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By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By Millard K. Shaler, Sydney H. Ball

During the past 50 years the attention of mining-men has been turned to Africa, and within the past decade prospecting-expeditions sent into Central Africa have resulted in the open-ing-up of several mines. Having recently spent two years in the Belgian Congo for the Societe Internationale Forestiere et Miniere du Congo, it is our purpose to outline briefly the mining-conditions in that part of Central Africa. Before it became, in 1908, a Belgian colony, this region was known as the Congo Free State. 11. Location and Area. The Belgian Congo lies in southwestern Central Africa, west of the continental divide, as illustrated in Fig. 1. It has a coastline of but 20 miles on the Atlantic, but widens rapidly eastward to points 5 north and 14 south of the equator. Its area is 908,000 sq. miles, which is almost one-quarter that of the United States and Alaska, or more than one and one-half times that of Alaska. Stated in other terms, its area is nearly one-third that of the United States, exclusive of Alaska and the insular possessions, or more than that of all the United States east of the Mississippi river. III. Topography and Drainage. From north to south, Africa is made up of three topographic elements: 1, the Atlas mountains, a highly-accentuated region

Jan 1, 1911

By Oliver C. Ralston

This paper reports the results of the use of salt in some research work carried on during the past 3 years at the Salt Lake City Station of the Bureau of Mines, which is quartered in the University of Utah, whose Metallurgical Research Department cooperates with the Bureau. Only the work involving the use of salt is described. The authors wish equal credit given to J. F. Cullen, C. L. Larson, C. Y. Pfoutz, C. E. Sims, H. C. Neeld, R. W. Johnson, F. G. Moses, N. C. Christensen, and G. H. Wigton, who have all in some way contributed toward the success of this work, while connected with the station in one way or another. Lead Metallurgy Popularly Supposed to be Without Problems In lead metallurgy it is difficult at first to find metallurgical problems, as the prevailing conception has been that lead is so easily concentrated in its various ores and so easily reduced to its metallic form that the only progress possible is that involved in cheapening methods of mining and of reduction. Most of the problems usually considered are of minor nature and do not involve radical metallurgical changes. During the three years of work of the Salt Lake Station, the following classification of problems in the metallurgy of lead has been made: Oxidized Ores. 1. Ores containing only lead. 2. Ores containing lead and silver or gold. 3. Ores containing lead and zinc, with or without silver. Sulphide Ores. 1. Ores of pyrite carrying some lead. 2. Ores of complex zinc-lead-iron sulphides. 3. Complex sulphides containing precious metals.

Jan 1, 1918

By Georges Millot

USUALLY the search for clays is left to chance in unexplored areas. A local working by the inhabitants or an outcrop is often the only guide. If the conditions of genesis of clays were always known, a set of general rules could be drawn up that would apply to this search. For example, a certain type of clay might be found wherever the sediment indicated a favorable environment. This paper sums up the considerable amount of knowledge that has been accumulated about the genesis of sedimentary days and offers some rules to be observed in prospecting for new clays. ANALYTICAL STUDY OF SEDIMENTARY CLAYS Clays may be found in many formations, both recent and ancient. All the intermediums exist between the deep-sea deposit and the mud deposited by a stream. In order to find out whether the nature of clay deposits depends on the environments in which they were formed, the samples used in the investigation described herein were very carefully chosen from: (1) ancient sedimentary series (a few from recent ones), (2) zones where conditions of genesis are typical. Ancient Formations Ancient formations were chosen because they are less difficult to sample than the bottom sediments of present-day lakes and seas. Moreover, a geo- logical section makes it possible to define the conditions of genesis of a deposit based on its facies, fossils, stratigraphic relations, and paleography. A present-day deposit is defined only by its aspect at the moment. Its previous history may have caused mixtures, alterations, and changes of environment, which escape detection. Typical Conditions of Genesis Samples from ancient deposits were taken from zones where typical conditions of genesis prevailed. Only clays from marine, lagoonal, and lacustrine environs are concerned in this study because the nature of the original en- vironments could be affirmed. In this way an inventory of the nature of sedimentary clays has been made for rocks formed in typical and individual environments; therefore the extent of the results that may be drawn from such a study will need discussion.

