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By M. G. Arthur

This paper is a theoretical analysis of fingering of water and coning of water and gas in homogeneous sand. Investigation of this idealized case illustrates the relative magnitude of the factors involved in actual conditions. The body of the report presents equations, example calculations, and charts that facilitate solution of such problems. Derivation of the equations introduced in this paper and a discussion of previously published equations are included in the appendix. Introduction Production of water from oil wells as a result of the pressure gradients established by flow of fluids through oil-~roducing sands is a common occurrence, which influences the cost of oil production, the degree of depletion and the efficiency of expulsion of oil from naturally occurring reservoirs. Control of water production and encroachment are important both in primary and secondary phases of of exploitation in order to produce oil and gas at lowest cost and in order to achieve the greatest ultimate recovery of the oil in the reservoir. Although many actual oil reservoirs present a multitude of variables that influence fingering and coning of water and gas, an inspection of the relationship and magnitude of the forces involved in the case of a homogeneous sand may indicate satisfactory methods of controlling water production. Application of equations relating the variables may indicate the geometric type of drainage that exists in a particular reservoir or in the vicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoir influenced by the well. Two geometric types of drainage are considered theoretically. The first is water fingering into an oil sand that is relatively thin compared with the lateral extent of the sand. This sand may represent the entire oil-producing reservoir or it may represent one interval in an oil reservoir, which is separated from other producing intervals by competent lithologic barriers to flow of fluids. For the condition of complete penetration of a well in such a sand body, it may be assumed that no flow occurs across bedding planes. A mathematical relation is developed between the limit of approach of a water finger to the well without being drawn into the well and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil well as the result of coning through bedding planes. The theory and graphical solution developed by Muskat' for the limit of approach of a water or gas cone to a well, without its entry into the well, related to the corresponding maximum pressure drawdown, is reviewed and amplified, Charts are presented, which facilitate graphical solution of the problem. A method is presented for the extension of this type of graphical solution to the case where gas and water coning occurs simultaneously~

Jan 1, 1944

By V. A. Zanadvoroff

The mine and concentrator of the Howe Sound Co., Chelan Division, are at Holden, in a remote section of the Cascade Mountains of northwestern Washington. Holden is at an elevation of 3200 ft., in the narrow valley of Railroad Creek. This creek drains into Lake Chelan, at a point some 40 miles up the lake from the town of Chelan. The concentrator treats 2000 to 2500 tons of low-grade copper-gold-zinc ore per day. Concentration is achieved by the differential flotation process, with recovery of 94 per cent copper and 82 per cent gold in the copper concentrate, followed by the recovery of 65 to 70 per cent zinc in the zinc flotation circuit. The final flotation tailing is deslimed, and coarse . sands, representing 60 to 70 percent of the total, are cyanided. The tonnage of tailing material amounts to 1900 to 2370 tons per day. General Considerations The property is within the Chelan National Forest. Railroad Creek is a fishing stream, being stocked regularly with trout from State hatcheries. Consequently, in planning a milling operation, the Howe Sound Co. was obliged to avoid any pollution of the stream by tailing material, and also destruction of valuable stands of timber. Moreover, the selected tailing- disposal sites should not mar the natural beauty of the valley. In addition to these requirements, the problem of tailing disposal at Holden was complicated by topography and climatic conditions. The valley is long and narrow, averaging 1200 to 1500 ft. in width. Its walls are flaring at a steep angle. There are no extensive flat areas suitable for deposition of tailing. All valleys tributary to Railroad Creek, also the well-marked paths of snowslides, must be avoided. Finally, the direction of prevailing winds and possible dust hazard arising therefrom dictated the necessity of selecting the tailing-disposal sites downstream from the mill building and two campsites. Heavy snowfall during the winter months of November to March, inclusive, impedes building of the retaining dike, making it necessary to prepare the needed storage space during the summer months. It is inadvisable, also, to do any dike building during the freezing weather, because the dike becomes unstable with the spring thaws, producing inevitable "sloughing" of the built-up borders. Tailing-disposal Sues The existing tailing-disposal areas are near the south wall of the valley. They were developed, and put to use in the following sequence: No. I. Area.—Covers approximately 10 acres. Built up to the height of 60 ft. and abandoned. Total length of dike border is 1900 feet.

