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By H. P. Stuwe

It is investigated whether a model of sphere packing permits the computation of the lattice parameters and their variation with concentration in various a phases; it does, except in phases containing silicon. Several observations indicate that a particular role is played by the "E-atoms" in the lattice. THE phase is formed by many alloys of the transition elements.'-' Its structure has been described by Bergman and Shoemaker,5,8 Dickins, Douglas, and Taylor,7 and Kasper, Decker, and elanger.' There are five kinds of crystallographically equivalent positions for the 30 atoms in the unit cell which have been designated by these authors I, 11, 111, IV, and V or, in the same sequence, A, B, C,D, and E, as shown in Fig, 1. For the purposes of the present paper two elements of the lattice will be discussed separately: The lattice planes perpendicular to the c-axis which are made up by the atoms A, B, C, and D and which determine the a-parameter; and the close-packed "vertical rows" of E-atoms which determine the c-parameter. asper,9 and Frank and kasper10 described the a phase and other complex structures as sphere packings. In these papers particular attention is paid to the coordination polyhedra. Lattice positions with an equal number of nearest neighbors are considered equivalent regardless of their crystallo-graphic description. This seems to work very well for the explanation of ordering phenomena in the a phase as far as information on this is available." If the description of the phase as a sphere packing is valid it should be possible to draw two further conclusions: 1) It should be possible to calculate the lattice parameters from the atomic radii of the components, and 2) It should be possible to predict the variation of the lattice parameters with concentration within one phase field. Both points are discussed in this paper. PROCEDURE Measurements of lattice constants were done with a symmetrical back-reflection X-ray camera. With Cr-radiation, about a dozen a1 lines could be observed with most samples. From the (550/710)- and 720-lines the a-value was computed. With this value the c-parameter was calculated from the (333)- and (413)-lines. Finally, the position of all the other lines was computed from the lattice parameters thus obtained. In this way the validity of the indexing could be checked and, at the same time, this proce- dure gave an estimate of the accuracy of the lattice parameters. A correction was made for film shrinkage. The atomic radii used in the computations are the Goldschmidt radii for coordination number 12. Actually, some of the atoms have a coordination number of 14 or 15, but the error thereby introduced is small. * For the computation of lattice constants from the atomic radii an "average atomic radius" of all components was used, i.e., complete disorder was assumed. Although this seems to be true for some systems like OS-Cr,4 it is not true in others.11,13,14 The ordering model, however, which has been suggested by Kasper on the basis of extensive research lets both kinds of atoms contribute to both the ''vertical rows" and the lattice planes perpendicular to them, so that even with ordering of this kind the assumption of complete disorder cannot introduce a very serious error in calculating lattice parameters. RESULTS Bergman and shoemaker6 gave a table of the interatomic distances in the Fe-Cr phase. If we disre-

Jan 1, 1960

By Robert F. Mehl

THE purpose of a symposium, I take it, is to gather together a group interested in a common intellectual field, in order to exchange views, and to appraise the state of knowledge. Symposia are the more successful, the greater the activity in the chosen field and the wider the range of applicability of the information gained. From time to time, as emphasis changes from one field of research to another, a given subject may enjoy popularity and later retire into a scientific somnolence, for fashions change even among engineers and scientists. The subject of this symposium, however, enjoys the advantages of wide applicability and of high current interest and productivity in results. It is a timely subject for a symposium; with much new information, surely metallurgical engineers should now devote an increasing attention to its application to practice. In beginning the symposium, I shall attempt briefly to appraise our basic knowledge in the field, to survey instances of practical usefulness, and to suggest where new work might be most productive of useful results. There are many examples of direct practical application of diffusion knowledge, and it is the purpose of the several papers in this symposium to review these. In this introduction I shall attempt to take a broad view, which, while it will but poorly serve the engineer in the solution of any given problem, may perhaps be of some use in assessing the state of knowledge in this field. RATE OF DIFFUSION Liquid Metals The process of diffusion among liquid metals, of gases in liquid or solid metals, or among solid metals, is ubiquitous, to say the least. The manufacture of alloys by the intermelting of metals, the addition of ferroalloys to molten steel, the deoxidation of molten alloys, all involve diffusion in the liquid state. The oxidation of molten copper for purposes of purification, the unsought oxidation of alloys generally during melting and casting, the reaction of liquid steel with oxidizing slags in the open-hearth furnace, the absorption of nitrogen by liquid steel, particularly in the bessemer furnace, all operate by the diffusion of gases in liquid metals. These processes have not been studied much from the viewpoint of rates of diffusion. Alloys are made by melting metals with stirring and with allowance of time for mixing (which is diffusion) but I know of no studies that seem to define the necessary times, and though in only very rare cases can faulty properties of the finished castings be ascribed to inadequate mixing, and though certainly in most cases, with stirring, the rate of diffusion is adequate to give sufficient mixing, a more quantitative treatment would be good to have. It is not wholly certain that thorough and sufficient mixing is at all times attained, for I suspect that ferroalloy additions to steel, and that additions of aluminum to steel as a deoxidizer, especially in the sampling of steels

