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By Walter L. Maxson, Fred C. Bond

SINCE the last publication of tabulated results of grindability tests by the authors1 the total number of ball-mill tests made has more than doubled, and rod-mill tests have become increasingly important. Nearly all of the standard closed-circuit ball-mill and rod-mill tests made to date are included in the present tabulation, together with additional information not previously published. STANDARD BALL-MILL GRINDABILITY TESTS The method of conducting these closed-circuit tests has not been altered. A sample of the ore or other material is stage-crushed in rolls set at 1/16-in. opening with a 6-mesh screen until all of it has passed the screen. The combined minus 6-mesh screen undersize is mixed, sampled and screen-analyzed, and its apparent specific gravity is determined by packing and shaking in a standard container, and weighing. The apparent specific gravity ordinarily is about 60 per cent of the true specific gravity. The unit volume present in the mill in all tests is 700 c.c. of the packed minus 6-mesh roll product, and the number of grams occupying 700 c.c. is the unit test weight. This weight is placed in the mill dry, ground for the number of revolutions estimated to be necessary, discharged, and screened mechanically in three testing sieves of the mesh size at which the test is to be conducted. The oversize, or circulating load, is weighed, sufficient fresh minus 6-mesh feed is added to bring the total weight up to that of 700 c.c., and the charge is returned to the mill for a second grinding period. All standard ball-mill tests are conducted at 250 per cent circulating load, and the number of revolutions in the mill necessary to obtain this circulating load at any grinding period is estimated from the results of the previous period. The number of net grams of screen undersize produced per revolution of the mill approaches its final equilibrium value after several grinding periods, and this is recorded as the grindability, or relative ease of grinding, of the sample. A cylindrical ball mill, 12 by 12 in. inside, with a smooth lining and rounded corners, is used with a revolution counter. Under standard grinding conditions it runs at 70 r.p.m., and contains a charge of 285 iron balls weighing 20,125 grams, ranging from I ½ to ¾ in. in diameter. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the capacity to be expected from a given mill is calculated by comparing the

Jan 1, 1943

By G. J. Wilson

Review of difficulties experienced in drilling directional wells in the offshore Grand Isle Block 43 field showed most failures of drill pipe, drill collars and casing to have been associated with excessive dog-legs. Alleviation of difficulties was approached by synthesizing theoretical and practical concepts in a planned dog-leg control program. Preventive measures necessary to control dog-leg severity and corrective measures used to reduce unacceptable doglegs are discussed. When other measures fail, deliberative measures as outlined can be employed after the probable cumulative fatigue damage to be sustained by the drill pipe has been determined. Results of a program successful in virtually eliminating problems stemming from excessive dog-legs indicate that control of dog-leg severity in directional wells is feasible and will cause no decrease in the over-all drilling rate. INTRODUCTION Prompted by an increasing frequency of drill pipe, drill collar and casing failures, a study of 50 directional wells representing 592,000 ft of hole, including 444,000 ft of deviated hole, drilled in the offshore Grand Isle Block 43 field was conducted in early 1965. A number of drill pipe washouts and six keyseating problems were recorded and a detailed review was made of 16 failures which had required fishing effort in 10 of the 50 directional wells drilled prior to June, 1965. These problem wells are exemplified by Wells G and F for which pertinent data are shown in Figs. 1 and 2. Data pertaining to all of the 16 failures are summarized in Table 1. Inspection of these data shows most of the problems to have been associated with dog-legs in excess of theoretical limits suggested by Lubinski' and excessive dog-legging is indicated to have been concomitant with whipstocking in several of the problem wells. Results of the investigation agreed with those reported by Schenck2 who had concluded that problems could be expected when dog-leg severity exceeded limits proposed by Lubinski. Since Schenck had demonstrated the desirability and feasibility of drilling directional wells without excessive dog-legging, a dog-leg control program was established in June, 1965 for wells drilled in the Grand Isle Block 43 field. This paper reviews the methods by which theoretical and practical concepts were synthesized to develop a program of preventive, corrective and deliberative measures which virtually eliminated problems stemming from excessive dog-legs in directional wells. Dog-legs of a magnitude causing no damage are referred to as permissible +1CONTINENTAL OIL CO. HARVEY, LA.

By O. D. Sherby, J. L. Lytton, C. R. Barrett

Randomly oriented polycryslalline copper of 99.995 pcl was tested in tension at temperatures of 626o, 496o, and 406o. The gvain-size mnge investigated was from 0.03 to 0.7 mm. Grain sizes were produced by two techniques: 1) varying the amount of prior cold work and the amealing time at constant annealing temperature so as to obtain various vecrystallized grain sizes with minimum grain growth, and 4 holding the prior cold work constant while varying the annealing time or temperature so as to obtain varying grain sizes by grain growth. Polycrystalline samples (grain size of 0.03 mm) with a strong. [001](100) texture were also studied. The relationship between the steady-state creep rate, Es, and pain size was found to be the same indepentent of the technique used to prepare the various grain sizes. For specimens with grain diameters above about 0.1 mm ea zuas esse)ztiallj~ independent of grain size, while for smaller grain diameters Cs increased slightly with decreasing grain size. Strongly textured polycrystalline copper, which contained low-angle grain boundaries, exhibited steady-state creep rates that were slightly lower than those observed in randomly oriented copper, of the same gain size. The results are explained by conside?%ng- the contribution of grain boundary shearing to the total strain and the effect of grain size on the resulting creep substructure. EXPERIMENTAL observations concerning the influence of grain size on steady-state creep rates are varied and oftentimes conflicting. Numerous early investigators found that an increase in the grain size resulted in a decrease in the high-temperature steady-state creep rate, i,.'-" Other workers have foundthat ef decreases with increasing grain size up to some optimum grain size and then increases with a further increase in grain size.'- '' It has been suggested that es, decreases with an increase in grain size only because the range of grain sizes studied normally lies to the left of the grain size for optimum creep resistance. However, sherbyl2 and Feltham and his co-worker13, 14 have found that even for small grain sizes 2, does not always decrease with an increase in grain diameter but may be proportional to the square of the grain diameter. A possible explanation for the different creep rate-grain size relationships which have been observed is that in most experimental studies different grain sizes have been prepared by annealing at various temperatures. For metals in which the impurity concentration is high (greater than about 0.1 at. pct) this type of

