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By J. W. Putman, N. J. Grant, D. S. Bloom

SEVERAL recent determinations of the melting S point of pure chromium have been reported which give values of 1845°C1; 1895°C,² 1930°C,³ 1860°C,' and 1890°C.5 because of this wide spread of values, it appeared desirable to make one additional attempt to obtain a more accurate, reliable figure. bloom and Grantx recently reported a phase transformation in chromium:.--- it was desired to check this, too, in the course of checking the melting point. To accomplish this, a much higher purity chromium was required. Electrolytic chromium containing about 0.5 pct 0 was crushed to a finer size and was then annealed in highly purified, dried hydrogen at 1375°C for 100 hr. This treatment produced chromium with about 0.008 pct 0, 0.002 pct N, and negligible carbon. The balance of the impurities was 0.3 pct Fe, 0.03 pct Si, 0.004 pct S, and less than 0.001 pct Mo. This chromium was melted in a stabilized zirconia crucible under pre-purified argon, using induction heating. Temperature measurements were made with annealed wolfram-molybdenum thermocouples and a Leeds and Northrup Speedomax Recording Potentiometer. The thermocouples were annealed for 1 min in hydrogen at a temperature of about 2400°C. Each leg of the thermocouple was immersed in an ice-water mixture using mechanical connectors to the lead wires. The thermocouple tip was immersed in the molten chromium in a zirconia protection tube which introduces an error of about 3°C as a temperature drop through the walls of the tube. The weight of chromium was about 183 g. The dimensions of the melt in the crucible were about 1.25 in. diam x 2 in. high. The tip of the thermocouple was held about ½ in. from the bottom of the crucible. Two new thermocouples were used with the above set-up giving the results shown in Table I. Since this chromium is purer than that used by Greenaway, Johnstone and McQuillan,' by Carlile et al.,4 and other investigators,²,3 it is believed to be the more accurate. Thermocouple aging effects which are believed responsible for the high value of 1930°C³ were avoided in this work. This value of 1903°C is correct to about ±10°C. The right hand column lists the temperature of the a ? ß transformation on heating and the ß ? a on cooling.3 A sample curve is shown in Fig. 1. The value so determined is 1840°C + 15°C. Fig. 1 gives adequate evidence that there is a transformation in chromium at high temperatures.' References 'H. T. Greenaway, S. T. M. Johnstone, and M. K. McQuillan: High Temperature Thermal Analysis USing the Tungsten-Molybdenum Thermocouple. Journal Inst. Metals (November 1951) 19, p. 109. ²J. W. Putman, R. D. Potter, and N. J. Grant: The Ternary System Chromium-Molybdenum-Iron. Trans. A.S.M. (1951) 43, p. 824. ³D. S. Bloom and N. J. Grant: Chromium-Nickel Phase Diagram. Trans. AIME (1951) 191, p. 1009; Journal of Metals (November 1951). ' S. J. Carlile, J. W. Christian, and W. Hume-Rothery: The Equilibrium Diagram of the System Chromium-Manganese. Journal Inst. Metals (1949) 76, p. 169. 5G. Grube and R. Knabe: Ztsch. Elektrochemie (1936) 42, p. 793.

Jan 1, 1953

[A session of the Institute of Metals held during the February, 1926, meeting of the Institute, was devoted to a symposium on ''gas" in copper. S. Skowronski, Perth Amboy, N. J., was chairman. On the program were papers by T. S. Fuller; W. H. Bassett and J. C. Bradley; Susan B. Leiter, and W. H. Bassett and H. A. Redworth. These papers follow the chairman's introductory discussion.] S. Skowronski, Perth Amboy, N. J.—There are today two groups of metallurgists, one group who believe in oxygen-free copper and another group who believe that oxygen is absolutely essential in copper; not that the two groups disagree, but that a certain grade of work calls for oxygen-free copper, while another grade of work does not. I can sum up the problem by reading the abstract of an article by Frederick Johnson of Great Britain in The Metal Industry of Sept. 4, 1925. Few, who have watched the trend of things during the last two decades, can have failed to notice the steady growth of opposition to the prevalent use of copper in the "tough-pitch" condition, which for many ages enjoyed an unchallenged supremacy. Broadly speaking, there are two schools of thought in the metallurgical world, one holding the view that copper containing a small proportion of oxygen is an eminently suitable material for users, the other expressing its preference, in no hesitating or uncertain manner, for copper from which oxygen has been removed by means of a deoxidizer. In the old days, before the advent of the converter and the electrolytic refining process, the copper of commerce was so impure that the presence of oxygen was imperative in order to neutralize the influence of impurities which militated against the hot-working properties of the metal. For electrical purposes, oxygen must be present, because sound bars and billets cannot be produced without it, except at the expense of electrical conductivity. For most engineering purposes, however, electro-deposited copper may be used either by itself or with the addition of alloying elements, e. g., arsenic and nickel, which experience has proved to be beneficial, such copper being freed from oxygen by the aid of a deoxidizer, e. g., phosphorus. Such material has positive advantages over "tough-pitch" copper as at present produced from refinery furnaces. It has greater toughness and malleability, and is immune from the action of reducing gases at high temperatures, the destructive action of which, in the case of "tough-pitch" copper, is well known. The reasons why there has been no wholesale replacement of "tough-pitch" copper by deoxidized copper are commercial in nature; copper can be more economically melted in large-capacity furnaces which lend themselves to the poling process and are not so suitable for control of uniformity of action of deoxidizers as the smaller electric or crucible furnaces, whilst they are also more convenient for the production of very large castings. Moreover, the equipment of most large copper manufacturing plants is designed for casting "tough-pitch " copper in open moulds, e. g., wire bars and cakes, and these could not be used for deoxidized copper, which must be cast in vertical moulds as in brass-shop practice. Further, there are still certain impure brands and

