks in the casing or tubing, or buoyancy of the gas phase when both gas and liquid are present in the well. Each of these movements can influence the pressure build-up, sometimes sufficiently to negate use of the data for computing permeability or stabilized build-up pressure. Examples of each of these phenomena are discussed below. FIELD OBSERVATIONS ON HUMP BUILD-UPS In approximately 75 per cent of the wells in a medium-sized field in South Texas the pressure build-up curves rise to 3 maximum and then decline to what appears to be a stabilized reservoir pressure as shown in Fig. I. Similar behavior has also been observed in wells in other fields in Texas and Louisian:,. Because of the possibility of such behavior being a mechanical failure of the pressure bomb. the bombs were run in tanden into one well which had been known to exhibit this behavior. When both bombs recorded identical curves with the characteristic hump, it was inferred that the unusual build-up is a result of well or forma-

By John W. Weeton, Max Quatinetz, Robert J. Schafer

Nickel powders of 1-, 0.4-, and 0.2- average particle size were combined with 0.05- p MgO powder. Oxide was added in quantities of 4, 12, and 20 vol pct. The mixtures were vacuum hot pressed and extruded at 2100°F. In spite of a general tendency to growth of oxide particles during processing, dispersions of fineness comparable to those of Sintered Aluminum Powder, SAP, were achieved. A small amount of oxide considerably improved 1800°F stress-rupture strength, but further oxide addition resulted in a decrease of strength. RECENTLY there has been much speculation concerning the requisites for strong and stable dispersion-strengthened alloys. The nature of the dispersed phase, the stability of the alloys, and variables influencing the mechanical properties of alloys have been given consideration. Such topics have been reviewed by Bunshah and Goetzel. Of the many parameters related to the mechanical properties of dispersion alloys, mean free path between dispersed particles (a measure of the fineness of the dispersion), particle size, and vol pct of the dispersed phase have been shown to be very important. Generally, strength increases with decreasing mean free path, and there is an optimum vol pct of dispersed phase. Just how fine a dispersion ought to be is somewhat open to debate, but Irmann, Lenel, Backensto, and Rose, Gregory and Grant,4 and others have shown in the original SAP-type alloys, aluminum plus aluminum oxide alloys, that better strength is generally obtained with finer dispersions and the best strengths were obtained when the mean free path was less than . Further, Cremens, and rant' showed that in nickel plus aluminum oxide alloys, stress-rupture strength at 1500°F was definitely increasing with decreasing mean free path. In their investigation, however, the finest dispersions that were produced were about 2.0 mean free path. To determine the potential of the nickel plus oxide type of product, it would be neces- sary to obtain dispersions analogous to those of SAP alloys; namely, ones where the mean free path between oxides is less than . Unfortunately, however, it is very difficult to produce extremely fine dispersions of oxides in metals other than those which naturally form refractory oxide skins. There are several approaches to this problem including such procedures as mechanical mixing, internal oxidation, reduction of mixed oxides, and metal deposition from solution. Work at the Lewis Research Center has shown that metal powders 0.1p or finer could be produced by ball milling, when selected grinding aids were utilized.' Because these unusually fine powders were available, it was an initial objective of this study to determine if by mixing of these fine Ni powders with various amounts of MgO (0.05) a fine dispersion of MgO in Ni comparable to those in Al-Al203 might be achieved. A second objective was then to attempt to relate the parameters of structure to 1800°F stress-rupture strength of the alloys. Nickel powders of 1-, 0.4-, and 0.2-p average particle size were combined with 0.05- average particle size MgO powder. This oxide was added in quantities of 4, 12, and 20 vol pct. The mixtures were hot pressed and extruded at 2100°F.