Jan 1, 1952

By F. L. Sizer

THE mining regulations of British Columbia and Mexico present some features which might well be copied in the United States, if we are to have a complete revision of the laws governing mining titles. 1. First and foremost is the "square" location, which would mean the abolition of extralateral rights. This is a condition in both of the countries above named which has seemed to work no hardship upon any one, and certainly the limitation of underground rights by vertical planes through all lines makes a locator's rights clear. In view of the long and costly litigation which has involved so seriously many of our most important mining districts, it would seem to be the part of wisdom to avoid a repetition of similar trouble on titles of lode mining claims, by the enactment of a law similar to that in force in British Columbia. Objections have been raised by representatives of English companies to the investment of large amounts of money in mining operations in the United States, because of the insecurity of title under the present apex law; and the statement has been made to me personally by one of the largest English operators, that he would never again consent to the purchase of mines in the United States, preferring Mexico with all its revolutionary troubles to the danger of encroachment upon his underground rights by an unscrupulous neighbor. Without going into further argument as to the desirability of the "square location," it should be sufficient to say to those who are inclined to "let well enough alone." and still stick to the "law of the apex" that there have never been any serious objections raised to this feature of the square location in either British Columbia or Mexico. There are well founded and logical reasons for abandoning the doctrine of extralateral rights since it is so difficult of interpretation; the most natural substitute being a law similar to that of British Columbia, giving to each locator an area 1,500 ft. square.

Jan 3, 1914

By Alden H. Emery, J. J. Forbes

The data contained in this paper were collected during the course of an investigation which covered 15 representative coal mines in six coalmining states. The purpose of the investigation was to determine by atmospheric sampling how much dust was raised into the air during the various operations of coal mining, such as undercutting with machines, loading coal by hand and transporting it from the working face to the surface. The data thus obtained were considered from two angles; namely, the possible physiological effect of inhalation and the explosion hazard of the dust. No attempt will be made to discuss the former factor in this paper. ConDitions of Mining The mines in which this investigation was conducted were considered representative, and it is believed that the results obtained will suffice for the average dustiness encountered in most coal mines. All of the coal mined was bituminous, from beds 30 to 120 in. thick. Only the ordinary room-and-pillar system of mining was employed. Daily production ranged from approximately 700 to 1500 tons and the men employed from 150 to 450. Coal was undercut by shortwall mining machines in all mines, with the exception of one in which pick mining was employed. Loading at the face wets done by miners; none of the mines used mechanical loaders. Electric drills, both for brushing roof and for shooting coal were commonly used, although some roof work was done with jack-hammers and a little of both with augers. Coal was hauled by motor, mule, or rope power in end-gate cars with capacities ranging from 1800 to 3600lb. With few exceptions, coal was won at the face by dry methods, that is to say, no water was employed for wetting down the dust either during undercutting, loading or transportation. Observations of Sources of Dust The common sources of coal dust as observed, arranged by decreasing amounts, were as follows: (1) Undercutting with mining machines; (2)

Jan 1, 1927

By M. E. Wadsworth, K. J. Richards

The oxidation rates of tantalum in various partial pressures of carbon dioxide in the temperature range 700°to 950°C were measured with a thermo-gravimetric balance. Oxidation involved a surface -controlled reaction associated with the formation of a nonprotective layer of Ta2O5. Below about 720°C, there was a change in the rate-determining mechanism, and above 830°C the linear rate was preceded by a complex region of nonlinear oxidation behavior. The linear oxidation of tantalum has been explained quantitatively in terms of carbon dioxide adsorption, followed by a rate-controlling surface reaction. The initial adsorption has been expressed both as an equilibrium process and as a steady-state reaction. The enthalpy for chemisorption of CO, was determined to be -17.3 kcal per mole. The surface-controlled reaction had an activation enthalpy of 40.4 kcal per mole. A considerable amount of interest has been shown in recent years in the oxidation of tantalum and the nature of the oxide film produced. This interest is associated with the increasing demand in our technology for structural materials to withstand high temperatures and corrosive atmospheres. The low oxidation resistance of tantalum has severely restricted its application as a high-strength, high-temperature material. As a fundamental approach to the realization of the full poten- tials of this metal, the kinetics of the oxidation of tantalum in oxygen and air have been extensively studied; however, very little work has been reported on the effect of other gases, including carbon dioxide. According to Miller,' the only reported study of the reaction between tantalum and dry carbon dioxide is a restricted observation by O'Driscoll et al.2 at 8 atm absolute pressure and 500°C. Therefore, this study was made to investigate the reaction of tantalum with carbon dioxide. EXPERIMENTAL MATERIALS AND METHODS The vacuum-annealed tantalum used in this study was obtained from Fansteel Metallurgical Corp. as 0.025-mm-thick sheet stock. This material had less than 0.1 pct total impurities, and the maximum individual impurity concentrations were

