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By C. C. Mattax, J. E. Bobek, M. O. Denekas

ABSTRACT investigations in recent years have shown that rock wettability can exert a profound influence on the displacement of oil by water from oil producing reservoirs. Core analyses frequently show oil recoveries from preferentially water-wet rock to be significantly greater than those from preferentially oil-wet rock. Thus, an accurate prediction of water-drive or waterflood oil recovery is dependent on the evaluation of reservoir rock wettability. Laboratory and field studies have been undertaken to examine and develop methods which may be used to measure rock wettahililiy, to investigate factors which may alter the wettability of reservoir rock, and to determine the wettability of specific reservoirs. It has been found that measurement of the rate and volume of spontaneous imbibition of the wet-ting phase by a rock is a reliable and reproducible test for semi-quantitarive determination of preferential rock wettability. Laboratory tests have shown that the wettability of reservoir rock may depend on both the crude oil composition and the rock type. Field and laboratory tests have indicated that coring flulids and core handling techniques can cause significant changes in the wettability of rock surfaces. However, a few fluids, brine in particular, appear not to affect core wettability and may be used when coring to determine reservoir wettability. Core handling and packing procedures have been developed which preserve core wettability during storage and laboratory testing. The wetfability characteristics of six reservoirs have been evaluated by wettabilify tests performed in the field on fresh cores cut with brine or special water-base muds. The tests indicated that all six reservoirs are water wet; however, the de-gree differed from one reservoir to another. INTRODUCTION Although surface properties of reservoir rock and interfacial characteristics of rock, crude oil, and water systems have been discussed for many years, the full significance of these properties to the production of oil is still in the process of evaluation. It is known, however, that one surface characteristic—preferential wettability of the reservoir rock—-is of paramount importance when the reservoir is being produced by water-flood or water-drive mechanisms. The importance of rock wettability has been pointed out by several authors'.',%* who have found that pref- erentially water-wet cores flood more efficiently than oil-wet cores; that is, more oil is recovered from water-wet cores in the early flooding stages than from oil-wet cores. Other authors'," indicate that waterflood oil recovery from cores of intermediate wettability may be greater than that from either strongly water-wet or strongly oil-wet cores. These recent investigations emphasize that the true wettability of a reservoir must be known before the performance of waterflood or water-drive reservoirs can be accurately evaluated. When reservoir wettability is to be determined by core analysis, precautions must be taken to maintain the original wettability which can be altered readily during coring5 nd testing.' In the coring operation the core may be partially or completely penetrated by the drilling fluid which, if it contains surface active materials, may drastically change the wettability of the core. Also, improper core handling during stcrage and testing may change its wettability because of evaporation of fluids or exposure to oxygen or surface active contaminants. One purpose of this paper is to discuss methods for obtaining, preserving, and testing cores without altering their original wettability. In addition, the results of wettability tests on fresh and preserved cores from six reservoirs are presented where special precautions were taken to obtain samples without altering their wettability during the coring operation.

By Alim Elibol, Rosbel Jimenez, Mustafa Can Suner, Deniz Tuncay, Zach Agioutantis

LaModel is a displacement-discontinuity variation of the boundary element method, which is utilized to analyze the displacement and stress in flat-lying, tabular orebodies. In coal mining, the accuracy and reliability of LaModel are proven with the utilization of the Mark- Bieniawski coal pillar strength and the stress gradient formula with proposed methodologies. However, the application of LaModel is limited to coal mines due to the default coal pillar strength properties. Recently, the stress gradient functions have been established and used to derive concentric rings of zones to simulate stone mine pillar yielding in LaModel. Also, to gain a robust understanding of the brittle failure mechanism and its effect on pillar strength, an S-Shaped failure envelope, where rock mass' cohesive and frictional strength components mobilize as a function of confinement (e.g., minimum principal stress), has been implemented into FLAC3D software. Therefore, by employing brittle failure criteria, the pillar strength stages at various width-to-height ratios and different pillar dimensions are estimated for four benching stages. The estimated pillar strengths and stress gradients for benching conditions are then used to calibrate LaModel in-seam material properties and compare stresses computed by LaModel and FLAC3D. Consequently, this study aims to increase the safety measures in the stone mining industry by implementing the practical use of LaModel for underground stone mines' initial development to various stages of bench mining.

Jun 25, 2024

By Daryl R. Tweeton

The Bureau of Mines has developed PC-based tomographic computer programs for geophysical applications, and is making them available to potential users as part of a Bureau plan to facilitate the transfer of technology to industry. These programs were initially developed for predicting and monitoring the flow pattern of leach solution during in situ mining. Seismic crosshole tomography has located fractured zones of low seismic velocity and saturated zones of high seismic velocit above the natural water table. The Bureau has applied tomography also to assessing high-wall blast damage, and examining the integrity of mine-related geological structures. The tomographic programs include the straight ray pro ram BOMTOM (Bureau of Mines Tomography? and the program BOMCRATR (Bureau of Mines Curved Ray Tomographic Reconstruction) that can be run with either curved or straight rays. Both programs provide optional mathematical constraints to help counteract the nonuniqueness of reconstructions that occurs with crosshole data. They are available from the Bureau free of charge. With typical data sets, they can be run on a 386 microcomputer with 640 Kb RAM. BOMTOM was described in the Bureau Report of Investigations 9159, so this report emphasizes BOMCRATR. Curved and straight ray reconstructions using seismic field data collected while simulating injection of leach solution were compared. The curved and straight ray tomograms were quite similar even with velocity variations of more than 50 percent.

