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By F. F. Skiba, J. E. Warren

An idealized miscible displacement process in a three-dimensional, heterogeneous porous medium has been studied via experimental computation based on a "Monte Carlo"' model. The macroscopic dispersion which results solely from variations in the permeability of the porous system is related to the scale of the heterogeneity as well as the distribution function for the permeabilities. The interpretation of laboratory data is often subjective and may bt? misleading since ambiguities are not always recognized. Furthermore, an experiment performed on a conventional oil-field core does not yield a valid measure of Macroscopic dispersion for reservoir engineering purposes since the scale of heterogeneity that is significant in the laboratory is not significant in the reservoir. The analysis of field-performance data is discussed and it is shown that a unique characterization of the reservoir can not be obtained from this information alone. A possible method based on a minimum of data, for estimating the spatial distribution of permeabilities in a reservoir is postulated INTRODUCTION Many studies concerned with diffusion and dispersion in porous media have been undertaken because of the potential importance of miscible displacement processes for increasing the recovery of oil. The results from a large number of these studies have been published; in a recent paper Perkins and Johnstonl presented a comprehensive survey of the pertinent literature and excellent appraisal of the "state of the art". In this investigation, dispersion resulting from macroscopic variations in the properties of the porous medium is of primary interest. Dispersion, in this sense, is caused by fluctuations in the velocities of the individual fluid elements as they move through the porous system. This phenomenon is the result of inhomogeneities in the permeability and/or porosity, but it can be amplified by differences in the characteristics of the fluids involved. The objectives of this study are the following: (1) to determine the qualitative manner in which macroscopic rock properties affect the observed dispersion coefficient; (2) to evaluate the possible influence of macroscopic dispersion on laboratory experiments; and (3) to appraise the significance of macroscopic dispersion with regard to reservoir performance. Investigations of this type are essential since many miscible displacement processes, while seemingly understood from a mechanistic point of view, do not behave in a predictable manner under field conditions. Although a plausible explanation is that the process is dominated by the environment, little serious effort has been devoted either to describing the reservoir itself or to determining the probable effect of the reservoir properties on the process. This study is intended to be exploratory in nature; however, it is hoped that it will provide additional insight into the physical problem and that it will suggest areas suitable for further investigation. EXPERIMENTAL COMPUTATION MODEL To limit the observed dispersion to that which results solely from variations in the properties of the porous medium, an idealized process in which one incompressible fluid displaces another identical fluid is simulated. This simulation is achieved by means of a modified Monte Carlo method — by tracking a number of mathematical particles (tracer) through the system according to the steady-state, single-phase velocity distribution. Then the system is characterized by the distribution of the residence times of the particles. Since any number of particles can be injected simultaneously (a true delta-function distribution) and only pressure conditions are imposed on the boundaries, the model is completely determinate. Furthermore molecular diffusion, microscopic dispersion, adsorption and/or reaction are automatically precluded from the model. The heterogeneous medium is represented by a rectangular, three-dimensional array of uniform, homogeneous porous blocks which are randomly arranged; it is assumed that any two opposing faces of the system are held at fixed potentials

Jan 1, 1965

By R. F. Mehl, G. T. Horne

Diffusion coefficients and mobilities were determined as functions of concentration in the a phase of the Cu-Zn system. Use was mode of incremental diffusion couples to determine the Kirkendall effect at various concentrations. Darken's analysis was used to calculate the individual diffusion coefficients and mobilities from these data. The general diffusion coefficient is a single-valued function of the concentration in this system to within the limits of accuracy of the experimental methods used. The form of the various functions (diffusion coefficients and mobilities) of concentration is the same in every case: it is essentially the same as the usual D vs c curve. AS Darken' has pointed out, the knowledge that the movements of different atoms diffusing in the same lattice need not proceed at the same rate is old. Ionic lattices are the classical examples; application of the generalization to lattices with metallic bonding was much more slowly accepted. It remained for Kirkendall'' to show clearly that metallic diffusion need not be symmetrical with respect to both species. Several investigators" have confirmed the initial observation of a "Kirkendall effect:" marker movement accompanying diffusion. They have extended it to other systems and conditions. The theoretical interpretations have been many; ne of the first and simplest of these is that of Darken"' which is essentially mechanism independent. Darken has shown that the Kirkendall experiment permlts a calculation of the individual diffusion coefficients and, coupled with activity data, offers a means of measuring the mobilities of the separateatoms in a binary diffusion process. There is no published information on the effects of concentration and temperature on the individual diffusion coefficients or on the mobility values in binary solid solution; this paper provides such information for zinc and copper in a brass. For purposes of clarity, the overall D value obtained, for example, from the Boltzmann-Matano solution to Fick's law, will be designated as the "general diffusion coefficient;" and the diffusion co- efficients for the separate diffusing species will be designated as the "individual diffusion coefficients." Experimental Procedure The authors have accepted Darken's analysis and have measured mobilities on this basis. The findings of da Silva and Mehl are accepted: that the Matano interface, defined as the origin of coordinates for the Boltzmann-Matano solution to Fick's law, coincides with the original weld interface; that the "shift" of a marker is the distance between the Matano interface and the marker; that the observed porosity is too small sensibly to affect this result; and that the shift is a linear function of the Matano area, the area defined as the absolute magnitude of the area on either side of the Matano interface. Alloys: The a-phase of the Cu-Zn system was chosen for investigation. The measurements were made on incremental couples for two separate reasons: l—it has been questioned whether D, the general diffusion coefficient, is a single-valued function of concentration (a comparison of the D-values for couples with small concentration range, e.g., 10 vs 20 pct Zn, against those from a wide concentration range, e.g., 0 vs 30 pct Zn, will answer that question); and 2—on the Darken analysis, the mobility can be determined only at the concentration at which the marker is observed to lie (this is but one concentration in a single couple) but choosing a series of incremental couples in the range between 0 and 30 pct Zn provides mobility values at several concentrations, thus giving mobility as a function of concentration. Four alloys were chosen; nominally, pure copper, copper with 10 pct Zn, copper with 20 pct Zn, and copper with 30 pct Zn. This allowed six different types of diffusion couples to be prepared, promising mobility determinations at six different concentrations, but having a minimum range of 10 pct Zn. The copper was an especially prepared pure copper supplied through the courtesy of the Ameri-