Jan 1, 1968

By Walter Knox, J. D. Doherty

IN 1939, at the request of The Koppers Coal Co., the Koppers Company Research Department established a Stoker Coal Research Laboratory for the purpose of investigating the performance characteristics of stoker coals in typical domestic stoker installations. Fig. I is a photograph of part of the laboratory. The material in this paper deals with the performance of one coal in a single installation. Presented are details of this installation, mechanical characteristics of the stoker, and the results of a series of burning tests in which adjustments were systematically varied. SUMMARY OF RESULTS Mechanical Features I. A large percentage of the total power consumed by a domestic stoker is used to operate the gear case and motor (Fig. 3). 2. The power consumption per ton goes down with an increase in rate of coal feed (Fig. 4). 3. The automatic air control in this stoker showed advantages over manual control (Fig. 5). 4. The air velocities through the retort tuyeres were uniform around the retort, but varied between the rows of tuyere rings (Fig. 6). 5. The crushing of coal with this stoker increased the minus 1/8-in. from 1 1.6 per cent to 19.2 per cent. There was a noticeable segregation of coal as it came from the retort and distribution was not uniform (Fig. 7). 6. Measurement of air entering over the fire showed that with some not uncommon adjustments this air may he a high percentage of the total air supply (Fig. 8 and Table I). Operating Performance I. The removal of clinker was shown to give a period of poor performance characterized by a high fuel-bed resistance and a high percentage of carbon monoxide in the flue gases (Fig. 10). 2. The fuel-bed resistance was found to decrease as the fuel bed built up in a normal response to heat demand after a prolonged hold-fire (Fig. II). 3. With intermittent operation the burning rate was almost always less than the feeding rate. The wide variations were found to be greatly dependent upon the length of the On period and the length of the intervals between On periods (Fig. 12). 4. The maintenance of a low furnace draft led to less fly ash, better clinker formation, and higher efficiencies (Fig. I3). 5. The maintenance of a minimum of excess air also resulted in less fly ash, better clinker formation, and higher efficiencies (Fig. 14). GUIDING PRINCIPLES In planning the investigations, the following principles were adopted: Selection of Healing Equipment.-Use only standard models of stokers and furnaces representative of those widely used.

Jan 1, 1942

By D. R. Miller

Internal friction and elastic modulus variations in electrorefined titanium, iodide refined titanium, and alloys of the latter material with oxygen, nitrogen, aluminum, and zirconium were investigated. No oxygen peak was detected with electrorefined titanium but, provided precautions were taken to prevent increases in background damping, an oxygen peak at about 410°C could be resolved with each of the other materials. An additional partially resolved peak was observed at 500°C in a Ti-N alloy. An anomaly in the variation of rigidity modulus with temperature was observed. Possible mechanisms for the formation of any oxygen peak have been discussed. PRATT, Bratina, and Chalmersl investigated the internal friction of commercial purity titanium and alloys of this material containing 1.5, 3.5, and 4.5 at. pct O. With commercial titanium the internal friction curve consisted of two components, a background which increased steadily with temperature and a peak at about 600" C which was due to grain boundary relaxation. In the Ti-O alloys, however, an additional internal friction peak was observed at 430" to 450°C and, since this peak increased in height as the oxygen content was increased, it was thought to be associated with the presence of oxygen. The diffusion of oxygen in titanium at temperatures between 300" and 500° C is believed to have marked effects in its tensile properties2'3 and the present internal friction measurements were undertaken to obtain further information on this diffusion, using material of higher purity than that of Pratt et d. and an apparatus of very much greater sensitivity. In the course of the investigation a number of important limitations on the work of Pratt et al. were revealed and results have been obtained which emphasize the need for ensuring that in this type of experiment, internal friction is independent of strain amplitude and that the values obtained are reproducible. 1) MATERIALS AND APPARATUS The basis material from which the majority of the specimens was prepared was iodide-refined titanium, the major impurities in which were oxygen and nitrogen—the metallic impurities being present at concentrations less than 0.001 at. pct. The hardness of this material after arc melting, forging, and swaging to rods 1/4 in. diameter was Dph = 110. Specimens 10 in. long and 0.020 in. (0.51 mm) diameter were prepared from these rods by further swaging and wire drawing and were finally annealed in vacuo (5 x 10-6 mmHg) for 24 hr at 800°C. The oxygen alloys were prepared from iodide-

Jan 1, 1962

By Henry Siegmann

HISTORY OF PRODUCTION AND USE In 1899 the consumption of fluorspar in the United States was reported as 16,000 tons. The invention of the open-hearth method of steel manufacture, plus the beginnings of a fluorine chemical industry, pushed consumption of fluorspar to 250,000 tons by 1918. In contrast to these consumption statistics of the past, the most recent statistics available (1972) indicate a total fluorspar usage in the United States of 1.352 million st (Table 15.4D.1). Fluorspar remains the world's cheapest source of fluorine, and its unique properties make the mineral the most desirable fluxing agent for steel refining. The linking of fluorine with carbon in the late 1930s resulted in the production of fluorocarbon, and constant growth in production over the years has formed the backbone of a strong fluorine chemical industry. For example, in 1972 it is estimated that total fluorocarbon production amounted to 2.113 million tons, and that, in this process, over 1.351 million tons of acid-grade fluorspar was consumed. The producers of primary aluminum long have been concerned about the fast dwindling reserves of natural cryolite. They found the solution to their problem by utilizing fluorspar for the manufacture of synthetic cryolite and aluminum fluoride. Nuclear weapons, as well as the growing number of peaceful uses for atomic reactors, constitute a market for uranium hexafluoride. This chemical and chlorine pentafluoride, used as an oxidizer with rocket fuels, are products that are as much a novelty as fluorocarbons were 25 years ago. Judging from past success in the field of fluorine chemistry research, it is safe to assume that the market for these chemicals will grow in the future. Three major industries account for the bulk of the fluorspar consumption: steel refining, fluorine chemical, and primary aluminum production. These industries have had a pattern of fabulous growth in the past, and their future plans point to a continuation of this pattern. It seems logical that the fluorspar usage also should continue its upward trend. Considering the growth of the fluorspar industry since 1899, and the obvious dependence on imports of fluorspar as a raw material, one of the most puzzling aspects of the past has been the apparent lack of coordination between fluorspar production and fluorspar consumption. A few authoritative voices have spoken out concerning the need to expand fluorspar production in order to meet consumption of the future. During World War II, the U.S. Government took positive steps in this direction by authorizing purchases at attractive prices for its "stockpile program." As a consequence, new fluorspar producing facilities were built, not only in

