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By Eric K. Albert, J. Kiusalaas

The paper presents an overview of SPASID (Kiusalaas and Albert, 1983), a new computer program developed under U.S. Bureau of Mines funding for the prediction of surface subsidence caused by under- ground mining operations. The presentation, which is illustrated with two case studies, also re-evaluates the influence function method as a tool of subsidence prediction, arriving at some rather unconventional recommendations. SPASID consists of four modules that communicate through common data bases: (1) Preprocessor. This module prepares and maintains the database for the entire site. The database contains all the information about the site and the mine operation that is necessary for the computation of subsidence. (2) Subsidence Predictor. The influence function method is used to predict the surface displacements that occur in any portion of the site that occur between two given dates. The computations take into account the time lag between extraction and displacement, and the effects of pitching seams and incomplete compaction at the edges of panels. The program contains i not he's influence function and the Green's function of transversely isotropic elasticity theory. (3) System Identification. The purpose of System Identification is to determine the optimal values of the various parameters associated with the influence functions in the Subsidence Module. System Identification requires measurements of subsidence from a site with a sirnilar overburden structure. The values of the subsidence parameters are obtained by minimizing the discrepancy between the measured and computed surface displacements. (4) Postprocessor. The Postprocessor is a graphics facility for displaying the data generated by the other program modules.

Jan 1, 1984

By Frank L. Nason

In the year 1904 an eminent Swedish geologist prepared a report on the iron-ore reserves of the world. His estimates follow: Countries. Tons. United States,.1,100,000,000 Great Britain,.1,000,000,000 Germany,.2,200,000,000 Spain,.. 500,000,000 Russia and Finland,...... 1,500,000,000 France,..1,500,000,000 Sweden,..1,000,000,000 Austria-Hungary,....... 1,000,000,000 Other countries,1,200,000,000 Total,.10,000,000,000 The iron-ore allotted to the United States by the Swedish geologist is barely sufficient to last 20 years at. the present rate of consumption. On the other hand (according to Edwin C. Eckel,' from whom the above and following statistics are quoted), there is hardly need for worry on the part of our iron industries for the next two centuries or more. Upon the basis of careful work by the U. S. Geological Survey, in which Mr. Eckel has taken an important part, the following estimates are definitely, but by no means finally, given for the United States: District. Tons. Lake Superior District,... 1,500,000,000 to 2,000,000,000 f red hematite,.. 1,000,000,000 Alabama, brown hematite, hematite, . 725,000,000 red hematite,.. 200,000,000 Georgia, { brown hematite, . 125,000,000 Tennessee, { red hematite,.. 600,000,000 Tennessee, { brown hematite,hematite, . 225,000,000 f red hematite,.. 50,000,000 Virginia, } brown hematite, . 300,000,000 Total,..4,725,000,000 to 5,225,000,000

Jan 1, 1913

By Clarence Linville

IN an article published in the Iron. Trade Review 1 I gave a convenient arrangement for the installation of wet and dry bulb thermometers for use in making moisture determinations in the air being blown into a blast furnace, and also gave a chart for use in obtaining moisture values from the thermometer readings. The data from which this chart was prepared were obtained from the tables in use by the U. S. Weather Bureau.2 The work of Carrier 3 has shown that these tables are somewhat in error. He has recalculated the values for moisture as referred to, wet and dry bulb thermometer readings, and he has prepared a psychrometric chart from the values thus obtained. This work has priced the subject of psychrometry upon a correct scientific basis. I think it is proper that we should recognize the importance of his work and give him credit for one of the most interesting and valuable researches that have been published in recent years. Blast-furnace men are not ready to use, as he suggests 4 a value expressed in grains of water accompanying a pound of dry air. However convenient this may be for heating and ventilating work and other engineering problems, there are several reasons for preferring the use of a value expressed in grains of water in a. cubic foot of mixed air and water vapor, in connection with combustion phenomena and the effects of moisture on blast-furnace operation. Previous papers presented to the Institute have used such values and we have

Jan 10, 1913

By Edward W. Parker, Marius R. Campbell

According to the estimates prepared by the U. S. Geological Survey, the area underlain by workable coal-beds in the United States is 496,776 sq. miles. Of this total area, 480 sq. miles contain the entire anthracite coal-fields of Pennsylvania. The bituminous coal-fields are estimated to be contained in areas, aggregating 250,051 sq. miles. The grade of coal between bituminous and lignite, and which is designated by the Geological Survey as " sub-bituminous," is estimated to be contained within areas aggregating 97,636 sq. miles, while the areas containing lignite aggregate 148,609 sq. miles. The coal-fields are divided, for the sake of convenience in classification, into six main provinces, as follows: 1. The Eastern. Province, containing the anthracite coal-fields of Pennsylvania and the bituminous coal-fields of the Appalachian region—namely, those of western Pennsylvania, Ohio, Virginia, West Virginia, Kentucky, Tennessee, Georgia, Ala bama, and small outlying areas in North Carolina. 2. The Interior Province, containing the bituminous coal-producing regions of Michigan, Illinois, Indiana, western Kentucky, Iowa, Kansas, Missouri, Oklahoma, Arkansas, and Texas. 3. The Gulf Province, containing the lignite-areas of Alabama, Mississippi, Louisiana, Arkansas, and Texas. 4. The Northern or Great Plains Province, containing the lignite and sub-bituminous areas of North and South Dakota, eastern Montana, and northeastern Wyoming. 5. The Rocky Mountain Province, containing the bituminous and sub-bituminous areas of western Montana and western Wyoming, Colorado, Utah, and New Mexico. 6. The Pacific Coast Province, containing the areas of Washington, Oregon, and California.