Jan 1, 1964

By Alfonso Rizo-Patrón, A. M. Gaudin

PREVIOUS studies of activation in flotation have directed attention to the action of the activator on the mineral to be floated rather than to the relationship of the activator to the collector. The latter phase of the problem, however, seems to have definite scientific, if not also practical, interest. In the investigation reported in this paper, experiments were carried out, largely with quartz as subject, barium as activator, and oleate as collector. The results obtained indicate that a I : I ratio of collector ion to activator ion gives optimum results, and that a 2:I ratio almost fails to achieve activation and flotation. Yet, a 2:I ratio would have been expected on stoichiometric grounds, had the coating been a normal salt of the activator ion with the collector ion, since barium is a divalent cation and oleate a monovalent anion. To interpret and rationalize the observations, considerations of the crystal chemistry of quartz are helpful. The point of view to which these considerations lead may be of general applicability to systems involving suspensions of solids in liquids; they confirm that an adsorbed coating is inescapable. APPARATUS AND SUPPLIES The experimental work consisted in barium-ion abstraction tests, hydrogen-ion and hydroxyl-ion abstraction tests, flotation tests, and determinations of the surface of the crushed quartz. The flotation machine was built according to the design of D. W. McGlashan.* It consists of a drill press in which the bit has been replaced by a stainless-steel impellor surrounding a stainless-steel stator, as in the Fagergren laboratory machine. The air intake is controlled by a valve, and the cell consists of a beaker. The quartz was obtained from vein quartz stored in large chunks. It was first crushed to 20 mesh, then sized on a 28-mesh screen. The 20 to 28-mesh size alone was retained for use. This size was freed of coarse iron by passage through a Ball Norton magnetic separator, bleached with boiling hydrochloric acid to remove residual abraded iron, washed with distilled water until the washings were thoroughly free of ferrous, ferric, and excess hydrogen ion, and stored in covered Pyrex beakers under water until used. The barium was used as barium chloride, Baker's analyzed C. P. The oleate was used as sodium oleate. It was prepared from sodium hydroxide, Baker's analyzed C. P., and oleic acid purified by R. R. de Arellano3 in the laboratories at the Massachusetts Institute of Technology. The purification procedure was elaborated from the recent researches of Brown and Shinowara.2 It consisted in: (I) saponification of olive oil with potassium

Jan 1, 1942

By GEO H. DEIKE

NOT much activity has been evident during the past year in the establishment of co-operative scholarships but the interest among the coal-mining companies is more pronounced than ever. This is apparent from the replies received to a letter sent out by the Committee on the Promotion of Student Interest in Coal Mining to over 120 coalmine operating officials. With that letter was forwarded a bulletin issued by the school of mineral industries of The Pennsylvania State College entitled ?Industrial Scholarships ? a Partnership of Industry and Education.? In that circular was outlined the need for trained men in the war and postwar world, and particularly as such demands pertain to the growth of the mineral industries.