Jan 1, 1976

By K. C. Mills, E. T. Turkdogan

The results on the rates of vaporization of Fe-Ni alloys, levitated by an electromagnetic field in a stagnant atmosphere of helium, are shown to be in close agreement with those predicted theoretically. AS shown in Part I of this series of papers, the rates of vaporization of metals enhanced by convection currents are increased further by the process of condensation of metal vapor when there is a steep temperature gradient in the boundary layer. At the time this theoretical work was completed one of the authors (K. C. Mills) had already carried out some experimental work on the rates of vaporization of molten Fe-Ni alloys. The experimental work was done under conditions which make it possible to compare the experimental rate data with those predicted on theoretical grounds. EXPERIMENTAL The object of the experiments was to evaluate the activities in a number of binary metal systems. The details of the experimental technique are given in another paper by Mills, Kinoshita, and Grieveson,2 and, for the present purpose, a brief mention of the relevant features of the experimental method will be adequate. Using an induction coil, the metal weighing about 1 to 1.5 g was levitated by the electromagnetic field in a stagnant atmosphere of pure helium. The helium was freed from oxygen and water vapor in the usual manner, and its pressure in the vaporization chamber was maintained at 1 atm through a bleeder device. The vaporization chamber consisted of a pyrex tube, 2.8 cm diam, with a side arm connected to the helium bleeder. The bottom of the tube, shaped conical, was surrounded by the induction coil, and the top was sealed with an optical flat for the purpose of measuring the melt temperature with a two-color optical pyrometer. By suitable adjustment of the high-frequency power input, the metal was brought to the desired temperature in about 30 sec of levitation. After a specified vaporization time, e.g., 3 to 4 min, the alloy was quenched by switching off the power. The amount of metal vaporized was determined from the difference between the initial and final weights of the sample. During the vaporization time, temperature fluctuations of about ±10°C were observed. COMPARISON OF EXPERIMENTAL DATA WITH THEORETICAL VALUES The experimental results are given in Table I. As already mentioned, the attainment of the vaporization temperature took about 30 sec from the moment of levitation. Therefore, the times recorded in Table I are 30 sec less than the total time; this is considered to be a reasonable estimate of actual vaporization times.

Jan 1, 1964

By D. B. Jugle, J. B. Darby, O. J. Kleppa

A systematic study has been made of the kinetics of solution under steady state, dynamic conditions of titanium, vanadium, chromium, iron, cobalt, and nickel in liquid aluminum. It was found that the temperature dependence of the solution rate obeyed an Arrhenius-type rate equation, and that at a given temperature the rate of solution of the various solutes correlates quantitatively with the equilibrium solubility of the solute in liquid aluminum. These results are consistent with a mechanism where the rate-controlling step is the diffusion of solute atoms through a liquid boundary layer. THE present study was initially started in order to explore the feasibility of liquid-metal solution calorimetry for transition metals and alloys. Previous work1 in this field employing liquid tin as a solvent at temperatures in the 500' to 600' range had indicated that the rates of solution of most transition metals in tin are very low. Under such conditions effective solution calorimetry is difficult. The objective of the present investigation was two-fold: a) To obtain, as far as possible, quantitative data on the rates of solution of a series of transition elements in liquid aluminum. b) To explore whether liquid aluminum might be a suitable solvent for liquid-metal calorimetry. In the course of this work a comprehensive set of data was obtained on the steady state rates of solution of transition metals in a common liquid-metal solvent. The results are consistent with the boundary layer model, which assumes that the rate-controlling step consists of diffusion of solute atoms through a viscous liquid layer. EXPERIMENTAL PROCEDURE A vacuum-tight stainless steel vessel was surrounded by a resistance furnace, as shown in Fig. 1. In all experiments the temperature of the liquid solvent was controlled to 2.5' by means of a Micromax controller. A high-vacuum manifold connected to the vessel maintained a vacuum of 1 x 105 mm of Hg or better. The vacuum vessel was equipped with a charging section isolated from the working chamber by a vacuum-tight gate valve. This arrangement allowed the specimen holder to be removed or inserted into the apparatus without removal of the liquid metal bath. The specimen holder was suspended from a closed end stainless steel tube, which also served as the thermocouple protection tube. The portion of the tube that was below the solvent level was surrounded by an alumina protection tube to isolate it from the liquid metal bath. The stainless steel tube was connected through a rotary vacuum seal and a gear train to a fractional horsepower motor. For most experiments the tube was rotated at a constant

Jan 1, 1963

By Enid C. Plante

INTRODUCTION To extend our knowledge of the flotation behavior of sulphide minerals, the response of the following minerals to ethyl xanthate as collector was studied by captive bubble and cylinder flotation tests: antimonite (Sb2S3), arsenopyrite (FeAsS), covellite (CuS), marcasite (FeS2), orpiment (As2S3), pyrrhotite (FeS) and tetrahedrite (4CU2S, Sb2S3). Lollingite (FeAs2) was also examined to determine if its behavior could be correlated with that of pyrite or marcasite (FeS2). EXPERIMENTAL METHOD Mineral for Flotation and Contact Tests Mineral was prepared in the manner already described' and its behavior both freshly ground and "oxidized" was studied. Tests in which the mineral was allowed to oxidize for various periods showed that a uniform response to xanthate was reached in two days or less. Oxidation Products The soluble oxidation products from most of the above minerals were measured and their effect on the flotation of the mineral studied. The mineral samples were wet ground to minus-52 mesh and deslimed, and 20 g of this material placed in 200 ml of distilled water of a measured pH value, and C02 free air bubbled through each suspension at a constant rate (about 1 bubble/sec) for 5 days. It has been shown1 that the size of the mineral is unimportant in the rate of formation of oxidation products and that probably the supply of oxygen to the mineral is the rate-determining step. At the end of 5 days the pH value of the supernatant liquid was measured again, the mineral filtered off and the soluble products determined. Methods for estimation of sulphur acids, ferrous and ferric iron and copper have already been described.1 No satisfactory method was found for antimony. Arsenic was estimated as the arsenate.2 FLOTATION OF "UNOXIDIZED" MINERALS WITH ETHYL XANTHATE AS COLLECTOR Fig I to 3, 4, 6, show the effect of alkali and cyanide as depressants for the minerals with 25 mg potassium ethyl xanthate per liter as collector at 35°C. Wark and Cox3 have shown that with ethyl xanthate as collector, galena, pyrite and chalcopyrite show a greater tolerance to cyanide and hydroxyl ions at room temperature than at 35°C. Covellite (Fig I), marcasite (Fig 2) and pyrrhotite (Fig 3) behave similarly. The independence of the curves for pyrrhotite at 35°C with respect to cyanide