Jan 1, 1992

A reliable laboratory method to characterize the response of free gold particles to flash flotation conditions has been developed. The test has been performed on free milling gold ores as well as synthetic ores, using either a gravity concentrate or gold powder as the gold source, to assess the floatability of gold particles. Trends in free gold flotation kinetics, as well as size and milling effects, were identified for gold recovery based on the different feed types, reagent dosages, and residence times. It was shown that the ultimate recoveries and kinetic trends of gold particles from the gravity concentrate could be enhanced with increased dosage of collector, potassium amyl xanthate. Interestingly, in comparison to gravity-recoverable gold, recovery from pure Au powders was better in collectorless flotation, and cumulative recovery decreased with higher levels of collector addition. Improved coarse particle recovery appeared linked to increased collector additions for both the gravity concentrate and the pure gold powders. In general, coarse gold particles demonstrated slower kinetic rates thaen the fine or intermediate components incomparable tests.

Jan 1, 2015

By Frank C. Kelton

A method is outlined for the analysis of large cores, developed primarily for the purpose of obtaining reliable data on fractured or vugular limestones. Porosity and fluid saturations are determined by a modified Dean-Stark extraction after initially bringing the samples to 100 per cent liquid saturation by a vacuum-pressure method. Horizontal permeabilities on the whole samples are determined in two directions, parallel and perpendicular to the di-rection of principal fracturing. Results are presented for various types of formations. A comparison is made between data obtained by this special method and the method of conventional analysis, and discussion is given of the relative advantages and limitations of each. In view of this comparison a modified method for the analysis of fractured and vugular formations is proposed, which method retains the advantages of the previously outlined techniques but gives promise of speeding up the analysis. INTRODUCTION For many years the greater part of the production in the Permian Basin was from formations of Permian and Pennsylvanian age. While production from these formations is still the predominant production. deeper prospecting has brought to light older formations with oil productive characteristics. Attempts to core these deeper horizons were at first usually characterized by poor recovery. The old rule of thumb, "good core recovery — poor well" was originated and remained in effect until recently. With the advent of diamond coring and the increased efficiency in drilling and coring operations. the old adage has lost its significance. Formations of Devonian. Silurian and Ordo-vician ages were successfully cored with varying degrees of recovery. The cores thus obtained were surprising and in some case; disappointing. Good recovery from these formations led to speculation as to the feasibility of analysis and the meaning of data obtained from conventional analysis. Commercial laboratories were engaged to analyze these cores. and their results indicated that data obtained by conventional methods would be of little value. From visual inspection it was apparent that in many cases the effective porosity for storage of hydrocarbons. and permeability. were contained largely in fractures and solution cavities rather than in the primary crystalline structure of the formation. In other cases the solution cavities augmented the effective porosity of the primary crystalline structure, or fractures enhanced the permeabiilty of the latter so that the formation might respond favorably to acidization and become commercially productive. Since the spacing of the cavities and fractures was often comparable to the core diameter, it was evident that the entire core should he analyzed instead of small fragments. On the basis of these observations, commercial laboratories were requested to devise a system of analysis which would yield data of practical value. Pro- cedures have accordingly been developed which seem to meet this requirement, and to date nearly 12,000 large core samples have been analyzed. It is the purpose of this paper to describe the methods used, to present typical results for several fractured formations and to compare the data obtained by this special analysis with that obtained by conventional analysis. Certain modifications and alternative procedures are finally suggested to speed up the analysis. CORE ANALYSIS PROCEDURE Fluid Saturations and Porosity The core sample, in segments up to 15 in. in length. is marked, weighed and examined under ultra-violet light to determine the presence of oil saturation. If present, the approximate quantity of oil and its location on intercrystalline, fracture or vugular surfaces is noted. This information is carefully recorded. The degree of fracturing and/or vugular development is also noted. The sample is then placed in a pressure cell and the air evacuated with a high speed vacuum pump. This evacuation is continued only long enough to reduce the pressure to approximately the vapor pressure of water in order not to remove excessive amounts of water. Water is admitted to the cell and allowed to penetrate the sample under atmospheric pressure, filling the pore space initially occupied by air and replacing the small amount of water removed by evacuation. Pressure up to 200 psi is applied to force water into the smaller capillaries, and the sample is left sub-