Jan 1, 1910

Writing the Technical Report, third edition, by J. Raleigh Nelson. McGraw-Hill Book Co. $4.50, 356 pp., 1952.-The aim of the book is to inspire a greater interest in report writing. Basis for the increased interest is a development of a keener understanding of the writer's own mental processes and the practical procedures involved in writing a report. The book is concerned with basic principles and procedures, rather than incidentals. It emphasizes the importance of correct attitudes and suggests a method of approach and organization. In the first part of the book, design and composition are considered. Next, the text gives directions for setting up both the long and short term report. The third part of, the book gives a systematic procecure for critical examination of the report. The fourth section presents a 16 week course in report writing. The Rocks of the Sekondi Series of the Gold Coast, by A T. Crow. Gold Coast Geological Survey. 7s. 6d, 73 pp., 1952.-The book describes the results of careful and detailed mapping of the Sekondi Series. The Sekondi-Takoradi area is undergoing intensive development, including extensions to Takoradi Harbor and to the railways. Details are given on the nature, extent, and structure of the Series and many faults which cut into them. The book is aimed at those with a practical interest in the area. It is illustrated with geological maps and drawings of horizontal sections. In the back, the terrain of the series is illustrated in a group of plates.

Jan 1, 1952

By Wilbur I. Duvall, Wilson Blake

The microseismic method of detecting instability in underground mines was developed by the U.S. Bureau of Mines (USBM) in the early 1940's. ,3 The method relies on the fact that as rock is stressed, strain energy is stored in the rock. Accompanying the buildup of strain energy are small-scale displacement adjustments that release small amounts of seismic and acoustic energy. These small-scale disturbances, which can be detected with the aid of special geophysical equipment, are called micro-seisims or self-gene rated rock noises. It was further determined that as failure of rock is approached, the rate at which rock noises are generated increases. Thus, by monitoring a rock structure at intervals and plotting rock noise rates vs. time, a semi quantitative estimate of the behavior and stability of the structure can be made. Since sufficient use of the microseismic method is still being made by various mining and construction companies, USBM undertook a comprehensive review of the method and a study of the fundamental properties of rock noises. As all prior work on rock noises has been done with resonant-type geophones, which prevented any analysis of their vibration records, it was necessary to develop the instrumentation and field techniques in order that their properties could be investigated, such as their frequency spectrum and absorption characteristics, and to determine if both P and S-waves are generated by a rock noise. The aim of this program is the design of microseismic instrumentation which can be better utilized as an engineering tool than the presently available microseismic equipment. This new design, based on the basic properties of rock noises, should allow better utilization of these phenomena in the study and location of zones of incipient instability in both underground and open-pit mines. EXPERIMENTAL PROCEDURE To study the waveform of rock noises, it was necessary to develop a microseismic system with a broad bandwidth. To achieve high sensitivity and broad frequency response, commercial ceramic accelerometers were used. The present broad-band microseismic system consists of accelerometers as geophones, low-noise preamplifiers, high-gain amplifiers, and an FM magnetic tape recorder. This seven-channel system has a flat frequency response from 20 to 10,000 Hz, a noise level of less than 2.0 kv, and a dynamic range (including manual set attenuation) of greater than 100 db; it can detect signals with acceleration levels as low as 2 ug. The entire system is solid state and hence battery operated and portable (Fig. 1) Analysis procedures consist of playing back the 30-in-per-sec (ips) magnetic tape recordings at 1 7/8 ips to expand the time scale of a recorded rock noise event and then recording this on a high-speed direct-writing oscillograph. The oscilIographic records are then digitized and run through Fourier integral analysis computer programs to determine the frequency spectrum of a rock noise event. The oscillographic records are also examined visually to determine if both P and S-waves can be recognized in a rock noise waveform. Broad-band microseismic recordings have been made at field sites in a wide variety of rock types and in both underground and open-pit mines. Sites include the Kimbley Pit, Ruth, Nev.; the Galena Mine, Wallace, Idaho; the Colony Development Mine. Grand Valley, Colo.; the Cliff Shaft Mine, Ishpeming, Mich; and the White Pine Mine, White Pine, Mich. DATA AND DISCUSSION Analyses of the recorded data have shown that rock noise frequencies are very broad. Fig. 2 and 3 show typical rock noise events and their frequency spectrums. In addition, it is evident from these figures that the wave form of a rock noise is very complex. The wide frequency variation, 50 to 7500 Hz, is due to many variables; the effect of travel distance is the only one examined in this study. The higher frequency components of the wave are rapidly absorbed with distance or increasing travel time. Fig. 4 shows the change in waveform resulting from an additional travel distance of 195 ft. From these data, it is apparent that a resonant-type microseismic geophone cannot respond to all frequencies generated by a rock noise, and in spite of the fact that the tuned geophone is more sensitive at resonance, a geophone with less sensitivity but broader band width is much more effective in detecting rock noises. In addition, a study of broad-band microseismic records shows that both P and S-wave arrivals are easily detected, as shown in Fig. 5. All records analyzed to date show that most of the energy is in the S portion of the wave; hence, microseismic geophones should be well