Jan 1, 1943

By A. B. Dyes, P. H. Braun, B. E. Cole

This paper presents a reservoir engineering analysis of the performance data for a waterflooding project in the Johnson Lease, South Ward field. This type of engineering analysis adds to the knowledge of the mechanics of water flooding. This study reveals that in general (a) high ultimate areal sweep-out efficiencies (95 to 100 per cent) can be expected, and (b) cross-flow among strata of different permeabilities during the fill-up phase can have an important influence on the behavior and should be dealt with in studying reservoirs for water flooding. The analysis further showed that the recovery predictions based on what was considered a consistent interpretation of core data and logs were low because little contribution was assumed from the low permeability, oil-bearing sand sections which have apparently yielded considerable waterflood oil. This project has yielded in excess of 2 1/2 times as much oil by water flooding as by primary depletion. These very favorable results were achieved without the use of any special injection well completion techniques. However, all of the low permeability material war included in the section open to injection despite its poor estimated primary yield. LEASE PERFORMANCE HISTORY The South Ward field lies in the southeast corner of Ward County near the southern tip of the tremendous Yates trend. Deposition of sand bodies along the seashore reefs during the latter part of the Permian period established what have turned out to be ideal conditions to form a great number of independent productive sands. Probably, these reservoirs in Ward and Winkler counties are providing operators with some of the nation's richest sources of secondary oil reserves through the use of waterflooding techniques. In South Ward field water has been very successfully used to flood oil from the Bennett sand occurring at a depth of about 2,300 to 2,400 ft. About 150 ft above the Bennett sand reservoir, the Grand Falls sand produced gas from a large cap extending over most of the field. The Atlantic Refining Co.'s 320-acre W. D. Johnson lease (Fig. 1) is on the northwest edge of the structure with only gas cap apparently present in the Grand Falls sand. The Bennett sand under this lease is oil productive, however, having a gross sand thickness averaging about 80 ft with a net of 18 ft of fairly clean, highly permeable sand, and about 36 ft of oil-bearing sand with low permeability and high water saturation. The lower permeability sand is interbedded with numerous layers of lime, shale, and anhydrite. Radioactivity logs from 12 wells and cores from two, examples of which are shown in Fig. 2, reveal that the total Bennett sand pore volume is about 71,000 bbl/acre. The estimated initial water saturation averages 41 per cent in the 54 ft of sand considered to contain oil; thus, also considering an estimated 18 per cent oil shrinkage, the lease originally contained about 34,000 bbl of oil per acre. Original pressure was probably about 1,400 psig. PVT correlations indicate that the reservoir fluid was originally saturated with gas. After discovery of the field in 1930, Atlantic completed the first well on the Johnson lease in March,

Jan 1, 1958

By O. Jay Myers

The war effort has furnished the necessary impetus for better magnesium foundry practice. Four or five years ago, there were but a few formulas in general use for core-sand mixtures for magnesium castings. Certain sands, binders, and inhibitors were specified and the proportions of these materials in each mixture were maintained between very narrow limits. As more and more war industries entered the field, much research was carried out and methods and practices were improved. Magnesium founding is still in a state of flux; therefore it is not uncommon to find one foundry spraying inhibitors on its cores, and another foundry using sand mixtures with incorporated protective agents. The basic core or dry-sand mold mixture for magnesium in use today is compounded with sand, core oil or resin binder, cereal, and moisture. Core oil or resin binder are added for baked strength while the cereal binder and moisture are for green strength. The normal mixtures (based on the weight of the sand) contain from o.5 to 1.5 per cent of both cereal binder and core oil, and the moisture content variesbetween 1.5 and 5 per cent. The ratio of core oil to cereal binder varies from 60:40 to 40:60, while the correct amount of moisture depends upon the method of coremaking. Protective Agents In all magnesium practice, protective agents are used in conjunction with the core and molding sands to prevent oxidation of the metal. The use of these inhibitors is not novel, but publications covering this field are not entirely adequate. Beck1 says: Magnesium alloys decompose water to form magnesium oxide, hydrogen being liberated in the process (Mg + H2O ? H2 ?+ MgO). This reaction results in the blackening of the skin and the appearance of areas of porosity on the casting surface, the cavities of which are filled with a grey oxide powder (these are termed 'burns'). Although sand cores for magnesium castings are thoroughly dried during the baking cycle, burning will take place on the casting5 unless the metal is protected properly. This type of burning is more difficult to define than the "water-magnesium" reaction cited by Beckl A possible explanation may lie in the following equation: 2Mg + O2—> 2MgO Here, the source of the oxygen is not water, but the air in the mold cavity, together with the chemically combined oxygen in the core-binding media. Generally, two methods are used to prevent this reaction from taking place.

Jan 1, 1945

By Stefan S. Kapusniak, Nichol Riggott, Stephen F. Smith

Stability investigations have been carried out in a number of major coal mining tunnels in the U.K. using various instrumentatcon techniques. The paper describes these instrumentation methods and presents results from studies in several tunnels. Both long and short term stability aspects are discussed. Prediction of tunnel stability is examined in relation to tunnel support requirements. Computer simulation techniques are used along with actual underground measurements to identify tunnel design parameters for influencing choice of support and prediction of long term stability.