Jan 1, 1950

By E. Martinez

Samples of chrysocolla, a hydrated copper silicate, from several sources were submitted to differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). Pure samples of chrysocolla are difficult to obtain, but comparison of the thermograms revealed that certain reactions occurred in all the samples and it is believed that these are due to chrysocolla. Endothermic reactions occurred at 50' to 175°C, 350° to 650°C, and 980° to 1100°C each of which caused a weight loss. The first was due to loss of absorbed water, the second to a dehydroxyla-tion, and the last to conversion of cupric oxide to cuprous oxide. In addition, two exotherms were detected at 685° to 695°C and 935° to 950°C. Infrared spectra of heated samples indicated the exotherms were due to changes in the Si-O bonds leading to the formation of cristobalite. The results suggest that thermoanalysis may be a more sensitive and reliable method for detection and identification of chrysocolla than X-ray diffraction, infrared spectroscopy, or optical techniques. The recovery of copper from oxide ores has been the subject of much research in recent years. One of the principal oxide copper minerals is chrysocolla, a hydrated copper silicate. The information available indicates that it has widely varying properties depending on the origin of the sample. Chrysocolla usually is found associated with cuprite, malachite, azurite, and native copper. Most of these other minerals are recoverable by present day flotation practice, but chrysocolla is lost in the tailings.1,2 Reagent combinations that are successful in laboratory chrysocolla flotation with ore from one source have been found to be ineffective with another. 3 The copper segregation process offers an altemative to beneficiation of oxide copper ores.4'5 The process is of particular interest in processing ores that cannot be treated by conventional hydrometal-lurgical methods because of high acid consumption.6 Fuller understanding of the properties of chryso- colla may prove of value in the search for improvements in both the flotation and segregation processes. Chrysocolla samples from Arizona, Nevada, Chile, Australia, and South Africa were studied by differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). In addition, a sample from Miami, Ariz., was submitted to X-ray diffraction, infrared spectrophotometry, and surface area determination. EQUlPMENT Differential thermal analysis (DTA) detects, amplifies, and records exothermic-endothermic reactions occurring in a sample as its temperature is raised at a constant rate, usually 10°C per minute. A unit made by the Robert L. Stone Co. was used in this study. The tests can be run if desired with a gas streaming through the sample. A thermobalance records weight losses or gains in a sample as its temperature is raised at a uniform rate. The gravimetric analyses (TGA) were run on a Chevenard thermobalance converted electronically for graphic recording. A heating rate of 5°C per minute up to 1100°C was used in these tests. A Perkin Elmer Infrared Spectrophotometer, Model 221, was used with sodium chloride optics obtaining IR spectra in the 2 to 15 region. A pressed pellet technique with potassium bromide was used in preparing the samples. DESCRIPTION OF SAMPLES Chrysocolla is found in the oxidation zones of copper deposits commonly associated with malachite, azurite, and limonite. It is described as varying in composition and in color from bluish green to brown or black. Inclusions of other minerals are usual so chemical analysis of chrysocolla samples may be suspect. However, it is considered by many to be a solid solution of CuO, SiO2 and H2O with a general formula of CuO.SiO2.2H2O or 2CuO.2SiO2. 3H20. Chukhrov7 has described a sample from the Urals as CU3,5(OH)2 (A1Si3) O10.nH2O and stated that chrysocolla is a montmorillonite-type mineral. On the basis of X-ray analyses, DTA, and infrared spectra of chrysocolla from the Inspiration Mine, Ariz., Sun8 concluded that there was no substantial evidence to classify it as a montmorillonite mineral. Chrysocolla samples from many sources throughout the world were used in this investigation. The following is a brief description of each:

Jan 1, 1963

By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.' In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant' but ~achinger' arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968

By Raynor Linzey, Karl M. Busen

The formation of thin films of silicon oxide by anodic oxidation of silicon and the subsequent removal of these films by an etch is a process often used for the evaluation of concentration distributions Profiles) in silicon layers by the differential sheet conductance method. The accuracy of the resulting profile is very strongly influenced by the uniformity of the thickness of the reacted silicon. Normally, it would be expected that for a constant number of coulombs passed the thickness would be the same from oxidation to oxidation. Investigations show that in certain electrolytes, for a given number of coulombs passed through an n-type silicon sample, the thickness of the reacted silicon increased with increasing resistivity. Even for the same resistivity the thickness varied sometimes by a factor of 1.5. When an electrolyte was used which consisted of 10 pct water by volume in ethylene glycol with 4.0 g KNO per 1000 ml of solution, anodiza-tion at 5 ma per sq cm led to satisfying results. Short-time anodizations gave oxide layers of a higher apparent density than those experienced from thermally gown silicon oxides. THE functioning and the electrical characteristics of semiconductor devices are based upon the incorporation of "impurities" into a single-crystalline body of suitable material and on the concentration distribution (profile) of this impurity. The incorporation can be achieved by well-known processes as, for example, by diffusion, epitaxial growth, alloying, or ion implantation. Often the profile resulting from these processes is not known. A powerful tool to learn about a concentration distribution is given by the method of differential sheet conductance which employs successive four-probe measurements on a layer subjected to stepwise removal of thin sublayers. Differential sheet conductance vs position (or penetration depth) of a sublayer is plotted and a smooth curve is drawn through the data. From this curve the profile is then calculated. When the semiconductor material is silicon, the sublayers are removed suitably by anodic oxidation of the silicon and subsequent dissolving of the formed silicon oxide by an etch. The accuracy of the resulting profile is very strongly influenced by the uniformity of the sublayer thickness. Normally, it would be expected that, for a constant number of coulombs passed, the thickness would be constant from oxidation to oxidation. Investigations showed that for sublayers several hundred angstroms thick the reproducibility can be rather poor. Therefore, efforts were made to obtain a reliable technique for uniform removal. The present paper describes such a technique and certain phenomena which were encountered during the investigations. APPARATUS AND TECHNIQUE The first report on the investigation of concentration distributions, where for differential sheet conductance measurements thin silicon sublayers were removed from a diffused layer by anodic oxidation, was given by Tannenbaum. The author reports the removal of sublayers which for the most part were 400 thick. More advanced device designs now require much narrower layers. When it was tried in these laboratories to determine profiles within such layers, difficulties were encountered with respect to sublayers which by necessity had to be thinner than the ones reported by Tannenbaum. The apparatus used for the investigations is sketched in Fig. 1. Two cylindrical containers connected by a wide tube are filled with an electrolyte. The left container receives the cathode whereas the right container is closed at the bottom end by a sample support consisting of a Teflon base and a copper pedestal. The silicon sample (1 by 1 cm) is mounted to the pedestal embedded flush in the Teflon base using silver paint (Degussa) for electrical contact. Pyseal is applied to the edges of the sample to protect the copper pedestal from the electrolyte. The base is mounted to the container using a water-tight silicon rubber gasket. Fig. 2 gives a view of the sample support. The copper pedestal is connected to the positive side of a power supply operating at a constant current output (Kepco Model ABC 425M). The electrolyte which has been reported by Duffek et al. consisted of either 2 or 10 pct water by volume in ethylene glycol and 4.0 g KNO3 in 1000-ml solution. The electrolyte is best prepared