Jan 1, 1956

By M. R. Geer, H. F. Yancey

THE performance of coal-washing equipment, that is, the effectiveness with which coal and impurity are separated, is a subject of undisputed interest to all concerned with the preparation of coal. Through the years much has been written in both American and European literature on the performance of coal-washing equipment and its interpretation, but until recently no effort has been made to consolidate this wealth of information into a single, comprehensive treatment of the subject. A splendid effort in this direction was made at the First International Conference on Coal Preparation held in Paris in June 1950 in which representatives from virtually every coal-producing country participated. Although the scope of the conference covered the entire field of coal preparation, many of the sixty-odd papers and a great deal of the discussion dealt with the subject of evaluating washery performance. Prominence was given this subject by the Centre d'Etudes et Re-cherches, des Charbonnages de France, which sponsored the conference. This research organization, generally referred to as Cerchar, was formed in 1948 following the nationalization of the French coal industry. Since that date it has conducted an intensive study of coal preparation. Perhaps because of a fresh viewpoint, Cerchar realized immediately that complete information on the performance of French washeries and a thorough understanding of the mechanism of gravity separation were the fundamental prerequisites in a program to improve preparation practice. For this reason Cerchar concentrated on obtaining performance data and on a comprehensive study of methods of evaluating such information. Some idea of the magnitude of this work will be appreciated from the fact that 175 performance tests were made in 44 plants. The work performed by Cerchar emphasized a condition that is recognized by many of those concerned with coal preparation, namely that the lack of uniformity in presenting data on washery performance, the diversity of methods used in evaluating such information, and the frequent confusion of the terms related to performance have been prime factors militating against the progress from art to science. Thus, Cerchar feels that standardization of the methods employed for evaluating washery performance, not only in France but in the entire world, is essential to progress, and the prime objective of the Paris conference was to seek international standardization of the evaluation methods advocated by Cerchar. At the conclusion of the conference the question of standardization was referred to the International Standards Organization. A careful study of the dozen papers on the subject of evaluating washery performance presented at the conference reveals that none of the methods is new; most of them date back over a decade. Nevertheless, the intensive scrutiny of these methods brought about by the conference unquestionably has resulted in a valuable exchange of ideas and a clarification of thought that could scarcely be achieved in any other way. The object of the present report is to make available to the American coal industry the ideas developed at the conference which seem most important from an American viewpoint and to provide a critical analysis of some of the evaluation methods advocated by Cerchar. The various methods of evaluating washery performance are illustrated partly with data that have been published in American literature, and some new data have been obtained as the result of experimental work undertaken since the conference to provide information on certain controversial points. An English translation of the proceedings of the conference, including the discussion as well as the papers, will be available,' and previous to the conference Coal Age2 published a very brief description of some of the principal evaluation methods used by Cerchar. Americans will appreciate as well as do the French the desirability of standardizing both the termi-

Jan 1, 1952

By David White

THE search for potash salts in the great "Red Beds? region of the Southwest, conducted for several years by the U. S. Geological Survey, the work being carried on for a part of the time in coöperation with the Bureau of Economic Geology and Technology of the University of Texas, has resulted in the discovery, within shafting depth, of potash salts, apparently of workable thickness and commercial quality, and prob-ably of great extent. Definite information is lacking as to the exact thickness of the potash beds, the size and boundaries of the areas underlain by workable strata, and the locations of the deposits richest and most favorably situated for exploitation. Briefly to review the salient features, of the general situation: We have in the great Red Beds region of the southwestern United States, embracing portions of central Kansas, western Oklahoma, eastern New Mexico, and northern and western Texas, .a series of sandstones. shales, anhydrite beds, clays and limestones, which; through an interval of 1000 ft., more or less, carry beds of salt, estimated by Darton1 to contain over 30,000 billions of tons of rock salt. It is the greatest known salt field of the world. At some points the intercalated beds of rock salt, one of which is reported by the driller to exceed 300 ft. in thickness, aggregate, accord-ing to the drillers' records, over 1000 ft. The sedi-mentary strata are similar in composition to those carrying the potash deposits of western Europe, and they were laid down at the same time and under condi-tions which, in many respects at least, were similar The stratigraphy and character of the beds are des-cribed by Darton2 and a, part of the area and the reported aggregate thicknesses of salt are shown, with some revision after Darton, in the accompanying map Fig. 1. The assumption that in the great areas of shallow evaporation basins spread over -the vast base-level region of saline deposition in the Southwest during Permo-Triassic time, potash salts were in some places, and at different stages, thrown down in crystalline deposits associated with the beds of rock salt, anhydrite, and gypsum, is, geologically speaking, more than reason-able. They are to be expected, and the conviction that they are probably present has long been held both in the Texas Bureau of Economic Geology and Tech-nology, under Dr. J. A. Udden, and in the- U. S. Geological Survey. Accordingly, for many years, efforts to determine whether potash deposits are present in this region have been made, though under very great difficulties, such as insufficient funds for boring, hack of drilling on private initiative in the more promising regions, hack of interest at first on the part of the drillers and companies, and, hater, inadequacy both of the methods of boring and of the sampling, to reveal in definite terms the thickness-of any saline stratum of given composition.