Jan 1, 1984

By D. L. Douglas

The ß decomposition of Zr-U-O alloys was studied during an interrupted quench from the a + ß region. Decomposition was more rapid than in binary Zr-U alloys of the same uranium content or qf equivalent ß composition. The rapid transformation has been ascribed to the presence of the primary a phase which provided nucleation sites and which permitted preferential partitioning of oxygen to the a phase and of uranium to the COMMERCLAL heat treatments are designed to produce certain strength and toughness character- istics by controlling the microstructure of an alloy. A desired distribution of microconstituents is achieved in practice by treating an alloy under the correct time-temperature conditions. A knowledge of the phase equilibria in any alloy system is essential in outlining heat treatments, but in addi-

Jan 1, 1961

By N. K. Chen, R. B. Pond

IN the study of slip band* formation, there have been many examples to show that they do not always appear as lines traversing the entire crystal, but as segments whose ends seem to vanish in their path through the crystal. This characteristic appearance of slip bands has been witnessed under the optical microscope at various magnifications'-' and also under the electron microscope.' A typical example of this behavior seen with the optical microscope is shown in Fig. 1. However, the slip band studies were generally conducted on polished surfaces of single or poly-crystalline metals which had been previously deformed; i.e., the load was generally released so that the observation could be made. Any picture of slip bands so obtained can represent the surface phenomenon only in a static state of the strained material. The conditions prior to their formation cannot be definitely and clearly assigned. Thus, while a segmented slip band may suggest that slip is a growth process as supposed by the theory of the nucleation of slip,V he usual appearance of suddenly and fully developed slip bands around the crystal has generally been considered as a consequence of uniform shear of the entire slip plane akin to a cataclysmic process. Little clear-cut information is available with regard to the speed at which a slip band forms, its direction of motion, the geometry of its position with regard to its neighbors, and its dependence on orientation. A description is given in this paper of experimental apparatus by which the progressive formation of slip bands can be recorded while the specimen is undergoing deformation. Qualitative and quantitative data on the dynamic formation of slip bands will be presented with special interest concerning the propagation of slip bands, the spacing of slip bands, and their relations to strain hardening. Views on the formation of slip bands are discussed and a mechanism of the unit process involved in the formation of a slip band is proposed. Preparation of Specimens Single-crystal specimens of high purity aluminum (99.997 pct), 1/8 in. square in cross-section and 1% in. long in gage length, were made by the method of gradual solidification from the liquid state. Since no machining work could be introduced in preparation of crystals of such small size, a special mold was designed for casting them to final shape. The mold consisted of two, separate, high purity graphite blocks. Generally, 20 molds were packed together in one container so that 20 specimens could be obtained by one casting operation. This was desirable since it was possible by this method to obtain groups of crystals with similar orientations. The as-cast crystals were carefully clipped from the gate, etched, and homogenized for 24 hr at 600°C. They were then very gently polished using a 4/0 paper, re-etched, and finally electrolytically polished after the method previously described by Chen and Mathewson.6 The crystallographic orientations were determined using a back-reflection, Laue method. Tensile Testing and Photographic Method The tensile testing equipment for these tests was composed of a specially designed microtensile machine, microload cell and microclip gage with necessary appurtenances. The members of the microtensile machine consisted of three parts, as shown in Fig. 2. The chassis is equipped with an oil cylinder, A, and piston, the piston being part of the movable cross-head, B. Pressure in the oil cylinder is controlled and regulated by an external pneumatic-hydraulic cell, C, which is connected to the cylinder by a Vs in. high pressure copper tube. This cell is half filled with hydraulic oil and has a needle valve, D, on the oil exit side as well as a needle valve, E, on the gas inlet side. A quick-acting valve, F, as well as a pressure gage is provided for the gas side. The oil exits into the load piston on the microtensile machine. By connecting a tank of inert gas to the gas inlet, regulated pressures were provided over the oil so that the oil would leave the cell at a rate determined by the setting of the exit needle valve, the gas pressure, and the pressure of the oil in the load piston of the microtensile machine. With this pneumatic-hydraulic appurtenance it was possible to