Jan 1, 1967

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By A. L. Pranatis, G. M. Pound

Changes in length of copper foils of varying thickness and grain size were measured under such conditions of low stress and high temperature that it is believed that creep was predominately the result of interboundary diffusion of the type recently discussed by Conyers Herring. The surface tension of copper was calculated and results confirmed previous work within the limits of experimental error. Under the assumption of viscous flow, viscosities were calculated as a function of temperature and grain size. Predictions of the Nabarro Herring theory of surface grain boundary flow were borne out fully and the Herring theory of diffusional viscosity is strongly supported. ONLY a relatively few techniques for obtaining the surface tension of solids are presently available. Of these, the simplest and most straight forward is the direct measurement of surface tension by the application of a balancing counterforce. Thin wires or foils are lightly loaded and strain rates (either positive due to the downward force of the applied load or negative if the contracting tendency of surface tension is sufficiently greater than the applied stress) are observed. By plotting strain rates against stress, the load which exactly balances the upward pull is found and a simple calculation yields a value for the surface tension. The technique is of comparative antiquity, and solid surface tension values were reported by Chapman and Porter,' Schottky; and Berggren" in the early part of the century. Later, the filament technique became fairly well established as a method for determining the surface tension of viscous liquids, and Tammann and coworkers,'. " Sawai and co-worker and Mackh howed good agreement between the values of surface tension for glasses and tars obtained by the filament technique and by more conventional methods. With the increased confidence in the technique gained in these experiments, the method was applied to solid metals and the first reliable values of surface tension of solid metals were reported by Sawai and coworkers10' " and by Tammann and Boehme." More recently, Udin and coworkersu-'" have reported the results of experiments with gold, silver, and copper wires. Similar experiments with gold wires were carried out by Alexander, Dawson, and Kling.'" The excellent review articles of Fisher and Dunn" and of Udinl@ should be referred to for detailed criticism of the foregoing work and for discussion of underlying theory. In all the foregoing calculations, it is assumed implicitly that the material contracts or extends uni- formly along the length of the specimen and also that it flows in a viscous fashion, i.e., that strain rates are proportional to stress. For an amorphous material, such as glass, tar, or pitch, the assumptions are quite valid and good agreement is obtained with values of surface tension measured by other techniques. The values reported for metals, however, are occasionally regarded with misgiving, since it can be argued that, because of their crystalline nature, true solids can not deform in a viscous fashion. If this is true, then the results reported for solid metals over a long period of years are of only doubtful value. Thus it is clearly necessary that a mechanism be established that would explain both the viscous flow and the uniform deformation that has been assumed. Such a mechanism has been proposed by Herring."' Briefly, he suggests that, under the conditions of the experiment, deformation takes place by means of a flow of vacancies between grain boundaries and surfaces. This is a direct but independent extension of the theory proposed by Nabarro" in an attempt to explain the microcreep observed by Chalmer~.In a condensed form the Herring viscosity equation is TRL there 7 is the viscosity, T the absolute temperature, R and L grain dimensions, and D the self-diffusion coefficient. In its complete form, all constants are calculable and it includes such factors as grain shape, specimen shape, and degree of grain boundary flow. When applied to existing data, good agreement was obtained between predicted and observed flow rates. The theory received provisional confirmation from the work of Buttner, Funk, and Udin" who observed viscosities in 5 mil Au wire much higher than those in the 1 mil wire used by Alexander, Dawson, and Kling.'" More significant were the completely negligible strain rates found by Greenough" in silver single crystals. Opposed to these observations were those of Udin, Shaler, and Wulff'" who found indications of viscosity decreasing as grain size increased. Thus, complete confirmation of the theory was lacking in that the data to which it could be applied contained only a limited number of grain sizes. Hence, it was proposed that a series of experiments be carried out with thin foils of varying grain size up to and including single crystals, where, according to the Herring theory, deformation would occur only at almost infinitely slow rates.