Jan 4, 1922

By F. B. Plummer

PETROLEUM ENGINEERING deals with the production, transportation, and refining of crude oil. Refining is chiefly the work of the chemical engineer; production, that of the petroleum engineer. Production engineering only is discussed in this paper. Petroleum production engineering is closest related to and, in fact, is a branch of mining engineering. Formerly, many petroleum engineers were trained as mining engineers or mining geologists. The profession is related also to mechanical and civil engineering to about the same extent that mining engineering is. Petroleum production draws upon the mechanical branch for drilling and pumping machinery and upon civil engineering for the construction of transportation lines, water supplies, and water-disposal plants. Fundamentally, petroleum production engineering deals with the removal of the oil from the reservoir rocks, just as mining is concerned with the removal of ore. The process of oil production demands a specialized knowledge just as distinct from mechanical and civil engineering as mining is distinct from operating a Diesel engine. Even though the chief tools of the petroleum engineer are the drill and the pump, these may be of little avail, and certainly not efficient, if their selection and use is not based on a knowledge of the physical chemistry of oil, the geology of the formations, the structure of the oil sand, the hydrodynamics of the reservoir, and the interrelation of all these many factors.

Jan 1, 1936

By H. Doi, Y. Fujiwara, K. Miyake

In order to throw light on the mechanism of plastic deformation of WC-Co alloys, compressive tests of WC-(7 to 43) vol pct Co alloys have been carried out at room temperature, and stress-micro strain relation has been investigated in detail. The analysis of the factors affecting the yield stresses reveals that the yield stresses can be predicted by modified Oro-wan's theory if one properly estimates the planar in-terfiarticle spacings. Conzpressive straining of some of the alloys by 0.066 to 0.17pct increases the decrements by a factor of as much as 3.4 to 14, whereas the corresponding increase in the electrical resistivities is less than 10 pct. The analysis of the decrement data in terms of -Gramto and Lücke theory shows that the marked increase is attributed to increased dislocation darnping itt the binder (cobalt) phase. By cornbilling the decrement data and the conzjwession duta, one obtains the relation between flow stress in shear (?t) and increase in dislocation density (p): At = const . v6 . This is interHeted to mean that the mechanism of strain hardening of CirC-Co alloys is essentially sarne as the one for dispersion strengthened alloys. The possible effect of bridge formations between the carbide particles has also been examined. OWING to the combination of hardness, strength, and other physical and chemical properties, WC-Co alloys have opened the way for unique fields of applications, the recent ones being, for instance, anvils for super-high-pressure generation apparatuses. In such applications, the alloys are frequently subjected to very high compressive stresses: these stresses may cause the alloys to deform plastically and eventually to fail. However, much remains obscure regarding the nature of the plasticity of the alloys. Evidently, the alloys owe their high strength to the hard carbide particles which frequently occupy as much as 80 to 90 pct in volume fraction, whereas the ductility required for practical applications is provided by the small amount of the binder phase between the carbide particles. When the volume fraction of the carbide phase is not very large, deformation behavior of the alloys may be described by some of the current dispersion strengthening theories. However, greatly increasing the carbide phase is thought to lead to some carbide skeleton structure or bridge formations owing to the increased chances for direct contacts between the carbide particles;1,2 this may appreciably affect the plasticity of the alloys. Regarding the effect of formation of the carbide skeleton structure, it is interesting to note the work by Ivensen et al.3 on compression tests of the alloys containing somewhat large carbide particles; they observe extensive generation of slip bands in the carbide particles after application of some preliminary compressive stresses. They interpret the results in terms of plastic deformatiot: of the carbide particles which are supposed to have formed a skeleton structure; the binder phase plays only a passive role, at least in the early stages of the deformation. That carbide crystals exhibit microplasticity at room temperature is apparent from the work of Takahashi and Freise4 and French and Thomas5 on indentation of WC single crystals. On the other hand, Dawihl and coworkers6-10 maintain that even when volume fraction of the carbide phase is very large (for instance, more than 90 pet), a very thin binder layer generally exists between the carbide particles. They interpret the results of the extensive mechanical tests in terms of the plasticity of such a layer. Gurland and Bardzil11 point out that decrease in ductility of the alloys with increase in the carbide phase is caused by the effect of plastic constraint exerted by the dispersed carbide particles. Drucker12 further develops this concept from a continuum-mechanics approach on an assumption that a continuous thin binder layer separates the carbide particles. A common feature of the studies reported so far on the plasticity of the alloys is that the information deduced is invariably qualitative in nature. Thus, very few systematic experiments for obtaining reliable and sufficiently detailed stress-strain curves of the alloys varying widely in the microstructural features have been carried out. In particular, it may be of special interest to investigate in detail the early stages of the plastic deformation of the alloys in order to shed light on the strengthening mechanism. However, such work appears to be extremely rare. Doi et al.13 recently reported a first brief account of the results of some quantitative analysis of the plasticity of the alloys in terms of dislocation theory. Their experiment was rather limited in the composition range covered (volume fraction occupied by the carbide phase: 79 to 83 pct), and thus they could not necessarily elucidate the controlling mechanism of plastic deformation of the alloys of a more general composition range. Consequently, in the present investigation, deformation behavior and some other physical properties of the alloys were investigated and discussed in more detail over a much wider composition range. SPECIMEN PREPARATION WC-Co alloys used in this experiment were prepared in cylindrical or rectangular form by sintering in vacuo compressed mixtures of tungsten carbide and cobalt