Jan 1, 1947

By V. A. Zanadvoroff

The mine and concentrator of the Howe Sound Co., Chelan Division, are at Holden, in a remote section of the Cascade Mountains of northwestern Washington. Holden is at an elevation of 3200 ft., in the narrow valley of Railroad Creek. This creek drains into Lake Chelan, at a point some 40 miles up the lake from the town of Chelan. The concentrator treats 2000 to 2500 tons of low-grade copper-gold-zinc ore per day. Concentration is achieved by the differential flotation process, with recovery of 94 per cent copper and 82 per cent gold in the copper concentrate, followed by the recovery of 65 to 70 per cent zinc in the zinc flotation circuit. The final flotation tailing is deslimed, and coarse . sands, representing 60 to 70 percent of the total, are cyanided. The tonnage of tailing material amounts to 1900 to 2370 tons per day. General Considerations The property is within the Chelan National Forest. Railroad Creek is a fishing stream, being stocked regularly with trout from State hatcheries. Consequently, in planning a milling operation, the Howe Sound Co. was obliged to avoid any pollution of the stream by tailing material, and also destruction of valuable stands of timber. Moreover, the selected tailing- disposal sites should not mar the natural beauty of the valley. In addition to these requirements, the problem of tailing disposal at Holden was complicated by topography and climatic conditions. The valley is long and narrow, averaging 1200 to 1500 ft. in width. Its walls are flaring at a steep angle. There are no extensive flat areas suitable for deposition of tailing. All valleys tributary to Railroad Creek, also the well-marked paths of snowslides, must be avoided. Finally, the direction of prevailing winds and possible dust hazard arising therefrom dictated the necessity of selecting the tailing-disposal sites downstream from the mill building and two campsites. Heavy snowfall during the winter months of November to March, inclusive, impedes building of the retaining dike, making it necessary to prepare the needed storage space during the summer months. It is inadvisable, also, to do any dike building during the freezing weather, because the dike becomes unstable with the spring thaws, producing inevitable "sloughing" of the built-up borders. Tailing-disposal Sues The existing tailing-disposal areas are near the south wall of the valley. They were developed, and put to use in the following sequence: No. I. Area.—Covers approximately 10 acres. Built up to the height of 60 ft. and abandoned. Total length of dike border is 1900 feet.

Jan 1, 1947

By A. E. Nehrenberg

R. A. Schmucker, Jr.—The writer wishes to point out that an acicular growth of austenite, similar to that described in the author's paper, was recently observed in an alloy steel of only 0.06 C content. This steel, which represents an 0.07 max C, 1.35 Cr, 0.55 Ni, 0.20 Mo analysis, combines the characteristics of minimum hardness in the annealed condition with maximum hardenability and is therefore suited primarily for cold-hobbing applications. The acicular austenite formation in this steel was observed accidentally during a determination of its Ac1 temperature. The samples used in this investigation represented as-forged bar stock which had been given a preliminary temper at 1300°F. The critical (Ac1) temperature was finally established at 1400 °F. Fig. 15 represents the microstructure of the sample which had been heated at 1450°F for ½ hr, water quenched, and tempered at 600°F for ½ hr (for the purpose of darkening the martensite). It will be observed from the distribution of the darkened areas of martensite that the parent austenite grains formed at 1450°F had grown in an acicular manner and still occupied only a small percentage of the total area. The remainder of the area contains the original equiaxed ferrite grains in which new austenite had as yet scarcely formed. However, the tiny isolated martensitic patches at several points where three or more ferrite grains intersect indicate that small austenite grains had formed and started to grow in an apparently equiaxed fashion. Fig. 16 represents the prior microstructure of an original sample in the as-forged and tempered condition, before it was heated -above the critical temperature. It is probable that there are two kinds of ferrite in this structure: (1) The equiaxed proeutectoid ferrite grains which separated from the austenite when the steel was cooled from the forging temperature, and (2) the acicular ferrite associated with the aggregate of fine carbide which is represented by the patches of