Jan 1, 1926

By R. E. Cole, A. M. Gaudin

OLEIC acid, a standard flotation reagent, has generally been preferred to other fatty acids. Because oleic acid differs from saturated fatty acids by the presence of one carbon-to-carbon double bond and because the flotation operation is one in which extremely intimate exposure of the reagent to oxygen is obtained, it appeared possible that the value of oleic acid as a flotation collector was related to the oxidizability of its double bond. To test this hypothesis, the floated mineral, fluor-ite, was leached with a solvent capable of extracting the adsorbed reagent and the extract was analyzed.' Results show that oleic acid is not oxidized during flotation, although some oxidation can be obtained if the flotation operation is repeated many times and if oxygen in place of air is employed as the gas during flotation. Incidentally, it was found that lino-leic acid which has two nonconjugated double bonds is not affected appreciably more than oleic acid. Linolenic acid which has three nonconjugated double bonds is measurably altered even during one flotation step, using air. The fatty acids used, from the Hormel Foundation, were of the highest purity. The quantity of fatty acids employed in each test was sufficient to float the mineral, but less than the theoretical amount required to form a monolayer at the mineral surface. The purpose of this limitation was to eliminate droplets of oil smeared on the adsorbate-covered mineral surface. The mineral was dried in vacuum at about 60 °C. Effective leaching was obtained by use of a solution of 1 pct hydrochloric acid in absolute alcohol. The extract was separated from the solvent by distillation, with final recovery of the extract in carbon tetrachloride. The identity of the extract was tested by a combination of analytical procedures including infrared spectroscopy, saponification number, iodine number, and index of refraction. At the outset, great hopes for accurate quantification of oleic acid oxidation had been entertained in regard to the method of infra-red spectroscopy. Unfortunately, because the double bond in the oleic acid is so sym- metrically located at the center of the molecule that it provides very weak absorption bands, accurate quantitative analyses were not obtained. Nevertheless, infra-red spectrograms suggested the absence of double-bond oxidation during flotation. Iodine number, semi-micro method, provided a critical test of the extent to which fatty acids oxidized during flotation, see Table I. The index of refraction was used in a qualitative rather than quantitative fashion, and its findings corroborated those obtained by the iodine-number method. It is concluded, in the case of fluorite and C-18 fatty acids having one or two nonconjugated double bonds, that there is practically no change of the fatty acid molecule or ion during the flotation operation. It would appear, therefore, that the extraordinary utility of these reagents is related to some property of the compounds other than the oxidizability of their double bonds. Acknowledgment The research reported herewith was sponsored by the Research Division, U. S. Atomic Energy Commission, and for this help the authors express their appreciation. Reference 'R. E. Cole: "Double-Bond Reactivity of Oleic Acid During Flotation." Thesis submitted in partial fulfillment of the requirements for the degree of M.S. at the Massachusetts Institute of Technology.

Jan 1, 1954

By Phillip E. La Moreaux

Fluoride, generally less than 0.5 ppm, is present in ground water from rocks of Paleozoic age and older, in northern and eastern Alabama. Some of the water-bearing formations in the Coastal Plain area of the State yield water with as much as 6.8 ppm fluoride. IN June 1940, the U. S. Geological Survey, in cooperation with the Geological Survey of Alabama, began a study of the ground-water resources of the part of Alabama where water is obtained from Cretaceous rocks. The purpose of the study was to determine the quality, quantity, occurrence, and availability of ground water in that area. These studies have been expanded to include ground-water investigations in the area of Tertiary rocks, or southern quarter of the State, and certain areas in northern Alabama. The first report issued on these studies was by C. W. Carlston,1 of the Alabama Geological Survey. In the present paper all references to ground-water data for the Cretaceous area are taken from this earlier publication. In 1945, the Dentistry Division of the Alabama Department of Public Health became interested in the correlation of tooth decay and mottled enamel with the chemical quality of ground water used for public supplies in the State. Through a cooperative arrangement between the State Department of Public Health and the Ground Water Division (now Branch) of the U. S. Geological Survey, a report by the author2 was published in 1948. These two reports give accurate information on the occurrence of fluoride in the Coastal Plain of Alabama. At present, only scattered information is available on fluoride in ground water of the crystalline-rock or Piedmont area and for the Paleozoic area of Alabama, but it is hoped that in the future more complete information on the presence of fluoride in ground water in these areas can be collected. Outline of Geology and Ground Water: As described by Adams,3 the State of Alabama includes parts of two major geologic divisions, the Appalachian region and the Coastal Plain. The boundary between these divisions is irregular and is known as the Fall Line of the Atlantic and Gulf Coast States. The Fall Line enters Alabama near Phoenix City, extends westward to Wetumpka, Clanton, and Tuscaloosa, and then swings northwestward to the northwest corner of the State. The Appalachian region in Alabama includes three major provinces, the Piedmont province, the Appalachian Ridge and Valley province, and the Appalachian Plateau province (fig. 1). The rock formations in the Piedmont province in east-central Alabama are mainly of pre-Cambrian age, chiefly crystalline schists and gneisses injected by younger igneous rocks (fig. 1, I). They are faulted and folded and have a complicated structure. These rocks are the oldest and among the most complex rocks in the State. Generally, only small yields of ground water are obtained from rocks in this area. Even though ground water is of great importance for the development of domestic and farm supplies in rural areas and a few small industrial and municipal wells, yields in the area from individual wells generally range from 5 to 25 gpm and rarely exceed 50 gpm. The geologic formations of the Appalachian Ridge and Valley province and the Appalachian Plateau province (see fig. 1, II, and III) are separated on the basis of their structure. These rocks are of Paleozoic age, ranging from Cambrian to Carboniferous, and comprise a succession of formations consisting chiefly of shale, sandstone, limestone, and dolomite, aggregating many thousands of feet in

Jan 1, 1951

By S. C. Sun

Most previous work on sedimentation of coal 1 and mineral 2-3 suspensions has been conducted in graduated 1-liter glass cylinders of 6-cm diam. With this type of large container it is often difficult to see through the suspension and tedious to perform a large number of tests. Furthermore, the heavy glass walls and the graduation lines of glass cylinders cause internal and stray reflections, respectively. To obviate these difficulties, an Atlab Emulsion Viewer from Arthur H. Thomas Co. was adopted as an alternative apparatus. Equipment: The viewer," shown in Fig. 1, consists of: 1) a stainless steel frame rack holding 21 flat-bottom Nessler tubes or an ungraduated replica 1.64 cm ID and 1.80 cm OD, 2) a movable masked 150-w lumaline lamp behind the tubes, and 3) a scaled glass panel with 100 vertical divisions in front of the tubes. The tubes are snugly held by springs in slots formed by spacer bars, which also serve as shields to eliminate stray light. The lumaline lamp is mounted behind a slit in a movable housing so that it can be positioned behind the suspension to be examined. The lowest or 100-divi-sion line on the front glass plate is leveled with the upper side of the bottom of all tubes. The scaled portion of each tube, roughly 19 cm high and 40 ml in volume, is used to study coal and mineral suspensions. Procedure: The following procedure was used in many tests. A 1.6-gm sample of dry coal was mixed with 16 ml of distilled water in an ordinary test tube and allowed to stand for three days, with occasional shaking to insure thorough wetting of all particles. The slurry was transferred to a Nessler tube and diluted to 32 ml. The pH regulator and flocculating reagent were added, and the slurry was diluted to reach the uppermost or zero-division line. The tube was immediately stoppered and inverted downward and up again ten times during a period of 35 to 40 sec. The lumaline lamp was turned on during the inversion period. After inversion the tube was quickly returned to the viewer rack. The time elapsed for each 10-division drop of the demarcation line between solid and liquid was recorded by stopwatch until the 80-division line was reached in the zone of compression. Additional readings were taken at 15, 30, and 60 min after settling began. The clarity of the supernatent liquid was observed also. As the settling rate became considerably slower at the 75-division line, it was convenient at this time to start the next test in a separate Nessler tube. This was continued until the suspensions in any number of the 21 tubes were tested. An attempt was made to correlate the experimental results between the Nessler tube and a 1-liter glass cylinder. Table I shows that coal particles settle much faster in the cylinder than in the tube, which has a large wall effect.' The correction factor for the tube impedance is 1.662 2 0.145 at the 40-division line in the hindered settling zone, and 1.614 & 0.139 at the 75-division line in the compression zone. This rough correlation was established by dividing the pulp height of each container into 100 divisions and comparing the settling rates of the two containers at the same divisions. Tests were also performed to determine the accuracy of the viewer. The results, not presented, showed that error was within 10 pct.