Jan 1, 1947

By Leonid V. Azároff, H. N. Murty

In the course of investigating the soft X-ray absorption spectra of Ni-A1 alloys, Das and ~zfiroff' observed an anomalous brittleness in solid solutions containing 3 to 5 at. pct Al. The brittle alloys also had anomalously larger lattice constants' and the fine structure at the nickel K edge of an alloy containing 3.96 at. pct A1 unexpectedly resembled that of NiA1 more closely than that of a solid solution containing 5.51 at. pct Al. This led them to suggest the possibility that short-range ordering was produced during the homogenization anneal to which each specimen was subjected, similar to that observed in dilute solutions of vanadium and of chromium in nickel: as the principal cause of embrittlement. It was decided to repeat the above measurements on several alloys in this composition range in order to test the above hypothesis and to establish the effect of heat treatment on the alloys' properties. Three solid solutions in this range were prepared containing, respectively, 3.16, 4.00, and 4.54 at. pct Al, in addition to alloys containing 6 and 9 pct. All samples were annealed in vacuum at 1800°F for 100 hr and then furnace-cooled to room temperature, as in the original study. The lattice constants of these alloys are shown by open circles in Fig. 1 and can be seen to fit quite closely the curve established by the previously measured values, indicated by solid circles. (The experimental errors are of the order of the size of the circles, +o.oo~R.) The three alloys containing 3 to 5 at. pct A1 were found to be quite brittle, as previously reported. In order to test the possibility of ordering, these three solid solutions were again heated to 1800°F and, following a few hours at that temperature, were quenched directly to room temperature. All three alloys lost their brittleness. In order to verify the proposed ordering hypothesis, it was decided to subject each sample to several cycles of quenching and annealing (disordering and ordering). After some experimentation, it was established that reproducible results could be obtained by anneal-

Jan 1, 1968

By J. B. Newkirk, R. W. Hendricks, R. Baro

STUDIES of the kinetics of precipitation in binary alkali halide systems are of interest from a theoretical point of view, because of the possibility of controlling diffusion rates by additions of aliovalent impurities. This note reports some preliminary results of a study of the kinetics of precipitation of AgCl from supersaturated solid solutions of AgCl in NaCl containing trace amounts of divalent cation impurities. In their study of the system NaC1- AgC1, Stokes and Li1 derived the phase diagram containing a mis-cibility gap with a broad maximum at approximately 170°C. They found that single crystals quenched from above the miscibility gap and aged at various temperatures within the two-phase region gradually turned light blue, then cloudy white, and finally opaque. The rate of transformation depended markedly on the aging temperature. The light-blue color in the early stages of aging was interpreted to be the result of Rayleigh scattering from precipitated particles less than 0.1 µ in diameter. These qualitative observations have been confirmed by us. However, a more precise tool was needed in order to quantitatively follow the growth kinetics of the precipitate particles. Because of the suspected small size of the precipitate particles and for other reasons, small-angle X-ray scattering was thought to be a suitable technique for this study. Small-angle X-ray intensities scattered from powder specimens were recorded on a General Electric XRD-5 diffractometer using the four-slit geometry described by Neynaber, Brammer, and Beeman.2 The slits were 0.08 mm wide by 10.00 mm high. It was found that, with very careful alignment, meaningful data could be obtained to within 3 min from the middle of the direct beam. Chromium radiation (?Ka = 2.29Å) was used in order to spread the scattered intensity to a relatively high angle, as indicated by Eq. [1]. A specimen containing 21.0 at. pet AgCl was prepared by melting analytic reagent-grade AgCl and NaCl under a chlorine atmosphere in a vycor cap-

Jan 1, 1964

By D. G. Westlake, E. S. Fisher

The habit planes for zirconium hydride precipitation in crystals of a zirconium have been determined at various hydrogen concentrations. The (10 • 0)planes are the predominant habit planes; some (10 • 5) and (10 -1) planes were observed after charging conditions which pevmitted formation of a surface layer of hydride. No platelets zrlere observed parallel to any of the twinning planes. Mechanisms for em-brittlement due to hydride precipitation are discussed. LANGERON and Lehr1 found, in 1956, that zirconium hydride precipitates in zirconium in platelets lying parallel to (10.0) slip planes. In 1960, Kunz and Bibbz reported observing the platelets in three different families of twinning planes, (10.2) {11.1), and {11.2), but never in the slip planes. The present study was undertaken to ascertain the cause of these seemingly contradictory results. EXPERIMENTAL Two specimens of iodide zirconium were used in the experiments. Specimen I was a single crystal, while specimen II contained three grains. Grain growth was accomplished by the technique of Lange-ron and Lehr. Three faces were ground on specimen I; the first was 2 deg from the (00.1) basal plane, a second was 2 deg from the (10.0) prism plane, and a third was 4 deg from the (12.0) plane. One face was ground on specimen II such that the poles of the surfaces of crystals A, B, and C were as shown in Fig. 1. After the faces were ground on 600 grit silicon carbide paper, they were chemically polished by dipping in a solution of 8 parts hydrofluoric acid, 50 parts nitric acid, and 50 parts water. This removed all cold worked metal from the surface. The samples were charged to various levels of hydrogen content by heating in hydrogen gas which had been purified by reaction with uranium powder. The various charging conditions are shown in Table I. Specimen I was heated to the reaction temperature at the indicated hydrogen pressure and allowed to react until essentially all the hydrogen was used up. Then the temperature was raised for homogenization. Specimen II was charged by making periodic addi-