Jan 1, 1970

By Leonard L. Melton, Calvin D. Saunders

The design and performance of many operations common to the petroleum industry depend upon the unique properties of a class of materials known as non-Newtonian fluids. The art of measuring and describing these properties, called rheology, has fallen far behind the field applica-tion of these fluids in this industry. Empirical methods are still employed although theoretically sound methods of analysis are now available. This paper illustrates a completely general method of analysis of the rheological properties of non-Newtonian fluids which id independent of the type of viscometer employed and also the rheological type of fluid encountered except those of a thixo-tropic or rheopectic nature. Values of the rheological properties of a fluid obtained using this method of analysis are based upon an absolute scale of measurement, eliminating the necessity of employ-jng arbitrary concepts of the flow properties of non-Newtonian fluids, The fundamental nature of this method of analysis is further demonstrated by evaluating the precision with which measurements have been made of these rheological properties by employing a dimensionless criteric: —the Fanning friction factor-Reynolds number correlation. INTRODUCTION Non-Newtonian fluids are not new in the petroleum industry. Particular properties of non-Newtonian materials have been recognized and used to advantage in drilling fluids and have found excellent application in the hydraulic fracturing process.'.' While usage of these fluids is not new in this industry, the art of measuring and describing their rheological properties is still in its infancy. This is reflected in the accepted method of evaluating drilling fluids, API RP 29, (1950), which recommends a one point "viscosity" measurement. These shortcomings are recognized by various groups in the industry and more adequate methods have been prposed.3,4 The efforts Of these people are to be commended; but, at the same time, the limitations of their method of analysis and viscometer must be appreciated. This method Of analysis is applicable Only to Bingham plastic fluids as is pointed out early in their articles. The consistency of a Bingham plastic fluid must also lie within the range of the viscometer which is also well defined by the author. It is believed that the apparent simplicity of this method of analysis and the utility Of Operation Of their viscometer will soon make the terms non-Newtonian fluid and Bingham plastic fluid synonymous as used in this industry; a tendency which has already been encountered. Application of this method of analysis to a non-Newtonian fluid other than a Bingham plastic can lead to erroneous results. The field of rheology has long been hampered by the adherence to arbitrary concepts of Of of the flow properties Of non-Newtonian fluids. This has resulted in the design and operation of viscometers so as to fulfill these concepts rather than following the more logical method of analyzing experimental data so as to yield a fundamental truth. completely Bingham proposed the concept Of plastic flow and yield asu rement. data presented by Buckingham could hardly be interpreted so as to substantiate this theory; but rather succeeded in establishing the fact that compliance with this flow concept could never be realized in the capillary tube vis-cometer.5 Bingham, in reply, sug-gested "Rather than complicate our formula, it would seem to me a much better plan to so change the conditions of flow that the formula will be linear... Reiner0 stated .This plan has been followed by me in collaboration with Miss Riwlin. . . . From the present paper (Reiner and Riwlin, 1929) it will be seen that it is possible to choose the conditions of flow so that the formula based on Bingham's law of plastic flow remains linear. This is realized in the rotation viscometer," Thus, a viscometer, with design and operation based on the Reiner and Riwlin equation for plastic flow, is restricted to a specific range of flow

Jan 1, 1958

By David R. Poirier

THE activity of carbon in Fe-C-Cr liquid solutions has been measured by Richardson and Dennis,1 Fuwa and chipman,2 and Goto et aL3 Fuwa and Chipman2 have presented their data along with data of Richardson and Dennis1 and utilized an interaction parameter. However, the interaction parameter is only valid for dilute solutions of carbon, because, as indicated, the same interaction parameter does not apply to more concentrated solutions of carbon (i.e., the effect of chromium on the saturation of graphite in liquid iron). Ohtani4 has attempted to account for the effect of carbon concentration on the interaction parameter; however even his analysis does not apply to the saturation data. Also, the effect of temperature on interaction parameters must be taken into account. Therefore, in any process where the concentration of carbon and/or the temperature changes (such as solidification), the use of an interaction parameter is not adequate to know the activity of carbon. The purpose of this communication is to make use of the existing data on the effect of chromium on the activity of carbon in liquid iron solutions in such a way that the activity can be described as a function of both composition and temperature. The method is an extension of Rist and chipman's5 analysis for the binary Fe-C solutions. As in Rist and Chipman's analysis, the activity coefficient is assumed to obey the relation: log y1 = at(l -X1)2 + It [1]

Jan 1, 1969

By B. E. Eakin, A. L. Lee

Atmospheric pressure viscosity values For light hydrocarbons were calculated by a simple mixing rule based on the Sutherland constants for pure components. This method was further extended so that the atmospheric pressure viscosity of a mixture may be calculated based on the molecular weight information only. INTRODUCTION A proven method for estimating the gas-phase viscosity of a mixture is the one by Herning and zipperer.l This mixing rule has the following form: One method for calculating the pure component viscosity i is the Sutherland equation,2 which has the following form: The Sutherland constants B and S are determined from experimental data. A set of Sutherland constants for light hydrocarbons based on the data of several investigators3-5 is presented in Table 1. APPLICATION The Herning-Zipperer equation and the Sutherland equation were used to obtain an equation for calculating the gas-phase viscosity of light hydrocarbons. This equation has the form, Eq. 3 was used successfully in the study of methane-n-butane mixtures.6 Further analysis indicated that the Sutherland constants are a function of molecular weight.7 The gas-phase viscosity may be calculated based on molecular weight information only. The following equation was developed: The atmospheric pressure viscosity of ethane, propane, n-butaneand four methane-propane mixtures calculated on the basis of Eq. 6 are compared with the data of other investigators in Tables 2, 3, 4 and 5, respectively. A plot of atmospheric pressure viscosity vs molecular weight based on Eq. 6 is presented in Fig. 1.

Jan 1, 1965

By V. Runolinna, R. T. Hukki

Preliminary separation of precious metals by flotation can offer a simplification of the conventional method of treatment of anode slimes. Laboratory flotation experiments show that rich gold and silver concentrate can be obtained with excellent recoveries. THE purpose of this paper is to present the results of an investigation into the possibilities of separating precious metals from anode slimes by selective flotation. The work was carried out at the State Research Institute in Helsinki, Finland. The sample of anode slimes tested was submitted by the Outo-kumpu Co. in Finland. In 1947 the average assay of filtered and dried anode slimes in the Outokumpu refinery in Pori was as follows: Au, 0.50 pct; Ag, 9.38 pct; Cu, 11.02 pct; Ni, 45.21 pct; Pb, 2.62 pct; Fe, 0.60 pct; Sn, 1.00 pct; Sb, 0.04 pct; As, 0.70 pct; Se, 4.33 pct; S, 2.32 pct; SO,, 2.17 pct; SiO2, 2.25 pct. The daily assay naturally varies considerably from the figures presented above. The present conventional method of treatment of anode slimes consists of the steps shown in the flowsheet in fig. 1. As seen from this simplified flowsheet, the present method of treatment involves many steps by which the components of the anode slimes are removed one after another until the main products, gold and silver, may be separated. Due to the small scale of operations, the above procedure is carried out in small batches requiring considerable amount of manual labor. If, however, the anode slimes could be treated in