Jan 1, 1951

By Allen Garrison

THE chemistry of clays and shales has been assuming increasing importance in the petroleum industry, and two factors have greatly influenced this trend. The first has been the growing evidence that the marine shales are source beds, and that the petroleum compounds have migrated to the sand reservoirs overlying or underlying these shales: the second has been the demand for drilling fluids better adapted to penetrate these marine shales without difficulty and expense. ORIGIN AND. GENERAL COMPOSITION OF CLAYS AND SHALES Clays, shales and- surface soils are all closely related materials. They are mixtures of finely divided compounds formed during the weathering of the solid crust of the earth. Their nature is essentially colloidal; that is, their behavior is determined by the state of division of the materials and the surface reactions of the smallest grains. Many of their chemical changes affect only the exposed areas and do not involve the interior of the grains of matter. The extent of these reactions is more nearly proportional to the area of the substances than to their mass, therefore it is possible for a small amount of a material in an extremely fine state of division to completely dominate the character of the mixture. More than 83 per cent of the crust of the earth is composed of three elements-oxygen, silicon and aluminum. Consequently, the corrosion products of the crust are predominantly aluminosilicates, or compounds of aluminum, silicon and oxygen. If we add the compounds of six elements-iron, calcium, sodium, potassium, magnesium and hydrogen-more than 98 per cent of the crust, has been accounted for. These six elements, together with the first three, also appear in soils, clays and shales.

Jan 1, 1939

By A. H. Miller

TEMPERATURE considerations are of prime importance in the manufacture of steel products-front the time the metal is produced in the melting furnace, where the chemical reactions have a direct dependence on the temperatures of the bath, to the final machining of work on which the expansion due to the rise in temperature of the forgings during machining must be allowed for. Methods employed and difficulties encountered in some of the more important steps are here outlined. These methods are the result of years of experience, with many methods of temperature determination, and have been successful in routine works practice in the manufacture of high-quality steels. In the operations of melting, forging, and heat treatment, if the product is to be of the best quality each operation must be carefully followed through. A high-quality product cannot be obtained even with the best heat treatment if the steel is poorly melted, and, conversely, the best steel ever made may he spoiled by inefficient heat treatment. To perform the best work in any of these operations, temperatures must be accurately regulated.

Jan 8, 1919

Sixteen executives, technicians and operative personnel from the French mining industry, now touring mining operations in the U.S., will wind up their visit to this country at the AIME Annual Meeting. Traveling under ECA auspices, they will be in Denver on Feb. 5, Salt Lake City, Feb. 8 to 13, Bonne Terre on Feb. 16. Four of the group are engaged in bauxite mining, nine in lead and zinc, two in pyrites mining. All are interested in American mining equipment and methods, and hope to contact manufacturers' representatives in the various areas they visit. A $600,000 manganese pilot plant is expected to be put into operation by Sept. 1, by the Bureau of Mines at Boulder City, Nev. S. R. Zimmerly, chief of the Bureau's metallurgical div. for the region, recently completed the mill design and flow sheet; and the Bureau is awaiting steel priorities before building. Ore from the Artillery Peak area, 60 miles south-west of Kingman, Ariz., will be used in the mill. Construction will be handled by Rex Lloyd of Boulder City.

Jan 2, 1951

The Institute's stock of Volumes XXXI, LI, and LII has become much reduced by sales: If members have copies of these volumes which they can spare, the price of $3 per volume will be paid for them, if in good condition. If desired, a copy of the Index for Volumes XXXVI to LV will he given for one of these volumes of the Transactions and one dollar additional. For two volumes of the Transactions, a copy of the Index will be sent and the balance will be credited to the payment of clues.