Jan 1, 1962

By H. S. Price, J. E. Warren

Techniques for studying the performance characteristics of heterogeneous reservoirs have been developed. The effect of permeability variation on both the steady-state and the transient flow of a single fluid has been investigated. Limited comparisons with field and laboratory data have been made. The physical models studied consist of random three-dimensional arrays of homogeneous porous blocks. The permeabilities of the individual elements are assigned according to a specific distribution function; uniform anisotropy is introduced by varying the relative dimensions of the blocks. A particular model is perturbed simply by re-arranging its elements at random. The behavior of a physical model is determined by digitally solving its numerical analogue. Based on computational experiments, subject to the restrictions implied by the assumptions that were made, the following general conclusions have been drawn. 1. The most probable behavior of a heterogeneous system approaches that of a homogeneous system with a permeability equal to the geometric mean of the individual permeabilities. 2. The effects of flow geometry and anisotropy on the most probable value of the effective permeability of a heterogeneous medium are finite but not significant. 3. The permeability determined from a pressure build-up curve lor a heterogeneous reservoir gives a reasonable value for the effective permeability of the drainage area. 4. A qualitative measure of the degree of heterogeneity and its spatial configuration are obtained from a comparative study of core analysis and pressure build-up data. It has been indicated that these conclusions are predicated on the assumption that the core analysis and the pressure build-up data represent true reservoir characteristics. Common sources of error in these data have been discussed. One of the most significant problems of reservoir engineering is that of determining the nature and the disposition of the heterogeneities that inevitably occur in petroliferous formations. It is with this problem that this paper is concerned. Extensive research, both theoretical and experimental, has provided reasonable descriptions of the physical processes that are associated with primary and secondaryrecovery mechanisms. Similar progress in the fie1d of numerical analysis and the evolution of truly high-speed digital computers have made it feasible to calculate the behavior of these mechanisms under almost any environmental conditions. It appears to be logical, then, to conclude that the mechanistic performance of any reservoir can be predicted with some confidence. Unfortunate1y, a necessary condition for the validity of this conclusion is that the formation be adequately described in a macroscopic sense. This condition cannot be satisfied ill general; therefore, a frustrating situation currently exists — it is possible to compute the effect of reservoir heterogeneity on behavior, but it is not possible to specify the heterogeneity itself. In many cases, the predicted behavior of a project is so completely dominated by irregularities in the formation's physical properties that the gratuitous assumptior, of a particular form for the variation can reduce the solution of the problem to a mere tautological exercise. While all porous media are microscopically heterogeneous, only macroscopic fluctuations need be considered since the fundamental concepts of reservoir mechanics are based on macroscopic quantities. For the simplest case in which only one physical property varies from point to point, the degree of heterogeneity that is apparent depends on three distinct factors, i.e., the nature of the property's variation (frequency distribution), its disposition (spatial distribution) and the inherent stability of the mechanism being studied. Consequently, any attempt to devise an unambiguous scale of heterogeneity must take these factors into account. Since this investigation is intended to be exploratory, it will be restricted to single-phase flow because of the simplification implied; both steady-state and unsteady-state behavior will be considered. Furthermore, to keep the number of parameters

By E. L. Claridge, K. S. Lee

Areal sweep efficiency of oil displacement by enhanced-viscosity water exhibiting pseudoplastic behavior was measured in a Hele-Shaw model representing one-quarter of a five-spot pattern. The pseudoplasticity of polymer solutions and the velocity distribution in the five-spot pattern produced a condition under which the mobility ratio between the displacing and the displaced fluid could not be assigned a single value. Instead, the movement of the displacement front is governed by local mobility ratios which are also time dependent. The areal sweep at breakthrough with polymer solutions was poorer than the sweep obtained with Newtonian fluids of comparable viscosity. However, the areal sweep at 1 PV throughput was greatly improved as compared to flood water without polymer. It was also demonstrated that, even after the oil-cut had declined to a low value during a regular waterflood, switching to polymer flood efficiently swept out the oil remaining in the model. INTRODUCTION The behavior of fluid displacements in isotropic porous media for various patterns of injection and production wells has been extensively investigated.1-7 These investigations all concerned Newtonian fluids, i.e., the viscosity of each fluid was constant regardless of flow rate. The generally unfavorable influence on areal sweep efficiency of higher mobility of the displacing fluid as compared to the mobility of the displaced fluid has been established for both miscible and immiscible fluids. The principle was also established that a close correspondence exists between miscible and immiscible flood front behavior,2, 3 although oil recovery in a waterflood at unfavorable mobility ratio may be less than that observed in a miscible displacement at the same mobility ratio. This is true even when oil recovery is expressed on the basis of movable oil. The reason is that oil saturation only slowly achieves its final value behind the water-flood front in accordance with the Buckley-Leverett8 simultaneous flow relations. It is convenient to use miscible displacements for laboratory simulation of waterflood frontal advance since the interfacial tension forces which are negligible in proportion to viscous forces on a reservoir scale9 are thus made nonoperative in the laboratory model. For miscible displacements, the Hele-Shaw type of model adequately represents a porous medium so long as the appropriate scaling rules5-10 are observed in its design and operation. During simulation of waterflood front behavior in the laboratory by using miscible displacements, the behavior of connate water may ordinarily be disregarded since it is usually indistinguishable from flood water in this process. However, when the flood water is deliberately thickened to improve the mobility ratio between water and oil. the effect on the sweep efficiency due to generation of a connate water bank during the process must be considered. In a uniform porous medium, such a bank is generated11 and efficiently displaced by injection of thickened water.l2 The oil originally in-place at the start of the waterflood is then displaced by connate water followed by thickened water. If the flood water must be thickened to obtain a favorable mobility ratio, the mobility of the oil phase is appreciably less than that of the connate water. Hence, the oil phase is inefficiently displaced by the connate water bank, and a considerable proportion of the oil comes in contact with and is displaced by the thickened waterflood front' A recent study 12 of five-spot displacements using miscible Newtonian fluids in which connate water banks of various sizes were simulated shows that, for connate water banks as large as 40 percent of 1 PV, major improvements in sweep efficiency resulted from use of a thickened