Jan 1, 1970

By C. H. Li, J. A. Sarteli, W. Bonfield

The stress to cause a permanent micros train of 2 x 10-6 in. per in. (defined as the microscopic yield stress) in beryllium is found to be very sensitive to surface condition. The initiation of plastic flow in as-machined specimens, which contain a high density of twins and large residual compressive stresses to a depth of about 0.010 in. from the surface, occurs by the nucleation of slip from high stress fields around twin tips in the surface layers. Removal of the damaged surface layers by chemical polishing results in an appreciable increase in the microscopic yield stress, which is attributed to the remoual of stress raising twins rather than to the release of residual stresses. IT is well known that the macroscopic mechanical properties of beryllium are very sensitive to the nature of its surface finish. Matthews and coworkers1 have shown that the tensile strength of rolled beryllium sheet can be considerably enhanced by chemical polishing, presumably due to the removal of the high concentration of notches, twins, and large residual compressive stresses normally found in the surface layers of ground specimens. There was no similar effect of surface condition on the macroscopic yield stress (the stress to produce 0.2 pct strain), a point to which we shall return. To date there have been no extensive studies on the effect of surface condition on the microstrain region of beryllium. Recent measurements2 of the stress to cause a permanent microstrain of the order of 10-6 in. per in. on machined hot pressed QMV beryllium, gave values ranging from about 600 to 3500 psi. Reasons for the considerable scatter in the results were not discussed. In this paper, we wish to show that the microstrain region of polycrystalline beryllium is, in fact, very sensitive to surface condition. The stress to cause a permanent strain of 2 x 10-6 in. per in. which for convenience we will refer to as the microscopic yield stress, can be increased by almost a factor of 2 by minimizing the amount of surface damage. The variation of microscopic yield stress is attributed to the presence of twins in the surface layers, rather than to residual compressive stresses. EXPERIMENTAL PROCEDURE The starting material for this investigation was commercial purity hot pressed QMV beryllium, with an average grain size of about 20 . The effects of surface treatment were assessed by comparing the microstructure with residual stress measurements and microstrain properties. Specimens were prepared for metallographic examination by wet grinding with 240, 400, and 600 papers, followed by polishing with a suspension of fine alumina in warm 20 pct oxalic acid. After this treatment, the surface could be examined, either in the unetched condition with polarized light, or after etching in 2 pct hydrofluoric or boiling 20 pct oxalic acid with normal light. Thin films of beryllium suitable for electron transmission study were prepared from bulk specimens by chemical polishing with hydrofluoric and phosphoric acids, and were examined in an RCA-EMU-3 electron microscope. Residual stress measurements were made by a procedure similar to that of Treuting and Read.3 Specimens 4.0 in. by 0.625 in. by 0.080 in. were prepared by three different machining procedures, namely: turning, grinding, and sawing, in order to introduce different levels of residual stresses. An electrical resistance strain gage was attached to one side of the specimen, and that surface was then protected by an acid-resistant enamel, while the opposite surface was removed by etching approximately one thousandth of an inch at a time. The change in specimen curvature in the longitudinal direction was noted and the residual stress was calculated by the following formula:

Jan 1, 1963

By J. Cervik, P. C. Thakur, S. D. Lauer

Methane drainage by cross-measure boreholes on retreat longwall faces can be a viable alternative to the vertical gob degas boreholes under favorable circumstances. The research was done in a mine working Pittsburgh coal seam in northern West Virginia under USBM Cooperative Agreement No. 14-09-0050-3252. The study was the first application of this technique to Pittsburgh coal seam. A total of 14 small diameter, inclined boreholes were drilled over a retreat longwall panel from gate roads, to intersect the overlying coal seams. All boreholes were manifolded to a pipeline and the gob gas was extracted by a surface exhaust fan. The methane capture ratio was poor at 7% to 18% at various stages of the longwall panel. A vertical gob degas borehole captured an additional 20% gas. Poor results were due to premature failures of the cross-measure boreholes leading to air leakage. For better performance, the boreholes should be drilled from a point 30 to 45 m (98 to 148 ft) from longwall pillar over the largest chain pillar. The standpipe should be grouted for at least 6 m (20 ft), and the entry containing boreholes and the pipeline must be supported to ensure access for maintenance and optimization of methane capture. Coursing the ventilation air around longwall such that it forces methane migration toward cross-measure boreholes can further improve methane capture. The optimum vertical inclination is 45º ± 10º.