Jan 12, 1918

By Sidney A. Swensrud

MUCH discussion has occurred as to the use or uses which might be made after the war of either or both .of the large diameter (24 inch and 20 inch) War Emergency pipe lines built by y the United States Government during the war, to move crude petroleum and refined products such as gasoline and light distillate fuels. Indeed, the disposition and future use of these lines constitutes, in the minds of many people, one of the most important problems of postwar readjustment in the Oil Industry. The two lines, running from points in Texas to the New York-New Jersey-Philadelphia area, were constructed only because of the inability during the war to continue normal ocean tanker movements from the Gulf Coast to the East Coast. Physically they could continue after the war to move crude or refined products, and it appears that lines of such large diameter as these, if operated at or near capacity, could move these liquids at costs per barrel which might be considered in the same general cost range as for tanker movements.1 If, therefore, we were to look forward at the end of the war to a shortage of tankers, it is probable that the continued use of these pipe lines for petroleum movements to the East Coast would be worth considering, as against building new tankers to take over the movement, provided there were no other economic or national defense reasons for restoring tanker fleets and no other better use for the pipe lines. Because of the extensive tanker construction program which has been and still is in progress, and because of our Navy's marked success in combating the submarine problem, it appears to be quite possible, however, that instead of a shortage of tankers at the end of the war, we may have a surplus instead. If this should turn out to be the case, then there would seem to be considerable doubt that these lines would continue to be used for moving petroleum or products to the East Coast at the expense of tying up tankers. It would hardly seem probable that the owner of any such tankers would ship via one of the large lines at the expense of tying up one of its own tankers, unless the pipe line tariff rate charged was lower than the out-of-pocket cost of operating a tanker as against the out-of-pocket cost of keeping it tied up. And considering that a substantial part of the cost of operating a tanker goes on even when it is tied up, it is very difficult to figure out how any pipeline tariff could be established that would be low enough to compete with individually owned tankers that otherwise would be idle. Certainly a pipe line tariff rate high enough to cover direct costs plus even a low rate of depreciation and return on the investment would be far above the out-of-pocket tanker operating costs. In view of these considerations, it has seemed desirable to examine with some care some of the various alternatives that have been suggested as to other possible uses to which these lines might be put. One of these is for transportation of natural gas to the New York-New Jersey Philadelphia area. This Eastern area, located at the destination of these lines, contains the heaviest concentration of population in the United States, and is not now served with natural gas. At the other end of the lines lie the greatest discovered natural gas reserves in the United States, if not in the world, and many

Jan 1, 1944

By Dave H. Barnett, Brij M. Moudgil

The flotation technique as employed by Florida phosphate producing companies for the beneficiation of fine phosphate particles has been standardized over the years. Lower recoveries of coarse Phosphate rock by froth flotation technique, however, led to the development of new methods based on skin flotation of phosphate agglomerates. Recent developments of floating coarse rock in large flotation machines have not yet convinced the rock Producers of their higher separation efficiency. It is interesting to note that the selection of a particular machine is still bared on equipment preference by an individual company as well as proven performance of a particular machine for upgrading a specific material. Various techniques which have been developed to beneficiate the coarse phosphate rock have been discussed. Performance of the individual techniques is presented.

Jan 3, 1979

By Earl Oliver, J. B. Umpleby

It is believed that in connection with the study of unit operation by the Petroleum Division of the A. I. M. E. a review of the simple principles of unit operation would be helpful. To that end, the following discussion is submitted. It is not to be considered in any sense as the conclusion of the committee, but rather as material submitted for its consideration and represents at this time only the viewpoints of its authors. Growth of the Oil Industry In 70 years the oil industry has grown from a single well on Oil Creek, Venango County, Pennsylvania, producing 25 bbl, per day, to more than 400,000 wells scattered over five continents with a daily output of 4,000,000 bbl. In that time petroleum has expanded from its simple use as a medicine in a few localities to a multitude of diverse uses in homes of every country the world over. During those years the oil fields of the United States have produced two-thirds of the world's output and have shipped their excess production into almost every country. In those years several hundred thousand good wells in the United States declined into small ones and depleted shallow deposits gave way to deep zones; so that the United States crude oil industry gradually changed from one of low cost production to one of higher cost. Throughout its entire life it has labored under two serious economic disadvantages, namely, constantly recurring periods of demoralization through overproduction, and competitive development methods that are wasteful. Development of Foreign Competition During the transition from low to higher cost production in the United States, events even more significant were taking place in foreign lands. Jungles were tamed and deserts conquered. Oil deposits were found and developed until, in the words of Sir John Cadman, "the globe is now drenched with a commodity which, although necessary to life, involves but an irregular and sometimes meager expenditure of life in its