Jan 1, 1960

By S. S. Shen, M. J. Pool, P. J. Spencer, J. R. Guadagno

VERY few thermodynamic data are available for rare-earth alloys, partly because of the difficulties of obtaining the metals in sufficiently pure form and also because of their comparative scarcity up to the present time. The rare earths form a very interesting series in the periodic table in view of the progressive filling of their 4f subvalence electron shell and would be expected to provide useful information with regard to alloying characteristics of transition elements. It has been found in recent calorimetric investigations that the heats of solution of a number of the rare-earth metals in liquid tin are highly exothermic.1-4 Exceptionally strong bonding between rare-earth and tin atoms is clearly indicated in the liquid solutions. Continued thermodynamic studies of the behavior of rare earths in solution could thus contribute a great deal to present theoretical knowledge of alloying behavior and would yield an insight into bonding of a strength hitherto unencountered in liquid alloys. The determination of the heats of solution of the pure components in liquid tin is an essential preliminary to calorimetric work of this nature. Heats of solution of praseodymium, neodymium, and samarium in liquid tin at 750" ' and the heats of mixing of Pr-Nd solid solutions' have already been determined in this laboratory. The present investigations with lanthanum continue the study of rare-earth elements. Details of the construction and operation of the liquid metal solution calorimeter used in this work have been published previously by Pool and Peluso and no further description will be given here. The lanthanum used in heat of solution determinations was supplied by Lunex who quoted the purity as 99.9 pct. Their detailed analysis of the material is given in Table I. Samples of 0.0003 to 0.0005 g-atom were used for each run and great care was taken to remove all surface oxide prior to weighing. The samples were stored at all other times in a beaker of oil to prevent their otherwise rapid oxidation. The compounds LaSn (Cudu, L1P type structure) and La&, (structure not classified) were prepared from the appropriate quantities of the two pure components by arc melting under a purified argon atmosphere and once again great precautions were taken to avoid any subsequent oxidation of the specimens. Although no structural examination of the compounds was made, the consistency of thermodynarnic measurements carried out on twenty or so individual samples of each indicates that the compounds were in fact homogeneous, single phase alloys. Samples of the compounds consisting of 0.0003 to 0.002 moles were used in the calorimetric measurements. A solvent bath consisting of approximately 80 g of 99.9 pct pure Sn was used for each series of runs and its heat capacity was determined at regular intervals throughout the experiments using pure tin or tungsten calibration samples. Measurements were made of the heat of solution of lanthanum in liquid tin at 725", 750C, and 775°K and at compositions up to 2.21, 4.76, and 5.25 at. pct La at the three temperatures respectively. In every case, the heat of solution of lanthanum remained constant at its limiting value, within experimental limits, up to the highest lanthanum concentration investigated. Since no change in was observed, it was concluded that the liquid/liquid + LaSn, phase boundary had not been

Jan 1, 1969

By R. C. Hall

The magnetic anisotropy and magnetostriction of single crystals of alloys between 25 and 59 wt pct Co in Fe have been determined in the disordered and ordered states. The magrzetostriction is large and positive for all alloys in both states of order (up to 150 x 10-6 for A,, and 40 x 10-6 for 111). The magnetic anisotropy becomes zero rzear 41 pct Co for the disordered state. Ordering shifts the zero-anisotropy composition to about 50 pct Co. COBALT-iron alloys have for many years been of interest as magnetic materials because they have unusually high magnetic saturation values.' This interest was increased recently by the development of Supermendur.' Supermendur is an alloy of 49 pct Co-49 pct Fe-2 pct V* which was found by suitable purification and heat treatments, including a magnetic anneal, to possess excellent magnetic properties. These included a square hysteresis loop with a low coercive force and a high magnetization, and a low total loss. Two factors which are important in determining the magnetic hysteresis properties are the basic magnetic properties of magnetostriction and anisotropy. Alloys having zero anisotropy and zero magnetostriction show improved hysteresis properties.3 Since very meager data4-' are available in the literature on the single-crystal anisotropy and magnetostriction of the cobalt-iron alloys, the present program was undertaken to determine these two properties in the disordered and ordered states. EXPERIMENTAL TECHNIQUES Ingots of the cobalt-iron alloys containing from 25 pct to 59 pct Co in iron were vacuum melted from electrolytic iron and cobalt of 99.9 pct purity. The ingots were cooled at a rate of about 1°C per hr through the transformation temperature (950" to 980°C dependent on the alloy content) for the growth of large grains. From these grains, single-crystal disks were fabricated with either the (110) or (100) plane parallel to the faces of the disk. The crystals were given two heat treatments to produce either the ordered state (cooling rate of 20°C per hr from 850 "C) or the disordered state (water quench from 850 °C). Since the iron-cobalt alloys order very rapidly, the water quench may not have produced complete disorder in all cases. Due to the method of growth, the crystals were not perfect. Most of the samples had low-angle boundaries and a few had some small included grains. These imperfections could and probably did affect the accuracy of both the magnetic anisotropy and magnetostriction measurements. Much of the scatter in the data may be attributed to the crystal imperfections. The methods of determining the spontaneous saturation magnetostriction and the anisotropy have been previously described.419110 MAGNETOSTRICTION The magnetostriction in the [loo] and [Ill] directions (hO0 and ?111 respectively) is illustrated in Fig. 1 for the disordered state. Both ?100 and ?111i became large positive values as cobalt was added to iron. The state of order did not have a large effect on the magnetostriction. The effect of order did not appear too consistent in these data. Tentative curves are shown in Fig. 1 for the ordered magnetostriction near the FeCo composition; here ?100 appeared to be lowered and ?111 raised as the degree of order was increased. These results agree qualitatively with the