Jan 1, 1986

By James W. Lower

IN developing the orebody on lower levels of the Star mine at Burke, Idaho, Hecla Mining Co. is faced with a serious problem in driving raises. Levels are at 200-ft intervals. As a raise is being driven between levels, at points about 70 and 130 ft from the sill, heavy pressure arches develop and the raise becomes extremely hazardous. Eventually, following a blast, caving occurs, making it impossible to recover the raise. In February 1957 it was decided to attempt sinking a small winze on the vein from the 5500 to the 5700 level. This shaft (winze-raise No. 2) was to be used as a raise prior to stoping. It was assumed, and correctly, that the heavy ground pressure could be controlled by timbering close to the bottom after each advance.

Jan 7, 1958

By J. F. Myers, R. J. Tower

"There is nothing new under the sun." All over the world, mineral-dressing engineers are working at their problems, no two of which are alike. Each encounters equipment and process problems. Many devise simple ways and means of overcoming their difficulties. Many of these problems are quite common in the industry, yet, since no one human being seems capable of thinking of everything, these problems at some plants often are looked upon as necessary evils. The purpose of this symposium is to gather together, from competent engineers, devices and practices that have been useful to them. Most of the ideas contributed are not new, yet there is no plant operator, old timer or youngster, who will not find some idea herein that will give him a suggestion for improving his operation. Space does not permit a complete elaboration on all of the contributions offered. Each item is summarized, but this will be ample for those skilled in the art of mineral dressing. A list of contributors appears at the end of the paper, and the superior number at the end of each item identifies its source. General Equipment A signal light to show that a steel bin, containing relatively line, moist ore, is full, can be made by suspending a copper rod in the bin to a sufficient depth to ensure ample contact with the ore. One wire of a 32-volt circuit should be attached to the rod and one to the side of the bin. Sufficient current will flow to make the signal light burn. A 110-volt circuit could be used, but 32 volts ensures safety.10 Fig I shows a circular bin for crushed ore. It is a concrete structure footed on the ground, using no supporting columns. Tailing from the sink-float was used for aggregate. Cross conveyors for discharging ore are not required, nor is a tripper for filling. Segregation is minimized by drawing from different gates. An exhaust fan on top of the bin eliminates condensation due to temperature of the ore.21 A beam with an adjustable point of suspension near the center permits rigging rolls for removal in a very few minutes. This makes unnecessary the lacing of the cable through the hub bolts on one side, around the shaft on the other, and the trouble of balancing the load.8 The ratchet handle on a Symons crusher may be replaced by a drum with a cable wound on it. When the cable is pulled by a crane or hoist it causes the drum to revolve and thus screws or unscrews the bowl. This reduces handwork and materially shortens the time required for the job.' TO Spread ore feed from an apron feeder over a belt conveyor, place a heavy steel bar about midway between the top

Jan 1, 1949

By Harry A. Lipsitt, Rollins E. Hook, Attwell M. Adair

A necessary condition for a uniaxial stress distribution in compression testing is that the specimen end surfaces make full contact with the apparatus compression plates. In addition all compression surfaces must be machined perpendicularly to the loading axis. In general this condition is not sufficiently fulfilled in a simple apparatus. Therefore on application of the load the compression plate may first touch the specimen at one point only. This may cause crumbling of the specimen if the material under investigation is brittle (e.g., ionic crystals). It also precludes a precise study of the beginning of deformation as the effective cross sectional area is unknown. In addition a complex stress state is set up which renders quantitative work impossible, e.g., on dislocation density and arrangement as a function of stress. To overcome these difficulties a "self-adjusting" upper compression plate is required. A simple and reliable method of achieving this is shown in Fig. 1: A steel hemisphere is placed on the specimen. As soon as the compression plate (which no longer needs precise machining) makes contact with this hemisphere the load is uniformly distributed over the whole specimen surface, and a homogeneous uniaxial state of stress results. An advantage of the method is that the loading is always central, even when the specimen surface is not parallel to the compression plate (Fig. 1, dashed line). Therefore to a first approximation a uniaxial state of stress is maintained if the misorientation of the specimen end surface is small. Two typical stress strain curves of identically prepared sodium chloride crystals are shown in Fig. 2; curve 1 was taken without and curve II with the hemisphere under otherwise identical conditions. The improvement in the accuracy of defining the beginning of elastic and plastic deformation is clearly indicated. The writer wishes to thank the Deutsche Forschungsgemeinschaft for financial support, and Professor P. Haasen for providing facilities for this work.

Jan 1, 1962

By P. F. Richardson, J. L. Perisho, W. J. Roe

Handling and transport of coal during the winter months can be a severe problem. The inability to unload frozen coal from rail cars produces serious economic and logistic problems due to transportation delays, rail car shortages, and demurrage on the rail cars. One method of dealing with the problem of unloading frozen coal has been to spray freeze conditioning agents onto the coal before it is loaded into rail cars. Both water soluble and oil based formulations have been used as freeze conditioning agents. The water soluble treatments generally contain a polyhydroxy alcohol, such as ethylene glycol, or salts of alkaline earth metals, such as magnesium chloride and calcium chloride, as freeze point depressants. The oil based treatments consist principally of hydrocarbons, such as No. 2 oil or diesel fuel. The authors' tests have shown significant differences in the effectiveness of these freeze conditioning agents, depending on the particular coal substrate being treated. These differences correlate with the coal porosity and inherent moisture of the substrate. In general, the greater the porosity of the coal, the smaller the effect of the freeze conditioning agents. Coal porosity has a greater impact on water soluble freeze conditioning agents than oil based products. The authors investigated the pore structure of a variety of coals using mercury intrusion. Findings were related to the effectiveness of different freeze conditioning agents as measured by unconfined compression strength tests. In general, coals with a large number of very small pores (between 0.05 µm and 0.03 µm) do not respond as well to freeze conditioning chemicals.