Jan 1, 1930

By Phillip B. Bucky, Fred D. Wright

The present known petroleum reserves are limited, and unless important new fields are discovered the Nation will be dependent, in the not too distant future, upon imports or upon synthetic liquid fuels to supplement domestic petroleum supplies. As a national defense measure, it would appear desirable to develop a substitute source of liquid fuels within the borders of the country if new discoveries of petroleum should Prove disappointing. Congress undoubtedly had this in mind when it passed the Synthetic Liquid Fuels Act (78th Congress, approved April 5, 1944). The act directed the Bureau of Mines to construct and operate demonstration plants for producing synthetic liquid fuels from coal and oil shale, and from forestry and agricultural products. As a part of this program, the Bureau of Mines has built a demonstration plant at Anvil Points, near Rifle, Colo., for retorting the oil shale, and has developed a mine to supply the plant with oil shale. At the beginning of mining operations, the physical qualities of the oil shale, which would have a bearing upon the selection of mining methods and practices for exploiting the deposits, were largely unknown. A comprehensive mining-research program has been set up to determine the best methods and practices to follow to obtain the lowest overall practicable mining cost for producing the oil shale on a large scale. Unusually low mining costs will be necessary for shale oil to be produced commercially. Consideration now is being given to exploiting a series of flat-lying beds 70 ft thick by a room-and-pillar method of three benches with the advance heading at the top. This report is one of a series giving the results obtained in research on mining problems, The structure and physical qualities of the oil shale indicate that the 70-ft interval of the oil-shale measure can be safely mined in open stopes; studies indicate that this method would be the most economical one to use.' As labor will be a major item of expense, the largest equipment that could be operated efficiently in the workings would be required to obtain the lowest practicable mining Cost. It Was therefore desirable to know the maximum safe span of unsupported rooms and the size of pillars necessary to support the overburden. This paper describes the work done at the Columbia School of Mines Barodynamic Laboratory in determining the maximum safe unsupported roof spans and the minimum safe pillar dimensions for the oil-shale mine at Rifle, Colo.

Jan 1, 1949

By H. M. Chance

In recent years an important function of the mining engineer has been the appraisal of the value of mining-properties required by those planning consolidations of a number of' individual operations. In no field of productive industry have the economic results attainable by consolidation been more clearly shown than in the mining-regions of the United States. In many important mining-centers unification of ownership of the most valuable properties has already partially or completely been attained, and, in other districts, projected absorptions and consolidations await only favorable financial conditions for their consummation. The iron-ore districts of the Lake Superior region, the coal-mines of Colorado, of Wyoming and of Utah, the anthracite mines of Pennsylvania, the Connellsville coking-coal mines, and large areas of bituminous coal-land in Pennsylvania, in Ohio, in the Indian Territory and in other portions of the United States, are now largely controlled by a few corporations operating on a large scale, or by a number of corporations working in harmony because of an affiliation and interleaving of interests. The tact of keen financiers and the diplomacy of men of great administrative ability are the chief operative forces in conceiving and accomplishing such consolidations, but in formulating and maturing them, the services of the mining engineer are often required to supply the facts upon which they must be based. For this purpose the expert is expected to furnish full and complete reports covering the quantity of ore, coal or other mineral available, its value per ton, cost of mining and treatment, etc. In reporting upon gold-, silver-, lead-, zinc-, copper- or iron-

Jan 1, 1905

The American Association of Petroleum Geologists, P. 0. Box 1552, Tulsa, Okla. J. P. D. Hull, Business Manager. The official publication of this Association is the Bulletin of the American Association of Petroleum Geologists, issued monthly. It contains illustrated papers, maps, current notes, discussions, reviews and personals. Annual subscription is $15 ($15.40 outside the United States). Back numbers of the Bulletin, practically all of which are available, cost from $1.50 to $3 each; for several years back a uniform price of $1.50 each is charged.

Jan 1, 1933

By William E. Ford, Edward Salisbury Dana

268. The greater part of the specimens or masses of minerals that occur may be described as aggregations of imperfect crystals. Many specimens whose structure appears to the eye quite homogeneous, and destitute internally of distinct crystallization, can be shown to be composed of crystalline grains. Under the above head, consequently, are included all the remaining varieties of structure among minerals. The individuals composing imperfectly crystallized individuals may be: 1. Columns, or fibers, in which case the structure is columnar or fibrous. 2. Thin lamina, producing a lamellar structure. 3. Grains, constituting a granular structure.