Jan 1, 1969

By H. Majima, E. Peters

The oxidation rates of pyrite, pyrrhotite, chalcopy-rite, chalcocite, covellite, bortzite, galem, sphalerite, and stibnite have beet2 carefully compared at 120 oC, using aqueous phosphate solutions buffered at pH 2.7, 7.1, and 11.2 as zvell as in 1.0 M NaOH and in am~onia-containing solutions. Under conditions of these studies, variations in rates of more than a factor of two per unit of mineral surface area were not observed for different minerals in phosphate buffered solutions, except that pyrrhotite showed unusually rapid oxidation rates In acid solutions, and stibnite showed very rapid oxidation rates in basic solutions. In caustic solutions, oxidation vates varied considerably, the most rapid being for pyrite and the slowest for sphalerite. In the presence of ammonia, only copper minerals showed more vapid oxidation rates in neutral solutions. Oxidation rates were measured on the basis of oxygen-consunzption rates per unit surface area of exposed mineral, using equivalent surface areas, mineral mesh sizes, pulp densities, agitation, and oxygen pressure. OXIDIZING pressure leaching of sulfide minerals has been a commercial method of treating concentrates of nickel, cobalt, and copper for over a decade, and recently the treatment of lead and zinc concentrates,' and even the recovery of sulfur from pyrrhotite by such processes, have been shown to be technically feasible.' Furthermore, the leaching of uranium ores by solutions acidified through the oxidation of pyrite and other sulfides present in the ore is commercially practicable.3 5 The mechanisms by which sulfide minerals oxidize in aqueous environments are not yet understood. However, certain generalities can be made for systems containing no unusual reagents, in which oxygen is the oxidizing agent. In acid solutions the oxidation of many sulfide minerals leads to the formation of elemental sulfur.8'7 The attack of some sulfides, notably galena (PbS), sphalerite (ZnS), and pyrrhotite (FeS), at temperatures below about 110°C leads to an almost quantitative conversion of the sulfide mineral to elemental sulfur according to the equation: On the other hand pyrite (FeS2) and copper minerals do not yield elemental sulfur quantitatively. Not more than 50 pct of the sulfur in pyrite is converted to the elemental form in acid oxidation, and this percentage is lowered by higher temperatures and possibly higher oxygen pressures.8'9 Copper minerals sometimes yield elemental sulfurlo'" but, since sulfur can reduce cupric ions with the precipitation of CuS or Cu2S, it is not likely that elemental sulfur is obtained in good yield. In acid solutions sulfur that is not converted to the elemental form always appears as sulfate salts or sulfuric acid. Sulfide minerals that yield elemental sulfur nearly quantitatively on oxidation in acid solutions tend to generate H2S when the conditions are not oxidizing. However, although it has been suggested that H2S is an essential intermediate in the mechanism of oxidation," this is doubtful because it is oxidized very slowly by oxygen. In basic solutions elemental sulfur is never formed, as predicted by thermodynamical considerations, summarized in the form of a potential-pH diagram in Fig. 1. However in neutral and basic solutions, unstable forms of sulfur not shown in the diagram appear during oxidation, notably thiosulfate (SOT-) and polythi-onates (S,O;-, x = 2 to 6).l3,l4 On prolonged oxidation only hexavalent sulfur as sulfate (SOi-) or sulfamate (NHzSO;) is found to remain, the latter appearing only in the presence of ammonia. The oxidation kinetics for thiosulfate by oxygen are the subject of a separate paper,'5 and were studied on the presumption that thiosulfate may, in fact, be a primary oxidation product for sulfide minerals, at least in neutral and basic solutions. A survey of the literature indicated that comparative oxidation rates for different sulfide minerals were needed to establish the role of the mineral structure and its thermodynamic properties on the oxidation rates and mechanisms.

Jan 1, 1967

By D. J. Freeh, W. E. Horst, R. C. Kellner

This paper is concerned with the description of grinding characteristics in a batch grinding system. A mathematical model was developed and used for simulating the system on an analog computer. A general equation describing the change of selected size fractions with respect to time is presented. The empirical verification of the model is discussed. In order to understand the performance of a grinding system, it would be desirable to have a mathematical description of the system's behavior. The development of a mathematical model to describe the performance of a batch dry-grinding operation was investigated. This is the first step toward reaching the objective of a practical mathematical description of a grinding system that could be employed for process control and optimization of a simple or complex grinding circuit. Although this article is concerned only with batch grinding performance, experimental work is being conducted to extend the model to continuous grinding systems. BASIC PROCESS CONSIDERATIONS In a paper dealing with the probability theory of wet ball milling, Roberts1 correlated the rate of change of oversize material, C, with energy input, E, as follows where the energy input is expressed in power/unit mass and k is a constant for each particle size. Experimental grinding studies were made by Bowdish2 to extend the previous work of Roberts. The work of Bowdish also showed that the rate of breaking of oversize particles in a ball mill is proportional to the concentration of oversize particles present. He further demonstrated that breaking of oversize particles is proportional to the surface area of the balls used for grinding. Rate equations were presented and it was concluded that grinding could be considered as a first order phenomenon according to the rate equation [2] di which is in accordance with Eq. 1. In Eq. 2, the effect of ball area is included in the constant k,. Other rate equations were reported to show the effect of a change in ball area and removal of fines during grinding. Correlation studies made by Arbiter and BhranY indicate a first-order rate equation for quartz; however, their data showed less than first-order rates existed for some of the other materials evaluated. More recently Kelsall4 has shown that the rate of breakage of any narrow size range of quartz could be described by a first-order rate equation. Several other investigators5-7 have described grinding behavior in terms of rate equations or kinetics. In general, the rate equations have been described for each particle size; however, the interactions between sizes and the overall relationships that exist have not been considered, at least not in the form of solving a group of simultaneous differential equations. Extensive work has been conducted by various investigators using a probabilistic approach which has expanded stein's' earlier work. Selection and breakage matrices are incorporated in the probabilistic model as contrasted with the deterministic method presented here. A batch grinding operation may be considered as an unsteady-state process from the standpoint that the conditions within the mill are a function of time. Therefore, a plot of mass fraction of the i-th size versus time would give a set of curves as shown in Fig. 1. In these curves X , represents the mass fraction of large size material, X2 intermediate size, and X3 small size material. An examination of these curves shows a strong similarity to the curves that would be obtained from a chemical reaction of the type9 A?B?C, [3] where A would be comparable to the largest size material being broken to an intermediate size, 3, and