Jan 1, 1951

By V. Runolinna, R. T. Hukki

Preliminary separation of precious metals by flotation can offer a simplification of the conventional method of treatment of anode slimes. Laboratory flotation experiments show that rich gold and silver concentrate can be obtained with excellent recoveries. THE purpose of this paper is to present the results of an investigation into the possibilities of separating precious metals from anode slimes by selective flotation. The work was carried out at the State Research Institute in Helsinki, Finland. The sample of anode slimes tested was submitted by the Outo-kumpu Co. in Finland. In 1947 the average assay of filtered and dried anode slimes in the Outokumpu refinery in Pori was as follows: Au, 0.50 pct; Ag, 9.38 pct; Cu, 11.02 pct; Ni, 45.21 pct; Pb, 2.62 pct; Fe, 0.60 pct; Sn, 1.00 pct; Sb, 0.04 pct; As, 0.70 pct; Se, 4.33 pct; S, 2.32 pct; SO,, 2.17 pct; SiO2, 2.25 pct. The daily assay naturally varies considerably from the figures presented above. The present conventional method of treatment of anode slimes consists of the steps shown in the flowsheet in fig. 1. As seen from this simplified flowsheet, the present method of treatment involves many steps by which the components of the anode slimes are removed one after another until the main products, gold and silver, may be separated. Due to the small scale of operations, the above procedure is carried out in small batches requiring considerable amount of manual labor. If, however, the anode slimes could be treated in

Jan 1, 1951

By A. T. Aldred

HIS note reports the existence of several new scandium intermetallic compounds of the A2B and AB stoichiometries where the A element is scandium and the B element is from group VIII or IB of the periodic table. Alloys were arc melted from high-purity materials using 2-g charges. Typical lot analyses for the materials used are given in Table I. Chemical analyses were not made on the alloys as there was little or no weight loss on melting. After annealing the specimens for 14 days at 600°C and water quenching, metallographic and X-ray techniques were used to determine the occurrence of the various phases. Table II lists the relevant data for the A2B phases. The Ti2Ni structure,2 has ninety-six atoms in a face-centered cubic cell, whilst the Al2Cu structure is body-centered tetragonal.3 The occurrence and stability of the various A2B type phases in transition metal alloy systems has recently been considered by Nevitt.4 The Ti2 Ni-type phases occur over a relatively narrow range of radius ratios from 1.14-1.26 with A partners mainly from the titanium group and B partners predominantly from the cobalt group. This suggests that both a favorable relative size of the atoms and a favorable electron concentration are necessary conditions for the existence of this structure type. A12Cu-type phases involving Ti group elements as A partners are formed with B partners from the cobalt and nickel groups, predominantly the latter, and have a higher radius ratio (1.27-1.29) than the Ti2Ni-type phases. The occurrence of both Sc2Pd and Sc2Co can be rationalized in terms of these considerations but SczNi is anomalous because of its high radius ratio. The radius ratios are calculated from the Goldschmidt CN12 radii and it might be postulated that the scandium atom is reduced in size in the compound. Unfortunately the apparent atomic size of scandium in the compound cannot be calculated from a knowledge of the structure and lattice dimensions. The crystal structure of the Sc2Au compound could not be identified from the powder diffraction pattern, but it is interesting to note that it is isostructural with a series of A2Au phases where A is a rare earth element.5 Pertinent information concerning the AB phases found in this investigation is given in Table 111. All the phases have the ordered bcc CsCl structure. The occurrence and stability of CsC1-type phases have recently been discussed by Dwight,7 who concludes that the relative sizes of the atoms do not appear to be a controlling factor (the radius ratios of all the known phases vary between 0.985 and 1.439) but that the occurrence of the phase is predominantly dependent on the relative positions of the A and B partners in the periodic table. As a measure of the stability of a given CsCl phase it has been customary to define a lattice contraction on alloying, DAB — dAB, where DAB is the AB interatomic spacing as calculated from the Goldschmidt CN8 radii and dAB is the AB interatomic distance in the compound (= v3/2 ao). Values of the parameter DscB -dScB for the compounds found in this investigation are given in column 5 of Table III and are plotted in Fig. 1. If the lattice contraction does in fact reflect the stability of a phase then Fig. 1 shows two very interesting trends when the position of the B partner in the periodic table is considered. Firstly, within any given group the stability increases in order on going from the first to third long period. Secondly, within any given period the stability increases in order as the B partner is taken from the copper, nickel, and cobalt groups. In the case of the second long period, the lattice contraction reaches a maximum at ScRh and then decreases to ScRu. The same trend could

Jan 1, 1962

By R. N. Hoffman

A new technique for determining capillary pressure curves has been developed and tested. The technique differs from previously reported centrifuge techniques in that the centrifuge is slowly accelerated from zero to the maximum desired speed rather than being held constant at particular, progressively higher speeds. An important advantage of this technique over other methods of determining capillary pressure curves is the short time required to obtain the desired amount of data over the chosen pressure range. For example, to obtain 30 data points between 1.2 and 104 psig with a 1.55-in. long, 3/4-in. diameter core using a brine-air system, 6.6 hours were required with this technique. An equally important development of this paper is an analytic method for the conversion of the data from the centrifuge experiment to capillary pressure curve data. Previously there has been only an approximate conversion available. Although the capillary pressure curves determined by this technique appear to be as accurate as those determined by other techniques, the accuracy could be improved if certain variables, not treated in this experiment, were investigated. Among these are the dynamic distortion of the centrifuge equipment and imperfect initial saturation of the cores. INTRODUCTION Pirson 1 defines capillary pressure in a porous medium as "the differential pressure that exists between two fluid phases at their interfaces when they are distributed under static equilibrium within a porous material". Capillary pressure in rocks is known to be a function of fluid saturation, among other things, and a capillary pressure curve is defined for the purposes of this paper as a plot of the capillary pressure-wetting phase saturation relationship for a particular rock sample. Several methods are used for determining capillary pressure curves for small rock cores. Prominent among these are the semi-permeable barrier, mercury injection, and, to a lesser extent, centrifuge methods. The semi-permeable barrier method is currently the most popular. It features simplicity in both execution and the mathematical conversion of the experimental data into a capillary pressure curve. The main disadvantages of the semi-permeable barrier method are the time required — as long as two months — to obtain several points for the curve, and a fairly low maximum pressure before breakthrough of the non-wetting phase into the barrier occurs, for example, about 32 psig for a brine-air system. It is for these reasons that other methods such as the centrifuge method have been introduced. High accelerations and the absence of a barrier result in quicker attainment of saturation equilibrium at a given pressure. However, the centrifuge method involves much more expensive equipment and more difficult procedures and calculations than does the barrier method. The purpose of this investigation has been to improve the equipment and procedures of the centrifuge method and to develop an analytic method for the conversion of the experimental data into a capillary pressure curve. Hassler and Brunner did the original work in the determination of capillary pressure using a centrifuge. In their work the centrifuge speed was increased in a step-wise manner, each speed being held constant until saturation equilibrium was reached in each core. Saturation equilibrium was indicated when the volume of liquid collected in the graduated pipette of the core holder remained constant. According to Hassler and Brunner, equilibrium was reached in "a few minutes to one-half hour or more". In the centrifuge method, as opposed to the barrier method, the fluid saturation of the core is not a constant throughout the length of the core, but varies with the radius of centrifugation. Also, the capillary pressure cannot be read directly but must be calculated from a knowledge of the centrifuge speed and other parameters. For these calculations, Hassler and Brunner derived the following equations:

By H. D. Outmans

Present first-order theory for frontal stability and viscous fingering of immiscible liquids is improved by including the nonlinear terms in the equations describing conditions at the interface of the liquids. This leads to the revision of several conclusions which were based on first-order theory. They concern the growth rate and changing shape of a sinusoidal disturbance, particularly in relation to the wave number of this disturbance. Nonlinear aspects of effective interfacial tension are discussed and it is shown that this tension is not simply a positive proportionality constant in a linear relation between pressure difference and curvature at the interface. Scaling requirements are determined from the dimensionless groups which govern fingering. Gravity and interfacial tension invalidate a previously formulated conclusion that the shape of a finger after a given displacement is independent of the displacement velocity. Also, similarity of fingering (and, hence, of sweep efficiency in case of an unstable front) requires geometrical similarity of the initial disturbance in the model and the reservoir with a scale factor which is the same as the one for scaling down the dimensions of the reservoir. INTRODUCTION The critical velocity at which the transition zone in the vertical displacement of immiscible liquids becomes unstable was calculated by ill. More recently, the same was done for nonvertical displacements and it was also shown that the stability is affected by an effective interfacial tension between the liquids. 2-4 Although in the oil reservoir a stable front is always desirable from a recovery point of view, the necessary velocity may have to be so low that the corresponding production rate is not economical. In that case, a knowledge of the fingering unstable front is necessary for predicting recovery at break- through. Studies in this direction have not gone beyond the very moment at which fingering first occurs.5,6 Conclusions about stability and fingering in these references are all based on linear theory. In this theory the nonlinear terms in the equations describing conditions at the front are neglected. The usual justification for this lack of mathematical rigor is that the nonlinear terms can be made small relative to the linear terms and, supposedly, small causes produce only small effects. It has been recognized, however, that this is not necessarily true in the nonlinear problems of hydrodynamics.7 The hydro-dynamic stability and fingering of the front between two liquids, accelerated in a direction normal to the front, for instance, is strongly influenced by the nonlinearity of the boundary conditions.8-10 Since these boundary conditions are not unlike those arising in the problem of stability and fingering of the front during a slow immiscible displacement in porous media, it was thought that there, too, the nonlinear terms should be taken into consideration. A summary of the results obtained in linear theory and a comparison with experimental data precede the nonlinear theory developed in this paper. This summary serves to introduce some quantities which will be used in the further develop ment. It should also be pointed out that the method of higher-order approximation by which the nonlinear stability problem is solved has application in other reservoir studies.11 SUMMARY OF LINEAR THEORY 1. A plane interface remains stable if its velocity is smaller than a critical velocity. vc = (p2-p1)gn/(l/A2- l/A1 .........(1.1) This equation is derived for uniform flow in a thin layer inclined to the horizontal plane. The displacement takes place in a direction normal to the intersection of this layer and the horizontal plane. The undisturbed (line) interface is normal to the velocity. Fluid 1, the upper fluid (gas), is displacing Fluid 2 (oil). (VcQS would be the injection rate in cc/

By R. E. Reed-Hill, W. H. Hartt, W. A. Slippy

An unusual form of double kinking has been observed at the ends of {1121} twins in deformed zirconium. These kinks lie partly outside of the twin and partly inside. While they are undoubtedly closely associated with accommodating the twinning shear into the matrix, they are apparently closely related to other important aspects of twin growth. A mechanism is proposed for {1121} twin growth involving interactions between 1/3 (1120) dislocations in the bend planes and twinning dislocations. It is also shown that boundaries without long range strain fields develop at the tapered ends of the twins. The {1121} twins can, therefore, grow without forming high-energy noncoherent twin boundaries containing large numbers of closely spaced twinning dislocations. NUMEROUS investigators have indicated that slip is often closely associated with deformation twinning. An example is twin accommodation kinking,1-3 where dislocations form bend planes and permit accommodation of a twinning shear within the parent crystal. Another is the incorporation of slip dislocations into twins, as proposed by Sleeswyk and verbraak4 and Ishii and Kiho5 for iron and ß-tin, respectively, and observed in hcp metals by Price.6 In addition, it has been shown that shear discontinuities exist at the points of twin intersections in zinc,7 magnesium,8 titanium,9 ß-tin,10 and bismuth," where the continuity conditions for twin intersections, originally proposed by cahn,12 are not satisfied. A similar situation occurs for zig-zag (1121) twins in zirconium13 and ?-phase silver-aluminum alloys,14 where the twinning shears of the two component twins are not parallel. In all these latter cases additional deformation by slip is believed to accommodate the twinning shear discontinuity. The present paper is concerned with a newly observed aspect of the slip and twinning interrelation, in which two kinks, one inside the twin and the other external to the twin, are formed. These kinks, observed in conjunction with (1121) twinning in zirconium, form to accommodate the twinning shear. A model has been constructed explaining the growth and accommodation of (1121) twins in terms of these kinks. This mechanism may be significant since it is concerned with an important twin mode, which occurs not only in zirconium but also in titanium and hafnium. The practical significance of (1121) twinning has been adequately demonstrated. At 77° K the high ductility of zirconium containing a large number of grains unfavorably oriented for slip is primarily due to (1121) twinning.'5 Also, (1121) twins nucleated at 77°K may grow during further deformation at room temperature. This growth can greatly increase the transverse ductility15 as well as produce large mechanical hysteresis effects.= EXPERIMENTAL PROCEDURE Arc-melted, sponge zirconium plate previously described17 was prestrained 0.65 pct at 77° K by cold-rolling to introduce {1121} twins into the structure. Tensile specimens were cut with axes normal to the plate rolling direction. These specimens were pulled in tension to near the point of failure in an Instron machine at room temperature at a cross-head speed of 2 x10-2 in. per min. This additional deformation caused growth of the twins nucleated by prestrain. Deformed specimens were then prepared for metallo-graphic examination. This included an anodizing treatment18 that made the surfaces sensitive to polarized light, permitting small lattice rotations to be revealed. EXPERIMENTAL RESULTS Nature of the Twin-Kink Band Structure. Fig. 1 is a photomicrograph of a typical specimen after prestrain at 77° K. The structure is characterized primarily by long, narrow, parallel sided (1121) twins which norma1ly traverse the entire grain. Fig. 2 shows several (1121) twins after additional straining at room temperature. These lie near the center of the polarized light photomicrograph and are inclined upward to the right. It is evident that this latter deformation has resulted in appreciable twin growth. The dark regions extending from the ends of these twins are accommodation kinks. The difference in reflected light intensity indicates the