Jan 1, 1922

The Institute's stock of Volumes XXXI, LI, and LII has become much reduced by sales. If members have copies of these volumes which they can spare, the price of $3 per volume will he paid for them, if in good condition. If desired, a copy of the Index for Volumes XXXVI to LV will be given for one of these volumes of the Transactions and one dollar additional. For two volumes of the Transactions, a copy of the Index will he sent and the balance will be credited to the payment of dues.

Jan 1, 1919

By P. W. Bridgman

FLOW and fracture are admittedly complicated phenomena of which we are yet only partially masters. There is not even universal agreement as to the details of the language best adapted merely to describe the phenomena, to say nothing of any theory. Certain points of view, however, are widely held, and there are certain general expectations as to what sort of procedures will prove permissible. A complete description of any situation involving fracture would demand a complete history of all the variables in the control of the experimenter. The experimenter endeavors so to choose his independent variables that they are adequate to determine completely the situation in the sense that when an experiment is repeated on the same initial material and with the independent variables running through the same sequence, all the other measurable properties of the system will also run through the same course. It is, I think, the universal conviction that when we are dealing with phenomena of flow and fracture, the most important of the necessary variables are the external forces acting on the various parts of the body; when the force history repeats, with certain obvious restrictions such as that temperature must be constant and non- mechanical forces, such as magnetic field, must be small enough to be ineffective, then the history of all measurable properties will repeat; in particular the alteration of geometrical shape due to flow will run through the same course, and when fracture comes, the character of the fracture will be reproduced. Complete mastery of merely the descriptive aspects of flow and fracture would demand the ability to predict the entire course of flow and complete characterization of the final fracture for every possible combination of forces, varying in time in all possible ways, when applied to bodies of all possible shapes. This full situation is obviously of prohibitive complexity. The first stage in reduction to manage- able simplicity is to resolve the total situation into the sum of contributions made by small elements. Our thesis is that if each of the elements is adequately characterized, the behavior of the whole system is fixed. The element is usually taken of a simple geometrical shape, suggested by the mathematics best adapted to the particular situation. The forces acting across the faces of the elements are ultimately determined by the forces acting across the free faces of the whole system. The detailed process of finding the precise forces on the faces of all the elements in terms of the external forces involves the use of a special mathematical invention, the stress, a constructional quantity consisting of six components. The stress at any point in the body is determined by both the external force system and by the physical properties of the body at all points; quite different stresses prevail at the interior of bodies of the same shape under the same external forces in the elastic and plastic ranges. The forces on the faces of any element are, however, uniquely determined by the stress system at the element. Our fundamental thesis