Jan 1, 1961

By Phillip E. La Moreaux

Fluoride, generally less than 0.5 ppm, is present in ground water from rocks of Paleozoic age and older, in northern and eastern Alabama. Some of the water-bearing formations in the Coastal Plain area of the State yield water with as much as 6.8 ppm fluoride. IN June 1940, the U. S. Geological Survey, in cooperation with the Geological Survey of Alabama, began a study of the ground-water resources of the part of Alabama where water is obtained from Cretaceous rocks. The purpose of the study was to determine the quality, quantity, occurrence, and availability of ground water in that area. These studies have been expanded to include ground-water investigations in the area of Tertiary rocks, or southern quarter of the State, and certain areas in northern Alabama. The first report issued on these studies was by C. W. Carlston,1 of the Alabama Geological Survey. In the present paper all references to ground-water data for the Cretaceous area are taken from this earlier publication. In 1945, the Dentistry Division of the Alabama Department of Public Health became interested in the correlation of tooth decay and mottled enamel with the chemical quality of ground water used for public supplies in the State. Through a cooperative arrangement between the State Department of Public Health and the Ground Water Division (now Branch) of the U. S. Geological Survey, a report by the author2 was published in 1948. These two reports give accurate information on the occurrence of fluoride in the Coastal Plain of Alabama. At present, only scattered information is available on fluoride in ground water of the crystalline-rock or Piedmont area and for the Paleozoic area of Alabama, but it is hoped that in the future more complete information on the presence of fluoride in ground water in these areas can be collected. Outline of Geology and Ground Water: As described by Adams,3 the State of Alabama includes parts of two major geologic divisions, the Appalachian region and the Coastal Plain. The boundary between these divisions is irregular and is known as the Fall Line of the Atlantic and Gulf Coast States. The Fall Line enters Alabama near Phoenix City, extends westward to Wetumpka, Clanton, and Tuscaloosa, and then swings northwestward to the northwest corner of the State. The Appalachian region in Alabama includes three major provinces, the Piedmont province, the Appalachian Ridge and Valley province, and the Appalachian Plateau province (fig. 1). The rock formations in the Piedmont province in east-central Alabama are mainly of pre-Cambrian age, chiefly crystalline schists and gneisses injected by younger igneous rocks (fig. 1, I). They are faulted and folded and have a complicated structure. These rocks are the oldest and among the most complex rocks in the State. Generally, only small yields of ground water are obtained from rocks in this area. Even though ground water is of great importance for the development of domestic and farm supplies in rural areas and a few small industrial and municipal wells, yields in the area from individual wells generally range from 5 to 25 gpm and rarely exceed 50 gpm. The geologic formations of the Appalachian Ridge and Valley province and the Appalachian Plateau province (see fig. 1, II, and III) are separated on the basis of their structure. These rocks are of Paleozoic age, ranging from Cambrian to Carboniferous, and comprise a succession of formations consisting chiefly of shale, sandstone, limestone, and dolomite, aggregating many thousands of feet in

Jan 1, 1951

The Institute conducts jointly with the American Society of Civil Engineers, American Society of Mechanical Engineers and American Institute of Electrical Engineers, certain activities as listed below, and is joint owner with them of certain properties. United Engineering Trustees, Inc.* When Mr. Carnegie made his gift which made possible a home for the engineering societies, a separate corporation was organized to act as a holding company and to manage the common property. This was long known as the United Engineering Society but the name has now been changed to one which more nearly reflects the real function of the corporation. It holds title to the Engineering societies Building and to various funds placed in its charge and is managed by a Board of Trustees of which three are chosen by each of the four societies, American Institute of Mining and Metallurgical Engineers, American Society of Mechanical Engineers, American Institute of Electrical Engineers and American Society of Civil Engineers, which own equal and undivided interests in the property. The land and building cost two million dollars. The interest of each of the Founders societies, aside from especial trust funds, is now valued at $493,352. The A. I. M. E. trustees are Arthur S. Dwight, J. V. N. Dorr and H. A. Guess. George D. Barron will succeed Mr. Guess as trustee at the end of this year. The President of the Board is Francis Lee Stuart and the Secretary, Alfred D. Flinn. The Engineering Foundation The Engnieering Foundation was established in 1814 as a result of a gift of $200,000 made by Ambrose Swasey. It is intended not only "for the Furtherance of research" along broad lines but also "for the advancement of" a wide variety of other activities of benefit to engineering as need arises. The endowment fund, which now amounts to $630,000, is administered by the United Engineering Trustees, Inc. Through The Engineering Foundation board, on which the Institute is now represented by J. V. N. Dorr, John M. Callow and Galen H. Clevenger, the income of the endowment, approximately $28,000 a year, and funds contributed for special projects are appropriated for the purposes intended. H. C. Bellinger will succeed Mr. Callow on the board at the end of this year. Alfred D. Flinn is Secretary- and Director. Researches of wide interest in many lines have been aided by Engineering Foundation. . A grant from it to the Mining Methods Committee assisted in the preparation of Volume 72 of the Transactions. For several years the Foundation has aided in support of the study of Blast-furnacc Slags by R. 8. McCaffery at the University of Wisconsin, sponsored by the Institute. The Foundation has raised over $230,000 to support the Alloys of Iron Research endorsed by the Institute and George B. Water-house is serving as Chairman and Director of the Iron Alloys Committee which has been brought together to direct this work. The Foundation has also on recommendation of the Institute made a grant in aid of the studies of Mining and Strata being conducted at Columbia University by P. B. Bucky, which promise information of great usefulness relative to mine subsidence and support of ground. John Fritz Medal Board of Award The medal was established in 1902 and lias since, been awarded not oftener than annually by a hoard of sixteen members, four representatives each from the American Societies of Civil, Mining and Metallurgical, Mechanical, and Electrical Engineers.

Jan 1, 1930

By B. Lustman

IT has been known for a number of years that the addition of certain alkaline-earth and rare-earth metals to nickel-chromium base electric resistance alloys causes marked increase in their oxidation resistance as measured in an intermittent oxidation test similar to the ASTM—B 76-39 test. However, the mechanism whereby such additions confer protection is still unknown. On the basis of the experimental observation that the increase in life in intermittent tests of nickel-base alloys is proportional to the atomic radius of the added element, Hessen-bruchl has proposed that the added metal ions occupy holes in the oxide lattice which prevent diffusion of nickel ions in the oxide. Horn2 has postulated that the effect of such additions is to accelerate the rate of diffusion of chromium atoms in the metal and thus to favor the formation of Cr2O3 scales. Hickman and Gulbransen3 concluded from electron diffraction observation that the addition of the elements in question results in the formation of a barrier to the diffusion of nickel ions to the surface. In connection with some experiments conducted to develop a test for the resistance to oxidation of alloys in massive form under conditions of intermittent heating and cooling, some features of the oxidation of nickel-chromium base alloys were revealed which may serve to elucidate the mechanism of protection conferred by rare-earth and alkaline-earth elements. Specimens of cylindrical shape 0.360 in. diam x 0.37 in. long were placed in alumina thimbles and inserted into and withdrawn from a Globar-heated furnace operating at 2150°F at 7.5-min intervals. The weight of oxygen absorbed as well as the weight of oxide spalled were measured at intervals. With the particular experimental conditions used, the specimens in a 7.5-min cycle were at temperature for 2 min which corresponds to the heating time of the ASTM test. The weight changes of similar specimens under conditions of continuous heating in air at 2150°F were also measured. The specimens after oxidation were examined metal- lographically and samples of the spalled oxide collected for X-ray diffraction identification of the phases. The specimens used were from the same lot of material used by Hickman and Gulbransen3 and had the compositions shown in table 1. Included in table I are results of ASTM life tests on the materials in the form of wires. These materials, their composition and the ASTM life test data thereon were all supplied by F. E. Bash of the Driver-Harris Co. It may be noted that alloy 13246 of 80 pct nickel, 20 pct chromium nominal composition showed the shortest life in the ASTM test; alloy 12246 with the addition of small amounts of the elements zirconium, calcium, and aluminum, intermediate life; and alloy 12046 with the further addition of silicon, the longest life. In fig. 1 are shown the results of intermittent oxidation tests made on bulk specimens at 2150°F as well as continuous tests conducted at the same temperature. Duplicate tests were made on each specimen. The ordinate scale, inches of metal oxidized, was derived from the experimentally observed weight gain of oxygen by assuming the scale to be entirely Cr2O3. It may be noted that the metal-loss curves during intermittent oxidation show a constant or continuously increasing rate of weight