Jan 1, 1953

By W. Mont Ferry

It is impossible to speak in exact terms of the effect that selective flotation has had, is having, and may have on the State of Utah. Its results enter into the economic structure of the state in so many ways and its ramifications are so widespread, that every line of industry is affectcd. Some effects can be definitely determined; others can be reasonably approximated; but the effect as a whole can not be set out in exact figures. Utah is essentially a mining state; mining is its basic industry and always will be. Agriculture, equally a basic industry, and of course, equally vital, can be practiced on only 6 per cent. of the 85,000 square miles of its area. It follows, therefore, that the economic future of this state depends upon a development of its natural resources. About 6 or 7 years ago, the mining industry in Utah was at a low ebb. This condition was caused partly by postwar conditions and other temporary causes, but prevailed also, which was most important, because the direet-smelting ores of the state were being rapidly exhausted and the cost of treatment of complex ores was almost prohibitive. Furthermore, the wet concentration of low-grade ores was unsatisfactory and did not result in producing a good smelting product. On visualizing this situation, one of the large smelting companies in the valley had the courage, ability and faith to develop and expand the principles involved in selective flotation of complex ores. This example has been followrd by other smelting and reduction companirs and the result has changed the entire aspect of the mining industry in Utah. The utilization of the zinc in the low-grade, lead-zinc-silvrr ores was the principal prob1t.m to be solvcd. The average yearly production from the State of Utah for the 10 years beginning 1914 and ending 1923, was something less than 10,000 tons of zinc corlcentrates. This period includes the world war, when abnormal priccs stimulated production. In 1924, selective flotation began to be practiced on a considerable scale, replacing concentration by gravity and bulk flotation which had been used generally until this time. Production and Value of Zinc Concentrates The production of zinc concentrates during 1924 was approximately 24,000 tons, or twice the average yearly production of the previous 10

Jan 1, 1928

By G. S. Hume

IN. THE autumn of 1922, British Petroleums Ltd. found oil of 14° Baumé in a sand 17 ft. thick in its. No. 2 well at Wainwright, 120 miles southeast of Edmonton. This greatly encouraged drilling in the Wainwright-Irma area and this past summer several wells were started, three of which are now completed and the others still being drilled. Of the three completed, No. 4 British Petroleums contains oil; No. 3 British Petroleums gave a show of oil but so far has not given much hope, of becoming a commercial producer; and No. 1 Maple Leaf Co., as now finished, is a. gas well with a daily flow of gas of about 2,500,000 cu. ft. at a closed pressure of 700 lb. An oil sand is reported to have been encountered below the producing gas horizon in the Maple Leaf well but has not been tested. Operations on this well have been suspended for the winter. The Geological Survey of Canada this past summer undertook a geological investigation of this area with the object of defining the structures with which the oil and gas are associated. The structure underlying this portion of the plains was supposed to be a terrace with the western edge dipping into the Alberta syncline and with a monoclinal structure to the east. By accurate leveling on known geological horizons on this terrace, a number of gentle folds were located and -it is in these folds that the oil and gas are found. At the British Petroleums Nos. 2 and 4 oil wells, the western flank of the fold has a gentle dip of only a few feet to the mile to the southwest whereas the strata on the eastern flank dip to the northeast about 40 ft. in ½ mile, the strike of the fold being northwest and southeast. How far oil will be found down the gentle southwest dip is unknown but probably the productive part of the fold will not exceed 1 mile in width, and possibly less. No. 3 British Petroleums well is on the strike of the fold 1 mile southeast of the two oil wells. The sand that was productive in Nos. 2 and 4 wells was not present in this well or, if present, was very thin and unproductive. Two other sand horizons, however, were encountered. The upper of these

Jan 3, 1925

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,'. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal's stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950