Jan 1, 1956

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By M. R. Yalamanchili, J. D. Miller

Discussion by M.R. Yalamanchili and J.D. Miller The authors, M. S. Celik et al., should be recognized for their efforts to describe the flotation behavior of boron minerals. In the case of borax and other soluble salt minerals, analysis of the flotation chemistry has been difficult because of the high ionic strengths associated with these soluble salt systems. However, considerable progress has been made in this area, and recently a surface charge/collector colloid adsorption model was proposed by Miller and his coworkers to explain the collector adsorption phenomena observed in soluble salt flotation systems (Milleret al, 1992; Yalamanchili et al., 1993; Miller and Yalamanchili, 1994; Yalamanchili and Miller, 1994a: Yalamanchili and Miller, 1994b). In this work, the sign of the surface charge of alkali halides in their saturated brines was established on the basis of nonequilibrium electrophoretic mobility measurements by laser-Doppler electrophoresis (Miller et al., 1992). Generally, these results are what would be expected from the simplified lattice-ionhydration theory. This electrokinetic information coupled with the stability and prevalence of collector colloids in such soluble salt flotation systems indicates that the selective flotation of alkali halides is due to the adsorption of oppositely charged collector colloids by heterocoagulation. Experimental flotation/bubble attachment results for 21 different alkali halides (Yalamanchili et al., 1993; Yalamanchili and Miller, I994b) confirmed that the flotation response of soluble salt minerals with weak electrolyte collectors can best be explained by the adsorption of oppositely charged collector colloids rather than by the adsorption collector ions and/or neutral molecular dipoles as originally suggested by many researchers (Fuerstenau and Fuerstenau, 1957; Schubert, 1967; Roman et al., 1968). In addition, the flotation of certain alkali oxyanions (Pizarro et al., 1993) and double salts such as schoenite and kainite can be explained by the same collector colloid adsorption mechanism (Miller and Yalamanchili, 1994). The borax flotation results reported by Celik et al. need to be examined in terms of the above mentioned surface charge/ collector colloid adsorption model. Unfortunately, the authors seem to be unaware of this recent work that nicely describes soluble salt flotation with weak electrolyte type collectors such as amines and carboxylates. In view of our past work, the flotation characteristics of borax were of particular interest, and, in this regard, the results of dodecyl amine flotation of borax reported by Celik et al. have been examined in further detail in the light of experimental results from our laboratory. In our research, a vacuum flotation technique was used to study the flotation response of borax (Na2B407.10H20), which has a solubility of 39 g/L at 25 °C) with dodecyl amine hydrochloride as collector. These chemicals were purchased from Eastman Kodak and used as received. Saturated solutions of borax at desired pH values were prepared by continuously stirring the salt solutions over a period of about 10 hrs. It should be mentioned that the conditioning time to achieve equilibrium is an important variable and can significantly change the flotation response of some soluble salts (Yalamanchili et al., 1993). Collector was added to the saturated borax solutions containing about one gram of 100x 150 mesh borax particles, and conditioning was done for about 20 minutes prior to flotation. The borax flotation recoveries from saturated brine are presented in Fig. 1 as a function of collector addition at the natural pH of 9.3, as reported both by Celik et al. and as measured in our laboratory. In addition, the region of precipitation for the dodecyl amine hydroborate is included in Fig. 1. It can be seen in Fig. 1 that the flotation response curves are separated by about one order of magnitude in R12NH3CI collector addition. The flotation results of Celik et al. show that the maximum borax recoveries can be obtained below the solubility limit of the dodecyl amine hydroborate collector. However, in our experiments borax flotation seems to occur only after the precipitation of the dodecyl amine hydroborate collector as might be expected from the collector colloid adsorption model (Yalamanchili et al., 1993) if borax were negatively charged. Further analysis by nonequilibrium and equilibrium electrophoretic mobility measurements for borax indicates that borax is negatively charged at the natural pH of 9.3, as discussed below. The reliability of the nonequilibrium electrophoretic measurements has been demonstrated previously for alkali halides and alkali oxyanions (Miller et al., 1992; Miller and Yalamanchili, 1994). The equilibrium and nonequlibrium electrophoretic measurements for borax were found to be consistent and are presented in Table 1. These results provide clear evidence that borax carries a negative surface charge in its saturated brine (pH 9.3), and the sign of the surface charge of borax reverses and becomes positive if the pH is reduced to 8.6. The equilibrium between borax and its saturated brine can be described by the following reaction: [2Na2B407.1OH2O-4Na++B407=+HB4O7 +OH+19H20] It appears that the oxyanions of the borax lattice provide