Jan 1, 1944

By F. Louis Grammer

THE difference between blast-furnace gas and ordinary producer-gas is chiefly that blast-furnace gas is richer in CO, and poorer in hydrocarbons and hydrogen, as is shown in Table I. TABLE I.-Volume-Composition of Producer-Gas and Blast-Furnace Gas.. Producer-Gas. Blast-Furnace Gas. Per Cent. Per Cent. (Volume.) (Volume.) CO . 22 to 33 25.5 00., . 6 to 3 13.0 H . . 13 to 7 1.5 CH, 3 to 1.5 0.0 N . 54 to 60 60.0 If natural gas, water-gas, or by-product coke-oven gas be available, blast-furnace gas can be made to resemble very closely in calorific value the average producer-gas by merely mixing in one of these products, which are richer in hydro-carbons and, hydrogen. Blast-furnace gas, however, possesses a virtue which is sometimes absent in producer-gas, especially with coals very high in sulphur-namely, that blast-furnace gas is relatively free from sulphur. In some regions the sulphur in coal is an acute problem, and it is highly desirable to find uses for the products which are specially high in sulphur-content. An advantage would be gained if coal was coked before charging into the gas-producers, but this adds to the expense. Sulphur may be partly eliminated from coal by washing it, the success depending upon the form in which the sulphur occurs, and upon the efficiency of the washer, but it cannot always be removed to the extent desired at most American plants. It is not practicable to remove all the sulphur from producer-gas by washing it, though Mr. Reinhardt, of Germany,

Sep 1, 1908

ROSWELL H. JOHNSON,* Pittsburgh, Pa.-The industry, I think, has suffered very severely from the lack of just such work as has been done by Messrs. Lewis and Beal. I think we owe a great deal to the Bureau of Mines for at last undertaking this much needed work, even though it is so belated. It could have been of very great assistance in so many properties where its usefulness has now passed. I think it is perhaps well to sound a note of caution, owing to the fact that so much of this information was derived from eastern Oklahoma; but with the new bulletin giving the decline for many fields, there will be far less danger of falling into error through assuming too much uniformity. The cumulative percentage curve seems to 'me to be a. particularly splendid idea. It should have a very important -influence, especially as the authors have themselves pointed out several variables that ought to be taken into consideration. The thickness, I think, is going to be an especially important one to work out along the general lines of method that they have advanced. Probably the most surprising thing in the paper is the general rule that the decline of a well is more correlated with its size than with its age. I can't help but think that that generalization, important as it is, is rather rough and will not apply so clearly when we have a larger number of fields before us. Still the generalization, rough as it is, is of very great importance, since the industry has been very largely basing a great many of its ideas on the ignorance of that principle. It leads to certain corollaries that are of great consequence. The first is that the undrilled portion of the property must be appraised on a. different basis from that used for the drilled portion.