Jan 1, 1986

By Claus Guenter Goetzeil

(New York Meeting, February, 1937) The object of this investigation was to determine whether silver alloys could be used instead of the currently employed insert of high-expansion Average Coefficient per Deg. C. over Range 20° to 200° C. Pure aluminum..................................... 24.6 X 10-6 Cast low-expansion Si-Cu-Ni-A1 piston alloy............ 20.0 X 10-6 High-expansion austenitic Cu-Ni cast iron.............. 19.3 X 10-6 Cast steel (0.25-0.35 C, 0.40-1.0 Mn).................. 12.6 X 10-6 Cast iron (3.15 total C, 2.16 Si)....................... 12.8 X 10-6 Pure silver.......................................... 18.9 X 10-6 austenitic ferronickel alloy, to reduce the wear of ring grooves in light metal pistons. A typical example of a piston containing a ferronickel insert is shown in Fig. 1. The high coefficient of expansion of silver made it worthy of consideration, while the small size of the insert would render its use feasible in Germany as an emergency measure. The coefficients of linear expansion of several metals and ailoys are as shown in the table above. Obviously the melting point of the insert must be high enough to prevent it from melting when the light alloy is cast around it. This imposes a lower limit of about 850" C. for the solidus of the silver alloy. Pure silver melts at about 961" C., so that the tolerable depression in the solidus is rather small. To avoid deformation of the insert during use a Brinell hardness number of at least 60 appears necessary.

Jan 1, 1937

By H. U. Schutt, J. M. Toguri

REGARDLESS of the degree of purification effected during the electrorefining of copper, a danger of re-introducing impurities exists in the operation of melting and casting of the refined copper. Logically only a combination of the purification and casting operation would remedy the situation. A well-known method of metal purification is the "Gross"-type process, whereby a volatile halide is produced, purified, and decomposed.' In the present case, this concept was used to remove the impurities rather than to form possible volatile copper halides. The object was to produce volatile halides of the impurities present and distill these away, leaving high-purity copper. It is interesting to note that such techniques are used in spectrographic procedures in order to shorten exposure time and enhance the density of impurity lines.' In the present investigation, copper hydroxy fluoride was used, since the temperature of decomposition of copper hydroxy fluoride and the melting point of copper nearly coincide. The fluorine released by the thermal decomposition of copper hydroxy fluoride purges the molten copper. Copper hydroxy fluoride was prepared by dissolving high-purity copper in nitric acid and adding hydrofluoric acid and ammonium hydroxide in the required proportions. The melt was made in a high-purity graphite crucible heated by an induction furnace. Trial experiments showed that impurities can be introduced from the crucible material. Therefore, preceding each cast, the crucible itself was cleaned by decomposing copper hydroxy fluoride and discarding the residual copper. Best experimental conditions were obtained by adding 30 g of copper hydroxy fluoride to 500 g of nor-

Jan 1, 1967

INTRODUCTION The preceding chapters have brought us to a point in the mineral appraisal process where the composited sample values can now be used to estimate the grade and tonnage of the total mineral deposit. There are many techniques whereby drill hole composites and/or other sample data are used to assign grade and estimates to the surrounding rock. Matheron and his students have properly called such techniques extension functions. Before embarking upon a detailed discussion of extension functions, it is necessary that we take time to consider the concept of geostatistics as advocated by George Matheron who developed the "Theory of Regionalized Variables," which he published in 1962 (Matheron, 1971). The concept of regionalized variables has important application in the techniques of mineral appraisal. The position or location of a mineral sample within a deposit can be almost as important as its value. Geostatistics, when defined as "the application of the theory of regionalized variables* to the study of mineralized volumes of rock," takes into consideration the position as well as the magnitude of the value of the sample. The principles of geostatistics, as outlined by Matheron, represent a major step forward in the mineral evaluation process, because they provide a sound theoretical and practical basis for quantifying the geological concepts of (1) area of influence of a sample, (2) the continuity or lack of continuity of mineralization within the ore body, and (3) the lateral changes in mineralization according to the trend direction of an ore body and its orthogonal components; or in other words, a measure of the anisotropy of the deposit. Royle (1971) has defined the objects of geostatistic as being: "1. To estimate the most likely value of blocks of ore, or the values of the whole deposit; and 2. to estimate the errors of such estimates. This latter is important as, in addition to providing a check on unwarranted optimism, it shows where more valuation work may be needed." Because of the great importance of these concepts in mineral evaluation, an introduction into the theory of regionalized variables, and the study of a practical approach to its application is outlined here. REGIONALIZED VARIABLES VS. RANDOM VARIABLES Classical statistics, as discussed in earlier chapters, grew out of the study and application of probability theory. Probability is concerned with the outcome of random events and therefore classical statistics is built upon the theory of random variables, i.e., the probability of independent events. The validity of most statistical inferences depends upon sample randomness being assured for unbiased results. Where independent events cannot be assumed the results of statistical inference becomes suspect. On the other hand, geostatistics is concerned with variables that have position in space as well as magnitude, hence the term regionalized variables. Mineral deposits are not the only field to which the theory of regionalized variables is applicable. Many natural phenomena that demonstrate a relationship between change in magnitude and position in space are amenable to application of geostatistical techniques. Mineral deposits vary greatly in their geosta-