Jan 1, 1995

By Kurt D. Mitchell

"This paper discusses general application for A C variable frequency drives in the mining industry. A review of induction motors characteristics, adjustable frequency controller fundamentals, and three commonly used controllers is presented. General application guidelines for the three different types of controllers; variable voltage input , current source input and pulse width modulated are then reviewed in detail, and an example of the economic benefit of this technology is discussed. IntroductionSoon after static DC variable speed drives were well established in industry, a need for static AC variable speed drives was seen. The first technical papers describing possible systems appeared in the mid-1960s, with commercially available units arriving in the early 1970s. Without exception, static AC drives are substantially more complex than their DC counterparts, but they have some very desirable properties. As compared to DC motors, AC motors are less costly, physically smaller, more reliable, require less maintenance , easily sealed, have good load regulation, are able to run at higher operating voltages, and have little danger of over-speed runaway . These properties are particularly desirable in explosion-proof, submersible or difficult accessibility applications.Variable speed AC drives are now a proven technology. available in packages from Sub-horsepower to hundreds of horsepower, from 115VAC to 4160 VAC. This paper covers the principles of operation of three common types of controllers, application criteria, motor consideration and finally an example of how an AC variable speed drive can pay for itself in terms of energy savings."

Jan 1, 1986

By D. J. Hutchinson, M. Lato, M. Diederichs

Light Detection and Ranging (LiDAR)-based applications for geomechanical purposes have recently proven to be a highly reliable and accurate form of remote analysis and documentation. The ability to remotely collect, process and evaluate rockmasses for structural geomechanical applications has benefits ranging from safety to efficiency, and provides a permanent record that can be assessed before and after an excavation has been completed. With the collaboration of Queen’s University and Rio Tinto, the Iron Ore Company of Canada (IOC) mines in Labrador City, Newfoundland and Labrador, evaluated the practical application of the I-Site 4400 LiDAR equipment, in conjunction with the Vulcan geotechnical module for geomechanical purposes. The project provided a comparative analysis between conventional hand-mapping and digital analysis. The analysis indicates that digital mapping could be employed as an active tool within the general geotechnical workflow, where results would be used in pit wall and rockmass support designs. As well, the field work enabled the generation of effective operational guidelines and protocols to maximize scanning efficiency.

Jan 1, 2009

By M. R. Tek, F. F. Craig, J. O. Wilkes, C. S. Goddin

The waterflood performance of a water-wet, stratified system with crossflow is computed by a finite difference procedure. The effects of five dimensionless parameters on tile oil displacement efficiency, water saturation con-tour.7 and crossflow rates are evaluated in the absence of gravity forces. Crossflow due to viscous and capillary forces is shown to exert a significant effect on oil recovery in a field-scale model of a two-layered. water-wet sandstone reservoir. The crossflow is at a maximum in the vicinity of the front advancing in the more permeable layer. Under favorable mobility ratio conditions, the comparted oil recovery with crossflow always is interrnerliate between that predicted for a uniform reservoir and that for a layered reservoir with no crossflow. INTRODUCTION The important erects of reservoir heterogeneity on waterflood performance are commanding increased attention in the technical literature. Much of this attention is centered on two categories of layered reservoirs: those in which layers are non-communicating and those in which crossflow of fluids occurs between the layers. In the first category, the reservoir is assumed to consist of discrete layers, each uniform within itself and differing from the others only in such properties as thickness, porosity and absolute permeability. The performance within each layer is calculated by one-dimensional flow theory, and the performance of the total reservoir is obtained by summing individual layer performances. Capillary and gravity effects usually are not considered. Representative publications dealing with thi5 type of reservoir are those of Stiles,' Dykstra and Parsons,' Hiatt,3 Warren and Cosgrove' and Higgins and Leighton." Prediction of performance for reservoirs in the second category is considerably more difficult since viscous, capillary and gravitational forces all play important roles in causing crossflow between layers. A number of authors have investigated the simpler problem of two-dimensional displacement flow in a stratified system with a mobility ratio of unity and negligible capillary and gravity effects.'; Others have considered two-dimensional, non-steady-state flow of a single, slightly compressible fluid in a stratified reservoir. A limited number of laboratory oil displacement tests in layered models with crossflow have been reported. Miscible floods (with resultant zero capillary forces) in layered five-spot models were conducted by Dyes and Braun," who studied the effect of mobility ratio with zero gravity forces, and by Craig et al. 12 who studied the effect of gravity forces at constant mobility ratio. Waterfloods in layered five-spot models (with cross-tlow due to capillary, viscous and gravity forces) were conducted by Gaucher and Lindley,"' who showed the effect of gravity forces in causing underrunning of the injected water and by Carpenter, Bail and Bobek, 14 who demonstrated the reliability of Rapoport's" dimension-less parameters for scaling layered systems. Waterfloods in rectangular layered models were conducted by Richardson and Perkins."' who investigated the effect of velocity at constant mobility ratio and with zero gravity forces, and by Hutchinson," who studied the effects of varying mobility, layer permeability and layer thickness ratios. The differential equations which rigorously describe waterflooding in a heterogenous porous medium are non-linear and do not facilitate analytical solution. By using finite difference approximations it is possible to obtain a solution to any desired degree of accuracy. Such a solution, using an alternating direction implicit procedure (ADJP), is described by Douglas, Peaceman and Rachford.18 In the present study, a computer program using ADJP explores systematically the effects of important parameters on waterflood performance of a two-dimensional, two-layered, field-scale model of a water-wet sandstone system. Particular attention is given to evaluation of the water saturation contours and crossflow rates at the interface between layers to gain improved understanding of the crossflow mechanism. PROCEDURE BASIC: FLOW EQUATIONS The basic flow equations for two-dimensional, two-phase, immiscible, incon~pressible flow in a porous medium are:

Jan 1, 1967

By P. H. Turnock, R. D. Pehlke

The effects of mutual interactions between elements on the solubility of nitrogen in liquid iron alloys containing chrormium, columbium, molybdenurn, nickel, or silicon have been determined. The equilibrium nitrogen solubilities in the liquid iron alloys were measured by the Sieverts method. The second-order effects caused by the presence of chrormium, columbium , or silicon in the melt were found to be significant. The solubility of nitrogen in liquid iron alloys containing several alloying elements has also been measured as a function of melt temperature and nitrogen pressure. The heat of solution of nitrogen in microcomponent iron alloys has been found to be a function of the logarithnz of the activity coefficient of nitrogen, irrvespectilje of the composition of the melt. The heat of solution of nitrogen in pure liquid iron was determined to be 1265 ± 450 cal per g-atom of N over the temperatxue range 1600° to 1800°. Sieverts ' law was obeyed for all melt compositions studied in the pressure interval 0.4 to 1.0 atm. The solubility of nitrogen in liquid pure iron and in many dilute binary liquid-iron alloys has been the subject of many investigations. Pehlke and Elliott' made a comprehensive investigation on this subject in which they summarized and compared previous researches. However, the practical application of these solubility studies requires prediction of the nitrogen solubility in the multicomponent alloys encountered in operating practice. The interaction parameter as defined by wagner2 has been used to predict the behavior of a solute in a complex alloy, and a modification of this approach has met with reasonable success in several instances.'1"5 The necessity for extending the nitrogen solubility data on binary alloys is caused by the lack of direct measurements of the solubility of nitrogen in molten alloy steels. A direct comparison between measured solubilities and those predicted for multicomponent alloys based on data in binary systems has been made in only a few instances, and most of these were reviewed by Langenberg,6 who developed a graphical technique for predicting nitrogen solubilities in multicomponent iron alloys. The solubility of nitrogen has also been studied over the entire Fe-Cr-Ni ternary system by Humbert and Elliott.? Both studies compared the solubilities computed from binary iron alloy data with those measured in ternary alloys in the liquid state at 1600°C. Most of the nitrogen solubility measurements referred to above were for iron alloys at 1600°C; thus, the ability to predict nitrogen solubilities in molten iron alloys has been restricted primarily to alloys at 1600°C. Recently, Nelsson8 devised an approximate method for calculating the change in nitrogen solubility in molten iron alloys as a function of temperature, but an assumption of regular solution behavior limits the applicability of the method. Chipman and Corrigan9,10 have developed an empirical correlation. based on the activity coefficient of nitrogen in the iron alloy at 1600°C, which facilitates the estimation of nitrogen solubilities at higher temperatures. This method also has limitations, due to the necessity of calculating the activity coefficient for nitrogen in a multicomponent iron alloy at 1600°C from the nitrogen solubility data for binary iron alloys. The shortcoming of such a straightforward approach to the problem of predicting nitrogen solubilities is the disregard of mutual interactions between elements in a complex iron melt. This investigation was conducted in an attempt to provide a more reliable method of predicting nitrogen solubilities in multicomponent iron alloys. The effects of the mutual interactions between chromium, nickel, silicon, molybdenum, or columbium in iron were studied, using the Sieverts' technique1,7 to measure the effects of alloy composition, temperature, and pressure on the solubility of nitrogen in ternary liquid iron alloys.