Jan 4, 1918

By Henry Sturgis Drinker, Rossiter W. Raymond

Jan 1, 1914

The Cuajone and Toquepala copper projects are located in the extreme southern area of Peru. Since 1960, Southern Peru Copper Company has operated the Toquepala open -pit mine, flotation mill, 110 smelter, townsites, power plants, and railroad. Toquepala and 10, the smelter and port location, are connected by a 110-mile-long (176 lun) railroad. Much of Toquepala's infrastructure has been used for the Cuajone project. Cuajone, at an elevation of 11,400 ft (3475 m), required five standard-guage railroad tunnels with a combined length of 17 miles (27.2 km) to connect with Toquepala so concentrates could be shipped to the no smelter. The total cost of Cuajone is estimated at $726 million for a designed annual capacity of 180,000 tons of copper, equivalent to about $4,000 per ton of installed production capacity. This relatively low cost per ton, by today's standards, has been made possible through the use of the 110-to Toquepala railroad, the ability to expand the 110 copper smelter, and other favorable factors. To mine the 468 million tons of copper sulfide or e at a grade of 1.0% copper, approximately 24 1 million tons of waste were stripped- before mining of ore to supply the new Botiflaca 45, 000 ton per day concentrator. The mining rate must exceed 300,000 tons of waste plus ore per day to maintain the 45, 0 00 tpd sulfide ore milling rate which was to be reached at the end of 1976. Waste stripping is done with 15 cu yd electric shovels and 120 -ton trucks. Ore mining is done with 8 and 9 yd shovels. A railroad connects the pit with the 60 in. by 89 in. Allis-Chalmers gyratory crusher. Side-dump railroad cars of 50.cu yd capacity dump onto a 0 16 ft 9 in. long (5. 1 m) grizzly inclined at 40º with 7 to 8 in. (178 to 203 rnrn) bar spacings. The grizzly is divided into two 22 ft 4 in. (6.8 m) wide sections and two side -dump railroad cars discharge simultaneously into the 150-ton capacity dump pocket. A Barco rock manipulator is used for breaking or removing oversize from the dump pocket. The bin receiving the grizzly undersize has a capacity of 5,000 tons, and the pocket beneath the crusher holds 900 tons. Each is equipped with an 84 in. apron feeder, which feeds a 60 in. (1.52 m) conveyor belt to the 150,000 ton coarse ore stockpile, where the ore is distributed by a 72 in. (1. 83 m) tripper conveyor. The 45, 000 live tons in the coarse ore stockpile are reclaimed by twelve 48 in. (1. 22 m) apron feeders. Maintenance on the crusher eccentric is made easy by an eccentric

Jan 1, 1978

By P. S. Kotval

THE nominal composition of "hconel" alloy 718 is 53 pct Ni-19 pct Cr-19 pct Fe-3 pct Mo-5 pct Cb-0.8 pct Ti-0.6 pct A1-0.05 pct C. The nature of the fine strengthening phase in this alloy has been open to debate. iseelstein' has identified the strengthening phase in the matrix of "Inconel" alloy 718 as a colum-bium-rich fcc y' precipitate. Wagner and Hall2 have noted that the metastable y' precipitate overages to an orthorhombic Ni3Cb precipitate which manifests itself as an acicular phase. These authors thus clarify Kaufman and Palty's earlier suggestion3 that the strengthening phase is orthorhombic NisCb. Wagner and Hall's review also reports work by cometto4 which suggests that the fine strengthening phase is not fcc / but bct with a Ni3V type structure and based on the Ni3Cb composition. Kir man and warringtons have shown by analysis of electron diffraction patterns that the metastable strengthening phase in a 55 pct Ni-15 pct 0-25 pct Fe-5 pct Cb alloy is bct and based on the Ni3Cb composition. Raymond~ has provided electron diffraction evidence which indicates that "y'" in "Inconel" alloy 718 is bct in structure. This note presents unambiguous data on the structure of the strengthening phase in "Inconel" alloy 718* ihe samples of this alloy were provided by courtesy of the ASTM task group on phase identification in 'superalloys. after prolonged aging. The electron diffraction patterns presented show that strengthening phase is not y' but bct as was proposed by cometto,' supported by Raymond,~ and identified by Kirman and warringtons in a similar system. Fig. 1 shows a selected-area diffraction pattern taken from a thin foil of "Inconel" alloy 718. The sample had received a final aging treatment of 1118 hr at 1200°F to precipitate the strengthening phase in the matrix. Fig. 2 is a schematic representation of the features in the diffraction pattern. The matrix orientation is (0i2)~,, as is shown by the indexed zone in Fig. 3. Figs. 4, 5, and 6 illustrate that the pattern, Fig. 1, is composed of three bct zones, viz., (0i4), (2i0), and (i01), respectively. These three zones correspond, respectively, to the alignment of the c axis of the bct unit cell with the [001], [loo], and [OlO] directions of the fcc matrix and serve to illustrate the fully coherent relationship of the precipitate structure with the matrix. The streaking of certain reflections is also consistent with the above orientation relationship. The interpretation of the diffraction effects presented here shows the metastable strengthening precipitate in "Inconel" 718 alloy to be bct in structure and demonstrates that it is not an ordered fcc y' phase.