Jan 1, 1951

By S. R. Goodman, Hsun Hu, R. S. Cline

The quenching technique has been used to study phase relations in the composition area 2FeO.SiO2-FeO-SiO2-MnO.Si02-ZMnO.SiO2 of the system iron oxide-manganese oxide-silica under strongly reducing conditions such as exist in a gas mixture consisting of equul parts of carbon dioxide and hydrogen. Liquidus and solidus temperatures of most mixtures in the composition area studied are in the range of 1173° to 1345°C. EQUILIBRIUM relations existing among the oxides of iron, manganese, and silicon are of particular interest in two areas of steelmaking: slags and ingot inclusions. Mixtures of these oxides represent about 90 pct of the slag in the acid steelmaking process, and so dominate the chemistry of the whole refining process. These constituents also play an important role in the early slags existing at the time of the "lime boil" in the basic open hearth process. If these slags are liquid, they "wet" the lumps of lime rising from the bottom of the bath, and react with them. A liquid slag rich in CaO is then formed at the very beginning of the refining. Because the temperature is still low, all conditions for a good dephosphoriza-tion are fulfilled at this stage of the operation. Metal deoxidized with ferromanganese or silico-manganese is likely to contain, as inclusions, phases made up from among the oxides of iron, manganese, and silicon. A knowledge of stability relations existing among the phases present in this system, therefore, enables one to predict the hardness of the inclusions encountered. Moreover, because the shape of the inclusions in steel has a profound influence on the physical properties of the metal, it is important to establish whether or not the oxidic material is present as liquid or crystalline phases during heating and rolling of the steel (-1150 to 1350°C). A knowledge of melting relations in synthetic mixtures of iron oxide, manganese oxide, and silica will give a clue to these problems. Methods for determining such relations and the results obtained are described iln this paper. I) PREVIOUS WORK A number cf previous studies have dealt with the three "binary"* systems bounding the system iron oxide-mangar,.ese oxide-silica. The system iron oxide-silica was studied by Bowen and shairerl in 1932. Their data were obtained by equilibration of mixtures in contact with metallic iron. Phase relations for the system iron oxide-silica ill atmospheres of different oxygen pressures car1 be derived from data on the system FeO-Fe2O3-SiO2 as determined by Muan.2 The diagram shown iri Fig. l is a section of this system in an atmosphere of CO2 and H2 in ratio 1:l. The system manganese oxide-silica has also been the subject of several investigations. Most of the early studies suffered from a lack of proper control of the atmosphere under which the equilibrations were carried mt. Phase diagrams for the system at two well defined levels of oxygen pressures have been determined recently. Glasser3 determined stability relations in an atmosphere consisting of carbon dioxide and hydrogen in ratio 5:1, diagram Fig. 2, and Muan4 studied phase relations in the system in air.

Jan 1, 1962

By Henry A. Stiff, and Lawrence E. Davis

The authors previously presented a method for predicting the tendency of oil field waters to deposit calcium sulfate. The present paper gives a similar method for calcium carbonate. Methods for predicting calcium carbonate scaling tendencies in fresh waters have been available for some time, but these could not be used for brines. By experimentally deriving the value of the K term in the Langelier equation, a method has been developed which applies to waters of high salt content. A statistical study is included which shows that the experimentally derived values of K are in good agreement with actual conditions. Several applications of the final equation to production practice are given. INTRODUCTION The authors previously presented a method for predicting the formation of calcium sulfate scale in oil field waters.' Although calcium sulfate deposition is important in production operations, the majority of scale problems involve calcium carbonate. The present communication discusses a method by which the formation of this type of scale in oil field waters can be predicted. Calcium carbonate precipitation is caused by a shift toward carbonate in the carbonate-bicarbonate-carbon dioxide equilibrium. When equilibrium shifts in the other direction, the precipitate goes back into solution. Since there is usually considerable delay between the establishment of an equilibrium and the precipitation or solution of calcium carbonate, unstable conditions exist in which a water will precipitate or dissolve calcium carbonate on standing. Tillmans? who did a major part of the early work on carbonate scaling, pointed out that the condition of equilibrium not only indicates the tendency of a water to scale but also is an indication of its corrosive properties. Previously precipitated calcium carbonate combines with iron to form a dense crust which inhibits corrosion. If the water tends to dissolve carbonate, the scale becomes porous, and electrolytic corrosion takes place. Tillmans1 work was extended by several investigators until in 1934 Langeliers developed an equation setting forth the conditions of carbonate equilibrium. By the use of this equation the pH of a water at equilibrium can be calculated. If the actual pH is higher than the calculated pH, the water has a tendency to form scale. If it is lower. the water has a tendency to be corrosive. Langelier's equation can be expressed in a simple form as follows: SI = pH-pCa-pA lk-K where: SI is the stability index. A positive index indicates scale formation. A negative index indicates corrosion. pH is the pH of the water sample, as actually determined. pCa is the negative logarithm of the calcium concentration. pAlk is the negative logarithm of the total alkalinity. K is a constant, the value of which depends on the total salt concentration and the temperature. This equation has been shown to apply to waters with totaI solid concentrations as high as 4.000 ppm. In fact, control of fresh water treatment by means of this equation has been standard text-book practice for a number of years. Nomographs have been worked out so that the stability index of a fresh water sample can be determined in a matter of minutes. Most oil field waters, however, contain well over 4,000 ppm of salts and for this reason the usual application of Langelier's equation can not be made. By an empirical method we have extended the application of the Langelier equation to waters of high salt concentration. By the use of this equation the tendency of oil field waters to deposit calcium carbonate can be predicted.