Jan 1, 1968

By C. van der Poel

When oil is displaced from a horizontal formation by another fluid of lower density, the latter tends to override the former in the shape of a tongue owing to gravity segregation. This gravity tongue has an adverse influence on the oil recovery. If the fluids are miscible, diffusion (mixing) takes place at the interfacial boundary of the gravity tongue. This mixing should have a favorable effect on oil recovery. The report describes a laboratory study of the magnitude of the mixing zone under various conditions, so as to assess the effect of diffusion on oil recovery both in laboratory experiments and under actual field conditions. The technique used enables visual observation and measurement of the size of the mixing zone in transparent glass-powder packs. The results show that in experiments in small models and cores the width of the mixing zone may well be of the same order of magnitude as the height of the model. In such cases oil recovery is favorably affected by mixing. It can further be concluded that, under conditions prevailing in the field, mixing of the injected fluid with reservoir oil is equal to that caused by molecular diffusion alone, eddy-mixing not taking place to any appreciable extent. A simple calculation, then, shows that molecular diffusion is too small for a beneficial effect to be expected from the injection of miscible fluids in horizontal or nearly horizontal reservoirs unless pay zones are thin. INTRODUCTION This paper gives results of experiments made on the mixing which occurs when a miscible displacement is carried out in a horizontal reservoir. This mixing takes place at the interfacial boundary of the gravity tongue formed when the lighter injected fluid overrides the oil present in the reservoir. The object of the experiments was to simulate the field case where, for example, propane with a viscosity of 0.075 cp under reservoir conditions displaces an oil of viscosity 0.6 cp. In the experiments the lighter fluid had a viscosity of about 1 cp and the heavier one a viscosity of about 8 cp, so as to obtain the same viscosity ratio. In order to enable the results to be compared with those published in the literature, a set of experiments with viscosity ratio equal to one was also performed. EXPERIMENTAL TECHNIQUE The technique developed for the purpose enables the width of the mixing zone to be studied as a function of time and place. A glass-powder pack is saturated with a water-glycerine mixture of suitable viscosity, which represents the reservoir fluid. The pack is then rendered transparent by dissolving sufficient ammonium thiocyanate in the mixture to obtain a solution with a refractive index matching that of the glass powder. Alkaline water to which phenol-phthalein has been added is used as the lighter and less-viscous displacing fluid. In those places where mixing or diffusion of the two liquids occurs, the slightly acidic ammonium-thiocyanate solution neutralizes the alkali in the water, and the glass pack shows up white against the red-colored invading water. If a black cloth is hung over the back of the apparatus, the transparent part of the glass pack appears black. In this way the position of the two phases and the transition zone between them is clearly visible, as shown in Fig. 1 (where the red-colored invading water is the grey-shaded zone lying uppermost). In all experiments the amount of alkali in the water was chosen such that the upper contour corresponded to a concentration of 5 per cent of the dense liquid. The lower contour is determined by the size of the glass grains and the thickness of the pack and, consequently, varies from experiment to experiment. Corresponding concentrations of the dense liquid range from about 97 per cent for packs of small grain size (permeability = 1 darcy) to about 95 per cent for those with large grains

By Peter Beardmore, Michael B. Bever

The effects of the temperature of deformation and the degvee of deformation on the annealing spectrum of a Au-Ag alloy have been determined by vesistance measurements. Specimens were deformed in torsion at 4°, 78K and room temperature up to strains nd/l of about 1.0 and were isochronally annealed. Discrete annealing stages similar to those found for pure metals were observed. Stage A occurred below room temperature; the decrease in reszstance associated with this stage increased as the temperature of deformation was lowered or the strain was increased. Stage B manifested itself as an increase in resistance; this is attributed to the restoration of short-range order promoted by vacancy or vacancy aggregate migration. At temperatures above 48S0K, recrystallization or Stage C occurred. Stages A, B, and C in the annealzng curves of this alloy may be considered to correspond to Stages II, Ill, and V, respectively, in the terminology used to describe the annealing spectrum of pure metals. ThE annealing behavior after deformation below room temperature has been thoroughly investigated on pure metals, in particular gold and copper. The occurrence of several discrete stages in the annealing spectrum of these metals has been established, but the interpretation of some of these stages in terms of specific mechanisms is still controversial.' The annealing of alloys deformed below room temperature has been the subject of only a few investigations. In the investigation reported here, a Au-Ag alloy was annealed after deformation at and below room temperature. This continues a research program on the deformation and annealing behavior of Au-Ag alloys.2-8s EXPERIMENTAL PROCEDURE An alloy rod of composition 82.6 wt pct Au-17.4 pct Ag was reduced to wire, 0.0428 in. diam, by swaging and drawing. After a recrystallization treatment, the grain size was 0.031 mm, as obtained from the average linear intercept.7 The ends of wires about 6 in. long were flattened and sealed into short brass tubes with cold setting cement to form the grips of the torsion specimens. The equipment used for deformation has been described elsewhere.6 The specimens were deformed at room temperature, 78", and 4°K to various strains nd/l, where n is the number of turns, d the diameter of the specimen, and 1 its length between grips. The strain rate ?max was 0.1 min-' at the sur- face of the specimen except where noted otherwise. The specimens were annealed isochronally for 30 min at intervals of approximately 30°K from the temperature of deformation to approximately 800°K, except that after deformation at 4°K the lowest annealing temperature was 78°K. A potentiometric method was used to measure the resistance: all measurements were made at 78°K with the exception of some measurements at 4°K mentioned below. Data obtained with a single specimen yielded a complete annealing curve: in several cases duplicate specimens were used to confirm the reproducibility of the curves. Since the surfaces of the specimens were rough after deformation, their diameters could not be measured accurately. The resistance increments after deformation and annealing are therefore reported as percentages of the resistance of the same specimen measured after completion of the annealing, that is, after full recrystallization. The corresponding resistivity values can be calculated by obtaining the effective diameter of a deformed specimen from the ratio of its resistance after recrystallization to the true resistivity, which was determined with a smooth specimen of known dimensions. This method of calculation was used to obtain data shown in several of the figures. RESULTS AND DISCUSSION The isochronal annealing curves after deformation to various strains at 4", 78K, and room temperature are shown in Figs. 1, 2, and 3, respectively. The resistance increment of the as-deformed specimens as a function of strain is shown in Fig. 4. For the specimens deformed at 4°K. values measured at 78°K are plotted with the exception of those for the as-deformed