Jan 1, 1980

By A. U. Seybolt, C. H. Mathewson

As is well known, many questions affecting the properties and uses of a metal cannot be answered without careful consideration of the state of purity realized in the various operations of preparation, refining, or special treatment that have brought the product to its final state. The occurrence of an impurity in minute quantity offers no guarantee that its effect will be inconsiderable because dissolved substances often modify the properties of a metal quite out of proportion to their concentration. In such cases the determination of solid solubility must be accepted as a problem of considerable difficulty, requiring the use of especially purified materials and methods not ordinarily used in the metallurgical laboratory. This aspect of the equilibrium between metals and their oxides is especially important and a search for fundamental data reveals little except conflicting opinion even concerning the systems of common occurrence and interest. Rhines and Mathewson1 in 1934 studied the solubility of oxygen in solid copper by annealing to equilibrium in air and gave reasons for the failure of other methods, notably the ordinary procedure of heat-treatment followed by microscopic examination, to yield reliable results. In this paper, a similar study has been made of the solubility of oxygen in cobalt. The simple theory of this method is outlined below.

Jan 1, 1935

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before breakage, which appears as heat An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories the romnnred. THE present status of the theory of comminution is extremely unsatisfactory. The amount of various ores and rock products crushed and ground annually approaches the staggering sum of perhaps one half billion tons. Yet the basic concepts underlying an operation of such magnitude are unknown, and actual knowledge of what takes place in comminution is almost entirely empirical. The responsibility for this situation cannot be charged to apathy or lack of appreciation of the importance of the problem. Many attempts have been made to evolve a workable hypothesis, but none has been completely successful. General Considerations In order to break rock, it must be subjected to a stress which strains the rock beyond its critical breaking point. The stress imparts energy to the rock, most of which is released in the form of heat when the stress and resulting strain are removed. If the strain induced exceeds the critical strain, the energy is released by breaking; if the induced strain does not reach the critical point, the energy is released with removal of the stress as energy of resilience. Rock is a brittle material and it is assumed that it breaks approximately at its yield point, so that no permanent deformation results from strains below the critical. When rock is broken the total energy input is accounted for by the heat liberated, and by the surface energy of the new surface produced. A small and probably negligible amount is released as noise. Rock is commonly broken under compression and the applied stress is ordinarily compressive. However, for breakage to occur, it is only necessary that the induced strain exceed the critical value, and this strain may represent the resultant of compressive, shearing, and tensile forces. The stress-strain diagram of rocks under compression, and the modulus of elasticity as determined therefrom, should be fundamental considerations in the development of any theories of rock breakage. Crushing in jaw or gyratory crushers results primarily from a squeezing action, and reduction in a hammer mill is the result of impact. The action in rod and ball mills is a combination of impacting, squeezing, and wearing away by attrition, or rubbing. In ordinary crushing and grinding, the forces are applied at protruding points and are not distributed evenly throughout the rock. This is one of the features of comminution which theoretical considerations have not covered adequately. Another feature is the effect of impact velocities, which may greatly influence the total energy required for breakage. Impact velocities may vary from 1 or 2 fps in crushers to 10 or 20 fps for ball mills, and as high as 100 or more for hammer mills. However, according to the findings of geophysicists, the velocity of sound and of compression waves in stone is many times greater; the primary longitudinal compression waves travel at perhaps 15,000 fps, and the secondary transverse waves, which may reach the surface and cause cracks to form thereon, travel at perhaps 5000 fps. When a crack tip forms, the total surrounding stresses are concentrated in this tip, which rapidly extends throughout the rock particle.1 It would seem that the energy required to deform the rock beyond its critical strain, resulting in the formation of a crack tip, represents practically all of the energy required. Most of the primary crack tips presumably form on the surface. A simple method of designating feed and product size is necessary for the evaluation of crushing and grinding results. Taggart's suggestion2 that the 80 pet passing size be used has been found very practical. In this paper, the square opening screen size which 80 pct of the feed passes is designated as the feed size F, and the size which 80 pct of the product passes, or the product size, is designated as P. The reduction ratio at the 80 pet passing size, or F/P is designated as n. The feed and prod-