Jan 1, 1962

By F. V. Lenel, J. A. Dromsky

The influence of thermal and mechanical treatments upon the elevated-temperature stability, the microstructure, and the mechanical properties of aluminumaluminum oxide alloys is investigated. Compacts from atomized and flake aluminum powders were sintered at temperatures just below the melting point of aluminum in a vacuum of 10-4 Torr for several hours and were then hot-extruded. During this treatment the hydrated oxide present on the surface of the powder particles decomposes, the water vapor produced reacts with the aluminum forming additional oxide, and the hydrogen developed is removed by diffusion to the surface. Extrusions of compacts so treated are stable at temperatures up to the melting point of aluminum and do not form blisters and internal defects typical of extrusions from untreated powder. Electron micrographs of extrusions from unsintered compacts show long parallel oriented platelets typical of the IN previous investigations1,2 the properties and structure of aluminum alloys were described which had been produced by cold compacting aluminum powder and then hot pressing and extruding the compacts. Both the structure and the properties of these alloys differ significantly from those of commercially produced aluminum-aluminum oxide alloys. When commercial alloys are produced, they are given a sintering treatment in air at about 600°C between cold compacting and hot pressing.3 During this treatment the hydrated oxide, which forms the coating on the aluminum-powder particles from which the alloys are prepared, is decomposed.4 The chemically bound water which is released reacts with the aluminum and forms aluminum oxide and hydrogen. Most of the hydrogen is eliminated by hydrated oxide skins on the original powder particles, while the oxide particles in extrusions from sintered compacts are broken up. The strength of extrusions from treated powder is somewhat lower, but their ductility is considerably improved over that of extrusions from untreated powder. The slip-trace patterns on electron microgvaphs of extrusions which had been strained in tension before replication indicated that the grain size of the extruded alloys was approximately the same as that of the original powder particles. Coarse-grained alloys were produced by severe cold work and annealing of the extrusions. They have significantly lower room-temperature strength, but about the same ductility as the vacuum-sintered fine-grained alloys. The size and shape of oxides in the coarsegrained alloys is similar to those of the fine-grained alloys, but the particles are somewhat more uniformly distributed. diffusing to the interior or exterior surfaces of the compact, but it is difficult to eliminate all of it because the solubility of hydrogen in solid aluminum is very low even near its melting point. Extruded alloys which are not sintered before hot pressing and extrusion appear quite sound upon metallo-graphic examination, but develop severe surface blistering and internal fissuring when they are heated to elevated temperatures after extrusion. Fissures and blisters have been observed even in commercial alloys which had been sintered in air, although they are much less severe.' Because of the importance of this sintering treatment it was studied in this investigation in a modified form, using vacuum sintering rather than sintering in air, to insure more complete elimination of occluded hydrogen. The technique is described and the effect of the treatment upon the structure of the alloys is documented. It has been known for some time that extruded aluminum-aluminum oxide alloys are very finegrained, but an exact delineation of grains in electron micrographs has not been possible. In the conventional metallographic-etching techniques etchants attack the interface between the second-phase particles and the matrix in the alloys much

Jan 1, 1964

By F. J. Fayers, R. L. Perrine

For many years the problem of increasing ultimate recovery of oil from a reservoir has been a subject of interest to the oil industry. At present, a standard secondary recovery technique is to flood the reservoir with water once natural forces of the system are depleted. The permeability characteristics of the rock, together with interfacial forces which exist between the two fluids and the porous material. allow only part of the oil in the rock formation to be recovered by the water-flooding process. Laboratory experiments have shown that when detergents are added to the flooding water, the flow properties of oil in a porous rock arc improved. This improvement results in greater oil recovery. Even though higher recoveries are obtained using detergents, the extra cost associated with the method may make it economically unsatisfactory. To establish economic feasibility requires experimental laboratory measurement of fluid and rock properties together with a calculational procedure to predict field results. Pilot tests in the field may also be required. This paper presents a mathematical procedure for predicting detergent flood behavior. A number of reasonable simplifying assumptions are made to obtain a tractable system of equations. The resulting method may be regarded as a generalization of Buckley-Lev-crett' theory to solve simultaneously for water saturation and detergent concentration profiles. Consequently this type of calculation can be used in much the same manner as Buckley-Leverett theory is used to evaluate a water flood. The mathematical method employed is the so-called method of characteristics for solving hyperbolic partial differential equations. This application of the method is instructive because several other problems in reservoir analysis may be analyzed in a similar manner. FLUID FLOW EQUATIONS The flow behavior of oil and water without detergent through porous reservoir rock is usually expressed by Darcy's law and a continuity equation for each phase. If gravitational forces are neglected, vrg = kr (s)µr v p rg.........(1) vrg = kr (s)µr v p rg.........(1) ? pa va = F ?/?t (sd) where v is the volumetric flux, k represents permeability, S is saturation, and P the pressure. Fluid viscosity is denoted by 11, p is the density, 4 is porosity, and I the time. The subscripts w and o refer to water and oil. The capillary forces in the system lead to a difference in pressure between phases. This may be expressed by the relation: Pm -P0 =Pc(S).........(5) The capillary pressure? P,, is determined experimentally as a function of saturation. DETERGENT BALANCE EQUATION Addition of detergent to the water phase affects the flow properties of the system. Capillary pressure and relative permeability become functions of detergent concentration, c, as well as fluid saturation. That is: P--P (S,c) and k,,,.- - -- k,,,. At low oil saturation values, the presence of detergent reduces capillary pressure and reduces the relative permeability ratio. Detergents are surface-active and adsorb on rock surfaces. The quantity adsorbed, a, will depend on the concentration c of detergent solution and may also depend on the saturation; thus, a = a(S,c). In this analysis we have assumed that the detergents used are water soluble but not oil soluble, and their movement is therefore restricted to the water phase. The dispersion of detergent in water is neglected by comparison with transfer by flow within the system. Detergent movement is determined by the water flux and adsorption: ? cv m = -F ?/?t (cs + a) We will assume that the quantity of detergent in solution is too small to significantly change water density or viscosity. When the permeability and capillary pres-