Jan 1, 1952

By P. G. Meikle, C. T. Holland

The effect of the condition of friction upon the ultimate unit compressive strength as determined between the compressed faces of precisely machined coal specimens and specially prepared testing platens has been examined. Reductions of 30 to 40% in the ultimate unit compressive strength of these model coal pillars have been verified when lubricants areused between the faces as compared to non-lubricated faces. Increase in unit compressive strength due to confinement at each of three levels of friction appears to follow generally the widely accepted "1/2 power law", i.e. S - C (L/T)1/2 where S is the unit ultimate strength, C is a constant dependent on the coal being tested and the coefficient of friction acting at the compression surfaces and L and T are the least width and thickness of the specimen, respectively. Results suggest that the surface condition of both the specimen and platens should be mentioned in detail in conjunction with compression testing, for although the term (L/T)1/2 is adequate for all practical purposes, the coefficient C is directly dependent on the condition of interfacial friction, all else remaining constant. One phase of the investigation of the confining effect of friction on the ultimate unit compressive strength of small coal specimens has recently been completed at the School of Mines of West Virginia University. The efficient control of ground is of fundamental importance to successful mining operations and the design of support pillars has always presented the mining engineer with a difficult and intriguing engineering problem. Since about the turn of the century, many investigators have performed extensive laboratory tests on small coal specimens in efforts to solve some of the perplexing problems of strata control and pillar action in coal mines. A detailed review of this work would serve no purpose here, but a brief mention of the more significant contributions is in order. Muller16 was perhaps the first to illustrate the effect of confining pressure on the strength of coal specimens in compression. His work has recently been more carefully expanded by the experiments of Murrell17 in Great Britain. Rice and Enzian l9 observed that as the size of cubical test specimens increased, the unit compressive strength decreased. These observations were later supplemented by Lawall and Holland, 13 by Greenwald4,5 et a1 at the U. S. Bureau of Mines, by Gaddy3 as well as by Steart,22 Millard15 et a1 and Evans2 et al. Gaddy3 seems to have been first to quantify this relationship with his equation: S = K/vd , where S - ultimate unit compressive strength (psi), K = a constant dependent on the coal, and D =edge dimension (in inches). Holland7 concluded that the strength of coal as affected by lateral dimensions and thickness could be expressed as where K = a coefficient dependent upon the coal, L = least width of pillar (in.) and T = thickness of pillar (in.). Data supplied by this formula have been compared to the estimated stresses in pillars that had been standing for long periods in coal mines and in the cases so far studied the results indicate that the formula predictions are sufficiently accurate for engineering purposes (Holland11 ). This equation therefore is believed to be the simplest and most accurate tool available at the present time for approximating the strength of a coal pillar (over a specified range of L/T) in situ. However, Holland7,9 has indicated that friction between the coal pillars and the top and bottom rock

Jan 1, 1965

By A. P. Young, F. C. Holden

IN many of the early investigations of the aging of titanium alloys, it was observed that the retained beta phase could be aged to a high hardness without an apparent change in microstructure; moreover, in some alloys it was found that even a very rapid quench produced beta having an anomalously high hardness. What appeared to be hard beta phase was designated as "beta prime," to distinguish it from the softer normal retained beta phase. Frost and co-workers'.' demonstrated that the increased hardness is caused by the formation of a metastable phase, omega, which can be identified from its X-ray diffraction pattern. This reaction also has been studied by Brotzen, et a1.,3 and the structure of the omega phase has been published by Silcock, et al.," and by Austin and Doig.3 The X-ray diffraction analysis by Austin and Doig indicated that omega is low in alloy content, approaching the composition of the stable alpha. The aging process proceeds by the path Thus, overaging results in the formation of alpha and the ultimate disappearance of omega. This is accompanied by a decrease in hardness and a recovery of ductility. The present work represents a study of the aging process in a high-purity Ti-6.4 Mn alloy, in which optical and electron microscopy, X-ray diffraction, and hardness data were correlated. The specimens, 1/8-in. sections cut from 1/4-in.-diam rod, were heated in argon to a temperature just into the beta field (810°C), held for 1 hr, and water-quenched. The aging samples were heated in air for 1 hr at 300 to 500°C. The specimens were ground and mechanically polished, finishing with alternate etching and polishing on a slow-speed wheel to remove disturbed metal from the surface. The surface finally was swab-etched, rinsed with tap water, and air-dried. The etchant used was an aqueous solution containing 1 1/2 pct HF and 3 1/2 pct HNO3. This procedure is identical with that used for preparing metallographic specimens, except that the optimum degree of final etching required for electron microscopy may vary from that used for light microscopy. Metal replicas, backed with silica, were prepared from plastic strip-pings for examination with the electron microscope. Complete details of the procedures used for preparing these replicas are available elsewhere." Fig. 1 shows a comparison between the structures revealed by the electron microscope and those obtained by conventional light microscopy. Hardness and X-ray diffraction data are listed in Table I. No evidence of a second phase is apparent in the optical micrographs for the as-quenched sample, or for the specimens aged at 300 or 400°C; fine alpha particles can be seen in the specimen aged at 500°C. In the electron micrographs, visible equiaxed pocks appear in the as-quenched specimen, and, with increasing density, in the samples aged at 300 and 400°C. After aging at 500°C, the structure becomes markedly coarser and develops an oriented appearance of a second phase, coincident with the appearance of visible alpha particles in the light micrographs. These observations are confirmed by X-ray diffraction and hardness data. In these specimens, aged for 1 hr, the intensity of the omega pattern increases to a maximum at the 400°C aging temperature, corresponding to maximum hardness and the maximum density of pocks in the electron micrographs. At this point the beta phase shows a definite enrichment in Mn. At 500°C, little or no omega re-

Jan 1, 1959

By H. H. Rachford, J. Douglas, D. W. Peaceman

A numerical solution of equations describing two-phase flow in porous media shows promise in providing a technique for predicting the displacermet from satlds of oil by water or gas. The description includes the influence of relative permeability, fluid viscosities and densities, graviry, and capillary pressure, and, tholrgh tested ortly for two-dimensional cases, should be eqlmlly applicable in three-dimensional geometry. Two memorical methods ore presented: the first method is quite general in its applicability; the second method can be used only with certain types of boundary conditions but requires less computing. Comparisons of computed results with data from Inhoratory models are presented. These data were taken on a water flood of a strarified model and on water floods of a five-spot model for favorable and unfavorable mobility ratios. On the stratified model, excellent agreement with recovery at breakthrough was obtained; agreement with recovery after breakthrough was poor. In the five-spot model, good agreement was obtainecl with recovery at and after breakthrough. The purpose of this paper is twofold: first, to present a reservoir engineering method requiring knowledge only of rock geometry and the normally measured rock and fluid properties for calculating the multi-dimensional flow of water displacing oil from porous, water-wet rock containing connate water; and, second, to investigate the validity of the method by comparing results of calculations with previously observed displacements in laboratory models. The availability of such a verified technique of reservoir analysis would afford major advantages. First, it would demonstrate that the fundamental macroscopic concepts of two-phase fluid mechanics, i.e., relative permeability and capillary pressure, yield an adequate description of the physical process. Also, since most reservoir rocks appear to be water-wet and contain connate water along with oil, it would provide a method of technical and economic value for calculating the course of oil displacement by water directly from measured reservoir and fluid properties. It is important to emphasize that the calculation is subject only to the limitations of detail and precision of reservoir information, but not to limitations introduced by simplifying assumptions. Further, it would providc almost the only means of examining the influence of factors such as the size and extent of reservoir inhomogeneities and uncertainties in the basic reservoir data. Knowledge of this influence is essential in stating quantitatively the detail required to define a reservoir and in establishing the relation between the uncertainty in the definition of reservoir properties and the reliability of predicted performance. Moreover, in the process of solving a particular problem much detailed information would become available about the displacement process. For example, at each point in the reservoir for all stages of the displace ment. the calculations would yield not only the water and oil saturations but also the direction and magnitude of fluid velocities and the local fluid mobilities. Such dctail is potentially of great value in giving insight into the mechanics of particular displacements. The development of such a method has long been the goal of research in the application of numerical an-alysis to petroleum reservoir enginecrinz. The most complete treatment of the displacement process published to date is that of Douglas. Blair, and Wagner,' which, however, was limited to flow in a single dimension. The method presented in the present work is hascd on the numerical solution of a finite difference analogue of the multi-dimensional differential system describing the displacement process. Although current work has considered only displacement of oil by water from water-wet sands, the differential system for other immiscible displacements, such as gas displacing oil with which it is in phase equilibrium, is quite similar. It should therefore be expected that the technique described will be applicable to displacement by gas as well. The description of the simultaneous flow of fluids through porous media in terms of relative perrncability and capillary pressure has been adequately discussed in the literature and standard textbooks. Sec, for exampje, Muskat. Chapter VII.'