Jan 1, 1951

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before breakage, which appears as heat An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories the romnnred. THE present status of the theory of comminution is extremely unsatisfactory. The amount of various ores and rock products crushed and ground annually approaches the staggering sum of perhaps one half billion tons. Yet the basic concepts underlying an operation of such magnitude are unknown, and actual knowledge of what takes place in comminution is almost entirely empirical. The responsibility for this situation cannot be charged to apathy or lack of appreciation of the importance of the problem. Many attempts have been made to evolve a workable hypothesis, but none has been completely successful. General Considerations In order to break rock, it must be subjected to a stress which strains the rock beyond its critical breaking point. The stress imparts energy to the rock, most of which is released in the form of heat when the stress and resulting strain are removed. If the strain induced exceeds the critical strain, the energy is released by breaking; if the induced strain does not reach the critical point, the energy is released with removal of the stress as energy of resilience. Rock is a brittle material and it is assumed that it breaks approximately at its yield point, so that no permanent deformation results from strains below the critical. When rock is broken the total energy input is accounted for by the heat liberated, and by the surface energy of the new surface produced. A small and probably negligible amount is released as noise. Rock is commonly broken under compression and the applied stress is ordinarily compressive. However, for breakage to occur, it is only necessary that the induced strain exceed the critical value, and this strain may represent the resultant of compressive, shearing, and tensile forces. The stress-strain diagram of rocks under compression, and the modulus of elasticity as determined therefrom, should be fundamental considerations in the development of any theories of rock breakage. Crushing in jaw or gyratory crushers results primarily from a squeezing action, and reduction in a hammer mill is the result of impact. The action in rod and ball mills is a combination of impacting, squeezing, and wearing away by attrition, or rubbing. In ordinary crushing and grinding, the forces are applied at protruding points and are not distributed evenly throughout the rock. This is one of the features of comminution which theoretical considerations have not covered adequately. Another feature is the effect of impact velocities, which may greatly influence the total energy required for breakage. Impact velocities may vary from 1 or 2 fps in crushers to 10 or 20 fps for ball mills, and as high as 100 or more for hammer mills. However, according to the findings of geophysicists, the velocity of sound and of compression waves in stone is many times greater; the primary longitudinal compression waves travel at perhaps 15,000 fps, and the secondary transverse waves, which may reach the surface and cause cracks to form thereon, travel at perhaps 5000 fps. When a crack tip forms, the total surrounding stresses are concentrated in this tip, which rapidly extends throughout the rock particle.1 It would seem that the energy required to deform the rock beyond its critical strain, resulting in the formation of a crack tip, represents practically all of the energy required. Most of the primary crack tips presumably form on the surface. A simple method of designating feed and product size is necessary for the evaluation of crushing and grinding results. Taggart's suggestion2 that the 80 pet passing size be used has been found very practical. In this paper, the square opening screen size which 80 pct of the feed passes is designated as the feed size F, and the size which 80 pct of the product passes, or the product size, is designated as P. The reduction ratio at the 80 pet passing size, or F/P is designated as n. The feed and prod-

Jan 1, 1951

By Vsevolod Krivobok

IT is generally recognized that "low temperatures" have a definite effect on the properties of metals and alloys. Furthermore, it is also generally understood that the effect is decidedly adverse. The possibility that the same low-temperature treatment might be employed for the purpose of improving certain properties of the .alloys has received less attention until recently, and the experimental and theoretical knowledge consequently is meager. The effect of low temperatures may be studied in two ways: by studying such properties as tensile strength, hardness, impact resistance, etc., at low temperature, and by studying the properties of alloys at room temperature after these alloys have been subjected to a low-temperature treatment. Even in the latter case, certain properties will differ materially from the same properties obtained on identical material but without cold treatment. In other words, subjecting alloys to cold treatment results in an irreversible change in mechanical properties. Changes of this character are usually indications of the appearance of a new phase or phases, and would be likely to occur in alloys which, either by virtue of their composition or by heat treatment, are retained at room temperature in a metastable condition. Consequently, studies of the effect of low temperatures logically should be conducted from the physicochemical point of view, since the results of such studies not only would furnish metallurgists with interesting theoretical data but would clearly indicate the classes of alloys that would hold promise of improvement, and, possibly, of new applications. As the present investigation deals with chromium and chromium-nickel alloys of iron of the stainless variety, it has been thought desirable to present the data concerning low-temperature properties of these alloys, available from the most recent and most comprehensive work of H: S. Russell.' A summary, of these data is given in Table 1. The data are confined to a limited number of alloys of the type dealt with in the present

Jan 1, 1931

By T. J. Whalen and Michael

The grain shape of the carbide in nickel-bowled ad cobalt-bonded titanium carbides was studied by microgiaphic examination, and the influcence of sintering atmosphere, sintering substl-after, ami the amount of metal binder on the grain shape was determined. If was found that the Carbide grain cross sections in the nickel and cobalt cermets ranged from round to angular, depending on the sintering conditions. The spheroidization of the carbides in both cobalt-bonded and nickel-bonded titanium carbides may be attribicted to oxygen. In the course of studies on titanium-carbide base cermets, various investigators have reported on the shape of the carbide grains, and it was noticed that grain shapes were obtained which were either spheroids, or polygons with rounded or square edges. It was also noted that the shapes of the carbide grains changed with time or composition. skolnickl showed that the titanium-carbide grains. after infiltration in vacuum with nickel tended to spheroi- dize with time. The titanium-carbide skeleton was located on a beryllia plate during infiltration. Gur-land,' who studied the microstructure of titanium carbide-cobalt compacts, showed that the carbide grains are round after 1 hr at 1450oC in a hydrogen atmosphere and angular after 7 hr at the same temperature. Goetzel3 has found that the carbide grains in compacts with a high binder content. 40 to 60 pet. tend to be spheroidized. whereas Blumenthal and silverman4 pointed out that the higher binder contents could yield either round or rectangular grains with rounded edges. depending on the nature of the binder. It is the purpose of this paper to present experi-

Jan 1, 1961