Jan 1, 1969

By George H. Found

DURING recent years considerable interest has been focused on the energy-absorption characteristics of metal when it is cyclically stressed in vibration. The most familiar manifestation of this phenomenon, which is called the "damping capacity" or "internal friction" of a material, is involved in the dissipation of mechanical energy of vibration, which otherwise would build up to stress levels where the problems of noise and fatigue are involved. In addition to its engineering importance in structures, the damping behavior of metals, particularly at low stress amplitudes, has also been used as a unique metallurgical research tool with which to provide sensitive means for indicating certain structural changes within metals. Important contributions toward understanding the energy-dissipating mechanisms that are responsible for internal friction in metals have been made in the last few years. The information is not yet sufficiently extensive, however, to provide a useful metallurgical concept describing exactly how the structure affects the internal friction, or to encourage more general use of this technique among metallurgists. Three fundamental mechanisms have been proposed, as a result of recent experimental investigations, to account for the internal friction in nonferrous metals in low-stress amplitude tests. These include damping due to internal thermal currents that are created and flow in metal because of differential vibratory stress effects,1 damping due to localized inelastic stress relaxation at inhomogeneities within the metal,2,3 and damping related to plastic flow of a localized type for which an explanation has been sought in terms of the dislocation theory.4 How each of these mechanisms functions as a result of structural changes in the metal is, in general, not well understood because of insufficient experimental data for which the controlling variables have been segregated and because of uncertainties in regard to the nature of the structural changes themselves. In several investigations the effects of cold-working on the internal friction of polycrystalline brass and aluminum have been described. As reported by Köster and Rosenthal,5 and by Förster and Breitfield,6 there is an initial large increase in the damping when the metal is worked. The initial high value is not stable, but declines rapidly, at first, in a hyperbolic manner. About 100 hr, after straining, a stable value is reached of magnitude proportional to the amount of strain.7 In Fig. I is shown the relationship found by Zener and his collaborators between the internal friction due to cold-working of alpha brass and the amount of cold-working.8 Several investigators have made internal-friction measurements on worked poly-

Jan 1, 1945

By Frederick Laist

F. N. FLYNN, Clifton, Ariz.-I would like to ask Mr. Mathewson what percentage of his leaching liquor is wasted at this time? It has a bearing on the question in connection with the New Cornelia, and I think it is a very important question. E. P. MATHEWSON, Anaconda, Mont.-I am not sure what the percentage is now, but we don't discard the strong liquors. Something like 25 per cent. of the wash water taken out each day is sent over a special set of scrap iron tanks, and the copper recovered there. We had a little trouble at first. We did not proceed to use the sponge iron for the reason that the plant we originally contemplated was abandoned for flotation. Our original idea was to use a leaching process on all the tailings of the mill, but we found it would take a great deal of time to build a plant; and the cost of operating the plant we estimated to be about the same and the recovery the same. It was a question of time with us, and we decided to adopt flotation. That changed our plans. We now have the leaching plant, treating the tailings of the old dump, and the flotation applied to the current tailings. The sponge iron was figured for the large plant. We can get all the scrap iron necessary for the small plant-plenty from the scrap produced in the main plant of the smelter.