Jan 1, 1969

By Richards R. Vandervoot

T HE creep behavior of many polycrystalline metals at moderate stresses can be described by the empirical relationship: where Em is the minimum creep rate, A is a constant, a is the applied stress, E is the average elastic modulus at the test temperature, and D is the self-diffusion coefficient.&apos; This equation is generally applicable for strain rates of less than around 10-5 per sec and temperatures greater than about one-half the melting point in absolute units. Under these conditions atomic mobility plays an important role in the deformation process, and steady-state creep occurs when a dynamic equilibrium is reached between the generation and recovery of dislocation substructure. Although several theoretical mechanisms have been proposed to explain the creep of polycrystalline solids,2"4 the dislocation climb model2 is in accord with most experimental observations. The majority of creep data used to develop Eq. [1] came from metals with either the fcc or hcp crystal structures. However, on the basis of results for a and 7 iron as well as those for a and a thallium, Sherby concluded that the high-temperature deformation behavior of close-packed metals and bcc metals is probably the same.&apos; The greater creep resistance of fcc and hcp metals and alloys on a relative temperature scale was attributed to lower diffusivities in the close-packed structures. To further compare the creep properties of fcc, hcp, and bcc metals, creep data for all six bcc refractory metals were analyzed according to Eq. [I]. The results are shown in Fig. 1. The sources of information for the quantities used to prepare this figure are listed in Table I, except for high-temperature elastic moduli. The latter data were obtained from Refs. 28 and 29. The dashed lines in the figure represent the range and breadth of data analyzed by Sherby for fcc and hcp metals. In general, the deformation behavior of all of the refractory metals, ex- cept possibly that of tungsten, can be represented by Eq. [1]. This correlation is strong evidence of the similarity that exists between creep of pure close-packed metals and creep of pure bcc metals. At (Em/D) < 108, the results of Flagella and Tarr on tungsten (W-1 in Fig. 1) agree with the five-power stress law, while those of Green (W-5 in Fig. 1) show a seven-power stress dependence. Where (Em/D) > 108, the stress exponents for other data on tungsten were in the range 10 to 15. It is possible that the creep rate dependence on stress in this region is not a power law but exponential (i.e., Em - eßo). However, it was not feasible to differentiate between these two cases because of the steep slope and scatter in the data. Note the inflection point in the curve for the data of Flagella and Tarr (W-1 in Fig. 1). The slope of the line changes from 5 to around 10 at Em/D = 108. The breakdown of the fifty-power stress law at high stresses is not uncommon in other metals, and this phenomenon may result from nonequilibrium conditions in the material such as excess lattice vacancies produced by rapid straining.30 The mechanical strength of a polycrystalline metal is related to its microstructure. Attempts to establish the influence of grain size on the creep rate of metals and alloys have led to a wide variety of results. For example, the following effects have been observed: creep rate decreases as grain size increases;31&apos;32 creep rate decreases as grain size decreases;&apos;,33 creep rate is a minimum at some critical grain size and increases with either an increase or decrease in