Jan 1, 1967

By W. N. Miner, R. O. Elliott

Electrical-resistivity )measurments were made be-trueetz room temperatrive and 1.5 oK on five different stocks of cerium metal, and the results were correlated with the types, amounts, and distribution of the impurities present. Magnesium, which appeared to be distributed as a solute throughout the cerium matrix, was found to have a large effect on the residual resistivity, 1 at. pct Mg being sufficient to increase the residual resistivity by about 10 microhm-cm. The formation of ß by repeated thermal cycling between room temperature and liquid-helium temperature is attributed to the deformation and faulting that occurs during the ? D a transformation. In preparation for starting a proposed study of cerium-rich alloys, we examined samples from severa1 stocks of cerium metal in order to choose the purest stock for future use in making the alloys. Low-temperature electrical-resistivity data were used to gain initial information about the purities of the stocks. Additional information was subsequently obtained from chemical analyses, density measurements, optical metallography, and electron-micro-probe analyses. Cerium that has been annealed at high temperature and cooled to room temperature has the fee crystal structure (? phase) with a = 5.16Å. When cooled further, in the region between about 250" and 150°K, some of the fee phase transforms to the double hcp form (ß phase) with a = 3.68 and c = 11.92Å. The remainder of the room-temperature fee form (and perhaps some of the hexagonal phase) transforms electronically in the vicinity of 100° K to the more dense or "collapsed" fee form (a phase), a - 4.85A, by transferring about 0.5 electron per atom from the 4f level to the valence band. Very little work related specifically to the effects of impurities on the physical properties of cerium has been reported in the literature. Gaume-Mahn1, 2 has studied the effects of calcium, magnesium. iron, silicon, and tantalum on the electrical resistivity and magnetic susceptibility of cerium between 60o and 300°K. Gschneidner, Elliott, and McDonald3 have discussed the effects of total impurity content on the hysteresis of the a —? (reversible) transformation and on the formation of the 4 and "a-? intermediate" phases. Smith and Morrice* have reported the effect of total impurity content on the resistivity of cerium at 4 and 293°K. In none of these reports, however, is it apparent that the distributions of the impurities were determined, L.r., whether the impurities were present in inclusions or in solid solution in the matrix is not mentioned; nor does it appear that the phase purity of the cerium was always considered. In the present study, five different stocks of cerium were involved. One was represented by a single sample of electrowon cerium, which was all that had remained from a stock of high-purity material obtained from the U.S. Bureau of Mines, Reno, Nev., in 1959. The other four stocks were recently purchased from commercial sources and were specified to be 99.9 wt pct pure. EXPERIMENTAL Cerium stocks designated as #1, #2, #4, and #5 were obtained from commercial suppliers for the specific purpose of finding a reliable source of high-purity cerium. Although the purity level of the cerium was specified to be 99.9 pet, the specifications did not include limits as to the amounts of various impurities that would be acceptable. Consequently the chemical analyses of the different stocks varied widely. Stock #3, which had been obtained from the U.S. Bureau of Mines and which was the purest on the basis of chemical analyses, consisted of a single specimen of electrowon cerium. It was included in the examination for purposes of comparison. Table I contains the chemical and spectrographic-

Jan 1, 1968

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967

By S. K. Mitra

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

Jan 1, 1962

By H. L. Hartman

The estimation of the magnitude of pressure changes which occur in mine ventilation circuits is of primary importance to the mining engineer in making changes in an existing mine or in projecting the ventilation requirements of a new mine. It is a formidable task in many cases, because no adequate theory is available and empirical data are unreliable or even lacking. The common practice of increasing one's estimate of the mine static pressure by an arbitrary "safety factor" to compensate for the unknown is a poor substitute for accuracy. Generally little difficulty is encountered in calculating friction losses in mine airways. As long as the friction factor can be reliably estimated, the well-known Atkinson formula gives accurate results. However, it is in the determination of shock losses that the ventilation engineer encounters difficulty and is apt to resort to an arbitrary allowance. Shock losses may constitute as little as five or as much as twenty-five percent or more of the overall pressure drop in the mine, and such allowances are generally completely unsatisfactory. Since other shock losses have been covered by McElroy (1), this paper deals with a long-neglected source of shock and pressure change in ventilation circuits, divergence and convergence of airflows, here referred to by their more common mining terms, splits and junctions. PREVIOUS WORK There is practically no fundamental information available in ventilation literature on the splitting and junction of airflows, either in mining or mechanical engineering periodicals or handbooks. Fluid mechanics textbooks seemingly avoid the subject of divergence and convergence, except for brief empirical treatment. The only investigation reported for mine ventilation systems was by Weeks, et a1 (21), in 1933. Although applicable to the case of line brattices in coal mines, it cannot be applied to the general case of mine splitting and junctions involving change of direction with little or no area change. In dealing briefly with the subject of shock losses at splits and junctions, McElroy (1) suggests only that they be considered comparable to bends, with losses at junctions being increased 50 pct to allow for interference of merging streams. He recognizes the importance of quantity ratio but concludes that exact quantitative data are lacking to compute losses at splits and junctions. A very capable summary and analysis of the state of knowledge in industrial ventilation and fluid mechanics regarding losses due to divergence has recently been reported by Gilman (3). In considering all earlier work dealing with both air and water as fluids, he compares results on a common basis and obtains good empirical agreement. For divergent flow, the controlling variable in each branch is the quantity ratio, although the deflection angle is of secondary importance. Empirical equations are presented for straight and 90-deg branches with varying velocity ratios, assuming branches smaller than the main duct. These formulas are modifications of the Borda equation for abrupt contraction and expansion. The only information available on shock losses in convergent flow are approximate experimental data presented by Alden (4) and the Manual of Recommended Practice for Industrial Ventilation of the American Conference of Governmental Industrial Hygienists. Alden considers the effects of both quantity ratio and deflection angle. The data indicate an effect opposite to that observed in divergence, the shock loss varying directly with quantity ratio. SHOCK LOSS THEORY Because pressure losses due to shock have been found to bear a constant relation to the mean velocity of flow in a given conduit, they are frequently expressed as a dimensionless function of the velocity head, termed the shock loss factor. For airflow in ducts and mine airways, the shock loss may be represented by the formula (1): Hx - XHv, (1)

Jan 1, 1961