Jan 12, 1916

By J. G. Hall

Introduction When one thinks about world metal economics today, it seems to me he must go beyond the traditional factors such as exploration, discovery, economic feasibility of development, management, labor, and the application of technology. These elements have been and will continue to be very important, of course, in making available the resources that experts believe the world will require during the remainder of this century. There are, however, some new forces as well as new or different emphasis on some of the old factors that could materially affect the development of the world metal mining industries. For example, in my own company two of the most significant considerations affecting our economics today have to do with foreign political decisions and with environmental concerns here in the U. S. -both of which play a far more significant role in our economic considerations than they did as recently as 10 years ago. After a brief look at some historical data and some projections of probable future demands for the world's major metals, I shall then identify and comment upon some of the factors that I believe will have an increasing impact on the future of the economics of our industries. I do not have any magic solutions to the problems we will face; nevertheless, we in the mining industries of the world are going to have to cope with these matters and find satisfactory answers to the problems they will create. The Past Although the age in which we live has been described as the atomic age, the space age and the computer age, we are, in fact, living in a metals age, and we have lived in a metals age for a very long time. The discovery of copper smelting, for example, is placed at about 4000 B.C. Gold was used in a primitive way before that. Other metals - lead, silver, tin, iron and mercury - were discovered and used before 2000 B.C. In all probability, we will be dependent upon metals beyond the vision of anyone living today. In industrialized nations of the world, man's mode of living is based to a great extent on metals, and it is extremely unlikely

Jan 1, 1971

By AIME AIME

THE 129th meeting of the American Institute of Mining and Metallurgical Engineers convened at New York City, in the Engineering Societies Building, Feb. 18-20, 1924. On February 21 an excursion was made to the Bethlehem Steel Co., at Bethlehem, where about 200 members and guests were splendidly entertained. An illustrated description of the Bethlehem Plant will be published next month. The meeting and excursion were largely attended; the registration at New York totalled 1276 versus 1201 in 1923. William Kelly, long identified with the iron-mining industry of the Lake Superior district, was elected President of the A. I. M. E. for the coming year, at ,the annual business meeting, Feb. 19, succeeding E. P. Mathewson. The following Directors were also elected (the date signifies year of termination of office; the final figure indicates the "District" the Director represents).

Jan 1, 1924

By J. R. Dunn

Planning quarry operations and control of the quality of rock materials at Hudson Cement Co. at East Kingston, N. Y., are special problems because of multiple uses for the stone and the great structural complexity of the rocks. Problems have been largely solved by detailed geologic work. These geologic studies have paid dividends in long and short range planning, in assessment of reserves, in vastly reduced cost of chemical analyses, and in reduced drilling costs. Limestones of the Hudson Valley outcrop along the Hudson River from Albany to Kingston. Old established cement companies are located just south of Catskill and just east and southeast of Hudson, N. Y. The new Atlantic Cement plant is being constructed at Ravena. Hudson Cement located at East Kingston, is a newcomer and is closest to the New York metropolitan area (Plate I).