Jan 1, 1970

By A. J. Griest, P. D. Frost, H. A. Robinson

The flow characteristics and uniform elongation of alpha-beta titanium alloys in the solution-treated condition were shown to be markedly affected by the solution temperature. Two classes of alpha-beta alloys were distinguished, based on the effect of solution temperature on the uniform elongation. Martensitic alpha-beta alloys, which are relatively weakly beta-stabilized, showed decreasing values of uniform elongation as the solution temperature was initially increased. However, after solution-treatment at still higher temperatures in the alpha-beta field, the uniform elongation of these alloys was again high, and often attained its maximum value. Nonmartensitic alpha-beta alloys, which are more heavily beta-stabilized, showed a continuous decrease of uniform elongation with increasing solution temperature. The behavior was rationalized in terms of the alpha-beta ratio and the alloy content of the beta existing at the solution temperature. The data indicate that in commercial practice close temperature control may be required to get maximum uniform elongotion, and hence, maximum potential formability, in solution-treated sheet. Bend-test data also were obtained for the solution-treated conditions. A MOST important objective of current titanium research is the development of age-hardenable alloys with superior formability in the solution -treated condition. Alpha-beta titanium alloys have been shown to be amenable to high-strength aging treatments after solution-treatment in the alpha-beta field.' However, heat-treatment data on the properties of solution-treated sheet, such as uniform elongation, minimum bend radius, and flow properties, which have a bearing on the potential formability, have not been widely available. This paper presents only the most significant results of a research program conducted at Battelle for the Air Force in an effort to develop sheet alloys that can be formed readily as solution-treated and subsequently aged to very high strengths. Data for 10 compositions representative of the more than 25 alloys studied in this program are presented. A primary objective of the paper is to demonstrate the pronounced dependence of the flow characteristics and uniform elongation on solution-treatment temperature. This effect is believed to be vitally important in the commercial heat-treatment of age-hardenable titanium sheet alloys. Experimental Procedures Melting and Fabrication—The nominal and actual compositions, beta transi temperatures, and rolling temperatures of 10 of the 30 alloys studied are presented in Table I. Stock :€or two of the alloys, E (Ti- 8Mn) and J (Ti-6A1-4V) was obtained from commercial heats. The remaining heats, except D and I, were double melted as 10-lb heats in a consumable-electrode furnace. Melting stock was 120 Brine11 hardness sponge. The oxygen and hydrogen analyses spotted throughout the heats indicate the range of interstitial levels resulting from the melting practice used. Heats D and I were melted as 20-lb ingots with the same grade of sponge. These ingots were cut in half and one portion used in the present evaluation. The ingots, which were about 4 in. diam and 4 in. in height, were upset forged and drawn at 1750°F to sheet bar 5/8 in. thick by 2 1/2 in. wide in such a manner that the top of the ingot corresponded to the top of the sheet bar. Slabs of the sheet bar, 5 1/2 in. in length were scalped to 1/2 in. thickness and rolled at the temperatures indicated in Table I to approximately 0.055 in. sheet. Elongation during rolling took place at 90" to the original forged length. The fabrication procedure used is described in some detail since the experimental heats showed considerable directionality in mechanical properties. The rolling procedures for the commercial heats were unknown, but were such as to produce essentially isotropic properties. All heats, as rolled, showed microstructures typical of alpha-beta alloys worked in the alpha-beta field; that is, the structures consisted of equiaxed alpha particles in a beta matrix. Heat Treatment— The effects of solution and aging heat-treatments on the properties of the alloys were evaluated uSing longitudinal and transverse tensile and bend coupons sheared from the sheet. Two or three solution-treated conditions were evaluated for each alloy. In addition, the alloys were also tested after annealing at 1200°F for 4 hr and furnace cooling. The solution-treated and annealed conditions were those in which the alloys might be expected to

Jan 1, 1959

By D. L. McDanels, J. W. Weeton, R. W. Jech

An investigation was conducted to determine the stress-strain behavior and tensile properties of metallic composites and to relate them to the properties of the base materials. Tungsten fibers in a copper matrix were chosen as the model sys-tem to investigate these properties. Room-temp-atzcre tensile and dynamic -modulus tests were used To meet the demand for improved structural materials, considerable effort is being directed toward the creation of composite materials. One such material under investigation is the fiber-reinforced composite, in which a ductile, relatively weak matrix is reinforced with high-strength fibers. Some work has been done on the reinforcement of metallic matrices with metallic fibers1"5 as well as with ceramic-whisker reinforcement. Summaries of much of this work have been published by Mach-lin7 and Baske~.' Work done at the Lewis Research Center of NASA-" has involved the making and testing of composites composed of a fiber, tungsten, and a matrix, copper, which were insoluble in each other. An equation was presented that showed the relation between the ultimate tensile strength of the composites and the strengths and relative volume percents of the components. This relation was verified experimentally for composites containing fibers extending the full length of the specimen as well as for composites reinforced with short-length or discontinuous fibers. Since the publication of the preliminary results,9'10 additional data have been obtained. This paper presents these data as well as analyses of the stress-strain behavior and the mechanics of deformation of uni-axially oriented, fiber-reinforced metallic composites, in which both components are mutually insoluble. EXPERIMENTAL PROCEDURE Composites were made with high-purity copper as the matrix and 3-, 5-, and 7-mil-diam tungsten wire as the reinforcing fiber. Some specimens were made in which the reinforcing fiber extended completely through the full length of the composite test section. The fibers were placed in ceramic to determine these properties. The composites were reinforced with either continuous or discontinuos tungsten fibers. The tensile properties and stress-strain behavior of composites reinforced with either type of reinforcement were similar, and in both cases the full strength of the fiber was utilized. tubes to insure axial orientation and infiltrated with copper at 2200°F for 1 hr. Composites were also made with short-length (3/8 in. long) 5-mil-diam tungsten fibers as discontinuous reinforcement and infiltrated under the same conditions. The reinforcing fibers in both cases were longitudinally oriented in the direction parallel to the tensile axis. Room-temperature tensile tests were conducted on the composites, stress-strain curves were obtained, and ultimate tensile strength and elongation were measured. Dynamic modulus of elasticity, based upon the resonant frequency induced in the flexural mode of vibration, was also determined for the composites and the components. A more detailed discussion of the experimental procedure employed in this investigation may be found in Ref. 11. RESULTS Room-temperature tensile tests were conducted on 3-, 5-, and 7-mil-diam tungsten wires which had been annealed for 1 hr at 2200°F and show the tensile strength of the wires to be 331,000, 327,000, and 290,000 psi, respectively. Since all the composites were infiltrated under these conditions, the strengths were considered to represent the strength of the fibers in the composites throughout this study. The average tensile strength of the annealed copper used as the matrix in this investigation was 27,800 psi. Results of room-temperature tensile tests on composites reinforced with 3-, 5-, or 7-mil-diam tungsten fibers are plotted as functions of composition in Fig. 1. These data represent previously reported datag,l0 as well as data more recently obtained. The line shown on each curve represents a prediction of tensile strength as a function of composition; the calculation of this line was explained in Refs. 9 and 10. A similar plot is presented in Fig. l(d) for composites reinforced with short-length, discontinuous 5-mil-diam tungsten fibers. Again, both the previously reported and the recent data are presented, and the line shown is identical to that shown for

Jan 1, 1965