By J. J. Gilvarry

Recently, Gilvarry1,2 has given a rigorous derivation of the proper distribution function for fragment size in single fracture, based on a closely defined physical model and deduced strictly by the laws of probability. The physical point of departure is Griffith's theory of brittle strength, identifying sub-microscopic flaws as the cause of the low strength of a solid in comparison with values implied by cohesive energies. Gilvarry and Bergstrom,4-7 and Gilvarry8 have compared the predictions of the theory with experiment, and have found excellent agreement, in general. The purpose of this communication is to sketch the extension of the theory to the case of comminution, and to indicate the applications to some examples in nature. The present treatment represents an amplification of a brief discussion appearing elsewhere. 9 Although the basic ideas of the Griffith theory are perfectly general for rupture of brittle solids, it was originally formulated with very brittle materials such as glass in mind. Moreover, Griffith's original experimental work was carried out on glass specimens. Recently, however, the theory has been extended by race" to apply directly to rocks. This extension makes the theory immediately applicable to the materials generally of interest from the standpoint of comminution. GENERAL CASE To obtain the distribution function for fragment size in single fracture, three assumptions are made, that: 1) Fracture proceeds by activation of preex-istent Griffith flaws in the volume, faces, and edges of a fragment; 2) the distributions of flaws of these three types are independent of each other; and 3) activated flaws of a particular type are distributed at random, individually and collectively, in the sense of Fry.11 The last assumption implies that each distribution is separately of Poisson type.

Jan 1, 1964

By William E. Hubbard

The production of the Texas Panhandle1 up to Jan. 1, 1932, was slightly under 179,000,000 bbl., 90 per cent of which came from Hutchin-son and Gray counties. About 21,500,000 bbl. were produced during 1931. This was about 35 per cent less than the 1930 production and the smallest annual production since the first boom started seven years ago. The present daily production is slightly under 55,000 bbl., which is the production permitted under statewide curtailment. The assumed potential for the purpose of curtailment is 108,708 bbl. and the actual capacity of the wells is probably in the neighborhood of 75,000 barrels. The total initial production of the oil wells completed in 1931 was 40,714 bbl. from 117 wells or 347 bbl. per well as compared to a 511-bbl. average from the 304 oil wells drilled during the preceding year. Gray County led with 71 completions and a total initial production of 29,209 barrels. Completions Two hundred wells were completed in the Panhandle in 1931, as against 526 in 1930. Of the year's completions, 117 were oil wells, 77 produced gas, and but six were dry holes. Of the 3197 wells drilled in the Panhandle to date, 2944 have produced oil, gas, or both, making the ratio of dry holes to producers about 1:11.7. Ignoring the 64 dry holes drilled in nonproductive counties the ratio becomes 190:2944 or 1:15.5, which is somewhat more favorable than that obtained at the end of 1930. Of the oil wells completed 374 have been plugged. Although it is but five years since the peak of drilling operations more than one-fifth of the oil wells in Hutchinson County have been plugged. The percentage of total wells plugged to total completed oil wells, by counties,

Jan 1, 1932

By M. R. Louthan

The susceptibility of titanium to stress orientation of hydride precipitates was investigated. It was determined that, when hydride precipitation occurred in titanium under an applied tensile stress of 30,000 psi, the hydrides precipitated on the titanium habit plane oriented most nearly perpendicular to the stress axis. Stress orientation of the hydride platelets occurred because the precipitation of the lower density hydride phase perpendicular to the stress axis caused expansion of the matrix in a direction that tended to relieve the applied stress. The Ti-H system has received considerable study in recent years, mainly because of concern over the effects of hydrogen on the mechanical properties of titanium. The amount of hydrogen present in commercial titanium is now quite low and should have no appreciable effect on its mechanical properties; however, many titanium applications require ex- posure to hydrogenous atmospheres under conditions in which hydrogen pickup is likely. In such cases continued exposures may cause the hydrogen content to increase to the extent that titanium hydride does precipitate as a second phase. The hydride phase has been shown 1,2 to have an adverse effect on the mechanical properties, particularly the impact properties, causing reductions in strength and ductility. BACKGROUND The behavior of titanium is often quite similar to that of zirconium and zirconium-base alloys, and the technology developed on one metal can often be applied to the other. Marshall and Louthan3,4 have shown that Zircaloy is susceptible to stress orientation* of zirconium hydride platelets, and that the platelet orientation has a pronounced effect on the mechanical properties of Zircaloy. They showed that when zirconium hydride precipitated in Zircaloy under an applied stress the hydride platelets tended to be aligned parallel to a compressive stress and perpendicular to a tensile stress. They also showed

Jan 1, 1963