Jan 11, 1961

ARTICLE I NAME AND OBJECT SEC. I. This Institute is incorporated under the Membership Corporations law of the State of New York; its corporate name is American Institute of Mining and Metallurgical Engineers, Inc.; and its objects are such as are stated in its Certificate of Incorporation. ARTICLE II MEMBERS SEC. 1. The membership of the Institute shall comprise four classes, namely: 1. Members; 2. Honorary Members; 3. Associates; 4. Junior Associates. All members shall be equally entitled to the privileges of membership, excepting that Honorary Members, Junior Associates, and Members and Associates whose residences shall be outside of the United States, Mexico, and Canada shall not be entitled to vote. Members and Associates residing within the United States of America, Mexico, and Canada, .and not in arrears for dues, shall be entitled to vote in person at the meetings of the Institute, or, as hereinafter provided for, by letter ballot. SEC. 2. Members shall comprise all those persons who on the third Monday of February, 1918, were members of the Institute, and in addition thereto, all those thereafter elected or transferred into the class of Members. A person to be eligible for election or transfer into the class of Members must be at least 27 years of age and must have had at least six years' employment in the practice of engineering, mining, geology, metallurgy or chemistry, during at least three years of which he must have held positions of responsibility in one or more of these fields. Graduation from the scientific course of a college, approved by the Committee on Membership, shall be considered equivalent to two years' employment, as required in the previous sentence. Employment as a teacher of engineering, mining, geology, metallurgy or chemistry, if in direct charge, may be considered a position of responsibility as specified in the second paragraph. Persons employed in research or any scientific literary work or in teaching in the scientific departments of colleges, approved by the Committee on Membership, who at the same time are engaged in consulting or in the active practice of mining, geology, or metallurgy, shall be entitled to consider the time so spent in active practice as equivalent to an equal length of time of employment in positions of responsibility, provided the work done or the positions held seem to the Committee on Membership to warrant the equivalency. The requirement of three years' employment in positions of responsibility maybe waived by the Committee on Membership in the case of persons who have done notable original work in mining, geology, or metallurgy, or have won distinction by

Jan 1, 1925

By John Dasher

Getting spodumene to float quickly and cleanly can be a problem. The author has presented an excellent account of a valid and useful approach to the scale-up of such problem floats. This indicated advantages for doubling retention time, i.e., buying another set of flotation cells. The author states that 21 pct of the spodumene floated in 2 min in the laboratory cell, that the grade of the rougher was about 75 pct spodumene, and that the final tailing contained 4 to 12 pct spodumene in different sizes with the present cells and 1 to 9 pct spodumene with twice as many cells.

Jan 6, 1959

By S. H. Ward, R. A. Barker

THE Juniper Prospect is in Carleton County, N. B., at approximately 46º 31' north latitude, 67º 20' west longitude. During the summer of 1955 an area in west-central New Brunswick was selected for aerial electromagnetic prospecting with American Metal Co.'s helicopter-mounted equipment. Generalized, small-scale government geologic maps had suggested that this area was located along the western border of the northeast-trending granitic backbone of northwestern New Brunswick and might be underlain by the Ordovician-Silurian sediments and volcanics that are the host rocks for the recently discovered sulfide deposits of the Bathurst-Newcastle district.

Jan 1, 1958

By Stanley J. Gasior, Albert J. Forney, Joseph H. Field

Most bituminous coal mined near Eastern industrial areas requiring high-Btu pipeline gas is caking and therefore unsuitable for fixed-bed pres- sure gasification by present techniques. If the caking property of such coal can be destroyed, the resulting fuel can be gasified in a fixed bed at pressure with steam and oxygen as a preliminary step in making a high-Btu gas. To find a practical way to convert strongly caking coals of granular or small lump size to noncaking fuel was the object of this study. In previous work, strongly caking coals of 1/8- to 1½ -in. size were converted to a noncaking coal char by treatment in a static bed in about 3 hours1 and coal of 18-100 Tyler mesh in a fluidized bed in about 5 min.2 An inert gas such as steam, nitrogen, carbon dioxide or a mixture of all three with a small amount of oxygen was used in both studies. In our work a strongly caking bituminous coal from the Pittsburgh seam of 4-8 Tyler mesh size was converted to a noncaking form in free-fall in about 2 sec by dropping it through a countercurrent flow of steam containing 4% to 7% oxygen at 1150º-1200°F and 300 psig. This method should also be applicable to smaller-sized material.