Jan 1, 1969

By G. E. Johnson

E. D. HYMAN*—How much sorting of scrap is done ? G. E. JOHNSON (author&apos;s reply)—We do practically no sorting. We charge "run of mine" scrap to the furnace. The unmeltables, mostly iron, are in such demand today that there is no difficulty in disposing of them. It may soon be desirable to sort out from the unmeltables as much of the brass as possible. J. J. BRUGMAN†—We have somewhat similar problems in the secondary aluminum business. What is your method of removing the unmelted material from the furnaces? Why have you such an apparently small space in which to charge your materials? Do you find that you have to seal that opening, or can you have it open and continuously charge at one end and pull out the other ? G. E. JOHNSON—Our means of melting scrap is efficient only to the extent that we use the waste heat from the vaporizing chamber to do the job. It is a batch process. We open the charge door and place the scrap on the hearth by hand shoveling. The door is then closed during the melting down period. After the melting is complete, the opposite door is opened and the unmeltables are raked out. The doors are approximately 3½ X 4½ ft and are not sealed during the process only closed. They are nominally tight. Some metal is oxidized in the process. We have visualized a means of conveying the materials through this melting unit with the metals that are melted trickling out during its travel. T. H. WELDON‡—Mr. Johnson, in line with the last question, is it necessary to seal the furnace between the melting down and the vaporizing unit, or have you got an inverted syphon in the bottom of the chamber? G. E. JOHNSON—That was one of the first things we encountered. We had to have a sealed opening, and it is a molten metal seal. You have indirectly asked me another question, which was: "Do you have to seal up the melting unit?" I would say we should exclude as much air as possible, although we are not too efficient in doing that. We allow the melting unit doors to be open when we charge and when we remove unmeltables. You can readily see that that would lead to the idea of having a controlled atmosphere in the melting unit, and I think this would do a more efficient job of melting the scrap. T. H. WELDON—How often do you charge the furnace? G. E. JOHNSON—We charge the melting unit, and rake out the unmeltables, about every hour. H. R. HANLEY*—Are any provisions made for controlling the rate of oxidation for the production of various size particles for certain characteristics of the zinc oxide product? G. E. JOHNSON—Yes, there are many. You are getting pretty much into the fine points of zinc oxide manufacture. Some of us still think we have something to learn about that. In general, this muffle furnace as I have described it to you produces a rounded particle of zinc oxide which is generally formed by a rapid oxidation of the zinc vapor, followed by rapid cooling. We have gone to the other extreme in some of our experiments. We have changed the furnace to produce a type of zinc oxide, such as we thought was peculiar to American process zinc oxide, by controlling the temperature at the point of oxidation and maintaining that temperature for a much longer period of time than we do when we make the rounded shape. There are other relationships that this furnace readily provides. One of the important factors is the ratio of air to zinc vapors. We can vary that by varying the air supply to the baghouse, or vary the rate at which we are vaporizing the zinc by the simple expedient of regulating the temperature over the carborundum arch. We have a number of variables that permit us to produce all of the grades of French process zinc oxide from lead-free up through the highest grades of seal oxides. There are many controls that we can apply to the operation. What I have said is but a brief condensation. K. MORGAN*—Can Mr. Johnson give us some idea of the fuel consumption of the furnace ? How much oil does he use per ton of zinc distilled? I am also interested to know what sort of heat transmission he gets through the arch? What is the thickness of the tiles used to construct the arch? Some time ago we built a small furnace for a different purpose, using a carborundum arch, and we found that the reflectivity of the molten zinc surface was so great we had to use a very high arch temperature. We found we made an improvement by having a layer of carbon on the surface of the zinc. Has Mr. Johnson had any experience on these points ? Does he make any sort of insolu-bles which he leaves in the furnace which he cannot tap out ? G. E. JOHNSON—I believe your first question was the fuel consumption. If I recall, somewhere in this paper there is a test that I quote. I believe we used 800 gal in a given period of time. Offhand I cannot translate that into tons of metal. I might also state that we have this understanding; that the carborundum arch, as the temperature becomes higher, becomes more efficient in heat transmission. As a matter of fact, I believe it is at about 2600°F or higher that the highest efficiency of heat transmission becomes available. We have calculations that I cannot quote from memory which indicate that the carborundum arch does a really very fine job for this type of furnace. Another point that we had considered was the fact that this furnace could be readily constructed so as to furnish an ideal source of heat for waste heat boilers. If a carborundum arch was used over the melting unit, we would have no zinc vapors in the gases at all— just clean combustion gases from which we would have removed some of the heat. L. P. DAVIDSON†— The insolubles

Jan 1, 1950

.MAX ROESLER, Firmeza, Oriente, Cuba (communication to the Secretary?).-It is substantially admitted by all who have recently been in touch with these deposits that the orebodies lie in the fine-grained dark-green rocks, called diorite by most writers and diabasic by myself. The three points of disagreement concern the agency of included limestone blocks as causes of deposition, the agency of the

Jan 5, 1917

By Hans-Jürgen Schaller, Horst A. Brodowsky

Activity coefficients of boron in palladium were determined at concentrations up to PdB0.23 by reducing B2O3 between 870" and 1050°C in a controlled H2-H2stream and measuring the resulting weight gain. The deviations from ideal behavior closely resemble those of the system Pd-H and are interpreted in terms of three principles: 1) The solute atoms occupy octahedral interstitial positions. 2) They donate their valence electrons to the 4 d and 5s bands of palladium, raising its Fermi energy. 3) The lattice strain energy is lower for two nearesl -neighbor interstitial particles than for two farther separate ones. SOLID solutions of hydrogen in palladium are a useful subject for studying thermodynamic aspects of the formation of alloys and of nonstoichiometric systems.1-3 The activity of hydrogen is readily measurable to a high degree of accuracy,4&apos;5 even at low temperatures where the deviations from ideal behavior are more pronounced, and its simple structure facilitates an interpretation of these deviations in terms of a detailed model. Two effects are discussed to account for the non-ideal properties:3 An "electronic" effect, connected with the rise of the Fermi energy, as electrons of the interstitial hydrogen atoms enter the electron gas of the metal, and an "elastic" effect, due to an interaction of the regions of strain around each interstitial atom. The electronic effect is based on the idea that the lowest energy levels of the dissolved hydrogen atoms are higher than the Fermi energy, so that the electron will not occupy a localized state but enter into the electron band of the metal.6 The elastic effect is based on the observation that dissolved hydrogen distorts and expands the palladium lattice. The hypothesis is put forward that the elastic strain energy is lower for two adjacent dilatational centers than for two separate ones; i.e., they attract each other. The resulting pair interaction can be used to calculate an elastic contribution to the thermodynamic excess functions by means of one of the statistical methods. This model permitted a detailed description of the solution properties of hydrogen in palladium3 and in palladium alloys.798 An extension of the approach to describe the excess functions of substitutional palladium alloys is possible.9 In order to further test and refine the model, an investigation of other interstitial alloys was started. Palladium dissolves considerable amounts of boron in homogeneous solid solution.10 The palladium lattice expands linearly up to nB = 0.23 (nB = B/Pd atomic ratio), the highest concentration studied." The expan- sion, extrapolated for 1 mole of interstitial per mole of palladium, is 17 pct of the lattice constant of pure palladium vs 5.7 pct in the case of hydrogen.12 The fact that the lattice expands rather than contracts is a strong indication that interstitial positions are occupied. According to neutron diffraction experiments, hydrogen occupies the octahedral sites of the fcc lattice.13 Unfortunately, this direct evidence is not available for the Pb-B system, mainly because of the high-reaction cross section of boron with thermal neutrons. However, by way of analogy and on the grounds of the rather close similarities between the two systems to be reported here, it seems safe to attribute octahedral positions to the dissolved boron, too. At higher boron contents, compounds of stoichiomet-ric compositions are reported such as Pd3B, which has the structure of cementite,14 so that a close structural relationship seems to exist with the system r Fe-C. In their study of hydrogen absorption in Pb-B alloys, Sieverts and Briining noted that alloys with an atomic ratio of about nB = 0.16 are no longer homogeneous15 This observation was confirmed in an extensive X-ray investigation.11,16 The phase boundaries of two miscibility gaps were established. One two-phase region was stable below a transition temperature of about 315°C and extended from nB = 0.015 to 0.178. The other one extended from nB = 0.021 to 0.114 slightly above the transition temperature and had an apex at nB = 0.065 and 410°C. All phases involved have the fcc structure of pure palladium with lattice expansions proportional to their boron contents. The occurrence of miscibility gaps, i.e., the coexistence of dilute and concentrated phases, points to an energy of attraction between the dissolved particles, in the Pb-B system as well as in the Pd-H system. The filling up of the electron bands seems to be analogous, too, in the two systems, as indicated by the hydrogen absorption capacit15,17,18 and by the suscepti bility of Pd-B alloys.l8 In both types of experiments, boron acts as an electron donor. A chemical method was used to measure the activity of boron in palladium. Boron trioxide was reduced in a moist hydrogen stream: B2O3 + 3H2 = 2B + 3H3O [l] At known activities or partial pressures of boron trioxide, hydrogen, and water, the activity of boron could be calculated from the law of mass action. The equilibrium concentration of boron corresponding to this activity was determined as the weight gain of the sample. EXPERIMENTAL The samples consisted of small pieces of foil of 0.1 mm thickness and about 100 mg weight. The palladium was supplied by DEGUSSA, Germany, and stated to be