By E. L. Claridge, K. S. Lee

Areal sweep efficiency of oil displacement by enhanced-viscosity water exhibiting pseudoplastic behavior was measured in a Hele-Shaw model representing one-quarter of a five-spot pattern. The pseudoplasticity of polymer solutions and the velocity distribution in the five-spot pattern produced a condition under which the mobility ratio between the displacing and the displaced fluid could not be assigned a single value. Instead, the movement of the displacement front is governed by local mobility ratios which are also time dependent. The areal sweep at breakthrough with polymer solutions was poorer than the sweep obtained with Newtonian fluids of comparable viscosity. However, the areal sweep at 1 PV throughput was greatly improved as compared to flood water without polymer. It was also demonstrated that, even after the oil-cut had declined to a low value during a regular waterflood, switching to polymer flood efficiently swept out the oil remaining in the model. INTRODUCTION The behavior of fluid displacements in isotropic porous media for various patterns of injection and production wells has been extensively investigated.1-7 These investigations all concerned Newtonian fluids, i.e., the viscosity of each fluid was constant regardless of flow rate. The generally unfavorable influence on areal sweep efficiency of higher mobility of the displacing fluid as compared to the mobility of the displaced fluid has been established for both miscible and immiscible fluids. The principle was also established that a close correspondence exists between miscible and immiscible flood front behavior,2, 3 although oil recovery in a waterflood at unfavorable mobility ratio may be less than that observed in a miscible displacement at the same mobility ratio. This is true even when oil recovery is expressed on the basis of movable oil. The reason is that oil saturation only slowly achieves its final value behind the water-flood front in accordance with the Buckley-Leverett8 simultaneous flow relations. It is convenient to use miscible displacements for laboratory simulation of waterflood frontal advance since the interfacial tension forces which are negligible in proportion to viscous forces on a reservoir scale9 are thus made nonoperative in the laboratory model. For miscible displacements, the Hele-Shaw type of model adequately represents a porous medium so long as the appropriate scaling rules5-10 are observed in its design and operation. During simulation of waterflood front behavior in the laboratory by using miscible displacements, the behavior of connate water may ordinarily be disregarded since it is usually indistinguishable from flood water in this process. However, when the flood water is deliberately thickened to improve the mobility ratio between water and oil. the effect on the sweep efficiency due to generation of a connate water bank during the process must be considered. In a uniform porous medium, such a bank is generated11 and efficiently displaced by injection of thickened water.l2 The oil originally in-place at the start of the waterflood is then displaced by connate water followed by thickened water. If the flood water must be thickened to obtain a favorable mobility ratio, the mobility of the oil phase is appreciably less than that of the connate water. Hence, the oil phase is inefficiently displaced by the connate water bank, and a considerable proportion of the oil comes in contact with and is displaced by the thickened waterflood front' A recent study 12 of five-spot displacements using miscible Newtonian fluids in which connate water banks of various sizes were simulated shows that, for connate water banks as large as 40 percent of 1 PV, major improvements in sweep efficiency resulted from use of a thickened

Jan 1, 1969

By P. F. Gnirk, J. B. Cheatham

Single bit-tooth penetration experiments under static load were conducted on six rocks at confining pressures of O to 5,000 psi using sharp wedge-shaped teeth with included angles ranging from 30 to 120° In general, the force-displacement curves for all rocks exhibit an increasingly nonlinear and discontinuous behavior with decreasing confining pressure. The confining pressure at which a rock exhibits a macroscopic transition from predominantly ductile to predominantly brittle behavior during penetration vmies from about 500 to 1,000 psi for the limestones to greater than 5,000 psi for dolomite. The correlation between calculated values of force per unit penetration based on plasticity theory and experimental values is quite encouraging, even at confining pressures as low as 1,000 psi A qualitative correlation between volume of fragmented rock per unit energy input for a single bit-tooth and drilling rate for microbits appears to exist over a confining pressure range of 0 to 5,000 psi. INTRODUCTION Laboratory experiments utilizing a small-scale drilling apparatus have demonstrated that penetration rates are reduced considerably as a result of increasing the confining pressure from atmospheric to a few thousand psi?-3 This undesirable situation can, in general, be attributed to a combination of decreased efficiency of chip removal at the bottom of the borehole, increased rock-failure strength, and a possible change in the mechanism of chip generation and rock fragmentation with increasing confining pressure. To more fully understand the principles underlying the last circumstance, it is the purpose of this investigation to experimentally study the mechanism of single bit-tooth penetration into dry rock at low confining pressures and, in particular, to establish the confining pressure at which the penetration mechanism may undergo a brittle to ductile transition for various rock types commonly encountered in drilling. Confining pressure as used here refers to the differential pressure between the borehole fluid pressure and the formation-pore fluid pressure. EXPERIMENTAL PROCEDURE Using an experimental apparatus previously described: a single, sharp wedge-shaped tool was forced under a "statically" applied load into an effectively semi-in finite dry rock sample subjected to a prescribed confining pressure. To prevent the invasion of the con fining-pressure fluid into the pores of the rock sample during penetration, the exposed surface of the rock was jacketed with a layer of silicon putty.* Electrical instrumentation incorporated into the apparatus yielded a graphical plot of force on the tool as a function of penetration or displacement of the tool into the rock during an experiment. During the course of the experimentation the following conditions were maintained constant: (1) pore pressure — atmospheric (i.e., the rock was dry); (2) temperature — 75F; (3) rate of loading — essentially static (approximately 0.002 in./sec); (4) bit tooth — a sharp wedge-shaped tool loaded normal to the rock surface; (5) rock surface — smooth and flat; (6) drilling fluid — hydraulic oil; and (7) maximum depth of penetration — approximateiy 0.1 in. In addition, each experiment was performed on a different rock sample so the rock surface is free of a layer of cuttings and of any previous indentation craters. The influence of the corners of a borehole was neglected, since each rock sample was cemented inta a section of aLuminum tubing to simulate a semi-infinite body. Indentation experiments were made on a sandstone, two limestones, a marble, a dolomite and a schist with a 60' bit-tooth over a range of confining pressures from atmospheric to 5,000 psi and at a constant confining pressure of 1,000 psi for a variety of bit-teeth with angles ranging from 30 to