Jan 3, 1965

By R. J. Wysor

Discussion of the paper of R. J. WYSOR, presented at the New York meeting, February, 1916, and printed in Bulletin No. 106, October, 1915, pp. 2161 to 2170. LEONARD WALDO, New York, N. Y.-Will Mr. Wysor kindly give us more information as to the pyrometers used and the temperature measurement? R. J. WYSOR, So. Bethlehem, Pa.-We used standard Bristol pyrometers with bare fire ends. These were standardized both before and after the tests with salt and pure aluminum. We also interchanged the pyrometers. J. W. RICHARDS, So. Bethlehem, Pa.-Did you attain any results which gave you approximately the value of the heat insulation at any of the furnaces? R. J. WYSOR.-In the first installation we were afraid to put in the insulation throughout the hot-blast main for the reasons mentioned in the paper, but we used the insulating brick in two 8-ft. sections in straight lengths of our hot-blast mains. Owing to the high conductivity of the steel shell, the temperatures which were taken on the outside were not representative of the two temperatures resulting from heat flow through the insulating brick. I believe that when a hot-blast main is insulated

Jan 5, 1916

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

Mrs. W. Y. Westervelt, Director of the New York Section, reports an interesting meeting at her house- on May 12. Dr. Cecile Griel, special worker of the division for work among foreign-born women of the National Board of the Y. W. C. A., spoke. As the Americanization Committee under Mrs. Scobey is planning an energetic campaign, Dr. Griel's stirring appeal was timely and suggestive. While Dr. Griel cited the usual avenues of approach to our alien population through the school children, the needs of the baby, sewing classes, English classes, etc., her especial appeal was for correct psychology on the part of the workers. She deplored the condescension, implied or expressed, so often manifest in persons attempting Americanism, work and emphasized many times the importance of an understanding heart and mind. At the close Mrs. Scobey brought forward plans for practical work to be done by the New York women, of which I hope to give some details next month.

Jan 7, 1919

By O. D. Sherby, J. L. Lytton, C. R. Barrett

Randomly oriented polycryslalline copper of 99.995 pcl was tested in tension at temperatures of 626o, 496o, and 406o. The gvain-size mnge investigated was from 0.03 to 0.7 mm. Grain sizes were produced by two techniques: 1) varying the amount of prior cold work and the amealing time at constant annealing temperature so as to obtain various vecrystallized grain sizes with minimum grain growth, and 4 holding the prior cold work constant while varying the annealing time or temperature so as to obtain varying grain sizes by grain growth. Polycrystalline samples (grain size of 0.03 mm) with a strong. [001](100) texture were also studied. The relationship between the steady-state creep rate, Es, and pain size was found to be the same indepentent of the technique used to prepare the various grain sizes. For specimens with grain diameters above about 0.1 mm ea zuas esse)ztiallj~ independent of grain size, while for smaller grain diameters Cs increased slightly with decreasing grain size. Strongly textured polycrystalline copper, which contained low-angle grain boundaries, exhibited steady-state creep rates that were slightly lower than those observed in randomly oriented copper, of the same gain size. The results are explained by conside?%ng- the contribution of grain boundary shearing to the total strain and the effect of grain size on the resulting creep substructure. EXPERIMENTAL observations concerning the influence of grain size on steady-state creep rates are varied and oftentimes conflicting. Numerous early investigators found that an increase in the grain size resulted in a decrease in the high-temperature steady-state creep rate, i,.'-" Other workers have foundthat ef decreases with increasing grain size up to some optimum grain size and then increases with a further increase in grain size.'- '' It has been suggested that es, decreases with an increase in grain size only because the range of grain sizes studied normally lies to the left of the grain size for optimum creep resistance. However, sherbyl2 and Feltham and his co-worker13, 14 have found that even for small grain sizes 2, does not always decrease with an increase in grain diameter but may be proportional to the square of the grain diameter. A possible explanation for the different creep rate-grain size relationships which have been observed is that in most experimental studies different grain sizes have been prepared by annealing at various temperatures. For metals in which the impurity concentration is high (greater than about 0.1 at. pct) this type of

Jan 1, 1968