Jan 1, 1944

By C. C. Harris

A critical literature review leads to a descriptive model of tumbling mill operation based upon energy partition concepts and the necessary requirements for particle fracture. As grinding proceeds into the ultra-fine region, conditions which are of little significance during normal operations gradually become controlling. These involve increasing resistance to fracture and an increasing tendency to aggregate as particles become smaller, and a growing fraction of the power input being consumed fruitlessly. The result is that fineness asymptotes to a maximum value as comminution proceeds indefinitely; thus where t is time, p and n are experimentally determined parameters, and Ø is a measure of fineness, which is presumed to be proportional to specific surface area, or proportional to the reciprocal of the size modulus (provided that the distribution modulus remains constant with time), or both. Ø, is the asymptotic value of Ø and is a measure of the grind limit. A method for its graphical determination is given. In a previous paper1 the physical and mathematical principles requisite to a study of the role of energy in comminution were reviewed. The micro-process of comminution — or the comminution event — can be investigated in terms of (a) the magnitude of the force-field localized around the individual particles which gives rise to the stresses generated in the particles, which in turn induces their fracture, and (b) the distribution of fragment sizes, should the event prove fruitful. The entire fragmentation operation can be considered to be the totality of its individual events, and in order to obtain a single independent variable of the process it is necessary to transform and sum the local stresses in terms of energy.1 This energy, however, will account for only a fraction of the energy input to the comminution process, the actual magnitude depending upon the kind of mill and several related factors. From the comminution viewpoint the primary function of a mill is that of stressing as many as possible of the individual particles of the charge to failure, with the maximum economy of energy expenditure. This is difficult indeed to achieve, for stressing a particle does not always break it, while the overwhelming portion of the energy input is involved with various internal mill processes which — almost incidentally — determine the magnitude, frequency, and manner in which the forces are applied to the particles. Essentially, these processes depend upon the mill dimensions, loading and speed, and they may be little affected whether fracture occurs or not. These processes must be delineated if a complete description of the role of energy in comminution is to be given; the energy account sheet1 (Fig. 1) in showing how the energy is partitioned for the requirements of the several functions it performs, provides a framework for the development of a model of the comminution process. Actual numerical values for the variables appearing in Fig. 1 will depend upon the mill, materials, and operating conditions. A possible general relationship between the variables will be suggested in this paper. Before proceeding further, a cautionary note must be issued. It was pointed out in an earlier paper' that while energy input is not changed by increasing the power and decreasing the time in the same proportion, and vice versa, the results of the process in terms of particle fineness may be different. Thus, although energy is chosen as the independent variable of a comminution process, it is not absolutely independent, and care must be exercised to ensure that it is used within its range of valid application. Time has the necessary independence, and it will be used in place of energy where it is appropriate. The residence time in a mill is usually of the order of minutes. Under these conditions the particles are subjected to "... a relatively constant fracture producing environment".2 However, under the more rigorous conditions of greatly extended time, which pertain in ultra-fine grinding, indications are that the fracture producing environment no longer remains constant; this is the major subject of this paper. At this extreme limit the mill is probably taxed to its utmost, and at the same time the bulk material properties are becoming closer to ideal, while the physico chemical effects associated with surfaces, edges and corners are multiplying. (The edge length per unit volume is proportional to the square of the specific

Jan 1, 1968

By H. R. Peiffer, R. Geckle

The silver phase of silver and finely divided alumina composites is shown to grow as single crystabs upon solidification from the melt. These crystals grow without the aid of an externally applied thermal gradient or a mold. The single-crystal growth is more readily disrupted as the alumina content varies from the optimum concentration of 20 wt pct. Pretreatment such as variation of fabrication pressure, and presintering of the specimens appear to play a lesser role in this phenomenon. In actual practice the growth of single crystals of metals from the melt is a tedious, painstaking process.' Care must be taken to insure the proper thermal gradients and rate of growth in a vibration-free environment. Excellent single crystals can be grown when these variables are controlled. When a second insoluble and finely divided phase is present in the melt the growth of single crystals is difficult, if not impossible, even under the most favorable conditions outlined above. During the past few years, a composite of silver and alumina has demonstrated an ability to resist flow even though the major phase, silver, is mo1ten. 2 A more surprising feature of this material is the ease with which single crystals of silver grow upon cooling the composite from temperatures above the melting point of silver to temperatures near room temperature. Observations have been made that demonstrate that single crystals of silver will grow even when conditions most unfavorable for growth of pure silver crystals exist. The crystals grown in this manner are imperfect in that a great deal of subgrain structure exists. It is the purpose of this manuscript to qualitatively describe this process and to attempt to isolate the influencing factors of this behavior. MATERIAL PREPARATION The composite material is prepared by powder-metallurgical techniques. Two items of great importance are the introduction of oxygen into the system and the obvious need for a thorough mixing of the metallic and refractory oxide phases. The oxygen is necessary in order that the silver wets the alumina. Without oxygen the phases separate and the material shows no unusual properties. In order to supply the needed oxygen the silver is added in the form of silver oxide which is readily decomposed to oxygen and silver upon heating. The silver oxide is readily obtained in a finely divided form that allows a uniform mixture of the alumina and silver oxide to be prepared. The correct ratio of alumina to silver oxide is mixed in the presence of alcohol in an ordinary food blender. The mixture has the consistency of a thin slurry and after mixing for approximately 20 min is dried and pressed into billets at various pressures. As is shown in Fig. 1, there is no limit to the shape of the specimens obtainable as single crystals. These billets are heated in air in a predeter-

Jan 1, 1964

Jan 3, 1953