Jan 1, 1966

By Gordon H. Geiger, J. Bruce Wagner

Electrical conductavity and therrnoelectvic nzeasuretnents on synthetic hematite slabs with 0.01 to 0.90 at. pet Ti and with 0.30 at. pet Ca were made. Additions of titanium and of calcium both increased the electronic conductivity with titanium yielding greater n-type behavior and calciurn p-type behavior. Reduction studies of hematite to magnetite in CO-CO2 atmospheres between 600° and 900°C initially exhibited linear kinetics. These linear rates were increased by additions of titanium and decreased by calcium. IN recent years many studies have been reported in the literature on the kinetics of the reduction of hematite and magnetite to iron. In addition, Hansen and Josephl and Schenck and Schultz2 have reported studies on the reduction of hematite to magnetite, the first step in total reduction to iron. In order to evaluate the results of the studies of over-all reduction in terms of the actual mechanism of the reaction and to define further the important factors in the rate- controlling mechanism of the magnetic roasting reaction, the following experiments were undertaken. Specimens of undoped hematite and hematite containing titanium or calcium in solution as doping agents were reduced to magnetite in CO-CO2 mixtures. In addition, electrical-conductivity measurements were correlated with the reduction kinetics using concepts of defect solid-state chemistry. EXPERIMENTAL Fisher certified Fe2O3 powder was used to make specimens for both the electrical and kinetic studies (see Table I for analysis). Doping with titanium and calcium was accomplished by adding TiO2 and CaO powders to the Fe2O3 powder. The powders were mixed in a Waring blender for minimum times of 1/2 hr. Satisfactory blending was achieved based on comparison of analyses of individual specimens af- ter reduction. The specimens were formed in a steel die using opposed punches with a rectangular opening 10.0 by 40.0 mm. The Fe2O3-TiO, platelets were pressed cold at 16,000 psi. They were sintered for approximately 16 hr at 1075°C in air, in accordance with information in the literature3, 4 on the time and temperature needed to obtain solution of the titanium in the hematite. The Fe2O3-CaO mixtures were first cold-pressed at 20,000 psi and sintered for 3 hr at 1225°C to insure solution of CaO. This material was then ground to -325 mesh in a 6-in. ball mill and the resulting powder was used to make platelets in the same manner as above. The sintered platelets were usually between 1/16 and 1/8 in. thick. They were ground on a carborundum wheel and polished on 2/0 paper. Typical dimensions of the kinetic-study specimens were 1.6 by 0.8 by 0.05 cm, and a typical weight was 0.3 g. Conductivity and thermoelectric specimens were approximately the same size, but were subjected to further sintering in order to ensure maximum densification. Finally, all specimens were measured to the nearest 0.0005 in. and weighed on a Mettler H-15 balance to the nearest 0.0001 g and the density calculated. The average density of the specimens used for the reduction studies was 4.87 g per cc, or 7.1 pet total porosity. The standard deviation ranged from 0.14 to 0.063 g per cc within a composition group. In the present study, the apparent surface area as measured with a micrometer was taken as the true surface area. The chemical analyses for calcium and for titanium within a group showed maximum variations of 50.04 pet from the average values used in Figs. 9 and 11. In order to suspend the specimen from the balance for the kinetic studies, a hole, 0.03 in. in

Jan 1, 1965

By F. C. Bond

Since the Third Theory of Comminution was presented eight years ago (I) it has found increasing use in crushing and grinding problems. The practical utility of its wok index equation is quite generally acknowledged (2). However, its theoretical basis has been questioned in at least three technical articles (3) (4) ('). The purpose of this paper is to present experimental proof that it is scientifically correct. Particles under compressive stress are strained and deformed. They absorb strain energy, and when this locally exceeds the breaking strength, a crack tip forms. The surrounding strain energy flows to the crack tip, which rapidly extends and splits the rock, releasing the strain energy as heat. The initial energy flow causes additional crack tips in highly strained areas. If the compression is rapidly applied by impact, crack tips may form before the strain energy has reached equilibrium in the particle, thus decreasing the total work input required for breakage. The energy necessary to break is essentially the energy necessary to produce crack tips, since the energy necessary to extend the cracks to breakage is already present as strain energy in the deformed particles. After breakage nearly all of this energy appears as heat. The crack length cannot be measured directly. However, in particles of regular and similar shape the crack tip length is considered as equal to the crack depth, or crack extension necessary to break, so that the crack length equals the square root of one-half of the surface area. The Third Theory states that the useful work done in crushing and grinding is directly proportional to the total length of the new cracks formed. It can be confirmed by showing that a constant work input produces a constant length of new cracks when reducing the same material to different product sizes. This is done in the present paper on a wide variety of material. The constant work input was supplied by one revolution of the 12" x 12" laboratory ball mill used in making grindability tests by the Allis-Chalmers method (12) (13) The new crack lengths produced per mill revolution were measured from all available grindability test results at 28, 35, 48, 65, and 100 mesh on fifteen different ores, and were found to remain substantially constant for each ore at all mesh sizes. A new technique is used for the measurement of crack lengths. Size distribution plots of the mill feed and product are made by the Third Theory method (9) and the crack lengths are obtained from these plots by the procedure described in the present paper. The energy input required to produce a unit length is of fundamental importance in the size reduction of brittle solids. The crack length Cr is expressed in centimeters per cubic centimeter of solid material. It bears a definite relationship to the external surface area of the crushed or ground solid. A uniform particle shape must be assumed before the surface area and crack length can be evaluated. In this paper it is assumed that the relationship between the surface area and the particle volume of a particle d microns in diameter is the same as that of cube d microns on a side. The external surface areas of particles with a cubical breakage probably agree approximately with this rule, and correction factors can be applied when physical measurements of the surface areas are available for comparison. However, the assumption of equivalent cubes has been found satisfactory for most calculation purposes. Assuming equivalent cubes, one cubic centimeter of particles d microns in diameter will have a crack length Cr of v30.000/d centimeters, and a surface area of 60,000/d square centimeters. The specific crack length is thus equal to the square root of one-half the specific surface area. Where Sa is the surface area in square centimeters per gram and Sg is the specific gravity of the ground solid, then Cr = vSg . Sa/2 = 173.2/ vd (1)

Jan 1, 1961

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