By J. W. Wolfe

The Benedict-Webb-Rmbin equation of state was used in digital computer programs to make rapid determinations of natural gas equilibrium phase compositions. Mixture components were the nine hydrocarbons, methane through heptane. Comparative tests were made with data from field separators, plant exchangers and literature sources. For most tests made, the B-W-R equations predrcted component K-vallles, mixture enthalpies and phase aensities within tile accuracy of available correlations for rune-component mixtures: significant deviations were noted when mixtures contained components heavier than heptune. INTRODUCTION Rapid, accurate methods for calculating the properties of hydrocarbon mixtures are needed for predicting the behavior of natural gas processes. For example, because of the common use of two-phase separation methods in gas proccssing, calculations must be made for the density and composition of equilibrium vapor and liquid phases. In addition, predictions must often be made for the temperature and pressure changes associated with the flow of single- and two-phase natural gas fluids through heat exchangers, chokes and turbines. The complex nature of non-ideal mixtures makes rigorous calculations for these natural gas properties difficult and time-consuming. Natural gas properties have conventionally been determined with generalized data correlations. These correlations, such as the K-values presented in the NGAA Equilibrium Ratio Data Book, are usually based on some average property of the mixture and have proven to give satisfactory estimates for the properties of most oil and gas systems. Digital computers, however, have not only increased the utility of these correlations, but also have made practical the use of equations of state for calculating the properties of natural gases. Potentially, if basic pure component data are available, all the desired thermodynamic properties of mixtures can be derived from a single equation of state describing the mixture. Currently. the best equation of state for describing the behavior of pure, light hydrocarbons over single-and two-phase regions, both below and above critical pressure, is that of Benedict. Webb and Rubin.' The equation contains eight constants which are determined by empirically fitting the equation to pure-component PVT data. Benedict and his co-workers presented the clevelopment of their equation as early as 1940.2 The B-W-R equation is a modification of the Beattie-Bridgeman equation of state and gives better PVT predictions than the Beattie equation at densities above the critical density. Benedict et al. made the equation applicable to mixtures by relating the mixture constants to composition and the constants for pure compounds. These authors, in a serics of articles in 1951,' showed the accuracy of the B-W-R equation when applied to light hydrocarbons and their simple mixtures, and demonstrated the equation's utility for making vapor-liquid equilibria calculations. Since its inception, the B-W-R equation has been the subject of many papers. Numerous additions and modifications have been proposed,'-',"'-':' the purpose of most being to improve the equation's ability to predict PVT properties of specific mixture systems. In 1959, Opfell, Pings and Sage summarized much of the work on the B-W-R equation in their book on equations of state." Since natural gases are primarily mixtures of light hydrocarbons, the B-W-R equation is a natural choice for an equation of state to compute both phase equilibria and thermodynamic properties of natural gases. Consequent-

Jan 1, 1967