Jan 1, 1970

By G. R. Leverant, C. P. Sullivan

Re crystallized TD-nickel mi-2Th0,) in both coated und uncoated conditions was fatigued at 1800°F at total strain ranges varying .from 0.2 to 0.75 pct. The fatigue life of uncoated inaferal, Nf, was related to the total strain range, ?eT, by (2Nf/021AeT = 0.014. A duplex Al-Cr pack coating increased the fatigue life by about a factor of two. The cracks that led to failure in both coated and uncoated material were initiated at the outer surface, indicating that the mechanical properties of the surface layers were important in determining fatigue life. Crack propagation and subsurface crack initiation in the TD-nickel occurred preferentially at grain boundaries with cavitation at thoria particle-matrix interfaces an integral part of the grain boundary fracture process. The importance of both the grain morphology developed during thermome chanical processing of TD-nickel and the distribution of thoria particle sizes to fatigue resistance are discussed. THE fatigue properties of only a few dispersion-strengthened metals have been studied at temperatures 0.5 Tm;1,2 among these have been lead and aluminum containing oxide dispersions. TD-nickel is a material of interest for application in aircraft gas turbine engines, but little fundamental information is available on its behavior under cyclic loading conditions. In this study, the low-cycle fatigue properties of TD-nickel were determined at 1800°F with emphasis on the 101-lowing; 1) the relation of the grain morphology produced during thermomechanical processing to crack initiation and propagation; 2) the role of thoria parti-cles in the fracture process; and 3) the effect of an oxidation resistant coating on fatigue life. I) MATERIAL AND EXPERIMENTAL PROCEDURE The TD-nickel was supplied by DuPont as a 5/8-in. thick plate which had been subjected to a proprietary series of thermomechanical treatments with a final anneal at 2000°F for 1 hr in hydrogen. The composition of the material is given in Table I. At the test temperature of 1800°F, the 0.2 pct offset yield stress was 15,000 psi, and the elongation and reduction in area were 4.6 and 3.0 pct, respectively. The microstructure of this material has been previously described.&apos; Briefly, it consists of an array of lath-shaped grains, about 0.15 mm in thickness, with the long dimension of each grain parallel to the primary working direction, Fig. 1(a). The presence of very small annealing twirls, Fig. l(b ), together with the absence of extensive dislocation networks, Fig. L/C), indicated that the material was in the recrystal- Table I. Composition of TD-Nickel ThO2 2.3 vol pct C 0.0073 wt pct lex 0.01 wt pct Cr 0.01 wt pct Cu 0.004 wt pct S 0.001 wt pct Ti <0.001 wt pct Co <0.01 wt pct Ni bal lized condition. Commercial TD-nickel sheet has a similar grain size and shape, but unlike the present material is not recrystallized as evidenced by the absence of annealing twins and the presence of a well-developed dislocation substructure.4 The plate material had Young&apos;s moduli in the rolling direction of 22 x 106 psi and 13 x 106 psi at room temperature and 1800°F, respectively, indicating a texture with a strong {100}<001> component in agreement with previous observations on recrystallized TD-nickel sheet.596 The 2.3 vol pct of thoria particles were uniformly distributed although some clustering and stringering of larger particles was occasionally seen. The average diameter of the particles was 450 and the calculated mean planar center-to-center spacing was 2100Å. Two specimens were coated with a duplex A1-Cr pack coating. The coating was somewhat nonuniform from one position to another along the gage length. An area of the coating after testing is shown in Fig. 2. Electron microprobe analysis revealed the following zones in the various lettered regions indicated in Fig. 2: A) a bcc matrix of B-NiA1 with some chromium in solid solution along with a fine dispersion of a chromium-rich second phase which was probably precipitated during cooling from the test temperature to room temperature; B) fcc y&apos;-Ni,Al with some chromium in solid solution; C) porosity; D) a two-phase mixture of a chromium-rich solid solution containing nickel and aluminum and a small volume fraction of a nickel-rich solid solution having approximately the same composition as the immediately adjacent portion of region E, E) the TD-nickel substrate containing chromium in solid solution to a depth of 5 to 10 mils. As expected from the nature of the diffusion processes involved,7 the thoria particles were present only up to the layer of porosity, region C, Fig. 2. The measured thickness of the coating proper, zones A to D, after testing was 1 to 2 mils. The specimen design and testing techniques have been previously discussed.&apos; Stressing was axial and parallel to the lath-shaped grains (i.e., parallel to the rolling direction). The total strain range was controlled between zero and a maximum tensile strain varying from 0.2 to 0.75 pct. (The test at 0.2 pct total strain range was switched to load control at 1030 cycles at which point the peak tensile and compres-

Jan 1, 1970